LMFDB - Embedded newform 6026.2.a.j.1.17

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			1.17
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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.189963 q^{3} +1.00000 q^{4} +2.89176 q^{5} -0.189963 q^{6} +3.54124 q^{7} -1.00000 q^{8} -2.96391 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.189963 q^{3} +1.00000 q^{4} +2.89176 q^{5} -0.189963 q^{6} +3.54124 q^{7} -1.00000 q^{8} -2.96391 q^{9} -2.89176 q^{10} -6.15219 q^{11} +0.189963 q^{12} +5.93249 q^{13} -3.54124 q^{14} +0.549327 q^{15} +1.00000 q^{16} -2.27288 q^{17} +2.96391 q^{18} +6.26758 q^{19} +2.89176 q^{20} +0.672703 q^{21} +6.15219 q^{22} +1.00000 q^{23} -0.189963 q^{24} +3.36228 q^{25} -5.93249 q^{26} -1.13292 q^{27} +3.54124 q^{28} +4.07624 q^{29} -0.549327 q^{30} +2.13061 q^{31} -1.00000 q^{32} -1.16869 q^{33} +2.27288 q^{34} +10.2404 q^{35} -2.96391 q^{36} -6.59833 q^{37} -6.26758 q^{38} +1.12695 q^{39} -2.89176 q^{40} +4.36217 q^{41} -0.672703 q^{42} +8.57089 q^{43} -6.15219 q^{44} -8.57093 q^{45} -1.00000 q^{46} -8.66705 q^{47} +0.189963 q^{48} +5.54036 q^{49} -3.36228 q^{50} -0.431762 q^{51} +5.93249 q^{52} +2.01626 q^{53} +1.13292 q^{54} -17.7906 q^{55} -3.54124 q^{56} +1.19061 q^{57} -4.07624 q^{58} -6.61282 q^{59} +0.549327 q^{60} +9.43486 q^{61} -2.13061 q^{62} -10.4959 q^{63} +1.00000 q^{64} +17.1553 q^{65} +1.16869 q^{66} +4.82797 q^{67} -2.27288 q^{68} +0.189963 q^{69} -10.2404 q^{70} +14.4802 q^{71} +2.96391 q^{72} -7.71772 q^{73} +6.59833 q^{74} +0.638707 q^{75} +6.26758 q^{76} -21.7864 q^{77} -1.12695 q^{78} -12.4987 q^{79} +2.89176 q^{80} +8.67653 q^{81} -4.36217 q^{82} +4.50864 q^{83} +0.672703 q^{84} -6.57261 q^{85} -8.57089 q^{86} +0.774333 q^{87} +6.15219 q^{88} -3.28752 q^{89} +8.57093 q^{90} +21.0084 q^{91} +1.00000 q^{92} +0.404736 q^{93} +8.66705 q^{94} +18.1243 q^{95} -0.189963 q^{96} +11.9909 q^{97} -5.54036 q^{98} +18.2346 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.189963	0.109675	0.0548375	−	0.998495i	$-0.482536\pi$
$3$	0.189963	0.109675	0.0548375	+	0.998495i	$0.482536\pi$
$4$	1.00000	0.500000
$5$	2.89176	1.29323	0.646617	−	0.762815i	$-0.276183\pi$
$5$	2.89176	1.29323	0.646617	+	0.762815i	$0.276183\pi$
$6$	−0.189963	−0.0775520
$7$	3.54124	1.33846	0.669231	−	0.743055i	$-0.266624\pi$
$7$	3.54124	1.33846	0.669231	+	0.743055i	$0.266624\pi$
$8$	−1.00000	−0.353553
$9$	−2.96391	−0.987971
$10$	−2.89176	−0.914455
$11$	−6.15219	−1.85495	−0.927477	−	0.373880i	$-0.878027\pi$
$11$	−6.15219	−1.85495	−0.927477	+	0.373880i	$0.878027\pi$
$12$	0.189963	0.0548375
$13$	5.93249	1.64538	0.822688	−	0.568492i	$-0.192473\pi$
$13$	5.93249	1.64538	0.822688	+	0.568492i	$0.192473\pi$
$14$	−3.54124	−0.946435
$15$	0.549327	0.141836
$16$	1.00000	0.250000
$17$	−2.27288	−0.551253	−0.275627	−	0.961265i	$-0.588885\pi$
$17$	−2.27288	−0.551253	−0.275627	+	0.961265i	$0.588885\pi$
$18$	2.96391	0.698601
$19$	6.26758	1.43788	0.718941	−	0.695071i	$-0.244627\pi$
$19$	6.26758	1.43788	0.718941	+	0.695071i	$0.244627\pi$
$20$	2.89176	0.646617
$21$	0.672703	0.146796
$22$	6.15219	1.31165
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.189963	−0.0387760
$25$	3.36228	0.672455
$26$	−5.93249	−1.16346
$27$	−1.13292	−0.218031
$28$	3.54124	0.669231
$29$	4.07624	0.756938	0.378469	−	0.925614i	$-0.376451\pi$
$29$	4.07624	0.756938	0.378469	+	0.925614i	$0.376451\pi$
$30$	−0.549327	−0.100293
$31$	2.13061	0.382669	0.191334	−	0.981525i	$-0.438719\pi$
$31$	2.13061	0.382669	0.191334	+	0.981525i	$0.438719\pi$
$32$	−1.00000	−0.176777
$33$	−1.16869	−0.203442
$34$	2.27288	0.389795
$35$	10.2404	1.73094
$36$	−2.96391	−0.493986
$37$	−6.59833	−1.08476	−0.542379	−	0.840134i	$-0.682476\pi$
$37$	−6.59833	−1.08476	−0.542379	+	0.840134i	$0.682476\pi$
$38$	−6.26758	−1.01674
$39$	1.12695	0.180457
$40$	−2.89176	−0.457227
$41$	4.36217	0.681256	0.340628	−	0.940198i	$-0.389360\pi$
$41$	4.36217	0.681256	0.340628	+	0.940198i	$0.389360\pi$
$42$	−0.672703	−0.103800
$43$	8.57089	1.30705	0.653524	−	0.756905i	$-0.273290\pi$
$43$	8.57089	1.30705	0.653524	+	0.756905i	$0.273290\pi$
$44$	−6.15219	−0.927477
$45$	−8.57093	−1.27768
$46$	−1.00000	−0.147442
$47$	−8.66705	−1.26422	−0.632110	−	0.774879i	$-0.717811\pi$
$47$	−8.66705	−1.26422	−0.632110	+	0.774879i	$0.717811\pi$
$48$	0.189963	0.0274188
$49$	5.54036	0.791480
$50$	−3.36228	−0.475498
$51$	−0.431762	−0.0604587
$52$	5.93249	0.822688
$53$	2.01626	0.276955	0.138478	−	0.990366i	$-0.455779\pi$
$53$	2.01626	0.276955	0.138478	+	0.990366i	$0.455779\pi$
$54$	1.13292	0.154171
$55$	−17.7906	−2.39889
$56$	−3.54124	−0.473218
$57$	1.19061	0.157700
$58$	−4.07624	−0.535236
$59$	−6.61282	−0.860915	−0.430458	−	0.902611i	$-0.641648\pi$
$59$	−6.61282	−0.860915	−0.430458	+	0.902611i	$0.641648\pi$
$60$	0.549327	0.0709178
$61$	9.43486	1.20801	0.604005	−	0.796980i	$-0.293571\pi$
$61$	9.43486	1.20801	0.604005	+	0.796980i	$0.293571\pi$
$62$	−2.13061	−0.270588
$63$	−10.4959	−1.32236
$64$	1.00000	0.125000
$65$	17.1553	2.12786
$66$	1.16869	0.143855
$67$	4.82797	0.589831	0.294915	−	0.955523i	$-0.404709\pi$
$67$	4.82797	0.589831	0.294915	+	0.955523i	$0.404709\pi$
$68$	−2.27288	−0.275627
$69$	0.189963	0.0228688
$70$	−10.2404	−1.22396
$71$	14.4802	1.71849	0.859244	−	0.511567i	$-0.170935\pi$
$71$	14.4802	1.71849	0.859244	+	0.511567i	$0.170935\pi$
$72$	2.96391	0.349301
$73$	−7.71772	−0.903291	−0.451645	−	0.892198i	$-0.649163\pi$
$73$	−7.71772	−0.903291	−0.451645	+	0.892198i	$0.649163\pi$
$74$	6.59833	0.767040
$75$	0.638707	0.0737516
$76$	6.26758	0.718941
