LMFDB - Embedded newform 6046.2.a.g.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$0$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.36493 q^{3} +1.00000 q^{4} -1.05232 q^{5} +2.36493 q^{6} -2.21269 q^{7} -1.00000 q^{8} +2.59290 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.36493 q^{3} +1.00000 q^{4} -1.05232 q^{5} +2.36493 q^{6} -2.21269 q^{7} -1.00000 q^{8} +2.59290 q^{9} +1.05232 q^{10} -1.54804 q^{11} -2.36493 q^{12} +1.46190 q^{13} +2.21269 q^{14} +2.48867 q^{15} +1.00000 q^{16} +0.691804 q^{17} -2.59290 q^{18} +6.01973 q^{19} -1.05232 q^{20} +5.23285 q^{21} +1.54804 q^{22} -8.55529 q^{23} +2.36493 q^{24} -3.89262 q^{25} -1.46190 q^{26} +0.962765 q^{27} -2.21269 q^{28} +1.90878 q^{29} -2.48867 q^{30} +3.61424 q^{31} -1.00000 q^{32} +3.66101 q^{33} -0.691804 q^{34} +2.32846 q^{35} +2.59290 q^{36} -2.60492 q^{37} -6.01973 q^{38} -3.45729 q^{39} +1.05232 q^{40} +5.47969 q^{41} -5.23285 q^{42} -9.02917 q^{43} -1.54804 q^{44} -2.72857 q^{45} +8.55529 q^{46} +1.59434 q^{47} -2.36493 q^{48} -2.10402 q^{49} +3.89262 q^{50} -1.63607 q^{51} +1.46190 q^{52} +5.63436 q^{53} -0.962765 q^{54} +1.62904 q^{55} +2.21269 q^{56} -14.2362 q^{57} -1.90878 q^{58} +5.80068 q^{59} +2.48867 q^{60} -3.60306 q^{61} -3.61424 q^{62} -5.73727 q^{63} +1.00000 q^{64} -1.53839 q^{65} -3.66101 q^{66} -6.63579 q^{67} +0.691804 q^{68} +20.2327 q^{69} -2.32846 q^{70} -8.82635 q^{71} -2.59290 q^{72} -2.30273 q^{73} +2.60492 q^{74} +9.20577 q^{75} +6.01973 q^{76} +3.42532 q^{77} +3.45729 q^{78} -10.8113 q^{79} -1.05232 q^{80} -10.0556 q^{81} -5.47969 q^{82} -10.6506 q^{83} +5.23285 q^{84} -0.728001 q^{85} +9.02917 q^{86} -4.51412 q^{87} +1.54804 q^{88} +10.4839 q^{89} +2.72857 q^{90} -3.23472 q^{91} -8.55529 q^{92} -8.54744 q^{93} -1.59434 q^{94} -6.33470 q^{95} +2.36493 q^{96} -11.0542 q^{97} +2.10402 q^{98} -4.01391 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 69 q^{2} + 69 q^{4} + 13 q^{5} - 27 q^{7} - 69 q^{8} + 99 q^{9}+O(q^{10}) $ 69 * q - 69 * q^2 + 69 * q^4 + 13 * q^5 - 27 * q^7 - 69 * q^8 + 99 * q^9	\( 69 q - 69 q^{2} + 69 q^{4} + 13 q^{5} - 27 q^{7} - 69 q^{8} + 99 q^{9} - 13 q^{10} + 42 q^{11} - 5 q^{13} + 27 q^{14} + 18 q^{15} + 69 q^{16} + 24 q^{17} - 99 q^{18} + q^{19} + 13 q^{20} + 7 q^{21} - 42 q^{22} + 25 q^{23} + 100 q^{25} + 5 q^{26} + 15 q^{27} - 27 q^{28} + 87 q^{29} - 18 q^{30} + 5 q^{31} - 69 q^{32} + 28 q^{33} - 24 q^{34} + 33 q^{35} + 99 q^{36} - 5 q^{37} - q^{38} + 22 q^{39} - 13 q^{40} + 47 q^{41} - 7 q^{42} - 23 q^{43} + 42 q^{44} + 14 q^{45} - 25 q^{46} + 13 q^{47} + 106 q^{49} - 100 q^{50} + 2 q^{51} - 5 q^{52} + 51 q^{53} - 15 q^{54} - 11 q^{55} + 27 q^{56} + 52 q^{57} - 87 q^{58} + 73 q^{59} + 18 q^{60} + 4 q^{61} - 5 q^{62} - 86 q^{63} + 69 q^{64} + 70 q^{65} - 28 q^{66} - 24 q^{67} + 24 q^{68} + 56 q^{69} - 33 q^{70} + 84 q^{71} - 99 q^{72} + 27 q^{73} + 5 q^{74} + 27 q^{75} + q^{76} + 45 q^{77} - 22 q^{78} + 42 q^{79} + 13 q^{80} + 205 q^{81} - 47 q^{82} + q^{83} + 7 q^{84} - 18 q^{85} + 23 q^{86} - q^{87} - 42 q^{88} + 94 q^{89} - 14 q^{90} + 6 q^{91} + 25 q^{92} - 13 q^{93} - 13 q^{94} + 86 q^{95} + 35 q^{97} - 106 q^{98} + 83 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 69 * q^4 + 13 * q^5 - 27 * q^7 - 69 * q^8 + 99 * q^9 - 13 * q^10 + 42 * q^11 - 5 * q^13 + 27 * q^14 + 18 * q^15 + 69 * q^16 + 24 * q^17 - 99 * q^18 + q^19 + 13 * q^20 + 7 * q^21 - 42 * q^22 + 25 * q^23 + 100 * q^25 + 5 * q^26 + 15 * q^27 - 27 * q^28 + 87 * q^29 - 18 * q^30 + 5 * q^31 - 69 * q^32 + 28 * q^33 - 24 * q^34 + 33 * q^35 + 99 * q^36 - 5 * q^37 - q^38 + 22 * q^39 - 13 * q^40 + 47 * q^41 - 7 * q^42 - 23 * q^43 + 42 * q^44 + 14 * q^45 - 25 * q^46 + 13 * q^47 + 106 * q^49 - 100 * q^50 + 2 * q^51 - 5 * q^52 + 51 * q^53 - 15 * q^54 - 11 * q^55 + 27 * q^56 + 52 * q^57 - 87 * q^58 + 73 * q^59 + 18 * q^60 + 4 * q^61 - 5 * q^62 - 86 * q^63 + 69 * q^64 + 70 * q^65 - 28 * q^66 - 24 * q^67 + 24 * q^68 + 56 * q^69 - 33 * q^70 + 84 * q^71 - 99 * q^72 + 27 * q^73 + 5 * q^74 + 27 * q^75 + q^76 + 45 * q^77 - 22 * q^78 + 42 * q^79 + 13 * q^80 + 205 * q^81 - 47 * q^82 + q^83 + 7 * q^84 - 18 * q^85 + 23 * q^86 - q^87 - 42 * q^88 + 94 * q^89 - 14 * q^90 + 6 * q^91 + 25 * q^92 - 13 * q^93 - 13 * q^94 + 86 * q^95 + 35 * q^97 - 106 * q^98 + 83 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.36493	−1.36539	−0.682697	−	0.730702i	$-0.739193\pi$
$3$	−2.36493	−1.36539	−0.682697	+	0.730702i	$0.739193\pi$
$4$	1.00000	0.500000
$5$	−1.05232	−0.470613	−0.235306	−	0.971921i	$-0.575609\pi$
$5$	−1.05232	−0.470613	−0.235306	+	0.971921i	$0.575609\pi$
$6$	2.36493	0.965479
$7$	−2.21269	−0.836316	−0.418158	−	0.908374i	$-0.637324\pi$
$7$	−2.21269	−0.836316	−0.418158	+	0.908374i	$0.637324\pi$
$8$	−1.00000	−0.353553
$9$	2.59290	0.864300
$10$	1.05232	0.332774
$11$	−1.54804	−0.466752	−0.233376	−	0.972387i	$-0.574977\pi$
$11$	−1.54804	−0.466752	−0.233376	+	0.972387i	$0.574977\pi$
$12$	−2.36493	−0.682697
$13$	1.46190	0.405458	0.202729	−	0.979235i	$-0.435019\pi$
$13$	1.46190	0.405458	0.202729	+	0.979235i	$0.435019\pi$
$14$	2.21269	0.591365
$15$	2.48867	0.642572
$16$	1.00000	0.250000
$17$	0.691804	0.167787	0.0838936	−	0.996475i	$-0.473264\pi$
$17$	0.691804	0.167787	0.0838936	+	0.996475i	$0.473264\pi$
$18$	−2.59290	−0.611152
$19$	6.01973	1.38102	0.690511	−	0.723322i	$-0.257386\pi$
$19$	6.01973	1.38102	0.690511	+	0.723322i	$0.257386\pi$
$20$	−1.05232	−0.235306
$21$	5.23285	1.14190
$22$	1.54804	0.330043
$23$	−8.55529	−1.78390	−0.891950	−	0.452134i	$-0.850663\pi$
$23$	−8.55529	−1.78390	−0.891950	+	0.452134i	$0.850663\pi$
$24$	2.36493	0.482740
$25$	−3.89262	−0.778524
$26$	−1.46190	−0.286702
$27$	0.962765	0.185284
$28$	−2.21269	−0.418158
$29$	1.90878	0.354451	0.177225	−	0.984170i	$-0.443288\pi$
$29$	1.90878	0.354451	0.177225	+	0.984170i	$0.443288\pi$
$30$	−2.48867	−0.454367
$31$	3.61424	0.649137	0.324569	−	0.945862i	$-0.394781\pi$
$31$	3.61424	0.649137	0.324569	+	0.945862i	$0.394781\pi$
$32$	−1.00000	−0.176777
$33$	3.66101	0.637300
$34$	−0.691804	−0.118643
$35$	2.32846	0.393581
$36$	2.59290	0.432150
$37$	−2.60492	−0.428246	−0.214123	−	0.976807i	$-0.568689\pi$
