LMFDB - Embedded newform 8007.2.a.f.1.47

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$48$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.47
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.55264 q^{2} -1.00000 q^{3} +4.51600 q^{4} -2.02616 q^{5} -2.55264 q^{6} -3.46941 q^{7} +6.42244 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.55264 q^{2} -1.00000 q^{3} +4.51600 q^{4} -2.02616 q^{5} -2.55264 q^{6} -3.46941 q^{7} +6.42244 q^{8} +1.00000 q^{9} -5.17206 q^{10} +2.24180 q^{11} -4.51600 q^{12} +2.20934 q^{13} -8.85617 q^{14} +2.02616 q^{15} +7.36222 q^{16} -1.00000 q^{17} +2.55264 q^{18} +1.23709 q^{19} -9.15012 q^{20} +3.46941 q^{21} +5.72251 q^{22} -6.14774 q^{23} -6.42244 q^{24} -0.894688 q^{25} +5.63965 q^{26} -1.00000 q^{27} -15.6678 q^{28} +6.11937 q^{29} +5.17206 q^{30} +7.08825 q^{31} +5.94826 q^{32} -2.24180 q^{33} -2.55264 q^{34} +7.02957 q^{35} +4.51600 q^{36} -8.56157 q^{37} +3.15784 q^{38} -2.20934 q^{39} -13.0129 q^{40} -10.8548 q^{41} +8.85617 q^{42} +0.242642 q^{43} +10.1239 q^{44} -2.02616 q^{45} -15.6930 q^{46} +5.56049 q^{47} -7.36222 q^{48} +5.03681 q^{49} -2.28382 q^{50} +1.00000 q^{51} +9.97735 q^{52} -2.50875 q^{53} -2.55264 q^{54} -4.54223 q^{55} -22.2821 q^{56} -1.23709 q^{57} +15.6206 q^{58} +2.25565 q^{59} +9.15012 q^{60} -5.32578 q^{61} +18.0938 q^{62} -3.46941 q^{63} +0.459342 q^{64} -4.47646 q^{65} -5.72251 q^{66} -4.75839 q^{67} -4.51600 q^{68} +6.14774 q^{69} +17.9440 q^{70} -7.79895 q^{71} +6.42244 q^{72} +9.40328 q^{73} -21.8547 q^{74} +0.894688 q^{75} +5.58668 q^{76} -7.77771 q^{77} -5.63965 q^{78} -2.68310 q^{79} -14.9170 q^{80} +1.00000 q^{81} -27.7085 q^{82} -7.70340 q^{83} +15.6678 q^{84} +2.02616 q^{85} +0.619378 q^{86} -6.11937 q^{87} +14.3978 q^{88} +1.43390 q^{89} -5.17206 q^{90} -7.66509 q^{91} -27.7632 q^{92} -7.08825 q^{93} +14.1940 q^{94} -2.50653 q^{95} -5.94826 q^{96} -8.34075 q^{97} +12.8572 q^{98} +2.24180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) $ 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * 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 $

$2$	2.55264	1.80499	0.902496	−	0.430698i	$-0.141732\pi$
$2$	2.55264	1.80499	0.902496	+	0.430698i	$0.141732\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.51600	2.25800
$5$	−2.02616	−0.906125	−0.453062	−	0.891479i	$-0.649669\pi$
$5$	−2.02616	−0.906125	−0.453062	+	0.891479i	$0.649669\pi$
$6$	−2.55264	−1.04211
$7$	−3.46941	−1.31131	−0.655657	−	0.755059i	$-0.727608\pi$
$7$	−3.46941	−1.31131	−0.655657	+	0.755059i	$0.727608\pi$
$8$	6.42244	2.27068
$9$	1.00000	0.333333
$10$	−5.17206	−1.63555
$11$	2.24180	0.675927	0.337964	−	0.941159i	$-0.390262\pi$
$11$	2.24180	0.675927	0.337964	+	0.941159i	$0.390262\pi$
$12$	−4.51600	−1.30366
$13$	2.20934	0.612759	0.306380	−	0.951909i	$-0.400882\pi$
$13$	2.20934	0.612759	0.306380	+	0.951909i	$0.400882\pi$
$14$	−8.85617	−2.36691
$15$	2.02616	0.523151
$16$	7.36222	1.84056
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.55264	0.601664
$19$	1.23709	0.283807	0.141904	−	0.989880i	$-0.454678\pi$
$19$	1.23709	0.283807	0.141904	+	0.989880i	$0.454678\pi$
$20$	−9.15012	−2.04603
$21$	3.46941	0.757087
$22$	5.72251	1.22004
$23$	−6.14774	−1.28189	−0.640946	−	0.767586i	$-0.721458\pi$
$23$	−6.14774	−1.28189	−0.640946	+	0.767586i	$0.721458\pi$
$24$	−6.42244	−1.31098
$25$	−0.894688	−0.178938
$26$	5.63965	1.10603
$27$	−1.00000	−0.192450
$28$	−15.6678	−2.96094
$29$	6.11937	1.13634	0.568169	−	0.822912i	$-0.307652\pi$
$29$	6.11937	1.13634	0.568169	+	0.822912i	$0.307652\pi$
$30$	5.17206	0.944284
$31$	7.08825	1.27309	0.636544	−	0.771240i	$-0.280363\pi$
$31$	7.08825	1.27309	0.636544	+	0.771240i	$0.280363\pi$
$32$	5.94826	1.05151
$33$	−2.24180	−0.390247
$34$	−2.55264	−0.437775
$35$	7.02957	1.18821
$36$	4.51600	0.752666
$37$	−8.56157	−1.40751	−0.703757	−	0.710441i	$-0.748496\pi$
$37$	−8.56157	−1.40751	−0.703757	+	0.710441i	$0.748496\pi$
$38$	3.15784	0.512270
$39$	−2.20934	−0.353777
$40$	−13.0129	−2.05752
$41$	−10.8548	−1.69524	−0.847619	−	0.530605i	$-0.821965\pi$
$41$	−10.8548	−1.69524	−0.847619	+	0.530605i	$0.821965\pi$
$42$	8.85617	1.36654
$43$	0.242642	0.0370025	0.0185012	−	0.999829i	$-0.494111\pi$
$43$	0.242642	0.0370025	0.0185012	+	0.999829i	$0.494111\pi$
$44$	10.1239	1.52624
$45$	−2.02616	−0.302042
$46$	−15.6930	−2.31381
$47$	5.56049	0.811081	0.405541	−	0.914077i	$-0.367083\pi$
$47$	5.56049	0.811081	0.405541	+	0.914077i	$0.367083\pi$
$48$	−7.36222	−1.06265
$49$	5.03681	0.719544
$50$	−2.28382	−0.322981
$51$	1.00000	0.140028
$52$	9.97735	1.38361
$53$	−2.50875	−0.344603	−0.172301	−	0.985044i	$-0.555120\pi$
$53$	−2.50875	−0.344603	−0.172301	+	0.985044i	$0.555120\pi$
$54$	−2.55264	−0.347371
$55$	−4.54223	−0.612474
$56$	−22.2821	−2.97757
$57$	−1.23709	−0.163856
$58$	15.6206	2.05108
$59$	2.25565	0.293661	0.146830	−	0.989162i	$-0.453093\pi$
$59$	2.25565	0.293661	0.146830	+	0.989162i	$0.453093\pi$
$60$	9.15012	1.18127
$61$	−5.32578	−0.681896	−0.340948	−	0.940082i	$-0.610748\pi$
$61$	−5.32578	−0.681896	−0.340948	+	0.940082i	$0.610748\pi$
$62$	18.0938	2.29791
$63$	−3.46941	−0.437105
$64$	0.459342	0.0574178
$65$	−4.47646	−0.555237
$66$	−5.72251	−0.704392
$67$	−4.75839	−0.581330	−0.290665	−	0.956825i	$-0.593876\pi$
$67$	−4.75839	−0.581330	−0.290665	+	0.956825i	$0.593876\pi$
$68$	−4.51600	−0.547645
$69$	6.14774	0.740101
$70$	17.9440	2.14472
$71$	−7.79895	−0.925565	−0.462782	−	0.886472i	$-0.653149\pi$
$71$	−7.79895	−0.925565	−0.462782	+	0.886472i	$0.653149\pi$
$72$	6.42244	0.756892