$77$	−21.7864	−2.48279
$78$	−1.12695	−0.127602
$79$	−12.4987	−1.40621	−0.703106	−	0.711085i	$-0.748204\pi$
$79$	−12.4987	−1.40621	−0.703106	+	0.711085i	$0.748204\pi$
$80$	2.89176	0.323309
$81$	8.67653	0.964059
$82$	−4.36217	−0.481721
$83$	4.50864	0.494888	0.247444	−	0.968902i	$-0.420409\pi$
$83$	4.50864	0.494888	0.247444	+	0.968902i	$0.420409\pi$
$84$	0.672703	0.0733979
$85$	−6.57261	−0.712900
$86$	−8.57089	−0.924223
$87$	0.774333	0.0830172
$88$	6.15219	0.655825
$89$	−3.28752	−0.348477	−0.174238	−	0.984704i	$-0.555746\pi$
$89$	−3.28752	−0.348477	−0.174238	+	0.984704i	$0.555746\pi$
$90$	8.57093	0.903455
$91$	21.0084	2.20227
$92$	1.00000	0.104257
$93$	0.404736	0.0419692
$94$	8.66705	0.893938
$95$	18.1243	1.85952
$96$	−0.189963	−0.0193880
$97$	11.9909	1.21750	0.608748	−	0.793364i	$-0.291672\pi$
$97$	11.9909	1.21750	0.608748	+	0.793364i	$0.291672\pi$
$98$	−5.54036	−0.559661
$99$	18.2346	1.83264
$100$	3.36228	0.336228
$101$	−18.0602	−1.79706	−0.898531	−	0.438910i	$-0.855365\pi$
$101$	−18.0602	−1.79706	−0.898531	+	0.438910i	$0.855365\pi$
$102$	0.431762	0.0427508
$103$	7.63955	0.752747	0.376374	−	0.926468i	$-0.377171\pi$
$103$	7.63955	0.752747	0.376374	+	0.926468i	$0.377171\pi$
$104$	−5.93249	−0.581729
$105$	1.94530	0.189841
$106$	−2.01626	−0.195837
$107$	17.9549	1.73577	0.867883	−	0.496768i	$-0.165480\pi$
$107$	17.9549	1.73577	0.867883	+	0.496768i	$0.165480\pi$
$108$	−1.13292	−0.109015
$109$	−1.98865	−0.190478	−0.0952390	−	0.995454i	$-0.530362\pi$
$109$	−1.98865	−0.190478	−0.0952390	+	0.995454i	$0.530362\pi$
$110$	17.7906	1.69627
$111$	−1.25344	−0.118971
$112$	3.54124	0.334615
$113$	−5.98359	−0.562889	−0.281445	−	0.959577i	$-0.590814\pi$
$113$	−5.98359	−0.562889	−0.281445	+	0.959577i	$0.590814\pi$
$114$	−1.19061	−0.111511
$115$	2.89176	0.269658
$116$	4.07624	0.378469
$117$	−17.5834	−1.62559
$118$	6.61282	0.608759
$119$	−8.04879	−0.737831
$120$	−0.549327	−0.0501464
$121$	26.8494	2.44086
$122$	−9.43486	−0.854192
$123$	0.828649	0.0747168
$124$	2.13061	0.191334
$125$	−4.73590	−0.423592
$126$	10.4959	0.935051
$127$	12.4352	1.10344	0.551721	−	0.834029i	$-0.313971\pi$
$127$	12.4352	1.10344	0.551721	+	0.834029i	$0.313971\pi$
$128$	−1.00000	−0.0883883
$129$	1.62815	0.143351
$130$	−17.1553	−1.50462
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−1.16869	−0.101721
$133$	22.1950	1.92455
$134$	−4.82797	−0.417073
$135$	−3.27614	−0.281965
$136$	2.27288	0.194897
$137$	12.5385	1.07123	0.535617	−	0.844461i	$-0.320079\pi$
$137$	12.5385	1.07123	0.535617	+	0.844461i	$0.320079\pi$
$138$	−0.189963	−0.0161707
$139$	−0.119746	−0.0101567	−0.00507835	−	0.999987i	$-0.501616\pi$
$139$	−0.119746	−0.0101567	−0.00507835	+	0.999987i	$0.501616\pi$
$140$	10.2404	0.865472
$141$	−1.64642	−0.138653
$142$	−14.4802	−1.21515
$143$	−36.4978	−3.05210
$144$	−2.96391	−0.246993
$145$	11.7875	0.978898
$146$	7.71772	0.638723
$147$	1.05246	0.0868056
$148$	−6.59833	−0.542379
$149$	−3.18575	−0.260986	−0.130493	−	0.991449i	$-0.541656\pi$
$149$	−3.18575	−0.260986	−0.130493	+	0.991449i	$0.541656\pi$
$150$	−0.638707	−0.0521502
$151$	−8.83049	−0.718615	−0.359308	−	0.933219i	$-0.616987\pi$
$151$	−8.83049	−0.718615	−0.359308	+	0.933219i	$0.616987\pi$
$152$	−6.26758	−0.508368
$153$	6.73661	0.544622
$154$	21.7864	1.75559
$155$	6.16121	0.494880
$156$	1.12695	0.0902284
$157$	15.1312	1.20760	0.603799	−	0.797136i	$-0.293653\pi$
$157$	15.1312	1.20760	0.603799	+	0.797136i	$0.293653\pi$
$158$	12.4987	0.994342
$159$	0.383015	0.0303751
$160$	−2.89176	−0.228614
$161$	3.54124	0.279089
$162$	−8.67653	−0.681693
$163$	17.8698	1.39967	0.699836	−	0.714304i	$-0.253257\pi$
$163$	17.8698	1.39967	0.699836	+	0.714304i	$0.253257\pi$
$164$	4.36217	0.340628
$165$	−3.37956	−0.263098
$166$	−4.50864	−0.349938
$167$	3.77569	0.292172	0.146086	−	0.989272i	$-0.453332\pi$
$167$	3.77569	0.292172	0.146086	+	0.989272i	$0.453332\pi$
$168$	−0.672703	−0.0519002
$169$	22.1945	1.70727
$170$	6.57261	0.504096
$171$	−18.5766	−1.42059
$172$	8.57089	0.653524
$173$	−0.0911958	−0.00693349	−0.00346674	−	0.999994i	$-0.501104\pi$
$173$	−0.0911958	−0.00693349	−0.00346674	+	0.999994i	$0.501104\pi$
$174$	−0.774333	−0.0587020
$175$	11.9066	0.900056
$176$	−6.15219	−0.463739
$177$	−1.25619	−0.0944209
$178$	3.28752	0.246410
$179$	0.0457866	0.00342225	0.00171112	−	0.999999i	$-0.499455\pi$
$179$	0.0457866	0.00342225	0.00171112	+	0.999999i	$0.499455\pi$
$180$	−8.57093	−0.638839
$181$	7.43760	0.552832	0.276416	−	0.961038i	$-0.410853\pi$
$181$	7.43760	0.552832	0.276416	+	0.961038i	$0.410853\pi$
$182$	−21.0084	−1.55724
$183$	1.79227	0.132489
$184$	−1.00000	−0.0737210
$185$	−19.0808	−1.40285
$186$	−0.404736	−0.0296767
$187$	13.9832	1.02255
$188$	−8.66705	−0.632110
$189$	−4.01194	−0.291826
$190$	−18.1243	−1.31488
$191$	7.98197	0.577555	0.288778	−	0.957396i	$-0.406751\pi$
$191$	7.98197	0.577555	0.288778	+	0.957396i	$0.406751\pi$
$192$	0.189963	0.0137094
$193$	6.63270	0.477432	0.238716	−	0.971089i	$-0.423273\pi$
$193$	6.63270	0.477432	0.238716	+	0.971089i	$0.423273\pi$
$194$	−11.9909	−0.860900
$195$	3.25888	0.233373
$196$	5.54036	0.395740
$197$	−4.19817	−0.299108	−0.149554	−	0.988754i	$-0.547784\pi$
$197$	−4.19817	−0.299108	−0.149554	+	0.988754i	$0.547784\pi$
$198$	−18.2346	−1.29587
$199$	18.3272	1.29918	0.649589	−	0.760285i	$-0.274941\pi$
$199$	18.3272	1.29918	0.649589	+	0.760285i	$0.274941\pi$
$200$	−3.36228	−0.237749
$201$	0.917135	0.0646897
$202$	18.0602	1.27071
$203$	14.4349	1.01313
$204$	−0.431762	−0.0302294
$205$	12.6143	0.881024
$206$	−7.63955	−0.532273
$207$	−2.96391	−0.206006