$37$	−2.60492	−0.428246	−0.214123	+	0.976807i	$0.568689\pi$
$38$	−6.01973	−0.976529
$39$	−3.45729	−0.553610
$40$	1.05232	0.166387
$41$	5.47969	0.855784	0.427892	−	0.903830i	$-0.359256\pi$
$41$	5.47969	0.855784	0.427892	+	0.903830i	$0.359256\pi$
$42$	−5.23285	−0.807446
$43$	−9.02917	−1.37694	−0.688468	−	0.725267i	$-0.741716\pi$
$43$	−9.02917	−1.37694	−0.688468	+	0.725267i	$0.741716\pi$
$44$	−1.54804	−0.233376
$45$	−2.72857	−0.406751
$46$	8.55529	1.26141
$47$	1.59434	0.232558	0.116279	−	0.993217i	$-0.462903\pi$
$47$	1.59434	0.232558	0.116279	+	0.993217i	$0.462903\pi$
$48$	−2.36493	−0.341348
$49$	−2.10402	−0.300575
$50$	3.89262	0.550499
$51$	−1.63607	−0.229096
$52$	1.46190	0.202729
$53$	5.63436	0.773938	0.386969	−	0.922093i	$-0.373522\pi$
$53$	5.63436	0.773938	0.386969	+	0.922093i	$0.373522\pi$
$54$	−0.962765	−0.131016
$55$	1.62904	0.219659
$56$	2.21269	0.295682
$57$	−14.2362	−1.88564
$58$	−1.90878	−0.250634
$59$	5.80068	0.755184	0.377592	−	0.925972i	$-0.376752\pi$
$59$	5.80068	0.755184	0.377592	+	0.925972i	$0.376752\pi$
$60$	2.48867	0.321286
$61$	−3.60306	−0.461324	−0.230662	−	0.973034i	$-0.574089\pi$
$61$	−3.60306	−0.461324	−0.230662	+	0.973034i	$0.574089\pi$
$62$	−3.61424	−0.459009
$63$	−5.73727	−0.722828
$64$	1.00000	0.125000
$65$	−1.53839	−0.190814
$66$	−3.66101	−0.450639
$67$	−6.63579	−0.810691	−0.405346	−	0.914164i	$-0.632849\pi$
$67$	−6.63579	−0.810691	−0.405346	+	0.914164i	$0.632849\pi$
$68$	0.691804	0.0838936
$69$	20.2327	2.43573
$70$	−2.32846	−0.278304
$71$	−8.82635	−1.04749	−0.523747	−	0.851874i	$-0.675466\pi$
$71$	−8.82635	−1.04749	−0.523747	+	0.851874i	$0.675466\pi$
$72$	−2.59290	−0.305576
$73$	−2.30273	−0.269514	−0.134757	−	0.990879i	$-0.543025\pi$
$73$	−2.30273	−0.269514	−0.134757	+	0.990879i	$0.543025\pi$
$74$	2.60492	0.302815
$75$	9.20577	1.06299
$76$	6.01973	0.690511
$77$	3.42532	0.390352
$78$	3.45729	0.391461
$79$	−10.8113	−1.21637	−0.608184	−	0.793796i	$-0.708102\pi$
$79$	−10.8113	−1.21637	−0.608184	+	0.793796i	$0.708102\pi$
$80$	−1.05232	−0.117653
$81$	−10.0556	−1.11729
$82$	−5.47969	−0.605131
$83$	−10.6506	−1.16906	−0.584529	−	0.811373i	$-0.698721\pi$
$83$	−10.6506	−1.16906	−0.584529	+	0.811373i	$0.698721\pi$
$84$	5.23285	0.570951
$85$	−0.728001	−0.0789628
$86$	9.02917	0.973641
$87$	−4.51412	−0.483965
$88$	1.54804	0.165022
$89$	10.4839	1.11129	0.555647	−	0.831418i	$-0.312471\pi$
$89$	10.4839	1.11129	0.555647	+	0.831418i	$0.312471\pi$
$90$	2.72857	0.287616
$91$	−3.23472	−0.339091
$92$	−8.55529	−0.891950
$93$	−8.54744	−0.886328
$94$	−1.59434	−0.164444
$95$	−6.33470	−0.649926
$96$	2.36493	0.241370
$97$	−11.0542	−1.12239	−0.561193	−	0.827685i	$-0.689657\pi$
$97$	−11.0542	−1.12239	−0.561193	+	0.827685i	$0.689657\pi$
$98$	2.10402	0.212539
$99$	−4.01391	−0.403413
$100$	−3.89262	−0.389262
$101$	5.56992	0.554227	0.277114	−	0.960837i	$-0.410622\pi$
$101$	5.56992	0.554227	0.277114	+	0.960837i	$0.410622\pi$
$102$	1.63607	0.161995
$103$	−15.8465	−1.56140	−0.780700	−	0.624906i	$-0.785137\pi$
$103$	−15.8465	−1.56140	−0.780700	+	0.624906i	$0.785137\pi$
$104$	−1.46190	−0.143351
$105$	−5.50664	−0.537393
$106$	−5.63436	−0.547257
$107$	5.81548	0.562204	0.281102	−	0.959678i	$-0.409300\pi$
$107$	5.81548	0.562204	0.281102	+	0.959678i	$0.409300\pi$
$108$	0.962765	0.0926421
$109$	−0.366852	−0.0351381	−0.0175690	−	0.999846i	$-0.505593\pi$
$109$	−0.366852	−0.0351381	−0.0175690	+	0.999846i	$0.505593\pi$
$110$	−1.62904	−0.155323
$111$	6.16045	0.584724
$112$	−2.21269	−0.209079
$113$	2.01156	0.189232	0.0946158	−	0.995514i	$-0.469838\pi$
$113$	2.01156	0.189232	0.0946158	+	0.995514i	$0.469838\pi$
$114$	14.2362	1.33335
$115$	9.00292	0.839527
$116$	1.90878	0.177225
$117$	3.79056	0.350437
$118$	−5.80068	−0.533996
$119$	−1.53075	−0.140323
$120$	−2.48867	−0.227183
$121$	−8.60357	−0.782143
$122$	3.60306	0.326206
$123$	−12.9591	−1.16848
$124$	3.61424	0.324569
$125$	9.35790	0.836996
$126$	5.73727	0.511117
$127$	−10.3020	−0.914156	−0.457078	−	0.889427i	$-0.651104\pi$
$127$	−10.3020	−0.914156	−0.457078	+	0.889427i	$0.651104\pi$
$128$	−1.00000	−0.0883883
$129$	21.3534	1.88006
$130$	1.53839	0.134926
$131$	16.1746	1.41318	0.706590	−	0.707623i	$-0.250233\pi$
$131$	16.1746	1.41318	0.706590	+	0.707623i	$0.250233\pi$
$132$	3.66101	0.318650
$133$	−13.3198	−1.15497
$134$	6.63579	0.573245
$135$	−1.01314	−0.0871972
$136$	−0.691804	−0.0593217
$137$	−4.72990	−0.404103	−0.202051	−	0.979375i	$-0.564761\pi$
$137$	−4.72990	−0.404103	−0.202051	+	0.979375i	$0.564761\pi$
$138$	−20.2327	−1.72232
$139$	4.33350	0.367563	0.183781	−	0.982967i	$-0.441166\pi$
$139$	4.33350	0.367563	0.183781	+	0.982967i	$0.441166\pi$
$140$	2.32846	0.196791
$141$	−3.77050	−0.317534
$142$	8.82635	0.740691
$143$	−2.26308	−0.189248
$144$	2.59290	0.216075
$145$	−2.00865	−0.166809
$146$	2.30273	0.190575
$147$	4.97587	0.410403
$148$	−2.60492	−0.214123
$149$	3.08300	0.252569	0.126285	−	0.991994i	$-0.459695\pi$
$149$	3.08300	0.252569	0.126285	+	0.991994i	$0.459695\pi$
$150$	−9.20577	−0.751648
$151$	5.51556	0.448850	0.224425	−	0.974491i	$-0.427950\pi$
$151$	5.51556	0.448850	0.224425	+	0.974491i	$0.427950\pi$
$152$	−6.01973	−0.488265
$153$	1.79378	0.145018
$154$	−3.42532	−0.276021
$155$	−3.80335	−0.305492
$156$	−3.45729	−0.276805
$157$	6.42463	0.512741	0.256370	−	0.966579i	$-0.417473\pi$
$157$	6.42463	0.512741	0.256370	+	0.966579i	$0.417473\pi$
$158$	10.8113	0.860102
$159$	−13.3249	−1.05673
$160$	1.05232	0.0831934
$161$	18.9302	1.49191
$162$	10.0556	0.790040
$163$	5.48135	0.429332	0.214666	−	0.976687i	$-0.431134\pi$
$163$	5.48135	0.429332	0.214666	+	0.976687i	$0.431134\pi$
$164$	5.47969	0.427892
$165$	−3.85256	−0.299921
$166$	10.6506	0.826648
$167$	12.1428	0.939642	0.469821	−	0.882762i	$-0.344318\pi$
$167$	12.1428	0.939642	0.469821	+	0.882762i	$0.344318\pi$
$168$	−5.23285	−0.403723
$169$	−10.8628	−0.835604
$170$	0.728001	0.0558351
$171$	15.6086	1.19362
$172$	−9.02917	−0.688468
$173$	−9.19686	−0.699224	−0.349612	−	0.936894i	$-0.613687\pi$
$173$	−9.19686	−0.699224	−0.349612	+	0.936894i	$0.613687\pi$
$174$	4.51412	0.342215
$175$	8.61314	0.651092
$176$	−1.54804	−0.116688
$177$	−13.7182	−1.03112
$178$	−10.4839	−0.785804
