LMFDB - Embedded newform 6026.2.a.j.1.11

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			1.11
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.46112 q^{3} +1.00000 q^{4} +2.24970 q^{5} +1.46112 q^{6} -0.440676 q^{7} -1.00000 q^{8} -0.865116 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.46112 q^{3} +1.00000 q^{4} +2.24970 q^{5} +1.46112 q^{6} -0.440676 q^{7} -1.00000 q^{8} -0.865116 q^{9} -2.24970 q^{10} -1.12539 q^{11} -1.46112 q^{12} -4.90241 q^{13} +0.440676 q^{14} -3.28710 q^{15} +1.00000 q^{16} +4.96419 q^{17} +0.865116 q^{18} -6.89044 q^{19} +2.24970 q^{20} +0.643882 q^{21} +1.12539 q^{22} +1.00000 q^{23} +1.46112 q^{24} +0.0611639 q^{25} +4.90241 q^{26} +5.64741 q^{27} -0.440676 q^{28} -0.760717 q^{29} +3.28710 q^{30} -8.34672 q^{31} -1.00000 q^{32} +1.64434 q^{33} -4.96419 q^{34} -0.991390 q^{35} -0.865116 q^{36} -7.03644 q^{37} +6.89044 q^{38} +7.16302 q^{39} -2.24970 q^{40} +4.52026 q^{41} -0.643882 q^{42} +6.09141 q^{43} -1.12539 q^{44} -1.94625 q^{45} -1.00000 q^{46} +6.01866 q^{47} -1.46112 q^{48} -6.80580 q^{49} -0.0611639 q^{50} -7.25331 q^{51} -4.90241 q^{52} -6.57361 q^{53} -5.64741 q^{54} -2.53180 q^{55} +0.440676 q^{56} +10.0678 q^{57} +0.760717 q^{58} -9.59430 q^{59} -3.28710 q^{60} -6.70180 q^{61} +8.34672 q^{62} +0.381236 q^{63} +1.00000 q^{64} -11.0290 q^{65} -1.64434 q^{66} +14.0502 q^{67} +4.96419 q^{68} -1.46112 q^{69} +0.991390 q^{70} +14.3353 q^{71} +0.865116 q^{72} -9.48910 q^{73} +7.03644 q^{74} -0.0893680 q^{75} -6.89044 q^{76} +0.495933 q^{77} -7.16302 q^{78} +1.45246 q^{79} +2.24970 q^{80} -5.65623 q^{81} -4.52026 q^{82} +15.5976 q^{83} +0.643882 q^{84} +11.1680 q^{85} -6.09141 q^{86} +1.11150 q^{87} +1.12539 q^{88} +17.9125 q^{89} +1.94625 q^{90} +2.16037 q^{91} +1.00000 q^{92} +12.1956 q^{93} -6.01866 q^{94} -15.5014 q^{95} +1.46112 q^{96} -10.2914 q^{97} +6.80580 q^{98} +0.973594 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.46112	−0.843581	−0.421790	−	0.906693i	$-0.638598\pi$
$3$	−1.46112	−0.843581	−0.421790	+	0.906693i	$0.638598\pi$
$4$	1.00000	0.500000
$5$	2.24970	1.00610	0.503049	−	0.864258i	$-0.332212\pi$
$5$	2.24970	1.00610	0.503049	+	0.864258i	$0.332212\pi$
$6$	1.46112	0.596502
$7$	−0.440676	−0.166560	−0.0832799	−	0.996526i	$-0.526540\pi$
$7$	−0.440676	−0.166560	−0.0832799	+	0.996526i	$0.526540\pi$
$8$	−1.00000	−0.353553
$9$	−0.865116	−0.288372
$10$	−2.24970	−0.711419
$11$	−1.12539	−0.339318	−0.169659	−	0.985503i	$-0.554267\pi$
$11$	−1.12539	−0.339318	−0.169659	+	0.985503i	$0.554267\pi$
$12$	−1.46112	−0.421790
$13$	−4.90241	−1.35968	−0.679841	−	0.733359i	$-0.737951\pi$
$13$	−4.90241	−1.35968	−0.679841	+	0.733359i	$0.737951\pi$
$14$	0.440676	0.117776
$15$	−3.28710	−0.848725
$16$	1.00000	0.250000
$17$	4.96419	1.20399	0.601997	−	0.798498i	$-0.294372\pi$
$17$	4.96419	1.20399	0.601997	+	0.798498i	$0.294372\pi$
$18$	0.865116	0.203910
$19$	−6.89044	−1.58077	−0.790387	−	0.612607i	$-0.790121\pi$
$19$	−6.89044	−1.58077	−0.790387	+	0.612607i	$0.790121\pi$
$20$	2.24970	0.503049
$21$	0.643882	0.140507
$22$	1.12539	0.239934
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.46112	0.298251
$25$	0.0611639	0.0122328
$26$	4.90241	0.961441
$27$	5.64741	1.08685
$28$	−0.440676	−0.0832799
$29$	−0.760717	−0.141262	−0.0706308	−	0.997503i	$-0.522501\pi$
$29$	−0.760717	−0.141262	−0.0706308	+	0.997503i	$0.522501\pi$
$30$	3.28710	0.600139
$31$	−8.34672	−1.49912	−0.749558	−	0.661939i	$-0.769734\pi$
$31$	−8.34672	−1.49912	−0.749558	+	0.661939i	$0.769734\pi$
$32$	−1.00000	−0.176777
$33$	1.64434	0.286242
$34$	−4.96419	−0.851352
$35$	−0.991390	−0.167575
$36$	−0.865116	−0.144186
$37$	−7.03644	−1.15678	−0.578392	−	0.815759i	$-0.696320\pi$
$37$	−7.03644	−1.15678	−0.578392	+	0.815759i	$0.696320\pi$
$38$	6.89044	1.11778
$39$	7.16302	1.14700
$40$	−2.24970	−0.355709
$41$	4.52026	0.705947	0.352973	−	0.935633i	$-0.385171\pi$
$41$	4.52026	0.705947	0.352973	+	0.935633i	$0.385171\pi$
$42$	−0.643882	−0.0993532
$43$	6.09141	0.928931	0.464466	−	0.885591i	$-0.346246\pi$
$43$	6.09141	0.928931	0.464466	+	0.885591i	$0.346246\pi$
$44$	−1.12539	−0.169659
$45$	−1.94625	−0.290130
$46$	−1.00000	−0.147442
$47$	6.01866	0.877912	0.438956	−	0.898508i	$-0.355348\pi$
$47$	6.01866	0.877912	0.438956	+	0.898508i	$0.355348\pi$
$48$	−1.46112	−0.210895
$49$	−6.80580	−0.972258
$50$	−0.0611639	−0.00864988
$51$	−7.25331	−1.01567
$52$	−4.90241	−0.679841
$53$	−6.57361	−0.902955	−0.451477	−	0.892283i	$-0.649103\pi$
$53$	−6.57361	−0.902955	−0.451477	+	0.892283i	$0.649103\pi$
$54$	−5.64741	−0.768516
$55$	−2.53180	−0.341388
$56$	0.440676	0.0588878
$57$	10.0678	1.33351
$58$	0.760717	0.0998870
$59$	−9.59430	−1.24907	−0.624536	−	0.780996i	$-0.714712\pi$
$59$	−9.59430	−1.24907	−0.624536	+	0.780996i	$0.714712\pi$
$60$	−3.28710	−0.424362
$61$	−6.70180	−0.858077	−0.429039	−	0.903286i	$-0.641148\pi$
$61$	−6.70180	−0.858077	−0.429039	+	0.903286i	$0.641148\pi$
$62$	8.34672	1.06003
$63$	0.381236	0.0480312
$64$	1.00000	0.125000
$65$	−11.0290	−1.36797
$66$	−1.64434	−0.202404
$67$	14.0502	1.71650	0.858250	−	0.513231i	$-0.171552\pi$
$67$	14.0502	1.71650	0.858250	+	0.513231i	$0.171552\pi$
$68$	4.96419	0.601997
$69$	−1.46112	−0.175899
$70$	0.991390	0.118494
$71$	14.3353	1.70129	0.850645	−	0.525740i	$-0.176212\pi$
$71$	14.3353	1.70129	0.850645	+	0.525740i	$0.176212\pi$
$72$	0.865116	0.101955
$73$	−9.48910	−1.11062	−0.555308	−	0.831645i	$-0.687400\pi$
$73$	−9.48910	−1.11062	−0.555308	+	0.831645i	$0.687400\pi$
$74$	7.03644	0.817970
$75$	−0.0893680	−0.0103193
$76$	−6.89044	−0.790387
