LMFDB - Embedded newform 6026.2.a.h.1.19

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:	$1$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.72713 q^{3} +1.00000 q^{4} +0.546511 q^{5} -1.72713 q^{6} +2.37970 q^{7} -1.00000 q^{8} -0.0170298 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.72713 q^{3} +1.00000 q^{4} +0.546511 q^{5} -1.72713 q^{6} +2.37970 q^{7} -1.00000 q^{8} -0.0170298 q^{9} -0.546511 q^{10} -1.95450 q^{11} +1.72713 q^{12} -3.17542 q^{13} -2.37970 q^{14} +0.943895 q^{15} +1.00000 q^{16} -0.643138 q^{17} +0.0170298 q^{18} +0.483782 q^{19} +0.546511 q^{20} +4.11005 q^{21} +1.95450 q^{22} -1.00000 q^{23} -1.72713 q^{24} -4.70133 q^{25} +3.17542 q^{26} -5.21080 q^{27} +2.37970 q^{28} +6.04235 q^{29} -0.943895 q^{30} -4.23490 q^{31} -1.00000 q^{32} -3.37568 q^{33} +0.643138 q^{34} +1.30053 q^{35} -0.0170298 q^{36} -6.91135 q^{37} -0.483782 q^{38} -5.48435 q^{39} -0.546511 q^{40} +1.46356 q^{41} -4.11005 q^{42} +7.54748 q^{43} -1.95450 q^{44} -0.00930697 q^{45} +1.00000 q^{46} -12.7339 q^{47} +1.72713 q^{48} -1.33702 q^{49} +4.70133 q^{50} -1.11078 q^{51} -3.17542 q^{52} +13.4183 q^{53} +5.21080 q^{54} -1.06816 q^{55} -2.37970 q^{56} +0.835553 q^{57} -6.04235 q^{58} -3.90994 q^{59} +0.943895 q^{60} +1.06084 q^{61} +4.23490 q^{62} -0.0405258 q^{63} +1.00000 q^{64} -1.73540 q^{65} +3.37568 q^{66} -9.73931 q^{67} -0.643138 q^{68} -1.72713 q^{69} -1.30053 q^{70} -15.5760 q^{71} +0.0170298 q^{72} -4.64800 q^{73} +6.91135 q^{74} -8.11979 q^{75} +0.483782 q^{76} -4.65113 q^{77} +5.48435 q^{78} +14.7471 q^{79} +0.546511 q^{80} -8.94862 q^{81} -1.46356 q^{82} +13.0716 q^{83} +4.11005 q^{84} -0.351482 q^{85} -7.54748 q^{86} +10.4359 q^{87} +1.95450 q^{88} -5.56625 q^{89} +0.00930697 q^{90} -7.55655 q^{91} -1.00000 q^{92} -7.31421 q^{93} +12.7339 q^{94} +0.264392 q^{95} -1.72713 q^{96} +8.21629 q^{97} +1.33702 q^{98} +0.0332848 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * 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
$3$	1.72713	0.997158	0.498579	−	0.866844i	$-0.333855\pi$
$3$	1.72713	0.997158	0.498579	+	0.866844i	$0.333855\pi$
$4$	1.00000	0.500000
$5$	0.546511	0.244407	0.122204	−	0.992505i	$-0.461004\pi$
$5$	0.546511	0.244407	0.122204	+	0.992505i	$0.461004\pi$
$6$	−1.72713	−0.705097
$7$	2.37970	0.899442	0.449721	−	0.893169i	$-0.351523\pi$
$7$	2.37970	0.899442	0.449721	+	0.893169i	$0.351523\pi$
$8$	−1.00000	−0.353553
$9$	−0.0170298	−0.00567659
$10$	−0.546511	−0.172822
$11$	−1.95450	−0.589305	−0.294652	−	0.955604i	$-0.595204\pi$
$11$	−1.95450	−0.589305	−0.294652	+	0.955604i	$0.595204\pi$
$12$	1.72713	0.498579
$13$	−3.17542	−0.880703	−0.440351	−	0.897826i	$-0.645146\pi$
$13$	−3.17542	−0.880703	−0.440351	+	0.897826i	$0.645146\pi$
$14$	−2.37970	−0.636002
$15$	0.943895	0.243713
$16$	1.00000	0.250000
$17$	−0.643138	−0.155984	−0.0779919	−	0.996954i	$-0.524851\pi$
$17$	−0.643138	−0.155984	−0.0779919	+	0.996954i	$0.524851\pi$
$18$	0.0170298	0.00401396
$19$	0.483782	0.110987	0.0554936	−	0.998459i	$-0.482327\pi$
$19$	0.483782	0.110987	0.0554936	+	0.998459i	$0.482327\pi$
$20$	0.546511	0.122204
$21$	4.11005	0.896886
$22$	1.95450	0.416701
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.72713	−0.352548
$25$	−4.70133	−0.940265
$26$	3.17542	0.622751
$27$	−5.21080	−1.00282
$28$	2.37970	0.449721
$29$	6.04235	1.12204	0.561019	−	0.827803i	$-0.310410\pi$
$29$	6.04235	1.12204	0.561019	+	0.827803i	$0.310410\pi$
$30$	−0.943895	−0.172331
$31$	−4.23490	−0.760610	−0.380305	−	0.924861i	$-0.624181\pi$
$31$	−4.23490	−0.760610	−0.380305	+	0.924861i	$0.624181\pi$
$32$	−1.00000	−0.176777
$33$	−3.37568	−0.587630
$34$	0.643138	0.110297
$35$	1.30053	0.219830
$36$	−0.0170298	−0.00283830
$37$	−6.91135	−1.13622	−0.568110	−	0.822953i	$-0.692325\pi$
$37$	−6.91135	−1.13622	−0.568110	+	0.822953i	$0.692325\pi$
$38$	−0.483782	−0.0784798
$39$	−5.48435	−0.878199
$40$	−0.546511	−0.0864111
$41$	1.46356	0.228570	0.114285	−	0.993448i	$-0.463542\pi$
$41$	1.46356	0.228570	0.114285	+	0.993448i	$0.463542\pi$
$42$	−4.11005	−0.634194
$43$	7.54748	1.15098	0.575490	−	0.817809i	$-0.304811\pi$
$43$	7.54748	1.15098	0.575490	+	0.817809i	$0.304811\pi$
$44$	−1.95450	−0.294652
$45$	−0.00930697	−0.00138740
$46$	1.00000	0.147442
$47$	−12.7339	−1.85742	−0.928712	−	0.370801i	$-0.879083\pi$
$47$	−12.7339	−1.85742	−0.928712	+	0.370801i	$0.879083\pi$
$48$	1.72713	0.249289
$49$	−1.33702	−0.191003
$50$	4.70133	0.664868
$51$	−1.11078	−0.155540
$52$	−3.17542	−0.440351
$53$	13.4183	1.84314	0.921570	−	0.388213i	$-0.126907\pi$
$53$	13.4183	1.84314	0.921570	+	0.388213i	$0.126907\pi$
$54$	5.21080	0.709099
$55$	−1.06816	−0.144030
$56$	−2.37970	−0.318001
$57$	0.835553	0.110672
$58$	−6.04235	−0.793400
$59$	−3.90994	−0.509030	−0.254515	−	0.967069i	$-0.581916\pi$
$59$	−3.90994	−0.509030	−0.254515	+	0.967069i	$0.581916\pi$
$60$	0.943895	0.121856
$61$	1.06084	0.135827	0.0679134	−	0.997691i	$-0.478366\pi$
$61$	1.06084	0.135827	0.0679134	+	0.997691i	$0.478366\pi$
$62$	4.23490	0.537833
$63$	−0.0405258	−0.00510577
$64$	1.00000	0.125000
$65$	−1.73540	−0.215250
$66$	3.37568	0.415517
$67$	−9.73931	−1.18985	−0.594923	−	0.803783i	$-0.702817\pi$
$67$	−9.73931	−1.18985	−0.594923	+	0.803783i	$0.702817\pi$
$68$	−0.643138	−0.0779919
$69$	−1.72713	−0.207922
$70$	−1.30053	−0.155444
$71$	−15.5760	−1.84854	−0.924268	−	0.381743i	$-0.875324\pi$
$71$	−15.5760	−1.84854	−0.924268	+	0.381743i	$0.875324\pi$
$72$	0.0170298	0.00200698
$73$	−4.64800	−0.544008	−0.272004	−	0.962296i	$-0.587686\pi$
$73$	−4.64800	−0.544008	−0.272004	+	0.962296i	$0.587686\pi$
$74$	6.91135	0.803429
$75$	−8.11979	−0.937592
