LMFDB - Embedded newform 1339.2.a.f.1.17

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			1.17
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)

$f(q)$	$=$	$q+0.835105 q^{2} -2.05058 q^{3} -1.30260 q^{4} +3.71011 q^{5} -1.71245 q^{6} -2.16987 q^{7} -2.75802 q^{8} +1.20488 q^{9} +O(q^{10})$	\(q+0.835105 q^{2} -2.05058 q^{3} -1.30260 q^{4} +3.71011 q^{5} -1.71245 q^{6} -2.16987 q^{7} -2.75802 q^{8} +1.20488 q^{9} +3.09833 q^{10} -3.85971 q^{11} +2.67109 q^{12} +1.00000 q^{13} -1.81207 q^{14} -7.60788 q^{15} +0.301965 q^{16} +7.10623 q^{17} +1.00620 q^{18} +0.0250324 q^{19} -4.83278 q^{20} +4.44949 q^{21} -3.22326 q^{22} +1.83736 q^{23} +5.65554 q^{24} +8.76490 q^{25} +0.835105 q^{26} +3.68103 q^{27} +2.82647 q^{28} -2.34392 q^{29} -6.35338 q^{30} -4.04802 q^{31} +5.76821 q^{32} +7.91464 q^{33} +5.93445 q^{34} -8.05044 q^{35} -1.56948 q^{36} -4.40189 q^{37} +0.0209047 q^{38} -2.05058 q^{39} -10.2325 q^{40} +9.81178 q^{41} +3.71579 q^{42} +12.6191 q^{43} +5.02765 q^{44} +4.47025 q^{45} +1.53439 q^{46} -5.53528 q^{47} -0.619203 q^{48} -2.29168 q^{49} +7.31961 q^{50} -14.5719 q^{51} -1.30260 q^{52} +6.18875 q^{53} +3.07405 q^{54} -14.3199 q^{55} +5.98453 q^{56} -0.0513310 q^{57} -1.95742 q^{58} +0.0829822 q^{59} +9.91002 q^{60} +1.65933 q^{61} -3.38053 q^{62} -2.61444 q^{63} +4.21313 q^{64} +3.71011 q^{65} +6.60956 q^{66} +3.94812 q^{67} -9.25657 q^{68} -3.76766 q^{69} -6.72296 q^{70} +13.0992 q^{71} -3.32309 q^{72} +14.4133 q^{73} -3.67604 q^{74} -17.9731 q^{75} -0.0326072 q^{76} +8.37505 q^{77} -1.71245 q^{78} +7.73607 q^{79} +1.12032 q^{80} -11.1629 q^{81} +8.19387 q^{82} +10.7312 q^{83} -5.79590 q^{84} +26.3649 q^{85} +10.5383 q^{86} +4.80641 q^{87} +10.6451 q^{88} -7.10557 q^{89} +3.73313 q^{90} -2.16987 q^{91} -2.39335 q^{92} +8.30080 q^{93} -4.62254 q^{94} +0.0928729 q^{95} -11.8282 q^{96} -3.68470 q^{97} -1.91379 q^{98} -4.65050 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.835105	0.590508	0.295254	−	0.955419i	$-0.404596\pi$
$2$	0.835105	0.590508	0.295254	+	0.955419i	$0.404596\pi$
$3$	−2.05058	−1.18390	−0.591952	−	0.805973i	$-0.701642\pi$
$3$	−2.05058	−1.18390	−0.591952	+	0.805973i	$0.701642\pi$
$4$	−1.30260	−0.651300
$5$	3.71011	1.65921	0.829605	−	0.558350i	$-0.188565\pi$
$5$	3.71011	1.65921	0.829605	+	0.558350i	$0.188565\pi$
$6$	−1.71245	−0.699105
$7$	−2.16987	−0.820133	−0.410066	−	0.912056i	$-0.634494\pi$
$7$	−2.16987	−0.820133	−0.410066	+	0.912056i	$0.634494\pi$
$8$	−2.75802	−0.975106
$9$	1.20488	0.401628
$10$	3.09833	0.979778
$11$	−3.85971	−1.16375	−0.581873	−	0.813280i	$-0.697680\pi$
$11$	−3.85971	−1.16375	−0.581873	+	0.813280i	$0.697680\pi$
$12$	2.67109	0.771076
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.81207	−0.484295
$15$	−7.60788	−1.96435
$16$	0.301965	0.0754912
$17$	7.10623	1.72351	0.861757	−	0.507322i	$-0.169365\pi$
$17$	7.10623	1.72351	0.861757	+	0.507322i	$0.169365\pi$
$18$	1.00620	0.237165
$19$	0.0250324	0.00574283	0.00287141	−	0.999996i	$-0.499086\pi$
$19$	0.0250324	0.00574283	0.00287141	+	0.999996i	$0.499086\pi$
$20$	−4.83278	−1.08064
$21$	4.44949	0.970958
$22$	−3.22326	−0.687201
$23$	1.83736	0.383117	0.191558	−	0.981481i	$-0.438646\pi$
$23$	1.83736	0.383117	0.191558	+	0.981481i	$0.438646\pi$
$24$	5.65554	1.15443
$25$	8.76490	1.75298
$26$	0.835105	0.163778
$27$	3.68103	0.708415
$28$	2.82647	0.534152
$29$	−2.34392	−0.435256	−0.217628	−	0.976032i	$-0.569832\pi$
$29$	−2.34392	−0.435256	−0.217628	+	0.976032i	$0.569832\pi$
$30$	−6.35338	−1.15996
$31$	−4.04802	−0.727047	−0.363523	−	0.931585i	$-0.618426\pi$
$31$	−4.04802	−0.727047	−0.363523	+	0.931585i	$0.618426\pi$
$32$	5.76821	1.01968
$33$	7.91464	1.37776
$34$	5.93445	1.01775
$35$	−8.05044	−1.36077
$36$	−1.56948	−0.261580
$37$	−4.40189	−0.723667	−0.361834	−	0.932243i	$-0.617849\pi$
$37$	−4.40189	−0.723667	−0.361834	+	0.932243i	$0.617849\pi$
$38$	0.0209047	0.00339119
$39$	−2.05058	−0.328356
$40$	−10.2325	−1.61791
$41$	9.81178	1.53234	0.766171	−	0.642636i	$-0.222159\pi$
$41$	9.81178	1.53234	0.766171	+	0.642636i	$0.222159\pi$
$42$	3.71579	0.573359
$43$	12.6191	1.92439	0.962195	−	0.272361i	$-0.0878045\pi$
$43$	12.6191	1.92439	0.962195	+	0.272361i	$0.0878045\pi$
$44$	5.02765	0.757947
$45$	4.47025	0.666385
$46$	1.53439	0.226234
$47$	−5.53528	−0.807403	−0.403702	−	0.914891i	$-0.632277\pi$
$47$	−5.53528	−0.807403	−0.403702	+	0.914891i	$0.632277\pi$
$48$	−0.619203	−0.0893743
$49$	−2.29168	−0.327383
$50$	7.31961	1.03515
$51$	−14.5719	−2.04047
$52$	−1.30260	−0.180638
$53$	6.18875	0.850090	0.425045	−	0.905172i	$-0.360258\pi$
$53$	6.18875	0.850090	0.425045	+	0.905172i	$0.360258\pi$
$54$	3.07405	0.418325
$55$	−14.3199	−1.93090
$56$	5.98453	0.799717
$57$	−0.0513310	−0.00679895
$58$	−1.95742	−0.257022
$59$	0.0829822	0.0108034	0.00540168	−	0.999985i	$-0.498281\pi$
$59$	0.0829822	0.0108034	0.00540168	+	0.999985i	$0.498281\pi$
$60$	9.91002	1.27938
$61$	1.65933	0.212455	0.106227	−	0.994342i	$-0.466123\pi$
$61$	1.65933	0.212455	0.106227	+	0.994342i	$0.466123\pi$
$62$	−3.38053	−0.429327
$63$	−2.61444	−0.329388
$64$	4.21313	0.526641
$65$	3.71011	0.460182
$66$	6.60956	0.813580
$67$	3.94812	0.482340	0.241170	−	0.970483i	$-0.422469\pi$
$67$	3.94812	0.482340	0.241170	+	0.970483i	$0.422469\pi$
$68$	−9.25657	−1.12252
$69$	−3.76766	−0.453573
$70$	−6.72296	−0.803548
$71$	13.0992	1.55459	0.777294	−	0.629137i	$-0.216592\pi$
$71$	13.0992	1.55459	0.777294	+	0.629137i	$0.216592\pi$
$72$	−3.32309	−0.391630
$73$	14.4133	1.68695	0.843474	−	0.537170i	$-0.180506\pi$
$73$	14.4133	1.68695	0.843474	+	0.537170i	$0.180506\pi$
