LMFDB - Embedded newform 8007.2.a.h.1.36

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:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.36
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)

$f(q)$	$=$	$q+1.15210 q^{2} +1.00000 q^{3} -0.672658 q^{4} +0.848798 q^{5} +1.15210 q^{6} +0.816661 q^{7} -3.07918 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.15210 q^{2} +1.00000 q^{3} -0.672658 q^{4} +0.848798 q^{5} +1.15210 q^{6} +0.816661 q^{7} -3.07918 q^{8} +1.00000 q^{9} +0.977904 q^{10} -2.54119 q^{11} -0.672658 q^{12} -3.28811 q^{13} +0.940878 q^{14} +0.848798 q^{15} -2.20222 q^{16} -1.00000 q^{17} +1.15210 q^{18} +3.28857 q^{19} -0.570951 q^{20} +0.816661 q^{21} -2.92772 q^{22} +1.55996 q^{23} -3.07918 q^{24} -4.27954 q^{25} -3.78824 q^{26} +1.00000 q^{27} -0.549334 q^{28} +9.06787 q^{29} +0.977904 q^{30} +1.68003 q^{31} +3.62118 q^{32} -2.54119 q^{33} -1.15210 q^{34} +0.693181 q^{35} -0.672658 q^{36} +7.01206 q^{37} +3.78878 q^{38} -3.28811 q^{39} -2.61360 q^{40} -7.71623 q^{41} +0.940878 q^{42} -0.842345 q^{43} +1.70935 q^{44} +0.848798 q^{45} +1.79724 q^{46} +4.62097 q^{47} -2.20222 q^{48} -6.33306 q^{49} -4.93047 q^{50} -1.00000 q^{51} +2.21177 q^{52} +9.47955 q^{53} +1.15210 q^{54} -2.15696 q^{55} -2.51465 q^{56} +3.28857 q^{57} +10.4471 q^{58} -4.79385 q^{59} -0.570951 q^{60} +4.88358 q^{61} +1.93557 q^{62} +0.816661 q^{63} +8.57640 q^{64} -2.79094 q^{65} -2.92772 q^{66} +13.3656 q^{67} +0.672658 q^{68} +1.55996 q^{69} +0.798616 q^{70} -4.96923 q^{71} -3.07918 q^{72} +12.5207 q^{73} +8.07862 q^{74} -4.27954 q^{75} -2.21208 q^{76} -2.07529 q^{77} -3.78824 q^{78} +8.83158 q^{79} -1.86924 q^{80} +1.00000 q^{81} -8.88989 q^{82} +8.38612 q^{83} -0.549334 q^{84} -0.848798 q^{85} -0.970469 q^{86} +9.06787 q^{87} +7.82479 q^{88} -10.0082 q^{89} +0.977904 q^{90} -2.68527 q^{91} -1.04932 q^{92} +1.68003 q^{93} +5.32383 q^{94} +2.79134 q^{95} +3.62118 q^{96} -10.7893 q^{97} -7.29635 q^{98} -2.54119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) $ 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.15210	0.814660	0.407330	−	0.913281i	$-0.366460\pi$
$2$	1.15210	0.814660	0.407330	+	0.913281i	$0.366460\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.672658	−0.336329
$5$	0.848798	0.379594	0.189797	−	0.981823i	$-0.439217\pi$
$5$	0.848798	0.379594	0.189797	+	0.981823i	$0.439217\pi$
$6$	1.15210	0.470344
$7$	0.816661	0.308669	0.154334	−	0.988019i	$-0.450677\pi$
$7$	0.816661	0.308669	0.154334	+	0.988019i	$0.450677\pi$
$8$	−3.07918	−1.08865
$9$	1.00000	0.333333
$10$	0.977904	0.309240
$11$	−2.54119	−0.766199	−0.383099	−	0.923707i	$-0.625143\pi$
$11$	−2.54119	−0.766199	−0.383099	+	0.923707i	$0.625143\pi$
$12$	−0.672658	−0.194180
$13$	−3.28811	−0.911957	−0.455979	−	0.889991i	$-0.650711\pi$
$13$	−3.28811	−0.911957	−0.455979	+	0.889991i	$0.650711\pi$
$14$	0.940878	0.251460
$15$	0.848798	0.219159
$16$	−2.20222	−0.550554
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.15210	0.271553
$19$	3.28857	0.754451	0.377225	−	0.926122i	$-0.376878\pi$
$19$	3.28857	0.754451	0.377225	+	0.926122i	$0.376878\pi$
$20$	−0.570951	−0.127668
$21$	0.816661	0.178210
$22$	−2.92772	−0.624192
$23$	1.55996	0.325275	0.162637	−	0.986686i	$-0.448000\pi$
$23$	1.55996	0.325275	0.162637	+	0.986686i	$0.448000\pi$
$24$	−3.07918	−0.628535
$25$	−4.27954	−0.855908
$26$	−3.78824	−0.742935
$27$	1.00000	0.192450
$28$	−0.549334	−0.103814
$29$	9.06787	1.68386	0.841931	−	0.539585i	$-0.181419\pi$