$77$	0.495933	0.0565168
$78$	−7.16302	−0.811053
$79$	1.45246	0.163415	0.0817073	−	0.996656i	$-0.473963\pi$
$79$	1.45246	0.163415	0.0817073	+	0.996656i	$0.473963\pi$
$80$	2.24970	0.251524
$81$	−5.65623	−0.628470
$82$	−4.52026	−0.499180
$83$	15.5976	1.71206	0.856030	−	0.516926i	$-0.172924\pi$
$83$	15.5976	1.71206	0.856030	+	0.516926i	$0.172924\pi$
$84$	0.643882	0.0702533
$85$	11.1680	1.21134
$86$	−6.09141	−0.656853
$87$	1.11150	0.119165
$88$	1.12539	0.119967
$89$	17.9125	1.89872	0.949359	−	0.314195i	$-0.101735\pi$
$89$	17.9125	1.89872	0.949359	+	0.314195i	$0.101735\pi$
$90$	1.94625	0.205153
$91$	2.16037	0.226469
$92$	1.00000	0.104257
$93$	12.1956	1.26462
$94$	−6.01866	−0.620778
$95$	−15.5014	−1.59041
$96$	1.46112	0.149125
$97$	−10.2914	−1.04494	−0.522468	−	0.852659i	$-0.674989\pi$
$97$	−10.2914	−1.04494	−0.522468	+	0.852659i	$0.674989\pi$
$98$	6.80580	0.687490
$99$	0.973594	0.0978499
$100$	0.0611639	0.00611639
$101$	8.68997	0.864684	0.432342	−	0.901710i	$-0.357687\pi$
$101$	8.68997	0.864684	0.432342	+	0.901710i	$0.357687\pi$
$102$	7.25331	0.718184
$103$	3.02852	0.298409	0.149205	−	0.988806i	$-0.452329\pi$
$103$	3.02852	0.298409	0.149205	+	0.988806i	$0.452329\pi$
$104$	4.90241	0.480720
$105$	1.44854	0.141363
$106$	6.57361	0.638485
$107$	2.69758	0.260785	0.130393	−	0.991462i	$-0.458376\pi$
$107$	2.69758	0.260785	0.130393	+	0.991462i	$0.458376\pi$
$108$	5.64741	0.543423
$109$	16.5926	1.58928	0.794642	−	0.607078i	$-0.207658\pi$
$109$	16.5926	1.58928	0.794642	+	0.607078i	$0.207658\pi$
$110$	2.53180	0.241397
$111$	10.2811	0.975841
$112$	−0.440676	−0.0416400
$113$	14.7889	1.39123	0.695613	−	0.718417i	$-0.255133\pi$
$113$	14.7889	1.39123	0.695613	+	0.718417i	$0.255133\pi$
$114$	−10.0678	−0.942935
$115$	2.24970	0.209786
$116$	−0.760717	−0.0706308
$117$	4.24115	0.392094
$118$	9.59430	0.883227
$119$	−2.18760	−0.200537
$120$	3.28710	0.300069
$121$	−9.73349	−0.884863
$122$	6.70180	0.606752
$123$	−6.60467	−0.595523
$124$	−8.34672	−0.749558
$125$	−11.1109	−0.993790
$126$	−0.381236	−0.0339632
$127$	−13.1248	−1.16464	−0.582318	−	0.812961i	$-0.697854\pi$
$127$	−13.1248	−1.16464	−0.582318	+	0.812961i	$0.697854\pi$
$128$	−1.00000	−0.0883883
$129$	−8.90031	−0.783628
$130$	11.0290	0.967303
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	1.64434	0.143121
$133$	3.03645	0.263294
$134$	−14.0502	−1.21375
$135$	12.7050	1.09347
$136$	−4.96419	−0.425676
$137$	−15.0747	−1.28791	−0.643957	−	0.765061i	$-0.722709\pi$
$137$	−15.0747	−1.28791	−0.643957	+	0.765061i	$0.722709\pi$
$138$	1.46112	0.124379
$139$	10.5681	0.896375	0.448187	−	0.893940i	$-0.352070\pi$
$139$	10.5681	0.896375	0.448187	+	0.893940i	$0.352070\pi$
$140$	−0.991390	−0.0837877
$141$	−8.79402	−0.740590
$142$	−14.3353	−1.20299
$143$	5.51713	0.461365
$144$	−0.865116	−0.0720930
$145$	−1.71139	−0.142123
$146$	9.48910	0.785324
$147$	9.94413	0.820178
$148$	−7.03644	−0.578392
$149$	14.5520	1.19215	0.596075	−	0.802929i	$-0.296726\pi$
$149$	14.5520	1.19215	0.596075	+	0.802929i	$0.296726\pi$
$150$	0.0893680	0.00729687
$151$	−0.269651	−0.0219439	−0.0109719	−	0.999940i	$-0.503493\pi$
$151$	−0.269651	−0.0219439	−0.0109719	+	0.999940i	$0.503493\pi$
$152$	6.89044	0.558888
$153$	−4.29460	−0.347198
$154$	−0.495933	−0.0399634
$155$	−18.7776	−1.50826
$156$	7.16302	0.573501
$157$	−1.20217	−0.0959440	−0.0479720	−	0.998849i	$-0.515276\pi$
$157$	−1.20217	−0.0959440	−0.0479720	+	0.998849i	$0.515276\pi$
$158$	−1.45246	−0.115552
$159$	9.60486	0.761715
$160$	−2.24970	−0.177855
$161$	−0.440676	−0.0347301
$162$	5.65623	0.444395
$163$	20.1883	1.58127	0.790634	−	0.612288i	$-0.209751\pi$
$163$	20.1883	1.58127	0.790634	+	0.612288i	$0.209751\pi$
$164$	4.52026	0.352973
$165$	3.69927	0.287988
$166$	−15.5976	−1.21061
$167$	−9.85766	−0.762809	−0.381404	−	0.924408i	$-0.624559\pi$
$167$	−9.85766	−0.762809	−0.381404	+	0.924408i	$0.624559\pi$
$168$	−0.643882	−0.0496766
$169$	11.0336	0.848737
$170$	−11.1680	−0.856544
$171$	5.96102	0.455851
$172$	6.09141	0.464466
$173$	3.43267	0.260981	0.130490	−	0.991450i	$-0.458345\pi$
$173$	3.43267	0.260981	0.130490	+	0.991450i	$0.458345\pi$
$174$	−1.11150	−0.0842627
$175$	−0.0269535	−0.00203749
$176$	−1.12539	−0.0848296
$177$	14.0185	1.05369
$178$	−17.9125	−1.34260
$179$	6.48909	0.485017	0.242509	−	0.970149i	$-0.422030\pi$
$179$	6.48909	0.485017	0.242509	+	0.970149i	$0.422030\pi$
$180$	−1.94625	−0.145065
$181$	−17.0889	−1.27021	−0.635106	−	0.772425i	$-0.719043\pi$
$181$	−17.0889	−1.27021	−0.635106	+	0.772425i	$0.719043\pi$
$182$	−2.16037	−0.160137
$183$	9.79216	0.723857
$184$	−1.00000	−0.0737210
$185$	−15.8299	−1.16384
$186$	−12.1956	−0.894225
$187$	−5.58666	−0.408537
$188$	6.01866	0.438956
$189$	−2.48868	−0.181025
$190$	15.5014	1.12459
$191$	12.6961	0.918659	0.459330	−	0.888266i	$-0.348090\pi$
$191$	12.6961	0.918659	0.459330	+	0.888266i	$0.348090\pi$
$192$	−1.46112	−0.105448
$193$	3.14487	0.226373	0.113186	−	0.993574i	$-0.463894\pi$
$193$	3.14487	0.226373	0.113186	+	0.993574i	$0.463894\pi$
$194$	10.2914	0.738881
$195$	16.1147	1.15400
$196$	−6.80580	−0.486129
$197$	−22.9086	−1.63217	−0.816087	−	0.577929i	$-0.803861\pi$
$197$	−22.9086	−1.63217	−0.816087	+	0.577929i	$0.803861\pi$
$198$	−0.973594	−0.0691903
$199$	9.20918	0.652822	0.326411	−	0.945228i	$-0.394161\pi$
$199$	9.20918	0.652822	0.326411	+	0.945228i	$0.394161\pi$
$200$	−0.0611639	−0.00432494
$201$	−20.5290	−1.44801
$202$	−8.68997	−0.611424
$203$	0.335229	0.0235285
$204$	−7.25331	−0.507833
$205$	10.1693	0.710251
$206$	−3.02852	−0.211007
$207$	−0.865116	−0.0601297
$208$	−4.90241	−0.339921
$209$	7.75444	0.536386