$73$	9.40328	1.10057	0.550285	−	0.834977i	$-0.314519\pi$
$73$	9.40328	1.10057	0.550285	+	0.834977i	$0.314519\pi$
$74$	−21.8547	−2.54055
$75$	0.894688	0.103310
$76$	5.58668	0.640836
$77$	−7.77771	−0.886352
$78$	−5.63965	−0.638564
$79$	−2.68310	−0.301872	−0.150936	−	0.988544i	$-0.548229\pi$
$79$	−2.68310	−0.301872	−0.150936	+	0.988544i	$0.548229\pi$
$80$	−14.9170	−1.66777
$81$	1.00000	0.111111
$82$	−27.7085	−3.05989
$83$	−7.70340	−0.845558	−0.422779	−	0.906233i	$-0.638945\pi$
$83$	−7.70340	−0.845558	−0.422779	+	0.906233i	$0.638945\pi$
$84$	15.6678	1.70950
$85$	2.02616	0.219768
$86$	0.619378	0.0667892
$87$	−6.11937	−0.656065
$88$	14.3978	1.53481
$89$	1.43390	0.151993	0.0759967	−	0.997108i	$-0.475786\pi$
$89$	1.43390	0.151993	0.0759967	+	0.997108i	$0.475786\pi$
$90$	−5.17206	−0.545183
$91$	−7.66509	−0.803520
$92$	−27.7632	−2.89451
$93$	−7.08825	−0.735018
$94$	14.1940	1.46400
$95$	−2.50653	−0.257165
$96$	−5.94826	−0.607092
$97$	−8.34075	−0.846875	−0.423438	−	0.905925i	$-0.639177\pi$
$97$	−8.34075	−0.846875	−0.423438	+	0.905925i	$0.639177\pi$
$98$	12.8572	1.29877
$99$	2.24180	0.225309
$100$	−4.04041	−0.404041
$101$	3.40536	0.338846	0.169423	−	0.985543i	$-0.445810\pi$
$101$	3.40536	0.338846	0.169423	+	0.985543i	$0.445810\pi$
$102$	2.55264	0.252749
$103$	−11.6200	−1.14495	−0.572477	−	0.819921i	$-0.694018\pi$
$103$	−11.6200	−1.14495	−0.572477	+	0.819921i	$0.694018\pi$
$104$	14.1893	1.39138
$105$	−7.02957	−0.686016
$106$	−6.40394	−0.622006
$107$	−12.3157	−1.19061	−0.595303	−	0.803501i	$-0.702968\pi$
$107$	−12.3157	−1.19061	−0.595303	+	0.803501i	$0.702968\pi$
$108$	−4.51600	−0.434552
$109$	−12.3401	−1.18197	−0.590986	−	0.806682i	$-0.701261\pi$
$109$	−12.3401	−1.18197	−0.590986	+	0.806682i	$0.701261\pi$
$110$	−11.5947	−1.10551
$111$	8.56157	0.812628
$112$	−25.5426	−2.41355
$113$	−14.4391	−1.35832	−0.679158	−	0.733992i	$-0.737655\pi$
$113$	−14.4391	−1.35832	−0.679158	+	0.733992i	$0.737655\pi$
$114$	−3.15784	−0.295759
$115$	12.4563	1.16155
$116$	27.6350	2.56585
$117$	2.20934	0.204253
$118$	5.75787	0.530055
$119$	3.46941	0.318040
$120$	13.0129	1.18791
$121$	−5.97435	−0.543123
$122$	−13.5948	−1.23082
$123$	10.8548	0.978746
$124$	32.0105	2.87463
$125$	11.9436	1.06826
$126$	−8.85617	−0.788971
$127$	−0.415656	−0.0368835	−0.0184417	−	0.999830i	$-0.505871\pi$
$127$	−0.415656	−0.0368835	−0.0184417	+	0.999830i	$0.505871\pi$
$128$	−10.7240	−0.947875
$129$	−0.242642	−0.0213634
$130$	−11.4268	−1.00220
$131$	8.39104	0.733129	0.366564	−	0.930393i	$-0.380534\pi$
$131$	8.39104	0.733129	0.366564	+	0.930393i	$0.380534\pi$
$132$	−10.1239	−0.881176
$133$	−4.29196	−0.372160
$134$	−12.1465	−1.04930
$135$	2.02616	0.174384
$136$	−6.42244	−0.550720
$137$	16.0274	1.36931	0.684655	−	0.728867i	$-0.259953\pi$
$137$	16.0274	1.36931	0.684655	+	0.728867i	$0.259953\pi$
$138$	15.6930	1.33588
$139$	−21.4805	−1.82195	−0.910975	−	0.412462i	$-0.864669\pi$
$139$	−21.4805	−1.82195	−0.910975	+	0.412462i	$0.864669\pi$
$140$	31.7455	2.68298
$141$	−5.56049	−0.468278
$142$	−19.9079	−1.67064
$143$	4.95288	0.414181
$144$	7.36222	0.613519
$145$	−12.3988	−1.02966
$146$	24.0032	1.98652
$147$	−5.03681	−0.415429
$148$	−38.6640	−3.17816
$149$	18.0206	1.47630	0.738151	−	0.674636i	$-0.235699\pi$
$149$	18.0206	1.47630	0.738151	+	0.674636i	$0.235699\pi$
$150$	2.28382	0.186473
$151$	−5.61690	−0.457097	−0.228549	−	0.973533i	$-0.573398\pi$
$151$	−5.61690	−0.457097	−0.228549	+	0.973533i	$0.573398\pi$
$152$	7.94512	0.644434
$153$	−1.00000	−0.0808452
$154$	−19.8537	−1.59986
$155$	−14.3619	−1.15358
$156$	−9.97735	−0.798827
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−6.84899	−0.544876
$159$	2.50875	0.198957
$160$	−12.0521	−0.952803
$161$	21.3290	1.68096
$162$	2.55264	0.200555
$163$	−7.04223	−0.551590	−0.275795	−	0.961216i	$-0.588941\pi$
$163$	−7.04223	−0.551590	−0.275795	+	0.961216i	$0.588941\pi$
$164$	−49.0203	−3.82785
$165$	4.54223	0.353612
$166$	−19.6640	−1.52623
$167$	1.98324	0.153467	0.0767337	−	0.997052i	$-0.475551\pi$
$167$	1.98324	0.153467	0.0767337	+	0.997052i	$0.475551\pi$
$168$	22.2821	1.71910
$169$	−8.11884	−0.624526
$170$	5.17206	0.396679
$171$	1.23709	0.0946024
$172$	1.09577	0.0835515
$173$	−18.7223	−1.42343	−0.711714	−	0.702470i	$-0.752081\pi$
$173$	−18.7223	−1.42343	−0.711714	+	0.702470i	$0.752081\pi$
$174$	−15.6206	−1.18419
$175$	3.10404	0.234643
$176$	16.5046	1.24408
$177$	−2.25565	−0.169545
$178$	3.66024	0.274347
$179$	−17.3665	−1.29804	−0.649018	−	0.760773i	$-0.724820\pi$
$179$	−17.3665	−1.29804	−0.649018	+	0.760773i	$0.724820\pi$
$180$	−9.15012	−0.682009
$181$	16.7875	1.24781	0.623903	−	0.781502i	$-0.285546\pi$
$181$	16.7875	1.24781	0.623903	+	0.781502i	$0.285546\pi$
$182$	−19.5663	−1.45035
$183$	5.32578	0.393693
$184$	−39.4835	−2.91076
$185$	17.3471	1.27538
$186$	−18.0938	−1.32670
$187$	−2.24180	−0.163936
$188$	25.1112	1.83142
$189$	3.46941	0.252362
$190$	−6.39828	−0.464180
$191$	−11.1355	−0.805734	−0.402867	−	0.915259i	$-0.631986\pi$
$191$	−11.1355	−0.805734	−0.402867	+	0.915259i	$0.631986\pi$
$192$	−0.459342	−0.0331502
$193$	13.7983	0.993221	0.496610	−	0.867974i	$-0.334578\pi$
$193$	13.7983	0.993221	0.496610	+	0.867974i	$0.334578\pi$
$194$	−21.2910	−1.52860
$195$	4.47646	0.320566
$196$	22.7462	1.62473
$197$	−3.21636	−0.229156	−0.114578	−	0.993414i	$-0.536552\pi$
$197$	−3.21636	−0.229156	−0.114578	+	0.993414i	$0.536552\pi$
$198$	5.72251	0.406681
$199$	9.70222	0.687772	0.343886	−	0.939011i	$-0.388257\pi$
$199$	9.70222	0.687772	0.343886	+	0.939011i	$0.388257\pi$
$200$	−5.74608	−0.406309
