LMFDB - Embedded newform 6026.2.a.k.1.18

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:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.0639197 q^{3} +1.00000 q^{4} +0.144901 q^{5} +0.0639197 q^{6} -1.36969 q^{7} +1.00000 q^{8} -2.99591 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.0639197 q^{3} +1.00000 q^{4} +0.144901 q^{5} +0.0639197 q^{6} -1.36969 q^{7} +1.00000 q^{8} -2.99591 q^{9} +0.144901 q^{10} -6.51381 q^{11} +0.0639197 q^{12} +1.08090 q^{13} -1.36969 q^{14} +0.00926200 q^{15} +1.00000 q^{16} -2.22525 q^{17} -2.99591 q^{18} +4.59606 q^{19} +0.144901 q^{20} -0.0875504 q^{21} -6.51381 q^{22} -1.00000 q^{23} +0.0639197 q^{24} -4.97900 q^{25} +1.08090 q^{26} -0.383257 q^{27} -1.36969 q^{28} +9.72921 q^{29} +0.00926200 q^{30} +5.03881 q^{31} +1.00000 q^{32} -0.416360 q^{33} -2.22525 q^{34} -0.198469 q^{35} -2.99591 q^{36} +8.33383 q^{37} +4.59606 q^{38} +0.0690909 q^{39} +0.144901 q^{40} -6.26144 q^{41} -0.0875504 q^{42} +10.6425 q^{43} -6.51381 q^{44} -0.434110 q^{45} -1.00000 q^{46} +1.53160 q^{47} +0.0639197 q^{48} -5.12394 q^{49} -4.97900 q^{50} -0.142237 q^{51} +1.08090 q^{52} +8.26590 q^{53} -0.383257 q^{54} -0.943854 q^{55} -1.36969 q^{56} +0.293779 q^{57} +9.72921 q^{58} -6.05341 q^{59} +0.00926200 q^{60} -12.1671 q^{61} +5.03881 q^{62} +4.10349 q^{63} +1.00000 q^{64} +0.156623 q^{65} -0.416360 q^{66} +7.89940 q^{67} -2.22525 q^{68} -0.0639197 q^{69} -0.198469 q^{70} +6.60601 q^{71} -2.99591 q^{72} +14.8468 q^{73} +8.33383 q^{74} -0.318256 q^{75} +4.59606 q^{76} +8.92192 q^{77} +0.0690909 q^{78} -6.96834 q^{79} +0.144901 q^{80} +8.96325 q^{81} -6.26144 q^{82} +11.8292 q^{83} -0.0875504 q^{84} -0.322441 q^{85} +10.6425 q^{86} +0.621888 q^{87} -6.51381 q^{88} -9.59523 q^{89} -0.434110 q^{90} -1.48051 q^{91} -1.00000 q^{92} +0.322079 q^{93} +1.53160 q^{94} +0.665971 q^{95} +0.0639197 q^{96} +14.8298 q^{97} -5.12394 q^{98} +19.5148 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * 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
$3$	0.0639197	0.0369040	0.0184520	−	0.999830i	$-0.494126\pi$
$3$	0.0639197	0.0369040	0.0184520	+	0.999830i	$0.494126\pi$
$4$	1.00000	0.500000
$5$	0.144901	0.0648015	0.0324007	−	0.999475i	$-0.489685\pi$
$5$	0.144901	0.0648015	0.0324007	+	0.999475i	$0.489685\pi$
$6$	0.0639197	0.0260951
$7$	−1.36969	−0.517696	−0.258848	−	0.965918i	$-0.583343\pi$
$7$	−1.36969	−0.517696	−0.258848	+	0.965918i	$0.583343\pi$
$8$	1.00000	0.353553
$9$	−2.99591	−0.998638
$10$	0.144901	0.0458216
$11$	−6.51381	−1.96399	−0.981993	−	0.188916i	$-0.939503\pi$
$11$	−6.51381	−1.96399	−0.981993	+	0.188916i	$0.939503\pi$
$12$	0.0639197	0.0184520
$13$	1.08090	0.299788	0.149894	−	0.988702i	$-0.452107\pi$
$13$	1.08090	0.299788	0.149894	+	0.988702i	$0.452107\pi$
$14$	−1.36969	−0.366066
$15$	0.00926200	0.00239144
$16$	1.00000	0.250000
$17$	−2.22525	−0.539703	−0.269852	−	0.962902i	$-0.586975\pi$
$17$	−2.22525	−0.539703	−0.269852	+	0.962902i	$0.586975\pi$
$18$	−2.99591	−0.706144
$19$	4.59606	1.05441	0.527204	−	0.849739i	$-0.323240\pi$
$19$	4.59606	1.05441	0.527204	+	0.849739i	$0.323240\pi$
$20$	0.144901	0.0324007
$21$	−0.0875504	−0.0191051
$22$	−6.51381	−1.38875
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.0639197	0.0130475
$25$	−4.97900	−0.995801
$26$	1.08090	0.211982
$27$	−0.383257	−0.0737578
$28$	−1.36969	−0.258848
$29$	9.72921	1.80667	0.903334	−	0.428937i	$-0.141112\pi$
$29$	9.72921	1.80667	0.903334	+	0.428937i	$0.141112\pi$
$30$	0.00926200	0.00169100
$31$	5.03881	0.904997	0.452498	−	0.891765i	$-0.350533\pi$
$31$	5.03881	0.904997	0.452498	+	0.891765i	$0.350533\pi$
$32$	1.00000	0.176777
$33$	−0.416360	−0.0724790
$34$	−2.22525	−0.381628
$35$	−0.198469	−0.0335475
$36$	−2.99591	−0.499319
$37$	8.33383	1.37007	0.685037	−	0.728509i	$-0.259786\pi$
$37$	8.33383	1.37007	0.685037	+	0.728509i	$0.259786\pi$
$38$	4.59606	0.745579
$39$	0.0690909	0.0110634
$40$	0.144901	0.0229108
$41$	−6.26144	−0.977873	−0.488937	−	0.872319i	$-0.662615\pi$
$41$	−6.26144	−0.977873	−0.488937	+	0.872319i	$0.662615\pi$
$42$	−0.0875504	−0.0135093
$43$	10.6425	1.62297	0.811484	−	0.584374i	$-0.198660\pi$
$43$	10.6425	1.62297	0.811484	+	0.584374i	$0.198660\pi$
$44$	−6.51381	−0.981993
$45$	−0.434110	−0.0647132
$46$	−1.00000	−0.147442
$47$	1.53160	0.223407	0.111703	−	0.993742i	$-0.464369\pi$
$47$	1.53160	0.223407	0.111703	+	0.993742i	$0.464369\pi$
$48$	0.0639197	0.00922601
$49$	−5.12394	−0.731991
$50$	−4.97900	−0.704137
$51$	−0.142237	−0.0199172
$52$	1.08090	0.149894
$53$	8.26590	1.13541	0.567704	−	0.823233i	$-0.307832\pi$
$53$	8.26590	1.13541	0.567704	+	0.823233i	$0.307832\pi$
$54$	−0.383257	−0.0521546
$55$	−0.943854	−0.127269
$56$	−1.36969	−0.183033
$57$	0.293779	0.0389119
$58$	9.72921	1.27751
$59$	−6.05341	−0.788086	−0.394043	−	0.919092i	$-0.628924\pi$
$59$	−6.05341	−0.788086	−0.394043	+	0.919092i	$0.628924\pi$
$60$	0.00926200	0.00119572
$61$	−12.1671	−1.55784	−0.778918	−	0.627125i	$-0.784231\pi$
$61$	−12.1671	−1.55784	−0.778918	+	0.627125i	$0.784231\pi$
$62$	5.03881	0.639929
$63$	4.10349	0.516991
$64$	1.00000	0.125000
$65$	0.156623	0.0194267
$66$	−0.416360	−0.0512504
$67$	7.89940	0.965065	0.482532	−	0.875878i	$-0.339717\pi$
$67$	7.89940	0.965065	0.482532	+	0.875878i	$0.339717\pi$
$68$	−2.22525	−0.269852
$69$	−0.0639197	−0.00769502
$70$	−0.198469	−0.0237216
$71$	6.60601	0.783989	0.391994	−	0.919968i	$-0.371785\pi$
$71$	6.60601	0.783989	0.391994	+	0.919968i	$0.371785\pi$
$72$	−2.99591	−0.353072
$73$	14.8468	1.73769	0.868843	−	0.495087i	$-0.164864\pi$
$73$	14.8468	1.73769	0.868843	+	0.495087i	$0.164864\pi$
$74$	8.33383	0.968788
$75$	−0.318256	−0.0367491
