LMFDB - Embedded newform 8007.2.a.c.1.20

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:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-0.177236 q^{2} -1.00000 q^{3} -1.96859 q^{4} -2.36208 q^{5} +0.177236 q^{6} -1.71756 q^{7} +0.703377 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.177236 q^{2} -1.00000 q^{3} -1.96859 q^{4} -2.36208 q^{5} +0.177236 q^{6} -1.71756 q^{7} +0.703377 q^{8} +1.00000 q^{9} +0.418646 q^{10} -5.41057 q^{11} +1.96859 q^{12} -2.15860 q^{13} +0.304413 q^{14} +2.36208 q^{15} +3.81251 q^{16} +1.00000 q^{17} -0.177236 q^{18} -4.14502 q^{19} +4.64996 q^{20} +1.71756 q^{21} +0.958949 q^{22} +2.94109 q^{23} -0.703377 q^{24} +0.579417 q^{25} +0.382583 q^{26} -1.00000 q^{27} +3.38116 q^{28} -2.08733 q^{29} -0.418646 q^{30} -2.15234 q^{31} -2.08247 q^{32} +5.41057 q^{33} -0.177236 q^{34} +4.05701 q^{35} -1.96859 q^{36} +10.6988 q^{37} +0.734648 q^{38} +2.15860 q^{39} -1.66143 q^{40} -3.45639 q^{41} -0.304413 q^{42} -0.623745 q^{43} +10.6512 q^{44} -2.36208 q^{45} -0.521267 q^{46} +7.24759 q^{47} -3.81251 q^{48} -4.05000 q^{49} -0.102694 q^{50} -1.00000 q^{51} +4.24940 q^{52} +1.29165 q^{53} +0.177236 q^{54} +12.7802 q^{55} -1.20809 q^{56} +4.14502 q^{57} +0.369950 q^{58} +2.53826 q^{59} -4.64996 q^{60} +13.5435 q^{61} +0.381473 q^{62} -1.71756 q^{63} -7.25593 q^{64} +5.09879 q^{65} -0.958949 q^{66} +3.19321 q^{67} -1.96859 q^{68} -2.94109 q^{69} -0.719048 q^{70} -2.85455 q^{71} +0.703377 q^{72} -9.51172 q^{73} -1.89622 q^{74} -0.579417 q^{75} +8.15984 q^{76} +9.29297 q^{77} -0.382583 q^{78} +2.33374 q^{79} -9.00545 q^{80} +1.00000 q^{81} +0.612597 q^{82} +13.6729 q^{83} -3.38116 q^{84} -2.36208 q^{85} +0.110550 q^{86} +2.08733 q^{87} -3.80567 q^{88} -0.446578 q^{89} +0.418646 q^{90} +3.70752 q^{91} -5.78979 q^{92} +2.15234 q^{93} -1.28453 q^{94} +9.79087 q^{95} +2.08247 q^{96} +16.7200 q^{97} +0.717806 q^{98} -5.41057 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + 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 $

$2$	−0.177236	−0.125325	−0.0626625	−	0.998035i	$-0.519959\pi$
$2$	−0.177236	−0.125325	−0.0626625	+	0.998035i	$0.519959\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.96859	−0.984294
$5$	−2.36208	−1.05635	−0.528177	−	0.849134i	$-0.677124\pi$
$5$	−2.36208	−1.05635	−0.528177	+	0.849134i	$0.677124\pi$
$6$	0.177236	0.0723564
$7$	−1.71756	−0.649176	−0.324588	−	0.945856i	$-0.605226\pi$
$7$	−1.71756	−0.649176	−0.324588	+	0.945856i	$0.605226\pi$
$8$	0.703377	0.248681
$9$	1.00000	0.333333
$10$	0.418646	0.132387
$11$	−5.41057	−1.63135	−0.815675	−	0.578511i	$-0.803634\pi$
$11$	−5.41057	−1.63135	−0.815675	+	0.578511i	$0.803634\pi$
$12$	1.96859	0.568282
$13$	−2.15860	−0.598689	−0.299344	−	0.954145i	$-0.596768\pi$
$13$	−2.15860	−0.598689	−0.299344	+	0.954145i	$0.596768\pi$
$14$	0.304413	0.0813579
$15$	2.36208	0.609886
$16$	3.81251	0.953128
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.177236	−0.0417750
$19$	−4.14502	−0.950933	−0.475467	−	0.879734i	$-0.657721\pi$
$19$	−4.14502	−0.950933	−0.475467	+	0.879734i	$0.657721\pi$
$20$	4.64996	1.03976
$21$	1.71756	0.374802
$22$	0.958949	0.204449
$23$	2.94109	0.613259	0.306630	−	0.951829i	$-0.400799\pi$
$23$	2.94109	0.613259	0.306630	+	0.951829i	$0.400799\pi$
$24$	−0.703377	−0.143576
$25$	0.579417	0.115883
$26$	0.382583	0.0750306
$27$	−1.00000	−0.192450
$28$	3.38116	0.638979
$29$	−2.08733	−0.387607	−0.193803	−	0.981040i	$-0.562082\pi$
$29$	−2.08733	−0.387607	−0.193803	+	0.981040i	$0.562082\pi$
$30$	−0.418646	−0.0764339
$31$	−2.15234	−0.386572	−0.193286	−	0.981142i	$-0.561914\pi$
$31$	−2.15234	−0.386572	−0.193286	+	0.981142i	$0.561914\pi$
$32$	−2.08247	−0.368132
$33$	5.41057	0.941860
$34$	−0.177236	−0.0303958
$35$	4.05701	0.685759
$36$	−1.96859	−0.328098
$37$	10.6988	1.75888	0.879440	−	0.476010i	$-0.157917\pi$
$37$	10.6988	1.75888	0.879440	+	0.476010i	$0.157917\pi$
$38$	0.734648	0.119176
$39$	2.15860	0.345653
$40$	−1.66143	−0.262696
$41$	−3.45639	−0.539797	−0.269898	−	0.962889i	$-0.586990\pi$
$41$	−3.45639	−0.539797	−0.269898	+	0.962889i	$0.586990\pi$
$42$	−0.304413	−0.0469720
$43$	−0.623745	−0.0951203	−0.0475601	−	0.998868i	$-0.515145\pi$
$43$	−0.623745	−0.0951203	−0.0475601	+	0.998868i	$0.515145\pi$
$44$	10.6512	1.60573
$45$	−2.36208	−0.352118
$46$	−0.521267	−0.0768567
$47$	7.24759	1.05717	0.528585	−	0.848881i	$-0.322723\pi$
$47$	7.24759	1.05717	0.528585	+	0.848881i	$0.322723\pi$
$48$	−3.81251	−0.550289
$49$	−4.05000	−0.578571
$50$	−0.102694	−0.0145231
$51$	−1.00000	−0.140028
$52$	4.24940	0.589286
$53$	1.29165	0.177421	0.0887106	−	0.996057i	$-0.471725\pi$
$53$	1.29165	0.177421	0.0887106	+	0.996057i	$0.471725\pi$
$54$	0.177236	0.0241188
$55$	12.7802	1.72328
$56$	−1.20809	−0.161438
$57$	4.14502	0.549021
$58$	0.369950	0.0485768
$59$	2.53826	0.330453	0.165226	−	0.986256i	$-0.447165\pi$
$59$	2.53826	0.330453	0.165226	+	0.986256i	$0.447165\pi$
$60$	−4.64996	−0.600307
$61$	13.5435	1.73407	0.867035	−	0.498247i	$-0.166023\pi$
$61$	13.5435	1.73407	0.867035	+	0.498247i	$0.166023\pi$
$62$	0.381473	0.0484471
$63$	−1.71756	−0.216392
$64$	−7.25593	−0.906992
$65$	5.09879	0.632427
$66$	−0.958949	−0.118039
$67$	3.19321	0.390113	0.195056	−	0.980792i	$-0.437511\pi$
$67$	3.19321	0.390113	0.195056	+	0.980792i	$0.437511\pi$
$68$	−1.96859	−0.238726
$69$	−2.94109	−0.354065
$70$	−0.719048	−0.0859427
$71$	−2.85455	−0.338772	−0.169386	−	0.985550i	$-0.554179\pi$
$71$	−2.85455	−0.338772	−0.169386	+	0.985550i	$0.554179\pi$
$72$	0.703377	0.0828938
$73$	−9.51172	−1.11326	−0.556631	−	0.830760i	$-0.687906\pi$
$73$	−9.51172	−1.11326	−0.556631	+	0.830760i	$0.687906\pi$