$74$	−3.67604	−0.427331
$75$	−17.9731	−2.07536
$76$	−0.0326072	−0.00374030
$77$	8.37505	0.954425
$78$	−1.71245	−0.193897
$79$	7.73607	0.870376	0.435188	−	0.900340i	$-0.356682\pi$
$79$	7.73607	0.870376	0.435188	+	0.900340i	$0.356682\pi$
$80$	1.12032	0.125256
$81$	−11.1629	−1.24032
$82$	8.19387	0.904861
$83$	10.7312	1.17791	0.588953	−	0.808167i	$-0.299540\pi$
$83$	10.7312	1.17791	0.588953	+	0.808167i	$0.299540\pi$
$84$	−5.79590	−0.632385
$85$	26.3649	2.85967
$86$	10.5383	1.13637
$87$	4.80641	0.515301
$88$	10.6451	1.13478
$89$	−7.10557	−0.753189	−0.376595	−	0.926378i	$-0.622905\pi$
$89$	−7.10557	−0.753189	−0.376595	+	0.926378i	$0.622905\pi$
$90$	3.73313	0.393506
$91$	−2.16987	−0.227464
$92$	−2.39335	−0.249524
$93$	8.30080	0.860753
$94$	−4.62254	−0.476778
$95$	0.0928729	0.00952856
$96$	−11.8282	−1.20721
$97$	−3.68470	−0.374124	−0.187062	−	0.982348i	$-0.559897\pi$
$97$	−3.68470	−0.374124	−0.187062	+	0.982348i	$0.559897\pi$
$98$	−1.91379	−0.193322
$99$	−4.65050	−0.467392
$100$	−11.4172	−1.14172
$101$	0.140850	0.0140151	0.00700757	−	0.999975i	$-0.497769\pi$
$101$	0.140850	0.0140151	0.00700757	+	0.999975i	$0.497769\pi$
$102$	−12.1691	−1.20492
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−2.75802	−0.270446
$105$	16.5081	1.61102
$106$	5.16825	0.501985
$107$	−7.18052	−0.694167	−0.347083	−	0.937834i	$-0.612828\pi$
$107$	−7.18052	−0.694167	−0.347083	+	0.937834i	$0.612828\pi$
$108$	−4.79491	−0.461391
$109$	17.6559	1.69112	0.845562	−	0.533877i	$-0.179265\pi$
$109$	17.6559	1.69112	0.845562	+	0.533877i	$0.179265\pi$
$110$	−11.9586	−1.14021
$111$	9.02644	0.856752
$112$	−0.655223	−0.0619128
$113$	−10.4134	−0.979606	−0.489803	−	0.871833i	$-0.662931\pi$
$113$	−10.4134	−0.979606	−0.489803	+	0.871833i	$0.662931\pi$
$114$	−0.0428667	−0.00401484
$115$	6.81682	0.635672
$116$	3.05319	0.283482
$117$	1.20488	0.111391
$118$	0.0692989	0.00637948
$119$	−15.4196	−1.41351
$120$	20.9827	1.91545
$121$	3.89734	0.354303
$122$	1.38571	0.125456
$123$	−20.1198	−1.81415
$124$	5.27295	0.473525
$125$	13.9682	1.24935
$126$	−2.18333	−0.194506
$127$	−0.463225	−0.0411046	−0.0205523	−	0.999789i	$-0.506542\pi$
$127$	−0.463225	−0.0411046	−0.0205523	+	0.999789i	$0.506542\pi$
$128$	−8.01801	−0.708699
$129$	−25.8764	−2.27829
$130$	3.09833	0.271741
$131$	−7.99878	−0.698857	−0.349428	−	0.936963i	$-0.613624\pi$
$131$	−7.99878	−0.698857	−0.349428	+	0.936963i	$0.613624\pi$
$132$	−10.3096	−0.897336
$133$	−0.0543170	−0.00470988
$134$	3.29710	0.284826
$135$	13.6570	1.17541
$136$	−19.5991	−1.68061
$137$	−8.08903	−0.691092	−0.345546	−	0.938402i	$-0.612306\pi$
$137$	−8.08903	−0.691092	−0.345546	+	0.938402i	$0.612306\pi$
$138$	−3.14640	−0.267839
$139$	−3.62933	−0.307836	−0.153918	−	0.988084i	$-0.549189\pi$
$139$	−3.62933	−0.307836	−0.153918	+	0.988084i	$0.549189\pi$
$140$	10.4865	0.886271
$141$	11.3505	0.955887
$142$	10.9392	0.917997
$143$	−3.85971	−0.322765
$144$	0.363832	0.0303193
$145$	−8.69621	−0.722181
$146$	12.0366	0.996157
$147$	4.69927	0.387589
$148$	5.73391	0.471324
$149$	0.718156	0.0588337	0.0294168	−	0.999567i	$-0.490635\pi$
$149$	0.718156	0.0588337	0.0294168	+	0.999567i	$0.490635\pi$
$150$	−15.0095	−1.22552
$151$	20.5542	1.67267	0.836337	−	0.548215i	$-0.184692\pi$
$151$	20.5542	1.67267	0.836337	+	0.548215i	$0.184692\pi$
$152$	−0.0690398	−0.00559987
$153$	8.56217	0.692211
$154$	6.99405	0.563596
$155$	−15.0186	−1.20632
$156$	2.67109	0.213858
$157$	−0.232342	−0.0185429	−0.00927147	−	0.999957i	$-0.502951\pi$
$157$	−0.232342	−0.0185429	−0.00927147	+	0.999957i	$0.502951\pi$
$158$	6.46044	0.513965
$159$	−12.6905	−1.00642
$160$	21.4007	1.69187
$161$	−3.98683	−0.314207
$162$	−9.32220	−0.732421
$163$	15.0717	1.18051	0.590255	−	0.807217i	$-0.299027\pi$
$163$	15.0717	1.18051	0.590255	+	0.807217i	$0.299027\pi$
$164$	−12.7808	−0.998014
$165$	29.3642	2.28600
$166$	8.96171	0.695563
$167$	7.96552	0.616390	0.308195	−	0.951323i	$-0.400275\pi$
$167$	7.96552	0.616390	0.308195	+	0.951323i	$0.400275\pi$
$168$	−12.2718	−0.946787
$169$	1.00000	0.0769231
$170$	22.0174	1.68866
$171$	0.0301611	0.00230648
$172$	−16.4376	−1.25335
$173$	16.8331	1.27980	0.639900	−	0.768458i	$-0.278976\pi$
$173$	16.8331	1.27980	0.639900	+	0.768458i	$0.278976\pi$
$174$	4.01385	0.304290
$175$	−19.0187	−1.43768
$176$	−1.16550	−0.0878525
$177$	−0.170162	−0.0127901
$178$	−5.93390	−0.444765
$179$	−16.2707	−1.21613	−0.608065	−	0.793887i	$-0.708054\pi$
$179$	−16.2707	−1.21613	−0.608065	+	0.793887i	$0.708054\pi$
$180$	−5.82294	−0.434016
$181$	−5.08034	−0.377619	−0.188809	−	0.982014i	$-0.560463\pi$
$181$	−5.08034	−0.377619	−0.188809	+	0.982014i	$0.560463\pi$
$182$	−1.81207	−0.134319
$183$	−3.40258	−0.251526
$184$	−5.06748	−0.373580
$185$	−16.3315	−1.20072
$186$	6.93204	0.508282
$187$	−27.4280	−2.00573
$188$	7.21025	0.525861
$189$	−7.98735	−0.580994
$190$	0.0775586	0.00562669
$191$	−5.58967	−0.404455	−0.202227	−	0.979339i	$-0.564818\pi$
$191$	−5.58967	−0.404455	−0.202227	+	0.979339i	$0.564818\pi$
$192$	−8.63936	−0.623492
$193$	−6.44072	−0.463613	−0.231807	−	0.972762i	$-0.574464\pi$
$193$	−6.44072	−0.463613	−0.231807	+	0.972762i	$0.574464\pi$
$194$	−3.07711	−0.220924
$195$	−7.60788	−0.544811
$196$	2.98514	0.213224
$197$	−9.74769	−0.694494	−0.347247	−	0.937774i	$-0.612883\pi$
$197$	−9.74769	−0.694494	−0.347247	+	0.937774i	$0.612883\pi$
$198$	−3.88365	−0.275999
$199$	−18.1166	−1.28425	−0.642125	−	0.766600i	$-0.721947\pi$
$199$	−18.1166	−1.28425	−0.642125	+	0.766600i	$0.721947\pi$
$200$	−24.1737	−1.70934
$201$	−8.09595	−0.571044
$202$	0.117625	0.00827605
$203$	5.08600	0.356967
