LMFDB - Embedded newform 6010.2.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.34202 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.34202 q^{6} +2.38251 q^{7} +1.00000 q^{8} -1.19898 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.34202 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.34202 q^{6} +2.38251 q^{7} +1.00000 q^{8} -1.19898 q^{9} -1.00000 q^{10} -3.62020 q^{11} +1.34202 q^{12} -2.92305 q^{13} +2.38251 q^{14} -1.34202 q^{15} +1.00000 q^{16} -2.81300 q^{17} -1.19898 q^{18} +1.26964 q^{19} -1.00000 q^{20} +3.19737 q^{21} -3.62020 q^{22} -5.29024 q^{23} +1.34202 q^{24} +1.00000 q^{25} -2.92305 q^{26} -5.63512 q^{27} +2.38251 q^{28} -1.21165 q^{29} -1.34202 q^{30} +9.48477 q^{31} +1.00000 q^{32} -4.85838 q^{33} -2.81300 q^{34} -2.38251 q^{35} -1.19898 q^{36} -4.43168 q^{37} +1.26964 q^{38} -3.92280 q^{39} -1.00000 q^{40} -2.70832 q^{41} +3.19737 q^{42} -7.47622 q^{43} -3.62020 q^{44} +1.19898 q^{45} -5.29024 q^{46} +4.08944 q^{47} +1.34202 q^{48} -1.32365 q^{49} +1.00000 q^{50} -3.77510 q^{51} -2.92305 q^{52} -6.18954 q^{53} -5.63512 q^{54} +3.62020 q^{55} +2.38251 q^{56} +1.70388 q^{57} -1.21165 q^{58} +10.0812 q^{59} -1.34202 q^{60} +6.82551 q^{61} +9.48477 q^{62} -2.85659 q^{63} +1.00000 q^{64} +2.92305 q^{65} -4.85838 q^{66} -9.43122 q^{67} -2.81300 q^{68} -7.09961 q^{69} -2.38251 q^{70} -13.2242 q^{71} -1.19898 q^{72} -13.1073 q^{73} -4.43168 q^{74} +1.34202 q^{75} +1.26964 q^{76} -8.62515 q^{77} -3.92280 q^{78} -4.26050 q^{79} -1.00000 q^{80} -3.96549 q^{81} -2.70832 q^{82} -5.16762 q^{83} +3.19737 q^{84} +2.81300 q^{85} -7.47622 q^{86} -1.62606 q^{87} -3.62020 q^{88} -0.599015 q^{89} +1.19898 q^{90} -6.96420 q^{91} -5.29024 q^{92} +12.7288 q^{93} +4.08944 q^{94} -1.26964 q^{95} +1.34202 q^{96} +8.31904 q^{97} -1.32365 q^{98} +4.34055 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.34202	0.774815	0.387408	−	0.921908i	$-0.373371\pi$
$3$	1.34202	0.774815	0.387408	+	0.921908i	$0.373371\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.34202	0.547877
$7$	2.38251	0.900504	0.450252	−	0.892902i	$-0.351334\pi$
$7$	2.38251	0.900504	0.450252	+	0.892902i	$0.351334\pi$
$8$	1.00000	0.353553
$9$	−1.19898	−0.399661
$10$	−1.00000	−0.316228
$11$	−3.62020	−1.09153	−0.545765	−	0.837938i	$-0.683761\pi$
$11$	−3.62020	−1.09153	−0.545765	+	0.837938i	$0.683761\pi$
$12$	1.34202	0.387408
$13$	−2.92305	−0.810709	−0.405355	−	0.914160i	$-0.632852\pi$
$13$	−2.92305	−0.810709	−0.405355	+	0.914160i	$0.632852\pi$
$14$	2.38251	0.636752
$15$	−1.34202	−0.346508
$16$	1.00000	0.250000
$17$	−2.81300	−0.682253	−0.341126	−	0.940017i	$-0.610808\pi$
$17$	−2.81300	−0.682253	−0.341126	+	0.940017i	$0.610808\pi$
$18$	−1.19898	−0.282603
$19$	1.26964	0.291275	0.145637	−	0.989338i	$-0.453477\pi$
$19$	1.26964	0.291275	0.145637	+	0.989338i	$0.453477\pi$
$20$	−1.00000	−0.223607
$21$	3.19737	0.697724
$22$	−3.62020	−0.771829
$23$	−5.29024	−1.10309	−0.551546	−	0.834145i	$-0.685962\pi$
$23$	−5.29024	−1.10309	−0.551546	+	0.834145i	$0.685962\pi$
$24$	1.34202	0.273939
$25$	1.00000	0.200000
$26$	−2.92305	−0.573258
$27$	−5.63512	−1.08448
$28$	2.38251	0.450252
$29$	−1.21165	−0.224998	−0.112499	−	0.993652i	$-0.535886\pi$
$29$	−1.21165	−0.224998	−0.112499	+	0.993652i	$0.535886\pi$
$30$	−1.34202	−0.245018
$31$	9.48477	1.70352	0.851758	−	0.523936i	$-0.175537\pi$
$31$	9.48477	1.70352	0.851758	+	0.523936i	$0.175537\pi$
$32$	1.00000	0.176777
$33$	−4.85838	−0.845735
$34$	−2.81300	−0.482425
$35$	−2.38251	−0.402718
$36$	−1.19898	−0.199831
$37$	−4.43168	−0.728564	−0.364282	−	0.931289i	$-0.618685\pi$
$37$	−4.43168	−0.728564	−0.364282	+	0.931289i	$0.618685\pi$
$38$	1.26964	0.205962
$39$	−3.92280	−0.628150
$40$	−1.00000	−0.158114
$41$	−2.70832	−0.422968	−0.211484	−	0.977381i	$-0.567830\pi$
$41$	−2.70832	−0.422968	−0.211484	+	0.977381i	$0.567830\pi$
$42$	3.19737	0.493366
$43$	−7.47622	−1.14011	−0.570057	−	0.821605i	$-0.693079\pi$
$43$	−7.47622	−1.14011	−0.570057	+	0.821605i	$0.693079\pi$
$44$	−3.62020	−0.545765
$45$	1.19898	0.178734
$46$	−5.29024	−0.780003
$47$	4.08944	0.596506	0.298253	−	0.954487i	$-0.403596\pi$
$47$	4.08944	0.596506	0.298253	+	0.954487i	$0.403596\pi$
$48$	1.34202	0.193704
$49$	−1.32365	−0.189093
$50$	1.00000	0.141421
$51$	−3.77510	−0.528620
$52$	−2.92305	−0.405355
$53$	−6.18954	−0.850199	−0.425099	−	0.905147i	$-0.639761\pi$
$53$	−6.18954	−0.850199	−0.425099	+	0.905147i	$0.639761\pi$
$54$	−5.63512	−0.766842
$55$	3.62020	0.488147
$56$	2.38251	0.318376
$57$	1.70388	0.225684
$58$	−1.21165	−0.159098
$59$	10.0812	1.31246	0.656228	−	0.754563i	$-0.272151\pi$
$59$	10.0812	1.31246	0.656228	+	0.754563i	$0.272151\pi$
$60$	−1.34202	−0.173254
$61$	6.82551	0.873917	0.436959	−	0.899482i	$-0.356056\pi$
$61$	6.82551	0.873917	0.436959	+	0.899482i	$0.356056\pi$
$62$	9.48477	1.20457
$63$	−2.85659	−0.359896
$64$	1.00000	0.125000
$65$	2.92305	0.362560
$66$	−4.85838	−0.598025
$67$	−9.43122	−1.15221	−0.576103	−	0.817377i	$-0.695427\pi$
$67$	−9.43122	−1.15221	−0.576103	+	0.817377i	$0.695427\pi$
$68$	−2.81300	−0.341126
$69$	−7.09961	−0.854692
$70$	−2.38251	−0.284764
$71$	−13.2242	−1.56943	−0.784713	−	0.619859i	$-0.787190\pi$
$71$	−13.2242	−1.56943	−0.784713	+	0.619859i	$0.787190\pi$
$72$	−1.19898	−0.141302
$73$	−13.1073	−1.53410	−0.767048	−	0.641590i	$-0.778275\pi$
$73$	−13.1073	−1.53410	−0.767048	+	0.641590i	$0.778275\pi$
$74$	−4.43168	−0.515172
$75$	1.34202	0.154963
$76$	1.26964	0.145637
$77$	−8.62515	−0.982927
$78$	−3.92280	−0.444169
$79$	−4.26050	−0.479344	−0.239672	−	0.970854i	$-0.577040\pi$