$210$	−1.44854	−0.0999590
$211$	16.7371	1.15223	0.576114	−	0.817369i	$-0.304568\pi$
$211$	16.7371	1.15223	0.576114	+	0.817369i	$0.304568\pi$
$212$	−6.57361	−0.451477
$213$	−20.9457	−1.43518
$214$	−2.69758	−0.184403
$215$	13.7039	0.934595
$216$	−5.64741	−0.384258
$217$	3.67820	0.249692
$218$	−16.5926	−1.12379
$219$	13.8648	0.936894
$220$	−2.53180	−0.170694
$221$	−24.3365	−1.63705
$222$	−10.2811	−0.690024
$223$	−15.1546	−1.01483	−0.507414	−	0.861703i	$-0.669398\pi$
$223$	−15.1546	−1.01483	−0.507414	+	0.861703i	$0.669398\pi$
$224$	0.440676	0.0294439
$225$	−0.0529138	−0.00352759
$226$	−14.7889	−0.983745
$227$	−0.897588	−0.0595750	−0.0297875	−	0.999556i	$-0.509483\pi$
$227$	−0.897588	−0.0595750	−0.0297875	+	0.999556i	$0.509483\pi$
$228$	10.0678	0.666755
$229$	0.656611	0.0433901	0.0216951	−	0.999765i	$-0.493094\pi$
$229$	0.656611	0.0433901	0.0216951	+	0.999765i	$0.493094\pi$
$230$	−2.24970	−0.148341
$231$	−0.724620	−0.0476765
$232$	0.760717	0.0499435
$233$	8.13109	0.532686	0.266343	−	0.963878i	$-0.414185\pi$
$233$	8.13109	0.532686	0.266343	+	0.963878i	$0.414185\pi$
$234$	−4.24115	−0.277252
$235$	13.5402	0.883266
$236$	−9.59430	−0.624536
$237$	−2.12223	−0.137853
$238$	2.18760	0.141801
$239$	7.49695	0.484937	0.242469	−	0.970159i	$-0.422043\pi$
$239$	7.49695	0.484937	0.242469	+	0.970159i	$0.422043\pi$
$240$	−3.28710	−0.212181
$241$	−26.8774	−1.73133	−0.865663	−	0.500627i	$-0.833103\pi$
$241$	−26.8774	−1.73133	−0.865663	+	0.500627i	$0.833103\pi$
$242$	9.73349	0.625693
$243$	−8.67779	−0.556681
$244$	−6.70180	−0.429039
$245$	−15.3110	−0.978186
$246$	6.60467	0.421098
$247$	33.7797	2.14935
$248$	8.34672	0.530017
$249$	−22.7900	−1.44426
$250$	11.1109	0.702716
$251$	20.5994	1.30022	0.650112	−	0.759838i	$-0.274722\pi$
$251$	20.5994	1.30022	0.650112	+	0.759838i	$0.274722\pi$
$252$	0.381236	0.0240156
$253$	−1.12539	−0.0707528
$254$	13.1248	0.823522
$255$	−16.3178	−1.02186
$256$	1.00000	0.0625000
$257$	15.8073	0.986033	0.493016	−	0.870020i	$-0.335894\pi$
$257$	15.8073	0.986033	0.493016	+	0.870020i	$0.335894\pi$
$258$	8.90031	0.554109
$259$	3.10079	0.192674
$260$	−11.0290	−0.683987
$261$	0.658108	0.0407358
$262$	1.00000	0.0617802
$263$	−13.7995	−0.850915	−0.425457	−	0.904978i	$-0.639887\pi$
$263$	−13.7995	−0.850915	−0.425457	+	0.904978i	$0.639887\pi$
$264$	−1.64434	−0.101202
$265$	−14.7887	−0.908461
$266$	−3.03645	−0.186177
$267$	−26.1723	−1.60172
$268$	14.0502	0.858250
$269$	−24.5422	−1.49637	−0.748183	−	0.663492i	$-0.769074\pi$
$269$	−24.5422	−1.49637	−0.748183	+	0.663492i	$0.769074\pi$
$270$	−12.7050	−0.773202
$271$	−15.8736	−0.964253	−0.482127	−	0.876101i	$-0.660136\pi$
$271$	−15.8736	−0.964253	−0.482127	+	0.876101i	$0.660136\pi$
$272$	4.96419	0.300998
$273$	−3.15657	−0.191044
$274$	15.0747	0.910693
$275$	−0.0688333	−0.00415081
$276$	−1.46112	−0.0879494
$277$	−1.02193	−0.0614020	−0.0307010	−	0.999529i	$-0.509774\pi$
$277$	−1.02193	−0.0614020	−0.0307010	+	0.999529i	$0.509774\pi$
$278$	−10.5681	−0.633833
$279$	7.22088	0.432303
$280$	0.991390	0.0592469
$281$	9.85093	0.587657	0.293829	−	0.955858i	$-0.405070\pi$
$281$	9.85093	0.587657	0.293829	+	0.955858i	$0.405070\pi$
$282$	8.79402	0.523676
$283$	27.3984	1.62867	0.814333	−	0.580398i	$-0.197103\pi$
$283$	27.3984	1.62867	0.814333	+	0.580398i	$0.197103\pi$
$284$	14.3353	0.850645
$285$	22.6495	1.34164
$286$	−5.51713	−0.326235
$287$	−1.99197	−0.117582
$288$	0.865116	0.0509774
$289$	7.64322	0.449601
$290$	1.71139	0.100496
$291$	15.0370	0.881487
$292$	−9.48910	−0.555308
$293$	16.1283	0.942228	0.471114	−	0.882072i	$-0.343852\pi$
$293$	16.1283	0.942228	0.471114	+	0.882072i	$0.343852\pi$
$294$	−9.94413	−0.579953
$295$	−21.5843	−1.25669
$296$	7.03644	0.408985
$297$	−6.35555	−0.368787
$298$	−14.5520	−0.842977
$299$	−4.90241	−0.283513
$300$	−0.0893680	−0.00515967
$301$	−2.68434	−0.154723
$302$	0.269651	0.0155167
$303$	−12.6971	−0.729431
$304$	−6.89044	−0.395194
$305$	−15.0771	−0.863310
$306$	4.29460	0.245506
$307$	9.47523	0.540780	0.270390	−	0.962751i	$-0.412847\pi$
$307$	9.47523	0.540780	0.270390	+	0.962751i	$0.412847\pi$
$308$	0.495933	0.0282584
$309$	−4.42505	−0.251732
$310$	18.7776	1.06650
$311$	−17.4063	−0.987020	−0.493510	−	0.869740i	$-0.664286\pi$
$311$	−17.4063	−0.987020	−0.493510	+	0.869740i	$0.664286\pi$
$312$	−7.16302	−0.405526
$313$	19.3980	1.09644	0.548219	−	0.836335i	$-0.315306\pi$
$313$	19.3980	1.09644	0.548219	+	0.836335i	$0.315306\pi$
$314$	1.20217	0.0678427
$315$	0.857667	0.0483241
$316$	1.45246	0.0817073
$317$	15.7321	0.883604	0.441802	−	0.897112i	$-0.354339\pi$
$317$	15.7321	0.883604	0.441802	+	0.897112i	$0.354339\pi$
$318$	−9.60486	−0.538614
$319$	0.856104	0.0479326
$320$	2.24970	0.125762
$321$	−3.94150	−0.219993
$322$	0.440676	0.0245579
$323$	−34.2055	−1.90324
$324$	−5.65623	−0.314235
$325$	−0.299850	−0.0166327
$326$	−20.1883	−1.11813
$327$	−24.2439	−1.34069
$328$	−4.52026	−0.249590
$329$	−2.65228	−0.146225
$330$	−3.69927	−0.203638
$331$	−19.5334	−1.07365	−0.536825	−	0.843694i	$-0.680376\pi$
$331$	−19.5334	−1.07365	−0.536825	+	0.843694i	$0.680376\pi$
$332$	15.5976	0.856030
$333$	6.08734	0.333584
$334$	9.85766	0.539387
$335$	31.6087	1.72697
$336$	0.643882	0.0351267
$337$	−34.7556	−1.89326	−0.946630	−	0.322322i	$-0.895537\pi$
$337$	−34.7556	−1.89326	−0.946630	+	0.322322i	$0.895537\pi$
$338$	−11.0336	−0.600148
$339$	−21.6085	−1.17361
$340$	11.1680	0.605668
$341$	9.39333	0.508678
$342$	−5.96102	−0.322335
$343$	6.08389	0.328499
$344$	−6.09141	−0.328427
$345$	−3.28710	−0.176971
$346$	−3.43267	−0.184541