$204$	18.9813	1.32896
$205$	36.4028	2.54248
$206$	−0.835105	−0.0581845
$207$	2.21381	0.153870
$208$	0.301965	0.0209375
$209$	−0.0966177	−0.00668319
$210$	13.7860	0.951323
$211$	19.9558	1.37382	0.686909	−	0.726744i	$-0.258967\pi$
$211$	19.9558	1.37382	0.686909	+	0.726744i	$0.258967\pi$
$212$	−8.06146	−0.553663
$213$	−26.8610	−1.84048
$214$	−5.99649	−0.409911
$215$	46.8181	3.19297
$216$	−10.1524	−0.690780
$217$	8.78367	0.596275
$218$	14.7445	0.998623
$219$	−29.5556	−1.99718
$220$	18.6531	1.25759
$221$	7.10623	0.478017
$222$	7.53803	0.505919
$223$	−19.4033	−1.29934	−0.649672	−	0.760215i	$-0.725094\pi$
$223$	−19.4033	−1.29934	−0.649672	+	0.760215i	$0.725094\pi$
$224$	−12.5162	−0.836277
$225$	10.5607	0.704045
$226$	−8.69624	−0.578466
$227$	−22.2583	−1.47734	−0.738668	−	0.674070i	$-0.764545\pi$
$227$	−22.2583	−1.47734	−0.738668	+	0.674070i	$0.764545\pi$
$228$	0.0668637	0.00442816
$229$	4.44102	0.293471	0.146735	−	0.989176i	$-0.453123\pi$
$229$	4.44102	0.293471	0.146735	+	0.989176i	$0.453123\pi$
$230$	5.69276	0.375369
$231$	−17.1737	−1.12995
$232$	6.46458	0.424421
$233$	−22.6668	−1.48495	−0.742477	−	0.669872i	$-0.766349\pi$
$233$	−22.6668	−1.48495	−0.742477	+	0.669872i	$0.766349\pi$
$234$	1.00620	0.0657776
$235$	−20.5365	−1.33965
$236$	−0.108093	−0.00703623
$237$	−15.8634	−1.03044
$238$	−12.8770	−0.834689
$239$	23.7515	1.53636	0.768179	−	0.640236i	$-0.221163\pi$
$239$	23.7515	1.53636	0.768179	+	0.640236i	$0.221163\pi$
$240$	−2.29731	−0.148291
$241$	−2.73466	−0.176155	−0.0880773	−	0.996114i	$-0.528072\pi$
$241$	−2.73466	−0.176155	−0.0880773	+	0.996114i	$0.528072\pi$
$242$	3.25468	0.209219
$243$	11.8473	0.760008
$244$	−2.16144	−0.138372
$245$	−8.50237	−0.543197
$246$	−16.8022	−1.07127
$247$	0.0250324	0.00159277
$248$	11.1645	0.708948
$249$	−22.0053	−1.39453
$250$	11.6649	0.737753
$251$	19.9716	1.26060	0.630298	−	0.776353i	$-0.282933\pi$
$251$	19.9716	1.26060	0.630298	+	0.776353i	$0.282933\pi$
$252$	3.40556	0.214530
$253$	−7.09169	−0.445850
$254$	−0.386842	−0.0242726
$255$	−54.0633	−3.38558
$256$	−15.1221	−0.945134
$257$	6.87546	0.428879	0.214440	−	0.976737i	$-0.431207\pi$
$257$	6.87546	0.428879	0.214440	+	0.976737i	$0.431207\pi$
$258$	−21.6095	−1.34535
$259$	9.55152	0.593503
$260$	−4.83278	−0.299717
$261$	−2.82415	−0.174811
$262$	−6.67982	−0.412681
$263$	6.05843	0.373579	0.186789	−	0.982400i	$-0.440192\pi$
$263$	6.05843	0.373579	0.186789	+	0.982400i	$0.440192\pi$
$264$	−21.8287	−1.34346
$265$	22.9609	1.41048
$266$	−0.0453604	−0.00278122
$267$	14.5706	0.891704
$268$	−5.14282	−0.314148
$269$	−25.7980	−1.57293	−0.786467	−	0.617632i	$-0.788092\pi$
$269$	−25.7980	−1.57293	−0.786467	+	0.617632i	$0.788092\pi$
$270$	11.4051	0.694089
$271$	−21.3247	−1.29538	−0.647691	−	0.761903i	$-0.724265\pi$
$271$	−21.3247	−1.29538	−0.647691	+	0.761903i	$0.724265\pi$
$272$	2.14583	0.130110
$273$	4.44949	0.269295
$274$	−6.75519	−0.408096
$275$	−33.8299	−2.04002
$276$	4.90776	0.295412
$277$	2.05229	0.123310	0.0616549	−	0.998098i	$-0.480362\pi$
$277$	2.05229	0.123310	0.0616549	+	0.998098i	$0.480362\pi$
$278$	−3.03087	−0.181780
$279$	−4.87740	−0.292002
$280$	22.2033	1.32690
$281$	2.84516	0.169728	0.0848640	−	0.996393i	$-0.472954\pi$
$281$	2.84516	0.169728	0.0848640	+	0.996393i	$0.472954\pi$
$282$	9.47889	0.564460
$283$	−9.02441	−0.536446	−0.268223	−	0.963357i	$-0.586436\pi$
$283$	−9.02441	−0.536446	−0.268223	+	0.963357i	$0.586436\pi$
$284$	−17.0630	−1.01250
$285$	−0.190443	−0.0112809
$286$	−3.22326	−0.190595
$287$	−21.2903	−1.25672
$288$	6.95002	0.409534
$289$	33.4985	1.97050
$290$	−7.26225	−0.426454
$291$	7.55577	0.442927
$292$	−18.7748	−1.09871
$293$	−24.8147	−1.44969	−0.724844	−	0.688913i	$-0.758088\pi$
$293$	−24.8147	−1.44969	−0.724844	+	0.688913i	$0.758088\pi$
$294$	3.92439	0.228875
$295$	0.307873	0.0179251
$296$	12.1405	0.705652
$297$	−14.2077	−0.824415
$298$	0.599736	0.0347418
$299$	1.83736	0.106257
$300$	23.4118	1.35168
$301$	−27.3817	−1.57826
$302$	17.1649	0.987729
$303$	−0.288825	−0.0165926
$304$	0.00755890	0.000433533 0
$305$	6.15627	0.352507
$306$	7.15031	0.408756
$307$	−0.592569	−0.0338197	−0.0169099	−	0.999857i	$-0.505383\pi$
$307$	−0.592569	−0.0338197	−0.0169099	+	0.999857i	$0.505383\pi$
$308$	−10.9093	−0.621617
$309$	2.05058	0.116653
$310$	−12.5421	−0.712344
$311$	3.58049	0.203031	0.101516	−	0.994834i	$-0.467631\pi$
$311$	3.58049	0.203031	0.101516	+	0.994834i	$0.467631\pi$
$312$	5.65554	0.320182
$313$	−13.4640	−0.761030	−0.380515	−	0.924775i	$-0.624253\pi$
$313$	−13.4640	−0.761030	−0.380515	+	0.924775i	$0.624253\pi$
$314$	−0.194030	−0.0109498
$315$	−9.69984	−0.546524
$316$	−10.0770	−0.566876
$317$	−8.88426	−0.498990	−0.249495	−	0.968376i	$-0.580265\pi$
$317$	−8.88426	−0.498990	−0.249495	+	0.968376i	$0.580265\pi$
$318$	−10.5979	−0.594302
$319$	9.04686	0.506527
$320$	15.6312	0.873809
$321$	14.7242	0.821826
$322$	−3.32943	−0.185542
$323$	0.177886	0.00989784
$324$	14.5408	0.807822
$325$	8.76490	0.486189
$326$	12.5865	0.697101
$327$	−36.2048	−2.00213
$328$	−27.0611	−1.49420
$329$	12.0108	0.662178
$330$	24.5222	1.34990
$331$	21.7001	1.19275	0.596374	−	0.802707i	$-0.296608\pi$
$331$	21.7001	1.19275	0.596374	+	0.802707i	$0.296608\pi$
$332$	−13.9785	−0.767170
$333$	−5.30377	−0.290645
$334$	6.65205	0.363984
$335$	14.6480	0.800304
$336$	1.34359	0.0732987
$337$	9.50271	0.517646	0.258823	−	0.965925i	$-0.416665\pi$
$337$	9.50271	0.517646	0.258823	+	0.965925i	$0.416665\pi$
$338$	0.835105	0.0454237
$339$	21.3534	1.15976
$340$	−34.3429	−1.86250
$341$	15.6242	0.846097
$342$	0.0251877	0.00136199
$343$	20.1617	1.08863