$79$	−4.26050	−0.479344	−0.239672	+	0.970854i	$0.577040\pi$
$80$	−1.00000	−0.111803
$81$	−3.96549	−0.440610
$82$	−2.70832	−0.299084
$83$	−5.16762	−0.567220	−0.283610	−	0.958940i	$-0.591532\pi$
$83$	−5.16762	−0.567220	−0.283610	+	0.958940i	$0.591532\pi$
$84$	3.19737	0.348862
$85$	2.81300	0.305113
$86$	−7.47622	−0.806182
$87$	−1.62606	−0.174332
$88$	−3.62020	−0.385914
$89$	−0.599015	−0.0634955	−0.0317477	−	0.999496i	$-0.510107\pi$
$89$	−0.599015	−0.0634955	−0.0317477	+	0.999496i	$0.510107\pi$
$90$	1.19898	0.126384
$91$	−6.96420	−0.730047
$92$	−5.29024	−0.551546
$93$	12.7288	1.31991
$94$	4.08944	0.421794
$95$	−1.26964	−0.130262
$96$	1.34202	0.136969
$97$	8.31904	0.844671	0.422336	−	0.906440i	$-0.361210\pi$
$97$	8.31904	0.844671	0.422336	+	0.906440i	$0.361210\pi$
$98$	−1.32365	−0.133709
$99$	4.34055	0.436242
$100$	1.00000	0.100000
$101$	12.0889	1.20290	0.601448	−	0.798912i	$-0.294591\pi$
$101$	12.0889	1.20290	0.601448	+	0.798912i	$0.294591\pi$
$102$	−3.77510	−0.373791
$103$	1.87317	0.184569	0.0922846	−	0.995733i	$-0.470583\pi$
$103$	1.87317	0.184569	0.0922846	+	0.995733i	$0.470583\pi$
$104$	−2.92305	−0.286629
$105$	−3.19737	−0.312032
$106$	−6.18954	−0.601181
$107$	−15.8632	−1.53355	−0.766776	−	0.641915i	$-0.778140\pi$
$107$	−15.8632	−1.53355	−0.766776	+	0.641915i	$0.778140\pi$
$108$	−5.63512	−0.542239
$109$	0.497921	0.0476922	0.0238461	−	0.999716i	$-0.492409\pi$
$109$	0.497921	0.0476922	0.0238461	+	0.999716i	$0.492409\pi$
$110$	3.62020	0.345172
$111$	−5.94740	−0.564502
$112$	2.38251	0.225126
$113$	3.79403	0.356913	0.178456	−	0.983948i	$-0.442890\pi$
$113$	3.79403	0.356913	0.178456	+	0.983948i	$0.442890\pi$
$114$	1.70388	0.159583
$115$	5.29024	0.493317
$116$	−1.21165	−0.112499
$117$	3.50469	0.324009
$118$	10.0812	0.928046
$119$	−6.70200	−0.614371
$120$	−1.34202	−0.122509
$121$	2.10582	0.191439
$122$	6.82551	0.617953
$123$	−3.63462	−0.327722
$124$	9.48477	0.851758
$125$	−1.00000	−0.0894427
$126$	−2.85659	−0.254485
$127$	−6.65489	−0.590526	−0.295263	−	0.955416i	$-0.595407\pi$
$127$	−6.65489	−0.590526	−0.295263	+	0.955416i	$0.595407\pi$
$128$	1.00000	0.0883883
$129$	−10.0332	−0.883377
$130$	2.92305	0.256369
$131$	3.70371	0.323594	0.161797	−	0.986824i	$-0.448271\pi$
$131$	3.70371	0.323594	0.161797	+	0.986824i	$0.448271\pi$
$132$	−4.85838	−0.422867
$133$	3.02492	0.262294
$134$	−9.43122	−0.814733
$135$	5.63512	0.484994
$136$	−2.81300	−0.241213
$137$	−2.24789	−0.192050	−0.0960250	−	0.995379i	$-0.530613\pi$
$137$	−2.24789	−0.192050	−0.0960250	+	0.995379i	$0.530613\pi$
$138$	−7.09961	−0.604359
$139$	−0.505292	−0.0428583	−0.0214292	−	0.999770i	$-0.506822\pi$
$139$	−0.505292	−0.0428583	−0.0214292	+	0.999770i	$0.506822\pi$
$140$	−2.38251	−0.201359
$141$	5.48811	0.462182
$142$	−13.2242	−1.10975
$143$	10.5820	0.884914
$144$	−1.19898	−0.0999153
$145$	1.21165	0.100622
$146$	−13.1073	−1.08477
$147$	−1.77636	−0.146512
$148$	−4.43168	−0.364282
$149$	−6.08013	−0.498104	−0.249052	−	0.968490i	$-0.580119\pi$
$149$	−6.08013	−0.498104	−0.249052	+	0.968490i	$0.580119\pi$
$150$	1.34202	0.109575
$151$	13.0783	1.06430	0.532148	−	0.846651i	$-0.321385\pi$
$151$	13.0783	1.06430	0.532148	+	0.846651i	$0.321385\pi$
$152$	1.26964	0.102981
$153$	3.37274	0.272670
$154$	−8.62515	−0.695035
$155$	−9.48477	−0.761835
$156$	−3.92280	−0.314075
$157$	−6.09119	−0.486130	−0.243065	−	0.970010i	$-0.578153\pi$
$157$	−6.09119	−0.486130	−0.243065	+	0.970010i	$0.578153\pi$
$158$	−4.26050	−0.338948
$159$	−8.30648	−0.658747
$160$	−1.00000	−0.0790569
$161$	−12.6040	−0.993338
$162$	−3.96549	−0.311558
$163$	−7.06457	−0.553340	−0.276670	−	0.960965i	$-0.589231\pi$
$163$	−7.06457	−0.553340	−0.276670	+	0.960965i	$0.589231\pi$
$164$	−2.70832	−0.211484
$165$	4.85838	0.378224
$166$	−5.16762	−0.401085
$167$	−11.3372	−0.877298	−0.438649	−	0.898658i	$-0.644543\pi$
$167$	−11.3372	−0.877298	−0.438649	+	0.898658i	$0.644543\pi$
$168$	3.19737	0.246683
$169$	−4.45576	−0.342751
$170$	2.81300	0.215747
$171$	−1.52227	−0.116411
$172$	−7.47622	−0.570057
$173$	−13.6092	−1.03469	−0.517343	−	0.855778i	$-0.673079\pi$
$173$	−13.6092	−1.03469	−0.517343	+	0.855778i	$0.673079\pi$
$174$	−1.62606	−0.123271
$175$	2.38251	0.180101
$176$	−3.62020	−0.272883
$177$	13.5291	1.01691
$178$	−0.599015	−0.0448981
$179$	8.70967	0.650991	0.325496	−	0.945544i	$-0.394469\pi$
$179$	8.70967	0.650991	0.325496	+	0.945544i	$0.394469\pi$
$180$	1.19898	0.0893669
$181$	17.3933	1.29284	0.646418	−	0.762983i	$-0.276266\pi$
$181$	17.3933	1.29284	0.646418	+	0.762983i	$0.276266\pi$
$182$	−6.96420	−0.516221
$183$	9.15997	0.677124
$184$	−5.29024	−0.390002
$185$	4.43168	0.325824
$186$	12.7288	0.933317
$187$	10.1836	0.744699
$188$	4.08944	0.298253
$189$	−13.4257	−0.976577
$190$	−1.26964	−0.0921091
$191$	−22.3689	−1.61856	−0.809279	−	0.587425i	$-0.800142\pi$
$191$	−22.3689	−1.61856	−0.809279	+	0.587425i	$0.800142\pi$
$192$	1.34202	0.0968519
$193$	−7.24221	−0.521305	−0.260653	−	0.965433i	$-0.583938\pi$
$193$	−7.24221	−0.521305	−0.260653	+	0.965433i	$0.583938\pi$
$194$	8.31904	0.597273
$195$	3.92280	0.280917
$196$	−1.32365	−0.0945464
$197$	16.5311	1.17779	0.588895	−	0.808209i	$-0.299563\pi$
$197$	16.5311	1.17779	0.588895	+	0.808209i	$0.299563\pi$
$198$	4.34055	0.308470
$199$	8.41322	0.596397	0.298199	−	0.954504i	$-0.403614\pi$
$199$	8.41322	0.596397	0.298199	+	0.954504i	$0.403614\pi$
$200$	1.00000	0.0707107
$201$	−12.6569	−0.892748
$202$	12.0889	0.850575
$203$	−2.88677	−0.202612
$204$	−3.77510	−0.264310
$205$	2.70832	0.189157
$206$	1.87317	0.130510