$74$	−1.89622	−0.220431
$75$	−0.579417	−0.0669053
$76$	8.15984	0.935997
$77$	9.29297	1.05903
$78$	−0.382583	−0.0433190
$79$	2.33374	0.262566	0.131283	−	0.991345i	$-0.458090\pi$
$79$	2.33374	0.262566	0.131283	+	0.991345i	$0.458090\pi$
$80$	−9.00545	−1.00684
$81$	1.00000	0.111111
$82$	0.612597	0.0676500
$83$	13.6729	1.50079	0.750396	−	0.660989i	$-0.229863\pi$
$83$	13.6729	1.50079	0.750396	+	0.660989i	$0.229863\pi$
$84$	−3.38116	−0.368915
$85$	−2.36208	−0.256203
$86$	0.110550	0.0119209
$87$	2.08733	0.223785
$88$	−3.80567	−0.405686
$89$	−0.446578	−0.0473372	−0.0236686	−	0.999720i	$-0.507535\pi$
$89$	−0.446578	−0.0473372	−0.0236686	+	0.999720i	$0.507535\pi$
$90$	0.418646	0.0441292
$91$	3.70752	0.388654
$92$	−5.78979	−0.603627
$93$	2.15234	0.223187
$94$	−1.28453	−0.132490
$95$	9.79087	1.00452
$96$	2.08247	0.212541
$97$	16.7200	1.69766	0.848830	−	0.528666i	$-0.177307\pi$
$97$	16.7200	1.69766	0.848830	+	0.528666i	$0.177307\pi$
$98$	0.717806	0.0725094
$99$	−5.41057	−0.543783
$100$	−1.14063	−0.114063
$101$	−4.44762	−0.442555	−0.221278	−	0.975211i	$-0.571023\pi$
$101$	−4.44762	−0.442555	−0.221278	+	0.975211i	$0.571023\pi$
$102$	0.177236	0.0175490
$103$	−13.9120	−1.37079	−0.685397	−	0.728170i	$-0.740371\pi$
$103$	−13.9120	−1.37079	−0.685397	+	0.728170i	$0.740371\pi$
$104$	−1.51831	−0.148883
$105$	−4.05701	−0.395923
$106$	−0.228926	−0.0222353
$107$	14.3042	1.38284	0.691418	−	0.722455i	$-0.256987\pi$
$107$	14.3042	1.38284	0.691418	+	0.722455i	$0.256987\pi$
$108$	1.96859	0.189427
$109$	−4.40712	−0.422125	−0.211063	−	0.977473i	$-0.567692\pi$
$109$	−4.40712	−0.422125	−0.211063	+	0.977473i	$0.567692\pi$
$110$	−2.26511	−0.215970
$111$	−10.6988	−1.01549
$112$	−6.54820	−0.618747
$113$	−6.16105	−0.579583	−0.289792	−	0.957090i	$-0.593586\pi$
$113$	−6.16105	−0.579583	−0.289792	+	0.957090i	$0.593586\pi$
$114$	−0.734648	−0.0688061
$115$	−6.94708	−0.647819
$116$	4.10909	0.381519
$117$	−2.15860	−0.199563
$118$	−0.449871	−0.0414140
$119$	−1.71756	−0.157448
$120$	1.66143	0.151667
$121$	18.2743	1.66130
$122$	−2.40040	−0.217322
$123$	3.45639	0.311652
$124$	4.23707	0.380500
$125$	10.4418	0.933940
$126$	0.304413	0.0271193
$127$	0.425213	0.0377315	0.0188658	−	0.999822i	$-0.493994\pi$
$127$	0.425213	0.0377315	0.0188658	+	0.999822i	$0.493994\pi$
$128$	5.45095	0.481801
$129$	0.623745	0.0549177
$130$	−0.903690	−0.0792589
$131$	6.37638	0.557107	0.278554	−	0.960421i	$-0.410145\pi$
$131$	6.37638	0.557107	0.278554	+	0.960421i	$0.410145\pi$
$132$	−10.6512	−0.927067
$133$	7.11931	0.617323
$134$	−0.565953	−0.0488909
$135$	2.36208	0.203295
$136$	0.703377	0.0603141
$137$	−2.75555	−0.235423	−0.117711	−	0.993048i	$-0.537556\pi$
$137$	−2.75555	−0.235423	−0.117711	+	0.993048i	$0.537556\pi$
$138$	0.521267	0.0443732
$139$	17.2732	1.46509	0.732547	−	0.680716i	$-0.238331\pi$
$139$	17.2732	1.46509	0.732547	+	0.680716i	$0.238331\pi$
$140$	−7.98657	−0.674988
$141$	−7.24759	−0.610357
$142$	0.505929	0.0424566
$143$	11.6793	0.976671
$144$	3.81251	0.317709
$145$	4.93043	0.409450
$146$	1.68582	0.139520
$147$	4.05000	0.334038
$148$	−21.0616	−1.73125
$149$	−8.86165	−0.725975	−0.362987	−	0.931794i	$-0.618243\pi$
$149$	−8.86165	−0.725975	−0.362987	+	0.931794i	$0.618243\pi$
$150$	0.102694	0.00838490
$151$	−8.90127	−0.724375	−0.362187	−	0.932105i	$-0.617970\pi$
$151$	−8.90127	−0.724375	−0.362187	+	0.932105i	$0.617970\pi$
$152$	−2.91551	−0.236479
$153$	1.00000	0.0808452
$154$	−1.64705	−0.132723
$155$	5.08400	0.408357
$156$	−4.24940	−0.340224
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−0.413623	−0.0329061
$159$	−1.29165	−0.102434
$160$	4.91896	0.388878
$161$	−5.05149	−0.398113
$162$	−0.177236	−0.0139250
$163$	19.0668	1.49342	0.746712	−	0.665147i	$-0.231631\pi$
$163$	19.0668	1.49342	0.746712	+	0.665147i	$0.231631\pi$
$164$	6.80420	0.531319
$165$	−12.7802	−0.994937
$166$	−2.42333	−0.188087
$167$	2.08568	0.161395	0.0806974	−	0.996739i	$-0.474285\pi$
$167$	2.08568	0.161395	0.0806974	+	0.996739i	$0.474285\pi$
$168$	1.20809	0.0932062
$169$	−8.34043	−0.641572
$170$	0.418646	0.0321087
$171$	−4.14502	−0.316978
$172$	1.22790	0.0936263
$173$	−0.862074	−0.0655423	−0.0327711	−	0.999463i	$-0.510433\pi$
$173$	−0.862074	−0.0655423	−0.0327711	+	0.999463i	$0.510433\pi$
$174$	−0.369950	−0.0280458
$175$	−0.995182	−0.0752287
$176$	−20.6279	−1.55488
$177$	−2.53826	−0.190787
$178$	0.0791498	0.00593253
$179$	11.8464	0.885444	0.442722	−	0.896659i	$-0.354013\pi$
$179$	11.8464	0.885444	0.442722	+	0.896659i	$0.354013\pi$
$180$	4.64996	0.346587
$181$	−22.2095	−1.65082	−0.825410	−	0.564533i	$-0.809056\pi$
$181$	−22.2095	−1.65082	−0.825410	+	0.564533i	$0.809056\pi$
$182$	−0.657108	−0.0487081
$183$	−13.5435	−1.00117
$184$	2.06869	0.152506
$185$	−25.2715	−1.85800
$186$	−0.381473	−0.0279709
$187$	−5.41057	−0.395660
$188$	−14.2675	−1.04056
$189$	1.71756	0.124934
$190$	−1.73530	−0.125892
$191$	20.3829	1.47485	0.737427	−	0.675426i	$-0.236040\pi$
$191$	20.3829	1.47485	0.737427	+	0.675426i	$0.236040\pi$
$192$	7.25593	0.523652
$193$	10.7301	0.772372	0.386186	−	0.922421i	$-0.373792\pi$
$193$	10.7301	0.772372	0.386186	+	0.922421i	$0.373792\pi$
$194$	−2.96339	−0.212759
$195$	−5.09879	−0.365132
$196$	7.97277	0.569484
$197$	−4.19088	−0.298588	−0.149294	−	0.988793i	$-0.547700\pi$
$197$	−4.19088	−0.298588	−0.149294	+	0.988793i	$0.547700\pi$
$198$	0.958949	0.0681496
$199$	−21.9341	−1.55487	−0.777434	−	0.628964i	$-0.783479\pi$
$199$	−21.9341	−1.55487	−0.777434	+	0.628964i	$0.783479\pi$
$200$	0.407549	0.0288181
$201$	−3.19321	−0.225232
$202$	0.788280	0.0554632
$203$	3.58510	0.251625
$204$	1.96859	0.137829