$179$	−23.5941	−1.76350	−0.881751	−	0.471714i	$-0.843635\pi$
$179$	−23.5941	−1.76350	−0.881751	+	0.471714i	$0.843635\pi$
$180$	−2.72857	−0.203375
$181$	−20.6771	−1.53692	−0.768460	−	0.639898i	$-0.778976\pi$
$181$	−20.6771	−1.53692	−0.768460	+	0.639898i	$0.778976\pi$
$182$	3.23472	0.239774
$183$	8.52098	0.629889
$184$	8.55529	0.630704
$185$	2.74121	0.201538
$186$	8.54744	0.626728
$187$	−1.07094	−0.0783150
$188$	1.59434	0.116279
$189$	−2.13030	−0.154956
$190$	6.33470	0.459567
$191$	−19.5172	−1.41221	−0.706107	−	0.708106i	$-0.749550\pi$
$191$	−19.5172	−1.41221	−0.706107	+	0.708106i	$0.749550\pi$
$192$	−2.36493	−0.170674
$193$	3.69898	0.266258	0.133129	−	0.991099i	$-0.457498\pi$
$193$	3.69898	0.266258	0.133129	+	0.991099i	$0.457498\pi$
$194$	11.0542	0.793646
$195$	3.63819	0.260536
$196$	−2.10402	−0.150287
$197$	9.02618	0.643088	0.321544	−	0.946895i	$-0.395798\pi$
$197$	9.02618	0.643088	0.321544	+	0.946895i	$0.395798\pi$
$198$	4.01391	0.285256
$199$	21.2031	1.50305	0.751524	−	0.659706i	$-0.229319\pi$
$199$	21.2031	1.50305	0.751524	+	0.659706i	$0.229319\pi$
$200$	3.89262	0.275250
$201$	15.6932	1.10691
$202$	−5.56992	−0.391898
$203$	−4.22352	−0.296433
$204$	−1.63607	−0.114548
$205$	−5.76641	−0.402743
$206$	15.8465	1.10408
$207$	−22.1830	−1.54182
$208$	1.46190	0.101365
$209$	−9.31878	−0.644594
$210$	5.50664	0.379994
$211$	−1.54318	−0.106237	−0.0531185	−	0.998588i	$-0.516916\pi$
$211$	−1.54318	−0.106237	−0.0531185	+	0.998588i	$0.516916\pi$
$212$	5.63436	0.386969
$213$	20.8737	1.43024
$214$	−5.81548	−0.397538
$215$	9.50160	0.648004
$216$	−0.962765	−0.0655079
$217$	−7.99718	−0.542884
$218$	0.366852	0.0248464
$219$	5.44580	0.367993
$220$	1.62904	0.109830
$221$	1.01135	0.0680307
$222$	−6.16045	−0.413462
$223$	−5.53988	−0.370978	−0.185489	−	0.982646i	$-0.559387\pi$
$223$	−5.53988	−0.370978	−0.185489	+	0.982646i	$0.559387\pi$
$224$	2.21269	0.147841
$225$	−10.0932	−0.672878
$226$	−2.01156	−0.133807
$227$	−4.49438	−0.298302	−0.149151	−	0.988814i	$-0.547654\pi$
$227$	−4.49438	−0.298302	−0.149151	+	0.988814i	$0.547654\pi$
$228$	−14.2362	−0.942819
$229$	6.70358	0.442985	0.221492	−	0.975162i	$-0.428907\pi$
$229$	6.70358	0.442985	0.221492	+	0.975162i	$0.428907\pi$
$230$	−9.00292	−0.593635
$231$	−8.10066	−0.532984
$232$	−1.90878	−0.125317
$233$	15.2141	0.996706	0.498353	−	0.866974i	$-0.333938\pi$
$233$	15.2141	0.996706	0.498353	+	0.866974i	$0.333938\pi$
$234$	−3.79056	−0.247797
$235$	−1.67776	−0.109445
$236$	5.80068	0.377592
$237$	25.5680	1.66082
$238$	1.53075	0.0992235
$239$	5.99076	0.387510	0.193755	−	0.981050i	$-0.437933\pi$
$239$	5.99076	0.387510	0.193755	+	0.981050i	$0.437933\pi$
$240$	2.48867	0.160643
$241$	15.1737	0.977426	0.488713	−	0.872445i	$-0.337467\pi$
$241$	15.1737	0.977426	0.488713	+	0.872445i	$0.337467\pi$
$242$	8.60357	0.553059
$243$	20.8924	1.34025
$244$	−3.60306	−0.230662
$245$	2.21411	0.141454
$246$	12.9591	0.826242
$247$	8.80025	0.559946
$248$	−3.61424	−0.229505
$249$	25.1880	1.59622
$250$	−9.35790	−0.591846
$251$	−26.2487	−1.65680	−0.828401	−	0.560136i	$-0.810749\pi$
$251$	−26.2487	−1.65680	−0.828401	+	0.560136i	$0.810749\pi$
$252$	−5.73727	−0.361414
$253$	13.2439	0.832638
$254$	10.3020	0.646406
$255$	1.72167	0.107815
$256$	1.00000	0.0625000
$257$	14.1270	0.881220	0.440610	−	0.897699i	$-0.354762\pi$
$257$	14.1270	0.881220	0.440610	+	0.897699i	$0.354762\pi$
$258$	−21.3534	−1.32940
$259$	5.76386	0.358149
$260$	−1.53839	−0.0954069
$261$	4.94926	0.306352
$262$	−16.1746	−0.999269
$263$	−15.7552	−0.971508	−0.485754	−	0.874096i	$-0.661455\pi$
$263$	−15.7552	−0.971508	−0.485754	+	0.874096i	$0.661455\pi$
$264$	−3.66101	−0.225319
$265$	−5.92916	−0.364225
$266$	13.3198	0.816687
$267$	−24.7938	−1.51735
$268$	−6.63579	−0.405346
$269$	−10.1167	−0.616827	−0.308413	−	0.951252i	$-0.599798\pi$
$269$	−10.1167	−0.616827	−0.308413	+	0.951252i	$0.599798\pi$
$270$	1.01314	0.0616577
$271$	6.33829	0.385024	0.192512	−	0.981295i	$-0.438337\pi$
$271$	6.33829	0.385024	0.192512	+	0.981295i	$0.438337\pi$
$272$	0.691804	0.0419468
$273$	7.64990	0.462993
$274$	4.72990	0.285744
$275$	6.02593	0.363377
$276$	20.2327	1.21786
$277$	2.22975	0.133973	0.0669863	−	0.997754i	$-0.478662\pi$
$277$	2.22975	0.133973	0.0669863	+	0.997754i	$0.478662\pi$
$278$	−4.33350	−0.259906
$279$	9.37137	0.561049
$280$	−2.32846	−0.139152
$281$	−0.379589	−0.0226444	−0.0113222	−	0.999936i	$-0.503604\pi$
$281$	−0.379589	−0.0226444	−0.0113222	+	0.999936i	$0.503604\pi$
$282$	3.77050	0.224530
$283$	−22.4607	−1.33515	−0.667574	−	0.744543i	$-0.732667\pi$
$283$	−22.4607	−1.33515	−0.667574	+	0.744543i	$0.732667\pi$
$284$	−8.82635	−0.523747
$285$	14.9811	0.887405
$286$	2.26308	0.133819
$287$	−12.1248	−0.715707
$288$	−2.59290	−0.152788
$289$	−16.5214	−0.971847
$290$	2.00865	0.117952
$291$	26.1424	1.53250
$292$	−2.30273	−0.134757
$293$	21.2633	1.24222	0.621109	−	0.783724i	$-0.286683\pi$
$293$	21.2633	1.24222	0.621109	+	0.783724i	$0.286683\pi$
$294$	−4.97587	−0.290199
$295$	−6.10418	−0.355399
$296$	2.60492	0.151408
$297$	−1.49040	−0.0864817
$298$	−3.08300	−0.178593
$299$	−12.5070	−0.723297
$300$	9.20577	0.531496
$301$	19.9787	1.15155
$302$	−5.51556	−0.317385
$303$	−13.1725	−0.756738
$304$	6.01973	0.345255
$305$	3.79158	0.217105
$306$	−1.79378	−0.102544
$307$	3.84635	0.219523	0.109761	−	0.993958i	$-0.464991\pi$
$307$	3.84635	0.219523	0.109761	+	0.993958i	$0.464991\pi$
$308$	3.42532	0.195176
$309$	37.4758	2.13192
$310$	3.80335	0.216016
$311$	−14.0090	−0.794375	−0.397187	−	0.917738i	$-0.630014\pi$
$311$	−14.0090	−0.794375	−0.397187	+	0.917738i	$0.630014\pi$
$312$	3.45729	0.195731
$313$	17.5987	0.994736	0.497368	−	0.867540i	$-0.334300\pi$
$313$	17.5987	0.994736	0.497368	+	0.867540i	$0.334300\pi$
$314$	−6.42463	−0.362563
$315$	6.03746	0.340172
$316$	−10.8113	−0.608184
$317$	−13.0098	−0.730701	−0.365351	−	0.930870i	$-0.619051\pi$
$317$	−13.0098	−0.730701	−0.365351	+	0.930870i	$0.619051\pi$
$318$	13.3249	0.747221
$319$	−2.95486	−0.165440
$320$	−1.05232	−0.0588266
$321$	−13.7532	−0.767629
$322$	−18.9302	−1.05494
$323$	4.16448	0.231718
$324$	−10.0556	−0.558643
$325$	−5.69062	−0.315659
$326$	−5.48135	−0.303584