$347$	8.75009	0.469729	0.234865	−	0.972028i	$-0.424535\pi$
$347$	8.75009	0.469729	0.234865	+	0.972028i	$0.424535\pi$
$348$	1.11150	0.0595827
$349$	19.2698	1.03149	0.515745	−	0.856742i	$-0.327515\pi$
$349$	19.2698	1.03149	0.515745	+	0.856742i	$0.327515\pi$
$350$	0.0269535	0.00144072
$351$	−27.6859	−1.47776
$352$	1.12539	0.0599836
$353$	13.9306	0.741453	0.370726	−	0.928742i	$-0.379109\pi$
$353$	13.9306	0.741453	0.370726	+	0.928742i	$0.379109\pi$
$354$	−14.0185	−0.745073
$355$	32.2502	1.71166
$356$	17.9125	0.949359
$357$	3.19636	0.169169
$358$	−6.48909	−0.342959
$359$	−4.47002	−0.235918	−0.117959	−	0.993018i	$-0.537635\pi$
$359$	−4.47002	−0.235918	−0.117959	+	0.993018i	$0.537635\pi$
$360$	1.94625	0.102577
$361$	28.4781	1.49885
$362$	17.0889	0.898175
$363$	14.2218	0.746453
$364$	2.16037	0.113234
$365$	−21.3477	−1.11739
$366$	−9.79216	−0.511844
$367$	−18.8441	−0.983653	−0.491826	−	0.870693i	$-0.663671\pi$
$367$	−18.8441	−0.983653	−0.491826	+	0.870693i	$0.663671\pi$
$368$	1.00000	0.0521286
$369$	−3.91055	−0.203575
$370$	15.8299	0.822958
$371$	2.89683	0.150396
$372$	12.1956	0.632312
$373$	−27.2719	−1.41209	−0.706043	−	0.708169i	$-0.749521\pi$
$373$	−27.2719	−1.41209	−0.706043	+	0.708169i	$0.749521\pi$
$374$	5.58666	0.288880
$375$	16.2344	0.838342
$376$	−6.01866	−0.310389
$377$	3.72934	0.192071
$378$	2.48868	0.128004
$379$	19.1748	0.984941	0.492471	−	0.870329i	$-0.336094\pi$
$379$	19.1748	0.984941	0.492471	+	0.870329i	$0.336094\pi$
$380$	−15.5014	−0.795207
$381$	19.1769	0.982464
$382$	−12.6961	−0.649590
$383$	−9.09482	−0.464724	−0.232362	−	0.972629i	$-0.574645\pi$
$383$	−9.09482	−0.464724	−0.232362	+	0.972629i	$0.574645\pi$
$384$	1.46112	0.0745627
$385$	1.11570	0.0568614
$386$	−3.14487	−0.160070
$387$	−5.26977	−0.267878
$388$	−10.2914	−0.522468
$389$	25.7793	1.30706	0.653531	−	0.756899i	$-0.273287\pi$
$389$	25.7793	1.30706	0.653531	+	0.756899i	$0.273287\pi$
$390$	−16.1147	−0.815998
$391$	4.96419	0.251050
$392$	6.80580	0.343745
$393$	1.46112	0.0737040
$394$	22.9086	1.15412
$395$	3.26761	0.164411
$396$	0.973594	0.0489249
$397$	34.2418	1.71855	0.859274	−	0.511515i	$-0.170915\pi$
$397$	34.2418	1.71855	0.859274	+	0.511515i	$0.170915\pi$
$398$	−9.20918	−0.461615
$399$	−4.43663	−0.222109
$400$	0.0611639	0.00305819
$401$	19.3466	0.966124	0.483062	−	0.875586i	$-0.339525\pi$
$401$	19.3466	0.966124	0.483062	+	0.875586i	$0.339525\pi$
$402$	20.5290	1.02390
$403$	40.9190	2.03832
$404$	8.68997	0.432342
$405$	−12.7248	−0.632302
$406$	−0.335229	−0.0166372
$407$	7.91876	0.392518
$408$	7.25331	0.359092
$409$	26.2502	1.29799	0.648995	−	0.760793i	$-0.275190\pi$
$409$	26.2502	1.29799	0.648995	+	0.760793i	$0.275190\pi$
$410$	−10.1693	−0.502223
$411$	22.0259	1.08646
$412$	3.02852	0.149205
$413$	4.22798	0.208045
$414$	0.865116	0.0425181
$415$	35.0900	1.72250
$416$	4.90241	0.240360
$417$	−15.4413	−0.756164
$418$	−7.75444	−0.379282
$419$	7.27774	0.355541	0.177770	−	0.984072i	$-0.443112\pi$
$419$	7.27774	0.355541	0.177770	+	0.984072i	$0.443112\pi$
$420$	1.44854	0.0706817
$421$	32.0130	1.56022	0.780109	−	0.625644i	$-0.215164\pi$
$421$	32.0130	1.56022	0.780109	+	0.625644i	$0.215164\pi$
$422$	−16.7371	−0.814748
$423$	−5.20684	−0.253165
$424$	6.57361	0.319243
$425$	0.303629	0.0147282
$426$	20.9457	1.01482
$427$	2.95332	0.142921
$428$	2.69758	0.130393
$429$	−8.06121	−0.389199
$430$	−13.7039	−0.660859
$431$	−26.2203	−1.26299	−0.631494	−	0.775381i	$-0.717558\pi$
$431$	−26.2203	−1.26299	−0.631494	+	0.775381i	$0.717558\pi$
$432$	5.64741	0.271711
$433$	7.34861	0.353152	0.176576	−	0.984287i	$-0.443498\pi$
$433$	7.34861	0.353152	0.176576	+	0.984287i	$0.443498\pi$
$434$	−3.67820	−0.176559
$435$	2.50055	0.119892
$436$	16.5926	0.794642
$437$	−6.89044	−0.329614
$438$	−13.8648	−0.662484
$439$	24.4884	1.16877	0.584383	−	0.811478i	$-0.301337\pi$
$439$	24.4884	1.16877	0.584383	+	0.811478i	$0.301337\pi$
$440$	2.53180	0.120699
$441$	5.88781	0.280372
$442$	24.3365	1.15757
$443$	13.5090	0.641832	0.320916	−	0.947108i	$-0.396009\pi$
$443$	13.5090	0.641832	0.320916	+	0.947108i	$0.396009\pi$
$444$	10.2811	0.487920
$445$	40.2977	1.91030
$446$	15.1546	0.717591
$447$	−21.2623	−1.00567
$448$	−0.440676	−0.0208200
$449$	18.0879	0.853620	0.426810	−	0.904341i	$-0.359637\pi$
$449$	18.0879	0.853620	0.426810	+	0.904341i	$0.359637\pi$
$450$	0.0529138	0.00249438
$451$	−5.08707	−0.239541
$452$	14.7889	0.695613
$453$	0.393993	0.0185114
$454$	0.897588	0.0421259
$455$	4.86020	0.227849
$456$	−10.0678	−0.471467
$457$	−34.8649	−1.63091	−0.815455	−	0.578821i	$-0.803513\pi$
$457$	−34.8649	−1.63091	−0.815455	+	0.578821i	$0.803513\pi$
$458$	−0.656611	−0.0306814
$459$	28.0349	1.30856
$460$	2.24970	0.104893
$461$	−24.7405	−1.15228	−0.576140	−	0.817351i	$-0.695442\pi$
$461$	−24.7405	−1.15228	−0.576140	+	0.817351i	$0.695442\pi$
$462$	0.724620	0.0337124
$463$	−0.617193	−0.0286834	−0.0143417	−	0.999897i	$-0.504565\pi$
$463$	−0.617193	−0.0286834	−0.0143417	+	0.999897i	$0.504565\pi$
$464$	−0.760717	−0.0353154
$465$	27.4365	1.27234
$466$	−8.13109	−0.376666
$467$	−2.86526	−0.132589	−0.0662943	−	0.997800i	$-0.521118\pi$
$467$	−2.86526	−0.132589	−0.0662943	+	0.997800i	$0.521118\pi$
$468$	4.24115	0.196047
$469$	−6.19157	−0.285900
$470$	−13.5402	−0.624563
$471$	1.75653	0.0809365
$472$	9.59430	0.441614
$473$	−6.85522	−0.315203
$474$	2.12223	0.0974771
$475$	−0.421446	−0.0193373
$476$	−2.18760	−0.100269
$477$	5.68693	0.260387
$478$	−7.49695	−0.342902
$479$	23.6493	1.08057	0.540283	−	0.841484i	$-0.318317\pi$
$479$	23.6493	1.08057	0.540283	+	0.841484i	$0.318317\pi$
$480$	3.28710	0.150035
$481$	34.4955	1.57286