$208$	5.93249	0.411344
$209$	−38.5593	−2.66721
$210$	−1.94530	−0.134238
$211$	−14.5397	−1.00095	−0.500475	−	0.865751i	$-0.666841\pi$
$211$	−14.5397	−1.00095	−0.500475	+	0.865751i	$0.666841\pi$
$212$	2.01626	0.138478
$213$	2.75070	0.188475
$214$	−17.9549	−1.22737
$215$	24.7850	1.69032
$216$	1.13292	0.0770855
$217$	7.54499	0.512187
$218$	1.98865	0.134688
$219$	−1.46608	−0.0990684
$220$	−17.7906	−1.19945
$221$	−13.4838	−0.907019
$222$	1.25344	0.0841251
$223$	3.62069	0.242459	0.121230	−	0.992624i	$-0.461316\pi$
$223$	3.62069	0.242459	0.121230	+	0.992624i	$0.461316\pi$
$224$	−3.54124	−0.236609
$225$	−9.96550	−0.664367
$226$	5.98359	0.398023
$227$	−22.0752	−1.46519	−0.732593	−	0.680667i	$-0.761690\pi$
$227$	−22.0752	−1.46519	−0.732593	+	0.680667i	$0.761690\pi$
$228$	1.19061	0.0788499
$229$	−17.0183	−1.12460	−0.562300	−	0.826933i	$-0.690083\pi$
$229$	−17.0183	−1.12460	−0.562300	+	0.826933i	$0.690083\pi$
$230$	−2.89176	−0.190677
$231$	−4.13860	−0.272300
$232$	−4.07624	−0.267618
$233$	−13.8317	−0.906146	−0.453073	−	0.891474i	$-0.649672\pi$
$233$	−13.8317	−0.906146	−0.453073	+	0.891474i	$0.649672\pi$
$234$	17.5834	1.14946
$235$	−25.0630	−1.63493
$236$	−6.61282	−0.430458
$237$	−2.37428	−0.154226
$238$	8.04879	0.521726
$239$	17.3802	1.12423	0.562116	−	0.827059i	$-0.309988\pi$
$239$	17.3802	1.12423	0.562116	+	0.827059i	$0.309988\pi$
$240$	0.549327	0.0354589
$241$	−20.4973	−1.32035	−0.660173	−	0.751113i	$-0.729517\pi$
$241$	−20.4973	−1.32035	−0.660173	+	0.751113i	$0.729517\pi$
$242$	−26.8494	−1.72595
$243$	5.04698	0.323764
$244$	9.43486	0.604005
$245$	16.0214	1.02357
$246$	−0.828649	−0.0528327
$247$	37.1824	2.36586
$248$	−2.13061	−0.135294
$249$	0.856474	0.0542768
$250$	4.73590	0.299525
$251$	−31.3790	−1.98063	−0.990314	−	0.138846i	$-0.955661\pi$
$251$	−31.3790	−1.98063	−0.990314	+	0.138846i	$0.955661\pi$
$252$	−10.4959	−0.661181
$253$	−6.15219	−0.386785
$254$	−12.4352	−0.780251
$255$	−1.24855	−0.0781873
$256$	1.00000	0.0625000
$257$	29.3092	1.82825	0.914127	−	0.405427i	$-0.132877\pi$
$257$	29.3092	1.82825	0.914127	+	0.405427i	$0.132877\pi$
$258$	−1.62815	−0.101364
$259$	−23.3662	−1.45191
$260$	17.1553	1.06393
$261$	−12.0816	−0.747833
$262$	1.00000	0.0617802
$263$	2.36319	0.145720	0.0728602	−	0.997342i	$-0.476787\pi$
$263$	2.36319	0.145720	0.0728602	+	0.997342i	$0.476787\pi$
$264$	1.16869	0.0719277
$265$	5.83055	0.358168
$266$	−22.1950	−1.36086
$267$	−0.624507	−0.0382192
$268$	4.82797	0.294915
$269$	−26.5681	−1.61989	−0.809943	−	0.586509i	$-0.800502\pi$
$269$	−26.5681	−1.61989	−0.809943	+	0.586509i	$0.800502\pi$
$270$	3.27614	0.199379
$271$	−9.59513	−0.582862	−0.291431	−	0.956592i	$-0.594131\pi$
$271$	−9.59513	−0.582862	−0.291431	+	0.956592i	$0.594131\pi$
$272$	−2.27288	−0.137813
$273$	3.99080	0.241535
$274$	−12.5385	−0.757476
$275$	−20.6854	−1.24737
$276$	0.189963	0.0114344
$277$	−11.5453	−0.693690	−0.346845	−	0.937922i	$-0.612747\pi$
$277$	−11.5453	−0.693690	−0.346845	+	0.937922i	$0.612747\pi$
$278$	0.119746	0.00718187
$279$	−6.31494	−0.378066
$280$	−10.2404	−0.611981
$281$	33.3589	1.99003	0.995013	−	0.0997476i	$-0.0318035\pi$
$281$	33.3589	1.99003	0.995013	+	0.0997476i	$0.0318035\pi$
$282$	1.64642	0.0980427
$283$	−2.17546	−0.129318	−0.0646589	−	0.997907i	$-0.520596\pi$
$283$	−2.17546	−0.129318	−0.0646589	+	0.997907i	$0.520596\pi$
$284$	14.4802	0.859244
$285$	3.44295	0.203943
$286$	36.4978	2.15816
$287$	15.4475	0.911835
$288$	2.96391	0.174650
$289$	−11.8340	−0.696120
$290$	−11.7875	−0.692186
$291$	2.27783	0.133529
$292$	−7.71772	−0.451645
$293$	22.9081	1.33831	0.669154	−	0.743124i	$-0.266657\pi$
$293$	22.9081	1.33831	0.669154	+	0.743124i	$0.266657\pi$
$294$	−1.05246	−0.0613808
$295$	−19.1227	−1.11337
$296$	6.59833	0.383520
$297$	6.96995	0.404437
$298$	3.18575	0.184545
$299$	5.93249	0.343085
$300$	0.638707	0.0368758
$301$	30.3516	1.74944
$302$	8.83049	0.508138
$303$	−3.43077	−0.197093
$304$	6.26758	0.359470
$305$	27.2834	1.56224
$306$	−6.73661	−0.385106
$307$	−10.2806	−0.586742	−0.293371	−	0.955999i	$-0.594777\pi$
$307$	−10.2806	−0.586742	−0.293371	+	0.955999i	$0.594777\pi$
$308$	−21.7864	−1.24139
$309$	1.45123	0.0825576
$310$	−6.16121	−0.349933
$311$	−3.30278	−0.187283	−0.0936417	−	0.995606i	$-0.529851\pi$
$311$	−3.30278	−0.187283	−0.0936417	+	0.995606i	$0.529851\pi$
$312$	−1.12695	−0.0638011
$313$	−34.9457	−1.97525	−0.987623	−	0.156848i	$-0.949867\pi$
$313$	−34.9457	−1.97525	−0.987623	+	0.156848i	$0.949867\pi$
$314$	−15.1312	−0.853901
$315$	−30.3517	−1.71012
$316$	−12.4987	−0.703106
$317$	26.9577	1.51409	0.757047	−	0.653360i	$-0.226641\pi$
$317$	26.9577	1.51409	0.757047	+	0.653360i	$0.226641\pi$
$318$	−0.383015	−0.0214784
$319$	−25.0778	−1.40409
$320$	2.89176	0.161654
$321$	3.41076	0.190370
$322$	−3.54124	−0.197345
$323$	−14.2454	−0.792637
$324$	8.67653	0.482029
$325$	19.9467	1.10644
$326$	−17.8698	−0.989717
$327$	−0.377769	−0.0208907
$328$	−4.36217	−0.240860
$329$	−30.6921	−1.69211
$330$	3.37956	0.186039
$331$	16.8104	0.923984	0.461992	−	0.886884i	$-0.347135\pi$
$331$	16.8104	0.923984	0.461992	+	0.886884i	$0.347135\pi$
$332$	4.50864	0.247444
$333$	19.5569	1.07171
$334$	−3.77569	−0.206597
$335$	13.9613	0.762789
$336$	0.672703	0.0366990
$337$	−36.3838	−1.98195	−0.990975	−	0.134044i	$-0.957204\pi$
$337$	−36.3838	−1.98195	−0.990975	+	0.134044i	$0.957204\pi$
$338$	−22.1945	−1.20722
$339$	−1.13666	−0.0617349
$340$	−6.57261	−0.356450
$341$	−13.1079	−0.709833
$342$	18.5766	1.00451
$343$	−5.16894	−0.279096
$344$	−8.57089	−0.462112
$345$	0.549327	0.0295748
$346$	0.0911958	0.00490272