$327$	0.867580	0.0479773
$328$	−5.47969	−0.302566
$329$	−3.52777	−0.194492
$330$	3.85256	0.212076
$331$	−30.2502	−1.66270	−0.831351	−	0.555748i	$-0.812432\pi$
$331$	−30.2502	−1.66270	−0.831351	+	0.555748i	$0.812432\pi$
$332$	−10.6506	−0.584529
$333$	−6.75429	−0.370133
$334$	−12.1428	−0.664427
$335$	6.98299	0.381522
$336$	5.23285	0.285475
$337$	−2.14102	−0.116629	−0.0583145	−	0.998298i	$-0.518573\pi$
$337$	−2.14102	−0.116629	−0.0583145	+	0.998298i	$0.518573\pi$
$338$	10.8628	0.590861
$339$	−4.75720	−0.258376
$340$	−0.728001	−0.0394814
$341$	−5.59499	−0.302986
$342$	−15.6086	−0.844014
$343$	20.1443	1.08769
$344$	9.02917	0.486820
$345$	−21.2913	−1.14628
$346$	9.19686	0.494426
$347$	8.51110	0.456900	0.228450	−	0.973556i	$-0.426634\pi$
$347$	8.51110	0.456900	0.228450	+	0.973556i	$0.426634\pi$
$348$	−4.51412	−0.241982
$349$	−16.7000	−0.893932	−0.446966	−	0.894551i	$-0.647496\pi$
$349$	−16.7000	−0.893932	−0.446966	+	0.894551i	$0.647496\pi$
$350$	−8.61314	−0.460392
$351$	1.40747	0.0751250
$352$	1.54804	0.0825108
$353$	26.6712	1.41956	0.709782	−	0.704421i	$-0.248793\pi$
$353$	26.6712	1.41956	0.709782	+	0.704421i	$0.248793\pi$
$354$	13.7182	0.729114
$355$	9.28816	0.492965
$356$	10.4839	0.555647
$357$	3.62011	0.191596
$358$	23.5941	1.24698
$359$	28.0211	1.47890	0.739449	−	0.673213i	$-0.235086\pi$
$359$	28.0211	1.47890	0.739449	+	0.673213i	$0.235086\pi$
$360$	2.72857	0.143808
$361$	17.2372	0.907219
$362$	20.6771	1.08677
$363$	20.3469	1.06793
$364$	−3.23472	−0.169546
$365$	2.42321	0.126837
$366$	−8.52098	−0.445399
$367$	23.2300	1.21259	0.606297	−	0.795238i	$-0.292654\pi$
$367$	23.2300	1.21259	0.606297	+	0.795238i	$0.292654\pi$
$368$	−8.55529	−0.445975
$369$	14.2083	0.739654
$370$	−2.74121	−0.142509
$371$	−12.4671	−0.647257
$372$	−8.54744	−0.443164
$373$	13.1317	0.679932	0.339966	−	0.940438i	$-0.389584\pi$
$373$	13.1317	0.679932	0.339966	+	0.940438i	$0.389584\pi$
$374$	1.07094	0.0553770
$375$	−22.1308	−1.14283
$376$	−1.59434	−0.0822218
$377$	2.79044	0.143715
$378$	2.13030	0.109571
$379$	−20.4158	−1.04869	−0.524344	−	0.851507i	$-0.675689\pi$
$379$	−20.4158	−1.04869	−0.524344	+	0.851507i	$0.675689\pi$
$380$	−6.33470	−0.324963
$381$	24.3635	1.24818
$382$	19.5172	0.998586
$383$	−1.14386	−0.0584483	−0.0292241	−	0.999573i	$-0.509304\pi$
$383$	−1.14386	−0.0584483	−0.0292241	+	0.999573i	$0.509304\pi$
$384$	2.36493	0.120685
$385$	−3.60455	−0.183705
$386$	−3.69898	−0.188273
$387$	−23.4117	−1.19009
$388$	−11.0542	−0.561193
$389$	4.60635	0.233551	0.116776	−	0.993158i	$-0.462744\pi$
$389$	4.60635	0.233551	0.116776	+	0.993158i	$0.462744\pi$
$390$	−3.63819	−0.184227
$391$	−5.91858	−0.299316
$392$	2.10402	0.106269
$393$	−38.2518	−1.92955
$394$	−9.02618	−0.454732
$395$	11.3770	0.572438
$396$	−4.01391	−0.201707
$397$	18.2570	0.916292	0.458146	−	0.888877i	$-0.348514\pi$
$397$	18.2570	0.916292	0.458146	+	0.888877i	$0.348514\pi$
$398$	−21.2031	−1.06281
$399$	31.5003	1.57699
$400$	−3.89262	−0.194631
$401$	13.7042	0.684357	0.342179	−	0.939635i	$-0.388835\pi$
$401$	13.7042	0.684357	0.342179	+	0.939635i	$0.388835\pi$
$402$	−15.6932	−0.782705
$403$	5.28366	0.263198
$404$	5.56992	0.277114
$405$	10.5817	0.525809
$406$	4.22352	0.209610
$407$	4.03252	0.199884
$408$	1.63607	0.0809975
$409$	32.1829	1.59134	0.795671	−	0.605729i	$-0.207118\pi$
$409$	32.1829	1.59134	0.795671	+	0.605729i	$0.207118\pi$
$410$	5.76641	0.284782
$411$	11.1859	0.551759
$412$	−15.8465	−0.780700
$413$	−12.8351	−0.631573
$414$	22.1830	1.09023
$415$	11.2079	0.550173
$416$	−1.46190	−0.0716756
$417$	−10.2484	−0.501868
$418$	9.31878	0.455797
$419$	15.3731	0.751027	0.375513	−	0.926817i	$-0.377466\pi$
$419$	15.3731	0.751027	0.375513	+	0.926817i	$0.377466\pi$
$420$	−5.50664	−0.268697
$421$	−11.1660	−0.544197	−0.272098	−	0.962269i	$-0.587718\pi$
$421$	−11.1660	−0.544197	−0.272098	+	0.962269i	$0.587718\pi$
$422$	1.54318	0.0751209
$423$	4.13396	0.201000
$424$	−5.63436	−0.273629
$425$	−2.69293	−0.130626
$426$	−20.8737	−1.01133
$427$	7.97243	0.385813
$428$	5.81548	0.281102
$429$	5.35203	0.258398
$430$	−9.50160	−0.458208
$431$	−4.76323	−0.229437	−0.114718	−	0.993398i	$-0.536597\pi$
$431$	−4.76323	−0.229437	−0.114718	+	0.993398i	$0.536597\pi$
$432$	0.962765	0.0463211
$433$	−2.12741	−0.102237	−0.0511184	−	0.998693i	$-0.516279\pi$
$433$	−2.12741	−0.102237	−0.0511184	+	0.998693i	$0.516279\pi$
$434$	7.99718	0.383877
$435$	4.75031	0.227760
$436$	−0.366852	−0.0175690
$437$	−51.5005	−2.46360
$438$	−5.44580	−0.260210
$439$	4.19829	0.200373	0.100187	−	0.994969i	$-0.468056\pi$
$439$	4.19829	0.200373	0.100187	+	0.994969i	$0.468056\pi$
$440$	−1.62904	−0.0776613
$441$	−5.45552	−0.259787
$442$	−1.01135	−0.0481050
$443$	23.2227	1.10334	0.551672	−	0.834061i	$-0.313990\pi$
$443$	23.2227	1.10334	0.551672	+	0.834061i	$0.313990\pi$
$444$	6.16045	0.292362
$445$	−11.0325	−0.522989
$446$	5.53988	0.262321
$447$	−7.29108	−0.344856
$448$	−2.21269	−0.104540
$449$	25.0587	1.18260	0.591298	−	0.806453i	$-0.298616\pi$
$449$	25.0587	1.18260	0.591298	+	0.806453i	$0.298616\pi$
$450$	10.0932	0.475796
$451$	−8.48279	−0.399439
$452$	2.01156	0.0946158
$453$	−13.0439	−0.612856
$454$	4.49438	0.210932
$455$	3.40397	0.159581
$456$	14.2362	0.666673
$457$	36.3747	1.70154	0.850768	−	0.525542i	$-0.176137\pi$
$457$	36.3747	1.70154	0.850768	+	0.525542i	$0.176137\pi$
$458$	−6.70358	−0.313238
$459$	0.666045	0.0310883
$460$	9.00292	0.419763
$461$	35.6387	1.65986	0.829929	−	0.557868i	$-0.188381\pi$
$461$	35.6387	1.65986	0.829929	+	0.557868i	$0.188381\pi$
$462$	8.10066	0.376877
$463$	−21.7529	−1.01094	−0.505471	−	0.862844i	$-0.668681\pi$
$463$	−21.7529	−1.01094	−0.505471	+	0.862844i	$0.668681\pi$
$464$	1.90878	0.0886127
$465$	8.99466	0.417117
$466$	−15.2141	−0.704778
$467$	25.7724	1.19260	0.596302	−	0.802760i	$-0.296636\pi$
$467$	25.7724	1.19260	0.596302	+	0.802760i	$0.296636\pi$
$468$	3.79056	0.175219
$469$	14.6829	0.677994
$470$	1.67776	0.0773893
$471$	−15.1938	−0.700093
$472$	−5.80068	−0.266998
$473$	13.9775	0.642687
$474$	−25.5680	−1.17438
$475$	−23.4325	−1.07516
$476$	−1.53075	−0.0701616
$477$	14.6093	0.668915
$478$	−5.99076	−0.274011
$479$	27.4992	1.25647	0.628235	−	0.778024i	$-0.283778\pi$