$76$	4.59606	0.527204
$77$	8.92192	1.01675
$78$	0.0690909	0.00782301
$79$	−6.96834	−0.783999	−0.392000	−	0.919965i	$-0.628217\pi$
$79$	−6.96834	−0.783999	−0.392000	+	0.919965i	$0.628217\pi$
$80$	0.144901	0.0162004
$81$	8.96325	0.995916
$82$	−6.26144	−0.691461
$83$	11.8292	1.29842	0.649212	−	0.760608i	$-0.275099\pi$
$83$	11.8292	1.29842	0.649212	+	0.760608i	$0.275099\pi$
$84$	−0.0875504	−0.00955253
$85$	−0.322441	−0.0349736
$86$	10.6425	1.14761
$87$	0.621888	0.0666734
$88$	−6.51381	−0.694374
$89$	−9.59523	−1.01709	−0.508546	−	0.861035i	$-0.669817\pi$
$89$	−9.59523	−1.01709	−0.508546	+	0.861035i	$0.669817\pi$
$90$	−0.434110	−0.0457592
$91$	−1.48051	−0.155199
$92$	−1.00000	−0.104257
$93$	0.322079	0.0333980
$94$	1.53160	0.157972
$95$	0.665971	0.0683272
$96$	0.0639197	0.00652377
$97$	14.8298	1.50574	0.752870	−	0.658170i	$-0.228669\pi$
$97$	14.8298	1.50574	0.752870	+	0.658170i	$0.228669\pi$
$98$	−5.12394	−0.517596
$99$	19.5148	1.96131
$100$	−4.97900	−0.497900
$101$	1.36950	0.136270	0.0681351	−	0.997676i	$-0.478295\pi$
$101$	1.36950	0.136270	0.0681351	+	0.997676i	$0.478295\pi$
$102$	−0.142237	−0.0140836
$103$	2.65327	0.261435	0.130717	−	0.991420i	$-0.458272\pi$
$103$	2.65327	0.261435	0.130717	+	0.991420i	$0.458272\pi$
$104$	1.08090	0.105991
$105$	−0.0126861	−0.00123804
$106$	8.26590	0.802855
$107$	8.71168	0.842190	0.421095	−	0.907017i	$-0.361646\pi$
$107$	8.71168	0.842190	0.421095	+	0.907017i	$0.361646\pi$
$108$	−0.383257	−0.0368789
$109$	0.472027	0.0452120	0.0226060	−	0.999744i	$-0.492804\pi$
$109$	0.472027	0.0452120	0.0226060	+	0.999744i	$0.492804\pi$
$110$	−0.943854	−0.0899930
$111$	0.532696	0.0505612
$112$	−1.36969	−0.129424
$113$	8.98808	0.845527	0.422764	−	0.906240i	$-0.361060\pi$
$113$	8.98808	0.845527	0.422764	+	0.906240i	$0.361060\pi$
$114$	0.293779	0.0275149
$115$	−0.144901	−0.0135120
$116$	9.72921	0.903334
$117$	−3.23829	−0.299380
$118$	−6.05341	−0.557261
$119$	3.04792	0.279402
$120$	0.00926200	0.000845501 0
$121$	31.4297	2.85724
$122$	−12.1671	−1.10156
$123$	−0.400229	−0.0360875
$124$	5.03881	0.452498
$125$	−1.44596	−0.129331
$126$	4.10349	0.365568
$127$	4.68959	0.416133	0.208067	−	0.978115i	$-0.433283\pi$
$127$	4.68959	0.416133	0.208067	+	0.978115i	$0.433283\pi$
$128$	1.00000	0.0883883
$129$	0.680266	0.0598941
$130$	0.156623	0.0137368
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−0.416360	−0.0362395
$133$	−6.29520	−0.545863
$134$	7.89940	0.682404
$135$	−0.0555341	−0.00477962
$136$	−2.22525	−0.190814
$137$	−8.99218	−0.768254	−0.384127	−	0.923280i	$-0.625497\pi$
$137$	−8.99218	−0.768254	−0.384127	+	0.923280i	$0.625497\pi$
$138$	−0.0639197	−0.00544120
$139$	7.41844	0.629224	0.314612	−	0.949220i	$-0.398126\pi$
$139$	7.41844	0.629224	0.314612	+	0.949220i	$0.398126\pi$
$140$	−0.198469	−0.0167737
$141$	0.0978994	0.00824461
$142$	6.60601	0.554364
$143$	−7.04079	−0.588780
$144$	−2.99591	−0.249660
$145$	1.40977	0.117075
$146$	14.8468	1.22873
$147$	−0.327520	−0.0270134
$148$	8.33383	0.685037
$149$	−2.51135	−0.205738	−0.102869	−	0.994695i	$-0.532802\pi$
$149$	−2.51135	−0.205738	−0.102869	+	0.994695i	$0.532802\pi$
$150$	−0.318256	−0.0259855
$151$	−14.4370	−1.17486	−0.587432	−	0.809273i	$-0.699861\pi$
$151$	−14.4370	−1.17486	−0.587432	+	0.809273i	$0.699861\pi$
$152$	4.59606	0.372790
$153$	6.66667	0.538968
$154$	8.92192	0.718949
$155$	0.730126	0.0586451
$156$	0.0690909	0.00553170
$157$	8.31461	0.663578	0.331789	−	0.943354i	$-0.392348\pi$
$157$	8.31461	0.663578	0.331789	+	0.943354i	$0.392348\pi$
$158$	−6.96834	−0.554371
$159$	0.528353	0.0419012
$160$	0.144901	0.0114554
$161$	1.36969	0.107947
$162$	8.96325	0.704219
$163$	−9.80477	−0.767969	−0.383985	−	0.923339i	$-0.625448\pi$
$163$	−9.80477	−0.767969	−0.383985	+	0.923339i	$0.625448\pi$
$164$	−6.26144	−0.488937
$165$	−0.0603308	−0.00469675
$166$	11.8292	0.918124
$167$	−19.1826	−1.48439	−0.742196	−	0.670183i	$-0.766216\pi$
$167$	−19.1826	−1.48439	−0.742196	+	0.670183i	$0.766216\pi$
$168$	−0.0875504	−0.00675466
$169$	−11.8316	−0.910127
$170$	−0.322441	−0.0247301
$171$	−13.7694	−1.05297
$172$	10.6425	0.811484
$173$	7.99229	0.607643	0.303821	−	0.952729i	$-0.401737\pi$
$173$	7.99229	0.607643	0.303821	+	0.952729i	$0.401737\pi$
$174$	0.621888	0.0471452
$175$	6.81971	0.515522
$176$	−6.51381	−0.490997
$177$	−0.386932	−0.0290836
$178$	−9.59523	−0.719193
$179$	−17.3138	−1.29410	−0.647048	−	0.762449i	$-0.723997\pi$
$179$	−17.3138	−1.29410	−0.647048	+	0.762449i	$0.723997\pi$
$180$	−0.434110	−0.0323566
$181$	20.1045	1.49435	0.747176	−	0.664626i	$-0.231409\pi$
$181$	20.1045	1.49435	0.747176	+	0.664626i	$0.231409\pi$
$182$	−1.48051	−0.109742
$183$	−0.777717	−0.0574905
$184$	−1.00000	−0.0737210
$185$	1.20758	0.0887828
$186$	0.322079	0.0236160
$187$	14.4949	1.05997
$188$	1.53160	0.111703
$189$	0.524945	0.0381841
$190$	0.665971	0.0483146
$191$	−7.39182	−0.534854	−0.267427	−	0.963578i	$-0.586173\pi$
$191$	−7.39182	−0.534854	−0.267427	+	0.963578i	$0.586173\pi$
$192$	0.0639197	0.00461300
$193$	−0.427294	−0.0307573	−0.0153787	−	0.999882i	$-0.504895\pi$
$193$	−0.427294	−0.0307573	−0.0153787	+	0.999882i	$0.504895\pi$
$194$	14.8298	1.06472
$195$	0.0100113	0.000716925 0
$196$	−5.12394	−0.365996
$197$	3.38825	0.241403	0.120702	−	0.992689i	$-0.461486\pi$
$197$	3.38825	0.241403	0.120702	+	0.992689i	$0.461486\pi$
$198$	19.5148	1.38686
$199$	−18.6439	−1.32163	−0.660815	−	0.750549i	$-0.729789\pi$
$199$	−18.6439	−1.32163	−0.660815	+	0.750549i	$0.729789\pi$
$200$	−4.97900	−0.352069
$201$	0.504927	0.0356148
$202$	1.36950	0.0963576
$203$	−13.3260	−0.935305
$204$	−0.142237	−0.00995862
$205$	−0.907287	−0.0633676
$206$	2.65327	0.184862
$207$	2.99591	0.208230