$347$	25.0536	1.34495	0.672474	−	0.740121i	$-0.265232\pi$
$347$	25.0536	1.34495	0.672474	+	0.740121i	$0.265232\pi$
$348$	0.774333	0.0415086
$349$	−27.6068	−1.47776	−0.738879	−	0.673838i	$-0.764644\pi$
$349$	−27.6068	−1.47776	−0.738879	+	0.673838i	$0.764644\pi$
$350$	−11.9066	−0.636436
$351$	−6.72105	−0.358743
$352$	6.15219	0.327913
$353$	−13.6199	−0.724914	−0.362457	−	0.932000i	$-0.618062\pi$
$353$	−13.6199	−0.724914	−0.362457	+	0.932000i	$0.618062\pi$
$354$	1.25619	0.0667657
$355$	41.8734	2.22241
$356$	−3.28752	−0.174238
$357$	−1.52897	−0.0809217
$358$	−0.0457866	−0.00241989
$359$	−8.09276	−0.427120	−0.213560	−	0.976930i	$-0.568506\pi$
$359$	−8.09276	−0.427120	−0.213560	+	0.976930i	$0.568506\pi$
$360$	8.57093	0.451728
$361$	20.2826	1.06750
$362$	−7.43760	−0.390912
$363$	5.10039	0.267701
$364$	21.0084	1.10114
$365$	−22.3178	−1.16817
$366$	−1.79227	−0.0936836
$367$	−11.1281	−0.580884	−0.290442	−	0.956893i	$-0.593802\pi$
$367$	−11.1281	−0.580884	−0.290442	+	0.956893i	$0.593802\pi$
$368$	1.00000	0.0521286
$369$	−12.9291	−0.673061
$370$	19.0808	0.991963
$371$	7.14006	0.370694
$372$	0.404736	0.0209846
$373$	7.98559	0.413478	0.206739	−	0.978396i	$-0.433715\pi$
$373$	7.98559	0.413478	0.206739	+	0.978396i	$0.433715\pi$
$374$	−13.9832	−0.723052
$375$	−0.899645	−0.0464575
$376$	8.66705	0.446969
$377$	24.1822	1.24545
$378$	4.01194	0.206352
$379$	−8.77145	−0.450559	−0.225280	−	0.974294i	$-0.572330\pi$
$379$	−8.77145	−0.450559	−0.225280	+	0.974294i	$0.572330\pi$
$380$	18.1243	0.929759
$381$	2.36222	0.121020
$382$	−7.98197	−0.408393
$383$	35.5386	1.81594	0.907968	−	0.419040i	$-0.137633\pi$
$383$	35.5386	1.81594	0.907968	+	0.419040i	$0.137633\pi$
$384$	−0.189963	−0.00969400
$385$	−63.0009	−3.21082
$386$	−6.63270	−0.337596
$387$	−25.4034	−1.29133
$388$	11.9909	0.608748
$389$	5.01037	0.254036	0.127018	−	0.991900i	$-0.459459\pi$
$389$	5.01037	0.254036	0.127018	+	0.991900i	$0.459459\pi$
$390$	−3.25888	−0.165020
$391$	−2.27288	−0.114944
$392$	−5.54036	−0.279830
$393$	−0.189963	−0.00958235
$394$	4.19817	0.211501
$395$	−36.1432	−1.81856
$396$	18.2346	0.916321
$397$	12.8764	0.646247	0.323123	−	0.946357i	$-0.395267\pi$
$397$	12.8764	0.646247	0.323123	+	0.946357i	$0.395267\pi$
$398$	−18.3272	−0.918658
$399$	4.21622	0.211075
$400$	3.36228	0.168114
$401$	24.5864	1.22779	0.613893	−	0.789389i	$-0.289603\pi$
$401$	24.5864	1.22779	0.613893	+	0.789389i	$0.289603\pi$
$402$	−0.917135	−0.0457425
$403$	12.6398	0.629634
$404$	−18.0602	−0.898531
$405$	25.0904	1.24675
$406$	−14.4349	−0.716393
$407$	40.5941	2.01218
$408$	0.431762	0.0213754
$409$	−13.2657	−0.655948	−0.327974	−	0.944687i	$-0.606366\pi$
$409$	−13.2657	−0.655948	−0.327974	+	0.944687i	$0.606366\pi$
$410$	−12.6143	−0.622978
$411$	2.38184	0.117488
$412$	7.63955	0.376374
$413$	−23.4175	−1.15230
$414$	2.96391	0.145668
$415$	13.0379	0.640006
$416$	−5.93249	−0.290864
$417$	−0.0227472	−0.00111394
$418$	38.5593	1.88600
$419$	−25.2875	−1.23538	−0.617689	−	0.786423i	$-0.711931\pi$
$419$	−25.2875	−1.23538	−0.617689	+	0.786423i	$0.711931\pi$
$420$	1.94530	0.0949207
$421$	11.4673	0.558881	0.279440	−	0.960163i	$-0.409851\pi$
$421$	11.4673	0.558881	0.279440	+	0.960163i	$0.409851\pi$
$422$	14.5397	0.707779
$423$	25.6884	1.24901
$424$	−2.01626	−0.0979184
$425$	−7.64204	−0.370693
$426$	−2.75070	−0.133272
$427$	33.4111	1.61688
$428$	17.9549	0.867883
$429$	−6.93322	−0.334739
$430$	−24.7850	−1.19524
$431$	15.6022	0.751534	0.375767	−	0.926714i	$-0.377379\pi$
$431$	15.6022	0.751534	0.375767	+	0.926714i	$0.377379\pi$
$432$	−1.13292	−0.0545077
$433$	−34.9616	−1.68015	−0.840073	−	0.542473i	$-0.817488\pi$
$433$	−34.9616	−1.68015	−0.840073	+	0.542473i	$0.817488\pi$
$434$	−7.54499	−0.362171
$435$	2.23919	0.107361
$436$	−1.98865	−0.0952390
$437$	6.26758	0.299819
$438$	1.46608	0.0700520
$439$	21.8011	1.04051	0.520254	−	0.854011i	$-0.325837\pi$
$439$	21.8011	1.04051	0.520254	+	0.854011i	$0.325837\pi$
$440$	17.7906	0.848136
$441$	−16.4211	−0.781959
$442$	13.4838	0.641360
$443$	28.4231	1.35042	0.675212	−	0.737624i	$-0.264052\pi$
$443$	28.4231	1.35042	0.675212	+	0.737624i	$0.264052\pi$
$444$	−1.25344	−0.0594855
$445$	−9.50673	−0.450662
$446$	−3.62069	−0.171445
$447$	−0.605173	−0.0286237
$448$	3.54124	0.167308
$449$	−6.16703	−0.291040	−0.145520	−	0.989355i	$-0.546486\pi$
$449$	−6.16703	−0.291040	−0.145520	+	0.989355i	$0.546486\pi$
$450$	9.96550	0.469778
$451$	−26.8369	−1.26370
$452$	−5.98359	−0.281445
$453$	−1.67746	−0.0788142
$454$	22.0752	1.03604
$455$	60.7511	2.84806
$456$	−1.19061	−0.0557553
$457$	10.6997	0.500510	0.250255	−	0.968180i	$-0.419486\pi$
$457$	10.6997	0.500510	0.250255	+	0.968180i	$0.419486\pi$
$458$	17.0183	0.795213
$459$	2.57499	0.120190
$460$	2.89176	0.134829
$461$	18.8432	0.877615	0.438808	−	0.898581i	$-0.355401\pi$
$461$	18.8432	0.877615	0.438808	+	0.898581i	$0.355401\pi$
$462$	4.13860	0.192545
$463$	28.3465	1.31737	0.658687	−	0.752417i	$-0.271112\pi$
$463$	28.3465	1.31737	0.658687	+	0.752417i	$0.271112\pi$
$464$	4.07624	0.189235
$465$	1.17040	0.0542760
$466$	13.8317	0.640742
$467$	1.87456	0.0867442	0.0433721	−	0.999059i	$-0.486190\pi$
$467$	1.87456	0.0867442	0.0433721	+	0.999059i	$0.486190\pi$
$468$	−17.5834	−0.812793
$469$	17.0970	0.789466
$470$	25.0630	1.15607
$471$	2.87436	0.132443
$472$	6.61282	0.304380
$473$	−52.7297	−2.42452
$474$	2.37428	0.109054
$475$	21.0733	0.966911
$476$	−8.04879	−0.368916
$477$	−5.97603	−0.273624
$478$	−17.3802	−0.794952
$479$	16.1755	0.739076	0.369538	−	0.929216i	$-0.379516\pi$
$479$	16.1755	0.739076	0.369538	+	0.929216i	$0.379516\pi$