$482$	26.8774	1.22423
$483$	0.643882	0.0292977
$484$	−9.73349	−0.442432
$485$	−23.1526	−1.05131
$486$	8.67779	0.393633
$487$	−18.7405	−0.849212	−0.424606	−	0.905378i	$-0.639587\pi$
$487$	−18.7405	−0.849212	−0.424606	+	0.905378i	$0.639587\pi$
$488$	6.70180	0.303376
$489$	−29.4976	−1.33393
$490$	15.3110	0.691682
$491$	22.2411	1.00373	0.501864	−	0.864947i	$-0.332648\pi$
$491$	22.2411	1.00373	0.501864	+	0.864947i	$0.332648\pi$
$492$	−6.60467	−0.297761
$493$	−3.77634	−0.170078
$494$	−33.7797	−1.51982
$495$	2.19030	0.0984465
$496$	−8.34672	−0.374779
$497$	−6.31723	−0.283367
$498$	22.7900	1.02125
$499$	−4.57517	−0.204813	−0.102406	−	0.994743i	$-0.532654\pi$
$499$	−4.57517	−0.204813	−0.102406	+	0.994743i	$0.532654\pi$
$500$	−11.1109	−0.496895
$501$	14.4033	0.643491
$502$	−20.5994	−0.919397
$503$	−4.75919	−0.212202	−0.106101	−	0.994355i	$-0.533837\pi$
$503$	−4.75919	−0.212202	−0.106101	+	0.994355i	$0.533837\pi$
$504$	−0.381236	−0.0169816
$505$	19.5498	0.869957
$506$	1.12539	0.0500298
$507$	−16.1214	−0.715978
$508$	−13.1248	−0.582318
$509$	20.1188	0.891750	0.445875	−	0.895095i	$-0.352893\pi$
$509$	20.1188	0.891750	0.445875	+	0.895095i	$0.352893\pi$
$510$	16.3178	0.722564
$511$	4.18162	0.184984
$512$	−1.00000	−0.0441942
$513$	−38.9132	−1.71806
$514$	−15.8073	−0.697230
$515$	6.81328	0.300229
$516$	−8.90031	−0.391814
$517$	−6.77336	−0.297892
$518$	−3.10079	−0.136241
$519$	−5.01555	−0.220158
$520$	11.0290	0.483652
$521$	2.16879	0.0950163	0.0475082	−	0.998871i	$-0.484872\pi$
$521$	2.16879	0.0950163	0.0475082	+	0.998871i	$0.484872\pi$
$522$	−0.658108	−0.0288046
$523$	−18.1405	−0.793229	−0.396614	−	0.917985i	$-0.629815\pi$
$523$	−18.1405	−0.793229	−0.396614	+	0.917985i	$0.629815\pi$
$524$	−1.00000	−0.0436852
$525$	0.0393823	0.00171879
$526$	13.7995	0.601688
$527$	−41.4348	−1.80493
$528$	1.64434	0.0715606
$529$	1.00000	0.0434783
$530$	14.7887	0.642379
$531$	8.30018	0.360197
$532$	3.03645	0.131647
$533$	−22.1602	−0.959863
$534$	26.1723	1.13259
$535$	6.06876	0.262375
$536$	−14.0502	−0.606875
$537$	−9.48137	−0.409151
$538$	24.5422	1.05809
$539$	7.65920	0.329905
$540$	12.7050	0.546736
$541$	−20.9832	−0.902138	−0.451069	−	0.892489i	$-0.648957\pi$
$541$	−20.9832	−0.902138	−0.451069	+	0.892489i	$0.648957\pi$
$542$	15.8736	0.681830
$543$	24.9691	1.07153
$544$	−4.96419	−0.212838
$545$	37.3285	1.59898
$546$	3.15657	0.135089
$547$	32.8179	1.40319	0.701597	−	0.712574i	$-0.252471\pi$
$547$	32.8179	1.40319	0.701597	+	0.712574i	$0.252471\pi$
$548$	−15.0747	−0.643957
$549$	5.79783	0.247445
$550$	0.0688333	0.00293506
$551$	5.24167	0.223303
$552$	1.46112	0.0621896
$553$	−0.640065	−0.0272183
$554$	1.02193	0.0434177
$555$	23.1295	0.981791
$556$	10.5681	0.448187
$557$	4.11931	0.174541	0.0872703	−	0.996185i	$-0.472186\pi$
$557$	4.11931	0.174541	0.0872703	+	0.996185i	$0.472186\pi$
$558$	−7.22088	−0.305684
$559$	−29.8626	−1.26305
$560$	−0.991390	−0.0418939
$561$	8.16281	0.344634
$562$	−9.85093	−0.415537
$563$	17.7614	0.748552	0.374276	−	0.927317i	$-0.377891\pi$
$563$	17.7614	0.748552	0.374276	+	0.927317i	$0.377891\pi$
$564$	−8.79402	−0.370295
$565$	33.2707	1.39971
$566$	−27.3984	−1.15164
$567$	2.49256	0.104678
$568$	−14.3353	−0.601497
$569$	44.2900	1.85673	0.928367	−	0.371665i	$-0.121213\pi$
$569$	44.2900	1.85673	0.928367	+	0.371665i	$0.121213\pi$
$570$	−22.6495	−0.948684
$571$	33.4458	1.39967	0.699833	−	0.714307i	$-0.253258\pi$
$571$	33.4458	1.39967	0.699833	+	0.714307i	$0.253258\pi$
$572$	5.51713	0.230683
$573$	−18.5506	−0.774963
$574$	1.99197	0.0831433
$575$	0.0611639	0.00255071
$576$	−0.865116	−0.0360465
$577$	−16.1893	−0.673967	−0.336984	−	0.941510i	$-0.609407\pi$
$577$	−16.1893	−0.673967	−0.336984	+	0.941510i	$0.609407\pi$
$578$	−7.64322	−0.317916
$579$	−4.59505	−0.190964
$580$	−1.71139	−0.0710614
$581$	−6.87349	−0.285160
$582$	−15.0370	−0.623306
$583$	7.39789	0.306389
$584$	9.48910	0.392662
$585$	9.54132	0.394485
$586$	−16.1283	−0.666256
$587$	−26.2784	−1.08462	−0.542312	−	0.840177i	$-0.682451\pi$
$587$	−26.2784	−1.08462	−0.542312	+	0.840177i	$0.682451\pi$
$588$	9.94413	0.410089
$589$	57.5126	2.36976
$590$	21.5843	0.888613
$591$	33.4724	1.37687
$592$	−7.03644	−0.289196
$593$	−22.2994	−0.915725	−0.457862	−	0.889023i	$-0.651385\pi$
$593$	−22.2994	−0.915725	−0.457862	+	0.889023i	$0.651385\pi$
$594$	6.35555	0.260772
$595$	−4.92145	−0.201760
$596$	14.5520	0.596075
$597$	−13.4558	−0.550708
$598$	4.90241	0.200474
$599$	−1.19471	−0.0488146	−0.0244073	−	0.999702i	$-0.507770\pi$
$599$	−1.19471	−0.0488146	−0.0244073	+	0.999702i	$0.507770\pi$
$600$	0.0893680	0.00364844
$601$	−21.1525	−0.862828	−0.431414	−	0.902154i	$-0.641985\pi$
$601$	−21.1525	−0.862828	−0.431414	+	0.902154i	$0.641985\pi$
$602$	2.68434	0.109405
$603$	−12.1550	−0.494990
$604$	−0.269651	−0.0109719
$605$	−21.8975	−0.890259
$606$	12.6971	0.515785
$607$	−21.6002	−0.876724	−0.438362	−	0.898799i	$-0.644441\pi$
$607$	−21.6002	−0.876724	−0.438362	+	0.898799i	$0.644441\pi$
$608$	6.89044	0.279444
$609$	−0.489812	−0.0198482
$610$	15.0771	0.610452
$611$	−29.5059	−1.19368
$612$	−4.29460	−0.173599
$613$	47.4821	1.91779	0.958893	−	0.283768i	$-0.0915846\pi$
$613$	47.4821	1.91779	0.958893	+	0.283768i	$0.0915846\pi$
$614$	−9.47523	−0.382389
$615$	−14.8585	−0.599154
$616$	−0.495933	−0.0199817
$617$	−24.2906	−0.977902	−0.488951	−	0.872311i	$-0.662620\pi$
$617$	−24.2906	−0.977902	−0.488951	+	0.872311i	$0.662620\pi$
$618$	4.42505	0.178002
$619$	13.1880	0.530071	0.265035	−	0.964239i	$-0.414616\pi$
$619$	13.1880	0.530071	0.265035	+	0.964239i	$0.414616\pi$