$207$	6.34291	0.440863
$208$	−2.92305	−0.202677
$209$	−4.59633	−0.317935
$210$	−3.19737	−0.220640
$211$	24.5338	1.68898	0.844488	−	0.535574i	$-0.179905\pi$
$211$	24.5338	1.68898	0.844488	+	0.535574i	$0.179905\pi$
$212$	−6.18954	−0.425099
$213$	−17.7472	−1.21602
$214$	−15.8632	−1.08438
$215$	7.47622	0.509874
$216$	−5.63512	−0.383421
$217$	22.5976	1.53402
$218$	0.497921	0.0337235
$219$	−17.5903	−1.18864
$220$	3.62020	0.244074
$221$	8.22255	0.553108
$222$	−5.94740	−0.399163
$223$	17.2392	1.15442	0.577210	−	0.816596i	$-0.304141\pi$
$223$	17.2392	1.15442	0.577210	+	0.816596i	$0.304141\pi$
$224$	2.38251	0.159188
$225$	−1.19898	−0.0799322
$226$	3.79403	0.252375
$227$	21.1448	1.40343	0.701713	−	0.712459i	$-0.252419\pi$
$227$	21.1448	1.40343	0.701713	+	0.712459i	$0.252419\pi$
$228$	1.70388	0.112842
$229$	26.1622	1.72885	0.864424	−	0.502763i	$-0.167683\pi$
$229$	26.1622	1.72885	0.864424	+	0.502763i	$0.167683\pi$
$230$	5.29024	0.348828
$231$	−11.5751	−0.761587
$232$	−1.21165	−0.0795489
$233$	−17.8562	−1.16980	−0.584900	−	0.811105i	$-0.698866\pi$
$233$	−17.8562	−1.16980	−0.584900	+	0.811105i	$0.698866\pi$
$234$	3.50469	0.229109
$235$	−4.08944	−0.266766
$236$	10.0812	0.656228
$237$	−5.71768	−0.371403
$238$	−6.70200	−0.434426
$239$	−16.6874	−1.07942	−0.539708	−	0.841852i	$-0.681465\pi$
$239$	−16.6874	−1.07942	−0.539708	+	0.841852i	$0.681465\pi$
$240$	−1.34202	−0.0866270
$241$	−6.93506	−0.446727	−0.223363	−	0.974735i	$-0.571704\pi$
$241$	−6.93506	−0.446727	−0.223363	+	0.974735i	$0.571704\pi$
$242$	2.10582	0.135367
$243$	11.5836	0.743088
$244$	6.82551	0.436959
$245$	1.32365	0.0845649
$246$	−3.63462	−0.231735
$247$	−3.71122	−0.236139
$248$	9.48477	0.602284
$249$	−6.93504	−0.439491
$250$	−1.00000	−0.0632456
$251$	−2.55057	−0.160991	−0.0804953	−	0.996755i	$-0.525650\pi$
$251$	−2.55057	−0.160991	−0.0804953	+	0.996755i	$0.525650\pi$
$252$	−2.85659	−0.179948
$253$	19.1517	1.20406
$254$	−6.65489	−0.417565
$255$	3.77510	0.236406
$256$	1.00000	0.0625000
$257$	6.43679	0.401516	0.200758	−	0.979641i	$-0.435660\pi$
$257$	6.43679	0.401516	0.200758	+	0.979641i	$0.435660\pi$
$258$	−10.0332	−0.624642
$259$	−10.5585	−0.656074
$260$	2.92305	0.181280
$261$	1.45275	0.0899230
$262$	3.70371	0.228816
$263$	23.9661	1.47781	0.738907	−	0.673808i	$-0.235342\pi$
$263$	23.9661	1.47781	0.738907	+	0.673808i	$0.235342\pi$
$264$	−4.85838	−0.299012
$265$	6.18954	0.380220
$266$	3.02492	0.185470
$267$	−0.803890	−0.0491973
$268$	−9.43122	−0.576103
$269$	7.30257	0.445246	0.222623	−	0.974905i	$-0.428538\pi$
$269$	7.30257	0.445246	0.222623	+	0.974905i	$0.428538\pi$
$270$	5.63512	0.342942
$271$	11.4662	0.696523	0.348261	−	0.937397i	$-0.386772\pi$
$271$	11.4662	0.696523	0.348261	+	0.937397i	$0.386772\pi$
$272$	−2.81300	−0.170563
$273$	−9.34610	−0.565652
$274$	−2.24789	−0.135800
$275$	−3.62020	−0.218306
$276$	−7.09961	−0.427346
$277$	19.9221	1.19700	0.598502	−	0.801121i	$-0.295763\pi$
$277$	19.9221	1.19700	0.598502	+	0.801121i	$0.295763\pi$
$278$	−0.505292	−0.0303054
$279$	−11.3721	−0.680829
$280$	−2.38251	−0.142382
$281$	−9.12481	−0.544341	−0.272170	−	0.962249i	$-0.587741\pi$
$281$	−9.12481	−0.544341	−0.272170	+	0.962249i	$0.587741\pi$
$282$	5.48811	0.326812
$283$	−7.77734	−0.462315	−0.231157	−	0.972916i	$-0.574251\pi$
$283$	−7.77734	−0.462315	−0.231157	+	0.972916i	$0.574251\pi$
$284$	−13.2242	−0.784713
$285$	−1.70388	−0.100929
$286$	10.5820	0.625729
$287$	−6.45259	−0.380885
$288$	−1.19898	−0.0706508
$289$	−9.08703	−0.534531
$290$	1.21165	0.0711507
$291$	11.1643	0.654464
$292$	−13.1073	−0.767048
$293$	−25.9635	−1.51680	−0.758402	−	0.651788i	$-0.774019\pi$
$293$	−25.9635	−1.51680	−0.758402	+	0.651788i	$0.774019\pi$
$294$	−1.77636	−0.103600
$295$	−10.0812	−0.586948
$296$	−4.43168	−0.257586
$297$	20.4002	1.18374
$298$	−6.08013	−0.352213
$299$	15.4637	0.894286
$300$	1.34202	0.0774815
$301$	−17.8122	−1.02668
$302$	13.0783	0.752571
$303$	16.2236	0.932022
$304$	1.26964	0.0728187
$305$	−6.82551	−0.390828
$306$	3.37274	0.192807
$307$	−1.74433	−0.0995539	−0.0497770	−	0.998760i	$-0.515851\pi$
$307$	−1.74433	−0.0995539	−0.0497770	+	0.998760i	$0.515851\pi$
$308$	−8.62515	−0.491464
$309$	2.51383	0.143007
$310$	−9.48477	−0.538699
$311$	−25.0483	−1.42036	−0.710180	−	0.704020i	$-0.751386\pi$
$311$	−25.0483	−1.42036	−0.710180	+	0.704020i	$0.751386\pi$
$312$	−3.92280	−0.222085
$313$	22.1159	1.25006	0.625032	−	0.780599i	$-0.285086\pi$
$313$	22.1159	1.25006	0.625032	+	0.780599i	$0.285086\pi$
$314$	−6.09119	−0.343746
$315$	2.85659	0.160951
$316$	−4.26050	−0.239672
$317$	−10.4323	−0.585935	−0.292968	−	0.956122i	$-0.594643\pi$
$317$	−10.4323	−0.585935	−0.292968	+	0.956122i	$0.594643\pi$
$318$	−8.30648	−0.465805
$319$	4.38642	0.245592
$320$	−1.00000	−0.0559017
$321$	−21.2887	−1.18822
$322$	−12.6040	−0.702396
$323$	−3.57149	−0.198723
$324$	−3.96549	−0.220305
$325$	−2.92305	−0.162142
$326$	−7.06457	−0.391270
$327$	0.668220	0.0369527
$328$	−2.70832	−0.149542
$329$	9.74313	0.537156
$330$	4.85838	0.267445
$331$	−15.7906	−0.867928	−0.433964	−	0.900930i	$-0.642886\pi$
$331$	−15.7906	−0.867928	−0.433964	+	0.900930i	$0.642886\pi$
$332$	−5.16762	−0.283610
$333$	5.31351	0.291178
$334$	−11.3372	−0.620344
$335$	9.43122	0.515283
$336$	3.19737	0.174431
$337$	23.3718	1.27315	0.636573	−	0.771217i	$-0.280351\pi$
$337$	23.3718	1.27315	0.636573	+	0.771217i	$0.280351\pi$
$338$	−4.45576	−0.242361
$339$	5.09167	0.276541
$340$	2.81300	0.152556
$341$	−34.3367	−1.85944
$342$	−1.52227	−0.0823151
$343$	−19.8312	−1.07078
$344$	−7.47622	−0.403091
$345$	7.09961	0.382230