$201$	4.75839	0.335631
$202$	8.69268	0.611614
$203$	−21.2306	−1.49010
$204$	4.51600	0.316183
$205$	21.9936	1.53610
$206$	−29.6618	−2.06663
$207$	−6.14774	−0.427297
$208$	16.2656	1.12782
$209$	2.77330	0.191833
$210$	−17.9440	−1.23825
$211$	24.6814	1.69914	0.849568	−	0.527479i	$-0.176863\pi$
$211$	24.6814	1.69914	0.849568	+	0.527479i	$0.176863\pi$
$212$	−11.3295	−0.778112
$213$	7.79895	0.534375
$214$	−31.4377	−2.14903
$215$	−0.491630	−0.0335289
$216$	−6.42244	−0.436992
$217$	−24.5921	−1.66942
$218$	−31.5000	−2.13345
$219$	−9.40328	−0.635415
$220$	−20.5127	−1.38297
$221$	−2.20934	−0.148616
$222$	21.8547	1.46679
$223$	−27.6445	−1.85121	−0.925605	−	0.378490i	$-0.876443\pi$
$223$	−27.6445	−1.85121	−0.925605	+	0.378490i	$0.876443\pi$
$224$	−20.6369	−1.37886
$225$	−0.894688	−0.0596459
$226$	−36.8579	−2.45175
$227$	−18.6791	−1.23977	−0.619887	−	0.784691i	$-0.712822\pi$
$227$	−18.6791	−1.23977	−0.619887	+	0.784691i	$0.712822\pi$
$228$	−5.58668	−0.369987
$229$	−4.98225	−0.329236	−0.164618	−	0.986357i	$-0.552639\pi$
$229$	−4.98225	−0.329236	−0.164618	+	0.986357i	$0.552639\pi$
$230$	31.7965	2.09660
$231$	7.77771	0.511736
$232$	39.3013	2.58026
$233$	15.7438	1.03141	0.515707	−	0.856765i	$-0.327529\pi$
$233$	15.7438	1.03141	0.515707	+	0.856765i	$0.327529\pi$
$234$	5.63965	0.368675
$235$	−11.2664	−0.734941
$236$	10.1865	0.663085
$237$	2.68310	0.174286
$238$	8.85617	0.574060
$239$	10.6517	0.689004	0.344502	−	0.938786i	$-0.388048\pi$
$239$	10.6517	0.689004	0.344502	+	0.938786i	$0.388048\pi$
$240$	14.9170	0.962890
$241$	20.4804	1.31926	0.659629	−	0.751591i	$-0.270713\pi$
$241$	20.4804	1.31926	0.659629	+	0.751591i	$0.270713\pi$
$242$	−15.2504	−0.980332
$243$	−1.00000	−0.0641500
$244$	−24.0512	−1.53972
$245$	−10.2054	−0.651997
$246$	27.7085	1.76663
$247$	2.73314	0.173905
$248$	45.5239	2.89077
$249$	7.70340	0.488183
$250$	30.4877	1.92821
$251$	22.1050	1.39526	0.697628	−	0.716460i	$-0.254239\pi$
$251$	22.1050	1.39526	0.697628	+	0.716460i	$0.254239\pi$
$252$	−15.6678	−0.986981
$253$	−13.7820	−0.866465
$254$	−1.06102	−0.0665744
$255$	−2.02616	−0.126883
$256$	−28.2932	−1.76832
$257$	2.02310	0.126198	0.0630988	−	0.998007i	$-0.479902\pi$
$257$	2.02310	0.126198	0.0630988	+	0.998007i	$0.479902\pi$
$258$	−0.619378	−0.0385608
$259$	29.7036	1.84569
$260$	−20.2157	−1.25372
$261$	6.11937	0.378779
$262$	21.4193	1.32329
$263$	2.18794	0.134914	0.0674572	−	0.997722i	$-0.478511\pi$
$263$	2.18794	0.134914	0.0674572	+	0.997722i	$0.478511\pi$
$264$	−14.3978	−0.886124
$265$	5.08311	0.312253
$266$	−10.9559	−0.671746
$267$	−1.43390	−0.0877534
$268$	−21.4889	−1.31264
$269$	−10.5208	−0.641463	−0.320731	−	0.947170i	$-0.603929\pi$
$269$	−10.5208	−0.641463	−0.320731	+	0.947170i	$0.603929\pi$
$270$	5.17206	0.314761
$271$	−21.3957	−1.29970	−0.649849	−	0.760063i	$-0.725168\pi$
$271$	−21.3957	−1.29970	−0.649849	+	0.760063i	$0.725168\pi$
$272$	−7.36222	−0.446400
$273$	7.66509	0.463912
$274$	40.9122	2.47159
$275$	−2.00571	−0.120949
$276$	27.7632	1.67115
$277$	10.2537	0.616087	0.308044	−	0.951372i	$-0.400326\pi$
$277$	10.2537	0.616087	0.308044	+	0.951372i	$0.400326\pi$
$278$	−54.8320	−3.28860
$279$	7.08825	0.424363
$280$	45.1470	2.69805
$281$	−16.8624	−1.00593	−0.502964	−	0.864308i	$-0.667757\pi$
$281$	−16.8624	−1.00593	−0.502964	+	0.864308i	$0.667757\pi$
$282$	−14.1940	−0.845238
$283$	−8.82997	−0.524887	−0.262444	−	0.964947i	$-0.584528\pi$
$283$	−8.82997	−0.524887	−0.262444	+	0.964947i	$0.584528\pi$
$284$	−35.2200	−2.08992
$285$	2.50653	0.148474
$286$	12.6429	0.747593
$287$	37.6598	2.22299
$288$	5.94826	0.350504
$289$	1.00000	0.0588235
$290$	−31.6497	−1.85854
$291$	8.34075	0.488944
$292$	42.4652	2.48509
$293$	−32.7904	−1.91563	−0.957816	−	0.287381i	$-0.907215\pi$
$293$	−32.7904	−1.91563	−0.957816	+	0.287381i	$0.907215\pi$
$294$	−12.8572	−0.749846
$295$	−4.57030	−0.266093
$296$	−54.9862	−3.19601
$297$	−2.24180	−0.130082
$298$	46.0001	2.66471
$299$	−13.5824	−0.785491
$300$	4.04041	0.233273
$301$	−0.841823	−0.0485219
$302$	−14.3380	−0.825057
$303$	−3.40536	−0.195633
$304$	9.10771	0.522363
$305$	10.7909	0.617883
$306$	−2.55264	−0.145925
$307$	23.3845	1.33462	0.667312	−	0.744778i	$-0.267445\pi$
$307$	23.3845	1.33462	0.667312	+	0.744778i	$0.267445\pi$
$308$	−35.1241	−2.00138
$309$	11.6200	0.661040
$310$	−36.6609	−2.08220
$311$	−2.92766	−0.166012	−0.0830062	−	0.996549i	$-0.526452\pi$
$311$	−2.92766	−0.166012	−0.0830062	+	0.996549i	$0.526452\pi$
$312$	−14.1893	−0.803313
$313$	3.54376	0.200305	0.100153	−	0.994972i	$-0.468067\pi$
$313$	3.54376	0.200305	0.100153	+	0.994972i	$0.468067\pi$
$314$	−2.55264	−0.144054
$315$	7.02957	0.396071
$316$	−12.1168	−0.681626
$317$	−27.9163	−1.56794	−0.783968	−	0.620801i	$-0.786808\pi$
$317$	−27.9163	−1.56794	−0.783968	+	0.620801i	$0.786808\pi$
$318$	6.40394	0.359115
$319$	13.7184	0.768081
$320$	−0.930699	−0.0520277
$321$	12.3157	0.687397
$322$	54.4454	3.03412
$323$	−1.23709	−0.0688333
$324$	4.51600	0.250889
$325$	−1.97667	−0.109646
$326$	−17.9763	−0.995616
$327$	12.3401	0.682412
$328$	−69.7145	−3.84934
$329$	−19.2916	−1.06358
$330$	11.5947	0.638267
$331$	−2.18898	−0.120317	−0.0601587	−	0.998189i	$-0.519161\pi$
$331$	−2.18898	−0.120317	−0.0601587	+	0.998189i	$0.519161\pi$
$332$	−34.7885	−1.90927
$333$	−8.56157	−0.469171
$334$	5.06249	0.277007
$335$	9.64124	0.526757
$336$	25.5426	1.39346
$337$	−32.6741	−1.77987	−0.889936	−	0.456085i	$-0.849251\pi$
$337$	−32.6741	−1.77987	−0.889936	+	0.456085i	$0.849251\pi$
$338$	−20.7245	−1.12726
$339$	14.4391	0.784224
$340$	9.15012	0.496235