$205$	8.16426	0.570217
$206$	2.46572	0.171795
$207$	2.94109	0.204420
$208$	−8.22970	−0.570627
$209$	22.4269	1.55130
$210$	0.719048	0.0496190
$211$	−18.1603	−1.25021	−0.625103	−	0.780543i	$-0.714943\pi$
$211$	−18.1603	−1.25021	−0.625103	+	0.780543i	$0.714943\pi$
$212$	−2.54272	−0.174635
$213$	2.85455	0.195590
$214$	−2.53521	−0.173304
$215$	1.47334	0.100481
$216$	−0.703377	−0.0478588
$217$	3.69677	0.250953
$218$	0.781101	0.0529028
$219$	9.51172	0.642742
$220$	−25.1589	−1.69622
$221$	−2.15860	−0.145203
$222$	1.89622	0.127266
$223$	13.3162	0.891719	0.445859	−	0.895103i	$-0.352898\pi$
$223$	13.3162	0.891719	0.445859	+	0.895103i	$0.352898\pi$
$224$	3.57676	0.238982
$225$	0.579417	0.0386278
$226$	1.09196	0.0726362
$227$	19.0076	1.26158	0.630790	−	0.775953i	$-0.282731\pi$
$227$	19.0076	1.26158	0.630790	+	0.775953i	$0.282731\pi$
$228$	−8.15984	−0.540398
$229$	5.77214	0.381434	0.190717	−	0.981645i	$-0.438919\pi$
$229$	5.77214	0.381434	0.190717	+	0.981645i	$0.438919\pi$
$230$	1.23127	0.0811878
$231$	−9.29297	−0.611432
$232$	−1.46818	−0.0963906
$233$	−12.1096	−0.793325	−0.396662	−	0.917965i	$-0.629832\pi$
$233$	−12.1096	−0.793325	−0.396662	+	0.917965i	$0.629832\pi$
$234$	0.382583	0.0250102
$235$	−17.1194	−1.11674
$236$	−4.99678	−0.325262
$237$	−2.33374	−0.151593
$238$	0.304413	0.0197322
$239$	−7.78534	−0.503592	−0.251796	−	0.967780i	$-0.581021\pi$
$239$	−7.78534	−0.503592	−0.251796	+	0.967780i	$0.581021\pi$
$240$	9.00545	0.581299
$241$	0.113944	0.00733980	0.00366990	−	0.999993i	$-0.498832\pi$
$241$	0.113944	0.00733980	0.00366990	+	0.999993i	$0.498832\pi$
$242$	−3.23887	−0.208202
$243$	−1.00000	−0.0641500
$244$	−26.6616	−1.70683
$245$	9.56641	0.611176
$246$	−0.612597	−0.0390578
$247$	8.94746	0.569313
$248$	−1.51391	−0.0961332
$249$	−13.6729	−0.866482
$250$	−1.85066	−0.117046
$251$	−22.1098	−1.39556	−0.697778	−	0.716314i	$-0.745828\pi$
$251$	−22.1098	−1.39556	−0.697778	+	0.716314i	$0.745828\pi$
$252$	3.38116	0.212993
$253$	−15.9130	−1.00044
$254$	−0.0753631	−0.00472870
$255$	2.36208	0.147919
$256$	13.5458	0.846610
$257$	−13.3347	−0.831793	−0.415896	−	0.909412i	$-0.636532\pi$
$257$	−13.3347	−0.831793	−0.415896	+	0.909412i	$0.636532\pi$
$258$	−0.110550	−0.00688256
$259$	−18.3759	−1.14182
$260$	−10.0374	−0.622494
$261$	−2.08733	−0.129202
$262$	−1.13013	−0.0698194
$263$	19.1519	1.18096	0.590479	−	0.807053i	$-0.298939\pi$
$263$	19.1519	1.18096	0.590479	+	0.807053i	$0.298939\pi$
$264$	3.80567	0.234223
$265$	−3.05097	−0.187420
$266$	−1.26180	−0.0773659
$267$	0.446578	0.0273301
$268$	−6.28612	−0.383986
$269$	20.3107	1.23837	0.619183	−	0.785247i	$-0.287464\pi$
$269$	20.3107	1.23837	0.619183	+	0.785247i	$0.287464\pi$
$270$	−0.418646	−0.0254780
$271$	−2.76499	−0.167961	−0.0839805	−	0.996467i	$-0.526763\pi$
$271$	−2.76499	−0.167961	−0.0839805	+	0.996467i	$0.526763\pi$
$272$	3.81251	0.231167
$273$	−3.70752	−0.224390
$274$	0.488383	0.0295043
$275$	−3.13498	−0.189046
$276$	5.78979	0.348504
$277$	−14.2976	−0.859060	−0.429530	−	0.903053i	$-0.641321\pi$
$277$	−14.2976	−0.859060	−0.429530	+	0.903053i	$0.641321\pi$
$278$	−3.06144	−0.183613
$279$	−2.15234	−0.128857
$280$	2.85361	0.170536
$281$	−11.6932	−0.697561	−0.348780	−	0.937205i	$-0.613404\pi$
$281$	−11.6932	−0.697561	−0.348780	+	0.937205i	$0.613404\pi$
$282$	1.28453	0.0764929
$283$	−2.28158	−0.135626	−0.0678130	−	0.997698i	$-0.521602\pi$
$283$	−2.28158	−0.135626	−0.0678130	+	0.997698i	$0.521602\pi$
$284$	5.61942	0.333451
$285$	−9.79087	−0.579961
$286$	−2.06999	−0.122401
$287$	5.93654	0.350423
$288$	−2.08247	−0.122711
$289$	1.00000	0.0588235
$290$	−0.873851	−0.0513143
$291$	−16.7200	−0.980145
$292$	18.7246	1.09578
$293$	−19.2530	−1.12477	−0.562385	−	0.826875i	$-0.690116\pi$
$293$	−19.2530	−1.12477	−0.562385	+	0.826875i	$0.690116\pi$
$294$	−0.717806	−0.0418633
$295$	−5.99556	−0.349075
$296$	7.52533	0.437401
$297$	5.41057	0.313953
$298$	1.57061	0.0909827
$299$	−6.34864	−0.367151
$300$	1.14063	0.0658545
$301$	1.07132	0.0617498
$302$	1.57763	0.0907822
$303$	4.44762	0.255509
$304$	−15.8029	−0.906361
$305$	−31.9909	−1.83179
$306$	−0.177236	−0.0101319
$307$	−3.81747	−0.217875	−0.108937	−	0.994049i	$-0.534745\pi$
$307$	−3.81747	−0.217875	−0.108937	+	0.994049i	$0.534745\pi$
$308$	−18.2940	−1.04240
$309$	13.9120	0.791428
$310$	−0.901069	−0.0511773
$311$	−9.36345	−0.530952	−0.265476	−	0.964117i	$-0.585529\pi$
$311$	−9.36345	−0.530952	−0.265476	+	0.964117i	$0.585529\pi$
$312$	1.51831	0.0859575
$313$	−10.6566	−0.602345	−0.301172	−	0.953570i	$-0.597378\pi$
$313$	−10.6566	−0.602345	−0.301172	+	0.953570i	$0.597378\pi$
$314$	−0.177236	−0.0100020
$315$	4.05701	0.228586
$316$	−4.59417	−0.258442
$317$	−20.7174	−1.16361	−0.581804	−	0.813329i	$-0.697653\pi$
$317$	−20.7174	−1.16361	−0.581804	+	0.813329i	$0.697653\pi$
$318$	0.228926	0.0128376
$319$	11.2936	0.632322
$320$	17.1391	0.958104
$321$	−14.3042	−0.798380
$322$	0.895306	0.0498935
$323$	−4.14502	−0.230635
$324$	−1.96859	−0.109366
$325$	−1.25073	−0.0693781
$326$	−3.37932	−0.187163
$327$	4.40712	0.243714
$328$	−2.43114	−0.134237
$329$	−12.4481	−0.686288
$330$	2.26511	0.124690
$331$	−18.1770	−0.999097	−0.499549	−	0.866286i	$-0.666501\pi$
$331$	−18.1770	−0.999097	−0.499549	+	0.866286i	$0.666501\pi$
$332$	−26.9162	−1.47722
$333$	10.6988	0.586293
$334$	−0.369658	−0.0202268
$335$	−7.54262	−0.412097
$336$	6.54820	0.357234
$337$	18.4788	1.00660	0.503302	−	0.864110i	$-0.332118\pi$
$337$	18.4788	1.00660	0.503302	+	0.864110i	$0.332118\pi$
$338$	1.47823	0.0804049
$339$	6.16105	0.334622
$340$	4.64996	0.252179
$341$	11.6454	0.630634
$342$	0.734648	0.0397252
$343$	18.9790	1.02477