$479$	27.4992	1.25647	0.628235	+	0.778024i	$0.283778\pi$
$480$	−2.48867	−0.113592
$481$	−3.80813	−0.173636
$482$	−15.1737	−0.691144
$483$	−44.7685	−2.03704
$484$	−8.60357	−0.391071
$485$	11.6326	0.528209
$486$	−20.8924	−0.947700
$487$	13.1392	0.595394	0.297697	−	0.954660i	$-0.403781\pi$
$487$	13.1392	0.595394	0.297697	+	0.954660i	$0.403781\pi$
$488$	3.60306	0.163103
$489$	−12.9630	−0.586208
$490$	−2.21411	−0.100023
$491$	−3.77326	−0.170285	−0.0851425	−	0.996369i	$-0.527135\pi$
$491$	−3.77326	−0.170285	−0.0851425	+	0.996369i	$0.527135\pi$
$492$	−12.9591	−0.584241
$493$	1.32050	0.0594723
$494$	−8.80025	−0.395942
$495$	4.22393	0.189851
$496$	3.61424	0.162284
$497$	19.5299	0.876037
$498$	−25.1880	−1.12870
$499$	27.7300	1.24137	0.620683	−	0.784061i	$-0.286855\pi$
$499$	27.7300	1.24137	0.620683	+	0.784061i	$0.286855\pi$
$500$	9.35790	0.418498
$501$	−28.7170	−1.28298
$502$	26.2487	1.17154
$503$	−29.4091	−1.31129	−0.655643	−	0.755071i	$-0.727602\pi$
$503$	−29.4091	−1.31129	−0.655643	+	0.755071i	$0.727602\pi$
$504$	5.73727	0.255558
$505$	−5.86135	−0.260827
$506$	−13.2439	−0.588764
$507$	25.6899	1.14093
$508$	−10.3020	−0.457078
$509$	10.2497	0.454308	0.227154	−	0.973859i	$-0.427058\pi$
$509$	10.2497	0.454308	0.227154	+	0.973859i	$0.427058\pi$
$510$	−1.72167	−0.0762370
$511$	5.09522	0.225399
$512$	−1.00000	−0.0441942
$513$	5.79559	0.255881
$514$	−14.1270	−0.623116
$515$	16.6756	0.734815
$516$	21.3534	0.940030
$517$	−2.46810	−0.108547
$518$	−5.76386	−0.253250
$519$	21.7499	0.954717
$520$	1.53839	0.0674629
$521$	39.9801	1.75156	0.875781	−	0.482709i	$-0.160347\pi$
$521$	39.9801	1.75156	0.875781	+	0.482709i	$0.160347\pi$
$522$	−4.94926	−0.216623
$523$	−7.91543	−0.346118	−0.173059	−	0.984912i	$-0.555365\pi$
$523$	−7.91543	−0.346118	−0.173059	+	0.984912i	$0.555365\pi$
$524$	16.1746	0.706590
$525$	−20.3695	−0.888997
$526$	15.7552	0.686960
$527$	2.50035	0.108917
$528$	3.66101	0.159325
$529$	50.1929	2.18230
$530$	5.92916	0.257546
$531$	15.0406	0.652705
$532$	−13.3198	−0.577485
$533$	8.01077	0.346985
$534$	24.7938	1.07293
$535$	−6.11976	−0.264580
$536$	6.63579	0.286623
$537$	55.7983	2.40788
$538$	10.1167	0.436162
$539$	3.25711	0.140294
$540$	−1.01314	−0.0435986
$541$	25.6825	1.10418	0.552088	−	0.833786i	$-0.313831\pi$
$541$	25.6825	1.10418	0.552088	+	0.833786i	$0.313831\pi$
$542$	−6.33829	−0.272253
$543$	48.9000	2.09850
$544$	−0.691804	−0.0296609
$545$	0.386047	0.0165364
$546$	−7.64990	−0.327386
$547$	16.4901	0.705064	0.352532	−	0.935800i	$-0.385321\pi$
$547$	16.4901	0.705064	0.352532	+	0.935800i	$0.385321\pi$
$548$	−4.72990	−0.202051
$549$	−9.34237	−0.398722
$550$	−6.02593	−0.256946
$551$	11.4903	0.489504
$552$	−20.2327	−0.861159
$553$	23.9220	1.01727
$554$	−2.22975	−0.0947330
$555$	−6.48278	−0.275179
$556$	4.33350	0.183781
$557$	−19.1138	−0.809877	−0.404938	−	0.914344i	$-0.632707\pi$
$557$	−19.1138	−0.809877	−0.404938	+	0.914344i	$0.632707\pi$
$558$	−9.37137	−0.396722
$559$	−13.1998	−0.558290
$560$	2.32846	0.0983953
$561$	2.53270	0.106931
$562$	0.379589	0.0160120
$563$	−40.4881	−1.70637	−0.853184	−	0.521609i	$-0.825332\pi$
$563$	−40.4881	−1.70637	−0.853184	+	0.521609i	$0.825332\pi$
$564$	−3.77050	−0.158767
$565$	−2.11681	−0.0890548
$566$	22.4607	0.944093
$567$	22.2498	0.934404
$568$	8.82635	0.370345
$569$	0.315500	0.0132265	0.00661323	−	0.999978i	$-0.497895\pi$
$569$	0.315500	0.0132265	0.00661323	+	0.999978i	$0.497895\pi$
$570$	−14.9811	−0.627490
$571$	32.0352	1.34063	0.670317	−	0.742075i	$-0.266158\pi$
$571$	32.0352	1.34063	0.670317	+	0.742075i	$0.266158\pi$
$572$	−2.26308	−0.0946241
$573$	46.1568	1.92823
$574$	12.1248	0.506081
$575$	33.3025	1.38881
$576$	2.59290	0.108037
$577$	24.0641	1.00180	0.500902	−	0.865504i	$-0.333002\pi$
$577$	24.0641	1.00180	0.500902	+	0.865504i	$0.333002\pi$
$578$	16.5214	0.687200
$579$	−8.74783	−0.363547
$580$	−2.00865	−0.0834045
$581$	23.5665	0.977702
$582$	−26.1424	−1.08364
$583$	−8.72221	−0.361237
$584$	2.30273	0.0952877
$585$	−3.98889	−0.164920
$586$	−21.2633	−0.878380
$587$	3.13876	0.129550	0.0647752	−	0.997900i	$-0.479367\pi$
$587$	3.13876	0.129550	0.0647752	+	0.997900i	$0.479367\pi$
$588$	4.97587	0.205202
$589$	21.7568	0.896472
$590$	6.10418	0.251305
$591$	−21.3463	−0.878069
$592$	−2.60492	−0.107061
$593$	−22.5511	−0.926061	−0.463031	−	0.886342i	$-0.653238\pi$
$593$	−22.5511	−0.926061	−0.463031	+	0.886342i	$0.653238\pi$
$594$	1.49040	0.0611518
$595$	1.61084	0.0660379
$596$	3.08300	0.126285
$597$	−50.1438	−2.05225
$598$	12.5070	0.511448
$599$	−28.3038	−1.15646	−0.578230	−	0.815874i	$-0.696256\pi$
$599$	−28.3038	−1.15646	−0.578230	+	0.815874i	$0.696256\pi$
$600$	−9.20577	−0.375824
$601$	4.11225	0.167742	0.0838710	−	0.996477i	$-0.473272\pi$
$601$	4.11225	0.167742	0.0838710	+	0.996477i	$0.473272\pi$
$602$	−19.9787	−0.814272
$603$	−17.2059	−0.700680
$604$	5.51556	0.224425
$605$	9.05373	0.368087
$606$	13.1725	0.535095
$607$	−1.20624	−0.0489599	−0.0244799	−	0.999700i	$-0.507793\pi$
$607$	−1.20624	−0.0489599	−0.0244799	+	0.999700i	$0.507793\pi$
$608$	−6.01973	−0.244132
$609$	9.98833	0.404748
$610$	−3.79158	−0.153517
$611$	2.33077	0.0942927
$612$	1.79378	0.0725092
$613$	−13.6908	−0.552964	−0.276482	−	0.961019i	$-0.589169\pi$
$613$	−13.6908	−0.552964	−0.276482	+	0.961019i	$0.589169\pi$
$614$	−3.84635	−0.155226
$615$	13.6372	0.549903
$616$	−3.42532	−0.138010
$617$	−5.79423	−0.233267	−0.116633	−	0.993175i	$-0.537210\pi$
$617$	−5.79423	−0.233267	−0.116633	+	0.993175i	$0.537210\pi$
$618$	−37.4758	−1.50750
$619$	−17.5258	−0.704423	−0.352211	−	0.935921i	$-0.614570\pi$
$619$	−17.5258	−0.704423	−0.352211	+	0.935921i	$0.614570\pi$
$620$	−3.80335	−0.152746
$621$	−8.23673	−0.330529
$622$	14.0090	0.561708
$623$	−23.1976	−0.929394
$624$	−3.45729	−0.138403
$625$	9.61556	0.384622
$626$	−17.5987	−0.703385
$627$	22.0383	0.880124
$628$	6.42463	0.256370
$629$	−1.80209	−0.0718542
$630$	−6.03746	−0.240538
$631$	7.79870	0.310462	0.155231	−	0.987878i	$-0.450388\pi$
$631$	7.79870	0.310462	0.155231	+	0.987878i	$0.450388\pi$
$632$	10.8113	0.430051
$633$	3.64952	0.145055
$634$	13.0098	0.516684
$635$	10.8410	0.430213
$636$	−13.3249	−0.528365