$620$	−18.7776	−0.754129
$621$	5.64741	0.226623
$622$	17.4063	0.697928
$623$	−7.89359	−0.316250
$624$	7.16302	0.286750
$625$	−25.3021	−1.01208
$626$	−19.3980	−0.775299
$627$	−11.3302	−0.452485
$628$	−1.20217	−0.0479720
$629$	−34.9303	−1.39276
$630$	−0.857667	−0.0341703
$631$	45.1020	1.79548	0.897740	−	0.440525i	$-0.145208\pi$
$631$	45.1020	1.79548	0.897740	+	0.440525i	$0.145208\pi$
$632$	−1.45246	−0.0577758
$633$	−24.4550	−0.971997
$634$	−15.7321	−0.624803
$635$	−29.5268	−1.17174
$636$	9.60486	0.380857
$637$	33.3648	1.32196
$638$	−0.856104	−0.0338935
$639$	−12.4017	−0.490604
$640$	−2.24970	−0.0889273
$641$	−5.50199	−0.217315	−0.108658	−	0.994079i	$-0.534655\pi$
$641$	−5.50199	−0.217315	−0.108658	+	0.994079i	$0.534655\pi$
$642$	3.94150	0.155559
$643$	47.4848	1.87262	0.936309	−	0.351176i	$-0.114218\pi$
$643$	47.4848	1.87262	0.936309	+	0.351176i	$0.114218\pi$
$644$	−0.440676	−0.0173651
$645$	−20.0230	−0.788407
$646$	34.2055	1.34580
$647$	−11.7711	−0.462770	−0.231385	−	0.972862i	$-0.574326\pi$
$647$	−11.7711	−0.462770	−0.231385	+	0.972862i	$0.574326\pi$
$648$	5.65623	0.222198
$649$	10.7973	0.423833
$650$	0.299850	0.0117611
$651$	−5.37431	−0.210636
$652$	20.1883	0.790634
$653$	0.815090	0.0318969	0.0159485	−	0.999873i	$-0.494923\pi$
$653$	0.815090	0.0318969	0.0159485	+	0.999873i	$0.494923\pi$
$654$	24.2439	0.948011
$655$	−2.24970	−0.0879032
$656$	4.52026	0.176487
$657$	8.20917	0.320270
$658$	2.65228	0.103397
$659$	30.1596	1.17485	0.587426	−	0.809278i	$-0.300141\pi$
$659$	30.1596	1.17485	0.587426	+	0.809278i	$0.300141\pi$
$660$	3.69927	0.143994
$661$	5.10247	0.198463	0.0992316	−	0.995064i	$-0.468362\pi$
$661$	5.10247	0.198463	0.0992316	+	0.995064i	$0.468362\pi$
$662$	19.5334	0.759185
$663$	35.5586	1.38098
$664$	−15.5976	−0.605305
$665$	6.83111	0.264899
$666$	−6.08734	−0.235879
$667$	−0.760717	−0.0294551
$668$	−9.85766	−0.381404
$669$	22.1428	0.856088
$670$	−31.6087	−1.22115
$671$	7.54215	0.291161
$672$	−0.643882	−0.0248383
$673$	5.98340	0.230643	0.115322	−	0.993328i	$-0.463210\pi$
$673$	5.98340	0.230643	0.115322	+	0.993328i	$0.463210\pi$
$674$	34.7556	1.33874
$675$	0.345418	0.0132951
$676$	11.0336	0.424368
$677$	19.7904	0.760606	0.380303	−	0.924862i	$-0.375820\pi$
$677$	19.7904	0.760606	0.380303	+	0.924862i	$0.375820\pi$
$678$	21.6085	0.829869
$679$	4.53518	0.174044
$680$	−11.1680	−0.428272
$681$	1.31149	0.0502563
$682$	−9.39333	−0.359689
$683$	−0.412644	−0.0157894	−0.00789469	−	0.999969i	$-0.502513\pi$
$683$	−0.412644	−0.0157894	−0.00789469	+	0.999969i	$0.502513\pi$
$684$	5.96102	0.227925
$685$	−33.9135	−1.29577
$686$	−6.08389	−0.232284
$687$	−0.959391	−0.0366031
$688$	6.09141	0.232233
$689$	32.2265	1.22773
$690$	3.28710	0.125138
$691$	23.1569	0.880928	0.440464	−	0.897770i	$-0.354814\pi$
$691$	23.1569	0.880928	0.440464	+	0.897770i	$0.354814\pi$
$692$	3.43267	0.130490
$693$	−0.429039	−0.0162979
$694$	−8.75009	−0.332149
$695$	23.7751	0.901841
$696$	−1.11150	−0.0421314
$697$	22.4395	0.849955
$698$	−19.2698	−0.729374
$699$	−11.8805	−0.449363
$700$	−0.0269535	−0.00101874
$701$	48.9193	1.84766	0.923829	−	0.382806i	$-0.125042\pi$
$701$	48.9193	1.84766	0.923829	+	0.382806i	$0.125042\pi$
$702$	27.6859	1.04494
$703$	48.4842	1.82862
$704$	−1.12539	−0.0424148
$705$	−19.7839	−0.745106
$706$	−13.9306	−0.524286
$707$	−3.82946	−0.144022
$708$	14.0185	0.526846
$709$	−20.5113	−0.770319	−0.385160	−	0.922850i	$-0.625854\pi$
$709$	−20.5113	−0.770319	−0.385160	+	0.922850i	$0.625854\pi$
$710$	−32.2502	−1.21033
$711$	−1.25655	−0.0471242
$712$	−17.9125	−0.671298
$713$	−8.34672	−0.312587
$714$	−3.19636	−0.119621
$715$	12.4119	0.464179
$716$	6.48909	0.242509
$717$	−10.9540	−0.409083
$718$	4.47002	0.166820
$719$	−25.2894	−0.943136	−0.471568	−	0.881830i	$-0.656312\pi$
$719$	−25.2894	−0.943136	−0.471568	+	0.881830i	$0.656312\pi$
$720$	−1.94625	−0.0725326
$721$	−1.33460	−0.0497030
$722$	−28.4781	−1.05985
$723$	39.2712	1.46051
$724$	−17.0889	−0.635106
$725$	−0.0465284	−0.00172802
$726$	−14.2218	−0.527822
$727$	−13.5470	−0.502430	−0.251215	−	0.967931i	$-0.580830\pi$
$727$	−13.5470	−0.502430	−0.251215	+	0.967931i	$0.580830\pi$
$728$	−2.16037	−0.0800687
$729$	29.6480	1.09807
$730$	21.3477	0.790112
$731$	30.2389	1.11843
$732$	9.79216	0.361929
$733$	−22.3218	−0.824476	−0.412238	−	0.911076i	$-0.635253\pi$
$733$	−22.3218	−0.824476	−0.412238	+	0.911076i	$0.635253\pi$
$734$	18.8441	0.695548
$735$	22.3713	0.825179
$736$	−1.00000	−0.0368605
$737$	−15.8119	−0.582440
$738$	3.91055	0.143949
$739$	38.4738	1.41528	0.707641	−	0.706572i	$-0.249759\pi$
$739$	38.4738	1.41528	0.707641	+	0.706572i	$0.249759\pi$
$740$	−15.8299	−0.581919
$741$	−49.3564	−1.81315
$742$	−2.89683	−0.106346
$743$	16.6339	0.610239	0.305120	−	0.952314i	$-0.401304\pi$
$743$	16.6339	0.610239	0.305120	+	0.952314i	$0.401304\pi$
$744$	−12.1956	−0.447112
$745$	32.7378	1.19942
$746$	27.2719	0.998495
$747$	−13.4937	−0.493710
$748$	−5.58666	−0.204269
$749$	−1.18876	−0.0434363
$750$	−16.2344	−0.592798
$751$	10.3402	0.377320	0.188660	−	0.982042i	$-0.439586\pi$
$751$	10.3402	0.377320	0.188660	+	0.982042i	$0.439586\pi$
$752$	6.01866	0.219478
$753$	−30.0983	−1.09684
$754$	−3.72934	−0.135815
$755$	−0.606634	−0.0220777
$756$	−2.48868	−0.0905124
$757$	−24.1973	−0.879467	−0.439734	−	0.898128i	$-0.644927\pi$
$757$	−24.1973	−0.879467	−0.439734	+	0.898128i	$0.644927\pi$
$758$	−19.1748	−0.696459
$759$	1.64434	0.0596857
$760$	15.5014	0.562296
$761$	37.8245	1.37114	0.685568	−	0.728009i	$-0.259554\pi$
$761$	37.8245	1.37114	0.685568	+	0.728009i	$0.259554\pi$
$762$	−19.1769	−0.694707