$76$	0.483782	0.0554936
$77$	−4.65113	−0.530046
$78$	5.48435	0.620981
$79$	14.7471	1.65918	0.829589	−	0.558375i	$-0.188575\pi$
$79$	14.7471	1.65918	0.829589	+	0.558375i	$0.188575\pi$
$80$	0.546511	0.0611018
$81$	−8.94862	−0.994291
$82$	−1.46356	−0.161624
$83$	13.0716	1.43479	0.717397	−	0.696665i	$-0.245333\pi$
$83$	13.0716	1.43479	0.717397	+	0.696665i	$0.245333\pi$
$84$	4.11005	0.448443
$85$	−0.351482	−0.0381236
$86$	−7.54748	−0.813865
$87$	10.4359	1.11885
$88$	1.95450	0.208351
$89$	−5.56625	−0.590021	−0.295011	−	0.955494i	$-0.595323\pi$
$89$	−5.56625	−0.590021	−0.295011	+	0.955494i	$0.595323\pi$
$90$	0.00930697	0.000981041 0
$91$	−7.55655	−0.792141
$92$	−1.00000	−0.104257
$93$	−7.31421	−0.758449
$94$	12.7339	1.31340
$95$	0.264392	0.0271261
$96$	−1.72713	−0.176274
$97$	8.21629	0.834238	0.417119	−	0.908852i	$-0.363040\pi$
$97$	8.21629	0.834238	0.417119	+	0.908852i	$0.363040\pi$
$98$	1.33702	0.135060
$99$	0.0332848	0.00334524
$100$	−4.70133	−0.470133
$101$	−7.17468	−0.713907	−0.356954	−	0.934122i	$-0.616185\pi$
$101$	−7.17468	−0.713907	−0.356954	+	0.934122i	$0.616185\pi$
$102$	1.11078	0.109984
$103$	−7.41808	−0.730925	−0.365462	−	0.930826i	$-0.619089\pi$
$103$	−7.41808	−0.730925	−0.365462	+	0.930826i	$0.619089\pi$
$104$	3.17542	0.311375
$105$	2.24619	0.219205
$106$	−13.4183	−1.30330
$107$	−11.5349	−1.11512	−0.557562	−	0.830136i	$-0.688263\pi$
$107$	−11.5349	−1.11512	−0.557562	+	0.830136i	$0.688263\pi$
$108$	−5.21080	−0.501409
$109$	1.66673	0.159644	0.0798220	−	0.996809i	$-0.474565\pi$
$109$	1.66673	0.159644	0.0798220	+	0.996809i	$0.474565\pi$
$110$	1.06816	0.101845
$111$	−11.9368	−1.13299
$112$	2.37970	0.224861
$113$	0.628262	0.0591019	0.0295510	−	0.999563i	$-0.490592\pi$
$113$	0.628262	0.0591019	0.0295510	+	0.999563i	$0.490592\pi$
$114$	−0.835553	−0.0782568
$115$	−0.546511	−0.0509625
$116$	6.04235	0.561019
$117$	0.0540767	0.00499939
$118$	3.90994	0.359939
$119$	−1.53048	−0.140298
$120$	−0.943895	−0.0861654
$121$	−7.17992	−0.652720
$122$	−1.06084	−0.0960441
$123$	2.52776	0.227921
$124$	−4.23490	−0.380305
$125$	−5.30189	−0.474215
$126$	0.0405258	0.00361032
$127$	−2.76031	−0.244938	−0.122469	−	0.992472i	$-0.539081\pi$
$127$	−2.76031	−0.244938	−0.122469	+	0.992472i	$0.539081\pi$
$128$	−1.00000	−0.0883883
$129$	13.0355	1.14771
$130$	1.73540	0.152205
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−3.37568	−0.293815
$133$	1.15126	0.0998266
$134$	9.73931	0.841348
$135$	−2.84776	−0.245096
$136$	0.643138	0.0551486
$137$	−13.4677	−1.15062	−0.575312	−	0.817934i	$-0.695119\pi$
$137$	−13.4677	−1.15062	−0.575312	+	0.817934i	$0.695119\pi$
$138$	1.72713	0.147023
$139$	−7.38074	−0.626026	−0.313013	−	0.949749i	$-0.601338\pi$
$139$	−7.38074	−0.626026	−0.313013	+	0.949749i	$0.601338\pi$
$140$	1.30053	0.109915
$141$	−21.9930	−1.85215
$142$	15.5760	1.30711
$143$	6.20636	0.519002
$144$	−0.0170298	−0.00141915
$145$	3.30222	0.274234
$146$	4.64800	0.384672
$147$	−2.30921	−0.190461
$148$	−6.91135	−0.568110
$149$	−19.9014	−1.63038	−0.815191	−	0.579192i	$-0.803368\pi$
$149$	−19.9014	−1.63038	−0.815191	+	0.579192i	$0.803368\pi$
$150$	8.11979	0.662978
$151$	−2.49936	−0.203395	−0.101697	−	0.994815i	$-0.532427\pi$
$151$	−2.49936	−0.203395	−0.101697	+	0.994815i	$0.532427\pi$
$152$	−0.483782	−0.0392399
$153$	0.0109525	0.000885457 0
$154$	4.65113	0.374799
$155$	−2.31442	−0.185899
$156$	−5.48435	−0.439100
$157$	−3.33070	−0.265819	−0.132909	−	0.991128i	$-0.542432\pi$
$157$	−3.33070	−0.265819	−0.132909	+	0.991128i	$0.542432\pi$
$158$	−14.7471	−1.17322
$159$	23.1750	1.83790
$160$	−0.546511	−0.0432055
$161$	−2.37970	−0.187547
$162$	8.94862	0.703070
$163$	−0.880629	−0.0689762	−0.0344881	−	0.999405i	$-0.510980\pi$
$163$	−0.880629	−0.0689762	−0.0344881	+	0.999405i	$0.510980\pi$
$164$	1.46356	0.114285
$165$	−1.84485	−0.143621
$166$	−13.0716	−1.01455
$167$	−9.52175	−0.736815	−0.368408	−	0.929664i	$-0.620097\pi$
$167$	−9.52175	−0.736815	−0.368408	+	0.929664i	$0.620097\pi$
$168$	−4.11005	−0.317097
$169$	−2.91672	−0.224363
$170$	0.351482	0.0269574
$171$	−0.00823870	−0.000630029 0
$172$	7.54748	0.575490
$173$	1.88911	0.143627	0.0718133	−	0.997418i	$-0.477121\pi$
$173$	1.88911	0.143627	0.0718133	+	0.997418i	$0.477121\pi$
$174$	−10.4359	−0.791145
$175$	−11.1877	−0.845714
$176$	−1.95450	−0.147326
$177$	−6.75296	−0.507584
$178$	5.56625	0.417208
$179$	17.6151	1.31661	0.658305	−	0.752751i	$-0.271274\pi$
$179$	17.6151	1.31661	0.658305	+	0.752751i	$0.271274\pi$
$180$	−0.00930697	−0.000693701 0
$181$	5.16895	0.384205	0.192103	−	0.981375i	$-0.438469\pi$
$181$	5.16895	0.384205	0.192103	+	0.981375i	$0.438469\pi$
$182$	7.55655	0.560128
$183$	1.83221	0.135441
$184$	1.00000	0.0737210
$185$	−3.77713	−0.277700
$186$	7.31421	0.536304
$187$	1.25701	0.0919220
$188$	−12.7339	−0.928712
$189$	−12.4001	−0.901977
$190$	−0.264392	−0.0191810
$191$	13.6429	0.987162	0.493581	−	0.869700i	$-0.335688\pi$
$191$	13.6429	0.987162	0.493581	+	0.869700i	$0.335688\pi$
$192$	1.72713	0.124645
$193$	−22.4970	−1.61937	−0.809685	−	0.586865i	$-0.800362\pi$
$193$	−22.4970	−1.61937	−0.809685	+	0.586865i	$0.800362\pi$
$194$	−8.21629	−0.589895
$195$	−2.99726	−0.214638
$196$	−1.33702	−0.0955017
$197$	18.2682	1.30155	0.650777	−	0.759269i	$-0.274443\pi$
$197$	18.2682	1.30155	0.650777	+	0.759269i	$0.274443\pi$
$198$	−0.0332848	−0.00236544
$199$	−12.1348	−0.860215	−0.430108	−	0.902778i	$-0.641524\pi$
$199$	−12.1348	−0.860215	−0.430108	+	0.902778i	$0.641524\pi$
$200$	4.70133	0.332434
$201$	−16.8210	−1.18646
$202$	7.17468	0.504809
$203$	14.3790	1.00921
$204$	−1.11078	−0.0777702
$205$	0.799854	0.0558642
$206$	7.41808	0.516842