$637$	−3.07587	−0.121871
$638$	2.95486	0.116984
$639$	−22.8858	−0.905350
$640$	1.05232	0.0415967
$641$	5.70326	0.225265	0.112633	−	0.993637i	$-0.464072\pi$
$641$	5.70326	0.225265	0.112633	+	0.993637i	$0.464072\pi$
$642$	13.7532	0.542796
$643$	2.45817	0.0969406	0.0484703	−	0.998825i	$-0.484565\pi$
$643$	2.45817	0.0969406	0.0484703	+	0.998825i	$0.484565\pi$
$644$	18.9302	0.745953
$645$	−22.4706	−0.884780
$646$	−4.16448	−0.163849
$647$	23.2681	0.914765	0.457382	−	0.889270i	$-0.348787\pi$
$647$	23.2681	0.914765	0.457382	+	0.889270i	$0.348787\pi$
$648$	10.0556	0.395020
$649$	−8.97968	−0.352483
$650$	5.69062	0.223204
$651$	18.9128	0.741250
$652$	5.48135	0.214666
$653$	−17.9312	−0.701702	−0.350851	−	0.936431i	$-0.614108\pi$
$653$	−17.9312	−0.701702	−0.350851	+	0.936431i	$0.614108\pi$
$654$	−0.867580	−0.0339251
$655$	−17.0209	−0.665061
$656$	5.47969	0.213946
$657$	−5.97075	−0.232941
$658$	3.52777	0.137527
$659$	27.8671	1.08555	0.542774	−	0.839879i	$-0.317374\pi$
$659$	27.8671	1.08555	0.542774	+	0.839879i	$0.317374\pi$
$660$	−3.85256	−0.149961
$661$	0.654716	0.0254655	0.0127327	−	0.999919i	$-0.495947\pi$
$661$	0.654716	0.0254655	0.0127327	+	0.999919i	$0.495947\pi$
$662$	30.2502	1.17571
$663$	−2.39177	−0.0928887
$664$	10.6506	0.413324
$665$	14.0167	0.543544
$666$	6.75429	0.261723
$667$	−16.3301	−0.632305
$668$	12.1428	0.469821
$669$	13.1014	0.506531
$670$	−6.98299	−0.269777
$671$	5.57768	0.215324
$672$	−5.23285	−0.201861
$673$	12.5984	0.485634	0.242817	−	0.970072i	$-0.421929\pi$
$673$	12.5984	0.485634	0.242817	+	0.970072i	$0.421929\pi$
$674$	2.14102	0.0824692
$675$	−3.74768	−0.144248
$676$	−10.8628	−0.417802
$677$	7.40048	0.284423	0.142212	−	0.989836i	$-0.454579\pi$
$677$	7.40048	0.284423	0.142212	+	0.989836i	$0.454579\pi$
$678$	4.75720	0.182699
$679$	24.4595	0.938669
$680$	0.728001	0.0279176
$681$	10.6289	0.407300
$682$	5.59499	0.214243
$683$	−5.93260	−0.227005	−0.113502	−	0.993538i	$-0.536207\pi$
$683$	−5.93260	−0.227005	−0.113502	+	0.993538i	$0.536207\pi$
$684$	15.6086	0.596808
$685$	4.97738	0.190176
$686$	−20.1443	−0.769114
$687$	−15.8535	−0.604849
$688$	−9.02917	−0.344234
$689$	8.23687	0.313800
$690$	21.2913	0.810545
$691$	18.2051	0.692554	0.346277	−	0.938132i	$-0.387446\pi$
$691$	18.2051	0.692554	0.346277	+	0.938132i	$0.387446\pi$
$692$	−9.19686	−0.349612
$693$	8.88152	0.337381
$694$	−8.51110	−0.323077
$695$	−4.56024	−0.172980
$696$	4.51412	0.171107
$697$	3.79088	0.143590
$698$	16.7000	0.632106
$699$	−35.9802	−1.36090
$700$	8.61314	0.325546
$701$	12.7752	0.482513	0.241257	−	0.970461i	$-0.422440\pi$
$701$	12.7752	0.482513	0.241257	+	0.970461i	$0.422440\pi$
$702$	−1.40747	−0.0531214
$703$	−15.6809	−0.591416
$704$	−1.54804	−0.0583439
$705$	3.96779	0.149435
$706$	−26.6712	−1.00378
$707$	−12.3245	−0.463509
$708$	−13.7182	−0.515562
$709$	−36.4723	−1.36975	−0.684873	−	0.728663i	$-0.740142\pi$
$709$	−36.4723	−1.36975	−0.684873	+	0.728663i	$0.740142\pi$
$710$	−9.28816	−0.348579
$711$	−28.0326	−1.05131
$712$	−10.4839	−0.392902
$713$	−30.9209	−1.15800
$714$	−3.62011	−0.135479
$715$	2.38149	0.0890627
$716$	−23.5941	−0.881751
$717$	−14.1677	−0.529104
$718$	−28.0211	−1.04574
$719$	23.5749	0.879195	0.439598	−	0.898195i	$-0.355121\pi$
$719$	23.5749	0.879195	0.439598	+	0.898195i	$0.355121\pi$
$720$	−2.72857	−0.101688
$721$	35.0633	1.30582
$722$	−17.2372	−0.641501
$723$	−35.8848	−1.33457
$724$	−20.6771	−0.768460
$725$	−7.43013	−0.275948
$726$	−20.3469	−0.755143
$727$	−14.2542	−0.528659	−0.264329	−	0.964432i	$-0.585151\pi$
$727$	−14.2542	−0.528659	−0.264329	+	0.964432i	$0.585151\pi$
$728$	3.23472	0.119887
$729$	−19.2425	−0.712684
$730$	−2.42321	−0.0896872
$731$	−6.24642	−0.231032
$732$	8.52098	0.314945
$733$	37.5272	1.38610	0.693049	−	0.720891i	$-0.256267\pi$
$733$	37.5272	1.38610	0.693049	+	0.720891i	$0.256267\pi$
$734$	−23.2300	−0.857434
$735$	−5.23622	−0.193141
$736$	8.55529	0.315352
$737$	10.2725	0.378391
$738$	−14.2083	−0.523015
$739$	−29.0734	−1.06948	−0.534742	−	0.845016i	$-0.679591\pi$
$739$	−29.0734	−1.06948	−0.534742	+	0.845016i	$0.679591\pi$
$740$	2.74121	0.100769
$741$	−20.8120	−0.764547
$742$	12.4671	0.457680
$743$	−40.7629	−1.49544	−0.747722	−	0.664012i	$-0.768853\pi$
$743$	−40.7629	−1.49544	−0.747722	+	0.664012i	$0.768853\pi$
$744$	8.54744	0.313364
$745$	−3.24431	−0.118862
$746$	−13.1317	−0.480785
$747$	−27.6160	−1.01042
$748$	−1.07094	−0.0391575
$749$	−12.8678	−0.470180
$750$	22.1308	0.808102
$751$	17.2118	0.628067	0.314034	−	0.949412i	$-0.398320\pi$
$751$	17.2118	0.628067	0.314034	+	0.949412i	$0.398320\pi$
$752$	1.59434	0.0581396
$753$	62.0763	2.26219
$754$	−2.79044	−0.101622
$755$	−5.80414	−0.211234
$756$	−2.13030	−0.0774781
$757$	−46.9208	−1.70536	−0.852682	−	0.522430i	$-0.825026\pi$
$757$	−46.9208	−1.70536	−0.852682	+	0.522430i	$0.825026\pi$
$758$	20.4158	0.741534
$759$	−31.3210	−1.13688
$760$	6.33470	0.229784
$761$	−8.16588	−0.296013	−0.148006	−	0.988986i	$-0.547286\pi$
$761$	−8.16588	−0.296013	−0.148006	+	0.988986i	$0.547286\pi$
$762$	−24.3635	−0.882598
$763$	0.811728	0.0293865
$764$	−19.5172	−0.706107
$765$	−1.88763	−0.0682476
$766$	1.14386	0.0413292
$767$	8.48001	0.306195
$768$	−2.36493	−0.0853371
$769$	−28.1705	−1.01586	−0.507928	−	0.861400i	$-0.669588\pi$
$769$	−28.1705	−1.01586	−0.507928	+	0.861400i	$0.669588\pi$
$770$	3.60455	0.129899
$771$	−33.4094	−1.20321
$772$	3.69898	0.133129
$773$	10.4879	0.377224	0.188612	−	0.982052i	$-0.439601\pi$
$773$	10.4879	0.377224	0.188612	+	0.982052i	$0.439601\pi$
$774$	23.4117	0.841518
$775$	−14.0689	−0.505369
$776$	11.0542	0.396823
$777$	−13.6311	−0.489014
$778$	−4.60635	−0.165146
$779$	32.9863	1.18186
$780$	3.63819	0.130268
$781$	13.6635	0.488920
$782$	5.91858	0.211648
$783$	1.83770	0.0656741
$784$	−2.10402	−0.0751437
$785$	−6.76078	−0.241303
$786$	38.2518	1.36440
$787$	44.4685	1.58513	0.792565	−	0.609788i	$-0.208745\pi$
$787$	44.4685	1.58513	0.792565	+	0.609788i	$0.208745\pi$
$788$	9.02618	0.321544
$789$	37.2600	1.32649
$790$	−11.3770	−0.404775
$791$	−4.45095	−0.158257
$792$	4.01391	0.142628
$793$	−5.26731	−0.187048
$794$	−18.2570	−0.647916
$795$	14.0221	0.497311
$796$	21.2031	0.751524