$344$	−34.8036	−1.87649
$345$	−13.9784	−0.752574
$346$	14.0574	0.755732
$347$	−1.58705	−0.0851971	−0.0425985	−	0.999092i	$-0.513564\pi$
$347$	−1.58705	−0.0851971	−0.0425985	+	0.999092i	$0.513564\pi$
$348$	−6.26082	−0.335615
$349$	5.95999	0.319031	0.159515	−	0.987195i	$-0.449007\pi$
$349$	5.95999	0.319031	0.159515	+	0.987195i	$0.449007\pi$
$350$	−15.8826	−0.848960
$351$	3.68103	0.196479
$352$	−22.2636	−1.18665
$353$	20.0153	1.06531	0.532653	−	0.846334i	$-0.321195\pi$
$353$	20.0153	1.06531	0.532653	+	0.846334i	$0.321195\pi$
$354$	−0.142103	−0.00755269
$355$	48.5994	2.57939
$356$	9.25572	0.490552
$357$	31.6191	1.67346
$358$	−13.5878	−0.718135
$359$	3.35016	0.176814	0.0884072	−	0.996084i	$-0.471822\pi$
$359$	3.35016	0.176814	0.0884072	+	0.996084i	$0.471822\pi$
$360$	−12.3290	−0.649796
$361$	−18.9994	−0.999967
$362$	−4.24262	−0.222987
$363$	−7.99180	−0.419461
$364$	2.82647	0.148147
$365$	53.4749	2.79900
$366$	−2.84151	−0.148528
$367$	28.6005	1.49294	0.746468	−	0.665421i	$-0.231748\pi$
$367$	28.6005	1.49294	0.746468	+	0.665421i	$0.231748\pi$
$368$	0.554819	0.0289219
$369$	11.8220	0.615431
$370$	−13.6385	−0.709033
$371$	−13.4288	−0.697186
$372$	−10.8126	−0.560608
$373$	32.2456	1.66961	0.834806	−	0.550544i	$-0.185580\pi$
$373$	32.2456	1.66961	0.834806	+	0.550544i	$0.185580\pi$
$374$	−22.9052	−1.18440
$375$	−28.6429	−1.47911
$376$	15.2664	0.787304
$377$	−2.34392	−0.120718
$378$	−6.67028	−0.343082
$379$	4.08562	0.209864	0.104932	−	0.994479i	$-0.466537\pi$
$379$	4.08562	0.209864	0.104932	+	0.994479i	$0.466537\pi$
$380$	−0.120976	−0.00620595
$381$	0.949881	0.0486639
$382$	−4.66796	−0.238834
$383$	27.4568	1.40298	0.701489	−	0.712680i	$-0.252519\pi$
$383$	27.4568	1.40298	0.701489	+	0.712680i	$0.252519\pi$
$384$	16.4416	0.839031
$385$	31.0723	1.58359
$386$	−5.37868	−0.273768
$387$	15.2045	0.772888
$388$	4.79969	0.243667
$389$	−31.3217	−1.58807	−0.794035	−	0.607871i	$-0.792024\pi$
$389$	−31.3217	−1.58807	−0.794035	+	0.607871i	$0.792024\pi$
$390$	−6.35338	−0.321716
$391$	13.0567	0.660307
$392$	6.32049	0.319233
$393$	16.4022	0.827379
$394$	−8.14034	−0.410105
$395$	28.7017	1.44414
$396$	6.05773	0.304413
$397$	−13.7774	−0.691468	−0.345734	−	0.938333i	$-0.612370\pi$
$397$	−13.7774	−0.691468	−0.345734	+	0.938333i	$0.612370\pi$
$398$	−15.1293	−0.758361
$399$	0.111381	0.00557604
$400$	2.64669	0.132335
$401$	23.8246	1.18974	0.594871	−	0.803821i	$-0.297203\pi$
$401$	23.8246	1.18974	0.594871	+	0.803821i	$0.297203\pi$
$402$	−6.76097	−0.337206
$403$	−4.04802	−0.201646
$404$	−0.183472	−0.00912805
$405$	−41.4156	−2.05796
$406$	4.24735	0.210792
$407$	16.9900	0.842164
$408$	40.1895	1.98968
$409$	32.2323	1.59378	0.796891	−	0.604123i	$-0.206476\pi$
$409$	32.2323	1.59378	0.796891	+	0.604123i	$0.206476\pi$
$410$	30.4001	1.50136
$411$	16.5872	0.818187
$412$	1.30260	0.0641745
$413$	−0.180060	−0.00886019
$414$	1.84876	0.0908617
$415$	39.8140	1.95439
$416$	5.76821	0.282810
$417$	7.44224	0.364448
$418$	−0.0806859	−0.00394648
$419$	19.1629	0.936171	0.468085	−	0.883683i	$-0.344944\pi$
$419$	19.1629	0.936171	0.468085	+	0.883683i	$0.344944\pi$
$420$	−21.5034	−1.04926
$421$	25.5599	1.24571	0.622857	−	0.782336i	$-0.285972\pi$
$421$	25.5599	1.24571	0.622857	+	0.782336i	$0.285972\pi$
$422$	16.6652	0.811251
$423$	−6.66936	−0.324275
$424$	−17.0687	−0.828928
$425$	62.2854	3.02128
$426$	−22.4317	−1.08682
$427$	−3.60051	−0.174241
$428$	9.35334	0.452111
$429$	7.91464	0.382123
$430$	39.0980	1.88548
$431$	22.0966	1.06436	0.532179	−	0.846632i	$-0.321373\pi$
$431$	22.0966	1.06436	0.532179	+	0.846632i	$0.321373\pi$
$432$	1.11154	0.0534791
$433$	1.28913	0.0619516	0.0309758	−	0.999520i	$-0.490139\pi$
$433$	1.28913	0.0619516	0.0309758	+	0.999520i	$0.490139\pi$
$434$	7.33529	0.352105
$435$	17.8323	0.854993
$436$	−22.9985	−1.10143
$437$	0.0459936	0.00220017
$438$	−24.6821	−1.17935
$439$	−34.1532	−1.63004	−0.815021	−	0.579431i	$-0.803275\pi$
$439$	−34.1532	−1.63004	−0.815021	+	0.579431i	$0.803275\pi$
$440$	39.4946	1.88283
$441$	−2.76120	−0.131486
$442$	5.93445	0.282273
$443$	−15.0188	−0.713562	−0.356781	−	0.934188i	$-0.616126\pi$
$443$	−15.0188	−0.713562	−0.356781	+	0.934188i	$0.616126\pi$
$444$	−11.7578	−0.558002
$445$	−26.3624	−1.24970
$446$	−16.2038	−0.767273
$447$	−1.47264	−0.0696534
$448$	−9.14193	−0.431916
$449$	5.21877	0.246289	0.123144	−	0.992389i	$-0.460702\pi$
$449$	5.21877	0.246289	0.123144	+	0.992389i	$0.460702\pi$
$450$	8.81928	0.415745
$451$	−37.8706	−1.78326
$452$	13.5644	0.638017
$453$	−42.1480	−1.98029
$454$	−18.5880	−0.872379
$455$	−8.05044	−0.377410
$456$	0.141572	0.00662970
$457$	−39.5569	−1.85039	−0.925197	−	0.379488i	$-0.876100\pi$
$457$	−39.5569	−1.85039	−0.925197	+	0.379488i	$0.876100\pi$
$458$	3.70872	0.173297
$459$	26.1583	1.22096
$460$	−8.87958	−0.414013
$461$	12.4589	0.580269	0.290135	−	0.956986i	$-0.406300\pi$
$461$	12.4589	0.580269	0.290135	+	0.956986i	$0.406300\pi$
$462$	−14.3419	−0.667244
$463$	13.3835	0.621983	0.310992	−	0.950413i	$-0.399339\pi$
$463$	13.3835	0.621983	0.310992	+	0.950413i	$0.399339\pi$
$464$	−0.707782	−0.0328580
$465$	30.7969	1.42817
$466$	−18.9292	−0.876877
$467$	−33.6211	−1.55580	−0.777900	−	0.628388i	$-0.783715\pi$
$467$	−33.6211	−1.55580	−0.777900	+	0.628388i	$0.783715\pi$
$468$	−1.56948	−0.0725493
$469$	−8.56690	−0.395583
$470$	−17.1501	−0.791076
$471$	0.476437	0.0219531
$472$	−0.228866	−0.0105344
$473$	−48.7059	−2.23950
$474$	−13.2476	−0.608485
$475$	0.219406	0.0100671
$476$	20.0855	0.920618
$477$	7.45672	0.341420
$478$	19.8350	0.907232
$479$	33.8522	1.54675	0.773373	−	0.633951i	$-0.218568\pi$