$207$	0.0170298	0.00118365
$208$	−3.17542	−0.220176
$209$	−0.945554	−0.0654053
$210$	−2.24619	−0.155002
$211$	12.8114	0.881973	0.440987	−	0.897514i	$-0.354629\pi$
$211$	12.8114	0.881973	0.440987	+	0.897514i	$0.354629\pi$
$212$	13.4183	0.921570
$213$	−26.9018	−1.84328
$214$	11.5349	0.788511
$215$	4.12478	0.281308
$216$	5.21080	0.354550
$217$	−10.0778	−0.684125
$218$	−1.66673	−0.112885
$219$	−8.02770	−0.542461
$220$	−1.06816	−0.0720152
$221$	2.04223	0.137375
$222$	11.9368	0.801145
$223$	−26.3483	−1.76442	−0.882208	−	0.470861i	$-0.843943\pi$
$223$	−26.3483	−1.76442	−0.882208	+	0.470861i	$0.843943\pi$
$224$	−2.37970	−0.159000
$225$	0.0800625	0.00533750
$226$	−0.628262	−0.0417914
$227$	20.9614	1.39126	0.695628	−	0.718402i	$-0.255126\pi$
$227$	20.9614	1.39126	0.695628	+	0.718402i	$0.255126\pi$
$228$	0.835553	0.0553359
$229$	−11.2178	−0.741291	−0.370645	−	0.928774i	$-0.620863\pi$
$229$	−11.2178	−0.741291	−0.370645	+	0.928774i	$0.620863\pi$
$230$	0.546511	0.0360359
$231$	−8.03310	−0.528539
$232$	−6.04235	−0.396700
$233$	21.6622	1.41914	0.709568	−	0.704637i	$-0.248890\pi$
$233$	21.6622	1.41914	0.709568	+	0.704637i	$0.248890\pi$
$234$	−0.0540767	−0.00353510
$235$	−6.95920	−0.453968
$236$	−3.90994	−0.254515
$237$	25.4701	1.65446
$238$	1.53048	0.0992060
$239$	−1.69920	−0.109912	−0.0549561	−	0.998489i	$-0.517502\pi$
$239$	−1.69920	−0.109912	−0.0549561	+	0.998489i	$0.517502\pi$
$240$	0.943895	0.0609282
$241$	−4.52346	−0.291382	−0.145691	−	0.989330i	$-0.546540\pi$
$241$	−4.52346	−0.291382	−0.145691	+	0.989330i	$0.546540\pi$
$242$	7.17992	0.461543
$243$	0.176977	0.0113531
$244$	1.06084	0.0679134
$245$	−0.730699	−0.0466827
$246$	−2.52776	−0.161164
$247$	−1.53621	−0.0977467
$248$	4.23490	0.268916
$249$	22.5763	1.43072
$250$	5.30189	0.335321
$251$	18.7370	1.18267	0.591335	−	0.806426i	$-0.298601\pi$
$251$	18.7370	1.18267	0.591335	+	0.806426i	$0.298601\pi$
$252$	−0.0405258	−0.00255288
$253$	1.95450	0.122879
$254$	2.76031	0.173197
$255$	−0.607054	−0.0380152
$256$	1.00000	0.0625000
$257$	12.2418	0.763624	0.381812	−	0.924240i	$-0.375300\pi$
$257$	12.2418	0.763624	0.381812	+	0.924240i	$0.375300\pi$
$258$	−13.0355	−0.811552
$259$	−16.4470	−1.02196
$260$	−1.73540	−0.107625
$261$	−0.102900	−0.00636935
$262$	1.00000	0.0617802
$263$	29.5109	1.81972	0.909860	−	0.414916i	$-0.136189\pi$
$263$	29.5109	1.81972	0.909860	+	0.414916i	$0.136189\pi$
$264$	3.37568	0.207759
$265$	7.33323	0.450477
$266$	−1.15126	−0.0705881
$267$	−9.61362	−0.588344
$268$	−9.73931	−0.594923
$269$	−4.96244	−0.302565	−0.151283	−	0.988491i	$-0.548340\pi$
$269$	−4.96244	−0.302565	−0.151283	+	0.988491i	$0.548340\pi$
$270$	2.84776	0.173309
$271$	−21.3809	−1.29880	−0.649399	−	0.760448i	$-0.724980\pi$
$271$	−21.3809	−1.29880	−0.649399	+	0.760448i	$0.724980\pi$
$272$	−0.643138	−0.0389959
$273$	−13.0511	−0.789890
$274$	13.4677	0.813614
$275$	9.18875	0.554103
$276$	−1.72713	−0.103961
$277$	21.2840	1.27883	0.639415	−	0.768862i	$-0.279177\pi$
$277$	21.2840	1.27883	0.639415	+	0.768862i	$0.279177\pi$
$278$	7.38074	0.442667
$279$	0.0721194	0.00431768
$280$	−1.30053	−0.0777218
$281$	16.7218	0.997536	0.498768	−	0.866735i	$-0.333786\pi$
$281$	16.7218	0.997536	0.498768	+	0.866735i	$0.333786\pi$
$282$	21.9930	1.30966
$283$	27.1756	1.61542	0.807711	−	0.589579i	$-0.200706\pi$
$283$	27.1756	1.61542	0.807711	+	0.589579i	$0.200706\pi$
$284$	−15.5760	−0.924268
$285$	0.456640	0.0270490
$286$	−6.20636	−0.366990
$287$	3.48284	0.205586
$288$	0.0170298	0.00100349
$289$	−16.5864	−0.975669
$290$	−3.30222	−0.193913
$291$	14.1906	0.831866
$292$	−4.64800	−0.272004
$293$	−1.47593	−0.0862249	−0.0431125	−	0.999070i	$-0.513727\pi$
$293$	−1.47593	−0.0862249	−0.0431125	+	0.999070i	$0.513727\pi$
$294$	2.30921	0.134676
$295$	−2.13683	−0.124411
$296$	6.91135	0.401714
$297$	10.1845	0.590966
$298$	19.9014	1.15285
$299$	3.17542	0.183639
$300$	−8.11979	−0.468796
$301$	17.9607	1.03524
$302$	2.49936	0.143822
$303$	−12.3916	−0.711878
$304$	0.483782	0.0277468
$305$	0.579762	0.0331971
$306$	−0.0109525	−0.000626112 0
$307$	−30.2166	−1.72455	−0.862275	−	0.506440i	$-0.830961\pi$
$307$	−30.2166	−1.72455	−0.862275	+	0.506440i	$0.830961\pi$
$308$	−4.65113	−0.265023
$309$	−12.8120	−0.728847
$310$	2.31442	0.131450
$311$	−7.36136	−0.417424	−0.208712	−	0.977977i	$-0.566927\pi$
$311$	−7.36136	−0.417424	−0.208712	+	0.977977i	$0.566927\pi$
$312$	5.48435	0.310490
$313$	1.26962	0.0717630	0.0358815	−	0.999356i	$-0.488576\pi$
$313$	1.26962	0.0717630	0.0358815	+	0.999356i	$0.488576\pi$
$314$	3.33070	0.187962
$315$	−0.0221478	−0.00124789
$316$	14.7471	0.829589
$317$	−29.5320	−1.65868	−0.829342	−	0.558742i	$-0.811284\pi$
$317$	−29.5320	−1.65868	−0.829342	+	0.558742i	$0.811284\pi$
$318$	−23.1750	−1.29959
$319$	−11.8098	−0.661222
$320$	0.546511	0.0305509
$321$	−19.9223	−1.11195
$322$	2.37970	0.132616
$323$	−0.311138	−0.0173122
$324$	−8.94862	−0.497146
$325$	14.9287	0.828094
$326$	0.880629	0.0487735
$327$	2.87866	0.159190
$328$	−1.46356	−0.0808118
$329$	−30.3028	−1.67065
$330$	1.84485	0.101555
$331$	14.3844	0.790640	0.395320	−	0.918543i	$-0.370634\pi$
$331$	14.3844	0.790640	0.395320	+	0.918543i	$0.370634\pi$
$332$	13.0716	0.717397
$333$	0.117699	0.00644986
$334$	9.52175	0.521007
$335$	−5.32265	−0.290807
$336$	4.11005	0.224221
$337$	−10.2218	−0.556815	−0.278408	−	0.960463i	$-0.589807\pi$
$337$	−10.2218	−0.556815	−0.278408	+	0.960463i	$0.589807\pi$
$338$	2.91672	0.158648
$339$	1.08509	0.0589339
$340$	−0.351482	−0.0190618
$341$	8.27712	0.448231
$342$	0.00823870	0.000445498 0
$343$	−19.8396	−1.07124
$344$	−7.54748	−0.406933
$345$	−0.943895	−0.0508176