$341$	15.8904	0.860514
$342$	3.15784	0.170757
$343$	6.81112	0.367766
$344$	1.55835	0.0840207
$345$	−12.4563	−0.670624
$346$	−47.7913	−2.56928
$347$	28.1445	1.51087	0.755437	−	0.655221i	$-0.227424\pi$
$347$	28.1445	1.51087	0.755437	+	0.655221i	$0.227424\pi$
$348$	−27.6350	−1.48139
$349$	26.0053	1.39203	0.696017	−	0.718025i	$-0.254954\pi$
$349$	26.0053	1.39203	0.696017	+	0.718025i	$0.254954\pi$
$350$	7.92351	0.423530
$351$	−2.20934	−0.117926
$352$	13.3348	0.710746
$353$	−10.9923	−0.585061	−0.292530	−	0.956256i	$-0.594497\pi$
$353$	−10.9923	−0.585061	−0.292530	+	0.956256i	$0.594497\pi$
$354$	−5.75787	−0.306027
$355$	15.8019	0.838677
$356$	6.47550	0.343201
$357$	−3.46941	−0.183621
$358$	−44.3306	−2.34294
$359$	22.3832	1.18134	0.590670	−	0.806913i	$-0.298863\pi$
$359$	22.3832	1.18134	0.590670	+	0.806913i	$0.298863\pi$
$360$	−13.0129	−0.685839
$361$	−17.4696	−0.919454
$362$	42.8525	2.25228
$363$	5.97435	0.313572
$364$	−34.6155	−1.81435
$365$	−19.0525	−0.997254
$366$	13.5948	0.710613
$367$	4.08640	0.213308	0.106654	−	0.994296i	$-0.465986\pi$
$367$	4.08640	0.213308	0.106654	+	0.994296i	$0.465986\pi$
$368$	−45.2610	−2.35939
$369$	−10.8548	−0.565080
$370$	44.2810	2.30206
$371$	8.70387	0.451882
$372$	−32.0105	−1.65967
$373$	−3.90386	−0.202134	−0.101067	−	0.994880i	$-0.532226\pi$
$373$	−3.90386	−0.202134	−0.101067	+	0.994880i	$0.532226\pi$
$374$	−5.72251	−0.295904
$375$	−11.9436	−0.616763
$376$	35.7119	1.84170
$377$	13.5197	0.696302
$378$	8.85617	0.455512
$379$	−30.3176	−1.55731	−0.778656	−	0.627451i	$-0.784098\pi$
$379$	−30.3176	−1.55731	−0.778656	+	0.627451i	$0.784098\pi$
$380$	−11.3195	−0.580677
$381$	0.415656	0.0212947
$382$	−28.4249	−1.45434
$383$	31.0815	1.58819	0.794096	−	0.607792i	$-0.207945\pi$
$383$	31.0815	1.58819	0.794096	+	0.607792i	$0.207945\pi$
$384$	10.7240	0.547256
$385$	15.7589	0.803146
$386$	35.2221	1.79276
$387$	0.242642	0.0123342
$388$	−37.6668	−1.91224
$389$	−14.2062	−0.720285	−0.360142	−	0.932897i	$-0.617272\pi$
$389$	−14.2062	−0.720285	−0.360142	+	0.932897i	$0.617272\pi$
$390$	11.4268	0.578619
$391$	6.14774	0.310904
$392$	32.3486	1.63385
$393$	−8.39104	−0.423272
$394$	−8.21022	−0.413625
$395$	5.43637	0.273534
$396$	10.1239	0.508747
$397$	31.2065	1.56621	0.783104	−	0.621891i	$-0.213635\pi$
$397$	31.2065	1.56621	0.783104	+	0.621891i	$0.213635\pi$
$398$	24.7663	1.24142
$399$	4.29196	0.214867
$400$	−6.58689	−0.329345
$401$	3.77384	0.188457	0.0942284	−	0.995551i	$-0.469962\pi$
$401$	3.77384	0.188457	0.0942284	+	0.995551i	$0.469962\pi$
$402$	12.1465	0.605811
$403$	15.6603	0.780096
$404$	15.3786	0.765114
$405$	−2.02616	−0.100681
$406$	−54.1942	−2.68961
$407$	−19.1933	−0.951376
$408$	6.42244	0.317958
$409$	17.3296	0.856893	0.428447	−	0.903567i	$-0.359061\pi$
$409$	17.3296	0.856893	0.428447	+	0.903567i	$0.359061\pi$
$410$	56.1418	2.77265
$411$	−16.0274	−0.790572
$412$	−52.4760	−2.58530
$413$	−7.82577	−0.385081
$414$	−15.6930	−0.771268
$415$	15.6083	0.766181
$416$	13.1417	0.644325
$417$	21.4805	1.05190
$418$	7.07924	0.346257
$419$	10.0593	0.491427	0.245714	−	0.969342i	$-0.420978\pi$
$419$	10.0593	0.491427	0.245714	+	0.969342i	$0.420978\pi$
$420$	−31.7455	−1.54902
$421$	−11.2473	−0.548161	−0.274080	−	0.961707i	$-0.588373\pi$
$421$	−11.2473	−0.548161	−0.274080	+	0.961707i	$0.588373\pi$
$422$	63.0028	3.06693
$423$	5.56049	0.270360
$424$	−16.1123	−0.782482
$425$	0.894688	0.0433987
$426$	19.9079	0.964543
$427$	18.4773	0.894180
$428$	−55.6178	−2.68839
$429$	−4.95288	−0.239127
$430$	−1.25496	−0.0605194
$431$	−3.75504	−0.180874	−0.0904370	−	0.995902i	$-0.528826\pi$
$431$	−3.75504	−0.180874	−0.0904370	+	0.995902i	$0.528826\pi$
$432$	−7.36222	−0.354215
$433$	30.4843	1.46498	0.732491	−	0.680777i	$-0.238358\pi$
$433$	30.4843	1.46498	0.732491	+	0.680777i	$0.238358\pi$
$434$	−62.7748	−3.01329
$435$	12.3988	0.594477
$436$	−55.7280	−2.66889
$437$	−7.60528	−0.363810
$438$	−24.0032	−1.14692
$439$	23.0191	1.09864	0.549321	−	0.835611i	$-0.314886\pi$
$439$	23.0191	1.09864	0.549321	+	0.835611i	$0.314886\pi$
$440$	−29.1722	−1.39073
$441$	5.03681	0.239848
$442$	−5.63965	−0.268251
$443$	24.6124	1.16937	0.584685	−	0.811260i	$-0.301218\pi$
$443$	24.6124	1.16937	0.584685	+	0.811260i	$0.301218\pi$
$444$	38.6640	1.83491
$445$	−2.90531	−0.137725
$446$	−70.5665	−3.34142
$447$	−18.0206	−0.852343
$448$	−1.59365	−0.0752927
$449$	14.0696	0.663987	0.331993	−	0.943282i	$-0.392279\pi$
$449$	14.0696	0.663987	0.331993	+	0.943282i	$0.392279\pi$
$450$	−2.28382	−0.107660
$451$	−24.3343	−1.14586
$452$	−65.2069	−3.06707
$453$	5.61690	0.263905
$454$	−47.6811	−2.23778
$455$	15.5307	0.728089
$456$	−7.94512	−0.372064
$457$	−21.1847	−0.990977	−0.495489	−	0.868614i	$-0.665011\pi$
$457$	−21.1847	−0.990977	−0.495489	+	0.868614i	$0.665011\pi$
$458$	−12.7179	−0.594269
$459$	1.00000	0.0466760
$460$	56.2525	2.62279
$461$	−10.6532	−0.496167	−0.248084	−	0.968739i	$-0.579801\pi$
$461$	−10.6532	−0.496167	−0.248084	+	0.968739i	$0.579801\pi$
$462$	19.8537	0.923679
$463$	38.2845	1.77923	0.889616	−	0.456709i	$-0.150972\pi$
$463$	38.2845	1.77923	0.889616	+	0.456709i	$0.150972\pi$
$464$	45.0521	2.09149
$465$	14.3619	0.666018
$466$	40.1884	1.86169
$467$	−28.5102	−1.31929	−0.659647	−	0.751575i	$-0.729294\pi$
$467$	−28.5102	−1.31929	−0.659647	+	0.751575i	$0.729294\pi$
$468$	9.97735	0.461203
$469$	16.5088	0.762306
$470$	−28.7592	−1.32656
$471$	1.00000	0.0460776
$472$	14.4868	0.666808
$473$	0.543953	0.0250110
$474$	6.84899	0.314585
$475$	−1.10681	−0.0507838
$476$	15.6678	0.718134
$477$	−2.50875	−0.114868