$480$	−0.549327	−0.0250732
$481$	−39.1445	−1.78484
$482$	20.4973	0.933626
$483$	0.672703	0.0306090
$484$	26.8494	1.22043
$485$	34.6749	1.57451
$486$	−5.04698	−0.228936
$487$	31.0984	1.40920	0.704602	−	0.709603i	$-0.251126\pi$
$487$	31.0984	1.40920	0.704602	+	0.709603i	$0.251126\pi$
$488$	−9.43486	−0.427096
$489$	3.39460	0.153509
$490$	−16.0214	−0.723773
$491$	22.9088	1.03386	0.516929	−	0.856028i	$-0.327075\pi$
$491$	22.9088	1.03386	0.516929	+	0.856028i	$0.327075\pi$
$492$	0.828649	0.0373584
$493$	−9.26478	−0.417265
$494$	−37.1824	−1.67291
$495$	52.7300	2.37004
$496$	2.13061	0.0956672
$497$	51.2779	2.30013
$498$	−0.856474	−0.0383795
$499$	13.1235	0.587489	0.293745	−	0.955884i	$-0.405098\pi$
$499$	13.1235	0.587489	0.293745	+	0.955884i	$0.405098\pi$
$500$	−4.73590	−0.211796
$501$	0.717240	0.0320439
$502$	31.3790	1.40052
$503$	2.90459	0.129509	0.0647547	−	0.997901i	$-0.479374\pi$
$503$	2.90459	0.129509	0.0647547	+	0.997901i	$0.479374\pi$
$504$	10.4959	0.467526
$505$	−52.2259	−2.32402
$506$	6.15219	0.273498
$507$	4.21612	0.187244
$508$	12.4352	0.551721
$509$	−28.2199	−1.25083	−0.625413	−	0.780294i	$-0.715070\pi$
$509$	−28.2199	−1.25083	−0.625413	+	0.780294i	$0.715070\pi$
$510$	1.24855	0.0552868
$511$	−27.3303	−1.20902
$512$	−1.00000	−0.0441942
$513$	−7.10068	−0.313503
$514$	−29.3092	−1.29277
$515$	22.0917	0.973479
$516$	1.62815	0.0716753
$517$	53.3213	2.34507
$518$	23.3662	1.02665
$519$	−0.0173238	−0.000760431 0
$520$	−17.1553	−0.752311
$521$	−15.7099	−0.688263	−0.344131	−	0.938921i	$-0.611827\pi$
$521$	−15.7099	−0.688263	−0.344131	+	0.938921i	$0.611827\pi$
$522$	12.0816	0.528798
$523$	−8.59959	−0.376034	−0.188017	−	0.982166i	$-0.560206\pi$
$523$	−8.59959	−0.376034	−0.188017	+	0.982166i	$0.560206\pi$
$524$	−1.00000	−0.0436852
$525$	2.26181	0.0987137
$526$	−2.36319	−0.103040
$527$	−4.84261	−0.210947
$528$	−1.16869	−0.0508605
$529$	1.00000	0.0434783
$530$	−5.83055	−0.253263
$531$	19.5998	0.850560
$532$	22.1950	0.962275
$533$	25.8785	1.12092
$534$	0.624507	0.0270251
$535$	51.9213	2.24475
$536$	−4.82797	−0.208537
$537$	0.00869774	0.000375335 0
$538$	26.5681	1.14543
$539$	−34.0853	−1.46816
$540$	−3.27614	−0.140983
$541$	−22.0860	−0.949553	−0.474777	−	0.880106i	$-0.657471\pi$
$541$	−22.0860	−0.949553	−0.474777	+	0.880106i	$0.657471\pi$
$542$	9.59513	0.412146
$543$	1.41287	0.0606319
$544$	2.27288	0.0974487
$545$	−5.75070	−0.246333
$546$	−3.99080	−0.170791
$547$	−6.99452	−0.299064	−0.149532	−	0.988757i	$-0.547777\pi$
$547$	−6.99452	−0.299064	−0.149532	+	0.988757i	$0.547777\pi$
$548$	12.5385	0.535617
$549$	−27.9641	−1.19348
$550$	20.6854	0.882027
$551$	25.5481	1.08839
$552$	−0.189963	−0.00808535
$553$	−44.2608	−1.88216
$554$	11.5453	0.490513
$555$	−3.62464	−0.153857
$556$	−0.119746	−0.00507835
$557$	−7.73926	−0.327923	−0.163961	−	0.986467i	$-0.552427\pi$
$557$	−7.73926	−0.327923	−0.163961	+	0.986467i	$0.552427\pi$
$558$	6.31494	0.267333
$559$	50.8467	2.15059
$560$	10.2404	0.432736
$561$	2.65628	0.112148
$562$	−33.3589	−1.40716
$563$	20.6649	0.870921	0.435461	−	0.900208i	$-0.356586\pi$
$563$	20.6649	0.870921	0.435461	+	0.900208i	$0.356586\pi$
$564$	−1.64642	−0.0693267
$565$	−17.3031	−0.727948
$566$	2.17546	0.0914416
$567$	30.7256	1.29036
$568$	−14.4802	−0.607577
$569$	39.1349	1.64062	0.820311	−	0.571918i	$-0.193801\pi$
$569$	39.1349	1.64062	0.820311	+	0.571918i	$0.193801\pi$
$570$	−3.44295	−0.144209
$571$	−5.70353	−0.238685	−0.119343	−	0.992853i	$-0.538079\pi$
$571$	−5.70353	−0.238685	−0.119343	+	0.992853i	$0.538079\pi$
$572$	−36.4978	−1.52605
$573$	1.51628	0.0633434
$574$	−15.4475	−0.644765
$575$	3.36228	0.140217
$576$	−2.96391	−0.123496
$577$	1.28479	0.0534864	0.0267432	−	0.999642i	$-0.491486\pi$
$577$	1.28479	0.0534864	0.0267432	+	0.999642i	$0.491486\pi$
$578$	11.8340	0.492231
$579$	1.25997	0.0523624
$580$	11.7875	0.489449
$581$	15.9662	0.662388
$582$	−2.27783	−0.0944192
$583$	−12.4044	−0.513739
$584$	7.71772	0.319361
$585$	−50.8470	−2.10226
$586$	−22.9081	−0.946326
$587$	−42.9656	−1.77338	−0.886690	−	0.462364i	$-0.847001\pi$
$587$	−42.9656	−1.77338	−0.886690	+	0.462364i	$0.847001\pi$
$588$	1.05246	0.0434028
$589$	13.3538	0.550232
$590$	19.1227	0.787268
$591$	−0.797497	−0.0328046
$592$	−6.59833	−0.271190
$593$	38.6031	1.58524	0.792620	−	0.609716i	$-0.208717\pi$
$593$	38.6031	1.58524	0.792620	+	0.609716i	$0.208717\pi$
$594$	−6.96995	−0.285980
$595$	−23.2752	−0.954189
$596$	−3.18575	−0.130493
$597$	3.48148	0.142487
$598$	−5.93249	−0.242598
$599$	−29.0780	−1.18810	−0.594048	−	0.804430i	$-0.702471\pi$
$599$	−29.0780	−1.18810	−0.594048	+	0.804430i	$0.702471\pi$
$600$	−0.638707	−0.0260751
$601$	33.6553	1.37283	0.686415	−	0.727210i	$-0.259183\pi$
$601$	33.6553	1.37283	0.686415	+	0.727210i	$0.259183\pi$
$602$	−30.3516	−1.23704
$603$	−14.3097	−0.582736
$604$	−8.83049	−0.359308
$605$	77.6420	3.15660
$606$	3.43077	0.139366
$607$	−20.3468	−0.825851	−0.412926	−	0.910765i	$-0.635493\pi$
$607$	−20.3468	−0.825851	−0.412926	+	0.910765i	$0.635493\pi$
$608$	−6.26758	−0.254184
$609$	2.74210	0.111115
$610$	−27.2834	−1.10467
$611$	−51.4172	−2.08012
$612$	6.73661	0.272311
$613$	−5.47852	−0.221275	−0.110638	−	0.993861i	$-0.535289\pi$
$613$	−5.47852	−0.221275	−0.110638	+	0.993861i	$0.535289\pi$
$614$	10.2806	0.414890
$615$	2.39625	0.0966263
$616$	21.7864	0.877797
$617$	−40.4693	−1.62923	−0.814615	−	0.580002i	$-0.803052\pi$
$617$	−40.4693	−1.62923	−0.814615	+	0.580002i	$0.803052\pi$
$618$	−1.45123	−0.0583770
$619$	15.0384	0.604443	0.302221	−	0.953238i	$-0.402272\pi$
$619$	15.0384	0.604443	0.302221	+	0.953238i	$0.402272\pi$