$346$	−13.6092	−0.731633
$347$	16.6600	0.894355	0.447177	−	0.894445i	$-0.352429\pi$
$347$	16.6600	0.894355	0.447177	+	0.894445i	$0.352429\pi$
$348$	−1.62606	−0.0871661
$349$	30.7520	1.64612	0.823058	−	0.567957i	$-0.192266\pi$
$349$	30.7520	1.64612	0.823058	+	0.567957i	$0.192266\pi$
$350$	2.38251	0.127350
$351$	16.4718	0.879197
$352$	−3.62020	−0.192957
$353$	2.00214	0.106563	0.0532815	−	0.998580i	$-0.483032\pi$
$353$	2.00214	0.106563	0.0532815	+	0.998580i	$0.483032\pi$
$354$	13.5291	0.719065
$355$	13.2242	0.701869
$356$	−0.599015	−0.0317477
$357$	−8.99421	−0.476024
$358$	8.70967	0.460320
$359$	−15.5122	−0.818705	−0.409352	−	0.912376i	$-0.634245\pi$
$359$	−15.5122	−0.818705	−0.409352	+	0.912376i	$0.634245\pi$
$360$	1.19898	0.0631920
$361$	−17.3880	−0.915159
$362$	17.3933	0.914173
$363$	2.82606	0.148330
$364$	−6.96420	−0.365023
$365$	13.1073	0.686069
$366$	9.15997	0.478799
$367$	−10.7962	−0.563559	−0.281780	−	0.959479i	$-0.590925\pi$
$367$	−10.7962	−0.563559	−0.281780	+	0.959479i	$0.590925\pi$
$368$	−5.29024	−0.275773
$369$	3.24723	0.169044
$370$	4.43168	0.230392
$371$	−14.7466	−0.765607
$372$	12.7288	0.659955
$373$	25.3421	1.31217	0.656083	−	0.754689i	$-0.272212\pi$
$373$	25.3421	1.31217	0.656083	+	0.754689i	$0.272212\pi$
$374$	10.1836	0.526582
$375$	−1.34202	−0.0693016
$376$	4.08944	0.210897
$377$	3.54173	0.182408
$378$	−13.4257	−0.690545
$379$	−10.7488	−0.552131	−0.276065	−	0.961139i	$-0.589031\pi$
$379$	−10.7488	−0.552131	−0.276065	+	0.961139i	$0.589031\pi$
$380$	−1.26964	−0.0651310
$381$	−8.93099	−0.457548
$382$	−22.3689	−1.14449
$383$	21.4554	1.09632	0.548161	−	0.836373i	$-0.315328\pi$
$383$	21.4554	1.09632	0.548161	+	0.836373i	$0.315328\pi$
$384$	1.34202	0.0684847
$385$	8.62515	0.439578
$386$	−7.24221	−0.368619
$387$	8.96386	0.455659
$388$	8.31904	0.422336
$389$	14.2584	0.722927	0.361464	−	0.932386i	$-0.382277\pi$
$389$	14.2584	0.722927	0.361464	+	0.932386i	$0.382277\pi$
$390$	3.92280	0.198638
$391$	14.8814	0.752587
$392$	−1.32365	−0.0668544
$393$	4.97045	0.250726
$394$	16.5311	0.832824
$395$	4.26050	0.214369
$396$	4.34055	0.218121
$397$	11.2652	0.565385	0.282693	−	0.959211i	$-0.408772\pi$
$397$	11.2652	0.565385	0.282693	+	0.959211i	$0.408772\pi$
$398$	8.41322	0.421716
$399$	4.05950	0.203229
$400$	1.00000	0.0500000
$401$	24.0953	1.20326	0.601631	−	0.798774i	$-0.294518\pi$
$401$	24.0953	1.20326	0.601631	+	0.798774i	$0.294518\pi$
$402$	−12.6569	−0.631268
$403$	−27.7245	−1.38106
$404$	12.0889	0.601448
$405$	3.96549	0.197047
$406$	−2.88677	−0.143268
$407$	16.0435	0.795249
$408$	−3.77510	−0.186895
$409$	−24.1388	−1.19359	−0.596793	−	0.802396i	$-0.703558\pi$
$409$	−24.1388	−1.19359	−0.596793	+	0.802396i	$0.703558\pi$
$410$	2.70832	0.133754
$411$	−3.01671	−0.148803
$412$	1.87317	0.0922846
$413$	24.0185	1.18187
$414$	6.34291	0.311737
$415$	5.16762	0.253668
$416$	−2.92305	−0.143315
$417$	−0.678112	−0.0332073
$418$	−4.59633	−0.224814
$419$	−1.20223	−0.0587329	−0.0293665	−	0.999569i	$-0.509349\pi$
$419$	−1.20223	−0.0587329	−0.0293665	+	0.999569i	$0.509349\pi$
$420$	−3.19737	−0.156016
$421$	18.3314	0.893417	0.446709	−	0.894679i	$-0.352596\pi$
$421$	18.3314	0.893417	0.446709	+	0.894679i	$0.352596\pi$
$422$	24.5338	1.19429
$423$	−4.90317	−0.238400
$424$	−6.18954	−0.300591
$425$	−2.81300	−0.136451
$426$	−17.7472	−0.859853
$427$	16.2618	0.786966
$428$	−15.8632	−0.766776
$429$	14.2013	0.685645
$430$	7.47622	0.360535
$431$	−25.0110	−1.20474	−0.602369	−	0.798218i	$-0.705776\pi$
$431$	−25.0110	−1.20474	−0.602369	+	0.798218i	$0.705776\pi$
$432$	−5.63512	−0.271120
$433$	24.9832	1.20062	0.600308	−	0.799769i	$-0.295045\pi$
$433$	24.9832	1.20062	0.600308	+	0.799769i	$0.295045\pi$
$434$	22.5976	1.08472
$435$	1.62606	0.0779637
$436$	0.497921	0.0238461
$437$	−6.71668	−0.321302
$438$	−17.5903	−0.840496
$439$	−36.7928	−1.75603	−0.878013	−	0.478636i	$-0.841131\pi$
$439$	−36.7928	−1.75603	−0.878013	+	0.478636i	$0.841131\pi$
$440$	3.62020	0.172586
$441$	1.58703	0.0755731
$442$	8.22255	0.391107
$443$	−27.1361	−1.28927	−0.644637	−	0.764489i	$-0.722991\pi$
$443$	−27.1361	−1.28927	−0.644637	+	0.764489i	$0.722991\pi$
$444$	−5.94740	−0.282251
$445$	0.599015	0.0283960
$446$	17.2392	0.816299
$447$	−8.15965	−0.385938
$448$	2.38251	0.112563
$449$	−41.4175	−1.95461	−0.977307	−	0.211827i	$-0.932059\pi$
$449$	−41.4175	−1.95461	−0.977307	+	0.211827i	$0.932059\pi$
$450$	−1.19898	−0.0565206
$451$	9.80465	0.461683
$452$	3.79403	0.178456
$453$	17.5513	0.824634
$454$	21.1448	0.992372
$455$	6.96420	0.326487
$456$	1.70388	0.0797914
$457$	−17.7643	−0.830980	−0.415490	−	0.909598i	$-0.636390\pi$
$457$	−17.7643	−0.830980	−0.415490	+	0.909598i	$0.636390\pi$
$458$	26.1622	1.22248
$459$	15.8516	0.739889
$460$	5.29024	0.246659
$461$	−26.0270	−1.21220	−0.606099	−	0.795390i	$-0.707266\pi$
$461$	−26.0270	−1.21220	−0.606099	+	0.795390i	$0.707266\pi$
$462$	−11.5751	−0.538523
$463$	−37.1290	−1.72553	−0.862765	−	0.505604i	$-0.831270\pi$
$463$	−37.1290	−1.72553	−0.862765	+	0.505604i	$0.831270\pi$
$464$	−1.21165	−0.0562496
$465$	−12.7288	−0.590282
$466$	−17.8562	−0.827174
$467$	−18.0901	−0.837108	−0.418554	−	0.908192i	$-0.637463\pi$
$467$	−18.0901	−0.837108	−0.418554	+	0.908192i	$0.637463\pi$
$468$	3.50469	0.162004
$469$	−22.4700	−1.03757
$470$	−4.08944	−0.188632
$471$	−8.17449	−0.376661
$472$	10.0812	0.464023
$473$	27.0654	1.24447
$474$	−5.71768	−0.262622
$475$	1.26964	0.0582549
$476$	−6.70200	−0.307186
$477$	7.42115	0.339791
$478$	−16.6874	−0.763262
$479$	29.6992	1.35699	0.678495	−	0.734605i	$-0.262633\pi$