$479$	33.8522	1.54675	0.773373	+	0.633951i	$0.218568\pi$
$480$	−43.8838	−2.00301
$481$	−4.40189	−0.200709
$482$	−2.28372	−0.104021
$483$	8.17533	0.371990
$484$	−5.07667	−0.230758
$485$	−13.6706	−0.620751
$486$	9.89378	0.448791
$487$	−28.8341	−1.30660	−0.653299	−	0.757100i	$-0.726615\pi$
$487$	−28.8341	−1.30660	−0.653299	+	0.757100i	$0.726615\pi$
$488$	−4.57645	−0.207166
$489$	−30.9058	−1.39761
$490$	−7.10038	−0.320762
$491$	12.7059	0.573408	0.286704	−	0.958019i	$-0.407440\pi$
$491$	12.7059	0.573408	0.286704	+	0.958019i	$0.407440\pi$
$492$	26.2081	1.18155
$493$	−16.6565	−0.750169
$494$	0.0209047	0.000940546 0
$495$	−17.2538	−0.775502
$496$	−1.22236	−0.0548856
$497$	−28.4235	−1.27497
$498$	−18.3767	−0.823480
$499$	42.1425	1.88656	0.943279	−	0.332001i	$-0.107724\pi$
$499$	42.1425	1.88656	0.943279	+	0.332001i	$0.107724\pi$
$500$	−18.1949	−0.813703
$501$	−16.3339	−0.729747
$502$	16.6784	0.744393
$503$	4.87935	0.217559	0.108780	−	0.994066i	$-0.465306\pi$
$503$	4.87935	0.217559	0.108780	+	0.994066i	$0.465306\pi$
$504$	7.21066	0.321188
$505$	0.522570	0.0232541
$506$	−5.92230	−0.263278
$507$	−2.05058	−0.0910695
$508$	0.603397	0.0267714
$509$	31.0439	1.37600	0.687998	−	0.725712i	$-0.258490\pi$
$509$	31.0439	1.37600	0.687998	+	0.725712i	$0.258490\pi$
$510$	−45.1485	−1.99921
$511$	−31.2749	−1.38352
$512$	3.40744	0.150589
$513$	0.0921451	0.00406830
$514$	5.74173	0.253257
$515$	−3.71011	−0.163487
$516$	33.7066	1.48385
$517$	21.3645	0.939612
$518$	7.97653	0.350468
$519$	−34.5177	−1.51516
$520$	−10.2325	−0.448727
$521$	16.1761	0.708686	0.354343	−	0.935116i	$-0.384705\pi$
$521$	16.1761	0.708686	0.354343	+	0.935116i	$0.384705\pi$
$522$	−2.35847	−0.103227
$523$	−9.92457	−0.433971	−0.216986	−	0.976175i	$-0.569622\pi$
$523$	−9.92457	−0.433971	−0.216986	+	0.976175i	$0.569622\pi$
$524$	10.4192	0.455165
$525$	38.9993	1.70207
$526$	5.05942	0.220601
$527$	−28.7662	−1.25307
$528$	2.38994	0.104009
$529$	−19.6241	−0.853221
$530$	19.1748	0.832899
$531$	0.0999839	0.00433893
$532$	0.0707533	0.00306754
$533$	9.81178	0.424995
$534$	12.1679	0.526558
$535$	−26.6405	−1.15177
$536$	−10.8890	−0.470333
$537$	33.3644	1.43978
$538$	−21.5441	−0.928831
$539$	8.84521	0.380990
$540$	−17.7896	−0.765544
$541$	−22.9610	−0.987173	−0.493586	−	0.869697i	$-0.664314\pi$
$541$	−22.9610	−0.987173	−0.493586	+	0.869697i	$0.664314\pi$
$542$	−17.8083	−0.764934
$543$	10.4176	0.447064
$544$	40.9902	1.75744
$545$	65.5051	2.80593
$546$	3.71579	0.159021
$547$	−20.4600	−0.874805	−0.437403	−	0.899266i	$-0.644102\pi$
$547$	−20.4600	−0.874805	−0.437403	+	0.899266i	$0.644102\pi$
$548$	10.5368	0.450108
$549$	1.99929	0.0853277
$550$	−28.2516	−1.20465
$551$	−0.0586740	−0.00249960
$552$	10.3913	0.442282
$553$	−16.7863	−0.713824
$554$	1.71387	0.0728155
$555$	33.4891	1.42153
$556$	4.72757	0.200494
$557$	37.9554	1.60822	0.804111	−	0.594479i	$-0.202642\pi$
$557$	37.9554	1.60822	0.804111	+	0.594479i	$0.202642\pi$
$558$	−4.07314	−0.172430
$559$	12.6191	0.533730
$560$	−2.43095	−0.102726
$561$	56.2432	2.37459
$562$	2.37601	0.100226
$563$	21.5256	0.907197	0.453598	−	0.891206i	$-0.350140\pi$
$563$	21.5256	0.907197	0.453598	+	0.891206i	$0.350140\pi$
$564$	−14.7852	−0.622569
$565$	−38.6347	−1.62537
$566$	−7.53633	−0.316776
$567$	24.2220	1.01723
$568$	−36.1278	−1.51589
$569$	18.2967	0.767038	0.383519	−	0.923533i	$-0.374712\pi$
$569$	18.2967	0.767038	0.383519	+	0.923533i	$0.374712\pi$
$570$	−0.159040	−0.00666146
$571$	−36.3440	−1.52095	−0.760475	−	0.649367i	$-0.775034\pi$
$571$	−36.3440	−1.52095	−0.760475	+	0.649367i	$0.775034\pi$
$572$	5.02765	0.210217
$573$	11.4621	0.478835
$574$	−17.7796	−0.742106
$575$	16.1043	0.671596
$576$	5.07633	0.211514
$577$	24.7549	1.03056	0.515280	−	0.857022i	$-0.327688\pi$
$577$	24.7549	1.03056	0.515280	+	0.857022i	$0.327688\pi$
$578$	27.9747	1.16360
$579$	13.2072	0.548874
$580$	11.3277	0.470356
$581$	−23.2853	−0.966039
$582$	6.30986	0.261552
$583$	−23.8867	−0.989288
$584$	−39.7521	−1.64495
$585$	4.47025	0.184822
$586$	−20.7229	−0.856053
$587$	16.0954	0.664329	0.332164	−	0.943222i	$-0.392221\pi$
$587$	16.0954	0.664329	0.332164	+	0.943222i	$0.392221\pi$
$588$	−6.12127	−0.252437
$589$	−0.101332	−0.00417530
$590$	0.257106	0.0105849
$591$	19.9884	0.822214
$592$	−1.32922	−0.0546305
$593$	−16.7750	−0.688867	−0.344434	−	0.938811i	$-0.611929\pi$
$593$	−16.7750	−0.688867	−0.344434	+	0.938811i	$0.611929\pi$
$594$	−11.8649	−0.486824
$595$	−57.2082	−2.34531
$596$	−0.935470	−0.0383184
$597$	37.1495	1.52043
$598$	1.53439	0.0627459
$599$	−29.0316	−1.18620	−0.593100	−	0.805129i	$-0.702096\pi$
$599$	−29.0316	−1.18620	−0.593100	+	0.805129i	$0.702096\pi$
$600$	49.5702	2.02370
$601$	27.1988	1.10946	0.554732	−	0.832029i	$-0.312821\pi$
$601$	27.1988	1.10946	0.554732	+	0.832029i	$0.312821\pi$
$602$	−22.8666	−0.931973
$603$	4.75703	0.193721
$604$	−26.7739	−1.08941
$605$	14.4595	0.587864
$606$	−0.241199	−0.00979805
$607$	10.6859	0.433725	0.216863	−	0.976202i	$-0.430418\pi$
$607$	10.6859	0.433725	0.216863	+	0.976202i	$0.430418\pi$
$608$	0.144392	0.00585587
$609$	−10.4293	−0.422615
$610$	5.14114	0.208159
$611$	−5.53528	−0.223933
$612$	−11.1531	−0.450837
$613$	−11.1608	−0.450780	−0.225390	−	0.974269i	$-0.572366\pi$
$613$	−11.1608	−0.450780	−0.225390	+	0.974269i	$0.572366\pi$
$614$	−0.494858	−0.0199708
$615$	−74.6468	−3.01005
$616$	−23.0985	−0.930666
$617$	−11.9201	−0.479886	−0.239943	−	0.970787i	$-0.577129\pi$
$617$	−11.9201	−0.479886	−0.239943	+	0.970787i	$0.577129\pi$
$618$	1.71245	0.0688849
$619$	−39.7413	−1.59734	−0.798668	−	0.601772i	$-0.794462\pi$