$763$	−7.31197	−0.264711
$764$	12.6961	0.459330
$765$	−9.66158	−0.349315
$766$	9.09482	0.328609
$767$	47.0352	1.69834
$768$	−1.46112	−0.0527238
$769$	16.1082	0.580877	0.290439	−	0.956894i	$-0.406199\pi$
$769$	16.1082	0.580877	0.290439	+	0.956894i	$0.406199\pi$
$770$	−1.11570	−0.0402071
$771$	−23.0964	−0.831798
$772$	3.14487	0.113186
$773$	27.5523	0.990988	0.495494	−	0.868611i	$-0.334987\pi$
$773$	27.5523	0.990988	0.495494	+	0.868611i	$0.334987\pi$
$774$	5.26977	0.189418
$775$	−0.510518	−0.0183384
$776$	10.2914	0.369441
$777$	−4.53064	−0.162536
$778$	−25.7793	−0.924233
$779$	−31.1466	−1.11594
$780$	16.1147	0.576998
$781$	−16.1329	−0.577279
$782$	−4.96419	−0.177519
$783$	−4.29608	−0.153529
$784$	−6.80580	−0.243064
$785$	−2.70454	−0.0965290
$786$	−1.46112	−0.0521166
$787$	17.5783	0.626600	0.313300	−	0.949654i	$-0.398565\pi$
$787$	17.5783	0.626600	0.313300	+	0.949654i	$0.398565\pi$
$788$	−22.9086	−0.816087
$789$	20.1628	0.717815
$790$	−3.26761	−0.116256
$791$	−6.51713	−0.231722
$792$	−0.973594	−0.0345952
$793$	32.8549	1.16671
$794$	−34.2418	−1.21520
$795$	21.6081	0.766360
$796$	9.20918	0.326411
$797$	−0.306197	−0.0108461	−0.00542304	−	0.999985i	$-0.501726\pi$
$797$	−0.306197	−0.0108461	−0.00542304	+	0.999985i	$0.501726\pi$
$798$	4.43663	0.157055
$799$	29.8778	1.05700
$800$	−0.0611639	−0.00216247
$801$	−15.4963	−0.547537
$802$	−19.3466	−0.683153
$803$	10.6790	0.376852
$804$	−20.5290	−0.724003
$805$	−0.991390	−0.0349419
$806$	−40.9190	−1.44131
$807$	35.8593	1.26231
$808$	−8.68997	−0.305712
$809$	−33.3630	−1.17298	−0.586490	−	0.809957i	$-0.699491\pi$
$809$	−33.3630	−1.17298	−0.586490	+	0.809957i	$0.699491\pi$
$810$	12.7248	0.447105
$811$	−33.8662	−1.18920	−0.594601	−	0.804021i	$-0.702690\pi$
$811$	−33.8662	−1.18920	−0.594601	+	0.804021i	$0.702690\pi$
$812$	0.335229	0.0117642
$813$	23.1933	0.813425
$814$	−7.91876	−0.277552
$815$	45.4177	1.59091
$816$	−7.25331	−0.253916
$817$	−41.9725	−1.46843
$818$	−26.2502	−0.917817
$819$	−1.86897	−0.0653071
$820$	10.1693	0.355126
$821$	−24.0597	−0.839688	−0.419844	−	0.907596i	$-0.637915\pi$
$821$	−24.0597	−0.839688	−0.419844	+	0.907596i	$0.637915\pi$
$822$	−22.0259	−0.768243
$823$	−27.6739	−0.964651	−0.482326	−	0.875992i	$-0.660208\pi$
$823$	−27.6739	−0.964651	−0.482326	+	0.875992i	$0.660208\pi$
$824$	−3.02852	−0.105504
$825$	0.100574	0.00350154
$826$	−4.22798	−0.147110
$827$	−0.323335	−0.0112435	−0.00562173	−	0.999984i	$-0.501789\pi$
$827$	−0.323335	−0.0112435	−0.00562173	+	0.999984i	$0.501789\pi$
$828$	−0.865116	−0.0300648
$829$	27.0142	0.938241	0.469120	−	0.883134i	$-0.344571\pi$
$829$	27.0142	0.938241	0.469120	+	0.883134i	$0.344571\pi$
$830$	−35.0900	−1.21799
$831$	1.49317	0.0517975
$832$	−4.90241	−0.169960
$833$	−33.7853	−1.17059
$834$	15.4413	0.534689
$835$	−22.1768	−0.767460
$836$	7.75444	0.268193
$837$	−47.1374	−1.62931
$838$	−7.27774	−0.251405
$839$	34.9316	1.20597	0.602986	−	0.797752i	$-0.293978\pi$
$839$	34.9316	1.20597	0.602986	+	0.797752i	$0.293978\pi$
$840$	−1.44854	−0.0499795
$841$	−28.4213	−0.980045
$842$	−32.0130	−1.10324
$843$	−14.3934	−0.495736
$844$	16.7371	0.576114
$845$	24.8223	0.853912
$846$	5.20684	0.179015
$847$	4.28932	0.147383
$848$	−6.57361	−0.225739
$849$	−40.0325	−1.37391
$850$	−0.303629	−0.0104144
$851$	−7.03644	−0.241206
$852$	−20.9457	−0.717588
$853$	−29.0586	−0.994949	−0.497475	−	0.867479i	$-0.665739\pi$
$853$	−29.0586	−0.994949	−0.497475	+	0.867479i	$0.665739\pi$
$854$	−2.95332	−0.101061
$855$	13.4105	0.458631
$856$	−2.69758	−0.0922015
$857$	−50.3724	−1.72069	−0.860345	−	0.509713i	$-0.829752\pi$
$857$	−50.3724	−1.72069	−0.860345	+	0.509713i	$0.829752\pi$
$858$	8.06121	0.275205
$859$	−49.4505	−1.68723	−0.843615	−	0.536948i	$-0.819577\pi$
$859$	−49.4505	−1.68723	−0.843615	+	0.536948i	$0.819577\pi$
$860$	13.7039	0.467298
$861$	2.91052	0.0991902
$862$	26.2203	0.893068
$863$	35.3316	1.20270	0.601351	−	0.798985i	$-0.294629\pi$
$863$	35.3316	1.20270	0.601351	+	0.798985i	$0.294629\pi$
$864$	−5.64741	−0.192129
$865$	7.72248	0.262572
$866$	−7.34861	−0.249716
$867$	−11.1677	−0.379275
$868$	3.67820	0.124846
$869$	−1.63459	−0.0554496
$870$	−2.50055	−0.0847765
$871$	−68.8796	−2.33390
$872$	−16.5926	−0.561897
$873$	8.90327	0.301330
$874$	6.89044	0.233073
$875$	4.89631	0.165526
$876$	13.8648	0.468447
$877$	−40.9967	−1.38436	−0.692181	−	0.721724i	$-0.743350\pi$
$877$	−40.9967	−1.38436	−0.692181	+	0.721724i	$0.743350\pi$
$878$	−24.4884	−0.826442
$879$	−23.5655	−0.794845
$880$	−2.53180	−0.0853469
$881$	52.9658	1.78446	0.892231	−	0.451580i	$-0.149139\pi$
$881$	52.9658	1.78446	0.892231	+	0.451580i	$0.149139\pi$
$882$	−5.88781	−0.198253
$883$	−14.6025	−0.491413	−0.245707	−	0.969344i	$-0.579020\pi$
$883$	−14.6025	−0.491413	−0.245707	+	0.969344i	$0.579020\pi$
$884$	−24.3365	−0.818525
$885$	31.5374	1.06012
$886$	−13.5090	−0.453844
$887$	11.9395	0.400891	0.200445	−	0.979705i	$-0.435761\pi$
$887$	11.9395	0.400891	0.200445	+	0.979705i	$0.435761\pi$
$888$	−10.2811	−0.345012
$889$	5.78377	0.193982
$890$	−40.2977	−1.35078
$891$	6.36547	0.213251
$892$	−15.1546	−0.507414
$893$	−41.4712	−1.38778
$894$	21.2623	0.711119
$895$	14.5985	0.487975
$896$	0.440676	0.0147219
$897$	7.16302	0.239166
$898$	−18.0879	−0.603600
$899$	6.34949	0.211767
$900$	−0.0529138	−0.00176379
$901$	−32.6327	−1.08715
$902$	5.08707	0.169381
$903$	3.92215	0.130521
$904$	−14.7889	−0.491873
$905$	−38.4450	−1.27796
$906$	−0.393993	−0.0130896
$907$	−21.0175	−0.697873	−0.348937	−	0.937146i	$-0.613457\pi$
$907$	−21.0175	−0.697873	−0.348937	+	0.937146i	$0.613457\pi$
$908$	−0.897588	−0.0297875