$478$	27.1901	1.24365
$479$	−9.40074	−0.429531	−0.214765	−	0.976666i	$-0.568899\pi$
$479$	−9.40074	−0.429531	−0.214765	+	0.976666i	$0.568899\pi$
$480$	12.0521	0.550101
$481$	−18.9154	−0.862467
$482$	52.2792	2.38125
$483$	−21.3290	−0.970504
$484$	−26.9801	−1.22637
$485$	16.8997	0.767375
$486$	−2.55264	−0.115790
$487$	25.7599	1.16729	0.583647	−	0.812008i	$-0.301625\pi$
$487$	25.7599	1.16729	0.583647	+	0.812008i	$0.301625\pi$
$488$	−34.2045	−1.54837
$489$	7.04223	0.318461
$490$	−26.0507	−1.17685
$491$	−23.1486	−1.04468	−0.522341	−	0.852737i	$-0.674941\pi$
$491$	−23.1486	−1.04468	−0.522341	+	0.852737i	$0.674941\pi$
$492$	49.0203	2.21001
$493$	−6.11937	−0.275602
$494$	6.97673	0.313898
$495$	−4.54223	−0.204158
$496$	52.1853	2.34319
$497$	27.0578	1.21371
$498$	19.6640	0.881167
$499$	11.6616	0.522047	0.261023	−	0.965332i	$-0.415940\pi$
$499$	11.6616	0.522047	0.261023	+	0.965332i	$0.415940\pi$
$500$	53.9371	2.41214
$501$	−1.98324	−0.0886044
$502$	56.4262	2.51843
$503$	27.1431	1.21025	0.605125	−	0.796131i	$-0.293123\pi$
$503$	27.1431	1.21025	0.605125	+	0.796131i	$0.293123\pi$
$504$	−22.2821	−0.992523
$505$	−6.89979	−0.307037
$506$	−35.1805	−1.56396
$507$	8.11884	0.360570
$508$	−1.87710	−0.0832829
$509$	41.4022	1.83512	0.917560	−	0.397596i	$-0.130156\pi$
$509$	41.4022	1.83512	0.917560	+	0.397596i	$0.130156\pi$
$510$	−5.17206	−0.229023
$511$	−32.6238	−1.44319
$512$	−50.7745	−2.24394
$513$	−1.23709	−0.0546187
$514$	5.16426	0.227786
$515$	23.5440	1.03747
$516$	−1.09577	−0.0482385
$517$	12.4655	0.548232
$518$	75.8227	3.33146
$519$	18.7223	0.821816
$520$	−28.7498	−1.26076
$521$	0.305682	0.0133922	0.00669608	−	0.999978i	$-0.497869\pi$
$521$	0.305682	0.0133922	0.00669608	+	0.999978i	$0.497869\pi$
$522$	15.6206	0.683694
$523$	1.77085	0.0774337	0.0387168	−	0.999250i	$-0.487673\pi$
$523$	1.77085	0.0774337	0.0387168	+	0.999250i	$0.487673\pi$
$524$	37.8939	1.65540
$525$	−3.10404	−0.135471
$526$	5.58505	0.243520
$527$	−7.08825	−0.308769
$528$	−16.5046	−0.718271
$529$	14.7947	0.643247
$530$	12.9754	0.563615
$531$	2.25565	0.0978868
$532$	−19.3825	−0.840337
$533$	−23.9819	−1.03877
$534$	−3.66024	−0.158394
$535$	24.9536	1.07884
$536$	−30.5605	−1.32001
$537$	17.3665	0.749421
$538$	−26.8558	−1.15784
$539$	11.2915	0.486359
$540$	9.15012	0.393758
$541$	−22.0126	−0.946397	−0.473198	−	0.880956i	$-0.656901\pi$
$541$	−22.0126	−0.946397	−0.473198	+	0.880956i	$0.656901\pi$
$542$	−54.6157	−2.34595
$543$	−16.7875	−0.720421
$544$	−5.94826	−0.255029
$545$	25.0031	1.07101
$546$	19.5663	0.837358
$547$	−34.3621	−1.46922	−0.734609	−	0.678491i	$-0.762634\pi$
$547$	−34.3621	−1.46922	−0.734609	+	0.678491i	$0.762634\pi$
$548$	72.3795	3.09190
$549$	−5.32578	−0.227299
$550$	−5.11986	−0.218312
$551$	7.57018	0.322501
$552$	39.4835	1.68053
$553$	9.30876	0.395849
$554$	26.1741	1.11203
$555$	−17.3471	−0.736343
$556$	−97.0057	−4.11396
$557$	−18.7764	−0.795581	−0.397790	−	0.917476i	$-0.630223\pi$
$557$	−18.7764	−0.795581	−0.397790	+	0.917476i	$0.630223\pi$
$558$	18.0938	0.765971
$559$	0.536077	0.0226736
$560$	51.7533	2.18697
$561$	2.24180	0.0946487
$562$	−43.0438	−1.81569
$563$	16.4630	0.693834	0.346917	−	0.937896i	$-0.387229\pi$
$563$	16.4630	0.693834	0.346917	+	0.937896i	$0.387229\pi$
$564$	−25.1112	−1.05737
$565$	29.2559	1.23080
$566$	−22.5398	−0.947417
$567$	−3.46941	−0.145702
$568$	−50.0883	−2.10166
$569$	−29.2442	−1.22598	−0.612990	−	0.790091i	$-0.710033\pi$
$569$	−29.2442	−1.22598	−0.612990	+	0.790091i	$0.710033\pi$
$570$	6.39828	0.267995
$571$	6.78996	0.284151	0.142075	−	0.989856i	$-0.454622\pi$
$571$	6.78996	0.284151	0.142075	+	0.989856i	$0.454622\pi$
$572$	22.3672	0.935219
$573$	11.1355	0.465190
$574$	96.1322	4.01248
$575$	5.50031	0.229379
$576$	0.459342	0.0191393
$577$	−5.25392	−0.218723	−0.109362	−	0.994002i	$-0.534881\pi$
$577$	−5.25392	−0.218723	−0.109362	+	0.994002i	$0.534881\pi$
$578$	2.55264	0.106176
$579$	−13.7983	−0.573436
$580$	−55.9929	−2.32498
$581$	26.7262	1.10879
$582$	21.2910	0.882540
$583$	−5.62410	−0.232926
$584$	60.3920	2.49904
$585$	−4.47646	−0.185079
$586$	−83.7021	−3.45770
$587$	29.1675	1.20387	0.601935	−	0.798545i	$-0.294396\pi$
$587$	29.1675	1.20387	0.601935	+	0.798545i	$0.294396\pi$
$588$	−22.7462	−0.938038
$589$	8.76878	0.361311
$590$	−11.6664	−0.480296
$591$	3.21636	0.132303
$592$	−63.0322	−2.59061
$593$	3.43837	0.141197	0.0705985	−	0.997505i	$-0.477509\pi$
$593$	3.43837	0.141197	0.0705985	+	0.997505i	$0.477509\pi$
$594$	−5.72251	−0.234797
$595$	−7.02957	−0.288184
$596$	81.3808	3.33349
$597$	−9.70222	−0.397085
$598$	−34.6711	−1.41781
$599$	2.03705	0.0832314	0.0416157	−	0.999134i	$-0.486749\pi$
$599$	2.03705	0.0832314	0.0416157	+	0.999134i	$0.486749\pi$
$600$	5.74608	0.234583
$601$	−7.62119	−0.310875	−0.155437	−	0.987846i	$-0.549679\pi$
$601$	−7.62119	−0.310875	−0.155437	+	0.987846i	$0.549679\pi$
$602$	−2.14888	−0.0875816
$603$	−4.75839	−0.193777
$604$	−25.3659	−1.03212
$605$	12.1050	0.492137
$606$	−8.69268	−0.353116
$607$	2.48850	0.101005	0.0505025	−	0.998724i	$-0.483918\pi$
$607$	2.48850	0.101005	0.0505025	+	0.998724i	$0.483918\pi$
$608$	7.35851	0.298427
$609$	21.2306	0.860307
$610$	27.5452	1.11527
$611$	12.2850	0.496998
$612$	−4.51600	−0.182548
$613$	29.7440	1.20135	0.600674	−	0.799494i	$-0.294899\pi$
$613$	29.7440	1.20135	0.600674	+	0.799494i	$0.294899\pi$
$614$	59.6923	2.40899
$615$	−21.9936	−0.886867
$616$	−49.9519	−2.01262
$617$	−47.1182	−1.89691	−0.948453	−	0.316919i	$-0.897352\pi$
$617$	−47.1182	−1.89691	−0.948453	+	0.316919i	$0.897352\pi$