$797$	−14.9553	−0.529744	−0.264872	−	0.964284i	$-0.585330\pi$
$797$	−14.9553	−0.529744	−0.264872	+	0.964284i	$0.585330\pi$
$798$	−31.5003	−1.11510
$799$	1.10297	0.0390203
$800$	3.89262	0.137625
$801$	27.1838	0.960491
$802$	−13.7042	−0.483914
$803$	3.56472	0.125796
$804$	15.6932	0.553456
$805$	−19.9206	−0.702110
$806$	−5.28366	−0.186109
$807$	23.9253	0.842212
$808$	−5.56992	−0.195949
$809$	32.7349	1.15090	0.575449	−	0.817838i	$-0.304828\pi$
$809$	32.7349	1.15090	0.575449	+	0.817838i	$0.304828\pi$
$810$	−10.5817	−0.371803
$811$	47.9910	1.68519	0.842596	−	0.538546i	$-0.181026\pi$
$811$	47.9910	1.68519	0.842596	+	0.538546i	$0.181026\pi$
$812$	−4.22352	−0.148216
$813$	−14.9896	−0.525709
$814$	−4.03252	−0.141340
$815$	−5.76815	−0.202049
$816$	−1.63607	−0.0572739
$817$	−54.3532	−1.90158
$818$	−32.1829	−1.12525
$819$	−8.38732	−0.293077
$820$	−5.76641	−0.201372
$821$	−1.36381	−0.0475972	−0.0237986	−	0.999717i	$-0.507576\pi$
$821$	−1.36381	−0.0475972	−0.0237986	+	0.999717i	$0.507576\pi$
$822$	−11.1859	−0.390153
$823$	45.4186	1.58319	0.791596	−	0.611045i	$-0.209250\pi$
$823$	45.4186	1.58319	0.791596	+	0.611045i	$0.209250\pi$
$824$	15.8465	0.552038
$825$	−14.2509	−0.496153
$826$	12.8351	0.446589
$827$	−54.4684	−1.89405	−0.947026	−	0.321156i	$-0.895929\pi$
$827$	−54.4684	−1.89405	−0.947026	+	0.321156i	$0.895929\pi$
$828$	−22.1830	−0.770912
$829$	−31.1746	−1.08274	−0.541370	−	0.840785i	$-0.682094\pi$
$829$	−31.1746	−1.08274	−0.541370	+	0.840785i	$0.682094\pi$
$830$	−11.2079	−0.389031
$831$	−5.27320	−0.182925
$832$	1.46190	0.0506823
$833$	−1.45557	−0.0504326
$834$	10.2484	0.354874
$835$	−12.7782	−0.442208
$836$	−9.31878	−0.322297
$837$	3.47967	0.120275
$838$	−15.3731	−0.531056
$839$	15.8477	0.547122	0.273561	−	0.961855i	$-0.411799\pi$
$839$	15.8477	0.547122	0.273561	+	0.961855i	$0.411799\pi$
$840$	5.50664	0.189997
$841$	−25.3566	−0.874365
$842$	11.1660	0.384805
$843$	0.897702	0.0309185
$844$	−1.54318	−0.0531185
$845$	11.4312	0.393246
$846$	−4.13396	−0.142129
$847$	19.0370	0.654119
$848$	5.63436	0.193485
$849$	53.1180	1.82300
$850$	2.69293	0.0923667
$851$	22.2858	0.763948
$852$	20.8737	0.715121
$853$	−33.9533	−1.16254	−0.581270	−	0.813711i	$-0.697444\pi$
$853$	−33.9533	−1.16254	−0.581270	+	0.813711i	$0.697444\pi$
$854$	−7.97243	−0.272811
$855$	−16.4252	−0.561731
$856$	−5.81548	−0.198769
$857$	−1.04103	−0.0355610	−0.0177805	−	0.999842i	$-0.505660\pi$
$857$	−1.04103	−0.0355610	−0.0177805	+	0.999842i	$0.505660\pi$
$858$	−5.35203	−0.182715
$859$	25.9729	0.886182	0.443091	−	0.896477i	$-0.353882\pi$
$859$	25.9729	0.886182	0.443091	+	0.896477i	$0.353882\pi$
$860$	9.50160	0.324002
$861$	28.6744	0.977221
$862$	4.76323	0.162236
$863$	−19.5721	−0.666243	−0.333122	−	0.942884i	$-0.608102\pi$
$863$	−19.5721	−0.666243	−0.333122	+	0.942884i	$0.608102\pi$
$864$	−0.962765	−0.0327539
$865$	9.67806	0.329064
$866$	2.12741	0.0722923
$867$	39.0720	1.32695
$868$	−7.99718	−0.271442
$869$	16.7363	0.567741
$870$	−4.75031	−0.161051
$871$	−9.70087	−0.328701
$872$	0.366852	0.0124232
$873$	−28.6625	−0.970077
$874$	51.5005	1.74203
$875$	−20.7061	−0.699994
$876$	5.44580	0.183996
$877$	41.0834	1.38729	0.693644	−	0.720318i	$-0.256004\pi$
$877$	41.0834	1.38729	0.693644	+	0.720318i	$0.256004\pi$
$878$	−4.19829	−0.141685
$879$	−50.2863	−1.69612
$880$	1.62904	0.0549148
$881$	38.0561	1.28214	0.641072	−	0.767481i	$-0.278490\pi$
$881$	38.0561	1.28214	0.641072	+	0.767481i	$0.278490\pi$
$882$	5.45552	0.183697
$883$	−3.83216	−0.128963	−0.0644813	−	0.997919i	$-0.520539\pi$
$883$	−3.83216	−0.128963	−0.0644813	+	0.997919i	$0.520539\pi$
$884$	1.01135	0.0340153
$885$	14.4360	0.485260
$886$	−23.2227	−0.780182
$887$	15.4917	0.520160	0.260080	−	0.965587i	$-0.416251\pi$
$887$	15.4917	0.520160	0.260080	+	0.965587i	$0.416251\pi$
$888$	−6.16045	−0.206731
$889$	22.7951	0.764523
$890$	11.0325	0.369809
$891$	15.5664	0.521495
$892$	−5.53988	−0.185489
$893$	9.59750	0.321168
$894$	7.29108	0.243850
$895$	24.8286	0.829927
$896$	2.21269	0.0739206
$897$	29.5781	0.987585
$898$	−25.0587	−0.836221
$899$	6.89878	0.230087
$900$	−10.0932	−0.336439
$901$	3.89787	0.129857
$902$	8.48279	0.282446
$903$	−47.2483	−1.57232
$904$	−2.01156	−0.0669035
$905$	21.7590	0.723294
$906$	13.0439	0.433355
$907$	−47.1142	−1.56440	−0.782201	−	0.623027i	$-0.785903\pi$
$907$	−47.1142	−1.56440	−0.782201	+	0.623027i	$0.785903\pi$
$908$	−4.49438	−0.149151
$909$	14.4422	0.479019
$910$	−3.40397	−0.112841
$911$	−4.99693	−0.165556	−0.0827779	−	0.996568i	$-0.526379\pi$
$911$	−4.99693	−0.165556	−0.0827779	+	0.996568i	$0.526379\pi$
$912$	−14.2362	−0.471409
$913$	16.4876	0.545659
$914$	−36.3747	−1.20317
$915$	−8.96682	−0.296434
$916$	6.70358	0.221492
$917$	−35.7893	−1.18187
$918$	−0.666045	−0.0219828
$919$	43.1564	1.42360	0.711799	−	0.702383i	$-0.247881\pi$
$919$	43.1564	1.42360	0.711799	+	0.702383i	$0.247881\pi$
$920$	−9.00292	−0.296817
$921$	−9.09635	−0.299735
$922$	−35.6387	−1.17370
$923$	−12.9032	−0.424715
$924$	−8.10066	−0.266492
$925$	10.1399	0.333399
$926$	21.7529	0.714844
$927$	−41.0883	−1.34952
$928$	−1.90878	−0.0626586
$929$	−29.1819	−0.957427	−0.478714	−	0.877971i	$-0.658897\pi$
$929$	−29.1819	−0.957427	−0.478714	+	0.877971i	$0.658897\pi$
$930$	−8.99466	−0.294946
$931$	−12.6657	−0.415100
$932$	15.2141	0.498353
$933$	33.1302	1.08463
$934$	−25.7724	−0.843299
$935$	1.12698	0.0368560
$936$	−3.79056	−0.123898
$937$	−60.7755	−1.98545	−0.992724	−	0.120409i	$-0.961579\pi$
$937$	−60.7755	−1.98545	−0.992724	+	0.120409i	$0.961579\pi$
$938$	−14.6829	−0.479414
$939$	−41.6197	−1.35821
$940$	−1.67776	−0.0547225
$941$	16.4090	0.534919	0.267459	−	0.963569i	$-0.413816\pi$
$941$	16.4090	0.534919	0.267459	+	0.963569i	$0.413816\pi$
$942$	15.1938	0.495041
$943$	−46.8804	−1.52663
$944$	5.80068	0.188796
$945$	2.24176	0.0729244
$946$	−13.9775	−0.454448
$947$	12.9791	0.421762	0.210881	−	0.977512i	$-0.432367\pi$
$947$	12.9791	0.421762	0.210881	+	0.977512i	$0.432367\pi$
$948$	25.5680	0.830410
$949$	−3.36636	−0.109277
$950$	23.4325	0.760251
$951$	30.7672	0.997695
$952$	1.53075	0.0496117
$953$	25.3461	0.821040	0.410520	−	0.911851i	$-0.365347\pi$