$479$	29.6992	1.35699	0.678495	+	0.734605i	$0.262633\pi$
$480$	−1.34202	−0.0612545
$481$	12.9540	0.590653
$482$	−6.93506	−0.315883
$483$	−16.9149	−0.769653
$484$	2.10582	0.0957193
$485$	−8.31904	−0.377748
$486$	11.5836	0.525442
$487$	−21.3770	−0.968686	−0.484343	−	0.874878i	$-0.660941\pi$
$487$	−21.3770	−0.968686	−0.484343	+	0.874878i	$0.660941\pi$
$488$	6.82551	0.308976
$489$	−9.48079	−0.428736
$490$	1.32365	0.0597964
$491$	−24.4558	−1.10368	−0.551838	−	0.833952i	$-0.686073\pi$
$491$	−24.4558	−1.10368	−0.551838	+	0.833952i	$0.686073\pi$
$492$	−3.63462	−0.163861
$493$	3.40838	0.153506
$494$	−3.71122	−0.166976
$495$	−4.34055	−0.195093
$496$	9.48477	0.425879
$497$	−31.5068	−1.41327
$498$	−6.93504	−0.310767
$499$	22.9474	1.02727	0.513634	−	0.858009i	$-0.328299\pi$
$499$	22.9474	1.02727	0.513634	+	0.858009i	$0.328299\pi$
$500$	−1.00000	−0.0447214
$501$	−15.2147	−0.679744
$502$	−2.55057	−0.113837
$503$	−3.68919	−0.164493	−0.0822463	−	0.996612i	$-0.526209\pi$
$503$	−3.68919	−0.164493	−0.0822463	+	0.996612i	$0.526209\pi$
$504$	−2.85659	−0.127243
$505$	−12.0889	−0.537951
$506$	19.1517	0.851397
$507$	−5.97971	−0.265568
$508$	−6.65489	−0.295263
$509$	41.1905	1.82574	0.912869	−	0.408253i	$-0.133862\pi$
$509$	41.1905	1.82574	0.912869	+	0.408253i	$0.133862\pi$
$510$	3.77510	0.167164
$511$	−31.2283	−1.38146
$512$	1.00000	0.0441942
$513$	−7.15455	−0.315881
$514$	6.43679	0.283914
$515$	−1.87317	−0.0825418
$516$	−10.0332	−0.441689
$517$	−14.8046	−0.651105
$518$	−10.5585	−0.463915
$519$	−18.2638	−0.801690
$520$	2.92305	0.128184
$521$	14.8133	0.648984	0.324492	−	0.945888i	$-0.394807\pi$
$521$	14.8133	0.648984	0.324492	+	0.945888i	$0.394807\pi$
$522$	1.45275	0.0635852
$523$	−25.1510	−1.09978	−0.549888	−	0.835239i	$-0.685329\pi$
$523$	−25.1510	−1.09978	−0.549888	+	0.835239i	$0.685329\pi$
$524$	3.70371	0.161797
$525$	3.19737	0.139545
$526$	23.9661	1.04497
$527$	−26.6807	−1.16223
$528$	−4.85838	−0.211434
$529$	4.98663	0.216810
$530$	6.18954	0.268856
$531$	−12.0871	−0.524537
$532$	3.02492	0.131147
$533$	7.91656	0.342904
$534$	−0.803890	−0.0347877
$535$	15.8632	0.685825
$536$	−9.43122	−0.407367
$537$	11.6886	0.504398
$538$	7.30257	0.314836
$539$	4.79187	0.206401
$540$	5.63512	0.242497
$541$	−20.0935	−0.863888	−0.431944	−	0.901901i	$-0.642172\pi$
$541$	−20.0935	−0.863888	−0.431944	+	0.901901i	$0.642172\pi$
$542$	11.4662	0.492516
$543$	23.3422	1.00171
$544$	−2.81300	−0.120606
$545$	−0.497921	−0.0213286
$546$	−9.34610	−0.399976
$547$	23.1297	0.988956	0.494478	−	0.869190i	$-0.335359\pi$
$547$	23.1297	0.988956	0.494478	+	0.869190i	$0.335359\pi$
$548$	−2.24789	−0.0960250
$549$	−8.18367	−0.349271
$550$	−3.62020	−0.154366
$551$	−1.53836	−0.0655363
$552$	−7.09961	−0.302179
$553$	−10.1507	−0.431651
$554$	19.9221	0.846410
$555$	5.94740	0.252453
$556$	−0.505292	−0.0214292
$557$	20.1393	0.853330	0.426665	−	0.904410i	$-0.359688\pi$
$557$	20.1393	0.853330	0.426665	+	0.904410i	$0.359688\pi$
$558$	−11.3721	−0.481419
$559$	21.8534	0.924300
$560$	−2.38251	−0.100679
$561$	13.6666	0.577005
$562$	−9.12481	−0.384907
$563$	2.55818	0.107814	0.0539072	−	0.998546i	$-0.482832\pi$
$563$	2.55818	0.107814	0.0539072	+	0.998546i	$0.482832\pi$
$564$	5.48811	0.231091
$565$	−3.79403	−0.159616
$566$	−7.77734	−0.326906
$567$	−9.44782	−0.396771
$568$	−13.2242	−0.554876
$569$	19.1283	0.801901	0.400951	−	0.916100i	$-0.368680\pi$
$569$	19.1283	0.801901	0.400951	+	0.916100i	$0.368680\pi$
$570$	−1.70388	−0.0713676
$571$	11.8082	0.494158	0.247079	−	0.968995i	$-0.420529\pi$
$571$	11.8082	0.494158	0.247079	+	0.968995i	$0.420529\pi$
$572$	10.5820	0.442457
$573$	−30.0195	−1.25408
$574$	−6.45259	−0.269326
$575$	−5.29024	−0.220618
$576$	−1.19898	−0.0499576
$577$	−21.6608	−0.901752	−0.450876	−	0.892587i	$-0.648888\pi$
$577$	−21.6608	−0.901752	−0.450876	+	0.892587i	$0.648888\pi$
$578$	−9.08703	−0.377971
$579$	−9.71918	−0.403916
$580$	1.21165	0.0503111
$581$	−12.3119	−0.510783
$582$	11.1643	0.462776
$583$	22.4074	0.928018
$584$	−13.1073	−0.542385
$585$	−3.50469	−0.144901
$586$	−25.9635	−1.07254
$587$	−18.0105	−0.743375	−0.371687	−	0.928358i	$-0.621221\pi$
$587$	−18.0105	−0.743375	−0.371687	+	0.928358i	$0.621221\pi$
$588$	−1.77636	−0.0732560
$589$	12.0422	0.496191
$590$	−10.0812	−0.415035
$591$	22.1850	0.912570
$592$	−4.43168	−0.182141
$593$	2.80581	0.115221	0.0576105	−	0.998339i	$-0.481652\pi$
$593$	2.80581	0.115221	0.0576105	+	0.998339i	$0.481652\pi$
$594$	20.4002	0.837032
$595$	6.70200	0.274755
$596$	−6.08013	−0.249052
$597$	11.2907	0.462098
$598$	15.4637	0.632356
$599$	43.7461	1.78742	0.893709	−	0.448648i	$-0.148094\pi$
$599$	43.7461	1.78742	0.893709	+	0.448648i	$0.148094\pi$
$600$	1.34202	0.0547877
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	−17.8122	−0.725970
$603$	11.3079	0.460492
$604$	13.0783	0.532148
$605$	−2.10582	−0.0856139
$606$	16.2236	0.659039
$607$	−33.1270	−1.34458	−0.672291	−	0.740287i	$-0.734690\pi$
$607$	−33.1270	−1.34458	−0.672291	+	0.740287i	$0.734690\pi$
$608$	1.26964	0.0514906
$609$	−3.87411	−0.156987
$610$	−6.82551	−0.276357
$611$	−11.9537	−0.483593
$612$	3.37274	0.136335
$613$	24.4257	0.986547	0.493273	−	0.869874i	$-0.335800\pi$
$613$	24.4257	0.986547	0.493273	+	0.869874i	$0.335800\pi$
$614$	−1.74433	−0.0703953
$615$	3.63462	0.146562
$616$	−8.62515	−0.347517
$617$	26.0841	1.05011	0.525054	−	0.851069i	$-0.324045\pi$
$617$	26.0841	1.05011	0.525054	+	0.851069i	$0.324045\pi$
$618$	2.51383	0.101121
$619$	45.9667	1.84756	0.923779	−	0.382927i	$-0.125084\pi$
$619$	45.9667	1.84756	0.923779	+	0.382927i	$0.125084\pi$