$344$	−0.438728	−0.0236546
$345$	6.94708	0.374018
$346$	0.152791	0.00821408
$347$	19.8423	1.06519	0.532594	−	0.846371i	$-0.321217\pi$
$347$	19.8423	1.06519	0.532594	+	0.846371i	$0.321217\pi$
$348$	−4.10909	−0.220270
$349$	2.34756	0.125662	0.0628310	−	0.998024i	$-0.479987\pi$
$349$	2.34756	0.125662	0.0628310	+	0.998024i	$0.479987\pi$
$350$	0.176382	0.00942803
$351$	2.15860	0.115218
$352$	11.2674	0.600552
$353$	28.5406	1.51906	0.759530	−	0.650472i	$-0.225429\pi$
$353$	28.5406	1.51906	0.759530	+	0.650472i	$0.225429\pi$
$354$	0.449871	0.0239104
$355$	6.74266	0.357863
$356$	0.879128	0.0465937
$357$	1.71756	0.0909028
$358$	−2.09962	−0.110968
$359$	−0.246614	−0.0130158	−0.00650789	−	0.999979i	$-0.502072\pi$
$359$	−0.246614	−0.0130158	−0.00650789	+	0.999979i	$0.502072\pi$
$360$	−1.66143	−0.0875652
$361$	−1.81880	−0.0957263
$362$	3.93633	0.206889
$363$	−18.2743	−0.959152
$364$	−7.29859	−0.382550
$365$	22.4674	1.17600
$366$	2.40040	0.125471
$367$	28.5863	1.49219	0.746097	−	0.665837i	$-0.231925\pi$
$367$	28.5863	1.49219	0.746097	+	0.665837i	$0.231925\pi$
$368$	11.2129	0.584514
$369$	−3.45639	−0.179932
$370$	4.47903	0.232854
$371$	−2.21848	−0.115177
$372$	−4.23707	−0.219682
$373$	−20.1457	−1.04311	−0.521554	−	0.853219i	$-0.674647\pi$
$373$	−20.1457	−1.04311	−0.521554	+	0.853219i	$0.674647\pi$
$374$	0.958949	0.0495861
$375$	−10.4418	−0.539210
$376$	5.09779	0.262898
$377$	4.50571	0.232056
$378$	−0.304413	−0.0156573
$379$	−19.1872	−0.985579	−0.492790	−	0.870149i	$-0.664023\pi$
$379$	−19.1872	−0.985579	−0.492790	+	0.870149i	$0.664023\pi$
$380$	−19.2742	−0.988744
$381$	−0.425213	−0.0217843
$382$	−3.61259	−0.184836
$383$	6.28651	0.321226	0.160613	−	0.987017i	$-0.448653\pi$
$383$	6.28651	0.321226	0.160613	+	0.987017i	$0.448653\pi$
$384$	−5.45095	−0.278168
$385$	−21.9507	−1.11871
$386$	−1.90177	−0.0967974
$387$	−0.623745	−0.0317068
$388$	−32.9148	−1.67100
$389$	−8.31838	−0.421759	−0.210879	−	0.977512i	$-0.567633\pi$
$389$	−8.31838	−0.421759	−0.210879	+	0.977512i	$0.567633\pi$
$390$	0.903690	0.0457601
$391$	2.94109	0.148737
$392$	−2.84868	−0.143880
$393$	−6.37638	−0.321646
$394$	0.742776	0.0374205
$395$	−5.51247	−0.277363
$396$	10.6512	0.535242
$397$	−10.3191	−0.517902	−0.258951	−	0.965890i	$-0.583377\pi$
$397$	−10.3191	−0.517902	−0.258951	+	0.965890i	$0.583377\pi$
$398$	3.88752	0.194864
$399$	−7.11931	−0.356411
$400$	2.20903	0.110452
$401$	27.1162	1.35412	0.677059	−	0.735929i	$-0.263254\pi$
$401$	27.1162	1.35412	0.677059	+	0.735929i	$0.263254\pi$
$402$	0.565953	0.0282272
$403$	4.64605	0.231436
$404$	8.75554	0.435604
$405$	−2.36208	−0.117373
$406$	−0.635410	−0.0315349
$407$	−57.8869	−2.86935
$408$	−0.703377	−0.0348224
$409$	−37.4389	−1.85123	−0.925616	−	0.378464i	$-0.876453\pi$
$409$	−37.4389	−1.85123	−0.925616	+	0.378464i	$0.876453\pi$
$410$	−1.44700	−0.0714623
$411$	2.75555	0.135921
$412$	27.3871	1.34926
$413$	−4.35960	−0.214522
$414$	−0.521267	−0.0256189
$415$	−32.2964	−1.58537
$416$	4.49523	0.220397
$417$	−17.2732	−0.845873
$418$	−3.97487	−0.194417
$419$	−6.44675	−0.314944	−0.157472	−	0.987523i	$-0.550334\pi$
$419$	−6.44675	−0.314944	−0.157472	+	0.987523i	$0.550334\pi$
$420$	7.98657	0.389705
$421$	−4.46703	−0.217710	−0.108855	−	0.994058i	$-0.534718\pi$
$421$	−4.46703	−0.217710	−0.108855	+	0.994058i	$0.534718\pi$
$422$	3.21866	0.156682
$423$	7.24759	0.352390
$424$	0.908514	0.0441214
$425$	0.579417	0.0281059
$426$	−0.505929	−0.0245123
$427$	−23.2618	−1.12572
$428$	−28.1590	−1.36112
$429$	−11.6793	−0.563881
$430$	−0.261128	−0.0125927
$431$	19.0784	0.918976	0.459488	−	0.888184i	$-0.348033\pi$
$431$	19.0784	0.918976	0.459488	+	0.888184i	$0.348033\pi$
$432$	−3.81251	−0.183430
$433$	5.56303	0.267342	0.133671	−	0.991026i	$-0.457323\pi$
$433$	5.56303	0.267342	0.133671	+	0.991026i	$0.457323\pi$
$434$	−0.655201	−0.0314507
$435$	−4.93043	−0.236396
$436$	8.67579	0.415495
$437$	−12.1909	−0.583169
$438$	−1.68582	−0.0805516
$439$	−2.90398	−0.138599	−0.0692997	−	0.997596i	$-0.522076\pi$
$439$	−2.90398	−0.138599	−0.0692997	+	0.997596i	$0.522076\pi$
$440$	8.98930	0.428548
$441$	−4.05000	−0.192857
$442$	0.382583	0.0181976
$443$	13.3009	0.631944	0.315972	−	0.948769i	$-0.397669\pi$
$443$	13.3009	0.631944	0.315972	+	0.948769i	$0.397669\pi$
$444$	21.0616	0.999540
$445$	1.05485	0.0500048
$446$	−2.36011	−0.111755
$447$	8.86165	0.419142
$448$	12.4625	0.588797
$449$	11.4255	0.539203	0.269602	−	0.962972i	$-0.413108\pi$
$449$	11.4255	0.539203	0.269602	+	0.962972i	$0.413108\pi$
$450$	−0.102694	−0.00484103
$451$	18.7010	0.880597
$452$	12.1286	0.570480
$453$	8.90127	0.418218
$454$	−3.36884	−0.158107
$455$	−8.75747	−0.410556
$456$	2.91551	0.136531
$457$	11.8924	0.556302	0.278151	−	0.960537i	$-0.410278\pi$
$457$	11.8924	0.556302	0.278151	+	0.960537i	$0.410278\pi$
$458$	−1.02303	−0.0478031
$459$	−1.00000	−0.0466760
$460$	13.6759	0.637644
$461$	−1.67332	−0.0779341	−0.0389671	−	0.999240i	$-0.512407\pi$
$461$	−1.67332	−0.0779341	−0.0389671	+	0.999240i	$0.512407\pi$
$462$	1.64705	0.0766277
$463$	25.3834	1.17967	0.589834	−	0.807524i	$-0.299193\pi$
$463$	25.3834	1.17967	0.589834	+	0.807524i	$0.299193\pi$
$464$	−7.95796	−0.369439
$465$	−5.08400	−0.235765
$466$	2.14625	0.0994233
$467$	−27.0110	−1.24992	−0.624959	−	0.780658i	$-0.714884\pi$
$467$	−27.0110	−1.24992	−0.624959	+	0.780658i	$0.714884\pi$
$468$	4.24940	0.196429
$469$	−5.48452	−0.253252
$470$	3.03417	0.139956
$471$	−1.00000	−0.0460776
$472$	1.78535	0.0821775
$473$	3.37482	0.155174
$474$	0.413623	0.0189983
$475$	−2.40170	−0.110197
$476$	3.38116	0.154975
$477$	1.29165	0.0591404
$478$	1.37984	0.0631126