$346$	−1.88911	−0.101559
$347$	11.9664	0.642390	0.321195	−	0.947013i	$-0.395916\pi$
$347$	11.9664	0.642390	0.321195	+	0.947013i	$0.395916\pi$
$348$	10.4359	0.559424
$349$	2.63119	0.140845	0.0704223	−	0.997517i	$-0.477565\pi$
$349$	2.63119	0.140845	0.0704223	+	0.997517i	$0.477565\pi$
$350$	11.1877	0.598010
$351$	16.5465	0.883185
$352$	1.95450	0.104175
$353$	−20.3242	−1.08175	−0.540874	−	0.841104i	$-0.681906\pi$
$353$	−20.3242	−1.08175	−0.540874	+	0.841104i	$0.681906\pi$
$354$	6.75296	0.358916
$355$	−8.51249	−0.451796
$356$	−5.56625	−0.295011
$357$	−2.64333	−0.139900
$358$	−17.6151	−0.930984
$359$	−10.2530	−0.541132	−0.270566	−	0.962701i	$-0.587211\pi$
$359$	−10.2530	−0.541132	−0.270566	+	0.962701i	$0.587211\pi$
$360$	0.00930697	0.000490520 0
$361$	−18.7660	−0.987682
$362$	−5.16895	−0.271674
$363$	−12.4006	−0.650865
$364$	−7.55655	−0.396071
$365$	−2.54019	−0.132959
$366$	−1.83221	−0.0957711
$367$	−13.1647	−0.687193	−0.343597	−	0.939117i	$-0.611645\pi$
$367$	−13.1647	−0.687193	−0.343597	+	0.939117i	$0.611645\pi$
$368$	−1.00000	−0.0521286
$369$	−0.0249242	−0.00129750
$370$	3.77713	0.196364
$371$	31.9314	1.65780
$372$	−7.31421	−0.379224
$373$	−27.9871	−1.44912	−0.724559	−	0.689213i	$-0.757956\pi$
$373$	−27.9871	−1.44912	−0.724559	+	0.689213i	$0.757956\pi$
$374$	−1.25701	−0.0649987
$375$	−9.15703	−0.472867
$376$	12.7339	0.656699
$377$	−19.1870	−0.988181
$378$	12.4001	0.637794
$379$	0.505238	0.0259523	0.0129762	−	0.999916i	$-0.495869\pi$
$379$	0.505238	0.0259523	0.0129762	+	0.999916i	$0.495869\pi$
$380$	0.264392	0.0135630
$381$	−4.76741	−0.244242
$382$	−13.6429	−0.698029
$383$	19.9129	1.01750	0.508752	−	0.860913i	$-0.330107\pi$
$383$	19.9129	1.01750	0.508752	+	0.860913i	$0.330107\pi$
$384$	−1.72713	−0.0881371
$385$	−2.54190	−0.129547
$386$	22.4970	1.14507
$387$	−0.128532	−0.00653364
$388$	8.21629	0.417119
$389$	−7.22207	−0.366174	−0.183087	−	0.983097i	$-0.558609\pi$
$389$	−7.22207	−0.366174	−0.183087	+	0.983097i	$0.558609\pi$
$390$	2.99726	0.151772
$391$	0.643138	0.0325249
$392$	1.33702	0.0675299
$393$	−1.72713	−0.0871221
$394$	−18.2682	−0.920338
$395$	8.05945	0.405515
$396$	0.0332848	0.00167262
$397$	37.1412	1.86406	0.932032	−	0.362375i	$-0.118034\pi$
$397$	37.1412	1.86406	0.932032	+	0.362375i	$0.118034\pi$
$398$	12.1348	0.608264
$399$	1.98837	0.0995429
$400$	−4.70133	−0.235066
$401$	−13.2667	−0.662507	−0.331254	−	0.943542i	$-0.607472\pi$
$401$	−13.2667	−0.662507	−0.331254	+	0.943542i	$0.607472\pi$
$402$	16.8210	0.838957
$403$	13.4476	0.669872
$404$	−7.17468	−0.356954
$405$	−4.89052	−0.243012
$406$	−14.3790	−0.713618
$407$	13.5083	0.669580
$408$	1.11078	0.0549918
$409$	22.9714	1.13586	0.567932	−	0.823075i	$-0.307743\pi$
$409$	22.9714	1.13586	0.567932	+	0.823075i	$0.307743\pi$
$410$	−0.799854	−0.0395020
$411$	−23.2604	−1.14735
$412$	−7.41808	−0.365462
$413$	−9.30448	−0.457843
$414$	−0.0170298	−0.000836968 0
$415$	7.14378	0.350674
$416$	3.17542	0.155688
$417$	−12.7475	−0.624247
$418$	0.945554	0.0462485
$419$	6.32609	0.309050	0.154525	−	0.987989i	$-0.450615\pi$
$419$	6.32609	0.309050	0.154525	+	0.987989i	$0.450615\pi$
$420$	2.24619	0.109603
$421$	30.0999	1.46698	0.733491	−	0.679699i	$-0.237890\pi$
$421$	30.0999	1.46698	0.733491	+	0.679699i	$0.237890\pi$
$422$	−12.8114	−0.623649
$423$	0.216855	0.0105438
$424$	−13.4183	−0.651648
$425$	3.02360	0.146666
$426$	26.9018	1.30340
$427$	2.52449	0.122168
$428$	−11.5349	−0.557562
$429$	10.7192	0.517527
$430$	−4.12478	−0.198915
$431$	6.24375	0.300751	0.150376	−	0.988629i	$-0.451952\pi$
$431$	6.24375	0.300751	0.150376	+	0.988629i	$0.451952\pi$
$432$	−5.21080	−0.250705
$433$	−5.09446	−0.244824	−0.122412	−	0.992479i	$-0.539063\pi$
$433$	−5.09446	−0.244824	−0.122412	+	0.992479i	$0.539063\pi$
$434$	10.0778	0.483750
$435$	5.70335	0.273455
$436$	1.66673	0.0798220
$437$	−0.483782	−0.0231424
$438$	8.02770	0.383578
$439$	−5.68741	−0.271446	−0.135723	−	0.990747i	$-0.543336\pi$
$439$	−5.68741	−0.271446	−0.135723	+	0.990747i	$0.543336\pi$
$440$	1.06816	0.0509224
$441$	0.0227692	0.00108425
$442$	−2.04223	−0.0971390
$443$	−10.0320	−0.476634	−0.238317	−	0.971187i	$-0.576596\pi$
$443$	−10.0320	−0.476634	−0.238317	+	0.971187i	$0.576596\pi$
$444$	−11.9368	−0.566495
$445$	−3.04202	−0.144206
$446$	26.3483	1.24763
$447$	−34.3722	−1.62575
$448$	2.37970	0.112430
$449$	5.34635	0.252310	0.126155	−	0.992011i	$-0.459736\pi$
$449$	5.34635	0.252310	0.126155	+	0.992011i	$0.459736\pi$
$450$	−0.0800625	−0.00377418
$451$	−2.86054	−0.134698
$452$	0.628262	0.0295510
$453$	−4.31671	−0.202817
$454$	−20.9614	−0.983766
$455$	−4.12974	−0.193605
$456$	−0.835553	−0.0391284
$457$	10.4118	0.487042	0.243521	−	0.969896i	$-0.421698\pi$
$457$	10.4118	0.487042	0.243521	+	0.969896i	$0.421698\pi$
$458$	11.2178	0.524172
$459$	3.35126	0.156423
$460$	−0.546511	−0.0254812
$461$	30.0568	1.39989	0.699943	−	0.714199i	$-0.253209\pi$
$461$	30.0568	1.39989	0.699943	+	0.714199i	$0.253209\pi$
$462$	8.03310	0.373734
$463$	22.3224	1.03741	0.518705	−	0.854953i	$-0.326414\pi$
$463$	22.3224	1.03741	0.518705	+	0.854953i	$0.326414\pi$
$464$	6.04235	0.280509
$465$	−3.99730	−0.185370
$466$	−21.6622	−1.00348
$467$	1.09494	0.0506677	0.0253339	−	0.999679i	$-0.491935\pi$
$467$	1.09494	0.0506677	0.0253339	+	0.999679i	$0.491935\pi$
$468$	0.0540767	0.00249970
$469$	−23.1766	−1.07020
$470$	6.95920	0.321004
$471$	−5.75254	−0.265063
$472$	3.90994	0.179969
$473$	−14.7516	−0.678278
$474$	−25.4701	−1.16988
$475$	−2.27442	−0.104357
$476$	−1.53048	−0.0701492
$477$	−0.228510	−0.0104628
$478$	1.69920	0.0777197
$479$	37.4579	1.71150	0.855748	−	0.517392i	$-0.173097\pi$
