LMFDB - Embedded newform 6026.2.a.j.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.71066 q^{3} +1.00000 q^{4} -2.38566 q^{5} +2.71066 q^{6} -4.13924 q^{7} -1.00000 q^{8} +4.34767 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.71066 q^{3} +1.00000 q^{4} -2.38566 q^{5} +2.71066 q^{6} -4.13924 q^{7} -1.00000 q^{8} +4.34767 q^{9} +2.38566 q^{10} +5.88183 q^{11} -2.71066 q^{12} -3.00540 q^{13} +4.13924 q^{14} +6.46671 q^{15} +1.00000 q^{16} +6.38564 q^{17} -4.34767 q^{18} +4.95540 q^{19} -2.38566 q^{20} +11.2201 q^{21} -5.88183 q^{22} +1.00000 q^{23} +2.71066 q^{24} +0.691371 q^{25} +3.00540 q^{26} -3.65307 q^{27} -4.13924 q^{28} +9.90084 q^{29} -6.46671 q^{30} -5.84263 q^{31} -1.00000 q^{32} -15.9436 q^{33} -6.38564 q^{34} +9.87481 q^{35} +4.34767 q^{36} -5.08044 q^{37} -4.95540 q^{38} +8.14661 q^{39} +2.38566 q^{40} +11.8844 q^{41} -11.2201 q^{42} +4.90671 q^{43} +5.88183 q^{44} -10.3721 q^{45} -1.00000 q^{46} +7.91740 q^{47} -2.71066 q^{48} +10.1333 q^{49} -0.691371 q^{50} -17.3093 q^{51} -3.00540 q^{52} -6.91165 q^{53} +3.65307 q^{54} -14.0320 q^{55} +4.13924 q^{56} -13.4324 q^{57} -9.90084 q^{58} +2.15411 q^{59} +6.46671 q^{60} +1.81870 q^{61} +5.84263 q^{62} -17.9960 q^{63} +1.00000 q^{64} +7.16986 q^{65} +15.9436 q^{66} -3.88011 q^{67} +6.38564 q^{68} -2.71066 q^{69} -9.87481 q^{70} +12.1503 q^{71} -4.34767 q^{72} +6.84974 q^{73} +5.08044 q^{74} -1.87407 q^{75} +4.95540 q^{76} -24.3463 q^{77} -8.14661 q^{78} -15.0931 q^{79} -2.38566 q^{80} -3.14079 q^{81} -11.8844 q^{82} -3.32560 q^{83} +11.2201 q^{84} -15.2340 q^{85} -4.90671 q^{86} -26.8378 q^{87} -5.88183 q^{88} -6.85600 q^{89} +10.3721 q^{90} +12.4401 q^{91} +1.00000 q^{92} +15.8374 q^{93} -7.91740 q^{94} -11.8219 q^{95} +2.71066 q^{96} -12.2823 q^{97} -10.1333 q^{98} +25.5723 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) $ 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * 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
$3$	−2.71066	−1.56500	−0.782500	−	0.622651i	$-0.786056\pi$
$3$	−2.71066	−1.56500	−0.782500	+	0.622651i	$0.786056\pi$
$4$	1.00000	0.500000
$5$	−2.38566	−1.06690	−0.533450	−	0.845832i	$-0.679105\pi$
$5$	−2.38566	−1.06690	−0.533450	+	0.845832i	$0.679105\pi$
$6$	2.71066	1.10662
$7$	−4.13924	−1.56448	−0.782242	−	0.622974i	$-0.785924\pi$
$7$	−4.13924	−1.56448	−0.782242	+	0.622974i	$0.785924\pi$
$8$	−1.00000	−0.353553
$9$	4.34767	1.44922
$10$	2.38566	0.754412
$11$	5.88183	1.77344	0.886720	−	0.462308i	$-0.152978\pi$
$11$	5.88183	1.77344	0.886720	+	0.462308i	$0.152978\pi$
$12$	−2.71066	−0.782500
$13$	−3.00540	−0.833548	−0.416774	−	0.909010i	$-0.636839\pi$
$13$	−3.00540	−0.833548	−0.416774	+	0.909010i	$0.636839\pi$
$14$	4.13924	1.10626
$15$	6.46671	1.66970
$16$	1.00000	0.250000
$17$	6.38564	1.54875	0.774373	−	0.632730i	$-0.218066\pi$
$17$	6.38564	1.54875	0.774373	+	0.632730i	$0.218066\pi$
$18$	−4.34767	−1.02476
$19$	4.95540	1.13685	0.568424	−	0.822736i	$-0.307553\pi$
$19$	4.95540	1.13685	0.568424	+	0.822736i	$0.307553\pi$
$20$	−2.38566	−0.533450
$21$	11.2201	2.44842
$22$	−5.88183	−1.25401
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.71066	0.553311
$25$	0.691371	0.138274
$26$	3.00540	0.589407
$27$	−3.65307	−0.703033
$28$	−4.13924	−0.782242
$29$	9.90084	1.83854	0.919270	−	0.393628i	$-0.128780\pi$
$29$	9.90084	1.83854	0.919270	+	0.393628i	$0.128780\pi$
$30$	−6.46671	−1.18065
$31$	−5.84263	−1.04937	−0.524684	−	0.851297i	$-0.675816\pi$
$31$	−5.84263	−1.04937	−0.524684	+	0.851297i	$0.675816\pi$
$32$	−1.00000	−0.176777
$33$	−15.9436	−2.77543
$34$	−6.38564	−1.09513
$35$	9.87481	1.66915
$36$	4.34767	0.724611
$37$	−5.08044	−0.835220	−0.417610	−	0.908626i	$-0.637132\pi$
$37$	−5.08044	−0.835220	−0.417610	+	0.908626i	$0.637132\pi$
$38$	−4.95540	−0.803873
$39$	8.14661	1.30450
$40$	2.38566	0.377206
$41$	11.8844	1.85603	0.928014	−	0.372546i	$-0.121515\pi$
$41$	11.8844	1.85603	0.928014	+	0.372546i	$0.121515\pi$
$42$	−11.2201	−1.73129
$43$	4.90671	0.748266	0.374133	−	0.927375i	$-0.377940\pi$
$43$	4.90671	0.748266	0.374133	+	0.927375i	$0.377940\pi$
$44$	5.88183	0.886720
$45$	−10.3721	−1.54617
$46$	−1.00000	−0.147442
$47$	7.91740	1.15487	0.577436	−	0.816436i	$-0.304053\pi$
$47$	7.91740	1.15487	0.577436	+	0.816436i	$0.304053\pi$
$48$	−2.71066	−0.391250
$49$	10.1333	1.44761
$50$	−0.691371	−0.0977746
$51$	−17.3093	−2.42379
$52$	−3.00540	−0.416774
$53$	−6.91165	−0.949389	−0.474694	−	0.880151i	$-0.657441\pi$
$53$	−6.91165	−0.949389	−0.474694	+	0.880151i	$0.657441\pi$
$54$	3.65307	0.497119
$55$	−14.0320	−1.89208
$56$	4.13924	0.553129
$57$	−13.4324	−1.77917
$58$	−9.90084	−1.30004
$59$	2.15411	0.280442	0.140221	−	0.990120i	$-0.455219\pi$
$59$	2.15411	0.280442	0.140221	+	0.990120i	$0.455219\pi$
$60$	6.46671	0.834848
$61$	1.81870	0.232861	0.116431	−	0.993199i	$-0.462855\pi$
$61$	1.81870	0.232861	0.116431	+	0.993199i	$0.462855\pi$
$62$	5.84263	0.742015
$63$	−17.9960	−2.26729
$64$	1.00000	0.125000
$65$	7.16986	0.889312
$66$	15.9436	1.96253
$67$	−3.88011	−0.474031	−0.237016	−	0.971506i	$-0.576169\pi$
$67$	−3.88011	−0.474031	−0.237016	+	0.971506i	$0.576169\pi$
$68$	6.38564	0.774373
$69$	−2.71066	−0.326325
$70$	−9.87481	−1.18027
$71$	12.1503	1.44197	0.720986	−	0.692950i	$-0.243689\pi$
$71$	12.1503	1.44197	0.720986	+	0.692950i	$0.243689\pi$
$72$	−4.34767	−0.512378
$73$	6.84974	0.801702	0.400851	−	0.916143i	$-0.368715\pi$
$73$	6.84974	0.801702	0.400851	+	0.916143i	$0.368715\pi$
$74$	5.08044	0.590590
$75$	−1.87407	−0.216399
$76$	4.95540	0.568424