$620$	6.16121	0.247440
$621$	−1.13292	−0.0454626
$622$	3.30278	0.132429
$623$	−11.6419	−0.466423
$624$	1.12695	0.0451142
$625$	−30.5065	−1.22026
$626$	34.9457	1.39671
$627$	−7.32484	−0.292526
$628$	15.1312	0.603799
$629$	14.9972	0.597977
$630$	30.3517	1.20924
$631$	30.3099	1.20662	0.603308	−	0.797508i	$-0.293849\pi$
$631$	30.3099	1.20662	0.603308	+	0.797508i	$0.293849\pi$
$632$	12.4987	0.497171
$633$	−2.76199	−0.109779
$634$	−26.9577	−1.07063
$635$	35.9595	1.42701
$636$	0.383015	0.0151875
$637$	32.8681	1.30228
$638$	25.0778	0.992838
$639$	−42.9182	−1.69782
$640$	−2.89176	−0.114307
$641$	45.3169	1.78991	0.894954	−	0.446158i	$-0.147208\pi$
$641$	45.3169	1.78991	0.894954	+	0.446158i	$0.147208\pi$
$642$	−3.41076	−0.134612
$643$	35.1771	1.38725	0.693624	−	0.720337i	$-0.256013\pi$
$643$	35.1771	1.38725	0.693624	+	0.720337i	$0.256013\pi$
$644$	3.54124	0.139544
$645$	4.70822	0.185386
$646$	14.2454	0.560479
$647$	8.85247	0.348026	0.174013	−	0.984743i	$-0.444326\pi$
$647$	8.85247	0.348026	0.174013	+	0.984743i	$0.444326\pi$
$648$	−8.67653	−0.340846
$649$	40.6833	1.59696
$650$	−19.9467	−0.782373
$651$	1.43327	0.0561742
$652$	17.8698	0.699836
$653$	−25.1951	−0.985959	−0.492980	−	0.870041i	$-0.664092\pi$
$653$	−25.1951	−0.985959	−0.492980	+	0.870041i	$0.664092\pi$
$654$	0.377769	0.0147720
$655$	−2.89176	−0.112990
$656$	4.36217	0.170314
$657$	22.8747	0.892425
$658$	30.6921	1.19650
$659$	4.18012	0.162834	0.0814172	−	0.996680i	$-0.474055\pi$
$659$	4.18012	0.162834	0.0814172	+	0.996680i	$0.474055\pi$
$660$	−3.37956	−0.131549
$661$	27.8615	1.08369	0.541844	−	0.840479i	$-0.317726\pi$
$661$	27.8615	1.08369	0.541844	+	0.840479i	$0.317726\pi$
$662$	−16.8104	−0.653355
$663$	−2.56142	−0.0994774
$664$	−4.50864	−0.174969
$665$	64.1826	2.48889
$666$	−19.5569	−0.757814
$667$	4.07624	0.157832
$668$	3.77569	0.146086
$669$	0.687796	0.0265917
$670$	−13.9613	−0.539374
$671$	−58.0450	−2.24080
$672$	−0.672703	−0.0259501
$673$	32.3848	1.24834	0.624171	−	0.781288i	$-0.285437\pi$
$673$	32.3848	1.24834	0.624171	+	0.781288i	$0.285437\pi$
$674$	36.3838	1.40145
$675$	−3.80920	−0.146616
$676$	22.1945	0.853633
$677$	7.97224	0.306398	0.153199	−	0.988195i	$-0.451042\pi$
$677$	7.97224	0.306398	0.153199	+	0.988195i	$0.451042\pi$
$678$	1.13666	0.0436532
$679$	42.4628	1.62957
$680$	6.57261	0.252048
$681$	−4.19347	−0.160694
$682$	13.1079	0.501928
$683$	−6.24812	−0.239078	−0.119539	−	0.992830i	$-0.538142\pi$
$683$	−6.24812	−0.239078	−0.119539	+	0.992830i	$0.538142\pi$
$684$	−18.5766	−0.710293
$685$	36.2582	1.38536
$686$	5.16894	0.197351
$687$	−3.23284	−0.123341
$688$	8.57089	0.326762
$689$	11.9615	0.455695
$690$	−0.549327	−0.0209125
$691$	−31.1292	−1.18421	−0.592105	−	0.805861i	$-0.701703\pi$
$691$	−31.1292	−1.18421	−0.592105	+	0.805861i	$0.701703\pi$
$692$	−0.0911958	−0.00346674
$693$	64.5729	2.45292
$694$	−25.0536	−0.951021
$695$	−0.346276	−0.0131350
$696$	−0.774333	−0.0293510
$697$	−9.91466	−0.375545
$698$	27.6068	1.04493
$699$	−2.62751	−0.0993816
$700$	11.9066	0.450028
$701$	−21.8112	−0.823796	−0.411898	−	0.911230i	$-0.635134\pi$
$701$	−21.8112	−0.823796	−0.411898	+	0.911230i	$0.635134\pi$
$702$	6.72105	0.253670
$703$	−41.3556	−1.55975
$704$	−6.15219	−0.231869
$705$	−4.76104	−0.179311
$706$	13.6199	0.512592
$707$	−63.9556	−2.40530
$708$	−1.25619	−0.0472105
$709$	−15.1891	−0.570438	−0.285219	−	0.958462i	$-0.592066\pi$
$709$	−15.1891	−0.570438	−0.285219	+	0.958462i	$0.592066\pi$
$710$	−41.8734	−1.57148
$711$	37.0450	1.38930
$712$	3.28752	0.123205
$713$	2.13061	0.0797919
$714$	1.52897	0.0572203
$715$	−105.543	−3.94708
$716$	0.0457866	0.00171112
$717$	3.30159	0.123300
$718$	8.09276	0.302019
$719$	−12.1156	−0.451834	−0.225917	−	0.974147i	$-0.572538\pi$
$719$	−12.1156	−0.451834	−0.225917	+	0.974147i	$0.572538\pi$
$720$	−8.57093	−0.319420
$721$	27.0535	1.00752
$722$	−20.2826	−0.754840
$723$	−3.89372	−0.144809
$724$	7.43760	0.276416
$725$	13.7054	0.509007
$726$	−5.10039	−0.189293
$727$	−11.0672	−0.410461	−0.205230	−	0.978714i	$-0.565794\pi$
$727$	−11.0672	−0.410461	−0.205230	+	0.978714i	$0.565794\pi$
$728$	−21.0084	−0.778621
$729$	−25.0709	−0.928550
$730$	22.3178	0.826019
$731$	−19.4806	−0.720515
$732$	1.79227	0.0662443
$733$	−29.8159	−1.10127	−0.550637	−	0.834745i	$-0.685615\pi$
$733$	−29.8159	−1.10127	−0.550637	+	0.834745i	$0.685615\pi$
$734$	11.1281	0.410747
$735$	3.04347	0.112260
$736$	−1.00000	−0.0368605
$737$	−29.7026	−1.09411
$738$	12.9291	0.475926
$739$	−20.5156	−0.754677	−0.377339	−	0.926075i	$-0.623161\pi$
$739$	−20.5156	−0.754677	−0.377339	+	0.926075i	$0.623161\pi$
$740$	−19.0808	−0.701424
$741$	7.06327	0.259476
$742$	−7.14006	−0.262120
$743$	−39.8890	−1.46338	−0.731692	−	0.681635i	$-0.761269\pi$
$743$	−39.8890	−1.46338	−0.731692	+	0.681635i	$0.761269\pi$
$744$	−0.404736	−0.0148384
$745$	−9.21241	−0.337517
$746$	−7.98559	−0.292373
$747$	−13.3632	−0.488935
$748$	13.9832	0.511275
$749$	63.5826	2.32326
$750$	0.899645	0.0328504
$751$	−7.12093	−0.259846	−0.129923	−	0.991524i	$-0.541473\pi$
$751$	−7.12093	−0.259846	−0.129923	+	0.991524i	$0.541473\pi$
$752$	−8.66705	−0.316055
$753$	−5.96085	−0.217225
$754$	−24.1822	−0.880665
$755$	−25.5357	−0.929338
$756$	−4.01194	−0.145913
$757$	25.4464	0.924867	0.462433	−	0.886654i	$-0.346976\pi$
$757$	25.4464	0.924867	0.462433	+	0.886654i	$0.346976\pi$
$758$	8.77145	0.318594
$759$	−1.16869	−0.0424206
$760$	−18.1243	−0.657439
$761$	−54.6140	−1.97975	−0.989877	−	0.141925i	$-0.954671\pi$
$761$	−54.6140	−1.97975	−0.989877	+	0.141925i	$0.954671\pi$