$479$	37.4579	1.71150	0.855748	+	0.517392i	$0.173097\pi$
$480$	−0.943895	−0.0430827
$481$	21.9464	1.00067
$482$	4.52346	0.206038
$483$	−4.11005	−0.187014
$484$	−7.17992	−0.326360
$485$	4.49029	0.203894
$486$	−0.176977	−0.00802782
$487$	10.6622	0.483149	0.241575	−	0.970382i	$-0.422336\pi$
$487$	10.6622	0.483149	0.241575	+	0.970382i	$0.422336\pi$
$488$	−1.06084	−0.0480220
$489$	−1.52096	−0.0687801
$490$	0.730699	0.0330096
$491$	−30.9746	−1.39787	−0.698933	−	0.715187i	$-0.746342\pi$
$491$	−30.9746	−1.39787	−0.698933	+	0.715187i	$0.746342\pi$
$492$	2.52776	0.113960
$493$	−3.88607	−0.175020
$494$	1.53621	0.0691174
$495$	0.0181905	0.000817602 0
$496$	−4.23490	−0.190153
$497$	−37.0663	−1.66265
$498$	−22.5763	−1.01167
$499$	−36.8800	−1.65098	−0.825488	−	0.564419i	$-0.809100\pi$
$499$	−36.8800	−1.65098	−0.825488	+	0.564419i	$0.809100\pi$
$500$	−5.30189	−0.237108
$501$	−16.4453	−0.734721
$502$	−18.7370	−0.836274
$503$	−10.0464	−0.447946	−0.223973	−	0.974595i	$-0.571903\pi$
$503$	−10.0464	−0.447946	−0.223973	+	0.974595i	$0.571903\pi$
$504$	0.0405258	0.00180516
$505$	−3.92104	−0.174484
$506$	−1.95450	−0.0868883
$507$	−5.03754	−0.223725
$508$	−2.76031	−0.122469
$509$	26.4236	1.17121	0.585604	−	0.810598i	$-0.300858\pi$
$509$	26.4236	1.17121	0.585604	+	0.810598i	$0.300858\pi$
$510$	0.607054	0.0268808
$511$	−11.0609	−0.489304
$512$	−1.00000	−0.0441942
$513$	−2.52089	−0.111300
$514$	−12.2418	−0.539964
$515$	−4.05406	−0.178643
$516$	13.0355	0.573854
$517$	24.8884	1.09459
$518$	16.4470	0.722638
$519$	3.26274	0.143218
$520$	1.73540	0.0761024
$521$	31.2568	1.36939	0.684694	−	0.728831i	$-0.259936\pi$
$521$	31.2568	1.36939	0.684694	+	0.728831i	$0.259936\pi$
$522$	0.102900	0.00450381
$523$	0.444611	0.0194415	0.00972074	−	0.999953i	$-0.496906\pi$
$523$	0.444611	0.0194415	0.00972074	+	0.999953i	$0.496906\pi$
$524$	−1.00000	−0.0436852
$525$	−19.3227	−0.843310
$526$	−29.5109	−1.28674
$527$	2.72362	0.118643
$528$	−3.37568	−0.146907
$529$	1.00000	0.0434783
$530$	−7.33323	−0.318535
$531$	0.0665854	0.00288956
$532$	1.15126	0.0499133
$533$	−4.64743	−0.201302
$534$	9.61362	0.416022
$535$	−6.30397	−0.272544
$536$	9.73931	0.420674
$537$	30.4234	1.31287
$538$	4.96244	0.213946
$539$	2.61322	0.112559
$540$	−2.84776	−0.122548
$541$	−36.1722	−1.55516	−0.777582	−	0.628781i	$-0.783554\pi$
$541$	−36.1722	−1.55516	−0.777582	+	0.628781i	$0.783554\pi$
$542$	21.3809	0.918389
$543$	8.92744	0.383113
$544$	0.643138	0.0275743
$545$	0.910888	0.0390182
$546$	13.0511	0.558536
$547$	2.08286	0.0890567	0.0445284	−	0.999008i	$-0.485821\pi$
$547$	2.08286	0.0890567	0.0445284	+	0.999008i	$0.485821\pi$
$548$	−13.4677	−0.575312
$549$	−0.0180659	−0.000771034 0
$550$	−9.18875	−0.391810
$551$	2.92318	0.124532
$552$	1.72713	0.0735114
$553$	35.0937	1.49233
$554$	−21.2840	−0.904269
$555$	−6.52359	−0.276911
$556$	−7.38074	−0.313013
$557$	−32.0391	−1.35754	−0.678769	−	0.734352i	$-0.737486\pi$
$557$	−32.0391	−1.35754	−0.678769	+	0.734352i	$0.737486\pi$
$558$	−0.0721194	−0.00305306
$559$	−23.9664	−1.01367
$560$	1.30053	0.0549576
$561$	2.17102	0.0916607
$562$	−16.7218	−0.705365
$563$	31.6883	1.33550	0.667750	−	0.744385i	$-0.267257\pi$
$563$	31.6883	1.33550	0.667750	+	0.744385i	$0.267257\pi$
$564$	−21.9930	−0.926073
$565$	0.343352	0.0144449
$566$	−27.1756	−1.14228
$567$	−21.2950	−0.894308
$568$	15.5760	0.653556
$569$	2.77931	0.116515	0.0582575	−	0.998302i	$-0.481446\pi$
$569$	2.77931	0.116515	0.0582575	+	0.998302i	$0.481446\pi$
$570$	−0.456640	−0.0191265
$571$	−30.8292	−1.29016	−0.645081	−	0.764115i	$-0.723176\pi$
$571$	−30.8292	−1.29016	−0.645081	+	0.764115i	$0.723176\pi$
$572$	6.20636	0.259501
$573$	23.5630	0.984357
$574$	−3.48284	−0.145371
$575$	4.70133	0.196059
$576$	−0.0170298	−0.000709574 0
$577$	23.8845	0.994325	0.497162	−	0.867657i	$-0.334375\pi$
$577$	23.8845	0.994325	0.497162	+	0.867657i	$0.334375\pi$
$578$	16.5864	0.689902
$579$	−38.8552	−1.61477
$580$	3.30222	0.137117
$581$	31.1065	1.29051
$582$	−14.1906	−0.588218
$583$	−26.2260	−1.08617
$584$	4.64800	0.192336
$585$	0.0295535	0.00122189
$586$	1.47593	0.0609702
$587$	−18.9053	−0.780305	−0.390152	−	0.920750i	$-0.627578\pi$
$587$	−18.9053	−0.780305	−0.390152	+	0.920750i	$0.627578\pi$
$588$	−2.30921	−0.0952303
$589$	−2.04877	−0.0844180
$590$	2.13683	0.0879717
$591$	31.5515	1.29786
$592$	−6.91135	−0.284055
$593$	31.2873	1.28482	0.642408	−	0.766363i	$-0.277936\pi$
$593$	31.2873	1.28482	0.642408	+	0.766363i	$0.277936\pi$
$594$	−10.1845	−0.417876
$595$	−0.836422	−0.0342900
$596$	−19.9014	−0.815191
$597$	−20.9584	−0.857770
$598$	−3.17542	−0.129853
$599$	1.49047	0.0608990	0.0304495	−	0.999536i	$-0.490306\pi$
$599$	1.49047	0.0608990	0.0304495	+	0.999536i	$0.490306\pi$
$600$	8.11979	0.331489
$601$	−30.8448	−1.25819	−0.629093	−	0.777330i	$-0.716574\pi$
$601$	−30.8448	−1.25819	−0.629093	+	0.777330i	$0.716574\pi$
$602$	−17.9607	−0.732025
$603$	0.165858	0.00675427
$604$	−2.49936	−0.101697
$605$	−3.92391	−0.159530
$606$	12.3916	0.503374
$607$	34.0014	1.38008	0.690038	−	0.723773i	$-0.257594\pi$
$607$	34.0014	1.38008	0.690038	+	0.723773i	$0.257594\pi$
$608$	−0.483782	−0.0196200
$609$	24.8344	1.00634
$610$	−0.579762	−0.0234739
$611$	40.4353	1.63584
$612$	0.0109525	0.000442728 0
$613$	−3.92414	−0.158495	−0.0792473	−	0.996855i	$-0.525252\pi$
$613$	−3.92414	−0.158495	−0.0792473	+	0.996855i	$0.525252\pi$
$614$	30.2166	1.21944
$615$	1.38145	0.0557055
$616$	4.65113	0.187399
$617$	7.93988	0.319648	0.159824	−	0.987146i	$-0.448907\pi$
$617$	7.93988	0.319648	0.159824	+	0.987146i	$0.448907\pi$
$618$	12.8120	0.515373
$619$	−8.76103	−0.352135	−0.176068	−	0.984378i	$-0.556338\pi$