$77$	−24.3463	−2.77452
$78$	−8.14661	−0.922422
$79$	−15.0931	−1.69811	−0.849054	−	0.528307i	$-0.822827\pi$
$79$	−15.0931	−1.69811	−0.849054	+	0.528307i	$0.822827\pi$
$80$	−2.38566	−0.266725
$81$	−3.14079	−0.348976
$82$	−11.8844	−1.31241
$83$	−3.32560	−0.365033	−0.182516	−	0.983203i	$-0.558424\pi$
$83$	−3.32560	−0.365033	−0.182516	+	0.983203i	$0.558424\pi$
$84$	11.2201	1.22421
$85$	−15.2340	−1.65236
$86$	−4.90671	−0.529104
$87$	−26.8378	−2.87731
$88$	−5.88183	−0.627005
$89$	−6.85600	−0.726735	−0.363367	−	0.931646i	$-0.618373\pi$
$89$	−6.85600	−0.726735	−0.363367	+	0.931646i	$0.618373\pi$
$90$	10.3721	1.09331
$91$	12.4401	1.30407
$92$	1.00000	0.104257
$93$	15.8374	1.64226
$94$	−7.91740	−0.816618
$95$	−11.8219	−1.21290
$96$	2.71066	0.276655
$97$	−12.2823	−1.24707	−0.623537	−	0.781794i	$-0.714305\pi$
$97$	−12.2823	−1.24707	−0.623537	+	0.781794i	$0.714305\pi$
$98$	−10.1333	−1.02362
$99$	25.5723	2.57011
$100$	0.691371	0.0691371
$101$	−15.8103	−1.57319	−0.786593	−	0.617472i	$-0.788157\pi$
$101$	−15.8103	−1.57319	−0.786593	+	0.617472i	$0.788157\pi$
$102$	17.3093	1.71388
$103$	8.01002	0.789250	0.394625	−	0.918842i	$-0.370874\pi$
$103$	8.01002	0.789250	0.394625	+	0.918842i	$0.370874\pi$
$104$	3.00540	0.294704
$105$	−26.7672	−2.61221
$106$	6.91165	0.671319
$107$	15.4256	1.49125	0.745625	−	0.666365i	$-0.232151\pi$
$107$	15.4256	1.49125	0.745625	+	0.666365i	$0.232151\pi$
$108$	−3.65307	−0.351517
$109$	−9.52403	−0.912237	−0.456118	−	0.889919i	$-0.650761\pi$
$109$	−9.52403	−0.912237	−0.456118	+	0.889919i	$0.650761\pi$
$110$	14.0320	1.33790
$111$	13.7713	1.30712
$112$	−4.13924	−0.391121
$113$	5.32705	0.501126	0.250563	−	0.968100i	$-0.419384\pi$
$113$	5.32705	0.501126	0.250563	+	0.968100i	$0.419384\pi$
$114$	13.4324	1.25806
$115$	−2.38566	−0.222464
$116$	9.90084	0.919270
$117$	−13.0665	−1.20800
$118$	−2.15411	−0.198302
$119$	−26.4317	−2.42299
$120$	−6.46671	−0.590327
$121$	23.5960	2.14509
$122$	−1.81870	−0.164658
$123$	−32.2145	−2.90468
$124$	−5.84263	−0.524684
$125$	10.2789	0.919375
$126$	17.9960	1.60321
$127$	1.09445	0.0971167	0.0485583	−	0.998820i	$-0.484537\pi$
$127$	1.09445	0.0971167	0.0485583	+	0.998820i	$0.484537\pi$
$128$	−1.00000	−0.0883883
$129$	−13.3004	−1.17104
$130$	−7.16986	−0.628838
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−15.9436	−1.38772
$133$	−20.5116	−1.77858
$134$	3.88011	0.335191
$135$	8.71497	0.750065
$136$	−6.38564	−0.547564
$137$	−2.31495	−0.197780	−0.0988898	−	0.995098i	$-0.531529\pi$
$137$	−2.31495	−0.197780	−0.0988898	+	0.995098i	$0.531529\pi$
$138$	2.71066	0.230747
$139$	12.4396	1.05511	0.527555	−	0.849521i	$-0.323109\pi$
$139$	12.4396	1.05511	0.527555	+	0.849521i	$0.323109\pi$
$140$	9.87481	0.834574
$141$	−21.4614	−1.80737
$142$	−12.1503	−1.01963
$143$	−17.6773	−1.47825
$144$	4.34767	0.362306
$145$	−23.6200	−1.96154
$146$	−6.84974	−0.566889
$147$	−27.4679	−2.26551
$148$	−5.08044	−0.417610
$149$	2.84408	0.232996	0.116498	−	0.993191i	$-0.462833\pi$
$149$	2.84408	0.232996	0.116498	+	0.993191i	$0.462833\pi$
$150$	1.87407	0.153017
$151$	15.8610	1.29075	0.645375	−	0.763866i	$-0.276701\pi$
$151$	15.8610	1.29075	0.645375	+	0.763866i	$0.276701\pi$
$152$	−4.95540	−0.401936
$153$	27.7627	2.24448
$154$	24.3463	1.96188
$155$	13.9385	1.11957
$156$	8.14661	0.652251
$157$	8.17821	0.652693	0.326346	−	0.945250i	$-0.394182\pi$
$157$	8.17821	0.652693	0.326346	+	0.945250i	$0.394182\pi$
$158$	15.0931	1.20074
$159$	18.7351	1.48579
$160$	2.38566	0.188603
$161$	−4.13924	−0.326218
$162$	3.14079	0.246764
$163$	18.9396	1.48347	0.741733	−	0.670695i	$-0.234004\pi$
$163$	18.9396	1.48347	0.741733	+	0.670695i	$0.234004\pi$
$164$	11.8844	0.928014
$165$	38.0361	2.96111
$166$	3.32560	0.258117
$167$	−17.6045	−1.36228	−0.681139	−	0.732154i	$-0.738515\pi$
$167$	−17.6045	−1.36228	−0.681139	+	0.732154i	$0.738515\pi$
$168$	−11.2201	−0.865646
$169$	−3.96757	−0.305198
$170$	15.2340	1.16839
$171$	21.5445	1.64755
$172$	4.90671	0.374133
$173$	−18.6923	−1.42115	−0.710573	−	0.703623i	$-0.751564\pi$
$173$	−18.6923	−1.42115	−0.710573	+	0.703623i	$0.751564\pi$
$174$	26.8378	2.03457
$175$	−2.86175	−0.216328
$176$	5.88183	0.443360
$177$	−5.83907	−0.438891
$178$	6.85600	0.513879
$179$	13.2311	0.988935	0.494468	−	0.869196i	$-0.335363\pi$
$179$	13.2311	0.988935	0.494468	+	0.869196i	$0.335363\pi$
$180$	−10.3721	−0.773087
$181$	−16.0123	−1.19018	−0.595091	−	0.803658i	$-0.702884\pi$
$181$	−16.0123	−1.19018	−0.595091	+	0.803658i	$0.702884\pi$
$182$	−12.4401	−0.922119
$183$	−4.92988	−0.364428
$184$	−1.00000	−0.0737210
$185$	12.1202	0.891095
$186$	−15.8374	−1.16125
$187$	37.5593	2.74661
$188$	7.91740	0.577436
$189$	15.1209	1.09988
$190$	11.8219	0.857651
$191$	2.70993	0.196083	0.0980417	−	0.995182i	$-0.468742\pi$
$191$	2.70993	0.196083	0.0980417	+	0.995182i	$0.468742\pi$
$192$	−2.71066	−0.195625
$193$	17.4917	1.25908	0.629541	−	0.776967i	$-0.283243\pi$
$193$	17.4917	1.25908	0.629541	+	0.776967i	$0.283243\pi$
$194$	12.2823	0.881814
$195$	−19.4350	−1.39177
$196$	10.1333	0.723806
$197$	22.2579	1.58581	0.792906	−	0.609344i	$-0.208567\pi$
$197$	22.2579	1.58581	0.792906	+	0.609344i	$0.208567\pi$
$198$	−25.5723	−1.81734
$199$	13.8502	0.981817	0.490909	−	0.871211i	$-0.336665\pi$
$199$	13.8502	0.981817	0.490909	+	0.871211i	$0.336665\pi$
$200$	−0.691371	−0.0488873
$201$	10.5177	0.741859
$202$	15.8103	1.11241
$203$	−40.9819	−2.87637
$204$	−17.3093	−1.21189
$205$	−28.3521	−1.98019
$206$	−8.01002	−0.558084
$207$	4.34767	0.302184
$208$	−3.00540	−0.208387