$762$	−2.36222	−0.0855741
$763$	−7.04228	−0.254948
$764$	7.98197	0.288778
$765$	19.4807	0.704325
$766$	−35.5386	−1.28406
$767$	−39.2305	−1.41653
$768$	0.189963	0.00685469
$769$	−25.5877	−0.922715	−0.461357	−	0.887214i	$-0.652637\pi$
$769$	−25.5877	−0.922715	−0.461357	+	0.887214i	$0.652637\pi$
$770$	63.0009	2.27040
$771$	5.56765	0.200514
$772$	6.63270	0.238716
$773$	−30.6616	−1.10282	−0.551411	−	0.834234i	$-0.685910\pi$
$773$	−30.6616	−1.10282	−0.551411	+	0.834234i	$0.685910\pi$
$774$	25.4034	0.913106
$775$	7.16370	0.257328
$776$	−11.9909	−0.430450
$777$	−4.43872	−0.159238
$778$	−5.01037	−0.179630
$779$	27.3402	0.979566
$780$	3.25888	0.116686
$781$	−89.0851	−3.18772
$782$	2.27288	0.0812779
$783$	−4.61806	−0.165036
$784$	5.54036	0.197870
$785$	43.7557	1.56171
$786$	0.189963	0.00677575
$787$	−32.0552	−1.14264	−0.571322	−	0.820726i	$-0.693569\pi$
$787$	−32.0552	−1.14264	−0.571322	+	0.820726i	$0.693569\pi$
$788$	−4.19817	−0.149554
$789$	0.448918	0.0159819
$790$	36.1432	1.28592
$791$	−21.1893	−0.753406
$792$	−18.2346	−0.647937
$793$	55.9722	1.98763
$794$	−12.8764	−0.456965
$795$	1.10759	0.0392821
$796$	18.3272	0.649589
$797$	−38.2678	−1.35551	−0.677757	−	0.735286i	$-0.737048\pi$
$797$	−38.2678	−1.35551	−0.677757	+	0.735286i	$0.737048\pi$
$798$	−4.21622	−0.149253
$799$	19.6991	0.696905
$800$	−3.36228	−0.118874
$801$	9.74394	0.344285
$802$	−24.5864	−0.868176
$803$	47.4808	1.67556
$804$	0.917135	0.0323449
$805$	10.2404	0.360927
$806$	−12.6398	−0.445219
$807$	−5.04695	−0.177661
$808$	18.0602	0.635357
$809$	24.9488	0.877153	0.438576	−	0.898694i	$-0.355483\pi$
$809$	24.9488	0.877153	0.438576	+	0.898694i	$0.355483\pi$
$810$	−25.0904	−0.881588
$811$	18.2170	0.639684	0.319842	−	0.947471i	$-0.396370\pi$
$811$	18.2170	0.639684	0.319842	+	0.947471i	$0.396370\pi$
$812$	14.4349	0.506566
$813$	−1.82272	−0.0639255
$814$	−40.5941	−1.42282
$815$	51.6752	1.81010
$816$	−0.431762	−0.0151147
$817$	53.7188	1.87938
$818$	13.2657	0.463825
$819$	−62.2670	−2.17578
$820$	12.6143	0.440512
$821$	−50.7069	−1.76968	−0.884841	−	0.465893i	$-0.845733\pi$
$821$	−50.7069	−1.76968	−0.884841	+	0.465893i	$0.845733\pi$
$822$	−2.38184	−0.0830762
$823$	−24.4435	−0.852046	−0.426023	−	0.904712i	$-0.640086\pi$
$823$	−24.4435	−0.852046	−0.426023	+	0.904712i	$0.640086\pi$
$824$	−7.63955	−0.266136
$825$	−3.92945	−0.136806
$826$	23.4175	0.814801
$827$	6.33668	0.220348	0.110174	−	0.993912i	$-0.464859\pi$
$827$	6.33668	0.220348	0.110174	+	0.993912i	$0.464859\pi$
$828$	−2.96391	−0.103003
$829$	−2.59608	−0.0901656	−0.0450828	−	0.998983i	$-0.514355\pi$
$829$	−2.59608	−0.0901656	−0.0450828	+	0.998983i	$0.514355\pi$
$830$	−13.0379	−0.452552
$831$	−2.19318	−0.0760805
$832$	5.93249	0.205672
$833$	−12.5925	−0.436306
$834$	0.0227472	0.000787672 0
$835$	10.9184	0.377846
$836$	−38.5593	−1.33360
$837$	−2.41381	−0.0834336
$838$	25.2875	0.873543
$839$	41.7678	1.44198	0.720992	−	0.692944i	$-0.243687\pi$
$839$	41.7678	1.44198	0.720992	+	0.692944i	$0.243687\pi$
$840$	−1.94530	−0.0671191
$841$	−12.3843	−0.427045
$842$	−11.4673	−0.395188
$843$	6.33695	0.218256
$844$	−14.5397	−0.500475
$845$	64.1810	2.20789
$846$	−25.6884	−0.883185
$847$	95.0801	3.26699
$848$	2.01626	0.0692388
$849$	−0.413257	−0.0141829
$850$	7.64204	0.262120
$851$	−6.59833	−0.226188
$852$	2.75070	0.0942376
$853$	−46.5023	−1.59221	−0.796103	−	0.605160i	$-0.793109\pi$
$853$	−46.5023	−1.59221	−0.796103	+	0.605160i	$0.793109\pi$
$854$	−33.4111	−1.14330
$855$	−53.7190	−1.83715
$856$	−17.9549	−0.613686
$857$	−38.5634	−1.31730	−0.658651	−	0.752449i	$-0.728873\pi$
$857$	−38.5634	−1.31730	−0.658651	+	0.752449i	$0.728873\pi$
$858$	6.93322	0.236696
$859$	−26.0303	−0.888142	−0.444071	−	0.895992i	$-0.646466\pi$
$859$	−26.0303	−0.888142	−0.444071	+	0.895992i	$0.646466\pi$
$860$	24.7850	0.845160
$861$	2.93444	0.100006
$862$	−15.6022	−0.531415
$863$	−50.5777	−1.72169	−0.860843	−	0.508870i	$-0.830063\pi$
$863$	−50.5777	−1.72169	−0.860843	+	0.508870i	$0.830063\pi$
$864$	1.13292	0.0385428
$865$	−0.263716	−0.00896663
$866$	34.9616	1.18804
$867$	−2.24803	−0.0763470
$868$	7.54499	0.256094
$869$	76.8942	2.60846
$870$	−2.23919	−0.0759155
$871$	28.6419	0.970494
$872$	1.98865	0.0673442
$873$	−35.5401	−1.20285
$874$	−6.26758	−0.212004
$875$	−16.7710	−0.566962
$876$	−1.46608	−0.0495342
$877$	43.3307	1.46317	0.731587	−	0.681748i	$-0.238780\pi$
$877$	43.3307	1.46317	0.731587	+	0.681748i	$0.238780\pi$
$878$	−21.8011	−0.735751
$879$	4.35169	0.146779
$880$	−17.7906	−0.599723
$881$	17.8541	0.601521	0.300760	−	0.953700i	$-0.402760\pi$
$881$	17.8541	0.601521	0.300760	+	0.953700i	$0.402760\pi$
$882$	16.4211	0.552929
$883$	39.8155	1.33990	0.669948	−	0.742408i	$-0.266316\pi$
$883$	39.8155	1.33990	0.669948	+	0.742408i	$0.266316\pi$
$884$	−13.4838	−0.453510
$885$	−3.63260	−0.122108
$886$	−28.4231	−0.954893
$887$	−34.6752	−1.16428	−0.582140	−	0.813089i	$-0.697784\pi$
$887$	−34.6752	−1.16428	−0.582140	+	0.813089i	$0.697784\pi$
$888$	1.25344	0.0420626
$889$	44.0359	1.47692
$890$	9.50673	0.318666
$891$	−53.3796	−1.78829
$892$	3.62069	0.121230
$893$	−54.3215	−1.81780
$894$	0.605173	0.0202400
$895$	0.132404	0.00442577
$896$	−3.54124	−0.118304
$897$	1.12695	0.0376278
$898$	6.16703	0.205796
$899$	8.68487	0.289656
$900$	−9.96550	−0.332183
$901$	−4.58271	−0.152672
$902$	26.8369	0.893570
$903$	5.76567	0.191869
$904$	5.98359	0.199011
$905$	21.5078	0.714942
$906$	1.67746	0.0557300
$907$	45.2896	1.50382	0.751908	−	0.659268i	$-0.229134\pi$
$907$	45.2896	1.50382	0.751908	+	0.659268i	$0.229134\pi$
$908$	−22.0752	−0.732593
$909$	53.5290	1.77545