$208$	1.08090	0.0749471
$209$	−29.9378	−2.07084
$210$	−0.0126861	−0.000875424 0
$211$	8.38699	0.577384	0.288692	−	0.957422i	$-0.406780\pi$
$211$	8.38699	0.577384	0.288692	+	0.957422i	$0.406780\pi$
$212$	8.26590	0.567704
$213$	0.422254	0.0289324
$214$	8.71168	0.595518
$215$	1.54211	0.105171
$216$	−0.383257	−0.0260773
$217$	−6.90163	−0.468513
$218$	0.472027	0.0319697
$219$	0.949002	0.0641276
$220$	−0.943854	−0.0636346
$221$	−2.40528	−0.161797
$222$	0.532696	0.0357522
$223$	−1.61238	−0.107973	−0.0539865	−	0.998542i	$-0.517193\pi$
$223$	−1.61238	−0.107973	−0.0539865	+	0.998542i	$0.517193\pi$
$224$	−1.36969	−0.0915166
$225$	14.9167	0.994445
$226$	8.98808	0.597878
$227$	5.00929	0.332478	0.166239	−	0.986085i	$-0.446838\pi$
$227$	5.00929	0.332478	0.166239	+	0.986085i	$0.446838\pi$
$228$	0.293779	0.0194560
$229$	12.5849	0.831632	0.415816	−	0.909449i	$-0.363496\pi$
$229$	12.5849	0.831632	0.415816	+	0.909449i	$0.363496\pi$
$230$	−0.144901	−0.00955446
$231$	0.570286	0.0375221
$232$	9.72921	0.638754
$233$	3.71797	0.243573	0.121786	−	0.992556i	$-0.461138\pi$
$233$	3.71797	0.243573	0.121786	+	0.992556i	$0.461138\pi$
$234$	−3.23829	−0.211694
$235$	0.221930	0.0144771
$236$	−6.05341	−0.394043
$237$	−0.445414	−0.0289327
$238$	3.04792	0.197567
$239$	−14.5079	−0.938436	−0.469218	−	0.883082i	$-0.655464\pi$
$239$	−14.5079	−0.938436	−0.469218	+	0.883082i	$0.655464\pi$
$240$	0.00926200	0.000597859 0
$241$	5.93050	0.382017	0.191009	−	0.981588i	$-0.438824\pi$
$241$	5.93050	0.382017	0.191009	+	0.981588i	$0.438824\pi$
$242$	31.4297	2.02038
$243$	1.72270	0.110511
$244$	−12.1671	−0.778918
$245$	−0.742461	−0.0474341
$246$	−0.400229	−0.0255177
$247$	4.96789	0.316099
$248$	5.03881	0.319965
$249$	0.756118	0.0479171
$250$	−1.44596	−0.0914507
$251$	23.5215	1.48466	0.742332	−	0.670033i	$-0.233720\pi$
$251$	23.5215	1.48466	0.742332	+	0.670033i	$0.233720\pi$
$252$	4.10349	0.258495
$253$	6.51381	0.409520
$254$	4.68959	0.294251
$255$	−0.0206103	−0.00129067
$256$	1.00000	0.0625000
$257$	−14.7711	−0.921397	−0.460699	−	0.887557i	$-0.652401\pi$
$257$	−14.7711	−0.921397	−0.460699	+	0.887557i	$0.652401\pi$
$258$	0.680266	0.0423515
$259$	−11.4148	−0.709281
$260$	0.156623	0.00971337
$261$	−29.1479	−1.80421
$262$	−1.00000	−0.0617802
$263$	14.6650	0.904281	0.452140	−	0.891947i	$-0.350661\pi$
$263$	14.6650	0.904281	0.452140	+	0.891947i	$0.350661\pi$
$264$	−0.416360	−0.0256252
$265$	1.19773	0.0735762
$266$	−6.29520	−0.385983
$267$	−0.613324	−0.0375348
$268$	7.89940	0.482532
$269$	8.80309	0.536734	0.268367	−	0.963317i	$-0.413516\pi$
$269$	8.80309	0.536734	0.268367	+	0.963317i	$0.413516\pi$
$270$	−0.0555341	−0.00337970
$271$	−13.0853	−0.794877	−0.397438	−	0.917629i	$-0.630101\pi$
$271$	−13.0853	−0.794877	−0.397438	+	0.917629i	$0.630101\pi$
$272$	−2.22525	−0.134926
$273$	−0.0946334	−0.00572748
$274$	−8.99218	−0.543237
$275$	32.4323	1.95574
$276$	−0.0639197	−0.00384751
$277$	10.7198	0.644089	0.322044	−	0.946725i	$-0.395630\pi$
$277$	10.7198	0.644089	0.322044	+	0.946725i	$0.395630\pi$
$278$	7.41844	0.444928
$279$	−15.0958	−0.903764
$280$	−0.198469	−0.0118608
$281$	11.8567	0.707309	0.353654	−	0.935376i	$-0.384939\pi$
$281$	11.8567	0.707309	0.353654	+	0.935376i	$0.384939\pi$
$282$	0.0978994	0.00582982
$283$	0.934556	0.0555536	0.0277768	−	0.999614i	$-0.491157\pi$
$283$	0.934556	0.0555536	0.0277768	+	0.999614i	$0.491157\pi$
$284$	6.60601	0.391994
$285$	0.0425687	0.00252155
$286$	−7.04079	−0.416331
$287$	8.57626	0.506241
$288$	−2.99591	−0.176536
$289$	−12.0482	−0.708720
$290$	1.40977	0.0827844
$291$	0.947917	0.0555679
$292$	14.8468	0.868843
$293$	−12.3560	−0.721844	−0.360922	−	0.932596i	$-0.617538\pi$
$293$	−12.3560	−0.721844	−0.360922	+	0.932596i	$0.617538\pi$
$294$	−0.327520	−0.0191014
$295$	−0.877142	−0.0510692
$296$	8.33383	0.484394
$297$	2.49646	0.144859
$298$	−2.51135	−0.145479
$299$	−1.08090	−0.0625102
$300$	−0.318256	−0.0183745
$301$	−14.5770	−0.840204
$302$	−14.4370	−0.830755
$303$	0.0875379	0.00502892
$304$	4.59606	0.263602
$305$	−1.76302	−0.100950
$306$	6.66667	0.381108
$307$	12.4904	0.712862	0.356431	−	0.934322i	$-0.383993\pi$
$307$	12.4904	0.712862	0.356431	+	0.934322i	$0.383993\pi$
$308$	8.92192	0.508374
$309$	0.169596	0.00964800
$310$	0.730126	0.0414684
$311$	−3.68277	−0.208830	−0.104415	−	0.994534i	$-0.533297\pi$
$311$	−3.68277	−0.208830	−0.104415	+	0.994534i	$0.533297\pi$
$312$	0.0690909	0.00391150
$313$	6.80012	0.384366	0.192183	−	0.981359i	$-0.438443\pi$
$313$	6.80012	0.384366	0.192183	+	0.981359i	$0.438443\pi$
$314$	8.31461	0.469220
$315$	0.594598	0.0335018
$316$	−6.96834	−0.392000
$317$	11.9802	0.672873	0.336436	−	0.941706i	$-0.390778\pi$
$317$	11.9802	0.672873	0.336436	+	0.941706i	$0.390778\pi$
$318$	0.528353	0.0296286
$319$	−63.3742	−3.54827
$320$	0.144901	0.00810019
$321$	0.556847	0.0310802
$322$	1.36969	0.0763301
$323$	−10.2274	−0.569068
$324$	8.96325	0.497958
$325$	−5.38182	−0.298530
$326$	−9.80477	−0.543036
$327$	0.0301718	0.00166850
$328$	−6.26144	−0.345730
$329$	−2.09782	−0.115657
$330$	−0.0603308	−0.00332110
$331$	10.0520	0.552509	0.276255	−	0.961084i	$-0.410907\pi$
$331$	10.0520	0.552509	0.276255	+	0.961084i	$0.410907\pi$
$332$	11.8292	0.649212
$333$	−24.9674	−1.36821
$334$	−19.1826	−1.04962
$335$	1.14463	0.0625377
$336$	−0.0875504	−0.00477627
$337$	−26.4212	−1.43925	−0.719626	−	0.694362i	$-0.755687\pi$
$337$	−26.4212	−1.43925	−0.719626	+	0.694362i	$0.755687\pi$
$338$	−11.8316	−0.643557
$339$	0.574515	0.0312034
$340$	−0.322441	−0.0174868
$341$	−32.8218	−1.77740
$342$	−13.7694	−0.744564
$343$	16.6061	0.896644
$344$	10.6425	0.573806
$345$	−0.00926200	−0.000498649 0
$346$	7.99229	0.429668