$479$	−15.1888	−0.693994	−0.346997	−	0.937866i	$-0.612799\pi$
$479$	−15.1888	−0.693994	−0.346997	+	0.937866i	$0.612799\pi$
$480$	−4.91896	−0.224519
$481$	−23.0946	−1.05302
$482$	−0.0201951	−0.000919860 0
$483$	5.05149	0.229851
$484$	−35.9746	−1.63521
$485$	−39.4940	−1.79333
$486$	0.177236	0.00803960
$487$	−2.38029	−0.107861	−0.0539306	−	0.998545i	$-0.517175\pi$
$487$	−2.38029	−0.107861	−0.0539306	+	0.998545i	$0.517175\pi$
$488$	9.52620	0.431231
$489$	−19.0668	−0.862229
$490$	−1.69551	−0.0765956
$491$	−25.8852	−1.16818	−0.584092	−	0.811687i	$-0.698549\pi$
$491$	−25.8852	−1.16818	−0.584092	+	0.811687i	$0.698549\pi$
$492$	−6.80420	−0.306757
$493$	−2.08733	−0.0940085
$494$	−1.58581	−0.0713491
$495$	12.7802	0.574427
$496$	−8.20582	−0.368452
$497$	4.90285	0.219923
$498$	2.42333	0.108592
$499$	−37.6553	−1.68568	−0.842841	−	0.538163i	$-0.819118\pi$
$499$	−37.6553	−1.68568	−0.842841	+	0.538163i	$0.819118\pi$
$500$	−20.5555	−0.919271
$501$	−2.08568	−0.0931814
$502$	3.91865	0.174898
$503$	−15.6707	−0.698720	−0.349360	−	0.936989i	$-0.613601\pi$
$503$	−15.6707	−0.698720	−0.349360	+	0.936989i	$0.613601\pi$
$504$	−1.20809	−0.0538126
$505$	10.5056	0.467495
$506$	2.82035	0.125380
$507$	8.34043	0.370412
$508$	−0.837069	−0.0371389
$509$	33.4171	1.48119	0.740593	−	0.671953i	$-0.234545\pi$
$509$	33.4171	1.48119	0.740593	+	0.671953i	$0.234545\pi$
$510$	−0.418646	−0.0185380
$511$	16.3369	0.722703
$512$	−13.3027	−0.587902
$513$	4.14502	0.183007
$514$	2.36338	0.104244
$515$	32.8613	1.44804
$516$	−1.22790	−0.0540552
$517$	−39.2136	−1.72461
$518$	3.25687	0.143099
$519$	0.862074	0.0378409
$520$	3.58637	0.157273
$521$	−1.81768	−0.0796342	−0.0398171	−	0.999207i	$-0.512678\pi$
$521$	−1.81768	−0.0796342	−0.0398171	+	0.999207i	$0.512678\pi$
$522$	0.369950	0.0161923
$523$	31.2660	1.36717	0.683584	−	0.729872i	$-0.260420\pi$
$523$	31.2660	1.36717	0.683584	+	0.729872i	$0.260420\pi$
$524$	−12.5525	−0.548357
$525$	0.995182	0.0434333
$526$	−3.39442	−0.148004
$527$	−2.15234	−0.0937574
$528$	20.6279	0.897713
$529$	−14.3500	−0.623913
$530$	0.540742	0.0234883
$531$	2.53826	0.110151
$532$	−14.0150	−0.607627
$533$	7.46097	0.323170
$534$	−0.0791498	−0.00342515
$535$	−33.7875	−1.46076
$536$	2.24603	0.0970138
$537$	−11.8464	−0.511211
$538$	−3.59979	−0.155198
$539$	21.9128	0.943851
$540$	−4.64996	−0.200102
$541$	15.0213	0.645818	0.322909	−	0.946430i	$-0.395339\pi$
$541$	15.0213	0.645818	0.322909	+	0.946430i	$0.395339\pi$
$542$	0.490056	0.0210497
$543$	22.2095	0.953102
$544$	−2.08247	−0.0892851
$545$	10.4100	0.445914
$546$	0.657108	0.0281216
$547$	10.8559	0.464167	0.232083	−	0.972696i	$-0.425446\pi$
$547$	10.8559	0.464167	0.232083	+	0.972696i	$0.425446\pi$
$548$	5.42454	0.231725
$549$	13.5435	0.578023
$550$	0.555632	0.0236922
$551$	8.65201	0.368588
$552$	−2.06869	−0.0880495
$553$	−4.00833	−0.170451
$554$	2.53405	0.107662
$555$	25.2715	1.07272
$556$	−34.0038	−1.44208
$557$	−27.6057	−1.16969	−0.584845	−	0.811145i	$-0.698845\pi$
$557$	−27.6057	−1.16969	−0.584845	+	0.811145i	$0.698845\pi$
$558$	0.381473	0.0161490
$559$	1.34642	0.0569475
$560$	15.4674	0.653616
$561$	5.41057	0.228435
$562$	2.07247	0.0874217
$563$	25.2585	1.06452	0.532260	−	0.846581i	$-0.321343\pi$
$563$	25.2585	1.06452	0.532260	+	0.846581i	$0.321343\pi$
$564$	14.2675	0.600770
$565$	14.5529	0.612245
$566$	0.404379	0.0169973
$567$	−1.71756	−0.0721306
$568$	−2.00782	−0.0842464
$569$	15.2790	0.640531	0.320265	−	0.947328i	$-0.396228\pi$
$569$	15.2790	0.640531	0.320265	+	0.947328i	$0.396228\pi$
$570$	1.73530	0.0726836
$571$	4.56380	0.190989	0.0954945	−	0.995430i	$-0.469557\pi$
$571$	4.56380	0.190989	0.0954945	+	0.995430i	$0.469557\pi$
$572$	−22.9917	−0.961331
$573$	−20.3829	−0.851508
$574$	−1.05217	−0.0439167
$575$	1.70412	0.0710666
$576$	−7.25593	−0.302331
$577$	−5.41583	−0.225464	−0.112732	−	0.993625i	$-0.535960\pi$
$577$	−5.41583	−0.225464	−0.112732	+	0.993625i	$0.535960\pi$
$578$	−0.177236	−0.00737205
$579$	−10.7301	−0.445929
$580$	−9.70598	−0.403019
$581$	−23.4839	−0.974277
$582$	2.96339	0.122837
$583$	−6.98854	−0.289436
$584$	−6.69033	−0.276848
$585$	5.09879	0.210809
$586$	3.41232	0.140962
$587$	11.5442	0.476478	0.238239	−	0.971207i	$-0.423430\pi$
$587$	11.5442	0.476478	0.238239	+	0.971207i	$0.423430\pi$
$588$	−7.97277	−0.328792
$589$	8.92150	0.367604
$590$	1.06263	0.0437478
$591$	4.19088	0.172390
$592$	40.7895	1.67644
$593$	2.31647	0.0951258	0.0475629	−	0.998868i	$-0.484855\pi$
$593$	2.31647	0.0951258	0.0475629	+	0.998868i	$0.484855\pi$
$594$	−0.958949	−0.0393462
$595$	4.05701	0.166321
$596$	17.4449	0.714572
$597$	21.9341	0.897704
$598$	1.12521	0.0460132
$599$	−39.1448	−1.59941	−0.799707	−	0.600390i	$-0.795012\pi$
$599$	−39.1448	−1.59941	−0.799707	+	0.600390i	$0.795012\pi$
$600$	−0.407549	−0.0166381
$601$	−36.2153	−1.47725	−0.738627	−	0.674114i	$-0.764526\pi$
$601$	−36.2153	−1.47725	−0.738627	+	0.674114i	$0.764526\pi$
$602$	−0.189876	−0.00773878
$603$	3.19321	0.130038
$604$	17.5229	0.712998
$605$	−43.1653	−1.75492
$606$	−0.788280	−0.0320217
$607$	−25.4222	−1.03185	−0.515927	−	0.856633i	$-0.672552\pi$
$607$	−25.4222	−1.03185	−0.515927	+	0.856633i	$0.672552\pi$
$608$	8.63188	0.350069
$609$	−3.58510	−0.145276
$610$	5.66994	0.229569
$611$	−15.6447	−0.632915
$612$	−1.96859	−0.0795754
$613$	−23.9022	−0.965399	−0.482700	−	0.875786i	$-0.660344\pi$
$613$	−23.9022	−0.965399	−0.482700	+	0.875786i	$0.660344\pi$
$614$	0.676594	0.0273051
$615$	−8.16426	−0.329215
$616$	6.53646	0.263362
$617$	5.78893	0.233054	0.116527	−	0.993188i	$-0.462824\pi$
$617$	5.78893	0.233054	0.116527	+	0.993188i	$0.462824\pi$
$618$	−2.46572	−0.0991856