$620$	−9.48477	−0.380918
$621$	29.8111	1.19628
$622$	−25.0483	−1.00435
$623$	−1.42716	−0.0571779
$624$	−3.92280	−0.157038
$625$	1.00000	0.0400000
$626$	22.1159	0.883928
$627$	−6.16837	−0.246341
$628$	−6.09119	−0.243065
$629$	12.4663	0.497064
$630$	2.85659	0.113809
$631$	15.6852	0.624420	0.312210	−	0.950013i	$-0.398931\pi$
$631$	15.6852	0.624420	0.312210	+	0.950013i	$0.398931\pi$
$632$	−4.26050	−0.169474
$633$	32.9248	1.30864
$634$	−10.4323	−0.414319
$635$	6.65489	0.264091
$636$	−8.30648	−0.329374
$637$	3.86910	0.153299
$638$	4.38642	0.173660
$639$	15.8556	0.627238
$640$	−1.00000	−0.0395285
$641$	11.4538	0.452397	0.226198	−	0.974081i	$-0.427370\pi$
$641$	11.4538	0.452397	0.226198	+	0.974081i	$0.427370\pi$
$642$	−21.2887	−0.840198
$643$	−34.6226	−1.36538	−0.682692	−	0.730707i	$-0.739191\pi$
$643$	−34.6226	−1.36538	−0.682692	+	0.730707i	$0.739191\pi$
$644$	−12.6040	−0.496669
$645$	10.0332	0.395058
$646$	−3.57149	−0.140518
$647$	2.76414	0.108670	0.0543349	−	0.998523i	$-0.482696\pi$
$647$	2.76414	0.108670	0.0543349	+	0.998523i	$0.482696\pi$
$648$	−3.96549	−0.155779
$649$	−36.4958	−1.43259
$650$	−2.92305	−0.114652
$651$	30.3264	1.18858
$652$	−7.06457	−0.276670
$653$	−29.0353	−1.13624	−0.568120	−	0.822946i	$-0.692329\pi$
$653$	−29.0353	−1.13624	−0.568120	+	0.822946i	$0.692329\pi$
$654$	0.668220	0.0261295
$655$	−3.70371	−0.144716
$656$	−2.70832	−0.105742
$657$	15.7155	0.613118
$658$	9.74313	0.379827
$659$	3.71873	0.144861	0.0724306	−	0.997373i	$-0.476924\pi$
$659$	3.71873	0.144861	0.0724306	+	0.997373i	$0.476924\pi$
$660$	4.85838	0.189112
$661$	−1.13820	−0.0442709	−0.0221354	−	0.999755i	$-0.507047\pi$
$661$	−1.13820	−0.0442709	−0.0221354	+	0.999755i	$0.507047\pi$
$662$	−15.7906	−0.613718
$663$	11.0348	0.428557
$664$	−5.16762	−0.200542
$665$	−3.02492	−0.117301
$666$	5.31351	0.205894
$667$	6.40993	0.248194
$668$	−11.3372	−0.438649
$669$	23.1353	0.894463
$670$	9.43122	0.364360
$671$	−24.7097	−0.953907
$672$	3.19737	0.123341
$673$	−13.0409	−0.502690	−0.251345	−	0.967898i	$-0.580873\pi$
$673$	−13.0409	−0.502690	−0.251345	+	0.967898i	$0.580873\pi$
$674$	23.3718	0.900250
$675$	−5.63512	−0.216896
$676$	−4.45576	−0.171375
$677$	2.51965	0.0968379	0.0484190	−	0.998827i	$-0.484582\pi$
$677$	2.51965	0.0968379	0.0484190	+	0.998827i	$0.484582\pi$
$678$	5.09167	0.195544
$679$	19.8202	0.760629
$680$	2.81300	0.107874
$681$	28.3767	1.08740
$682$	−34.3367	−1.31482
$683$	7.39775	0.283067	0.141534	−	0.989933i	$-0.454797\pi$
$683$	7.39775	0.283067	0.141534	+	0.989933i	$0.454797\pi$
$684$	−1.52227	−0.0582056
$685$	2.24789	0.0858874
$686$	−19.8312	−0.757158
$687$	35.1102	1.33954
$688$	−7.47622	−0.285028
$689$	18.0924	0.689264
$690$	7.09961	0.270277
$691$	−2.66025	−0.101201	−0.0506004	−	0.998719i	$-0.516113\pi$
$691$	−2.66025	−0.101201	−0.0506004	+	0.998719i	$0.516113\pi$
$692$	−13.6092	−0.517343
$693$	10.3414	0.392838
$694$	16.6600	0.632404
$695$	0.505292	0.0191668
$696$	−1.62606	−0.0616357
$697$	7.61850	0.288571
$698$	30.7520	1.16398
$699$	−23.9634	−0.906380
$700$	2.38251	0.0900504
$701$	−35.2848	−1.33269	−0.666344	−	0.745644i	$-0.732142\pi$
$701$	−35.2848	−1.33269	−0.666344	+	0.745644i	$0.732142\pi$
$702$	16.4718	0.621686
$703$	−5.62662	−0.212212
$704$	−3.62020	−0.136441
$705$	−5.48811	−0.206694
$706$	2.00214	0.0753514
$707$	28.8020	1.08321
$708$	13.5291	0.508456
$709$	−6.79105	−0.255043	−0.127522	−	0.991836i	$-0.540702\pi$
$709$	−6.79105	−0.255043	−0.127522	+	0.991836i	$0.540702\pi$
$710$	13.2242	0.496296
$711$	5.10827	0.191575
$712$	−0.599015	−0.0224490
$713$	−50.1767	−1.87913
$714$	−8.99421	−0.336600
$715$	−10.5820	−0.395745
$716$	8.70967	0.325496
$717$	−22.3948	−0.836348
$718$	−15.5122	−0.578912
$719$	−18.4413	−0.687744	−0.343872	−	0.939016i	$-0.611739\pi$
$719$	−18.4413	−0.687744	−0.343872	+	0.939016i	$0.611739\pi$
$720$	1.19898	0.0446835
$721$	4.46285	0.166205
$722$	−17.3880	−0.647115
$723$	−9.30699	−0.346131
$724$	17.3933	0.646418
$725$	−1.21165	−0.0449997
$726$	2.82606	0.104885
$727$	0.119257	0.00442298	0.00221149	−	0.999998i	$-0.499296\pi$
$727$	0.119257	0.00442298	0.00221149	+	0.999998i	$0.499296\pi$
$728$	−6.96420	−0.258111
$729$	27.4419	1.01637
$730$	13.1073	0.485124
$731$	21.0306	0.777845
$732$	9.15997	0.338562
$733$	−10.4774	−0.386990	−0.193495	−	0.981101i	$-0.561982\pi$
$733$	−10.4774	−0.386990	−0.193495	+	0.981101i	$0.561982\pi$
$734$	−10.7962	−0.398497
$735$	1.77636	0.0655222
$736$	−5.29024	−0.195001
$737$	34.1429	1.25767
$738$	3.24723	0.119532
$739$	1.30303	0.0479329	0.0239665	−	0.999713i	$-0.492371\pi$
$739$	1.30303	0.0479329	0.0239665	+	0.999713i	$0.492371\pi$
$740$	4.43168	0.162912
$741$	−4.98053	−0.182964
$742$	−14.7466	−0.541366
$743$	−32.7290	−1.20071	−0.600356	−	0.799733i	$-0.704974\pi$
$743$	−32.7290	−1.20071	−0.600356	+	0.799733i	$0.704974\pi$
$744$	12.7288	0.466659
$745$	6.08013	0.222759
$746$	25.3421	0.927841
$747$	6.19589	0.226696
$748$	10.1836	0.372350
$749$	−37.7942	−1.38097
$750$	−1.34202	−0.0490036
$751$	9.39169	0.342708	0.171354	−	0.985210i	$-0.445186\pi$
$751$	9.39169	0.342708	0.171354	+	0.985210i	$0.445186\pi$
$752$	4.08944	0.149127
$753$	−3.42291	−0.124738
$754$	3.54173	0.128982
$755$	−13.0783	−0.475968
$756$	−13.4257	−0.488289
$757$	24.9355	0.906294	0.453147	−	0.891436i	$-0.350301\pi$
$757$	24.9355	0.906294	0.453147	+	0.891436i	$0.350301\pi$
$758$	−10.7488	−0.390415
$759$	25.7020	0.932922
$760$	−1.26964	−0.0460546
$761$	−17.5984	−0.637942	−0.318971	−	0.947764i	$-0.603337\pi$
$761$	−17.5984	−0.637942	−0.318971	+	0.947764i	$0.603337\pi$