$619$	−39.7413	−1.59734	−0.798668	+	0.601772i	$0.794462\pi$
$620$	19.5632	0.785678
$621$	6.76340	0.271406
$622$	2.99009	0.119892
$623$	15.4181	0.617715
$624$	−0.619203	−0.0247880
$625$	7.99896	0.319959
$626$	−11.2439	−0.449395
$627$	0.198122	0.00791225
$628$	0.302649	0.0120770
$629$	−31.2809	−1.24725
$630$	−8.10038	−0.322727
$631$	−20.2199	−0.804940	−0.402470	−	0.915433i	$-0.631848\pi$
$631$	−20.2199	−0.804940	−0.402470	+	0.915433i	$0.631848\pi$
$632$	−21.3362	−0.848710
$633$	−40.9211	−1.62647
$634$	−7.41929	−0.294658
$635$	−1.71861	−0.0682011
$636$	16.5307	0.655484
$637$	−2.29168	−0.0907996
$638$	7.55508	0.299108
$639$	15.7830	0.624366
$640$	−29.7477	−1.17588
$641$	−23.3505	−0.922291	−0.461145	−	0.887325i	$-0.652561\pi$
$641$	−23.3505	−0.922291	−0.461145	+	0.887325i	$0.652561\pi$
$642$	12.2963	0.485295
$643$	22.1200	0.872329	0.436165	−	0.899867i	$-0.356337\pi$
$643$	22.1200	0.872329	0.436165	+	0.899867i	$0.356337\pi$
$644$	5.19325	0.204643
$645$	−96.0043	−3.78017
$646$	0.148553	0.00584476
$647$	20.0247	0.787251	0.393625	−	0.919271i	$-0.371221\pi$
$647$	20.0247	0.787251	0.393625	+	0.919271i	$0.371221\pi$
$648$	30.7875	1.20945
$649$	−0.320287	−0.0125724
$650$	7.31961	0.287099
$651$	−18.0116	−0.705932
$652$	−19.6324	−0.768866
$653$	−5.64991	−0.221098	−0.110549	−	0.993871i	$-0.535261\pi$
$653$	−5.64991	−0.221098	−0.110549	+	0.993871i	$0.535261\pi$
$654$	−30.2348	−1.18227
$655$	−29.6763	−1.15955
$656$	2.96281	0.115678
$657$	17.3663	0.677525
$658$	10.0303	0.391021
$659$	16.8150	0.655020	0.327510	−	0.944848i	$-0.393791\pi$
$659$	16.8150	0.655020	0.327510	+	0.944848i	$0.393791\pi$
$660$	−38.2498	−1.48887
$661$	47.3485	1.84164	0.920821	−	0.389985i	$-0.127520\pi$
$661$	47.3485	1.84164	0.920821	+	0.389985i	$0.127520\pi$
$662$	18.1219	0.704327
$663$	−14.5719	−0.565925
$664$	−29.5969	−1.14858
$665$	−0.201522	−0.00781468
$666$	−4.42920	−0.171628
$667$	−4.30664	−0.166754
$668$	−10.3759	−0.401455
$669$	39.7881	1.53830
$670$	12.2326	0.472586
$671$	−6.40451	−0.247243
$672$	25.6656	0.990071
$673$	−31.6196	−1.21885	−0.609423	−	0.792845i	$-0.708599\pi$
$673$	−31.6196	−1.21885	−0.609423	+	0.792845i	$0.708599\pi$
$674$	7.93576	0.305674
$675$	32.2639	1.24184
$676$	−1.30260	−0.0501000
$677$	19.9356	0.766187	0.383093	−	0.923710i	$-0.374859\pi$
$677$	19.9356	0.766187	0.383093	+	0.923710i	$0.374859\pi$
$678$	17.8324	0.684847
$679$	7.99530	0.306832
$680$	−72.7148	−2.78848
$681$	45.6425	1.74902
$682$	13.0478	0.499628
$683$	−14.1683	−0.542135	−0.271067	−	0.962560i	$-0.587377\pi$
$683$	−14.1683	−0.542135	−0.271067	+	0.962560i	$0.587377\pi$
$684$	−0.0392879	−0.00150221
$685$	−30.0112	−1.14667
$686$	16.8371	0.642845
$687$	−9.10667	−0.347441
$688$	3.81051	0.145274
$689$	6.18875	0.235772
$690$	−11.6735	−0.444401
$691$	−4.69646	−0.178662	−0.0893309	−	0.996002i	$-0.528473\pi$
$691$	−4.69646	−0.178662	−0.0893309	+	0.996002i	$0.528473\pi$
$692$	−21.9268	−0.833533
$693$	10.0910	0.383324
$694$	−1.32535	−0.0503096
$695$	−13.4652	−0.510765
$696$	−13.2562	−0.502473
$697$	69.7247	2.64101
$698$	4.97721	0.188390
$699$	46.4802	1.75804
$700$	24.7737	0.936358
$701$	27.0833	1.02292	0.511461	−	0.859307i	$-0.329105\pi$
$701$	27.0833	1.02292	0.511461	+	0.859307i	$0.329105\pi$
$702$	3.07405	0.116023
$703$	−0.110190	−0.00415589
$704$	−16.2614	−0.612876
$705$	42.1117	1.58602
$706$	16.7149	0.629073
$707$	−0.305626	−0.0114943
$708$	0.221653	0.00833022
$709$	−26.6386	−1.00043	−0.500217	−	0.865900i	$-0.666747\pi$
$709$	−26.6386	−1.00043	−0.500217	+	0.865900i	$0.666747\pi$
$710$	40.5856	1.52315
$711$	9.32107	0.349567
$712$	19.5973	0.734440
$713$	−7.43769	−0.278544
$714$	26.4052	0.988191
$715$	−14.3199	−0.535535
$716$	21.1942	0.792066
$717$	−48.7044	−1.81890
$718$	2.79773	0.104410
$719$	−27.7074	−1.03331	−0.516656	−	0.856193i	$-0.672823\pi$
$719$	−27.7074	−1.03331	−0.516656	+	0.856193i	$0.672823\pi$
$720$	1.34986	0.0503062
$721$	2.16987	0.0808101
$722$	−15.8665	−0.590489
$723$	5.60763	0.208550
$724$	6.61765	0.245943
$725$	−20.5443	−0.762995
$726$	−6.67400	−0.247695
$727$	−31.8609	−1.18166	−0.590828	−	0.806798i	$-0.701199\pi$
$727$	−31.8609	−1.18166	−0.590828	+	0.806798i	$0.701199\pi$
$728$	5.98453	0.221801
$729$	9.19477	0.340547
$730$	44.6571	1.65283
$731$	89.6740	3.31671
$732$	4.43220	0.163819
$733$	28.0703	1.03680	0.518400	−	0.855138i	$-0.326528\pi$
$733$	28.0703	1.03680	0.518400	+	0.855138i	$0.326528\pi$
$734$	23.8845	0.881592
$735$	17.4348	0.643093
$736$	10.5983	0.390658
$737$	−15.2386	−0.561321
$738$	9.87265	0.363417
$739$	−33.4232	−1.22949	−0.614747	−	0.788725i	$-0.710742\pi$
$739$	−33.4232	−1.22949	−0.614747	+	0.788725i	$0.710742\pi$
$740$	21.2734	0.782026
$741$	−0.0513310	−0.00188569
$742$	−11.2144	−0.411694
$743$	0.866497	0.0317887	0.0158943	−	0.999874i	$-0.494940\pi$
$743$	0.866497	0.0317887	0.0158943	+	0.999874i	$0.494940\pi$
$744$	−22.8938	−0.839326
$745$	2.66444	0.0976174
$746$	26.9284	0.985920
$747$	12.9299	0.473080
$748$	35.7276	1.30633
$749$	15.5808	0.569309
$750$	−23.9198	−0.873428
$751$	37.4207	1.36550	0.682750	−	0.730653i	$-0.260784\pi$
$751$	37.4207	1.36550	0.682750	+	0.730653i	$0.260784\pi$
$752$	−1.67146	−0.0609518
$753$	−40.9534	−1.49242
$754$	−1.95742	−0.0712851
$755$	76.2582	2.77532
$756$	10.4043	0.378401
$757$	−22.5372	−0.819129	−0.409564	−	0.912281i	$-0.634319\pi$
$757$	−22.5372	−0.819129	−0.409564	+	0.912281i	$0.634319\pi$
$758$	3.41192	0.123927
$759$	14.5421	0.527844
$760$	−0.256145	−0.00929136
$761$	40.7444	1.47698	0.738492	−	0.674262i	$-0.235538\pi$
$761$	40.7444	1.47698	0.738492	+	0.674262i	$0.235538\pi$