$619$	−8.76103	−0.352135	−0.176068	+	0.984378i	$0.556338\pi$
$620$	−2.31442	−0.0929494
$621$	5.21080	0.209102
$622$	7.36136	0.295164
$623$	−13.2460	−0.530690
$624$	−5.48435	−0.219550
$625$	20.6091	0.824363
$626$	−1.26962	−0.0507441
$627$	−1.63309	−0.0652194
$628$	−3.33070	−0.132909
$629$	4.44495	0.177232
$630$	0.0221478	0.000882390 0
$631$	−9.12805	−0.363382	−0.181691	−	0.983356i	$-0.558157\pi$
$631$	−9.12805	−0.363382	−0.181691	+	0.983356i	$0.558157\pi$
$632$	−14.7471	−0.586608
$633$	22.1269	0.879466
$634$	29.5320	1.17287
$635$	−1.50854	−0.0598647
$636$	23.1750	0.918950
$637$	4.24561	0.168217
$638$	11.8098	0.467554
$639$	0.265257	0.0104934
$640$	−0.546511	−0.0216028
$641$	−25.5876	−1.01065	−0.505325	−	0.862929i	$-0.668627\pi$
$641$	−25.5876	−1.01065	−0.505325	+	0.862929i	$0.668627\pi$
$642$	19.9223	0.786270
$643$	−13.0608	−0.515069	−0.257534	−	0.966269i	$-0.582910\pi$
$643$	−13.0608	−0.515069	−0.257534	+	0.966269i	$0.582910\pi$
$644$	−2.37970	−0.0937733
$645$	7.12403	0.280508
$646$	0.311138	0.0122416
$647$	−20.6107	−0.810290	−0.405145	−	0.914252i	$-0.632779\pi$
$647$	−20.6107	−0.810290	−0.405145	+	0.914252i	$0.632779\pi$
$648$	8.94862	0.351535
$649$	7.64198	0.299974
$650$	−14.9287	−0.585551
$651$	−17.4056	−0.682181
$652$	−0.880629	−0.0344881
$653$	9.83847	0.385009	0.192505	−	0.981296i	$-0.438339\pi$
$653$	9.83847	0.385009	0.192505	+	0.981296i	$0.438339\pi$
$654$	−2.87866	−0.112564
$655$	−0.546511	−0.0213540
$656$	1.46356	0.0571426
$657$	0.0791545	0.00308811
$658$	30.3028	1.18133
$659$	25.0150	0.974447	0.487224	−	0.873277i	$-0.338010\pi$
$659$	25.0150	0.974447	0.487224	+	0.873277i	$0.338010\pi$
$660$	−1.84485	−0.0718105
$661$	16.9679	0.659976	0.329988	−	0.943985i	$-0.392955\pi$
$661$	16.9679	0.659976	0.329988	+	0.943985i	$0.392955\pi$
$662$	−14.3844	−0.559067
$663$	3.52719	0.136985
$664$	−13.0716	−0.507276
$665$	0.629175	0.0243984
$666$	−0.117699	−0.00456074
$667$	−6.04235	−0.233961
$668$	−9.52175	−0.368408
$669$	−45.5069	−1.75940
$670$	5.32265	0.205632
$671$	−2.07342	−0.0800434
$672$	−4.11005	−0.158549
$673$	−37.5800	−1.44860	−0.724301	−	0.689484i	$-0.757837\pi$
$673$	−37.5800	−1.44860	−0.724301	+	0.689484i	$0.757837\pi$
$674$	10.2218	0.393728
$675$	24.4976	0.942915
$676$	−2.91672	−0.112181
$677$	−29.0960	−1.11825	−0.559125	−	0.829083i	$-0.688863\pi$
$677$	−29.0960	−1.11825	−0.559125	+	0.829083i	$0.688863\pi$
$678$	−1.08509	−0.0416726
$679$	19.5523	0.750349
$680$	0.351482	0.0134787
$681$	36.2030	1.38730
$682$	−8.27712	−0.316947
$683$	−45.8677	−1.75508	−0.877540	−	0.479503i	$-0.840817\pi$
$683$	−45.8677	−1.75508	−0.877540	+	0.479503i	$0.840817\pi$
$684$	−0.00823870	−0.000315015 0
$685$	−7.36025	−0.281221
$686$	19.8396	0.757480
$687$	−19.3745	−0.739184
$688$	7.54748	0.287745
$689$	−42.6086	−1.62326
$690$	0.943895	0.0359335
$691$	19.4795	0.741034	0.370517	−	0.928826i	$-0.379180\pi$
$691$	19.4795	0.741034	0.370517	+	0.928826i	$0.379180\pi$
$692$	1.88911	0.0718133
$693$	0.0792078	0.00300885
$694$	−11.9664	−0.454238
$695$	−4.03366	−0.153005
$696$	−10.4359	−0.395572
$697$	−0.941273	−0.0356532
$698$	−2.63119	−0.0995922
$699$	37.4133	1.41510
$700$	−11.1877	−0.422857
$701$	2.42730	0.0916780	0.0458390	−	0.998949i	$-0.485404\pi$
$701$	2.42730	0.0916780	0.0458390	+	0.998949i	$0.485404\pi$
$702$	−16.5465	−0.624506
$703$	−3.34359	−0.126106
$704$	−1.95450	−0.0736631
$705$	−12.0194	−0.452678
$706$	20.3242	0.764912
$707$	−17.0736	−0.642118
$708$	−6.75296	−0.253792
$709$	−10.6282	−0.399149	−0.199575	−	0.979883i	$-0.563956\pi$
$709$	−10.6282	−0.399149	−0.199575	+	0.979883i	$0.563956\pi$
$710$	8.51249	0.319468
$711$	−0.251140	−0.00941847
$712$	5.56625	0.208604
$713$	4.23490	0.158598
$714$	2.64333	0.0989240
$715$	3.39185	0.126848
$716$	17.6151	0.658305
$717$	−2.93474	−0.109600
$718$	10.2530	0.382638
$719$	18.2529	0.680717	0.340358	−	0.940296i	$-0.389452\pi$
$719$	18.2529	0.680717	0.340358	+	0.940296i	$0.389452\pi$
$720$	−0.00930697	−0.000346850 0
$721$	−17.6528	−0.657425
$722$	18.7660	0.698397
$723$	−7.81259	−0.290553
$724$	5.16895	0.192103
$725$	−28.4071	−1.05501
$726$	12.4006	0.460231
$727$	42.3362	1.57016	0.785082	−	0.619392i	$-0.212621\pi$
$727$	42.3362	1.57016	0.785082	+	0.619392i	$0.212621\pi$
$728$	7.55655	0.280064
$729$	27.1515	1.00561
$730$	2.54019	0.0940166
$731$	−4.85407	−0.179534
$732$	1.83221	0.0677204
$733$	13.5595	0.500833	0.250417	−	0.968138i	$-0.419432\pi$
$733$	13.5595	0.500833	0.250417	+	0.968138i	$0.419432\pi$
$734$	13.1647	0.485919
$735$	−1.26201	−0.0465500
$736$	1.00000	0.0368605
$737$	19.0355	0.701182
$738$	0.0249242	0.000917471 0
$739$	10.5758	0.389038	0.194519	−	0.980899i	$-0.437685\pi$
$739$	10.5758	0.389038	0.194519	+	0.980899i	$0.437685\pi$
$740$	−3.77713	−0.138850
$741$	−2.65323	−0.0974689
$742$	−31.9314	−1.17224
$743$	13.3752	0.490690	0.245345	−	0.969436i	$-0.421099\pi$
$743$	13.3752	0.490690	0.245345	+	0.969436i	$0.421099\pi$
$744$	7.31421	0.268152
$745$	−10.8763	−0.398477
$746$	27.9871	1.02468
$747$	−0.222606	−0.00814474
$748$	1.25701	0.0459610
$749$	−27.4497	−1.00299
$750$	9.15703	0.334368
$751$	−47.8751	−1.74699	−0.873493	−	0.486837i	$-0.838151\pi$
$751$	−47.8751	−1.74699	−0.873493	+	0.486837i	$0.838151\pi$
$752$	−12.7339	−0.464356
$753$	32.3612	1.17931
$754$	19.1870	0.698750
$755$	−1.36593	−0.0497112
$756$	−12.4001	−0.450989
$757$	11.1899	0.406703	0.203351	−	0.979106i	$-0.434817\pi$
$757$	11.1899	0.406703	0.203351	+	0.979106i	$0.434817\pi$
$758$	−0.505238	−0.0183511
$759$	3.37568	0.122529
$760$	−0.264392	−0.00959052
$761$	−45.7341	−1.65786	−0.828929	−	0.559353i	$-0.811050\pi$
$761$	−45.7341	−1.65786	−0.828929	+	0.559353i	$0.811050\pi$