$347$	−17.6246	−0.946137	−0.473069	−	0.881026i	$-0.656854\pi$
$347$	−17.6246	−0.946137	−0.473069	+	0.881026i	$0.656854\pi$
$348$	0.621888	0.0333367
$349$	23.4963	1.25773	0.628865	−	0.777514i	$-0.283520\pi$
$349$	23.4963	1.25773	0.628865	+	0.777514i	$0.283520\pi$
$350$	6.81971	0.364529
$351$	−0.414263	−0.0221117
$352$	−6.51381	−0.347187
$353$	30.9743	1.64860	0.824299	−	0.566155i	$-0.191570\pi$
$353$	30.9743	1.64860	0.824299	+	0.566155i	$0.191570\pi$
$354$	−0.386932	−0.0205652
$355$	0.957214	0.0508037
$356$	−9.59523	−0.508546
$357$	0.194822	0.0103111
$358$	−17.3138	−0.915064
$359$	−30.4711	−1.60820	−0.804102	−	0.594491i	$-0.797354\pi$
$359$	−30.4711	−1.60820	−0.804102	+	0.594491i	$0.797354\pi$
$360$	−0.434110	−0.0228796
$361$	2.12375	0.111777
$362$	20.1045	1.05667
$363$	2.00897	0.105444
$364$	−1.48051	−0.0775996
$365$	2.15131	0.112605
$366$	−0.777717	−0.0406519
$367$	16.8433	0.879215	0.439608	−	0.898190i	$-0.355117\pi$
$367$	16.8433	0.879215	0.439608	+	0.898190i	$0.355117\pi$
$368$	−1.00000	−0.0521286
$369$	18.7587	0.976541
$370$	1.20758	0.0627789
$371$	−11.3218	−0.587796
$372$	0.322079	0.0166990
$373$	30.6318	1.58605	0.793027	−	0.609186i	$-0.208504\pi$
$373$	30.6318	1.58605	0.793027	+	0.609186i	$0.208504\pi$
$374$	14.4949	0.749512
$375$	−0.0924255	−0.00477283
$376$	1.53160	0.0789862
$377$	10.5163	0.541618
$378$	0.524945	0.0270002
$379$	2.65837	0.136551	0.0682756	−	0.997666i	$-0.478250\pi$
$379$	2.65837	0.136551	0.0682756	+	0.997666i	$0.478250\pi$
$380$	0.665971	0.0341636
$381$	0.299757	0.0153570
$382$	−7.39182	−0.378199
$383$	−28.4203	−1.45221	−0.726106	−	0.687583i	$-0.758672\pi$
$383$	−28.4203	−1.45221	−0.726106	+	0.687583i	$0.758672\pi$
$384$	0.0639197	0.00326189
$385$	1.29279	0.0658868
$386$	−0.427294	−0.0217487
$387$	−31.8841	−1.62076
$388$	14.8298	0.752870
$389$	−27.1274	−1.37541	−0.687707	−	0.725988i	$-0.741383\pi$
$389$	−27.1274	−1.37541	−0.687707	+	0.725988i	$0.741383\pi$
$390$	0.0100113	0.000506943 0
$391$	2.22525	0.112536
$392$	−5.12394	−0.258798
$393$	−0.0639197	−0.00322432
$394$	3.38825	0.170698
$395$	−1.00972	−0.0508043
$396$	19.5148	0.980656
$397$	−10.4592	−0.524930	−0.262465	−	0.964942i	$-0.584535\pi$
$397$	−10.4592	−0.524930	−0.262465	+	0.964942i	$0.584535\pi$
$398$	−18.6439	−0.934533
$399$	−0.402387	−0.0201445
$400$	−4.97900	−0.248950
$401$	−10.7612	−0.537389	−0.268694	−	0.963225i	$-0.586592\pi$
$401$	−10.7612	−0.537389	−0.268694	+	0.963225i	$0.586592\pi$
$402$	0.504927	0.0251835
$403$	5.44646	0.271308
$404$	1.36950	0.0681351
$405$	1.29878	0.0645369
$406$	−13.3260	−0.661360
$407$	−54.2850	−2.69081
$408$	−0.142237	−0.00704181
$409$	25.5337	1.26256	0.631279	−	0.775556i	$-0.282530\pi$
$409$	25.5337	1.26256	0.631279	+	0.775556i	$0.282530\pi$
$410$	−0.907287	−0.0448077
$411$	−0.574777	−0.0283517
$412$	2.65327	0.130717
$413$	8.29132	0.407989
$414$	2.99591	0.147241
$415$	1.71406	0.0841398
$416$	1.08090	0.0529956
$417$	0.474184	0.0232209
$418$	−29.9378	−1.46431
$419$	32.2303	1.57455	0.787276	−	0.616601i	$-0.211491\pi$
$419$	32.2303	1.57455	0.787276	+	0.616601i	$0.211491\pi$
$420$	−0.0126861	−0.000619018 0
$421$	23.4563	1.14319	0.571595	−	0.820536i	$-0.306325\pi$
$421$	23.4563	1.14319	0.571595	+	0.820536i	$0.306325\pi$
$422$	8.38699	0.408272
$423$	−4.58854	−0.223103
$424$	8.26590	0.401428
$425$	11.0795	0.537437
$426$	0.422254	0.0204583
$427$	16.6652	0.806486
$428$	8.71168	0.421095
$429$	−0.450045	−0.0217284
$430$	1.54211	0.0743670
$431$	−7.56604	−0.364443	−0.182222	−	0.983257i	$-0.558329\pi$
$431$	−7.56604	−0.364443	−0.182222	+	0.983257i	$0.558329\pi$
$432$	−0.383257	−0.0184395
$433$	−14.2675	−0.685651	−0.342826	−	0.939399i	$-0.611384\pi$
$433$	−14.2675	−0.685651	−0.342826	+	0.939399i	$0.611384\pi$
$434$	−6.90163	−0.331289
$435$	0.0901119	0.00432053
$436$	0.472027	0.0226060
$437$	−4.59606	−0.219859
$438$	0.949002	0.0453451
$439$	−25.2258	−1.20396	−0.601981	−	0.798511i	$-0.705622\pi$
$439$	−25.2258	−1.20396	−0.601981	+	0.798511i	$0.705622\pi$
$440$	−0.943854	−0.0449965
$441$	15.3509	0.730994
$442$	−2.40528	−0.114408
$443$	−14.5159	−0.689673	−0.344836	−	0.938663i	$-0.612066\pi$
$443$	−14.5159	−0.689673	−0.344836	+	0.938663i	$0.612066\pi$
$444$	0.532696	0.0252806
$445$	−1.39035	−0.0659091
$446$	−1.61238	−0.0763484
$447$	−0.160525	−0.00759256
$448$	−1.36969	−0.0647120
$449$	22.0227	1.03932	0.519658	−	0.854375i	$-0.326060\pi$
$449$	22.0227	1.03932	0.519658	+	0.854375i	$0.326060\pi$
$450$	14.9167	0.703179
$451$	40.7858	1.92053
$452$	8.98808	0.422764
$453$	−0.922807	−0.0433572
$454$	5.00929	0.235098
$455$	−0.214526	−0.0100571
$456$	0.293779	0.0137574
$457$	35.0010	1.63728	0.818639	−	0.574308i	$-0.194729\pi$
$457$	35.0010	1.63728	0.818639	+	0.574308i	$0.194729\pi$
$458$	12.5849	0.588053
$459$	0.852844	0.0398073
$460$	−0.144901	−0.00675602
$461$	−16.3963	−0.763654	−0.381827	−	0.924234i	$-0.624705\pi$
$461$	−16.3963	−0.763654	−0.381827	+	0.924234i	$0.624705\pi$
$462$	0.570286	0.0265321
$463$	−18.2034	−0.845982	−0.422991	−	0.906134i	$-0.639020\pi$
$463$	−18.2034	−0.845982	−0.422991	+	0.906134i	$0.639020\pi$
$464$	9.72921	0.451667
$465$	0.0466694	0.00216424
$466$	3.71797	0.172232
$467$	20.8751	0.965982	0.482991	−	0.875625i	$-0.339550\pi$
$467$	20.8751	0.965982	0.482991	+	0.875625i	$0.339550\pi$
$468$	−3.23829	−0.149690
$469$	−10.8198	−0.499610
$470$	0.221930	0.0102369
$471$	0.531467	0.0244887
$472$	−6.05341	−0.278631
$473$	−69.3233	−3.18749
$474$	−0.445414	−0.0204585
$475$	−22.8838	−1.04998
$476$	3.04792	0.139701
$477$	−24.7639	−1.13386
$478$	−14.5079	−0.663574
$479$	12.2014	0.557496	0.278748	−	0.960364i	$-0.410081\pi$