$762$	0.793250	0.0287364
$763$	−38.3109	−1.38695
$764$	7.28111	0.263421
$765$	31.7666	1.14852
$766$	22.9293	0.828470
$767$	0.0829822	0.00299631
$768$	31.0092	1.11895
$769$	−38.4768	−1.38751	−0.693755	−	0.720211i	$-0.744045\pi$
$769$	−38.4768	−1.38751	−0.693755	+	0.720211i	$0.744045\pi$
$770$	25.9487	0.935125
$771$	−14.0987	−0.507752
$772$	8.38968	0.301951
$773$	−41.6871	−1.49938	−0.749691	−	0.661788i	$-0.769798\pi$
$773$	−41.6871	−1.49938	−0.749691	+	0.661788i	$0.769798\pi$
$774$	12.6974	0.456397
$775$	−35.4805	−1.27450
$776$	10.1625	0.364811
$777$	−19.5862	−0.702650
$778$	−26.1569	−0.937769
$779$	0.245612	0.00879998
$780$	9.91002	0.354836
$781$	−50.5590	−1.80914
$782$	10.9037	0.389917
$783$	−8.62806	−0.308342
$784$	−0.692006	−0.0247145
$785$	−0.862016	−0.0307667
$786$	13.6975	0.488574
$787$	−11.2224	−0.400037	−0.200018	−	0.979792i	$-0.564100\pi$
$787$	−11.2224	−0.400037	−0.200018	+	0.979792i	$0.564100\pi$
$788$	12.6973	0.452324
$789$	−12.4233	−0.442281
$790$	23.9689	0.852776
$791$	22.5956	0.803407
$792$	12.8261	0.455757
$793$	1.65933	0.0589244
$794$	−11.5056	−0.408318
$795$	−47.0832	−1.66987
$796$	23.5987	0.836432
$797$	−15.6743	−0.555211	−0.277605	−	0.960695i	$-0.589541\pi$
$797$	−15.6743	−0.555211	−0.277605	+	0.960695i	$0.589541\pi$
$798$	0.0930151	0.00329270
$799$	−39.3349	−1.39157
$800$	50.5578	1.78749
$801$	−8.56139	−0.302502
$802$	19.8960	0.702553
$803$	−55.6311	−1.96318
$804$	10.5458	0.371921
$805$	−14.7916	−0.521335
$806$	−3.38053	−0.119074
$807$	52.9010	1.86220
$808$	−0.388468	−0.0136662
$809$	27.5190	0.967518	0.483759	−	0.875201i	$-0.339271\pi$
$809$	27.5190	0.967518	0.483759	+	0.875201i	$0.339271\pi$
$810$	−34.5864	−1.21524
$811$	46.3169	1.62641	0.813203	−	0.581979i	$-0.197722\pi$
$811$	46.3169	1.62641	0.813203	+	0.581979i	$0.197722\pi$
$812$	−6.62503	−0.232493
$813$	43.7280	1.53361
$814$	14.1885	0.497305
$815$	55.9178	1.95871
$816$	−4.40020	−0.154038
$817$	0.315886	0.0110514
$818$	26.9173	0.941142
$819$	−2.61444	−0.0913558
$820$	−47.4182	−1.65592
$821$	50.2855	1.75498	0.877488	−	0.479598i	$-0.159217\pi$
$821$	50.2855	1.75498	0.877488	+	0.479598i	$0.159217\pi$
$822$	13.8521	0.483146
$823$	−15.3373	−0.534626	−0.267313	−	0.963610i	$-0.586136\pi$
$823$	−15.3373	−0.534626	−0.267313	+	0.963610i	$0.586136\pi$
$824$	2.75802	0.0960801
$825$	69.3710	2.41519
$826$	−0.150369	−0.00523202
$827$	−45.4498	−1.58044	−0.790222	−	0.612821i	$-0.790035\pi$
$827$	−45.4498	−1.58044	−0.790222	+	0.612821i	$0.790035\pi$
$828$	−2.88371	−0.100216
$829$	−9.61822	−0.334055	−0.167027	−	0.985952i	$-0.553417\pi$
$829$	−9.61822	−0.334055	−0.167027	+	0.985952i	$0.553417\pi$
$830$	33.2489	1.15409
$831$	−4.20838	−0.145987
$832$	4.21313	0.146064
$833$	−16.2852	−0.564248
$834$	6.21506	0.215210
$835$	29.5529	1.02272
$836$	0.125854	0.00435276
$837$	−14.9009	−0.515051
$838$	16.0031	0.552817
$839$	29.7327	1.02649	0.513244	−	0.858243i	$-0.328444\pi$
$839$	29.7327	1.02649	0.513244	+	0.858243i	$0.328444\pi$
$840$	−45.5296	−1.57092
$841$	−23.5060	−0.810552
$842$	21.3452	0.735604
$843$	−5.83423	−0.200942
$844$	−25.9945	−0.894767
$845$	3.71011	0.127632
$846$	−5.56962	−0.191487
$847$	−8.45670	−0.290576
$848$	1.86878	0.0641743
$849$	18.5053	0.635100
$850$	52.0148	1.78409
$851$	−8.08788	−0.277249
$852$	34.9891	1.19871
$853$	−47.5286	−1.62735	−0.813675	−	0.581320i	$-0.802536\pi$
$853$	−47.5286	−1.62735	−0.813675	+	0.581320i	$0.802536\pi$
$854$	−3.00681	−0.102891
$855$	0.111901	0.00382693
$856$	19.8040	0.676886
$857$	−27.6692	−0.945160	−0.472580	−	0.881288i	$-0.656677\pi$
$857$	−27.6692	−0.945160	−0.472580	+	0.881288i	$0.656677\pi$
$858$	6.60956	0.225647
$859$	22.3058	0.761063	0.380532	−	0.924768i	$-0.375741\pi$
$859$	22.3058	0.761063	0.380532	+	0.924768i	$0.375741\pi$
$860$	−60.9853	−2.07958
$861$	43.6574	1.48784
$862$	18.4530	0.628512
$863$	21.6516	0.737028	0.368514	−	0.929622i	$-0.379867\pi$
$863$	21.6516	0.737028	0.368514	+	0.929622i	$0.379867\pi$
$864$	21.2330	0.722360
$865$	62.4527	2.12346
$866$	1.07656	0.0365829
$867$	−68.6913	−2.33288
$868$	−11.4416	−0.388354
$869$	−29.8590	−1.01290
$870$	14.8918	0.504880
$871$	3.94812	0.133777
$872$	−48.6952	−1.64903
$873$	−4.43963	−0.150259
$874$	0.0384095	0.00129922
$875$	−30.3091	−1.02463
$876$	38.4992	1.30077
$877$	42.1201	1.42230	0.711148	−	0.703042i	$-0.248175\pi$
$877$	42.1201	1.42230	0.711148	+	0.703042i	$0.248175\pi$
$878$	−28.5215	−0.962554
$879$	50.8845	1.71629
$880$	−4.32411	−0.145766
$881$	−10.3173	−0.347599	−0.173799	−	0.984781i	$-0.555604\pi$
$881$	−10.3173	−0.347599	−0.173799	+	0.984781i	$0.555604\pi$
$882$	−2.30590	−0.0776436
$883$	−42.2001	−1.42015	−0.710073	−	0.704128i	$-0.751338\pi$
$883$	−42.2001	−1.42015	−0.710073	+	0.704128i	$0.751338\pi$
$884$	−9.25657	−0.311332
$885$	−0.631319	−0.0212215
$886$	−12.5422	−0.421365
$887$	−23.7810	−0.798486	−0.399243	−	0.916845i	$-0.630727\pi$
$887$	−23.7810	−0.798486	−0.399243	+	0.916845i	$0.630727\pi$
$888$	−24.8951	−0.835424
$889$	1.00514	0.0337112
$890$	−22.0154	−0.737958
$891$	43.0855	1.44342
$892$	25.2748	0.846262
$893$	−0.138561	−0.00463678
$894$	−1.22981	−0.0411309
$895$	−60.3661	−2.01782
$896$	17.3980	0.581227
$897$	−3.76766	−0.125799
$898$	4.35822	0.145436
$899$	9.48826	0.316451
$900$	−13.7563	−0.458545
$901$	43.9786	1.46514
$902$	−31.6259	−1.05303
$903$	56.1484	1.86850
$904$	28.7202	0.955220
$905$	−18.8486	−0.626549
$906$	−35.1980	−1.16938
$907$	49.4359	1.64149	0.820746	−	0.571293i	$-0.193558\pi$
$907$	49.4359	1.64149	0.820746	+	0.571293i	$0.193558\pi$
$908$	28.9937	0.962188
$909$	0.169708	0.00562887