$209$	29.1469	2.01613
$210$	26.7672	1.84711
$211$	−26.8651	−1.84947	−0.924734	−	0.380615i	$-0.875712\pi$
$211$	−26.8651	−1.84947	−0.924734	+	0.380615i	$0.875712\pi$
$212$	−6.91165	−0.474694
$213$	−32.9352	−2.25668
$214$	−15.4256	−1.05447
$215$	−11.7057	−0.798324
$216$	3.65307	0.248560
$217$	24.1840	1.64172
$218$	9.52403	0.645049
$219$	−18.5673	−1.25466
$220$	−14.0320	−0.946041
$221$	−19.1914	−1.29095
$222$	−13.7713	−0.924272
$223$	−6.96803	−0.466614	−0.233307	−	0.972403i	$-0.574955\pi$
$223$	−6.96803	−0.466614	−0.233307	+	0.972403i	$0.574955\pi$
$224$	4.13924	0.276564
$225$	3.00585	0.200390
$226$	−5.32705	−0.354350
$227$	−25.7398	−1.70841	−0.854206	−	0.519935i	$-0.825956\pi$
$227$	−25.7398	−1.70841	−0.854206	+	0.519935i	$0.825956\pi$
$228$	−13.4324	−0.889583
$229$	12.8125	0.846671	0.423335	−	0.905973i	$-0.360859\pi$
$229$	12.8125	0.846671	0.423335	+	0.905973i	$0.360859\pi$
$230$	2.38566	0.157306
$231$	65.9945	4.34212
$232$	−9.90084	−0.650022
$233$	−0.631185	−0.0413503	−0.0206751	−	0.999786i	$-0.506582\pi$
$233$	−0.631185	−0.0413503	−0.0206751	+	0.999786i	$0.506582\pi$
$234$	13.0665	0.854183
$235$	−18.8882	−1.23213
$236$	2.15411	0.140221
$237$	40.9123	2.65754
$238$	26.4317	1.71331
$239$	−5.02452	−0.325009	−0.162505	−	0.986708i	$-0.551957\pi$
$239$	−5.02452	−0.325009	−0.162505	+	0.986708i	$0.551957\pi$
$240$	6.46671	0.417424
$241$	8.90254	0.573463	0.286732	−	0.958011i	$-0.407431\pi$
$241$	8.90254	0.573463	0.286732	+	0.958011i	$0.407431\pi$
$242$	−23.5960	−1.51681
$243$	19.4728	1.24918
$244$	1.81870	0.116431
$245$	−24.1746	−1.54446
$246$	32.2145	2.05392
$247$	−14.8930	−0.947617
$248$	5.84263	0.371008
$249$	9.01458	0.571276
$250$	−10.2789	−0.650096
$251$	−4.72263	−0.298090	−0.149045	−	0.988830i	$-0.547620\pi$
$251$	−4.72263	−0.298090	−0.149045	+	0.988830i	$0.547620\pi$
$252$	−17.9960	−1.13364
$253$	5.88183	0.369788
$254$	−1.09445	−0.0686719
$255$	41.2941	2.58594
$256$	1.00000	0.0625000
$257$	4.86977	0.303768	0.151884	−	0.988398i	$-0.451466\pi$
$257$	4.86977	0.303768	0.151884	+	0.988398i	$0.451466\pi$
$258$	13.3004	0.828047
$259$	21.0292	1.30669
$260$	7.16986	0.444656
$261$	43.0456	2.66445
$262$	1.00000	0.0617802
$263$	15.3165	0.944456	0.472228	−	0.881476i	$-0.343450\pi$
$263$	15.3165	0.944456	0.472228	+	0.881476i	$0.343450\pi$
$264$	15.9436	0.981263
$265$	16.4889	1.01290
$266$	20.5116	1.25765
$267$	18.5843	1.13734
$268$	−3.88011	−0.237016
$269$	−0.765831	−0.0466935	−0.0233468	−	0.999727i	$-0.507432\pi$
$269$	−0.765831	−0.0466935	−0.0233468	+	0.999727i	$0.507432\pi$
$270$	−8.71497	−0.530376
$271$	−23.9597	−1.45545	−0.727723	−	0.685871i	$-0.759421\pi$
$271$	−23.9597	−1.45545	−0.727723	+	0.685871i	$0.759421\pi$
$272$	6.38564	0.387186
$273$	−33.7208	−2.04087
$274$	2.31495	0.139851
$275$	4.06653	0.245221
$276$	−2.71066	−0.163162
$277$	−9.83278	−0.590794	−0.295397	−	0.955375i	$-0.595452\pi$
$277$	−9.83278	−0.590794	−0.295397	+	0.955375i	$0.595452\pi$
$278$	−12.4396	−0.746076
$279$	−25.4018	−1.52077
$280$	−9.87481	−0.590133
$281$	−15.3981	−0.918574	−0.459287	−	0.888288i	$-0.651895\pi$
$281$	−15.3981	−0.918574	−0.459287	+	0.888288i	$0.651895\pi$
$282$	21.4614	1.27801
$283$	−8.59002	−0.510624	−0.255312	−	0.966859i	$-0.582178\pi$
$283$	−8.59002	−0.510624	−0.255312	+	0.966859i	$0.582178\pi$
$284$	12.1503	0.720986
$285$	32.0452	1.89819
$286$	17.6773	1.04528
$287$	−49.1923	−2.90373
$288$	−4.34767	−0.256189
$289$	23.7764	1.39861
$290$	23.6200	1.38702
$291$	33.2930	1.95167
$292$	6.84974	0.400851
$293$	−12.8382	−0.750018	−0.375009	−	0.927021i	$-0.622360\pi$
$293$	−12.8382	−0.750018	−0.375009	+	0.927021i	$0.622360\pi$
$294$	27.4679	1.60196
$295$	−5.13898	−0.299203
$296$	5.08044	0.295295
$297$	−21.4867	−1.24679
$298$	−2.84408	−0.164753
$299$	−3.00540	−0.173807
$300$	−1.87407	−0.108199
$301$	−20.3100	−1.17065
$302$	−15.8610	−0.912699
$303$	42.8564	2.46204
$304$	4.95540	0.284212
$305$	−4.33881	−0.248439
$306$	−27.7627	−1.58709
$307$	26.0778	1.48834	0.744169	−	0.667992i	$-0.232846\pi$
$307$	26.0778	1.48834	0.744169	+	0.667992i	$0.232846\pi$
$308$	−24.3463	−1.38726
$309$	−21.7124	−1.23518
$310$	−13.9385	−0.791655
$311$	−26.8027	−1.51984	−0.759920	−	0.650017i	$-0.774762\pi$
$311$	−26.8027	−1.51984	−0.759920	+	0.650017i	$0.774762\pi$
$312$	−8.14661	−0.461211
$313$	−19.0729	−1.07806	−0.539032	−	0.842285i	$-0.681210\pi$
$313$	−19.0729	−1.07806	−0.539032	+	0.842285i	$0.681210\pi$
$314$	−8.17821	−0.461523
$315$	42.9324	2.41897
$316$	−15.0931	−0.849054
$317$	17.2407	0.968332	0.484166	−	0.874976i	$-0.339123\pi$
$317$	17.2407	0.968332	0.484166	+	0.874976i	$0.339123\pi$
$318$	−18.7351	−1.05061
$319$	58.2351	3.26054
$320$	−2.38566	−0.133362
$321$	−41.8136	−2.33381
$322$	4.13924	0.230671
$323$	31.6434	1.76069
$324$	−3.14079	−0.174488
$325$	−2.07784	−0.115258
$326$	−18.9396	−1.04897
$327$	25.8164	1.42765
$328$	−11.8844	−0.656205
$329$	−32.7720	−1.80678
$330$	−38.0361	−2.09382
$331$	−3.43622	−0.188872	−0.0944358	−	0.995531i	$-0.530105\pi$
$331$	−3.43622	−0.188872	−0.0944358	+	0.995531i	$0.530105\pi$
$332$	−3.32560	−0.182516
$333$	−22.0881	−1.21042
$334$	17.6045	0.963276
$335$	9.25663	0.505744
$336$	11.2201	0.612104
$337$	−2.03552	−0.110882	−0.0554408	−	0.998462i	$-0.517656\pi$
$337$	−2.03552	−0.110882	−0.0554408	+	0.998462i	$0.517656\pi$
$338$	3.96757	0.215807
$339$	−14.4398	−0.784262
$340$	−15.2340	−0.826178
$341$	−34.3654	−1.86099
$342$	−21.5445	−1.16499
$343$	−12.9694	−0.700283
$344$	−4.90671	−0.264552
$345$	6.46671	0.348156
$346$	18.6923	1.00490