$619$	27.7056	1.11358	0.556792	−	0.830652i	$-0.312032\pi$
$619$	27.7056	1.11358	0.556792	+	0.830652i	$0.312032\pi$
$620$	−10.0083	−0.401943
$621$	−2.94109	−0.118022
$622$	1.65954	0.0665416
$623$	0.767024	0.0307301
$624$	8.22970	0.329452
$625$	−27.5614	−1.10245
$626$	1.88873	0.0754888
$627$	−22.4269	−0.895646
$628$	−1.96859	−0.0785552
$629$	10.6988	0.426591
$630$	−0.719048	−0.0286476
$631$	−24.7181	−0.984012	−0.492006	−	0.870592i	$-0.663736\pi$
$631$	−24.7181	−0.984012	−0.492006	+	0.870592i	$0.663736\pi$
$632$	1.64150	0.0652953
$633$	18.1603	0.721806
$634$	3.67188	0.145829
$635$	−1.00439	−0.0398578
$636$	2.54272	0.100825
$637$	8.74234	0.346384
$638$	−2.00164	−0.0792457
$639$	−2.85455	−0.112924
$640$	−12.8756	−0.508952
$641$	−35.0610	−1.38483	−0.692413	−	0.721501i	$-0.743453\pi$
$641$	−35.0610	−1.38483	−0.692413	+	0.721501i	$0.743453\pi$
$642$	2.53521	0.100057
$643$	22.8153	0.899746	0.449873	−	0.893093i	$-0.351469\pi$
$643$	22.8153	0.899746	0.449873	+	0.893093i	$0.351469\pi$
$644$	9.94429	0.391860
$645$	−1.47334	−0.0580125
$646$	0.734648	0.0289043
$647$	−11.1718	−0.439210	−0.219605	−	0.975589i	$-0.570477\pi$
$647$	−11.1718	−0.439210	−0.219605	+	0.975589i	$0.570477\pi$
$648$	0.703377	0.0276313
$649$	−13.7334	−0.539084
$650$	0.221675	0.00869481
$651$	−3.69677	−0.144888
$652$	−37.5346	−1.46997
$653$	−14.7728	−0.578105	−0.289053	−	0.957313i	$-0.593340\pi$
$653$	−14.7728	−0.578105	−0.289053	+	0.957313i	$0.593340\pi$
$654$	−0.781101	−0.0305435
$655$	−15.0615	−0.588502
$656$	−13.1775	−0.514495
$657$	−9.51172	−0.371087
$658$	2.20626	0.0860090
$659$	31.4646	1.22569	0.612843	−	0.790205i	$-0.290026\pi$
$659$	31.4646	1.22569	0.612843	+	0.790205i	$0.290026\pi$
$660$	25.1589	0.979310
$661$	2.38230	0.0926607	0.0463304	−	0.998926i	$-0.485247\pi$
$661$	2.38230	0.0926607	0.0463304	+	0.998926i	$0.485247\pi$
$662$	3.22162	0.125212
$663$	2.15860	0.0838332
$664$	9.61718	0.373219
$665$	−16.8164	−0.652111
$666$	−1.89622	−0.0734772
$667$	−6.13901	−0.237704
$668$	−4.10585	−0.158860
$669$	−13.3162	−0.514834
$670$	1.33682	0.0516461
$671$	−73.2782	−2.82887
$672$	−3.57676	−0.137977
$673$	−22.3914	−0.863124	−0.431562	−	0.902083i	$-0.642037\pi$
$673$	−22.3914	−0.863124	−0.431562	+	0.902083i	$0.642037\pi$
$674$	−3.27511	−0.126153
$675$	−0.579417	−0.0223018
$676$	16.4189	0.631495
$677$	−17.9283	−0.689040	−0.344520	−	0.938779i	$-0.611958\pi$
$677$	−17.9283	−0.689040	−0.344520	+	0.938779i	$0.611958\pi$
$678$	−1.09196	−0.0419365
$679$	−28.7176	−1.10208
$680$	−1.66143	−0.0637130
$681$	−19.0076	−0.728374
$682$	−2.06399	−0.0790341
$683$	−8.60660	−0.329322	−0.164661	−	0.986350i	$-0.552653\pi$
$683$	−8.60660	−0.329322	−0.164661	+	0.986350i	$0.552653\pi$
$684$	8.15984	0.311999
$685$	6.50883	0.248690
$686$	−3.36377	−0.128429
$687$	−5.77214	−0.220221
$688$	−2.37804	−0.0906618
$689$	−2.78815	−0.106220
$690$	−1.23127	−0.0468738
$691$	38.6257	1.46939	0.734696	−	0.678396i	$-0.237325\pi$
$691$	38.6257	1.46939	0.734696	+	0.678396i	$0.237325\pi$
$692$	1.69707	0.0645129
$693$	9.29297	0.353011
$694$	−3.51677	−0.133495
$695$	−40.8007	−1.54766
$696$	1.46818	0.0556512
$697$	−3.45639	−0.130920
$698$	−0.416072	−0.0157486
$699$	12.1096	0.458026
$700$	1.95910	0.0740471
$701$	43.9672	1.66062	0.830308	−	0.557304i	$-0.188164\pi$
$701$	43.9672	1.66062	0.830308	+	0.557304i	$0.188164\pi$
$702$	−0.382583	−0.0144397
$703$	−44.3470	−1.67258
$704$	39.2588	1.47962
$705$	17.1194	0.644753
$706$	−5.05842	−0.190376
$707$	7.63905	0.287296
$708$	4.99678	0.187790
$709$	−16.0825	−0.603992	−0.301996	−	0.953309i	$-0.597653\pi$
$709$	−16.0825	−0.603992	−0.301996	+	0.953309i	$0.597653\pi$
$710$	−1.19504	−0.0448492
$711$	2.33374	0.0875220
$712$	−0.314113	−0.0117719
$713$	−6.33022	−0.237069
$714$	−0.304413	−0.0113924
$715$	−27.5874	−1.03171
$716$	−23.3207	−0.871537
$717$	7.78534	0.290749
$718$	0.0437089	0.00163120
$719$	51.3841	1.91630	0.958152	−	0.286260i	$-0.0924121\pi$
$719$	51.3841	1.91630	0.958152	+	0.286260i	$0.0924121\pi$
$720$	−9.00545	−0.335613
$721$	23.8947	0.889886
$722$	0.322357	0.0119969
$723$	−0.113944	−0.00423763
$724$	43.7214	1.62489
$725$	−1.20943	−0.0449172
$726$	3.23887	0.120206
$727$	−13.6403	−0.505890	−0.252945	−	0.967481i	$-0.581399\pi$
$727$	−13.6403	−0.505890	−0.252945	+	0.967481i	$0.581399\pi$
$728$	2.60779	0.0966511
$729$	1.00000	0.0370370
$730$	−3.98204	−0.147382
$731$	−0.623745	−0.0230701
$732$	26.6616	0.985441
$733$	−15.2500	−0.563270	−0.281635	−	0.959522i	$-0.590877\pi$
$733$	−15.2500	−0.563270	−0.281635	+	0.959522i	$0.590877\pi$
$734$	−5.06653	−0.187009
$735$	−9.56641	−0.352863
$736$	−6.12473	−0.225760
$737$	−17.2771	−0.636410
$738$	0.612597	0.0225500
$739$	−45.4574	−1.67218	−0.836088	−	0.548595i	$-0.815163\pi$
$739$	−45.4574	−1.67218	−0.836088	+	0.548595i	$0.815163\pi$
$740$	49.7492	1.82882
$741$	−8.94746	−0.328693
$742$	0.393194	0.0144346
$743$	10.1250	0.371452	0.185726	−	0.982602i	$-0.440536\pi$
$743$	10.1250	0.371452	0.185726	+	0.982602i	$0.440536\pi$
$744$	1.51391	0.0555026
$745$	20.9319	0.766886
$746$	3.57055	0.130727
$747$	13.6729	0.500264
$748$	10.6512	0.389446
$749$	−24.5682	−0.897703
$750$	1.85066	0.0675765
$751$	19.8144	0.723037	0.361518	−	0.932365i	$-0.382258\pi$
$751$	19.8144	0.723037	0.361518	+	0.932365i	$0.382258\pi$
$752$	27.6315	1.00762
$753$	22.1098	0.805725
$754$	−0.798575	−0.0290824
$755$	21.0255	0.765196
$756$	−3.38116	−0.122972
$757$	−4.19773	−0.152569	−0.0762846	−	0.997086i	$-0.524306\pi$
$757$	−4.19773	−0.152569	−0.0762846	+	0.997086i	$0.524306\pi$
$758$	3.40066	0.123518
$759$	15.9130	0.577604
$760$	6.88667	0.249806
$761$	−30.4434	−1.10357	−0.551786	−	0.833986i	$-0.686054\pi$