$762$	4.76741	0.172705
$763$	3.96632	0.143591
$764$	13.6429	0.493581
$765$	0.00598566	0.000216412 0
$766$	−19.9129	−0.719483
$767$	12.4157	0.448304
$768$	1.72713	0.0623224
$769$	−10.4570	−0.377090	−0.188545	−	0.982065i	$-0.560377\pi$
$769$	−10.4570	−0.377090	−0.188545	+	0.982065i	$0.560377\pi$
$770$	2.54190	0.0916036
$771$	21.1432	0.761454
$772$	−22.4970	−0.809685
$773$	−43.3159	−1.55797	−0.778983	−	0.627046i	$-0.784264\pi$
$773$	−43.3159	−1.55797	−0.778983	+	0.627046i	$0.784264\pi$
$774$	0.128532	0.00461998
$775$	19.9096	0.715175
$776$	−8.21629	−0.294948
$777$	−28.4060	−1.01906
$778$	7.22207	0.258924
$779$	0.708046	0.0253684
$780$	−2.99726	−0.107319
$781$	30.4434	1.08935
$782$	−0.643138	−0.0229986
$783$	−31.4855	−1.12520
$784$	−1.33702	−0.0477509
$785$	−1.82027	−0.0649681
$786$	1.72713	0.0616046
$787$	−27.1636	−0.968278	−0.484139	−	0.874991i	$-0.660867\pi$
$787$	−27.1636	−0.968278	−0.484139	+	0.874991i	$0.660867\pi$
$788$	18.2682	0.650777
$789$	50.9691	1.81455
$790$	−8.05945	−0.286742
$791$	1.49508	0.0531588
$792$	−0.0332848	−0.00118272
$793$	−3.36862	−0.119623
$794$	−37.1412	−1.31809
$795$	12.6654	0.449196
$796$	−12.1348	−0.430108
$797$	−19.1475	−0.678239	−0.339119	−	0.940743i	$-0.610129\pi$
$797$	−19.1475	−0.678239	−0.339119	+	0.940743i	$0.610129\pi$
$798$	−1.98837	−0.0703874
$799$	8.18963	0.289728
$800$	4.70133	0.166217
$801$	0.0947920	0.00334931
$802$	13.2667	0.468463
$803$	9.08454	0.320586
$804$	−16.8210	−0.593232
$805$	−1.30053	−0.0458378
$806$	−13.4476	−0.473671
$807$	−8.57076	−0.301705
$808$	7.17468	0.252404
$809$	27.6318	0.971482	0.485741	−	0.874103i	$-0.338550\pi$
$809$	27.6318	0.971482	0.485741	+	0.874103i	$0.338550\pi$
$810$	4.89052	0.171835
$811$	−41.5638	−1.45950	−0.729751	−	0.683713i	$-0.760364\pi$
$811$	−41.5638	−1.45950	−0.729751	+	0.683713i	$0.760364\pi$
$812$	14.3790	0.504604
$813$	−36.9276	−1.29511
$814$	−13.5083	−0.473464
$815$	−0.481274	−0.0168583
$816$	−1.11078	−0.0388851
$817$	3.65133	0.127744
$818$	−22.9714	−0.803178
$819$	0.128686	0.00449666
$820$	0.799854	0.0279321
$821$	9.63216	0.336165	0.168082	−	0.985773i	$-0.446243\pi$
$821$	9.63216	0.336165	0.168082	+	0.985773i	$0.446243\pi$
$822$	23.2604	0.811301
$823$	−32.4335	−1.13056	−0.565280	−	0.824899i	$-0.691232\pi$
$823$	−32.4335	−1.13056	−0.565280	+	0.824899i	$0.691232\pi$
$824$	7.41808	0.258421
$825$	15.8702	0.552528
$826$	9.30448	0.323744
$827$	−20.7850	−0.722767	−0.361383	−	0.932417i	$-0.617695\pi$
$827$	−20.7850	−0.722767	−0.361383	+	0.932417i	$0.617695\pi$
$828$	0.0170298	0.000591826 0
$829$	−31.8344	−1.10565	−0.552827	−	0.833296i	$-0.686451\pi$
$829$	−31.8344	−1.10565	−0.552827	+	0.833296i	$0.686451\pi$
$830$	−7.14378	−0.247964
$831$	36.7601	1.27520
$832$	−3.17542	−0.110088
$833$	0.859891	0.0297934
$834$	12.7475	0.441409
$835$	−5.20375	−0.180083
$836$	−0.945554	−0.0327027
$837$	22.0672	0.762754
$838$	−6.32609	−0.218531
$839$	14.1644	0.489010	0.244505	−	0.969648i	$-0.421375\pi$
$839$	14.1644	0.489010	0.244505	+	0.969648i	$0.421375\pi$
$840$	−2.24619	−0.0775008
$841$	7.51005	0.258967
$842$	−30.0999	−1.03731
$843$	28.8806	0.994701
$844$	12.8114	0.440987
$845$	−1.59402	−0.0548359
$846$	−0.216855	−0.00745563
$847$	−17.0861	−0.587084
$848$	13.4183	0.460785
$849$	46.9357	1.61083
$850$	−3.02360	−0.103709
$851$	6.91135	0.236918
$852$	−26.9018	−0.921641
$853$	16.6441	0.569883	0.284942	−	0.958545i	$-0.408026\pi$
$853$	16.6441	0.569883	0.284942	+	0.958545i	$0.408026\pi$
$854$	−2.52449	−0.0863861
$855$	−0.00450255	−0.000153984 0
$856$	11.5349	0.394256
$857$	−16.6186	−0.567680	−0.283840	−	0.958872i	$-0.591608\pi$
$857$	−16.6186	−0.567680	−0.283840	+	0.958872i	$0.591608\pi$
$858$	−10.7192	−0.365947
$859$	−6.30950	−0.215277	−0.107639	−	0.994190i	$-0.534329\pi$
$859$	−6.30950	−0.215277	−0.107639	+	0.994190i	$0.534329\pi$
$860$	4.12478	0.140654
$861$	6.01531	0.205001
$862$	−6.24375	−0.212663
$863$	40.4821	1.37803	0.689013	−	0.724749i	$-0.258044\pi$
$863$	40.4821	1.37803	0.689013	+	0.724749i	$0.258044\pi$
$864$	5.21080	0.177275
$865$	1.03242	0.0351034
$866$	5.09446	0.173117
$867$	−28.6468	−0.972896
$868$	−10.0778	−0.342063
$869$	−28.8232	−0.977761
$870$	−5.70335	−0.193362
$871$	30.9264	1.04790
$872$	−1.66673	−0.0564427
$873$	−0.139922	−0.00473563
$874$	0.483782	0.0163642
$875$	−12.6169	−0.426529
$876$	−8.02770	−0.271231
$877$	−24.4482	−0.825557	−0.412778	−	0.910831i	$-0.635442\pi$
$877$	−24.4482	−0.825557	−0.412778	+	0.910831i	$0.635442\pi$
$878$	5.68741	0.191941
$879$	−2.54912	−0.0859798
$880$	−1.06816	−0.0360076
$881$	17.2779	0.582107	0.291054	−	0.956707i	$-0.405994\pi$
$881$	17.2779	0.582107	0.291054	+	0.956707i	$0.405994\pi$
$882$	−0.0227692	−0.000766680 0
$883$	1.67355	0.0563194	0.0281597	−	0.999603i	$-0.491035\pi$
$883$	1.67355	0.0563194	0.0281597	+	0.999603i	$0.491035\pi$
$884$	2.04223	0.0686877
$885$	−3.69057	−0.124057
$886$	10.0320	0.337031
$887$	−1.47471	−0.0495160	−0.0247580	−	0.999693i	$-0.507882\pi$
$887$	−1.47471	−0.0495160	−0.0247580	+	0.999693i	$0.507882\pi$
$888$	11.9368	0.400573
$889$	−6.56872	−0.220308
$890$	3.04202	0.101969
$891$	17.4901	0.585941
$892$	−26.3483	−0.882208
$893$	−6.16042	−0.206150
$894$	34.3722	1.14958
$895$	9.62683	0.321789
$896$	−2.37970	−0.0795002
$897$	5.48435	0.183117
$898$	−5.34635	−0.178410
$899$	−25.5888	−0.853433
$900$	0.0800625	0.00266875
$901$	−8.62979	−0.287500
$902$	2.86054	0.0952455
$903$	31.0205	1.03230
$904$	−0.628262	−0.0208957
$905$	2.82489	0.0939026
$906$	4.31671	0.143413
$907$	−37.5448	−1.24666	−0.623328	−	0.781961i	$-0.714220\pi$
$907$	−37.5448	−1.24666	−0.623328	+	0.781961i	$0.714220\pi$