$347$	23.5016	1.26163	0.630816	−	0.775932i	$-0.282720\pi$
$347$	23.5016	1.26163	0.630816	+	0.775932i	$0.282720\pi$
$348$	−26.8378	−1.43866
$349$	7.65930	0.409993	0.204996	−	0.978763i	$-0.434282\pi$
$349$	7.65930	0.409993	0.204996	+	0.978763i	$0.434282\pi$
$350$	2.86175	0.152967
$351$	10.9789	0.586012
$352$	−5.88183	−0.313503
$353$	−20.9952	−1.11746	−0.558732	−	0.829348i	$-0.688712\pi$
$353$	−20.9952	−1.11746	−0.558732	+	0.829348i	$0.688712\pi$
$354$	5.83907	0.310343
$355$	−28.9864	−1.53844
$356$	−6.85600	−0.363367
$357$	71.6473	3.79198
$358$	−13.2311	−0.699283
$359$	33.0019	1.74177	0.870887	−	0.491484i	$-0.163545\pi$
$359$	33.0019	1.74177	0.870887	+	0.491484i	$0.163545\pi$
$360$	10.3721	0.546655
$361$	5.55604	0.292423
$362$	16.0123	0.841586
$363$	−63.9606	−3.35706
$364$	12.4401	0.652036
$365$	−16.3412	−0.855335
$366$	4.92988	0.257689
$367$	18.1997	0.950016	0.475008	−	0.879982i	$-0.342445\pi$
$367$	18.1997	0.950016	0.475008	+	0.879982i	$0.342445\pi$
$368$	1.00000	0.0521286
$369$	51.6693	2.68980
$370$	−12.1202	−0.630100
$371$	28.6090	1.48530
$372$	15.8374	0.821130
$373$	30.8630	1.59802	0.799012	−	0.601315i	$-0.205356\pi$
$373$	30.8630	1.59802	0.799012	+	0.601315i	$0.205356\pi$
$374$	−37.5593	−1.94214
$375$	−27.8626	−1.43882
$376$	−7.91740	−0.408309
$377$	−29.7560	−1.53251
$378$	−15.1209	−0.777736
$379$	−25.7683	−1.32363	−0.661815	−	0.749667i	$-0.730213\pi$
$379$	−25.7683	−1.32363	−0.661815	+	0.749667i	$0.730213\pi$
$380$	−11.8219	−0.606451
$381$	−2.96668	−0.151988
$382$	−2.70993	−0.138652
$383$	21.9984	1.12406	0.562032	−	0.827115i	$-0.310020\pi$
$383$	21.9984	1.12406	0.562032	+	0.827115i	$0.310020\pi$
$384$	2.71066	0.138328
$385$	58.0820	2.96013
$386$	−17.4917	−0.890305
$387$	21.3327	1.08440
$388$	−12.2823	−0.623537
$389$	3.67047	0.186100	0.0930500	−	0.995661i	$-0.470338\pi$
$389$	3.67047	0.186100	0.0930500	+	0.995661i	$0.470338\pi$
$390$	19.4350	0.984132
$391$	6.38564	0.322936
$392$	−10.1333	−0.511808
$393$	2.71066	0.136735
$394$	−22.2579	−1.12134
$395$	36.0070	1.81171
$396$	25.5723	1.28505
$397$	13.4636	0.675718	0.337859	−	0.941197i	$-0.390297\pi$
$397$	13.4636	0.675718	0.337859	+	0.941197i	$0.390297\pi$
$398$	−13.8502	−0.694249
$399$	55.5999	2.78348
$400$	0.691371	0.0345685
$401$	23.2149	1.15930	0.579648	−	0.814867i	$-0.303190\pi$
$401$	23.2149	1.15930	0.579648	+	0.814867i	$0.303190\pi$
$402$	−10.5177	−0.524573
$403$	17.5594	0.874698
$404$	−15.8103	−0.786593
$405$	7.49285	0.372323
$406$	40.9819	2.03390
$407$	−29.8823	−1.48121
$408$	17.3093	0.856938
$409$	−7.67855	−0.379680	−0.189840	−	0.981815i	$-0.560797\pi$
$409$	−7.67855	−0.379680	−0.189840	+	0.981815i	$0.560797\pi$
$410$	28.3521	1.40021
$411$	6.27504	0.309525
$412$	8.01002	0.394625
$413$	−8.91639	−0.438747
$414$	−4.34767	−0.213676
$415$	7.93376	0.389453
$416$	3.00540	0.147352
$417$	−33.7194	−1.65125
$418$	−29.1469	−1.42562
$419$	−10.6058	−0.518126	−0.259063	−	0.965860i	$-0.583414\pi$
$419$	−10.6058	−0.518126	−0.259063	+	0.965860i	$0.583414\pi$
$420$	−26.7672	−1.30611
$421$	−12.4768	−0.608082	−0.304041	−	0.952659i	$-0.598336\pi$
$421$	−12.4768	−0.608082	−0.304041	+	0.952659i	$0.598336\pi$
$422$	26.8651	1.30777
$423$	34.4222	1.67367
$424$	6.91165	0.335660
$425$	4.41484	0.214151
$426$	32.9352	1.59572
$427$	−7.52805	−0.364308
$428$	15.4256	0.745625
$429$	47.9170	2.31345
$430$	11.7057	0.564500
$431$	34.9085	1.68148	0.840741	−	0.541438i	$-0.182120\pi$
$431$	34.9085	1.68148	0.840741	+	0.541438i	$0.182120\pi$
$432$	−3.65307	−0.175758
$433$	−8.85392	−0.425492	−0.212746	−	0.977107i	$-0.568241\pi$
$433$	−8.85392	−0.425492	−0.212746	+	0.977107i	$0.568241\pi$
$434$	−24.1840	−1.16087
$435$	64.0258	3.06980
$436$	−9.52403	−0.456118
$437$	4.95540	0.237049
$438$	18.5673	0.887181
$439$	−22.7520	−1.08590	−0.542948	−	0.839767i	$-0.682692\pi$
$439$	−22.7520	−1.08590	−0.542948	+	0.839767i	$0.682692\pi$
$440$	14.0320	0.668952
$441$	44.0562	2.09791
$442$	19.1914	0.912842
$443$	12.7729	0.606859	0.303429	−	0.952854i	$-0.401868\pi$
$443$	12.7729	0.606859	0.303429	+	0.952854i	$0.401868\pi$
$444$	13.7713	0.653559
$445$	16.3561	0.775353
$446$	6.96803	0.329946
$447$	−7.70934	−0.364639
$448$	−4.13924	−0.195561
$449$	12.4793	0.588936	0.294468	−	0.955661i	$-0.404858\pi$
$449$	12.4793	0.588936	0.294468	+	0.955661i	$0.404858\pi$
$450$	−3.00585	−0.141697
$451$	69.9019	3.29155
$452$	5.32705	0.250563
$453$	−42.9938	−2.02002
$454$	25.7398	1.20803
$455$	−29.6778	−1.39131
$456$	13.4324	0.629030
$457$	−3.85726	−0.180435	−0.0902175	−	0.995922i	$-0.528756\pi$
$457$	−3.85726	−0.180435	−0.0902175	+	0.995922i	$0.528756\pi$
$458$	−12.8125	−0.598687
$459$	−23.3272	−1.08882
$460$	−2.38566	−0.111232
$461$	10.1757	0.473929	0.236964	−	0.971518i	$-0.423848\pi$
$461$	10.1757	0.473929	0.236964	+	0.971518i	$0.423848\pi$
$462$	−65.9945	−3.07034
$463$	−14.3261	−0.665790	−0.332895	−	0.942964i	$-0.608025\pi$
$463$	−14.3261	−0.665790	−0.332895	+	0.942964i	$0.608025\pi$
$464$	9.90084	0.459635
$465$	−37.7826	−1.75213
$466$	0.631185	0.0292391
$467$	36.0707	1.66915	0.834577	−	0.550891i	$-0.185712\pi$
$467$	36.0707	1.66915	0.834577	+	0.550891i	$0.185712\pi$
$468$	−13.0665	−0.603998
$469$	16.0607	0.741615
$470$	18.8882	0.871249
$471$	−22.1683	−1.02146
$472$	−2.15411	−0.0991511
$473$	28.8604	1.32700
$474$	−40.9123	−1.87916
$475$	3.42602	0.157197
$476$	−26.4317	−1.21149
$477$	−30.0496	−1.37588
$478$	5.02452	0.229816
$479$	8.60771	0.393296	0.196648	−	0.980474i	$-0.436994\pi$
$479$	8.60771	0.393296	0.196648	+	0.980474i	$0.436994\pi$