$479$	12.2014	0.557496	0.278748	+	0.960364i	$0.410081\pi$
$480$	0.00926200	0.000422750 0
$481$	9.00806	0.410732
$482$	5.93050	0.270127
$483$	0.0875504	0.00398368
$484$	31.4297	1.42862
$485$	2.14885	0.0975742
$486$	1.72270	0.0781432
$487$	−25.0139	−1.13349	−0.566745	−	0.823893i	$-0.691798\pi$
$487$	−25.0139	−1.13349	−0.566745	+	0.823893i	$0.691798\pi$
$488$	−12.1671	−0.550779
$489$	−0.626718	−0.0283412
$490$	−0.742461	−0.0335410
$491$	−0.785519	−0.0354500	−0.0177250	−	0.999843i	$-0.505642\pi$
$491$	−0.785519	−0.0354500	−0.0177250	+	0.999843i	$0.505642\pi$
$492$	−0.400229	−0.0180437
$493$	−21.6500	−0.975065
$494$	4.96789	0.223516
$495$	2.82771	0.127096
$496$	5.03881	0.226249
$497$	−9.04821	−0.405868
$498$	0.756118	0.0338825
$499$	37.4757	1.67764	0.838821	−	0.544407i	$-0.183245\pi$
$499$	37.4757	1.67764	0.838821	+	0.544407i	$0.183245\pi$
$500$	−1.44596	−0.0646654
$501$	−1.22614	−0.0547800
$502$	23.5215	1.04982
$503$	−0.282916	−0.0126146	−0.00630731	−	0.999980i	$-0.502008\pi$
$503$	−0.282916	−0.0126146	−0.00630731	+	0.999980i	$0.502008\pi$
$504$	4.10349	0.182784
$505$	0.198441	0.00883051
$506$	6.51381	0.289574
$507$	−0.756275	−0.0335874
$508$	4.68959	0.208067
$509$	1.52629	0.0676516	0.0338258	−	0.999428i	$-0.489231\pi$
$509$	1.52629	0.0676516	0.0338258	+	0.999428i	$0.489231\pi$
$510$	−0.0206103	−0.000912639 0
$511$	−20.3356	−0.899593
$512$	1.00000	0.0441942
$513$	−1.76147	−0.0777708
$514$	−14.7711	−0.651526
$515$	0.384461	0.0169414
$516$	0.680266	0.0299470
$517$	−9.97655	−0.438768
$518$	−11.4148	−0.501537
$519$	0.510864	0.0224245
$520$	0.156623	0.00686839
$521$	3.39263	0.148634	0.0743169	−	0.997235i	$-0.476322\pi$
$521$	3.39263	0.148634	0.0743169	+	0.997235i	$0.476322\pi$
$522$	−29.1479	−1.27577
$523$	−5.55710	−0.242995	−0.121498	−	0.992592i	$-0.538770\pi$
$523$	−5.55710	−0.242995	−0.121498	+	0.992592i	$0.538770\pi$
$524$	−1.00000	−0.0436852
$525$	0.435914	0.0190248
$526$	14.6650	0.639423
$527$	−11.2126	−0.488430
$528$	−0.416360	−0.0181198
$529$	1.00000	0.0434783
$530$	1.19773	0.0520262
$531$	18.1355	0.787013
$532$	−6.29520	−0.272931
$533$	−6.76801	−0.293155
$534$	−0.613324	−0.0265411
$535$	1.26233	0.0545751
$536$	7.89940	0.341202
$537$	−1.10669	−0.0477574
$538$	8.80309	0.379528
$539$	33.3763	1.43762
$540$	−0.0555341	−0.00238981
$541$	3.18909	0.137110	0.0685548	−	0.997647i	$-0.478161\pi$
$541$	3.18909	0.137110	0.0685548	+	0.997647i	$0.478161\pi$
$542$	−13.0853	−0.562063
$543$	1.28507	0.0551476
$544$	−2.22525	−0.0954070
$545$	0.0683970	0.00292980
$546$	−0.0946334	−0.00404994
$547$	3.99210	0.170690	0.0853449	−	0.996351i	$-0.472801\pi$
$547$	3.99210	0.170690	0.0853449	+	0.996351i	$0.472801\pi$
$548$	−8.99218	−0.384127
$549$	36.4516	1.55572
$550$	32.4323	1.38292
$551$	44.7160	1.90497
$552$	−0.0639197	−0.00272060
$553$	9.54450	0.405873
$554$	10.7198	0.455439
$555$	0.0771879	0.00327644
$556$	7.41844	0.314612
$557$	40.4537	1.71408	0.857038	−	0.515253i	$-0.172302\pi$
$557$	40.4537	1.71408	0.857038	+	0.515253i	$0.172302\pi$
$558$	−15.0958	−0.639058
$559$	11.5035	0.486547
$560$	−0.198469	−0.00838687
$561$	0.926508	0.0391172
$562$	11.8567	0.500143
$563$	20.8141	0.877209	0.438605	−	0.898680i	$-0.355473\pi$
$563$	20.8141	0.877209	0.438605	+	0.898680i	$0.355473\pi$
$564$	0.0978994	0.00412231
$565$	1.30238	0.0547914
$566$	0.934556	0.0392823
$567$	−12.2769	−0.515582
$568$	6.60601	0.277182
$569$	−29.4234	−1.23349	−0.616746	−	0.787162i	$-0.711549\pi$
$569$	−29.4234	−1.23349	−0.616746	+	0.787162i	$0.711549\pi$
$570$	0.0425687	0.00178301
$571$	35.5079	1.48596	0.742979	−	0.669314i	$-0.233412\pi$
$571$	35.5079	1.48596	0.742979	+	0.669314i	$0.233412\pi$
$572$	−7.04079	−0.294390
$573$	−0.472483	−0.0197383
$574$	8.57626	0.357966
$575$	4.97900	0.207639
$576$	−2.99591	−0.124830
$577$	3.55626	0.148049	0.0740245	−	0.997256i	$-0.476416\pi$
$577$	3.55626	0.148049	0.0740245	+	0.997256i	$0.476416\pi$
$578$	−12.0482	−0.501141
$579$	−0.0273125	−0.00113507
$580$	1.40977	0.0585374
$581$	−16.2024	−0.672188
$582$	0.947917	0.0392924
$583$	−53.8425	−2.22993
$584$	14.8468	0.614365
$585$	−0.469230	−0.0194003
$586$	−12.3560	−0.510421
$587$	7.29538	0.301113	0.150556	−	0.988601i	$-0.451894\pi$
$587$	7.29538	0.301113	0.150556	+	0.988601i	$0.451894\pi$
$588$	−0.327520	−0.0135067
$589$	23.1587	0.954236
$590$	−0.877142	−0.0361114
$591$	0.216576	0.00890875
$592$	8.33383	0.342518
$593$	8.33292	0.342192	0.171096	−	0.985254i	$-0.445269\pi$
$593$	8.33292	0.342192	0.171096	+	0.985254i	$0.445269\pi$
$594$	2.49646	0.102431
$595$	0.441645	0.0181057
$596$	−2.51135	−0.102869
$597$	−1.19171	−0.0487735
$598$	−1.08090	−0.0442014
$599$	18.2263	0.744705	0.372353	−	0.928091i	$-0.378551\pi$
$599$	18.2263	0.744705	0.372353	+	0.928091i	$0.378551\pi$
$600$	−0.318256	−0.0129928
$601$	12.5137	0.510444	0.255222	−	0.966882i	$-0.417851\pi$
$601$	12.5137	0.510444	0.255222	+	0.966882i	$0.417851\pi$
$602$	−14.5770	−0.594114
$603$	−23.6659	−0.963751
$604$	−14.4370	−0.587432
$605$	4.55418	0.185154
$606$	0.0875379	0.00355598
$607$	−22.2771	−0.904199	−0.452099	−	0.891968i	$-0.649325\pi$
$607$	−22.2771	−0.904199	−0.452099	+	0.891968i	$0.649325\pi$
$608$	4.59606	0.186395
$609$	−0.851796	−0.0345165
$610$	−1.76302	−0.0713826
$611$	1.65551	0.0669748
$612$	6.66667	0.269484
$613$	36.8864	1.48983	0.744915	−	0.667160i	$-0.232490\pi$
$613$	36.8864	1.48983	0.744915	+	0.667160i	$0.232490\pi$
$614$	12.4904	0.504070
$615$	−0.0579935	−0.00233852
$616$	8.92192	0.359475
$617$	37.8826	1.52510	0.762548	−	0.646932i	$-0.223948\pi$
$617$	37.8826	1.52510	0.762548	+	0.646932i	$0.223948\pi$
$618$	0.169596	0.00682217
$619$	−46.2182	−1.85767	−0.928834	−	0.370497i	$-0.879187\pi$