$909$	−7.51783	−0.249351
$910$	−4.86020	−0.161114
$911$	−37.3786	−1.23841	−0.619204	−	0.785230i	$-0.712545\pi$
$911$	−37.3786	−1.23841	−0.619204	+	0.785230i	$0.712545\pi$
$912$	10.0678	0.333378
$913$	−17.5534	−0.580933
$914$	34.8649	1.15323
$915$	22.0295	0.728271
$916$	0.656611	0.0216951
$917$	0.440676	0.0145524
$918$	−28.0349	−0.925288
$919$	29.0999	0.959915	0.479958	−	0.877292i	$-0.340652\pi$
$919$	29.0999	0.959915	0.479958	+	0.877292i	$0.340652\pi$
$920$	−2.24970	−0.0741705
$921$	−13.8445	−0.456191
$922$	24.7405	0.814785
$923$	−70.2776	−2.31322
$924$	−0.724620	−0.0238382
$925$	−0.430376	−0.0141507
$926$	0.617193	0.0202822
$927$	−2.62002	−0.0860528
$928$	0.760717	0.0249717
$929$	28.2873	0.928076	0.464038	−	0.885815i	$-0.346400\pi$
$929$	28.2873	0.928076	0.464038	+	0.885815i	$0.346400\pi$
$930$	−27.4365	−0.899678
$931$	46.8950	1.53692
$932$	8.13109	0.266343
$933$	25.4327	0.832631
$934$	2.86526	0.0937543
$935$	−12.5683	−0.411028
$936$	−4.24115	−0.138626
$937$	38.8749	1.26999	0.634993	−	0.772518i	$-0.281003\pi$
$937$	38.8749	1.26999	0.634993	+	0.772518i	$0.281003\pi$
$938$	6.19157	0.202162
$939$	−28.3429	−0.924934
$940$	13.5402	0.441633
$941$	29.0308	0.946378	0.473189	−	0.880961i	$-0.343103\pi$
$941$	29.0308	0.946378	0.473189	+	0.880961i	$0.343103\pi$
$942$	−1.75653	−0.0572307
$943$	4.52026	0.147200
$944$	−9.59430	−0.312268
$945$	−5.59879	−0.182129
$946$	6.85522	0.222882
$947$	3.29686	0.107134	0.0535668	−	0.998564i	$-0.482941\pi$
$947$	3.29686	0.107134	0.0535668	+	0.998564i	$0.482941\pi$
$948$	−2.12223	−0.0689267
$949$	46.5194	1.51008
$950$	0.421446	0.0136735
$951$	−22.9866	−0.745392
$952$	2.18760	0.0709006
$953$	−58.8537	−1.90646	−0.953229	−	0.302248i	$-0.902263\pi$
$953$	−58.8537	−1.90646	−0.953229	+	0.302248i	$0.902263\pi$
$954$	−5.68693	−0.184121
$955$	28.5625	0.924261
$956$	7.49695	0.242469
$957$	−1.25087	−0.0404350
$958$	−23.6493	−0.764075
$959$	6.64304	0.214515
$960$	−3.28710	−0.106091
$961$	38.6678	1.24735
$962$	−34.4955	−1.11218
$963$	−2.33372	−0.0752031
$964$	−26.8774	−0.865663
$965$	7.07503	0.227753
$966$	−0.643882	−0.0207166
$967$	41.1153	1.32218	0.661089	−	0.750307i	$-0.270094\pi$
$967$	41.1153	1.32218	0.661089	+	0.750307i	$0.270094\pi$
$968$	9.73349	0.312846
$969$	49.9784	1.60554
$970$	23.1526	0.743387
$971$	−34.1607	−1.09627	−0.548135	−	0.836390i	$-0.684662\pi$
$971$	−34.1607	−1.09627	−0.548135	+	0.836390i	$0.684662\pi$
$972$	−8.67779	−0.278340
$973$	−4.65711	−0.149300
$974$	18.7405	0.600483
$975$	0.438118	0.0140310
$976$	−6.70180	−0.214519
$977$	5.06679	0.162101	0.0810505	−	0.996710i	$-0.474172\pi$
$977$	5.06679	0.162101	0.0810505	+	0.996710i	$0.474172\pi$
$978$	29.4976	0.943229
$979$	−20.1585	−0.644270
$980$	−15.3110	−0.489093
$981$	−14.3545	−0.458305
$982$	−22.2411	−0.709743
$983$	−26.1039	−0.832584	−0.416292	−	0.909231i	$-0.636671\pi$
$983$	−26.1039	−0.832584	−0.416292	+	0.909231i	$0.636671\pi$
$984$	6.60467	0.210549
$985$	−51.5377	−1.64213
$986$	3.77634	0.120263
$987$	3.87531	0.123353
$988$	33.7797	1.07468
$989$	6.09141	0.193696
$990$	−2.19030	−0.0696122
$991$	47.4750	1.50809	0.754047	−	0.656821i	$-0.228099\pi$
$991$	47.4750	1.50809	0.754047	+	0.656821i	$0.228099\pi$
$992$	8.34672	0.265009
$993$	28.5407	0.905710
$994$	6.31723	0.200371
$995$	20.7179	0.656803
$996$	−22.7900	−0.722130
$997$	16.1313	0.510883	0.255441	−	0.966825i	$-0.417779\pi$
$997$	16.1313	0.510883	0.255441	+	0.966825i	$0.417779\pi$
$998$	4.57517	0.144824
$999$	−39.7377	−1.25725

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.j.1.11	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.j.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.46112 q^{3} +1.00000 q^{4} +2.24970 q^{5} +1.46112 q^{6} -0.440676 q^{7} -1.00000 q^{8} -0.865116 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.46112 q^{3} +1.00000 q^{4} +2.24970 q^{5} +1.46112 q^{6} -0.440676 q^{7} -1.00000 q^{8} -0.865116 q^{9} -2.24970 q^{10} -1.12539 q^{11} -1.46112 q^{12} -4.90241 q^{13} +0.440676 q^{14} -3.28710 q^{15} +1.00000 q^{16} +4.96419 q^{17} +0.865116 q^{18} -6.89044 q^{19} +2.24970 q^{20} +0.643882 q^{21} +1.12539 q^{22} +1.00000 q^{23} +1.46112 q^{24} +0.0611639 q^{25} +4.90241 q^{26} +5.64741 q^{27} -0.440676 q^{28} -0.760717 q^{29} +3.28710 q^{30} -8.34672 q^{31} -1.00000 q^{32} +1.64434 q^{33} -4.96419 q^{34} -0.991390 q^{35} -0.865116 q^{36} -7.03644 q^{37} +6.89044 q^{38} +7.16302 q^{39} -2.24970 q^{40} +4.52026 q^{41} -0.643882 q^{42} +6.09141 q^{43} -1.12539 q^{44} -1.94625 q^{45} -1.00000 q^{46} +6.01866 q^{47} -1.46112 q^{48} -6.80580 q^{49} -0.0611639 q^{50} -7.25331 q^{51} -4.90241 q^{52} -6.57361 q^{53} -5.64741 q^{54} -2.53180 q^{55} +0.440676 q^{56} +10.0678 q^{57} +0.760717 q^{58} -9.59430 q^{59} -3.28710 q^{60} -6.70180 q^{61} +8.34672 q^{62} +0.381236 q^{63} +1.00000 q^{64} -11.0290 q^{65} -1.64434 q^{66} +14.0502 q^{67} +4.96419 q^{68} -1.46112 q^{69} +0.991390 q^{70} +14.3353 q^{71} +0.865116 q^{72} -9.48910 q^{73} +7.03644 q^{74} -0.0893680 q^{75} -6.89044 q^{76} +0.495933 q^{77} -7.16302 q^{78} +1.45246 q^{79} +2.24970 q^{80} -5.65623 q^{81} -4.52026 q^{82} +15.5976 q^{83} +0.643882 q^{84} +11.1680 q^{85} -6.09141 q^{86} +1.11150 q^{87} +1.12539 q^{88} +17.9125 q^{89} +1.94625 q^{90} +2.16037 q^{91} +1.00000 q^{92} +12.1956 q^{93} -6.01866 q^{94} -15.5014 q^{95} +1.46112 q^{96} -10.2914 q^{97} +6.80580 q^{98} +0.973594 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) \) 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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