$480$	−6.46671	−0.295163
$481$	15.2688	0.696196
$482$	−8.90254	−0.405500
$483$	11.2201	0.510530
$484$	23.5960	1.07254
$485$	29.3013	1.33050
$486$	−19.4728	−0.883304
$487$	3.09068	0.140052	0.0700261	−	0.997545i	$-0.477692\pi$
$487$	3.09068	0.140052	0.0700261	+	0.997545i	$0.477692\pi$
$488$	−1.81870	−0.0823288
$489$	−51.3389	−2.32162
$490$	24.1746	1.09210
$491$	−10.8886	−0.491396	−0.245698	−	0.969346i	$-0.579017\pi$
$491$	−10.8886	−0.491396	−0.245698	+	0.969346i	$0.579017\pi$
$492$	−32.2145	−1.45234
$493$	63.2232	2.84743
$494$	14.8930	0.670067
$495$	−61.0067	−2.74205
$496$	−5.84263	−0.262342
$497$	−50.2928	−2.25594
$498$	−9.01458	−0.403953
$499$	16.5771	0.742092	0.371046	−	0.928614i	$-0.378999\pi$
$499$	16.5771	0.742092	0.371046	+	0.928614i	$0.378999\pi$
$500$	10.2789	0.459687
$501$	47.7198	2.13196
$502$	4.72263	0.210782
$503$	−8.17175	−0.364360	−0.182180	−	0.983265i	$-0.558315\pi$
$503$	−8.17175	−0.364360	−0.182180	+	0.983265i	$0.558315\pi$
$504$	17.9960	0.801607
$505$	37.7181	1.67843
$506$	−5.88183	−0.261479
$507$	10.7547	0.477634
$508$	1.09445	0.0485583
$509$	5.70567	0.252900	0.126450	−	0.991973i	$-0.459642\pi$
$509$	5.70567	0.252900	0.126450	+	0.991973i	$0.459642\pi$
$510$	−41.2941	−1.82853
$511$	−28.3527	−1.25425
$512$	−1.00000	−0.0441942
$513$	−18.1024	−0.799242
$514$	−4.86977	−0.214796
$515$	−19.1092	−0.842051
$516$	−13.3004	−0.585518
$517$	46.5688	2.04810
$518$	−21.0292	−0.923968
$519$	50.6683	2.22409
$520$	−7.16986	−0.314419
$521$	−20.5288	−0.899384	−0.449692	−	0.893184i	$-0.648466\pi$
$521$	−20.5288	−0.899384	−0.449692	+	0.893184i	$0.648466\pi$
$522$	−43.0456	−1.88405
$523$	−7.87261	−0.344245	−0.172123	−	0.985076i	$-0.555062\pi$
$523$	−7.87261	−0.344245	−0.172123	+	0.985076i	$0.555062\pi$
$524$	−1.00000	−0.0436852
$525$	7.75722	0.338553
$526$	−15.3165	−0.667831
$527$	−37.3090	−1.62520
$528$	−15.9436	−0.693858
$529$	1.00000	0.0434783
$530$	−16.4889	−0.716230
$531$	9.36537	0.406422
$532$	−20.5116	−0.889291
$533$	−35.7173	−1.54709
$534$	−18.5843	−0.804220
$535$	−36.8003	−1.59101
$536$	3.88011	0.167595
$537$	−35.8649	−1.54768
$538$	0.765831	0.0330173
$539$	59.6023	2.56725
$540$	8.71497	0.375033
$541$	3.88437	0.167002	0.0835010	−	0.996508i	$-0.473390\pi$
$541$	3.88437	0.167002	0.0835010	+	0.996508i	$0.473390\pi$
$542$	23.9597	1.02916
$543$	43.4038	1.86264
$544$	−6.38564	−0.273782
$545$	22.7211	0.973265
$546$	33.7208	1.44312
$547$	2.58204	0.110400	0.0552000	−	0.998475i	$-0.482420\pi$
$547$	2.58204	0.110400	0.0552000	+	0.998475i	$0.482420\pi$
$548$	−2.31495	−0.0988898
$549$	7.90712	0.337468
$550$	−4.06653	−0.173397
$551$	49.0627	2.09014
$552$	2.71066	0.115373
$553$	62.4740	2.65666
$554$	9.83278	0.417755
$555$	−32.8537	−1.39456
$556$	12.4396	0.527555
$557$	−15.6940	−0.664977	−0.332488	−	0.943107i	$-0.607888\pi$
$557$	−15.6940	−0.664977	−0.332488	+	0.943107i	$0.607888\pi$
$558$	25.4018	1.07535
$559$	−14.7466	−0.623715
$560$	9.87481	0.417287
$561$	−101.810	−4.29844
$562$	15.3981	0.649530
$563$	32.1403	1.35455	0.677275	−	0.735730i	$-0.263161\pi$
$563$	32.1403	1.35455	0.677275	+	0.735730i	$0.263161\pi$
$564$	−21.4614	−0.903687
$565$	−12.7085	−0.534651
$566$	8.59002	0.361065
$567$	13.0005	0.545968
$568$	−12.1503	−0.509814
$569$	−34.2096	−1.43414	−0.717071	−	0.697000i	$-0.754518\pi$
$569$	−34.2096	−1.43414	−0.717071	+	0.697000i	$0.754518\pi$
$570$	−32.0452	−1.34222
$571$	−12.0779	−0.505443	−0.252722	−	0.967539i	$-0.581326\pi$
$571$	−12.0779	−0.505443	−0.252722	+	0.967539i	$0.581326\pi$
$572$	−17.6773	−0.739123
$573$	−7.34569	−0.306870
$574$	49.1923	2.05324
$575$	0.691371	0.0288321
$576$	4.34767	0.181153
$577$	−42.1912	−1.75644	−0.878221	−	0.478255i	$-0.841269\pi$
$577$	−42.1912	−1.75644	−0.878221	+	0.478255i	$0.841269\pi$
$578$	−23.7764	−0.988969
$579$	−47.4141	−1.97046
$580$	−23.6200	−0.980768
$581$	13.7655	0.571088
$582$	−33.2930	−1.38004
$583$	−40.6532	−1.68368
$584$	−6.84974	−0.283444
$585$	31.1722	1.28881
$586$	12.8382	0.530343
$587$	6.83568	0.282139	0.141069	−	0.990000i	$-0.454946\pi$
$587$	6.83568	0.282139	0.141069	+	0.990000i	$0.454946\pi$
$588$	−27.4679	−1.13276
$589$	−28.9526	−1.19297
$590$	5.13898	0.211568
$591$	−60.3336	−2.48179
$592$	−5.08044	−0.208805
$593$	−6.87158	−0.282182	−0.141091	−	0.989997i	$-0.545061\pi$
$593$	−6.87158	−0.282182	−0.141091	+	0.989997i	$0.545061\pi$
$594$	21.4867	0.881611
$595$	63.0570	2.58509
$596$	2.84408	0.116498
$597$	−37.5432	−1.53654
$598$	3.00540	0.122900
$599$	3.65186	0.149211	0.0746055	−	0.997213i	$-0.476230\pi$
$599$	3.65186	0.149211	0.0746055	+	0.997213i	$0.476230\pi$
$600$	1.87407	0.0765086
$601$	−30.7565	−1.25459	−0.627293	−	0.778783i	$-0.715837\pi$
$601$	−30.7565	−1.25459	−0.627293	+	0.778783i	$0.715837\pi$
$602$	20.3100	0.827775
$603$	−16.8694	−0.686977
$604$	15.8610	0.645375
$605$	−56.2919	−2.28859
$606$	−42.8564	−1.74092
$607$	29.3815	1.19256	0.596279	−	0.802777i	$-0.296645\pi$
$607$	29.3815	1.19256	0.596279	+	0.802777i	$0.296645\pi$
$608$	−4.95540	−0.200968
$609$	111.088	4.50151
$610$	4.33881	0.175673
$611$	−23.7950	−0.962641
$612$	27.7627	1.12224
$613$	−38.8176	−1.56783	−0.783915	−	0.620868i	$-0.786780\pi$
$613$	−38.8176	−1.56783	−0.783915	+	0.620868i	$0.786780\pi$
$614$	−26.0778	−1.05241
$615$	76.8528	3.09900
$616$	24.3463	0.980940
$617$	−20.5115	−0.825763	−0.412881	−	0.910785i	$-0.635478\pi$
$617$	−20.5115	−0.825763	−0.412881	+	0.910785i	$0.635478\pi$
$618$	21.7124	0.873401
$619$	−3.40452	−0.136839	−0.0684196	−	0.997657i	$-0.521796\pi$