$619$	−46.2182	−1.85767	−0.928834	+	0.370497i	$0.879187\pi$
$620$	0.730126	0.0293226
$621$	0.383257	0.0153796
$622$	−3.68277	−0.147665
$623$	13.1425	0.526545
$624$	0.0690909	0.00276585
$625$	24.6855	0.987420
$626$	6.80012	0.271788
$627$	−1.91362	−0.0764225
$628$	8.31461	0.331789
$629$	−18.5449	−0.739433
$630$	0.594598	0.0236893
$631$	−8.34158	−0.332073	−0.166037	−	0.986120i	$-0.553097\pi$
$631$	−8.34158	−0.332073	−0.166037	+	0.986120i	$0.553097\pi$
$632$	−6.96834	−0.277186
$633$	0.536093	0.0213078
$634$	11.9802	0.475793
$635$	0.679524	0.0269661
$636$	0.528353	0.0209506
$637$	−5.53848	−0.219442
$638$	−63.3742	−2.50901
$639$	−19.7910	−0.782921
$640$	0.144901	0.00572770
$641$	−12.3628	−0.488303	−0.244151	−	0.969737i	$-0.578509\pi$
$641$	−12.3628	−0.488303	−0.244151	+	0.969737i	$0.578509\pi$
$642$	0.556847	0.0219770
$643$	39.2472	1.54776	0.773879	−	0.633334i	$-0.218314\pi$
$643$	39.2472	1.54776	0.773879	+	0.633334i	$0.218314\pi$
$644$	1.36969	0.0539735
$645$	0.0985709	0.00388123
$646$	−10.2274	−0.402392
$647$	−16.3410	−0.642430	−0.321215	−	0.947006i	$-0.604091\pi$
$647$	−16.3410	−0.642430	−0.321215	+	0.947006i	$0.604091\pi$
$648$	8.96325	0.352110
$649$	39.4307	1.54779
$650$	−5.38182	−0.211092
$651$	−0.441150	−0.0172900
$652$	−9.80477	−0.383985
$653$	41.5677	1.62667	0.813336	−	0.581794i	$-0.197649\pi$
$653$	41.5677	1.62667	0.813336	+	0.581794i	$0.197649\pi$
$654$	0.0301718	0.00117981
$655$	−0.144901	−0.00566173
$656$	−6.26144	−0.244468
$657$	−44.4797	−1.73532
$658$	−2.09782	−0.0817817
$659$	−8.06990	−0.314359	−0.157179	−	0.987570i	$-0.550240\pi$
$659$	−8.06990	−0.314359	−0.157179	+	0.987570i	$0.550240\pi$
$660$	−0.0603308	−0.00234838
$661$	21.8899	0.851418	0.425709	−	0.904860i	$-0.360025\pi$
$661$	21.8899	0.851418	0.425709	+	0.904860i	$0.360025\pi$
$662$	10.0520	0.390683
$663$	−0.153745	−0.00597096
$664$	11.8292	0.459062
$665$	−0.912177	−0.0353727
$666$	−24.9674	−0.967469
$667$	−9.72921	−0.376716
$668$	−19.1826	−0.742196
$669$	−0.103063	−0.00398464
$670$	1.14463	0.0442208
$671$	79.2541	3.05957
$672$	−0.0875504	−0.00337733
$673$	−28.7260	−1.10731	−0.553654	−	0.832747i	$-0.686767\pi$
$673$	−28.7260	−1.10731	−0.553654	+	0.832747i	$0.686767\pi$
$674$	−26.4212	−1.01770
$675$	1.90824	0.0734481
$676$	−11.8316	−0.455063
$677$	−26.2866	−1.01028	−0.505138	−	0.863038i	$-0.668559\pi$
$677$	−26.2866	−1.01028	−0.505138	+	0.863038i	$0.668559\pi$
$678$	0.574515	0.0220641
$679$	−20.3123	−0.779515
$680$	−0.322441	−0.0123650
$681$	0.320192	0.0122698
$682$	−32.8218	−1.25681
$683$	13.9216	0.532695	0.266347	−	0.963877i	$-0.414183\pi$
$683$	13.9216	0.532695	0.266347	+	0.963877i	$0.414183\pi$
$684$	−13.7694	−0.526486
$685$	−1.30297	−0.0497840
$686$	16.6061	0.634023
$687$	0.804421	0.0306906
$688$	10.6425	0.405742
$689$	8.93463	0.340382
$690$	−0.00926200	−0.000352598 0
$691$	−49.4549	−1.88135	−0.940676	−	0.339306i	$-0.889808\pi$
$691$	−49.4549	−1.88135	−0.940676	+	0.339306i	$0.889808\pi$
$692$	7.99229	0.303821
$693$	−26.7293	−1.01536
$694$	−17.6246	−0.669020
$695$	1.07494	0.0407746
$696$	0.621888	0.0235726
$697$	13.9333	0.527761
$698$	23.4963	0.889350
$699$	0.237652	0.00898881
$700$	6.81971	0.257761
$701$	−37.3814	−1.41187	−0.705937	−	0.708274i	$-0.749474\pi$
$701$	−37.3814	−1.41187	−0.705937	+	0.708274i	$0.749474\pi$
$702$	−0.414263	−0.0156354
$703$	38.3028	1.44462
$704$	−6.51381	−0.245498
$705$	0.0141857	0.000534263 0
$706$	30.9743	1.16573
$707$	−1.87579	−0.0705465
$708$	−0.386932	−0.0145418
$709$	11.3814	0.427438	0.213719	−	0.976895i	$-0.431442\pi$
$709$	11.3814	0.427438	0.213719	+	0.976895i	$0.431442\pi$
$710$	0.957214	0.0359236
$711$	20.8765	0.782932
$712$	−9.59523	−0.359597
$713$	−5.03881	−0.188705
$714$	0.194822	0.00729103
$715$	−1.02021	−0.0381539
$716$	−17.3138	−0.647048
$717$	−0.927338	−0.0346321
$718$	−30.4711	−1.13717
$719$	−31.9895	−1.19301	−0.596503	−	0.802611i	$-0.703444\pi$
$719$	−31.9895	−1.19301	−0.596503	+	0.802611i	$0.703444\pi$
$720$	−0.434110	−0.0161783
$721$	−3.63417	−0.135344
$722$	2.12375	0.0790380
$723$	0.379076	0.0140980
$724$	20.1045	0.747176
$725$	−48.4418	−1.79908
$726$	2.00897	0.0745600
$727$	40.7426	1.51106	0.755530	−	0.655114i	$-0.227379\pi$
$727$	40.7426	1.51106	0.755530	+	0.655114i	$0.227379\pi$
$728$	−1.48051	−0.0548712
$729$	−26.7796	−0.991838
$730$	2.15131	0.0796235
$731$	−23.6823	−0.875921
$732$	−0.777717	−0.0287452
$733$	−12.0280	−0.444264	−0.222132	−	0.975017i	$-0.571302\pi$
$733$	−12.0280	−0.444264	−0.222132	+	0.975017i	$0.571302\pi$
$734$	16.8433	0.621699
$735$	−0.0474579	−0.00175051
$736$	−1.00000	−0.0368605
$737$	−51.4551	−1.89537
$738$	18.7587	0.690519
$739$	25.3256	0.931616	0.465808	−	0.884886i	$-0.345764\pi$
$739$	25.3256	0.931616	0.465808	+	0.884886i	$0.345764\pi$
$740$	1.20758	0.0443914
$741$	0.317546	0.0116653
$742$	−11.3218	−0.415635
$743$	31.2839	1.14770	0.573848	−	0.818962i	$-0.305450\pi$
$743$	31.2839	1.14770	0.573848	+	0.818962i	$0.305450\pi$
$744$	0.322079	0.0118080
$745$	−0.363896	−0.0133321
$746$	30.6318	1.12151
$747$	−35.4393	−1.29665
$748$	14.4949	0.529985
$749$	−11.9323	−0.435998
$750$	−0.0924255	−0.00337490
$751$	23.9088	0.872445	0.436223	−	0.899839i	$-0.356316\pi$
$751$	23.9088	0.872445	0.436223	+	0.899839i	$0.356316\pi$
$752$	1.53160	0.0558517
$753$	1.50349	0.0547901
$754$	10.5163	0.382982
$755$	−2.09193	−0.0761330
$756$	0.524945	0.0190921
$757$	−10.4606	−0.380197	−0.190099	−	0.981765i	$-0.560881\pi$
$757$	−10.4606	−0.380197	−0.190099	+	0.981765i	$0.560881\pi$
$758$	2.65837	0.0965563
$759$	0.416360	0.0151129
$760$	0.665971	0.0241573
$761$	−4.18916	−0.151857	−0.0759285	−	0.997113i	$-0.524192\pi$
$761$	−4.18916	−0.151857	−0.0759285	+	0.997113i	$0.524192\pi$