$762$	−8.93099	−0.323536
$763$	1.18630	0.0429470
$764$	−22.3689	−0.809279
$765$	−3.37274	−0.121942
$766$	21.4554	0.775217
$767$	−29.4678	−1.06402
$768$	1.34202	0.0484260
$769$	−11.7196	−0.422620	−0.211310	−	0.977419i	$-0.567773\pi$
$769$	−11.7196	−0.422620	−0.211310	+	0.977419i	$0.567773\pi$
$770$	8.62515	0.310829
$771$	8.63829	0.311101
$772$	−7.24221	−0.260653
$773$	−47.2398	−1.69910	−0.849548	−	0.527512i	$-0.823125\pi$
$773$	−47.2398	−1.69910	−0.849548	+	0.527512i	$0.823125\pi$
$774$	8.96386	0.322199
$775$	9.48477	0.340703
$776$	8.31904	0.298636
$777$	−14.1697	−0.508336
$778$	14.2584	0.511187
$779$	−3.43858	−0.123200
$780$	3.92280	0.140459
$781$	47.8743	1.71308
$782$	14.8814	0.532159
$783$	6.82781	0.244006
$784$	−1.32365	−0.0472732
$785$	6.09119	0.217404
$786$	4.97045	0.177290
$787$	29.3196	1.04513	0.522566	−	0.852599i	$-0.324975\pi$
$787$	29.3196	1.04513	0.522566	+	0.852599i	$0.324975\pi$
$788$	16.5311	0.588895
$789$	32.1630	1.14503
$790$	4.26050	0.151582
$791$	9.03932	0.321401
$792$	4.34055	0.154235
$793$	−19.9513	−0.708493
$794$	11.2652	0.399788
$795$	8.30648	0.294601
$796$	8.41322	0.298199
$797$	47.3644	1.67773	0.838866	−	0.544338i	$-0.183219\pi$
$797$	47.3644	1.67773	0.838866	+	0.544338i	$0.183219\pi$
$798$	4.05950	0.143705
$799$	−11.5036	−0.406968
$800$	1.00000	0.0353553
$801$	0.718209	0.0253767
$802$	24.0953	0.850835
$803$	47.4511	1.67451
$804$	−12.6569	−0.446374
$805$	12.6040	0.444234
$806$	−27.7245	−0.976554
$807$	9.80019	0.344983
$808$	12.0889	0.425288
$809$	18.8357	0.662228	0.331114	−	0.943591i	$-0.392575\pi$
$809$	18.8357	0.662228	0.331114	+	0.943591i	$0.392575\pi$
$810$	3.96549	0.139333
$811$	−11.0302	−0.387322	−0.193661	−	0.981068i	$-0.562036\pi$
$811$	−11.0302	−0.387322	−0.193661	+	0.981068i	$0.562036\pi$
$812$	−2.88677	−0.101306
$813$	15.3879	0.539677
$814$	16.0435	0.562326
$815$	7.06457	0.247461
$816$	−3.77510	−0.132155
$817$	−9.49208	−0.332086
$818$	−24.1388	−0.843992
$819$	8.34996	0.291771
$820$	2.70832	0.0945786
$821$	5.48261	0.191345	0.0956723	−	0.995413i	$-0.469500\pi$
$821$	5.48261	0.191345	0.0956723	+	0.995413i	$0.469500\pi$
$822$	−3.01671	−0.105220
$823$	15.9422	0.555712	0.277856	−	0.960623i	$-0.410376\pi$
$823$	15.9422	0.555712	0.277856	+	0.960623i	$0.410376\pi$
$824$	1.87317	0.0652550
$825$	−4.85838	−0.169147
$826$	24.0185	0.835709
$827$	−32.8718	−1.14306	−0.571532	−	0.820579i	$-0.693651\pi$
$827$	−32.8718	−1.14306	−0.571532	+	0.820579i	$0.693651\pi$
$828$	6.34291	0.220431
$829$	44.1097	1.53199	0.765997	−	0.642844i	$-0.222246\pi$
$829$	44.1097	1.53199	0.765997	+	0.642844i	$0.222246\pi$
$830$	5.16762	0.179371
$831$	26.7359	0.927457
$832$	−2.92305	−0.101339
$833$	3.72343	0.129009
$834$	−0.678112	−0.0234811
$835$	11.3372	0.392340
$836$	−4.59633	−0.158968
$837$	−53.4478	−1.84743
$838$	−1.20223	−0.0415304
$839$	37.9873	1.31147	0.655734	−	0.754992i	$-0.272359\pi$
$839$	37.9873	1.31147	0.655734	+	0.754992i	$0.272359\pi$
$840$	−3.19737	−0.110320
$841$	−27.5319	−0.949376
$842$	18.3314	0.631741
$843$	−12.2457	−0.421764
$844$	24.5338	0.844488
$845$	4.45576	0.153283
$846$	−4.90317	−0.168575
$847$	5.01714	0.172391
$848$	−6.18954	−0.212550
$849$	−10.4373	−0.358209
$850$	−2.81300	−0.0964851
$851$	23.4446	0.803672
$852$	−17.7472	−0.608008
$853$	30.2336	1.03518	0.517589	−	0.855630i	$-0.326830\pi$
$853$	30.2336	1.03518	0.517589	+	0.855630i	$0.326830\pi$
$854$	16.2618	0.556469
$855$	1.52227	0.0520606
$856$	−15.8632	−0.542192
$857$	1.73974	0.0594283	0.0297141	−	0.999558i	$-0.490540\pi$
$857$	1.73974	0.0594283	0.0297141	+	0.999558i	$0.490540\pi$
$858$	14.2013	0.484824
$859$	0.215283	0.00734538	0.00367269	−	0.999993i	$-0.498831\pi$
$859$	0.215283	0.00734538	0.00367269	+	0.999993i	$0.498831\pi$
$860$	7.47622	0.254937
$861$	−8.65951	−0.295115
$862$	−25.0110	−0.851878
$863$	−29.6753	−1.01016	−0.505080	−	0.863073i	$-0.668537\pi$
$863$	−29.6753	−1.01016	−0.505080	+	0.863073i	$0.668537\pi$
$864$	−5.63512	−0.191711
$865$	13.6092	0.462725
$866$	24.9832	0.848964
$867$	−12.1950	−0.414163
$868$	22.5976	0.767011
$869$	15.4239	0.523219
$870$	1.62606	0.0551287
$871$	27.5680	0.934105
$872$	0.497921	0.0168617
$873$	−9.97439	−0.337582
$874$	−6.71668	−0.227195
$875$	−2.38251	−0.0805435
$876$	−17.5903	−0.594321
$877$	7.53574	0.254464	0.127232	−	0.991873i	$-0.459391\pi$
$877$	7.53574	0.254464	0.127232	+	0.991873i	$0.459391\pi$
$878$	−36.7928	−1.24170
$879$	−34.8435	−1.17524
$880$	3.62020	0.122037
$881$	3.36096	0.113234	0.0566168	−	0.998396i	$-0.481969\pi$
$881$	3.36096	0.113234	0.0566168	+	0.998396i	$0.481969\pi$
$882$	1.58703	0.0534382
$883$	50.4356	1.69729	0.848646	−	0.528960i	$-0.177418\pi$
$883$	50.4356	1.69729	0.848646	+	0.528960i	$0.177418\pi$
$884$	8.22255	0.276554
$885$	−13.5291	−0.454776
$886$	−27.1361	−0.911654
$887$	−18.7200	−0.628558	−0.314279	−	0.949331i	$-0.601763\pi$
$887$	−18.7200	−0.628558	−0.314279	+	0.949331i	$0.601763\pi$
$888$	−5.94740	−0.199582
$889$	−15.8553	−0.531771
$890$	0.599015	0.0200790
$891$	14.3559	0.480939
$892$	17.2392	0.577210
$893$	5.19211	0.173747
$894$	−8.15965	−0.272900
$895$	−8.70967	−0.291132
$896$	2.38251	0.0795940
$897$	20.7525	0.692907
$898$	−41.4175	−1.38212
$899$	−11.4923	−0.383288
$900$	−1.19898	−0.0399661
$901$	17.4112	0.580050
$902$	9.80465	0.326459
$903$	−23.9043	−0.795485
$904$	3.79403	0.126188
$905$	−17.3933	−0.578174
$906$	17.5513	0.583104
$907$	−4.75132	−0.157765	−0.0788825	−	0.996884i	$-0.525135\pi$
$907$	−4.75132	−0.157765	−0.0788825	+	0.996884i	$0.525135\pi$
$908$	21.1448	0.701713