$619$	−3.40452	−0.136839	−0.0684196	+	0.997657i	$0.521796\pi$
$620$	13.9385	0.559785
$621$	−3.65307	−0.146593
$622$	26.8027	1.07469
$623$	28.3786	1.13697
$624$	8.14661	0.326125
$625$	−27.9789	−1.11915
$626$	19.0729	0.762307
$627$	−79.0072	−3.15524
$628$	8.17821	0.326346
$629$	−32.4419	−1.29354
$630$	−42.9324	−1.71047
$631$	20.0502	0.798187	0.399094	−	0.916910i	$-0.369325\pi$
$631$	20.0502	0.798187	0.399094	+	0.916910i	$0.369325\pi$
$632$	15.0931	0.600372
$633$	72.8220	2.89441
$634$	−17.2407	−0.684714
$635$	−2.61098	−0.103614
$636$	18.7351	0.742896
$637$	−30.4546	−1.20665
$638$	−58.2351	−2.30555
$639$	52.8253	2.08974
$640$	2.38566	0.0943015
$641$	−18.4682	−0.729448	−0.364724	−	0.931116i	$-0.618837\pi$
$641$	−18.4682	−0.729448	−0.364724	+	0.931116i	$0.618837\pi$
$642$	41.8136	1.65025
$643$	−6.45660	−0.254624	−0.127312	−	0.991863i	$-0.540635\pi$
$643$	−6.45660	−0.254624	−0.127312	+	0.991863i	$0.540635\pi$
$644$	−4.13924	−0.163109
$645$	31.7302	1.24938
$646$	−31.6434	−1.24499
$647$	−9.83802	−0.386773	−0.193386	−	0.981123i	$-0.561947\pi$
$647$	−9.83802	−0.386773	−0.193386	+	0.981123i	$0.561947\pi$
$648$	3.14079	0.123382
$649$	12.6701	0.497346
$650$	2.07784	0.0814998
$651$	−65.5547	−2.56929
$652$	18.9396	0.741733
$653$	37.1050	1.45203	0.726016	−	0.687678i	$-0.241370\pi$
$653$	37.1050	1.45203	0.726016	+	0.687678i	$0.241370\pi$
$654$	−25.8164	−1.00950
$655$	2.38566	0.0932154
$656$	11.8844	0.464007
$657$	29.7804	1.16184
$658$	32.7720	1.27759
$659$	40.6174	1.58223	0.791114	−	0.611669i	$-0.209502\pi$
$659$	40.6174	1.58223	0.791114	+	0.611669i	$0.209502\pi$
$660$	38.0361	1.48055
$661$	−7.72935	−0.300637	−0.150318	−	0.988638i	$-0.548030\pi$
$661$	−7.72935	−0.300637	−0.150318	+	0.988638i	$0.548030\pi$
$662$	3.43622	0.133552
$663$	52.0213	2.02034
$664$	3.32560	0.129058
$665$	48.9337	1.89757
$666$	22.0881	0.855896
$667$	9.90084	0.383362
$668$	−17.6045	−0.681139
$669$	18.8880	0.730251
$670$	−9.25663	−0.357615
$671$	10.6973	0.412965
$672$	−11.2201	−0.432823
$673$	−37.4606	−1.44400	−0.721999	−	0.691894i	$-0.756777\pi$
$673$	−37.4606	−1.44400	−0.721999	+	0.691894i	$0.756777\pi$
$674$	2.03552	0.0784052
$675$	−2.52562	−0.0972113
$676$	−3.96757	−0.152599
$677$	14.0659	0.540597	0.270298	−	0.962777i	$-0.412878\pi$
$677$	14.0659	0.540597	0.270298	+	0.962777i	$0.412878\pi$
$678$	14.4398	0.554557
$679$	50.8392	1.95103
$680$	15.2340	0.584196
$681$	69.7718	2.67366
$682$	34.3654	1.31592
$683$	19.1420	0.732450	0.366225	−	0.930526i	$-0.380650\pi$
$683$	19.1420	0.732450	0.366225	+	0.930526i	$0.380650\pi$
$684$	21.5445	0.823773
$685$	5.52268	0.211011
$686$	12.9694	0.495175
$687$	−34.7302	−1.32504
$688$	4.90671	0.187066
$689$	20.7723	0.791361
$690$	−6.46671	−0.246183
$691$	−33.4075	−1.27088	−0.635440	−	0.772150i	$-0.719181\pi$
$691$	−33.4075	−1.27088	−0.635440	+	0.772150i	$0.719181\pi$
$692$	−18.6923	−0.710573
$693$	−105.850	−4.02089
$694$	−23.5016	−0.892109
$695$	−29.6766	−1.12570
$696$	26.8378	1.01728
$697$	75.8894	2.87451
$698$	−7.65930	−0.289909
$699$	1.71093	0.0647132
$700$	−2.86175	−0.108164
$701$	−17.7718	−0.671231	−0.335616	−	0.941999i	$-0.608944\pi$
$701$	−17.7718	−0.671231	−0.335616	+	0.941999i	$0.608944\pi$
$702$	−10.9789	−0.414373
$703$	−25.1757	−0.949518
$704$	5.88183	0.221680
$705$	51.1995	1.92829
$706$	20.9952	0.790166
$707$	65.4427	2.46123
$708$	−5.83907	−0.219446
$709$	19.2695	0.723682	0.361841	−	0.932240i	$-0.382148\pi$
$709$	19.2695	0.723682	0.361841	+	0.932240i	$0.382148\pi$
$710$	28.9864	1.08784
$711$	−65.6198	−2.46094
$712$	6.85600	0.256940
$713$	−5.84263	−0.218808
$714$	−71.6473	−2.68133
$715$	42.1719	1.57714
$716$	13.2311	0.494468
$717$	13.6198	0.508639
$718$	−33.0019	−1.23162
$719$	−8.46843	−0.315819	−0.157910	−	0.987454i	$-0.550475\pi$
$719$	−8.46843	−0.315819	−0.157910	+	0.987454i	$0.550475\pi$
$720$	−10.3721	−0.386544
$721$	−33.1554	−1.23477
$722$	−5.55604	−0.206774
$723$	−24.1317	−0.897469
$724$	−16.0123	−0.595091
$725$	6.84515	0.254222
$726$	63.9606	2.37380
$727$	38.3879	1.42373	0.711865	−	0.702317i	$-0.247851\pi$
$727$	38.3879	1.42373	0.711865	+	0.702317i	$0.247851\pi$
$728$	−12.4401	−0.461059
$729$	−43.3617	−1.60599
$730$	16.3412	0.604813
$731$	31.3325	1.15887
$732$	−4.92988	−0.182214
$733$	49.5137	1.82883	0.914415	−	0.404778i	$-0.132651\pi$
$733$	49.5137	1.82883	0.914415	+	0.404778i	$0.132651\pi$
$734$	−18.1997	−0.671762
$735$	65.5290	2.41707
$736$	−1.00000	−0.0368605
$737$	−22.8222	−0.840666
$738$	−51.6693	−1.90197
$739$	−35.7350	−1.31453	−0.657266	−	0.753658i	$-0.728287\pi$
$739$	−35.7350	−1.31453	−0.657266	+	0.753658i	$0.728287\pi$
$740$	12.1202	0.445548
$741$	40.3698	1.48302
$742$	−28.6090	−1.05027
$743$	−22.1147	−0.811309	−0.405655	−	0.914026i	$-0.632956\pi$
$743$	−22.1147	−0.811309	−0.405655	+	0.914026i	$0.632956\pi$
$744$	−15.8374	−0.580627
$745$	−6.78501	−0.248584
$746$	−30.8630	−1.12997
$747$	−14.4586	−0.529013
$748$	37.5593	1.37330
$749$	−63.8503	−2.33304
$750$	27.8626	1.01740
$751$	−36.4495	−1.33006	−0.665031	−	0.746815i	$-0.731582\pi$
$751$	−36.4495	−1.33006	−0.665031	+	0.746815i	$0.731582\pi$
$752$	7.91740	0.288718
$753$	12.8014	0.466511
$754$	29.7560	1.08365
$755$	−37.8390	−1.37710
$756$	15.1209	0.549942
$757$	20.2260	0.735127	0.367564	−	0.929998i	$-0.380192\pi$
$757$	20.2260	0.735127	0.367564	+	0.929998i	$0.380192\pi$
$758$	25.7683	0.935947
$759$	−15.9436	−0.578717
$760$	11.8219	0.428826
$761$	−5.60262	−0.203095	−0.101547	−	0.994831i	$-0.532379\pi$
$761$	−5.60262	−0.203095	−0.101547	+	0.994831i	$0.532379\pi$