$762$	0.299757	0.0108590
$763$	−0.646533	−0.0234061
$764$	−7.39182	−0.267427
$765$	0.966004	0.0349260
$766$	−28.4203	−1.02687
$767$	−6.54314	−0.236259
$768$	0.0639197	0.00230650
$769$	38.4606	1.38692	0.693462	−	0.720493i	$-0.256084\pi$
$769$	38.4606	1.38692	0.693462	+	0.720493i	$0.256084\pi$
$770$	1.29279	0.0465890
$771$	−0.944165	−0.0340033
$772$	−0.427294	−0.0153787
$773$	−14.1303	−0.508230	−0.254115	−	0.967174i	$-0.581784\pi$
$773$	−14.1303	−0.508230	−0.254115	+	0.967174i	$0.581784\pi$
$774$	−31.8841	−1.14605
$775$	−25.0882	−0.901197
$776$	14.8298	0.532359
$777$	−0.729630	−0.0261753
$778$	−27.1274	−0.972565
$779$	−28.7780	−1.03108
$780$	0.0100113	0.000358463 0
$781$	−43.0303	−1.53974
$782$	2.22525	0.0795749
$783$	−3.72879	−0.133256
$784$	−5.12394	−0.182998
$785$	1.20479	0.0430008
$786$	−0.0639197	−0.00227994
$787$	−36.6430	−1.30618	−0.653090	−	0.757280i	$-0.726528\pi$
$787$	−36.6430	−1.30618	−0.653090	+	0.757280i	$0.726528\pi$
$788$	3.38825	0.120702
$789$	0.937380	0.0333716
$790$	−1.00972	−0.0359241
$791$	−12.3109	−0.437726
$792$	19.5148	0.693428
$793$	−13.1514	−0.467021
$794$	−10.4592	−0.371181
$795$	0.0765587	0.00271526
$796$	−18.6439	−0.660815
$797$	52.1629	1.84770	0.923852	−	0.382750i	$-0.125023\pi$
$797$	52.1629	1.84770	0.923852	+	0.382750i	$0.125023\pi$
$798$	−0.402387	−0.0142443
$799$	−3.40820	−0.120573
$800$	−4.97900	−0.176034
$801$	28.7465	1.01571
$802$	−10.7612	−0.379991
$803$	−96.7092	−3.41279
$804$	0.504927	0.0178074
$805$	0.198469	0.00699513
$806$	5.44646	0.191843
$807$	0.562690	0.0198076
$808$	1.36950	0.0481788
$809$	33.4706	1.17676	0.588381	−	0.808584i	$-0.299766\pi$
$809$	33.4706	1.17676	0.588381	+	0.808584i	$0.299766\pi$
$810$	1.29878	0.0456345
$811$	−45.3338	−1.59189	−0.795943	−	0.605372i	$-0.793024\pi$
$811$	−45.3338	−1.59189	−0.795943	+	0.605372i	$0.793024\pi$
$812$	−13.3260	−0.467652
$813$	−0.836409	−0.0293342
$814$	−54.2850	−1.90269
$815$	−1.42072	−0.0497656
$816$	−0.142237	−0.00497931
$817$	48.9136	1.71127
$818$	25.5337	0.892763
$819$	4.43547	0.154988
$820$	−0.907287	−0.0316838
$821$	20.9516	0.731217	0.365609	−	0.930769i	$-0.380861\pi$
$821$	20.9516	0.731217	0.365609	+	0.930769i	$0.380861\pi$
$822$	−0.574777	−0.0200476
$823$	−18.0371	−0.628735	−0.314368	−	0.949301i	$-0.601792\pi$
$823$	−18.0371	−0.628735	−0.314368	+	0.949301i	$0.601792\pi$
$824$	2.65327	0.0924312
$825$	2.07306	0.0721747
$826$	8.29132	0.288492
$827$	31.8232	1.10660	0.553300	−	0.832982i	$-0.313368\pi$
$827$	31.8232	1.10660	0.553300	+	0.832982i	$0.313368\pi$
$828$	2.99591	0.104115
$829$	31.6009	1.09754	0.548771	−	0.835972i	$-0.315096\pi$
$829$	31.6009	1.09754	0.548771	+	0.835972i	$0.315096\pi$
$830$	1.71406	0.0594958
$831$	0.685204	0.0237695
$832$	1.08090	0.0374735
$833$	11.4021	0.395058
$834$	0.474184	0.0164197
$835$	−2.77956	−0.0961908
$836$	−29.9378	−1.03542
$837$	−1.93116	−0.0667506
$838$	32.2303	1.11338
$839$	−10.5961	−0.365818	−0.182909	−	0.983130i	$-0.558551\pi$
$839$	−10.5961	−0.365818	−0.182909	+	0.983130i	$0.558551\pi$
$840$	−0.0126861	−0.000437712 0
$841$	65.6575	2.26405
$842$	23.4563	0.808357
$843$	0.757873	0.0261025
$844$	8.38699	0.288692
$845$	−1.71441	−0.0589776
$846$	−4.58854	−0.157757
$847$	−43.0491	−1.47918
$848$	8.26590	0.283852
$849$	0.0597365	0.00205015
$850$	11.0795	0.380025
$851$	−8.33383	−0.285680
$852$	0.422254	0.0144662
$853$	−26.3022	−0.900571	−0.450286	−	0.892885i	$-0.648678\pi$
$853$	−26.3022	−0.900571	−0.450286	+	0.892885i	$0.648678\pi$
$854$	16.6652	0.570271
$855$	−1.99519	−0.0682342
$856$	8.71168	0.297759
$857$	−10.3827	−0.354666	−0.177333	−	0.984151i	$-0.556747\pi$
$857$	−10.3827	−0.354666	−0.177333	+	0.984151i	$0.556747\pi$
$858$	−0.450045	−0.0153643
$859$	−16.7525	−0.571589	−0.285795	−	0.958291i	$-0.592258\pi$
$859$	−16.7525	−0.571589	−0.285795	+	0.958291i	$0.592258\pi$
$860$	1.54211	0.0525854
$861$	0.548192	0.0186823
$862$	−7.56604	−0.257700
$863$	20.3606	0.693082	0.346541	−	0.938035i	$-0.387356\pi$
$863$	20.3606	0.693082	0.346541	+	0.938035i	$0.387356\pi$
$864$	−0.383257	−0.0130387
$865$	1.15809	0.0393761
$866$	−14.2675	−0.484829
$867$	−0.770120	−0.0261546
$868$	−6.90163	−0.234257
$869$	45.3904	1.53976
$870$	0.0901119	0.00305508
$871$	8.53848	0.289315
$872$	0.472027	0.0159849
$873$	−44.4288	−1.50369
$874$	−4.59606	−0.155464
$875$	1.98053	0.0669541
$876$	0.949002	0.0320638
$877$	−44.5787	−1.50532	−0.752658	−	0.658411i	$-0.771229\pi$
$877$	−44.5787	−1.50532	−0.752658	+	0.658411i	$0.771229\pi$
$878$	−25.2258	−0.851329
$879$	−0.789790	−0.0266389
$880$	−0.943854	−0.0318173
$881$	−16.7933	−0.565781	−0.282891	−	0.959152i	$-0.591293\pi$
$881$	−16.7933	−0.565781	−0.282891	+	0.959152i	$0.591293\pi$
$882$	15.3509	0.516891
$883$	32.4222	1.09109	0.545546	−	0.838081i	$-0.316322\pi$
$883$	32.4222	1.09109	0.545546	+	0.838081i	$0.316322\pi$
$884$	−2.40528	−0.0808984
$885$	−0.0560666	−0.00188466
$886$	−14.5159	−0.487672
$887$	15.9790	0.536523	0.268262	−	0.963346i	$-0.413551\pi$
$887$	15.9790	0.536523	0.268262	+	0.963346i	$0.413551\pi$
$888$	0.532696	0.0178761
$889$	−6.42330	−0.215431
$890$	−1.39035	−0.0466048
$891$	−58.3848	−1.95597
$892$	−1.61238	−0.0539865
$893$	7.03932	0.235562
$894$	−0.160525	−0.00536875
$895$	−2.50878	−0.0838594
$896$	−1.36969	−0.0457583
$897$	−0.0690909	−0.00230688
$898$	22.0227	0.734907
$899$	49.0236	1.63503
$900$	14.9167	0.497222
$901$	−18.3937	−0.612784
$902$	40.7858	1.35802
$903$	−0.931756	−0.0310069
$904$	8.98808	0.298939
$905$	2.91315	0.0968363
$906$	−0.922807	−0.0306582
$907$	−5.15503	−0.171170	−0.0855850	−	0.996331i	$-0.527276\pi$
$907$	−5.15503	−0.171170	−0.0855850	+	0.996331i	$0.527276\pi$