$761$	−30.4434	−1.10357	−0.551786	+	0.833986i	$0.686054\pi$
$762$	0.0753631	0.00273012
$763$	7.56947	0.274033
$764$	−40.1255	−1.45169
$765$	−2.36208	−0.0854011
$766$	−1.11420	−0.0402576
$767$	−5.47909	−0.197838
$768$	−13.5458	−0.488790
$769$	42.4422	1.53051	0.765253	−	0.643730i	$-0.222614\pi$
$769$	42.4422	1.53051	0.765253	+	0.643730i	$0.222614\pi$
$770$	3.89046	0.140203
$771$	13.3347	0.480236
$772$	−21.1232	−0.760241
$773$	−7.67442	−0.276030	−0.138015	−	0.990430i	$-0.544072\pi$
$773$	−7.67442	−0.276030	−0.138015	+	0.990430i	$0.544072\pi$
$774$	0.110550	0.00397365
$775$	−1.24710	−0.0447973
$776$	11.7605	0.422177
$777$	18.3759	0.659231
$778$	1.47432	0.0528569
$779$	14.3268	0.513311
$780$	10.0374	0.359397
$781$	15.4447	0.552656
$782$	−0.521267	−0.0186405
$783$	2.08733	0.0745950
$784$	−15.4407	−0.551452
$785$	−2.36208	−0.0843062
$786$	1.13013	0.0403103
$787$	5.95248	0.212183	0.106092	−	0.994356i	$-0.466166\pi$
$787$	5.95248	0.212183	0.106092	+	0.994356i	$0.466166\pi$
$788$	8.25012	0.293898
$789$	−19.1519	−0.681827
$790$	0.977009	0.0347604
$791$	10.5820	0.376251
$792$	−3.80567	−0.135229
$793$	−29.2351	−1.03817
$794$	1.82892	0.0649060
$795$	3.05097	0.108207
$796$	43.1792	1.53045
$797$	−9.22048	−0.326606	−0.163303	−	0.986576i	$-0.552215\pi$
$797$	−9.22048	−0.326606	−0.163303	+	0.986576i	$0.552215\pi$
$798$	1.26180	0.0446672
$799$	7.24759	0.256401
$800$	−1.20662	−0.0426604
$801$	−0.446578	−0.0157791
$802$	−4.80597	−0.169705
$803$	51.4638	1.81612
$804$	6.28612	0.221694
$805$	11.9320	0.420548
$806$	−0.823448	−0.0290047
$807$	−20.3107	−0.714971
$808$	−3.12836	−0.110055
$809$	40.1263	1.41076	0.705382	−	0.708827i	$-0.250775\pi$
$809$	40.1263	1.41076	0.705382	+	0.708827i	$0.250775\pi$
$810$	0.418646	0.0147097
$811$	17.9898	0.631706	0.315853	−	0.948808i	$-0.397709\pi$
$811$	17.9898	0.631706	0.315853	+	0.948808i	$0.397709\pi$
$812$	−7.05759	−0.247673
$813$	2.76499	0.0969723
$814$	10.2597	0.359601
$815$	−45.0372	−1.57759
$816$	−3.81251	−0.133465
$817$	2.58544	0.0904530
$818$	6.63552	0.232006
$819$	3.70752	0.129551
$820$	−16.0721	−0.561261
$821$	17.0296	0.594336	0.297168	−	0.954825i	$-0.403958\pi$
$821$	17.0296	0.594336	0.297168	+	0.954825i	$0.403958\pi$
$822$	−0.488383	−0.0170343
$823$	2.35440	0.0820692	0.0410346	−	0.999158i	$-0.486935\pi$
$823$	2.35440	0.0820692	0.0410346	+	0.999158i	$0.486935\pi$
$824$	−9.78541	−0.340891
$825$	3.13498	0.109146
$826$	0.772679	0.0268849
$827$	15.2593	0.530618	0.265309	−	0.964163i	$-0.414526\pi$
$827$	15.2593	0.530618	0.265309	+	0.964163i	$0.414526\pi$
$828$	−5.78979	−0.201209
$829$	−9.04771	−0.314240	−0.157120	−	0.987580i	$-0.550221\pi$
$829$	−9.04771	−0.314240	−0.157120	+	0.987580i	$0.550221\pi$
$830$	5.72409	0.198686
$831$	14.2976	0.495978
$832$	15.6627	0.543006
$833$	−4.05000	−0.140324
$834$	3.06144	0.106009
$835$	−4.92654	−0.170490
$836$	−44.1494	−1.52694
$837$	2.15234	0.0743958
$838$	1.14260	0.0394704
$839$	18.3919	0.634959	0.317479	−	0.948265i	$-0.397164\pi$
$839$	18.3919	0.634959	0.317479	+	0.948265i	$0.397164\pi$
$840$	−2.85361	−0.0984587
$841$	−24.6431	−0.849761
$842$	0.791720	0.0272845
$843$	11.6932	0.402737
$844$	35.7501	1.23057
$845$	19.7008	0.677727
$846$	−1.28453	−0.0441632
$847$	−31.3872	−1.07848
$848$	4.92441	0.169105
$849$	2.28158	0.0783037
$850$	−0.102694	−0.00352236
$851$	31.4663	1.07865
$852$	−5.61942	−0.192518
$853$	16.7595	0.573833	0.286917	−	0.957956i	$-0.407370\pi$
$853$	16.7595	0.573833	0.286917	+	0.957956i	$0.407370\pi$
$854$	4.12283	0.141080
$855$	9.79087	0.334841
$856$	10.0612	0.343885
$857$	−1.73772	−0.0593595	−0.0296797	−	0.999559i	$-0.509449\pi$
$857$	−1.73772	−0.0593595	−0.0296797	+	0.999559i	$0.509449\pi$
$858$	2.06999	0.0706683
$859$	33.3187	1.13682	0.568409	−	0.822746i	$-0.307559\pi$
$859$	33.3187	1.13682	0.568409	+	0.822746i	$0.307559\pi$
$860$	−2.90039	−0.0989025
$861$	−5.93654	−0.202317
$862$	−3.38139	−0.115171
$863$	13.4646	0.458341	0.229170	−	0.973386i	$-0.426399\pi$
$863$	13.4646	0.458341	0.229170	+	0.973386i	$0.426399\pi$
$864$	2.08247	0.0708471
$865$	2.03629	0.0692358
$866$	−0.985970	−0.0335046
$867$	−1.00000	−0.0339618
$868$	−7.27741	−0.247011
$869$	−12.6269	−0.428337
$870$	0.873851	0.0296263
$871$	−6.89288	−0.233556
$872$	−3.09987	−0.104975
$873$	16.7200	0.565887
$874$	2.16066	0.0730855
$875$	−17.9343	−0.606291
$876$	−18.7246	−0.632647
$877$	−20.2623	−0.684209	−0.342104	−	0.939662i	$-0.611140\pi$
$877$	−20.2623	−0.684209	−0.342104	+	0.939662i	$0.611140\pi$
$878$	0.514690	0.0173699
$879$	19.2530	0.649387
$880$	48.7247	1.64251
$881$	−5.05908	−0.170445	−0.0852223	−	0.996362i	$-0.527160\pi$
$881$	−5.05908	−0.170445	−0.0852223	+	0.996362i	$0.527160\pi$
$882$	0.717806	0.0241698
$883$	16.2057	0.545366	0.272683	−	0.962104i	$-0.412089\pi$
$883$	16.2057	0.545366	0.272683	+	0.962104i	$0.412089\pi$
$884$	4.24940	0.142923
$885$	5.99556	0.201539
$886$	−2.35740	−0.0791983
$887$	38.9318	1.30720	0.653601	−	0.756839i	$-0.273257\pi$
$887$	38.9318	1.30720	0.653601	+	0.756839i	$0.273257\pi$
$888$	−7.52533	−0.252533
$889$	−0.730327	−0.0244944
$890$	−0.186958	−0.00626685
$891$	−5.41057	−0.181261
$892$	−26.2141	−0.877713
$893$	−30.0414	−1.00530
$894$	−1.57061	−0.0525289
$895$	−27.9822	−0.935342
$896$	−9.36232	−0.312773
$897$	6.34864	0.211975
$898$	−2.02501	−0.0675756
$899$	4.49264	0.149838
$900$	−1.14063	−0.0380211
$901$	1.29165	0.0430310
$902$	−3.31450	−0.110361
$903$	−1.07132	−0.0356512
$904$	−4.33355	−0.144132
$905$	52.4606	1.74385
$906$	−1.57763	−0.0524131
$907$	50.0380	1.66149	0.830743	−	0.556656i	$-0.187916\pi$
$907$	50.0380	1.66149	0.830743	+	0.556656i	$0.187916\pi$