$618$	29.6618	1.19317
$619$	8.48363	0.340986	0.170493	−	0.985359i	$-0.445464\pi$
$619$	8.48363	0.340986	0.170493	+	0.985359i	$0.445464\pi$
$620$	−64.8583	−2.60477
$621$	6.14774	0.246700
$622$	−7.47327	−0.299651
$623$	−4.97480	−0.199311
$624$	−16.2656	−0.651146
$625$	−19.7261	−0.789044
$626$	9.04597	0.361549
$627$	−2.77330	−0.110755
$628$	−4.51600	−0.180208
$629$	8.56157	0.341372
$630$	17.9440	0.714906
$631$	−23.0457	−0.917434	−0.458717	−	0.888582i	$-0.651691\pi$
$631$	−23.0457	−0.917434	−0.458717	+	0.888582i	$0.651691\pi$
$632$	−17.2320	−0.685453
$633$	−24.6814	−0.980996
$634$	−71.2604	−2.83011
$635$	0.842184	0.0334211
$636$	11.3295	0.449243
$637$	11.1280	0.440907
$638$	35.0181	1.38638
$639$	−7.79895	−0.308522
$640$	21.7285	0.858893
$641$	31.8566	1.25826	0.629131	−	0.777300i	$-0.283411\pi$
$641$	31.8566	1.25826	0.629131	+	0.777300i	$0.283411\pi$
$642$	31.4377	1.24075
$643$	−29.5534	−1.16547	−0.582736	−	0.812662i	$-0.698018\pi$
$643$	−29.5534	−1.16547	−0.582736	+	0.812662i	$0.698018\pi$
$644$	96.3218	3.79561
$645$	0.491630	0.0193579
$646$	−3.15784	−0.124244
$647$	38.1367	1.49931	0.749653	−	0.661831i	$-0.230220\pi$
$647$	38.1367	1.49931	0.749653	+	0.661831i	$0.230220\pi$
$648$	6.42244	0.252297
$649$	5.05671	0.198493
$650$	−5.04573	−0.197910
$651$	24.5921	0.963839
$652$	−31.8027	−1.24549
$653$	−30.5698	−1.19629	−0.598144	−	0.801388i	$-0.704095\pi$
$653$	−30.5698	−1.19629	−0.598144	+	0.801388i	$0.704095\pi$
$654$	31.5000	1.23175
$655$	−17.0016	−0.664306
$656$	−79.9156	−3.12018
$657$	9.40328	0.366857
$658$	−49.2447	−1.91976
$659$	50.6158	1.97171	0.985855	−	0.167598i	$-0.0536010\pi$
$659$	50.6158	1.97171	0.985855	+	0.167598i	$0.0536010\pi$
$660$	20.5127	0.798456
$661$	10.7008	0.416211	0.208106	−	0.978106i	$-0.433270\pi$
$661$	10.7008	0.416211	0.208106	+	0.978106i	$0.433270\pi$
$662$	−5.58769	−0.217172
$663$	2.20934	0.0858035
$664$	−49.4746	−1.91999
$665$	8.69619	0.337224
$666$	−21.8547	−0.846850
$667$	−37.6203	−1.45666
$668$	8.95628	0.346529
$669$	27.6445	1.06880
$670$	24.6107	0.950793
$671$	−11.9393	−0.460912
$672$	20.6369	0.796088
$673$	5.40360	0.208293	0.104147	−	0.994562i	$-0.466789\pi$
$673$	5.40360	0.208293	0.104147	+	0.994562i	$0.466789\pi$
$674$	−83.4054	−3.21266
$675$	0.894688	0.0344366
$676$	−36.6646	−1.41018
$677$	−3.10063	−0.119167	−0.0595835	−	0.998223i	$-0.518977\pi$
$677$	−3.10063	−0.119167	−0.0595835	+	0.998223i	$0.518977\pi$
$678$	36.8579	1.41552
$679$	28.9375	1.11052
$680$	13.0129	0.499021
$681$	18.6791	0.715784
$682$	40.5626	1.55322
$683$	23.3315	0.892755	0.446378	−	0.894845i	$-0.352714\pi$
$683$	23.3315	0.892755	0.446378	+	0.894845i	$0.352714\pi$
$684$	5.58668	0.213612
$685$	−32.4740	−1.24077
$686$	17.3864	0.663815
$687$	4.98225	0.190085
$688$	1.78638	0.0681052
$689$	−5.54266	−0.211159
$690$	−31.7965	−1.21047
$691$	−9.35985	−0.356065	−0.178033	−	0.984025i	$-0.556973\pi$
$691$	−9.35985	−0.356065	−0.178033	+	0.984025i	$0.556973\pi$
$692$	−84.5497	−3.21410
$693$	−7.77771	−0.295451
$694$	71.8429	2.72712
$695$	43.5228	1.65091
$696$	−39.3013	−1.48971
$697$	10.8548	0.411156
$698$	66.3824	2.51261
$699$	−15.7438	−0.595487
$700$	14.0178	0.529824
$701$	31.5119	1.19019	0.595095	−	0.803655i	$-0.297114\pi$
$701$	31.5119	1.19019	0.595095	+	0.803655i	$0.297114\pi$
$702$	−5.63965	−0.212855
$703$	−10.5914	−0.399462
$704$	1.02975	0.0388102
$705$	11.2664	0.424318
$706$	−28.0594	−1.05603
$707$	−11.8146	−0.444333
$708$	−10.1865	−0.382832
$709$	−35.2079	−1.32226	−0.661131	−	0.750270i	$-0.729923\pi$
$709$	−35.2079	−1.32226	−0.661131	+	0.750270i	$0.729923\pi$
$710$	40.3366	1.51381
$711$	−2.68310	−0.100624
$712$	9.20916	0.345128
$713$	−43.5767	−1.63196
$714$	−8.85617	−0.331434
$715$	−10.0353	−0.375299
$716$	−78.4272	−2.93096
$717$	−10.6517	−0.397796
$718$	57.1364	2.13231
$719$	42.9730	1.60262	0.801311	−	0.598248i	$-0.204136\pi$
$719$	42.9730	1.60262	0.801311	+	0.598248i	$0.204136\pi$
$720$	−14.9170	−0.555925
$721$	40.3146	1.50139
$722$	−44.5937	−1.65961
$723$	−20.4804	−0.761675
$724$	75.8123	2.81754
$725$	−5.47492	−0.203334
$726$	15.2504	0.565995
$727$	23.5392	0.873022	0.436511	−	0.899699i	$-0.356214\pi$
$727$	23.5392	0.873022	0.436511	+	0.899699i	$0.356214\pi$
$728$	−49.2286	−1.82453
$729$	1.00000	0.0370370
$730$	−48.6343	−1.80004
$731$	−0.242642	−0.00897442
$732$	24.0512	0.888957
$733$	−21.0888	−0.778934	−0.389467	−	0.921040i	$-0.627341\pi$
$733$	−21.0888	−0.778934	−0.389467	+	0.921040i	$0.627341\pi$
$734$	10.4311	0.385020
$735$	10.2054	0.376430
$736$	−36.5683	−1.34793
$737$	−10.6673	−0.392936
$738$	−27.7085	−1.01996
$739$	−41.2274	−1.51657	−0.758287	−	0.651921i	$-0.773963\pi$
$739$	−41.2274	−1.51657	−0.758287	+	0.651921i	$0.773963\pi$
$740$	78.3394	2.87981
$741$	−2.73314	−0.100404
$742$	22.2179	0.815644
$743$	−4.37009	−0.160323	−0.0801616	−	0.996782i	$-0.525544\pi$
$743$	−4.37009	−0.160323	−0.0801616	+	0.996782i	$0.525544\pi$
$744$	−45.5239	−1.66899
$745$	−36.5125	−1.33771
$746$	−9.96516	−0.364851
$747$	−7.70340	−0.281853
$748$	−10.1239	−0.370168
$749$	42.7283	1.56126
$750$	−30.4877	−1.11325
$751$	−6.63680	−0.242180	−0.121090	−	0.992642i	$-0.538639\pi$
$751$	−6.63680	−0.242180	−0.121090	+	0.992642i	$0.538639\pi$
$752$	40.9376	1.49284
$753$	−22.1050	−0.805551
$754$	34.5111	1.25682
$755$	11.3807	0.414187
$756$	15.6678	0.569834
$757$	−32.8572	−1.19422	−0.597108	−	0.802161i	$-0.703684\pi$
$757$	−32.8572	−1.19422	−0.597108	+	0.802161i	$0.703684\pi$
$758$	−77.3902	−2.81094
$759$	13.7820	0.500254
$760$	−16.0981	−0.583938