$910$	−60.7511	−2.01388
$911$	22.7157	0.752606	0.376303	−	0.926497i	$-0.377195\pi$
$911$	22.7157	0.752606	0.376303	+	0.926497i	$0.377195\pi$
$912$	1.19061	0.0394249
$913$	−27.7380	−0.917994
$914$	−10.6997	−0.353914
$915$	5.18282	0.171339
$916$	−17.0183	−0.562300
$917$	−3.54124	−0.116942
$918$	−2.57499	−0.0849873
$919$	−29.6297	−0.977392	−0.488696	−	0.872454i	$-0.662527\pi$
$919$	−29.6297	−0.977392	−0.488696	+	0.872454i	$0.662527\pi$
$920$	−2.89176	−0.0953385
$921$	−1.95292	−0.0643510
$922$	−18.8432	−0.620568
$923$	85.9038	2.82756
$924$	−4.13860	−0.136150
$925$	−22.1854	−0.729452
$926$	−28.3465	−0.931523
$927$	−22.6430	−0.743693
$928$	−4.07624	−0.133809
$929$	12.8120	0.420347	0.210174	−	0.977664i	$-0.432597\pi$
$929$	12.8120	0.420347	0.210174	+	0.977664i	$0.432597\pi$
$930$	−1.17040	−0.0383789
$931$	34.7247	1.13805
$932$	−13.8317	−0.453073
$933$	−0.627405	−0.0205403
$934$	−1.87456	−0.0613374
$935$	40.4359	1.32240
$936$	17.5834	0.574731
$937$	28.7942	0.940665	0.470332	−	0.882489i	$-0.344134\pi$
$937$	28.7942	0.940665	0.470332	+	0.882489i	$0.344134\pi$
$938$	−17.0970	−0.558237
$939$	−6.63837	−0.216635
$940$	−25.0630	−0.817466
$941$	−20.7913	−0.677776	−0.338888	−	0.940827i	$-0.610051\pi$
$941$	−20.7913	−0.677776	−0.338888	+	0.940827i	$0.610051\pi$
$942$	−2.87436	−0.0936516
$943$	4.36217	0.142052
$944$	−6.61282	−0.215229
$945$	−11.6016	−0.377399
$946$	52.7297	1.71439
$947$	29.1211	0.946310	0.473155	−	0.880979i	$-0.343115\pi$
$947$	29.1211	0.946310	0.473155	+	0.880979i	$0.343115\pi$
$948$	−2.37428	−0.0771132
$949$	−45.7853	−1.48625
$950$	−21.0733	−0.683710
$951$	5.12095	0.166058
$952$	8.04879	0.260863
$953$	9.68198	0.313630	0.156815	−	0.987628i	$-0.449877\pi$
$953$	9.68198	0.313630	0.156815	+	0.987628i	$0.449877\pi$
$954$	5.97603	0.193481
$955$	23.0819	0.746914
$956$	17.3802	0.562116
$957$	−4.76384	−0.153993
$958$	−16.1755	−0.522606
$959$	44.4017	1.43380
$960$	0.549327	0.0177294
$961$	−26.4605	−0.853565
$962$	39.1445	1.26207
$963$	−53.2168	−1.71489
$964$	−20.4973	−0.660173
$965$	19.1802	0.617432
$966$	−0.672703	−0.0216439
$967$	3.46730	0.111501	0.0557505	−	0.998445i	$-0.482245\pi$
$967$	3.46730	0.111501	0.0557505	+	0.998445i	$0.482245\pi$
$968$	−26.8494	−0.862973
$969$	−2.70610	−0.0869325
$970$	−34.6749	−1.11335
$971$	28.1547	0.903528	0.451764	−	0.892137i	$-0.350795\pi$
$971$	28.1547	0.903528	0.451764	+	0.892137i	$0.350795\pi$
$972$	5.04698	0.161882
$973$	−0.424048	−0.0135944
$974$	−31.0984	−0.996458
$975$	3.78913	0.121349
$976$	9.43486	0.302003
$977$	10.5354	0.337058	0.168529	−	0.985697i	$-0.446098\pi$
$977$	10.5354	0.337058	0.168529	+	0.985697i	$0.446098\pi$
$978$	−3.39460	−0.108547
$979$	20.2255	0.646408
$980$	16.0214	0.511784
$981$	5.89419	0.188187
$982$	−22.9088	−0.731048
$983$	−20.8543	−0.665150	−0.332575	−	0.943077i	$-0.607917\pi$
$983$	−20.8543	−0.665150	−0.332575	+	0.943077i	$0.607917\pi$
$984$	−0.828649	−0.0264164
$985$	−12.1401	−0.386816
$986$	9.26478	0.295051
$987$	−5.83035	−0.185582
$988$	37.1824	1.18293
$989$	8.57089	0.272539
$990$	−52.7300	−1.67587
$991$	−29.3567	−0.932545	−0.466272	−	0.884641i	$-0.654403\pi$
$991$	−29.3567	−0.932545	−0.466272	+	0.884641i	$0.654403\pi$
$992$	−2.13061	−0.0676469
$993$	3.19335	0.101338
$994$	−51.2779	−1.62644
$995$	52.9978	1.68014
$996$	0.856474	0.0271384
$997$	−41.0929	−1.30142	−0.650712	−	0.759325i	$-0.725529\pi$
$997$	−41.0929	−1.30142	−0.650712	+	0.759325i	$0.725529\pi$
$998$	−13.1235	−0.415418
$999$	7.47539	0.236511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.j.1.17	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.j.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.189963 q^{3} +1.00000 q^{4} +2.89176 q^{5} -0.189963 q^{6} +3.54124 q^{7} -1.00000 q^{8} -2.96391 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.189963 q^{3} +1.00000 q^{4} +2.89176 q^{5} -0.189963 q^{6} +3.54124 q^{7} -1.00000 q^{8} -2.96391 q^{9} -2.89176 q^{10} -6.15219 q^{11} +0.189963 q^{12} +5.93249 q^{13} -3.54124 q^{14} +0.549327 q^{15} +1.00000 q^{16} -2.27288 q^{17} +2.96391 q^{18} +6.26758 q^{19} +2.89176 q^{20} +0.672703 q^{21} +6.15219 q^{22} +1.00000 q^{23} -0.189963 q^{24} +3.36228 q^{25} -5.93249 q^{26} -1.13292 q^{27} +3.54124 q^{28} +4.07624 q^{29} -0.549327 q^{30} +2.13061 q^{31} -1.00000 q^{32} -1.16869 q^{33} +2.27288 q^{34} +10.2404 q^{35} -2.96391 q^{36} -6.59833 q^{37} -6.26758 q^{38} +1.12695 q^{39} -2.89176 q^{40} +4.36217 q^{41} -0.672703 q^{42} +8.57089 q^{43} -6.15219 q^{44} -8.57093 q^{45} -1.00000 q^{46} -8.66705 q^{47} +0.189963 q^{48} +5.54036 q^{49} -3.36228 q^{50} -0.431762 q^{51} +5.93249 q^{52} +2.01626 q^{53} +1.13292 q^{54} -17.7906 q^{55} -3.54124 q^{56} +1.19061 q^{57} -4.07624 q^{58} -6.61282 q^{59} +0.549327 q^{60} +9.43486 q^{61} -2.13061 q^{62} -10.4959 q^{63} +1.00000 q^{64} +17.1553 q^{65} +1.16869 q^{66} +4.82797 q^{67} -2.27288 q^{68} +0.189963 q^{69} -10.2404 q^{70} +14.4802 q^{71} +2.96391 q^{72} -7.71772 q^{73} +6.59833 q^{74} +0.638707 q^{75} +6.26758 q^{76} -21.7864 q^{77} -1.12695 q^{78} -12.4987 q^{79} +2.89176 q^{80} +8.67653 q^{81} -4.36217 q^{82} +4.50864 q^{83} +0.672703 q^{84} -6.57261 q^{85} -8.57089 q^{86} +0.774333 q^{87} +6.15219 q^{88} -3.28752 q^{89} +8.57093 q^{90} +21.0084 q^{91} +1.00000 q^{92} +0.404736 q^{93} +8.66705 q^{94} +18.1243 q^{95} -0.189963 q^{96} +11.9909 q^{97} -5.54036 q^{98} +18.2346 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) \) 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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