$908$	20.9614	0.695628
$909$	0.122183	0.00405256
$910$	4.12974	0.136900
$911$	32.8640	1.08883	0.544416	−	0.838815i	$-0.316751\pi$
$911$	32.8640	1.08883	0.544416	+	0.838815i	$0.316751\pi$
$912$	0.835553	0.0276679
$913$	−25.5485	−0.845531
$914$	−10.4118	−0.344391
$915$	1.00132	0.0331027
$916$	−11.2178	−0.370645
$917$	−2.37970	−0.0785846
$918$	−3.35126	−0.110608
$919$	−46.6207	−1.53788	−0.768938	−	0.639323i	$-0.779215\pi$
$919$	−46.6207	−1.53788	−0.768938	+	0.639323i	$0.779215\pi$
$920$	0.546511	0.0180179
$921$	−52.1878	−1.71965
$922$	−30.0568	−0.989869
$923$	49.4605	1.62801
$924$	−8.03310	−0.264270
$925$	32.4925	1.06835
$926$	−22.3224	−0.733560
$927$	0.126328	0.00414916
$928$	−6.04235	−0.198350
$929$	48.1697	1.58040	0.790199	−	0.612850i	$-0.209977\pi$
$929$	48.1697	1.58040	0.790199	+	0.612850i	$0.209977\pi$
$930$	3.99730	0.131077
$931$	−0.646828	−0.0211989
$932$	21.6622	0.709568
$933$	−12.7140	−0.416238
$934$	−1.09494	−0.0358275
$935$	0.686973	0.0224664
$936$	−0.0540767	−0.00176755
$937$	−36.1130	−1.17976	−0.589879	−	0.807491i	$-0.700825\pi$
$937$	−36.1130	−1.17976	−0.589879	+	0.807491i	$0.700825\pi$
$938$	23.1766	0.756744
$939$	2.19279	0.0715590
$940$	−6.95920	−0.226984
$941$	−5.16644	−0.168421	−0.0842106	−	0.996448i	$-0.526837\pi$
$941$	−5.16644	−0.168421	−0.0842106	+	0.996448i	$0.526837\pi$
$942$	5.75254	0.187428
$943$	−1.46356	−0.0476602
$944$	−3.90994	−0.127258
$945$	−6.77682	−0.220450
$946$	14.7516	0.479615
$947$	−34.5463	−1.12260	−0.561302	−	0.827611i	$-0.689699\pi$
$947$	−34.5463	−1.12260	−0.561302	+	0.827611i	$0.689699\pi$
$948$	25.4701	0.827231
$949$	14.7594	0.479109
$950$	2.27442	0.0737918
$951$	−51.0056	−1.65397
$952$	1.53048	0.0496030
$953$	−7.60552	−0.246367	−0.123183	−	0.992384i	$-0.539310\pi$
$953$	−7.60552	−0.246367	−0.123183	+	0.992384i	$0.539310\pi$
$954$	0.228510	0.00739828
$955$	7.45598	0.241270
$956$	−1.69920	−0.0549561
$957$	−20.3970	−0.659342
$958$	−37.4579	−1.21021
$959$	−32.0491	−1.03492
$960$	0.943895	0.0304641
$961$	−13.0656	−0.421472
$962$	−21.9464	−0.707582
$963$	0.196437	0.00633010
$964$	−4.52346	−0.145691
$965$	−12.2949	−0.395786
$966$	4.11005	0.132239
$967$	−2.09433	−0.0673490	−0.0336745	−	0.999433i	$-0.510721\pi$
$967$	−2.09433	−0.0673490	−0.0336745	+	0.999433i	$0.510721\pi$
$968$	7.17992	0.230771
$969$	−0.537376	−0.0172630
$970$	−4.49029	−0.144175
$971$	38.5936	1.23853	0.619264	−	0.785183i	$-0.287431\pi$
$971$	38.5936	1.23853	0.619264	+	0.785183i	$0.287431\pi$
$972$	0.176977	0.00567653
$973$	−17.5640	−0.563075
$974$	−10.6622	−0.341638
$975$	25.7837	0.825740
$976$	1.06084	0.0339567
$977$	24.8868	0.796199	0.398100	−	0.917342i	$-0.369670\pi$
$977$	24.8868	0.796199	0.398100	+	0.917342i	$0.369670\pi$
$978$	1.52096	0.0486349
$979$	10.8792	0.347702
$980$	−0.730699	−0.0233413
$981$	−0.0283841	−0.000906234 0
$982$	30.9746	0.988441
$983$	−36.0099	−1.14854	−0.574268	−	0.818667i	$-0.694713\pi$
$983$	−36.0099	−1.14854	−0.574268	+	0.818667i	$0.694713\pi$
$984$	−2.52776	−0.0805821
$985$	9.98377	0.318109
$986$	3.88607	0.123758
$987$	−52.3368	−1.66590
$988$	−1.53621	−0.0488734
$989$	−7.54748	−0.239996
$990$	−0.0181905	−0.000578132 0
$991$	7.78476	0.247291	0.123646	−	0.992326i	$-0.460541\pi$
$991$	7.78476	0.247291	0.123646	+	0.992326i	$0.460541\pi$
$992$	4.23490	0.134458
$993$	24.8438	0.788393
$994$	37.0663	1.17567
$995$	−6.63182	−0.210243
$996$	22.5763	0.715358
$997$	−6.89443	−0.218349	−0.109174	−	0.994023i	$-0.534821\pi$
$997$	−6.89443	−0.218349	−0.109174	+	0.994023i	$0.534821\pi$
$998$	36.8800	1.16742
$999$	36.0137	1.13942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.19	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.19	✓	24	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.72713 q^{3} +1.00000 q^{4} +0.546511 q^{5} -1.72713 q^{6} +2.37970 q^{7} -1.00000 q^{8} -0.0170298 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.72713 q^{3} +1.00000 q^{4} +0.546511 q^{5} -1.72713 q^{6} +2.37970 q^{7} -1.00000 q^{8} -0.0170298 q^{9} -0.546511 q^{10} -1.95450 q^{11} +1.72713 q^{12} -3.17542 q^{13} -2.37970 q^{14} +0.943895 q^{15} +1.00000 q^{16} -0.643138 q^{17} +0.0170298 q^{18} +0.483782 q^{19} +0.546511 q^{20} +4.11005 q^{21} +1.95450 q^{22} -1.00000 q^{23} -1.72713 q^{24} -4.70133 q^{25} +3.17542 q^{26} -5.21080 q^{27} +2.37970 q^{28} +6.04235 q^{29} -0.943895 q^{30} -4.23490 q^{31} -1.00000 q^{32} -3.37568 q^{33} +0.643138 q^{34} +1.30053 q^{35} -0.0170298 q^{36} -6.91135 q^{37} -0.483782 q^{38} -5.48435 q^{39} -0.546511 q^{40} +1.46356 q^{41} -4.11005 q^{42} +7.54748 q^{43} -1.95450 q^{44} -0.00930697 q^{45} +1.00000 q^{46} -12.7339 q^{47} +1.72713 q^{48} -1.33702 q^{49} +4.70133 q^{50} -1.11078 q^{51} -3.17542 q^{52} +13.4183 q^{53} +5.21080 q^{54} -1.06816 q^{55} -2.37970 q^{56} +0.835553 q^{57} -6.04235 q^{58} -3.90994 q^{59} +0.943895 q^{60} +1.06084 q^{61} +4.23490 q^{62} -0.0405258 q^{63} +1.00000 q^{64} -1.73540 q^{65} +3.37568 q^{66} -9.73931 q^{67} -0.643138 q^{68} -1.72713 q^{69} -1.30053 q^{70} -15.5760 q^{71} +0.0170298 q^{72} -4.64800 q^{73} +6.91135 q^{74} -8.11979 q^{75} +0.483782 q^{76} -4.65113 q^{77} +5.48435 q^{78} +14.7471 q^{79} +0.546511 q^{80} -8.94862 q^{81} -1.46356 q^{82} +13.0716 q^{83} +4.11005 q^{84} -0.351482 q^{85} -7.54748 q^{86} +10.4359 q^{87} +1.95450 q^{88} -5.56625 q^{89} +0.00930697 q^{90} -7.55655 q^{91} -1.00000 q^{92} -7.31421 q^{93} +12.7339 q^{94} +0.264392 q^{95} -1.72713 q^{96} +8.21629 q^{97} +1.33702 q^{98} +0.0332848 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

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