$762$	2.96668	0.107471
$763$	39.4222	1.42718
$764$	2.70993	0.0980417
$765$	−66.2322	−2.39463
$766$	−21.9984	−0.794833
$767$	−6.47397	−0.233762
$768$	−2.71066	−0.0978125
$769$	−2.27729	−0.0821211	−0.0410606	−	0.999157i	$-0.513074\pi$
$769$	−2.27729	−0.0821211	−0.0410606	+	0.999157i	$0.513074\pi$
$770$	−58.0820	−2.09313
$771$	−13.2003	−0.475397
$772$	17.4917	0.629541
$773$	21.8837	0.787104	0.393552	−	0.919302i	$-0.371246\pi$
$773$	21.8837	0.787104	0.393552	+	0.919302i	$0.371246\pi$
$774$	−21.3327	−0.766789
$775$	−4.03942	−0.145100
$776$	12.2823	0.440907
$777$	−57.0029	−2.04497
$778$	−3.67047	−0.131593
$779$	58.8919	2.11002
$780$	−19.4350	−0.695886
$781$	71.4658	2.55725
$782$	−6.38564	−0.228350
$783$	−36.1684	−1.29255
$784$	10.1333	0.361903
$785$	−19.5104	−0.696357
$786$	−2.71066	−0.0966860
$787$	−47.7652	−1.70265	−0.851323	−	0.524642i	$-0.824199\pi$
$787$	−47.7652	−1.70265	−0.851323	+	0.524642i	$0.824199\pi$
$788$	22.2579	0.792906
$789$	−41.5178	−1.47807
$790$	−36.0070	−1.28107
$791$	−22.0499	−0.784005
$792$	−25.5723	−0.908670
$793$	−5.46593	−0.194101
$794$	−13.4636	−0.477805
$795$	−44.6956	−1.58519
$796$	13.8502	0.490909
$797$	−31.6497	−1.12109	−0.560545	−	0.828124i	$-0.689408\pi$
$797$	−31.6497	−1.12109	−0.560545	+	0.828124i	$0.689408\pi$
$798$	−55.5999	−1.96822
$799$	50.5577	1.78860
$800$	−0.691371	−0.0244436
$801$	−29.8076	−1.05320
$802$	−23.2149	−0.819746
$803$	40.2890	1.42177
$804$	10.5177	0.370929
$805$	9.87481	0.348041
$806$	−17.5594	−0.618505
$807$	2.07591	0.0730754
$808$	15.8103	0.556205
$809$	−0.839075	−0.0295003	−0.0147501	−	0.999891i	$-0.504695\pi$
$809$	−0.839075	−0.0295003	−0.0147501	+	0.999891i	$0.504695\pi$
$810$	−7.49285	−0.263272
$811$	45.0159	1.58072	0.790361	−	0.612641i	$-0.209893\pi$
$811$	45.0159	1.58072	0.790361	+	0.612641i	$0.209893\pi$
$812$	−40.9819	−1.43818
$813$	64.9465	2.27777
$814$	29.8823	1.04737
$815$	−45.1835	−1.58271
$816$	−17.3093	−0.605946
$817$	24.3147	0.850664
$818$	7.67855	0.268474
$819$	54.0853	1.88989
$820$	−28.3521	−0.990097
$821$	17.3117	0.604182	0.302091	−	0.953279i	$-0.402315\pi$
$821$	17.3117	0.604182	0.302091	+	0.953279i	$0.402315\pi$
$822$	−6.27504	−0.218867
$823$	−15.1825	−0.529227	−0.264613	−	0.964355i	$-0.585244\pi$
$823$	−15.1825	−0.529227	−0.264613	+	0.964355i	$0.585244\pi$
$824$	−8.01002	−0.279042
$825$	−11.0230	−0.383770
$826$	8.91639	0.310241
$827$	−5.52460	−0.192109	−0.0960545	−	0.995376i	$-0.530622\pi$
$827$	−5.52460	−0.192109	−0.0960545	+	0.995376i	$0.530622\pi$
$828$	4.34767	0.151092
$829$	−6.68908	−0.232321	−0.116161	−	0.993230i	$-0.537059\pi$
$829$	−6.68908	−0.232321	−0.116161	+	0.993230i	$0.537059\pi$
$830$	−7.93376	−0.275385
$831$	26.6533	0.924593
$832$	−3.00540	−0.104193
$833$	64.7075	2.24198
$834$	33.7194	1.16761
$835$	41.9984	1.45341
$836$	29.1469	1.00807
$837$	21.3435	0.737740
$838$	10.6058	0.366370
$839$	−2.94065	−0.101522	−0.0507612	−	0.998711i	$-0.516165\pi$
$839$	−2.94065	−0.101522	−0.0507612	+	0.998711i	$0.516165\pi$
$840$	26.7672	0.923557
$841$	69.0266	2.38023
$842$	12.4768	0.429979
$843$	41.7390	1.43757
$844$	−26.8651	−0.924734
$845$	9.46528	0.325615
$846$	−34.4222	−1.18346
$847$	−97.6692	−3.35596
$848$	−6.91165	−0.237347
$849$	23.2846	0.799126
$850$	−4.41484	−0.151428
$851$	−5.08044	−0.174155
$852$	−32.9352	−1.12834
$853$	14.3018	0.489684	0.244842	−	0.969563i	$-0.421264\pi$
$853$	14.3018	0.489684	0.244842	+	0.969563i	$0.421264\pi$
$854$	7.52805	0.257604
$855$	−51.3977	−1.75777
$856$	−15.4256	−0.527237
$857$	−30.8476	−1.05374	−0.526868	−	0.849947i	$-0.676634\pi$
$857$	−30.8476	−1.05374	−0.526868	+	0.849947i	$0.676634\pi$
$858$	−47.9170	−1.63586
$859$	40.4644	1.38063	0.690314	−	0.723510i	$-0.257473\pi$
$859$	40.4644	1.38063	0.690314	+	0.723510i	$0.257473\pi$
$860$	−11.7057	−0.399162
$861$	133.343	4.54433
$862$	−34.9085	−1.18899
$863$	47.1175	1.60390	0.801949	−	0.597393i	$-0.203797\pi$
$863$	47.1175	1.60390	0.801949	+	0.597393i	$0.203797\pi$
$864$	3.65307	0.124280
$865$	44.5934	1.51622
$866$	8.85392	0.300869
$867$	−64.4498	−2.18883
$868$	24.1840	0.820860
$869$	−88.7751	−3.01149
$870$	−64.0258	−2.17068
$871$	11.6613	0.395128
$872$	9.52403	0.322524
$873$	−53.3992	−1.80729
$874$	−4.95540	−0.167619
$875$	−42.5469	−1.43835
$876$	−18.5673	−0.627331
$877$	23.6839	0.799750	0.399875	−	0.916570i	$-0.369054\pi$
$877$	23.6839	0.799750	0.399875	+	0.916570i	$0.369054\pi$
$878$	22.7520	0.767844
$879$	34.8001	1.17378
$880$	−14.0320	−0.473020
$881$	34.0677	1.14777	0.573885	−	0.818936i	$-0.305436\pi$
$881$	34.0677	1.14777	0.573885	+	0.818936i	$0.305436\pi$
$882$	−44.0562	−1.48345
$883$	30.7018	1.03320	0.516599	−	0.856227i	$-0.327198\pi$
$883$	30.7018	1.03320	0.516599	+	0.856227i	$0.327198\pi$
$884$	−19.1914	−0.645477
$885$	13.9300	0.468253
$886$	−12.7729	−0.429114
$887$	33.6847	1.13102	0.565511	−	0.824741i	$-0.308679\pi$
$887$	33.6847	1.13102	0.565511	+	0.824741i	$0.308679\pi$
$888$	−13.7713	−0.462136
$889$	−4.53019	−0.151938
$890$	−16.3561	−0.548257
$891$	−18.4736	−0.618888
$892$	−6.96803	−0.233307
$893$	39.2339	1.31291
$894$	7.70934	0.257839
$895$	−31.5648	−1.05509
$896$	4.13924	0.138282
$897$	8.14661	0.272007
$898$	−12.4793	−0.416441
$899$	−57.8470	−1.92930
$900$	3.00585	0.100195
$901$	−44.1353	−1.47036
$902$	−69.9019	−2.32748
$903$	55.0535	1.83207
$904$	−5.32705	−0.177175
$905$	38.1998	1.26981
$906$	42.9938	1.42837
$907$	42.8532	1.42292	0.711459	−	0.702728i	$-0.248035\pi$
$907$	42.8532	1.42292	0.711459	+	0.702728i	$0.248035\pi$