$908$	−37.4182	−1.24177
$909$	−4.44762	−0.147518
$910$	1.55214	0.0514529
$911$	−9.41879	−0.312059	−0.156029	−	0.987752i	$-0.549869\pi$
$911$	−9.41879	−0.312059	−0.156029	+	0.987752i	$0.549869\pi$
$912$	15.8029	0.523288
$913$	−73.9780	−2.44831
$914$	−2.10776	−0.0697185
$915$	31.9909	1.05759
$916$	−11.3630	−0.375443
$917$	−10.9518	−0.361660
$918$	0.177236	0.00584967
$919$	−53.7411	−1.77275	−0.886377	−	0.462963i	$-0.846786\pi$
$919$	−53.7411	−1.77275	−0.886377	+	0.462963i	$0.846786\pi$
$920$	−4.88642	−0.161101
$921$	3.81747	0.125790
$922$	0.296572	0.00976709
$923$	6.16183	0.202819
$924$	18.2940	0.601829
$925$	6.19909	0.203825
$926$	−4.49886	−0.147842
$927$	−13.9120	−0.456931
$928$	4.34679	0.142691
$929$	9.74182	0.319619	0.159809	−	0.987148i	$-0.448912\pi$
$929$	9.74182	0.319619	0.159809	+	0.987148i	$0.448912\pi$
$930$	0.901069	0.0295472
$931$	16.7873	0.550182
$932$	23.8388	0.780864
$933$	9.36345	0.306546
$934$	4.78732	0.156646
$935$	12.7802	0.417957
$936$	−1.51831	−0.0496276
$937$	5.70782	0.186466	0.0932332	−	0.995644i	$-0.470280\pi$
$937$	5.70782	0.186466	0.0932332	+	0.995644i	$0.470280\pi$
$938$	0.972056	0.0317388
$939$	10.6566	0.347764
$940$	33.7010	1.09920
$941$	36.6126	1.19354	0.596768	−	0.802414i	$-0.296451\pi$
$941$	36.6126	1.19354	0.596768	+	0.802414i	$0.296451\pi$
$942$	0.177236	0.00577467
$943$	−10.1655	−0.331035
$944$	9.67713	0.314964
$945$	−4.05701	−0.131974
$946$	−0.598140	−0.0194472
$947$	41.1388	1.33683	0.668416	−	0.743788i	$-0.266973\pi$
$947$	41.1388	1.33683	0.668416	+	0.743788i	$0.266973\pi$
$948$	4.59417	0.149212
$949$	20.5320	0.666498
$950$	0.425667	0.0138105
$951$	20.7174	0.671809
$952$	−1.20809	−0.0391544
$953$	−11.0244	−0.357114	−0.178557	−	0.983930i	$-0.557143\pi$
$953$	−11.0244	−0.357114	−0.178557	+	0.983930i	$0.557143\pi$
$954$	−0.228926	−0.00741176
$955$	−48.1460	−1.55797
$956$	15.3261	0.495682
$957$	−11.2936	−0.365071
$958$	2.69200	0.0869747
$959$	4.73282	0.152831
$960$	−17.1391	−0.553162
$961$	−26.3674	−0.850562
$962$	4.09319	0.131970
$963$	14.3042	0.460945
$964$	−0.224309	−0.00722452
$965$	−25.3454	−0.815898
$966$	−0.895306	−0.0288060
$967$	29.4495	0.947032	0.473516	−	0.880785i	$-0.342985\pi$
$967$	29.4495	0.947032	0.473516	+	0.880785i	$0.342985\pi$
$968$	12.8537	0.413134
$969$	4.14502	0.133157
$970$	6.99977	0.224749
$971$	21.6431	0.694561	0.347280	−	0.937761i	$-0.387105\pi$
$971$	21.6431	0.694561	0.347280	+	0.937761i	$0.387105\pi$
$972$	1.96859	0.0631425
$973$	−29.6677	−0.951104
$974$	0.421873	0.0135177
$975$	1.25073	0.0400555
$976$	51.6348	1.65279
$977$	−1.21261	−0.0387949	−0.0193974	−	0.999812i	$-0.506175\pi$
$977$	−1.21261	−0.0387949	−0.0193974	+	0.999812i	$0.506175\pi$
$978$	3.37932	0.108059
$979$	2.41624	0.0772235
$980$	−18.8323	−0.601576
$981$	−4.40712	−0.140708
$982$	4.58780	0.146403
$983$	1.24768	0.0397948	0.0198974	−	0.999802i	$-0.493666\pi$
$983$	1.24768	0.0397948	0.0198974	+	0.999802i	$0.493666\pi$
$984$	2.43114	0.0775020
$985$	9.89919	0.315415
$986$	0.369950	0.0117816
$987$	12.4481	0.396229
$988$	−17.6138	−0.560371
$989$	−1.83449	−0.0583334
$990$	−2.26511	−0.0719901
$991$	−50.2832	−1.59730	−0.798649	−	0.601798i	$-0.794451\pi$
$991$	−50.2832	−1.59730	−0.798649	+	0.601798i	$0.794451\pi$
$992$	4.48218	0.142310
$993$	18.1770	0.576829
$994$	−0.868962	−0.0275618
$995$	51.8101	1.64249
$996$	26.9162	0.852873
$997$	37.3658	1.18339	0.591693	−	0.806163i	$-0.298460\pi$
$997$	37.3658	1.18339	0.591693	+	0.806163i	$0.298460\pi$
$998$	6.67388	0.211258
$999$	−10.6988	−0.338497

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.20	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.20	✓	39	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)

\(f(q)\)	\(=\)	\(q-0.177236 q^{2} -1.00000 q^{3} -1.96859 q^{4} -2.36208 q^{5} +0.177236 q^{6} -1.71756 q^{7} +0.703377 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.177236 q^{2} -1.00000 q^{3} -1.96859 q^{4} -2.36208 q^{5} +0.177236 q^{6} -1.71756 q^{7} +0.703377 q^{8} +1.00000 q^{9} +0.418646 q^{10} -5.41057 q^{11} +1.96859 q^{12} -2.15860 q^{13} +0.304413 q^{14} +2.36208 q^{15} +3.81251 q^{16} +1.00000 q^{17} -0.177236 q^{18} -4.14502 q^{19} +4.64996 q^{20} +1.71756 q^{21} +0.958949 q^{22} +2.94109 q^{23} -0.703377 q^{24} +0.579417 q^{25} +0.382583 q^{26} -1.00000 q^{27} +3.38116 q^{28} -2.08733 q^{29} -0.418646 q^{30} -2.15234 q^{31} -2.08247 q^{32} +5.41057 q^{33} -0.177236 q^{34} +4.05701 q^{35} -1.96859 q^{36} +10.6988 q^{37} +0.734648 q^{38} +2.15860 q^{39} -1.66143 q^{40} -3.45639 q^{41} -0.304413 q^{42} -0.623745 q^{43} +10.6512 q^{44} -2.36208 q^{45} -0.521267 q^{46} +7.24759 q^{47} -3.81251 q^{48} -4.05000 q^{49} -0.102694 q^{50} -1.00000 q^{51} +4.24940 q^{52} +1.29165 q^{53} +0.177236 q^{54} +12.7802 q^{55} -1.20809 q^{56} +4.14502 q^{57} +0.369950 q^{58} +2.53826 q^{59} -4.64996 q^{60} +13.5435 q^{61} +0.381473 q^{62} -1.71756 q^{63} -7.25593 q^{64} +5.09879 q^{65} -0.958949 q^{66} +3.19321 q^{67} -1.96859 q^{68} -2.94109 q^{69} -0.719048 q^{70} -2.85455 q^{71} +0.703377 q^{72} -9.51172 q^{73} -1.89622 q^{74} -0.579417 q^{75} +8.15984 q^{76} +9.29297 q^{77} -0.382583 q^{78} +2.33374 q^{79} -9.00545 q^{80} +1.00000 q^{81} +0.612597 q^{82} +13.6729 q^{83} -3.38116 q^{84} -2.36208 q^{85} +0.110550 q^{86} +2.08733 q^{87} -3.80567 q^{88} -0.446578 q^{89} +0.418646 q^{90} +3.70752 q^{91} -5.78979 q^{92} +2.15234 q^{93} -1.28453 q^{94} +9.79087 q^{95} +2.08247 q^{96} +16.7200 q^{97} +0.717806 q^{98} -5.41057 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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