$953$	25.3461	0.821040	0.410520	+	0.911851i	$0.365347\pi$
$954$	−14.6093	−0.472994
$955$	20.5384	0.664606
$956$	5.99076	0.193755
$957$	6.98804	0.225891
$958$	−27.4992	−0.888458
$959$	10.4658	0.337958
$960$	2.48867	0.0803215
$961$	−17.9372	−0.578621
$962$	3.80813	0.122779
$963$	15.0790	0.485913
$964$	15.1737	0.488713
$965$	−3.89252	−0.125305
$966$	44.7685	1.44040
$967$	−29.4685	−0.947642	−0.473821	−	0.880621i	$-0.657126\pi$
$967$	−29.4685	−0.947642	−0.473821	+	0.880621i	$0.657126\pi$
$968$	8.60357	0.276529
$969$	−9.84870	−0.316386
$970$	−11.6326	−0.373500
$971$	−16.5758	−0.531942	−0.265971	−	0.963981i	$-0.585693\pi$
$971$	−16.5758	−0.531942	−0.265971	+	0.963981i	$0.585693\pi$
$972$	20.8924	0.670125
$973$	−9.58868	−0.307399
$974$	−13.1392	−0.421007
$975$	13.4579	0.430998
$976$	−3.60306	−0.115331
$977$	45.4704	1.45473	0.727363	−	0.686253i	$-0.240746\pi$
$977$	45.4704	1.45473	0.727363	+	0.686253i	$0.240746\pi$
$978$	12.9630	0.414511
$979$	−16.2295	−0.518698
$980$	2.21411	0.0707272
$981$	−0.951211	−0.0303698
$982$	3.77326	0.120410
$983$	−28.4154	−0.906310	−0.453155	−	0.891432i	$-0.649702\pi$
$983$	−28.4154	−0.906310	−0.453155	+	0.891432i	$0.649702\pi$
$984$	12.9591	0.413121
$985$	−9.49845	−0.302646
$986$	−1.32050	−0.0420533
$987$	8.34294	0.265559
$988$	8.80025	0.279973
$989$	77.2472	2.45632
$990$	−4.22393	−0.134245
$991$	−15.7688	−0.500914	−0.250457	−	0.968128i	$-0.580581\pi$
$991$	−15.7688	−0.500914	−0.250457	+	0.968128i	$0.580581\pi$
$992$	−3.61424	−0.114752
$993$	71.5397	2.27024
$994$	−19.5299	−0.619452
$995$	−22.3125	−0.707353
$996$	25.1880	0.798112
$997$	−4.55197	−0.144162	−0.0720811	−	0.997399i	$-0.522964\pi$
$997$	−4.55197	−0.144162	−0.0720811	+	0.997399i	$0.522964\pi$
$998$	−27.7300	−0.877779
$999$	−2.50792	−0.0793472

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.g.1.11	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.g.1.11	✓	69	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.36493 q^{3} +1.00000 q^{4} -1.05232 q^{5} +2.36493 q^{6} -2.21269 q^{7} -1.00000 q^{8} +2.59290 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.36493 q^{3} +1.00000 q^{4} -1.05232 q^{5} +2.36493 q^{6} -2.21269 q^{7} -1.00000 q^{8} +2.59290 q^{9} +1.05232 q^{10} -1.54804 q^{11} -2.36493 q^{12} +1.46190 q^{13} +2.21269 q^{14} +2.48867 q^{15} +1.00000 q^{16} +0.691804 q^{17} -2.59290 q^{18} +6.01973 q^{19} -1.05232 q^{20} +5.23285 q^{21} +1.54804 q^{22} -8.55529 q^{23} +2.36493 q^{24} -3.89262 q^{25} -1.46190 q^{26} +0.962765 q^{27} -2.21269 q^{28} +1.90878 q^{29} -2.48867 q^{30} +3.61424 q^{31} -1.00000 q^{32} +3.66101 q^{33} -0.691804 q^{34} +2.32846 q^{35} +2.59290 q^{36} -2.60492 q^{37} -6.01973 q^{38} -3.45729 q^{39} +1.05232 q^{40} +5.47969 q^{41} -5.23285 q^{42} -9.02917 q^{43} -1.54804 q^{44} -2.72857 q^{45} +8.55529 q^{46} +1.59434 q^{47} -2.36493 q^{48} -2.10402 q^{49} +3.89262 q^{50} -1.63607 q^{51} +1.46190 q^{52} +5.63436 q^{53} -0.962765 q^{54} +1.62904 q^{55} +2.21269 q^{56} -14.2362 q^{57} -1.90878 q^{58} +5.80068 q^{59} +2.48867 q^{60} -3.60306 q^{61} -3.61424 q^{62} -5.73727 q^{63} +1.00000 q^{64} -1.53839 q^{65} -3.66101 q^{66} -6.63579 q^{67} +0.691804 q^{68} +20.2327 q^{69} -2.32846 q^{70} -8.82635 q^{71} -2.59290 q^{72} -2.30273 q^{73} +2.60492 q^{74} +9.20577 q^{75} +6.01973 q^{76} +3.42532 q^{77} +3.45729 q^{78} -10.8113 q^{79} -1.05232 q^{80} -10.0556 q^{81} -5.47969 q^{82} -10.6506 q^{83} +5.23285 q^{84} -0.728001 q^{85} +9.02917 q^{86} -4.51412 q^{87} +1.54804 q^{88} +10.4839 q^{89} +2.72857 q^{90} -3.23472 q^{91} -8.55529 q^{92} -8.54744 q^{93} -1.59434 q^{94} -6.33470 q^{95} +2.36493 q^{96} -11.0542 q^{97} +2.10402 q^{98} -4.01391 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 69 q^{2} + 69 q^{4} + 13 q^{5} - 27 q^{7} - 69 q^{8} + 99 q^{9}+O(q^{10}) \) 69 * q - 69 * q^2 + 69 * q^4 + 13 * q^5 - 27 * q^7 - 69 * q^8 + 99 * q^9	\( 69 q - 69 q^{2} + 69 q^{4} + 13 q^{5} - 27 q^{7} - 69 q^{8} + 99 q^{9} - 13 q^{10} + 42 q^{11} - 5 q^{13} + 27 q^{14} + 18 q^{15} + 69 q^{16} + 24 q^{17} - 99 q^{18} + q^{19} + 13 q^{20} + 7 q^{21} - 42 q^{22} + 25 q^{23} + 100 q^{25} + 5 q^{26} + 15 q^{27} - 27 q^{28} + 87 q^{29} - 18 q^{30} + 5 q^{31} - 69 q^{32} + 28 q^{33} - 24 q^{34} + 33 q^{35} + 99 q^{36} - 5 q^{37} - q^{38} + 22 q^{39} - 13 q^{40} + 47 q^{41} - 7 q^{42} - 23 q^{43} + 42 q^{44} + 14 q^{45} - 25 q^{46} + 13 q^{47} + 106 q^{49} - 100 q^{50} + 2 q^{51} - 5 q^{52} + 51 q^{53} - 15 q^{54} - 11 q^{55} + 27 q^{56} + 52 q^{57} - 87 q^{58} + 73 q^{59} + 18 q^{60} + 4 q^{61} - 5 q^{62} - 86 q^{63} + 69 q^{64} + 70 q^{65} - 28 q^{66} - 24 q^{67} + 24 q^{68} + 56 q^{69} - 33 q^{70} + 84 q^{71} - 99 q^{72} + 27 q^{73} + 5 q^{74} + 27 q^{75} + q^{76} + 45 q^{77} - 22 q^{78} + 42 q^{79} + 13 q^{80} + 205 q^{81} - 47 q^{82} + q^{83} + 7 q^{84} - 18 q^{85} + 23 q^{86} - q^{87} - 42 q^{88} + 94 q^{89} - 14 q^{90} + 6 q^{91} + 25 q^{92} - 13 q^{93} - 13 q^{94} + 86 q^{95} + 35 q^{97} - 106 q^{98} + 83 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 69 * q^4 + 13 * q^5 - 27 * q^7 - 69 * q^8 + 99 * q^9 - 13 * q^10 + 42 * q^11 - 5 * q^13 + 27 * q^14 + 18 * q^15 + 69 * q^16 + 24 * q^17 - 99 * q^18 + q^19 + 13 * q^20 + 7 * q^21 - 42 * q^22 + 25 * q^23 + 100 * q^25 + 5 * q^26 + 15 * q^27 - 27 * q^28 + 87 * q^29 - 18 * q^30 + 5 * q^31 - 69 * q^32 + 28 * q^33 - 24 * q^34 + 33 * q^35 + 99 * q^36 - 5 * q^37 - q^38 + 22 * q^39 - 13 * q^40 + 47 * q^41 - 7 * q^42 - 23 * q^43 + 42 * q^44 + 14 * q^45 - 25 * q^46 + 13 * q^47 + 106 * q^49 - 100 * q^50 + 2 * q^51 - 5 * q^52 + 51 * q^53 - 15 * q^54 - 11 * q^55 + 27 * q^56 + 52 * q^57 - 87 * q^58 + 73 * q^59 + 18 * q^60 + 4 * q^61 - 5 * q^62 - 86 * q^63 + 69 * q^64 + 70 * q^65 - 28 * q^66 - 24 * q^67 + 24 * q^68 + 56 * q^69 - 33 * q^70 + 84 * q^71 - 99 * q^72 + 27 * q^73 + 5 * q^74 + 27 * q^75 + q^76 + 45 * q^77 - 22 * q^78 + 42 * q^79 + 13 * q^80 + 205 * q^81 - 47 * q^82 + q^83 + 7 * q^84 - 18 * q^85 + 23 * q^86 - q^87 - 42 * q^88 + 94 * q^89 - 14 * q^90 + 6 * q^91 + 25 * q^92 - 13 * q^93 - 13 * q^94 + 86 * q^95 + 35 * q^97 - 106 * q^98 + 83 * q^99

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