$908$	−25.7398	−0.854206
$909$	−68.7380	−2.27990
$910$	29.6778	0.983808
$911$	44.3851	1.47054	0.735272	−	0.677772i	$-0.237054\pi$
$911$	44.3851	1.47054	0.735272	+	0.677772i	$0.237054\pi$
$912$	−13.4324	−0.444792
$913$	−19.5606	−0.647363
$914$	3.85726	0.127587
$915$	11.7610	0.388807
$916$	12.8125	0.423335
$917$	4.13924	0.136690
$918$	23.3272	0.769912
$919$	31.1900	1.02886	0.514432	−	0.857531i	$-0.328003\pi$
$919$	31.1900	1.02886	0.514432	+	0.857531i	$0.328003\pi$
$920$	2.38566	0.0786529
$921$	−70.6879	−2.32925
$922$	−10.1757	−0.335118
$923$	−36.5164	−1.20195
$924$	65.9945	2.17106
$925$	−3.51247	−0.115489
$926$	14.3261	0.470785
$927$	34.8249	1.14380
$928$	−9.90084	−0.325011
$929$	−1.19644	−0.0392538	−0.0196269	−	0.999807i	$-0.506248\pi$
$929$	−1.19644	−0.0392538	−0.0196269	+	0.999807i	$0.506248\pi$
$930$	37.7826	1.23894
$931$	50.2145	1.64571
$932$	−0.631185	−0.0206751
$933$	72.6529	2.37855
$934$	−36.0707	−1.18027
$935$	−89.6036	−2.93035
$936$	13.0665	0.427091
$937$	−42.6154	−1.39218	−0.696092	−	0.717953i	$-0.745079\pi$
$937$	−42.6154	−1.39218	−0.696092	+	0.717953i	$0.745079\pi$
$938$	−16.0607	−0.524401
$939$	51.7001	1.68717
$940$	−18.8882	−0.616066
$941$	−16.7403	−0.545718	−0.272859	−	0.962054i	$-0.587969\pi$
$941$	−16.7403	−0.545718	−0.272859	+	0.962054i	$0.587969\pi$
$942$	22.1683	0.722284
$943$	11.8844	0.387009
$944$	2.15411	0.0701104
$945$	−36.0733	−1.17347
$946$	−28.8604	−0.938333
$947$	26.2855	0.854165	0.427083	−	0.904213i	$-0.359541\pi$
$947$	26.2855	0.854165	0.427083	+	0.904213i	$0.359541\pi$
$948$	40.9123	1.32877
$949$	−20.5862	−0.668257
$950$	−3.42602	−0.111155
$951$	−46.7335	−1.51544
$952$	26.4317	0.856656
$953$	−5.22481	−0.169248	−0.0846241	−	0.996413i	$-0.526969\pi$
$953$	−5.22481	−0.169248	−0.0846241	+	0.996413i	$0.526969\pi$
$954$	30.0496	0.972891
$955$	−6.46496	−0.209201
$956$	−5.02452	−0.162505
$957$	−157.855	−5.10274
$958$	−8.60771	−0.278102
$959$	9.58213	0.309423
$960$	6.46671	0.208712
$961$	3.13636	0.101173
$962$	−15.2688	−0.492285
$963$	67.0655	2.16115
$964$	8.90254	0.286732
$965$	−41.7293	−1.34331
$966$	−11.2201	−0.360999
$967$	−12.4704	−0.401020	−0.200510	−	0.979692i	$-0.564260\pi$
$967$	−12.4704	−0.401020	−0.200510	+	0.979692i	$0.564260\pi$
$968$	−23.5960	−0.758403
$969$	−85.7746	−2.75548
$970$	−29.3013	−0.940807
$971$	19.3949	0.622413	0.311207	−	0.950342i	$-0.399267\pi$
$971$	19.3949	0.622413	0.311207	+	0.950342i	$0.399267\pi$
$972$	19.4728	0.624590
$973$	−51.4903	−1.65070
$974$	−3.09068	−0.0990319
$975$	5.63233	0.180379
$976$	1.81870	0.0582153
$977$	6.37157	0.203845	0.101922	−	0.994792i	$-0.467501\pi$
$977$	6.37157	0.203845	0.101922	+	0.994792i	$0.467501\pi$
$978$	51.3389	1.64164
$979$	−40.3259	−1.28882
$980$	−24.1746	−0.772228
$981$	−41.4073	−1.32203
$982$	10.8886	0.347469
$983$	−5.31690	−0.169583	−0.0847913	−	0.996399i	$-0.527022\pi$
$983$	−5.31690	−0.169583	−0.0847913	+	0.996399i	$0.527022\pi$
$984$	32.2145	1.02696
$985$	−53.0998	−1.69190
$986$	−63.2232	−2.01344
$987$	88.8337	2.82761
$988$	−14.8930	−0.473809
$989$	4.90671	0.156024
$990$	61.0067	1.93892
$991$	10.0086	0.317934	0.158967	−	0.987284i	$-0.449184\pi$
$991$	10.0086	0.317934	0.158967	+	0.987284i	$0.449184\pi$
$992$	5.84263	0.185504
$993$	9.31441	0.295584
$994$	50.2928	1.59519
$995$	−33.0419	−1.04750
$996$	9.01458	0.285638
$997$	−50.9504	−1.61362	−0.806808	−	0.590813i	$-0.798807\pi$
$997$	−50.9504	−1.61362	−0.806808	+	0.590813i	$0.798807\pi$
$998$	−16.5771	−0.524738
$999$	18.5592	0.587187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.j.1.5	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.j.1.5	✓	33	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.71066 q^{3} +1.00000 q^{4} -2.38566 q^{5} +2.71066 q^{6} -4.13924 q^{7} -1.00000 q^{8} +4.34767 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.71066 q^{3} +1.00000 q^{4} -2.38566 q^{5} +2.71066 q^{6} -4.13924 q^{7} -1.00000 q^{8} +4.34767 q^{9} +2.38566 q^{10} +5.88183 q^{11} -2.71066 q^{12} -3.00540 q^{13} +4.13924 q^{14} +6.46671 q^{15} +1.00000 q^{16} +6.38564 q^{17} -4.34767 q^{18} +4.95540 q^{19} -2.38566 q^{20} +11.2201 q^{21} -5.88183 q^{22} +1.00000 q^{23} +2.71066 q^{24} +0.691371 q^{25} +3.00540 q^{26} -3.65307 q^{27} -4.13924 q^{28} +9.90084 q^{29} -6.46671 q^{30} -5.84263 q^{31} -1.00000 q^{32} -15.9436 q^{33} -6.38564 q^{34} +9.87481 q^{35} +4.34767 q^{36} -5.08044 q^{37} -4.95540 q^{38} +8.14661 q^{39} +2.38566 q^{40} +11.8844 q^{41} -11.2201 q^{42} +4.90671 q^{43} +5.88183 q^{44} -10.3721 q^{45} -1.00000 q^{46} +7.91740 q^{47} -2.71066 q^{48} +10.1333 q^{49} -0.691371 q^{50} -17.3093 q^{51} -3.00540 q^{52} -6.91165 q^{53} +3.65307 q^{54} -14.0320 q^{55} +4.13924 q^{56} -13.4324 q^{57} -9.90084 q^{58} +2.15411 q^{59} +6.46671 q^{60} +1.81870 q^{61} +5.84263 q^{62} -17.9960 q^{63} +1.00000 q^{64} +7.16986 q^{65} +15.9436 q^{66} -3.88011 q^{67} +6.38564 q^{68} -2.71066 q^{69} -9.87481 q^{70} +12.1503 q^{71} -4.34767 q^{72} +6.84974 q^{73} +5.08044 q^{74} -1.87407 q^{75} +4.95540 q^{76} -24.3463 q^{77} -8.14661 q^{78} -15.0931 q^{79} -2.38566 q^{80} -3.14079 q^{81} -11.8844 q^{82} -3.32560 q^{83} +11.2201 q^{84} -15.2340 q^{85} -4.90671 q^{86} -26.8378 q^{87} -5.88183 q^{88} -6.85600 q^{89} +10.3721 q^{90} +12.4401 q^{91} +1.00000 q^{92} +15.8374 q^{93} -7.91740 q^{94} -11.8219 q^{95} +2.71066 q^{96} -12.2823 q^{97} -10.1333 q^{98} +25.5723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * q^99

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