$909$	−14.4944	−0.480750
$910$	6.96420	0.230861
$911$	−1.70760	−0.0565753	−0.0282877	−	0.999600i	$-0.509005\pi$
$911$	−1.70760	−0.0565753	−0.0282877	+	0.999600i	$0.509005\pi$
$912$	1.70388	0.0564210
$913$	18.7078	0.619137
$914$	−17.7643	−0.587592
$915$	−9.15997	−0.302819
$916$	26.1622	0.864424
$917$	8.82412	0.291398
$918$	15.8516	0.523180
$919$	6.20441	0.204665	0.102332	−	0.994750i	$-0.467369\pi$
$919$	6.20441	0.204665	0.102332	+	0.994750i	$0.467369\pi$
$920$	5.29024	0.174414
$921$	−2.34092	−0.0771359
$922$	−26.0270	−0.857153
$923$	38.6551	1.27235
$924$	−11.5751	−0.380794
$925$	−4.43168	−0.145713
$926$	−37.1290	−1.22013
$927$	−2.24590	−0.0737651
$928$	−1.21165	−0.0397745
$929$	−34.1079	−1.11904	−0.559522	−	0.828815i	$-0.689015\pi$
$929$	−34.1079	−1.11904	−0.559522	+	0.828815i	$0.689015\pi$
$930$	−12.7288	−0.417392
$931$	−1.68055	−0.0550780
$932$	−17.8562	−0.584900
$933$	−33.6153	−1.10052
$934$	−18.0901	−0.591925
$935$	−10.1836	−0.333040
$936$	3.50469	0.114554
$937$	8.49974	0.277674	0.138837	−	0.990315i	$-0.455664\pi$
$937$	8.49974	0.277674	0.138837	+	0.990315i	$0.455664\pi$
$938$	−22.4700	−0.733670
$939$	29.6799	0.968568
$940$	−4.08944	−0.133383
$941$	−55.2545	−1.80124	−0.900622	−	0.434603i	$-0.856889\pi$
$941$	−55.2545	−1.80124	−0.900622	+	0.434603i	$0.856889\pi$
$942$	−8.17449	−0.266339
$943$	14.3277	0.466573
$944$	10.0812	0.328114
$945$	13.4257	0.436739
$946$	27.0654	0.879972
$947$	22.6053	0.734574	0.367287	−	0.930108i	$-0.380287\pi$
$947$	22.6053	0.734574	0.367287	+	0.930108i	$0.380287\pi$
$948$	−5.71768	−0.185702
$949$	38.3134	1.24371
$950$	1.26964	0.0411925
$951$	−14.0003	−0.453992
$952$	−6.70200	−0.217213
$953$	4.88913	0.158374	0.0791872	−	0.996860i	$-0.474768\pi$
$953$	4.88913	0.158374	0.0791872	+	0.996860i	$0.474768\pi$
$954$	7.42115	0.240269
$955$	22.3689	0.723841
$956$	−16.6874	−0.539708
$957$	5.88666	0.190289
$958$	29.6992	0.959536
$959$	−5.35561	−0.172942
$960$	−1.34202	−0.0433135
$961$	58.9609	1.90196
$962$	12.9540	0.417655
$963$	19.0197	0.612901
$964$	−6.93506	−0.223363
$965$	7.24221	0.233135
$966$	−16.9149	−0.544227
$967$	5.72738	0.184180	0.0920900	−	0.995751i	$-0.470645\pi$
$967$	5.72738	0.184180	0.0920900	+	0.995751i	$0.470645\pi$
$968$	2.10582	0.0676837
$969$	−4.79301	−0.153974
$970$	−8.31904	−0.267108
$971$	15.0950	0.484422	0.242211	−	0.970224i	$-0.422127\pi$
$971$	15.0950	0.484422	0.242211	+	0.970224i	$0.422127\pi$
$972$	11.5836	0.371544
$973$	−1.20386	−0.0385941
$974$	−21.3770	−0.684964
$975$	−3.92280	−0.125630
$976$	6.82551	0.218479
$977$	58.0419	1.85692	0.928462	−	0.371426i	$-0.121131\pi$
$977$	58.0419	1.85692	0.928462	+	0.371426i	$0.121131\pi$
$978$	−9.48079	−0.303162
$979$	2.16855	0.0693072
$980$	1.32365	0.0422825
$981$	−0.596999	−0.0190607
$982$	−24.4558	−0.780416
$983$	7.92629	0.252809	0.126405	−	0.991979i	$-0.459656\pi$
$983$	7.92629	0.252809	0.126405	+	0.991979i	$0.459656\pi$
$984$	−3.63462	−0.115867
$985$	−16.5311	−0.526724
$986$	3.40838	0.108545
$987$	13.0755	0.416197
$988$	−3.71122	−0.118070
$989$	39.5510	1.25765
$990$	−4.34055	−0.137952
$991$	4.35107	0.138216	0.0691081	−	0.997609i	$-0.477985\pi$
$991$	4.35107	0.138216	0.0691081	+	0.997609i	$0.477985\pi$
$992$	9.48477	0.301142
$993$	−21.1913	−0.672484
$994$	−31.5068	−0.999336
$995$	−8.41322	−0.266717
$996$	−6.93504	−0.219745
$997$	−44.4625	−1.40814	−0.704070	−	0.710130i	$-0.748636\pi$
$997$	−44.4625	−1.40814	−0.704070	+	0.710130i	$0.748636\pi$
$998$	22.9474	0.726389
$999$	24.9730	0.790112

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.f.1.17	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.f.1.17	✓	22	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.34202 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.34202 q^{6} +2.38251 q^{7} +1.00000 q^{8} -1.19898 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.34202 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.34202 q^{6} +2.38251 q^{7} +1.00000 q^{8} -1.19898 q^{9} -1.00000 q^{10} -3.62020 q^{11} +1.34202 q^{12} -2.92305 q^{13} +2.38251 q^{14} -1.34202 q^{15} +1.00000 q^{16} -2.81300 q^{17} -1.19898 q^{18} +1.26964 q^{19} -1.00000 q^{20} +3.19737 q^{21} -3.62020 q^{22} -5.29024 q^{23} +1.34202 q^{24} +1.00000 q^{25} -2.92305 q^{26} -5.63512 q^{27} +2.38251 q^{28} -1.21165 q^{29} -1.34202 q^{30} +9.48477 q^{31} +1.00000 q^{32} -4.85838 q^{33} -2.81300 q^{34} -2.38251 q^{35} -1.19898 q^{36} -4.43168 q^{37} +1.26964 q^{38} -3.92280 q^{39} -1.00000 q^{40} -2.70832 q^{41} +3.19737 q^{42} -7.47622 q^{43} -3.62020 q^{44} +1.19898 q^{45} -5.29024 q^{46} +4.08944 q^{47} +1.34202 q^{48} -1.32365 q^{49} +1.00000 q^{50} -3.77510 q^{51} -2.92305 q^{52} -6.18954 q^{53} -5.63512 q^{54} +3.62020 q^{55} +2.38251 q^{56} +1.70388 q^{57} -1.21165 q^{58} +10.0812 q^{59} -1.34202 q^{60} +6.82551 q^{61} +9.48477 q^{62} -2.85659 q^{63} +1.00000 q^{64} +2.92305 q^{65} -4.85838 q^{66} -9.43122 q^{67} -2.81300 q^{68} -7.09961 q^{69} -2.38251 q^{70} -13.2242 q^{71} -1.19898 q^{72} -13.1073 q^{73} -4.43168 q^{74} +1.34202 q^{75} +1.26964 q^{76} -8.62515 q^{77} -3.92280 q^{78} -4.26050 q^{79} -1.00000 q^{80} -3.96549 q^{81} -2.70832 q^{82} -5.16762 q^{83} +3.19737 q^{84} +2.81300 q^{85} -7.47622 q^{86} -1.62606 q^{87} -3.62020 q^{88} -0.599015 q^{89} +1.19898 q^{90} -6.96420 q^{91} -5.29024 q^{92} +12.7288 q^{93} +4.08944 q^{94} -1.26964 q^{95} +1.34202 q^{96} +8.31904 q^{97} -1.32365 q^{98} +4.34055 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

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