$910$	−6.72296	−0.222864
$911$	−19.0033	−0.629608	−0.314804	−	0.949157i	$-0.601939\pi$
$911$	−19.0033	−0.629608	−0.314804	+	0.949157i	$0.601939\pi$
$912$	−0.0155001	−0.000513261 0
$913$	−41.4194	−1.37078
$914$	−33.0342	−1.09267
$915$	−12.6239	−0.417335
$916$	−5.78487	−0.191137
$917$	17.3563	0.573155
$918$	21.8449	0.720989
$919$	−56.8938	−1.87675	−0.938377	−	0.345613i	$-0.887671\pi$
$919$	−56.8938	−1.87675	−0.938377	+	0.345613i	$0.887671\pi$
$920$	−18.8009	−0.619847
$921$	1.21511	0.0400393
$922$	10.4045	0.342654
$923$	13.0992	0.431165
$924$	22.3705	0.735935
$925$	−38.5822	−1.26857
$926$	11.1766	0.367286
$927$	−1.20488	−0.0395736
$928$	−13.5202	−0.443824
$929$	−40.6903	−1.33500	−0.667502	−	0.744608i	$-0.732636\pi$
$929$	−40.6903	−1.33500	−0.667502	+	0.744608i	$0.732636\pi$
$930$	25.7186	0.843347
$931$	−0.0573662	−0.00188010
$932$	29.5258	0.967150
$933$	−7.34209	−0.240369
$934$	−28.0772	−0.918713
$935$	−101.761	−3.32793
$936$	−3.32309	−0.108619
$937$	20.3076	0.663421	0.331711	−	0.943381i	$-0.392374\pi$
$937$	20.3076	0.663421	0.331711	+	0.943381i	$0.392374\pi$
$938$	−7.15426	−0.233595
$939$	27.6090	0.900986
$940$	26.7508	0.872515
$941$	−42.0297	−1.37013	−0.685064	−	0.728482i	$-0.740226\pi$
$941$	−42.0297	−1.37013	−0.685064	+	0.728482i	$0.740226\pi$
$942$	0.397875	0.0129635
$943$	18.0278	0.587066
$944$	0.0250577	0.000815559 0
$945$	−29.6339	−0.963992
$946$	−40.6746	−1.32244
$947$	31.5740	1.02602	0.513008	−	0.858384i	$-0.328531\pi$
$947$	31.5740	1.02602	0.513008	+	0.858384i	$0.328531\pi$
$948$	20.6637	0.671127
$949$	14.4133	0.467875
$950$	0.183227	0.00594468
$951$	18.2179	0.590756
$952$	42.5274	1.37832
$953$	11.1477	0.361110	0.180555	−	0.983565i	$-0.442211\pi$
$953$	11.1477	0.361110	0.180555	+	0.983565i	$0.442211\pi$
$954$	6.22714	0.201611
$955$	−20.7383	−0.671075
$956$	−30.9387	−1.00063
$957$	−18.5513	−0.599679
$958$	28.2701	0.913366
$959$	17.5521	0.566787
$960$	−32.0530	−1.03451
$961$	−14.6135	−0.471403
$962$	−3.67604	−0.118520
$963$	−8.65168	−0.278797
$964$	3.56216	0.114729
$965$	−23.8958	−0.769232
$966$	6.82726	0.219663
$967$	47.5837	1.53019	0.765095	−	0.643918i	$-0.222692\pi$
$967$	47.5837	1.53019	0.765095	+	0.643918i	$0.222692\pi$
$968$	−10.7489	−0.345483
$969$	−0.364769	−0.0117181
$970$	−11.4164	−0.366559
$971$	−25.9477	−0.832700	−0.416350	−	0.909204i	$-0.636691\pi$
$971$	−25.9477	−0.832700	−0.416350	+	0.909204i	$0.636691\pi$
$972$	−15.4323	−0.494993
$973$	7.87517	0.252466
$974$	−24.0795	−0.771557
$975$	−17.9731	−0.575601
$976$	0.501058	0.0160385
$977$	26.4595	0.846514	0.423257	−	0.906010i	$-0.360887\pi$
$977$	26.4595	0.846514	0.423257	+	0.906010i	$0.360887\pi$
$978$	−25.8096	−0.825300
$979$	27.4254	0.876521
$980$	11.0752	0.353784
$981$	21.2732	0.679203
$982$	10.6107	0.338602
$983$	10.3453	0.329963	0.164981	−	0.986297i	$-0.447244\pi$
$983$	10.3453	0.329963	0.164981	+	0.986297i	$0.447244\pi$
$984$	55.4909	1.76899
$985$	−36.1650	−1.15231
$986$	−13.9099	−0.442981
$987$	−24.6291	−0.783954
$988$	−0.0326072	−0.00103737
$989$	23.1858	0.737266
$990$	−14.4088	−0.457941
$991$	−9.70724	−0.308361	−0.154180	−	0.988043i	$-0.549274\pi$
$991$	−9.70724	−0.308361	−0.154180	+	0.988043i	$0.549274\pi$
$992$	−23.3498	−0.741358
$993$	−44.4979	−1.41210
$994$	−23.7366	−0.752880
$995$	−67.2145	−2.13084
$996$	28.6641	0.908255
$997$	42.4432	1.34419	0.672094	−	0.740465i	$-0.265395\pi$
$997$	42.4432	1.34419	0.672094	+	0.740465i	$0.265395\pi$
$998$	35.1934	1.11403
$999$	−16.2035	−0.512657

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.f.1.17	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.f.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+0.835105 q^{2} -2.05058 q^{3} -1.30260 q^{4} +3.71011 q^{5} -1.71245 q^{6} -2.16987 q^{7} -2.75802 q^{8} +1.20488 q^{9} +O(q^{10})\)	\(q+0.835105 q^{2} -2.05058 q^{3} -1.30260 q^{4} +3.71011 q^{5} -1.71245 q^{6} -2.16987 q^{7} -2.75802 q^{8} +1.20488 q^{9} +3.09833 q^{10} -3.85971 q^{11} +2.67109 q^{12} +1.00000 q^{13} -1.81207 q^{14} -7.60788 q^{15} +0.301965 q^{16} +7.10623 q^{17} +1.00620 q^{18} +0.0250324 q^{19} -4.83278 q^{20} +4.44949 q^{21} -3.22326 q^{22} +1.83736 q^{23} +5.65554 q^{24} +8.76490 q^{25} +0.835105 q^{26} +3.68103 q^{27} +2.82647 q^{28} -2.34392 q^{29} -6.35338 q^{30} -4.04802 q^{31} +5.76821 q^{32} +7.91464 q^{33} +5.93445 q^{34} -8.05044 q^{35} -1.56948 q^{36} -4.40189 q^{37} +0.0209047 q^{38} -2.05058 q^{39} -10.2325 q^{40} +9.81178 q^{41} +3.71579 q^{42} +12.6191 q^{43} +5.02765 q^{44} +4.47025 q^{45} +1.53439 q^{46} -5.53528 q^{47} -0.619203 q^{48} -2.29168 q^{49} +7.31961 q^{50} -14.5719 q^{51} -1.30260 q^{52} +6.18875 q^{53} +3.07405 q^{54} -14.3199 q^{55} +5.98453 q^{56} -0.0513310 q^{57} -1.95742 q^{58} +0.0829822 q^{59} +9.91002 q^{60} +1.65933 q^{61} -3.38053 q^{62} -2.61444 q^{63} +4.21313 q^{64} +3.71011 q^{65} +6.60956 q^{66} +3.94812 q^{67} -9.25657 q^{68} -3.76766 q^{69} -6.72296 q^{70} +13.0992 q^{71} -3.32309 q^{72} +14.4133 q^{73} -3.67604 q^{74} -17.9731 q^{75} -0.0326072 q^{76} +8.37505 q^{77} -1.71245 q^{78} +7.73607 q^{79} +1.12032 q^{80} -11.1629 q^{81} +8.19387 q^{82} +10.7312 q^{83} -5.79590 q^{84} +26.3649 q^{85} +10.5383 q^{86} +4.80641 q^{87} +10.6451 q^{88} -7.10557 q^{89} +3.73313 q^{90} -2.16987 q^{91} -2.39335 q^{92} +8.30080 q^{93} -4.62254 q^{94} +0.0928729 q^{95} -11.8282 q^{96} -3.68470 q^{97} -1.91379 q^{98} -4.65050 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9}+O(q^{10}) \) 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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