$761$	−28.3486	−1.02764	−0.513818	−	0.857899i	$-0.671770\pi$
$761$	−28.3486	−1.02764	−0.513818	+	0.857899i	$0.671770\pi$
$762$	1.06102	0.0384368
$763$	42.8130	1.54994
$764$	−50.2877	−1.81934
$765$	2.02616	0.0732559
$766$	79.3401	2.86667
$767$	4.98349	0.179943
$768$	28.2932	1.02094
$769$	21.7056	0.782724	0.391362	−	0.920237i	$-0.372004\pi$
$769$	21.7056	0.782724	0.391362	+	0.920237i	$0.372004\pi$
$770$	40.2268	1.44967
$771$	−2.02310	−0.0728603
$772$	62.3129	2.24269
$773$	−13.2436	−0.476339	−0.238169	−	0.971224i	$-0.576547\pi$
$773$	−13.2436	−0.476339	−0.238169	+	0.971224i	$0.576547\pi$
$774$	0.619378	0.0222631
$775$	−6.34178	−0.227803
$776$	−53.5680	−1.92298
$777$	−29.7036	−1.06561
$778$	−36.2635	−1.30011
$779$	−13.4284	−0.481121
$780$	20.2157	0.723837
$781$	−17.4837	−0.625614
$782$	15.6930	0.561180
$783$	−6.11937	−0.218688
$784$	37.0821	1.32436
$785$	2.02616	0.0723166
$786$	−21.4193	−0.764003
$787$	−7.09225	−0.252811	−0.126406	−	0.991979i	$-0.540344\pi$
$787$	−7.09225	−0.252811	−0.126406	+	0.991979i	$0.540344\pi$
$788$	−14.5251	−0.517434
$789$	−2.18794	−0.0778929
$790$	13.8771	0.493726
$791$	50.0951	1.78118
$792$	14.3978	0.511604
$793$	−11.7664	−0.417838
$794$	79.6590	2.82699
$795$	−5.08311	−0.180279
$796$	43.8152	1.55299
$797$	21.4434	0.759564	0.379782	−	0.925076i	$-0.375999\pi$
$797$	21.4434	0.759564	0.379782	+	0.925076i	$0.375999\pi$
$798$	10.9559	0.387833
$799$	−5.56049	−0.196716
$800$	−5.32184	−0.188155
$801$	1.43390	0.0506645
$802$	9.63328	0.340163
$803$	21.0802	0.743905
$804$	21.4889	0.757854
$805$	−43.2159	−1.52316
$806$	39.9753	1.40807
$807$	10.5208	0.370349
$808$	21.8707	0.769410
$809$	36.3473	1.27790	0.638951	−	0.769248i	$-0.279369\pi$
$809$	36.3473	1.27790	0.638951	+	0.769248i	$0.279369\pi$
$810$	−5.17206	−0.181728
$811$	15.7654	0.553597	0.276799	−	0.960928i	$-0.410726\pi$
$811$	15.7654	0.553597	0.276799	+	0.960928i	$0.410726\pi$
$812$	−95.8773	−3.36463
$813$	21.3957	0.750381
$814$	−48.9937	−1.71723
$815$	14.2687	0.499809
$816$	7.36222	0.257729
$817$	0.300169	0.0105016
$818$	44.2363	1.54669
$819$	−7.66509	−0.267840
$820$	99.3229	3.46851
$821$	14.9671	0.522357	0.261178	−	0.965291i	$-0.415889\pi$
$821$	14.9671	0.522357	0.261178	+	0.965291i	$0.415889\pi$
$822$	−40.9122	−1.42698
$823$	13.1155	0.457177	0.228589	−	0.973523i	$-0.426589\pi$
$823$	13.1155	0.457177	0.228589	+	0.973523i	$0.426589\pi$
$824$	−74.6289	−2.59982
$825$	2.00571	0.0698298
$826$	−19.9764	−0.695068
$827$	10.5864	0.368126	0.184063	−	0.982914i	$-0.441075\pi$
$827$	10.5864	0.368126	0.184063	+	0.982914i	$0.441075\pi$
$828$	−27.7632	−0.964836
$829$	−31.9709	−1.11040	−0.555198	−	0.831718i	$-0.687357\pi$
$829$	−31.9709	−1.11040	−0.555198	+	0.831718i	$0.687357\pi$
$830$	39.8424	1.38295
$831$	−10.2537	−0.355698
$832$	1.01484	0.0351833
$833$	−5.03681	−0.174515
$834$	54.8320	1.89868
$835$	−4.01835	−0.139061
$836$	12.5242	0.433158
$837$	−7.08825	−0.245006
$838$	25.6777	0.887023
$839$	29.9980	1.03565	0.517823	−	0.855488i	$-0.326743\pi$
$839$	29.9980	1.03565	0.517823	+	0.855488i	$0.326743\pi$
$840$	−45.1470	−1.55772
$841$	8.44664	0.291263
$842$	−28.7104	−0.989426
$843$	16.8624	0.580772
$844$	111.461	3.83664
$845$	16.4500	0.565899
$846$	14.1940	0.487998
$847$	20.7275	0.712204
$848$	−18.4700	−0.634261
$849$	8.82997	0.303044
$850$	2.28382	0.0783344
$851$	52.6343	1.80428
$852$	35.2200	1.20662
$853$	−29.8090	−1.02064	−0.510321	−	0.859984i	$-0.670473\pi$
$853$	−29.8090	−1.02064	−0.510321	+	0.859984i	$0.670473\pi$
$854$	47.1660	1.61399
$855$	−2.50653	−0.0857216
$856$	−79.0970	−2.70348
$857$	−16.6775	−0.569691	−0.284846	−	0.958573i	$-0.591942\pi$
$857$	−16.6775	−0.569691	−0.284846	+	0.958573i	$0.591942\pi$
$858$	−12.6429	−0.431623
$859$	32.2577	1.10062	0.550309	−	0.834961i	$-0.314510\pi$
$859$	32.2577	1.10062	0.550309	+	0.834961i	$0.314510\pi$
$860$	−2.22020	−0.0757081
$861$	−37.6598	−1.28344
$862$	−9.58529	−0.326476
$863$	−55.9577	−1.90482	−0.952411	−	0.304818i	$-0.901404\pi$
$863$	−55.9577	−1.90482	−0.952411	+	0.304818i	$0.901404\pi$
$864$	−5.94826	−0.202364
$865$	37.9343	1.28980
$866$	77.8156	2.64428
$867$	−1.00000	−0.0339618
$868$	−111.058	−3.76954
$869$	−6.01495	−0.204043
$870$	31.6497	1.07303
$871$	−10.5129	−0.356215
$872$	−79.2539	−2.68387
$873$	−8.34075	−0.282292
$874$	−19.4136	−0.656674
$875$	−41.4371	−1.40083
$876$	−42.4652	−1.43476
$877$	49.0256	1.65548	0.827739	−	0.561114i	$-0.189627\pi$
$877$	49.0256	1.65548	0.827739	+	0.561114i	$0.189627\pi$
$878$	58.7596	1.98304
$879$	32.7904	1.10599
$880$	−33.4409	−1.12729
$881$	−4.52658	−0.152504	−0.0762522	−	0.997089i	$-0.524295\pi$
$881$	−4.52658	−0.152504	−0.0762522	+	0.997089i	$0.524295\pi$
$882$	12.8572	0.432924
$883$	−43.4739	−1.46301	−0.731507	−	0.681834i	$-0.761183\pi$
$883$	−43.4739	−1.46301	−0.731507	+	0.681834i	$0.761183\pi$
$884$	−9.97735	−0.335575
$885$	4.57030	0.153629
$886$	62.8267	2.11070
$887$	31.7212	1.06509	0.532546	−	0.846401i	$-0.321235\pi$
$887$	31.7212	1.06509	0.532546	+	0.846401i	$0.321235\pi$
$888$	54.9862	1.84522
$889$	1.44208	0.0483658
$890$	−7.41623	−0.248593
$891$	2.24180	0.0751030
$892$	−124.842	−4.18003
$893$	6.87881	0.230191
$894$	−46.0001	−1.53847
$895$	35.1873	1.17618
$896$	37.2059	1.24296
$897$	13.5824	0.453504
$898$	35.9148	1.19849
$899$	43.3756	1.44666
$900$	−4.04041	−0.134680
$901$	2.50875	0.0835785
$902$	−62.1168	−2.06826
$903$	0.841823	0.0280141
$904$	−92.7343	−3.08430
$905$	−34.0141	−1.13067
$906$	14.3380	0.476347
$907$	−20.5033	−0.680802	−0.340401	−	0.940280i	$-0.610563\pi$
$907$	−20.5033	−0.680802	−0.340401	+	0.940280i	$0.610563\pi$