$908$	5.00929	0.166239
$909$	−4.10290	−0.136085
$910$	−0.214526	−0.00711147
$911$	54.7360	1.81348	0.906742	−	0.421686i	$-0.138562\pi$
$911$	54.7360	1.81348	0.906742	+	0.421686i	$0.138562\pi$
$912$	0.293779	0.00972798
$913$	−77.0531	−2.55009
$914$	35.0010	1.15773
$915$	−0.112692	−0.00372547
$916$	12.5849	0.415816
$917$	1.36969	0.0452313
$918$	0.852844	0.0281480
$919$	−28.9165	−0.953868	−0.476934	−	0.878939i	$-0.658252\pi$
$919$	−28.9165	−0.953868	−0.476934	+	0.878939i	$0.658252\pi$
$920$	−0.144901	−0.00477723
$921$	0.798379	0.0263075
$922$	−16.3963	−0.539985
$923$	7.14045	0.235031
$924$	0.570286	0.0187610
$925$	−41.4942	−1.36432
$926$	−18.2034	−0.598200
$927$	−7.94898	−0.261079
$928$	9.72921	0.319377
$929$	−54.1701	−1.77726	−0.888632	−	0.458622i	$-0.848343\pi$
$929$	−54.1701	−1.77726	−0.888632	+	0.458622i	$0.848343\pi$
$930$	0.0466694	0.00153035
$931$	−23.5499	−0.771817
$932$	3.71797	0.121786
$933$	−0.235401	−0.00770669
$934$	20.8751	0.683053
$935$	2.10032	0.0686877
$936$	−3.23829	−0.105847
$937$	43.8467	1.43241	0.716205	−	0.697890i	$-0.245878\pi$
$937$	43.8467	1.43241	0.716205	+	0.697890i	$0.245878\pi$
$938$	−10.8198	−0.353278
$939$	0.434662	0.0141846
$940$	0.221930	0.00723855
$941$	33.1028	1.07912	0.539560	−	0.841947i	$-0.318590\pi$
$941$	33.1028	1.07912	0.539560	+	0.841947i	$0.318590\pi$
$942$	0.531467	0.0173161
$943$	6.26144	0.203901
$944$	−6.05341	−0.197022
$945$	0.0760648	0.00247439
$946$	−69.3233	−2.25389
$947$	−33.1584	−1.07750	−0.538751	−	0.842465i	$-0.681104\pi$
$947$	−33.1584	−1.07750	−0.538751	+	0.842465i	$0.681104\pi$
$948$	−0.445414	−0.0144664
$949$	16.0479	0.520938
$950$	−22.8838	−0.742448
$951$	0.765768	0.0248317
$952$	3.04792	0.0987836
$953$	−5.67178	−0.183727	−0.0918635	−	0.995772i	$-0.529282\pi$
$953$	−5.67178	−0.183727	−0.0918635	+	0.995772i	$0.529282\pi$
$954$	−24.7639	−0.801762
$955$	−1.07108	−0.0346593
$956$	−14.5079	−0.469218
$957$	−4.05086	−0.130946
$958$	12.2014	0.394209
$959$	12.3165	0.397722
$960$	0.00926200	0.000298930 0
$961$	−5.61040	−0.180981
$962$	9.00806	0.290431
$963$	−26.0994	−0.841043
$964$	5.93050	0.191009
$965$	−0.0619152	−0.00199312
$966$	0.0875504	0.00281689
$967$	−38.7461	−1.24599	−0.622995	−	0.782226i	$-0.714084\pi$
$967$	−38.7461	−1.24599	−0.622995	+	0.782226i	$0.714084\pi$
$968$	31.4297	1.01019
$969$	−0.653732	−0.0210009
$970$	2.14885	0.0689954
$971$	−43.6847	−1.40191	−0.700954	−	0.713206i	$-0.747242\pi$
$971$	−43.6847	−1.40191	−0.700954	+	0.713206i	$0.747242\pi$
$972$	1.72270	0.0552556
$973$	−10.1610	−0.325746
$974$	−25.0139	−0.801498
$975$	−0.344004	−0.0110169
$976$	−12.1671	−0.389459
$977$	−41.3602	−1.32323	−0.661615	−	0.749844i	$-0.730129\pi$
$977$	−41.3602	−1.32323	−0.661615	+	0.749844i	$0.730129\pi$
$978$	−0.626718	−0.0200402
$979$	62.5015	1.99756
$980$	−0.742461	−0.0237171
$981$	−1.41415	−0.0451504
$982$	−0.785519	−0.0250669
$983$	50.4296	1.60846	0.804228	−	0.594322i	$-0.202579\pi$
$983$	50.4296	1.60846	0.804228	+	0.594322i	$0.202579\pi$
$984$	−0.400229	−0.0127588
$985$	0.490960	0.0156433
$986$	−21.6500	−0.689475
$987$	−0.134092	−0.00426820
$988$	4.96789	0.158050
$989$	−10.6425	−0.338412
$990$	2.82771	0.0898704
$991$	−47.5155	−1.50938	−0.754691	−	0.656081i	$-0.772213\pi$
$991$	−47.5155	−1.50938	−0.754691	+	0.656081i	$0.772213\pi$
$992$	5.03881	0.159982
$993$	0.642522	0.0203898
$994$	−9.04821	−0.286992
$995$	−2.70151	−0.0856436
$996$	0.756118	0.0239585
$997$	−33.6828	−1.06674	−0.533372	−	0.845881i	$-0.679076\pi$
$997$	−33.6828	−1.06674	−0.533372	+	0.845881i	$0.679076\pi$
$998$	37.4757	1.18627
$999$	−3.19400	−0.101054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.18	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.18	✓	35	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.0639197 q^{3} +1.00000 q^{4} +0.144901 q^{5} +0.0639197 q^{6} -1.36969 q^{7} +1.00000 q^{8} -2.99591 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.0639197 q^{3} +1.00000 q^{4} +0.144901 q^{5} +0.0639197 q^{6} -1.36969 q^{7} +1.00000 q^{8} -2.99591 q^{9} +0.144901 q^{10} -6.51381 q^{11} +0.0639197 q^{12} +1.08090 q^{13} -1.36969 q^{14} +0.00926200 q^{15} +1.00000 q^{16} -2.22525 q^{17} -2.99591 q^{18} +4.59606 q^{19} +0.144901 q^{20} -0.0875504 q^{21} -6.51381 q^{22} -1.00000 q^{23} +0.0639197 q^{24} -4.97900 q^{25} +1.08090 q^{26} -0.383257 q^{27} -1.36969 q^{28} +9.72921 q^{29} +0.00926200 q^{30} +5.03881 q^{31} +1.00000 q^{32} -0.416360 q^{33} -2.22525 q^{34} -0.198469 q^{35} -2.99591 q^{36} +8.33383 q^{37} +4.59606 q^{38} +0.0690909 q^{39} +0.144901 q^{40} -6.26144 q^{41} -0.0875504 q^{42} +10.6425 q^{43} -6.51381 q^{44} -0.434110 q^{45} -1.00000 q^{46} +1.53160 q^{47} +0.0639197 q^{48} -5.12394 q^{49} -4.97900 q^{50} -0.142237 q^{51} +1.08090 q^{52} +8.26590 q^{53} -0.383257 q^{54} -0.943854 q^{55} -1.36969 q^{56} +0.293779 q^{57} +9.72921 q^{58} -6.05341 q^{59} +0.00926200 q^{60} -12.1671 q^{61} +5.03881 q^{62} +4.10349 q^{63} +1.00000 q^{64} +0.156623 q^{65} -0.416360 q^{66} +7.89940 q^{67} -2.22525 q^{68} -0.0639197 q^{69} -0.198469 q^{70} +6.60601 q^{71} -2.99591 q^{72} +14.8468 q^{73} +8.33383 q^{74} -0.318256 q^{75} +4.59606 q^{76} +8.92192 q^{77} +0.0690909 q^{78} -6.96834 q^{79} +0.144901 q^{80} +8.96325 q^{81} -6.26144 q^{82} +11.8292 q^{83} -0.0875504 q^{84} -0.322441 q^{85} +10.6425 q^{86} +0.621888 q^{87} -6.51381 q^{88} -9.59523 q^{89} -0.434110 q^{90} -1.48051 q^{91} -1.00000 q^{92} +0.322079 q^{93} +1.53160 q^{94} +0.665971 q^{95} +0.0639197 q^{96} +14.8298 q^{97} -5.12394 q^{98} +19.5148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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