$908$	−84.3546	−2.79941
$909$	3.40536	0.112949
$910$	39.6443	1.31420
$911$	9.12407	0.302294	0.151147	−	0.988511i	$-0.451703\pi$
$911$	9.12407	0.302294	0.151147	+	0.988511i	$0.451703\pi$
$912$	−9.10771	−0.301586
$913$	−17.2694	−0.571535
$914$	−54.0770	−1.78871
$915$	−10.7909	−0.356735
$916$	−22.4998	−0.743414
$917$	−29.1120	−0.961362
$918$	2.55264	0.0842498
$919$	2.74670	0.0906054	0.0453027	−	0.998973i	$-0.485575\pi$
$919$	2.74670	0.0906054	0.0453027	+	0.998973i	$0.485575\pi$
$920$	79.9998	2.63751
$921$	−23.3845	−0.770546
$922$	−27.1937	−0.895578
$923$	−17.2305	−0.567149
$924$	35.1241	1.15550
$925$	7.65994	0.251857
$926$	97.7268	3.21150
$927$	−11.6200	−0.381651
$928$	36.3996	1.19487
$929$	5.53981	0.181755	0.0908777	−	0.995862i	$-0.471033\pi$
$929$	5.53981	0.181755	0.0908777	+	0.995862i	$0.471033\pi$
$930$	36.6609	1.20216
$931$	6.23097	0.204212
$932$	71.0991	2.32893
$933$	2.92766	0.0958473
$934$	−72.7764	−2.38132
$935$	4.54223	0.148547
$936$	14.1893	0.463793
$937$	−14.2715	−0.466228	−0.233114	−	0.972449i	$-0.574892\pi$
$937$	−14.2715	−0.466228	−0.233114	+	0.972449i	$0.574892\pi$
$938$	42.1411	1.37596
$939$	−3.54376	−0.115646
$940$	−50.8791	−1.65949
$941$	−21.3378	−0.695593	−0.347796	−	0.937570i	$-0.613070\pi$
$941$	−21.3378	−0.695593	−0.347796	+	0.937570i	$0.613070\pi$
$942$	2.55264	0.0831697
$943$	66.7326	2.17311
$944$	16.6066	0.540499
$945$	−7.02957	−0.228672
$946$	1.38852	0.0451446
$947$	46.8591	1.52271	0.761357	−	0.648333i	$-0.224533\pi$
$947$	46.8591	1.52271	0.761357	+	0.648333i	$0.224533\pi$
$948$	12.1168	0.393537
$949$	20.7750	0.674385
$950$	−2.82528	−0.0916643
$951$	27.9163	0.905249
$952$	22.2821	0.722167
$953$	4.02202	0.130286	0.0651430	−	0.997876i	$-0.479250\pi$
$953$	4.02202	0.130286	0.0651430	+	0.997876i	$0.479250\pi$
$954$	−6.40394	−0.207335
$955$	22.5622	0.730095
$956$	48.1032	1.55577
$957$	−13.7184	−0.443452
$958$	−23.9968	−0.775300
$959$	−55.6055	−1.79560
$960$	0.930699	0.0300382
$961$	19.2433	0.620753
$962$	−48.2843	−1.55675
$963$	−12.3157	−0.396869
$964$	92.4894	2.97888
$965$	−27.9574	−0.899982
$966$	−54.4454	−1.75175
$967$	−7.94737	−0.255570	−0.127785	−	0.991802i	$-0.540787\pi$
$967$	−7.94737	−0.255570	−0.127785	+	0.991802i	$0.540787\pi$
$968$	−38.3699	−1.23326
$969$	1.23709	0.0397409
$970$	43.1389	1.38511
$971$	50.0346	1.60569	0.802843	−	0.596190i	$-0.203320\pi$
$971$	50.0346	1.60569	0.802843	+	0.596190i	$0.203320\pi$
$972$	−4.51600	−0.144851
$973$	74.5246	2.38915
$974$	65.7559	2.10696
$975$	1.97667	0.0633040
$976$	−39.2096	−1.25507
$977$	−13.4519	−0.430366	−0.215183	−	0.976574i	$-0.569035\pi$
$977$	−13.4519	−0.430366	−0.215183	+	0.976574i	$0.569035\pi$
$978$	17.9763	0.574819
$979$	3.21452	0.102736
$980$	−46.0874	−1.47221
$981$	−12.3401	−0.393991
$982$	−59.0902	−1.88564
$983$	16.3993	0.523057	0.261529	−	0.965196i	$-0.415773\pi$
$983$	16.3993	0.523057	0.261529	+	0.965196i	$0.415773\pi$
$984$	69.7145	2.22242
$985$	6.51684	0.207644
$986$	−15.6206	−0.497460
$987$	19.2916	0.614059
$988$	12.3428	0.392678
$989$	−1.49170	−0.0474332
$990$	−11.5947	−0.368504
$991$	40.6463	1.29117	0.645587	−	0.763687i	$-0.276613\pi$
$991$	40.6463	1.29117	0.645587	+	0.763687i	$0.276613\pi$
$992$	42.1628	1.33867
$993$	2.18898	0.0694653
$994$	69.0688	2.19073
$995$	−19.6582	−0.623208
$996$	34.7885	1.10232
$997$	−28.6143	−0.906223	−0.453111	−	0.891454i	$-0.649686\pi$
$997$	−28.6143	−0.906223	−0.453111	+	0.891454i	$0.649686\pi$
$998$	29.7680	0.942290
$999$	8.56157	0.270876

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.f.1.47	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.f.1.47	✓	48	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+2.55264 q^{2} -1.00000 q^{3} +4.51600 q^{4} -2.02616 q^{5} -2.55264 q^{6} -3.46941 q^{7} +6.42244 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.55264 q^{2} -1.00000 q^{3} +4.51600 q^{4} -2.02616 q^{5} -2.55264 q^{6} -3.46941 q^{7} +6.42244 q^{8} +1.00000 q^{9} -5.17206 q^{10} +2.24180 q^{11} -4.51600 q^{12} +2.20934 q^{13} -8.85617 q^{14} +2.02616 q^{15} +7.36222 q^{16} -1.00000 q^{17} +2.55264 q^{18} +1.23709 q^{19} -9.15012 q^{20} +3.46941 q^{21} +5.72251 q^{22} -6.14774 q^{23} -6.42244 q^{24} -0.894688 q^{25} +5.63965 q^{26} -1.00000 q^{27} -15.6678 q^{28} +6.11937 q^{29} +5.17206 q^{30} +7.08825 q^{31} +5.94826 q^{32} -2.24180 q^{33} -2.55264 q^{34} +7.02957 q^{35} +4.51600 q^{36} -8.56157 q^{37} +3.15784 q^{38} -2.20934 q^{39} -13.0129 q^{40} -10.8548 q^{41} +8.85617 q^{42} +0.242642 q^{43} +10.1239 q^{44} -2.02616 q^{45} -15.6930 q^{46} +5.56049 q^{47} -7.36222 q^{48} +5.03681 q^{49} -2.28382 q^{50} +1.00000 q^{51} +9.97735 q^{52} -2.50875 q^{53} -2.55264 q^{54} -4.54223 q^{55} -22.2821 q^{56} -1.23709 q^{57} +15.6206 q^{58} +2.25565 q^{59} +9.15012 q^{60} -5.32578 q^{61} +18.0938 q^{62} -3.46941 q^{63} +0.459342 q^{64} -4.47646 q^{65} -5.72251 q^{66} -4.75839 q^{67} -4.51600 q^{68} +6.14774 q^{69} +17.9440 q^{70} -7.79895 q^{71} +6.42244 q^{72} +9.40328 q^{73} -21.8547 q^{74} +0.894688 q^{75} +5.58668 q^{76} -7.77771 q^{77} -5.63965 q^{78} -2.68310 q^{79} -14.9170 q^{80} +1.00000 q^{81} -27.7085 q^{82} -7.70340 q^{83} +15.6678 q^{84} +2.02616 q^{85} +0.619378 q^{86} -6.11937 q^{87} +14.3978 q^{88} +1.43390 q^{89} -5.17206 q^{90} -7.66509 q^{91} -27.7632 q^{92} -7.08825 q^{93} +14.1940 q^{94} -2.50653 q^{95} -5.94826 q^{96} -8.34075 q^{97} +12.8572 q^{98} +2.24180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

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