$29$	9.06787	1.68386	0.841931	+	0.539585i	$0.181419\pi$
$30$	0.977904	0.178540
$31$	1.68003	0.301742	0.150871	−	0.988553i	$-0.451792\pi$
$31$	1.68003	0.301742	0.150871	+	0.988553i	$0.451792\pi$
$32$	3.62118	0.640139
$33$	−2.54119	−0.442365
$34$	−1.15210	−0.197584
$35$	0.693181	0.117169
$36$	−0.672658	−0.112110
$37$	7.01206	1.15278	0.576388	−	0.817176i	$-0.304462\pi$
$37$	7.01206	1.15278	0.576388	+	0.817176i	$0.304462\pi$
$38$	3.78878	0.614621
$39$	−3.28811	−0.526519
$40$	−2.61360	−0.413247
$41$	−7.71623	−1.20507	−0.602536	−	0.798092i	$-0.705843\pi$
$41$	−7.71623	−1.20507	−0.602536	+	0.798092i	$0.705843\pi$
$42$	0.940878	0.145181
$43$	−0.842345	−0.128456	−0.0642282	−	0.997935i	$-0.520459\pi$
$43$	−0.842345	−0.128456	−0.0642282	+	0.997935i	$0.520459\pi$
$44$	1.70935	0.257695
$45$	0.848798	0.126531
$46$	1.79724	0.264988
$47$	4.62097	0.674037	0.337019	−	0.941498i	$-0.390581\pi$
$47$	4.62097	0.674037	0.337019	+	0.941498i	$0.390581\pi$
$48$	−2.20222	−0.317863
$49$	−6.33306	−0.904723
$50$	−4.93047	−0.697274
$51$	−1.00000	−0.140028
$52$	2.21177	0.306718
$53$	9.47955	1.30212	0.651058	−	0.759028i	$-0.274325\pi$
$53$	9.47955	1.30212	0.651058	+	0.759028i	$0.274325\pi$
$54$	1.15210	0.156781
$55$	−2.15696	−0.290845
$56$	−2.51465	−0.336034
$57$	3.28857	0.435582
$58$	10.4471	1.37177
$59$	−4.79385	−0.624106	−0.312053	−	0.950065i	$-0.601017\pi$
$59$	−4.79385	−0.624106	−0.312053	+	0.950065i	$0.601017\pi$
$60$	−0.570951	−0.0737094
$61$	4.88358	0.625279	0.312639	−	0.949872i	$-0.398787\pi$
$61$	4.88358	0.625279	0.312639	+	0.949872i	$0.398787\pi$
$62$	1.93557	0.245818
$63$	0.816661	0.102890
$64$	8.57640	1.07205
$65$	−2.79094	−0.346174
$66$	−2.92772	−0.360377
$67$	13.3656	1.63287	0.816436	−	0.577436i	$-0.195947\pi$
$67$	13.3656	1.63287	0.816436	+	0.577436i	$0.195947\pi$
$68$	0.672658	0.0815717
$69$	1.55996	0.187797
$70$	0.798616	0.0954529
$71$	−4.96923	−0.589740	−0.294870	−	0.955537i	$-0.595276\pi$
$71$	−4.96923	−0.589740	−0.294870	+	0.955537i	$0.595276\pi$
$72$	−3.07918	−0.362885
$73$	12.5207	1.46544	0.732719	−	0.680531i	$-0.238251\pi$
$73$	12.5207	1.46544	0.732719	+	0.680531i	$0.238251\pi$
$74$	8.07862	0.939120
$75$	−4.27954	−0.494159
$76$	−2.21208	−0.253744
$77$	−2.07529	−0.236502
$78$	−3.78824	−0.428934
$79$	8.83158	0.993631	0.496815	−	0.867856i	$-0.334503\pi$
$79$	8.83158	0.993631	0.496815	+	0.867856i	$0.334503\pi$
$80$	−1.86924	−0.208987
$81$	1.00000	0.111111
$82$	−8.88989	−0.981724
$83$	8.38612	0.920497	0.460248	−	0.887790i	$-0.347760\pi$
$83$	8.38612	0.920497	0.460248	+	0.887790i	$0.347760\pi$
$84$	−0.549334	−0.0599372
$85$	−0.848798	−0.0920651
$86$	−0.970469	−0.104648
$87$	9.06787	0.972178
$88$	7.82479	0.834125
$89$	−10.0082	−1.06086	−0.530432	−	0.847727i	$-0.677970\pi$
$89$	−10.0082	−1.06086	−0.530432	+	0.847727i	$0.677970\pi$
$90$	0.977904	0.103080
$91$	−2.68527	−0.281493
$92$	−1.04932	−0.109399
$93$	1.68003	0.174211
$94$	5.32383	0.549111
$95$	2.79134	0.286385
$96$	3.62118	0.369585
$97$	−10.7893	−1.09549	−0.547744	−	0.836646i	$-0.684513\pi$
$97$	−10.7893	−1.09549	−0.547744	+	0.836646i	$0.684513\pi$
$98$	−7.29635	−0.737042
$99$	−2.54119	−0.255400
$100$	2.87867	0.287867
$101$	8.70442	0.866122	0.433061	−	0.901365i	$-0.357433\pi$
$101$	8.70442	0.866122	0.433061	+	0.901365i	$0.357433\pi$
$102$	−1.15210	−0.114075
$103$	−0.438833	−0.0432395	−0.0216197	−	0.999766i	$-0.506882\pi$
$103$	−0.438833	−0.0432395	−0.0216197	+	0.999766i	$0.506882\pi$
$104$	10.1247	0.992806
$105$	0.693181	0.0676475
$106$	10.9214	1.06078
$107$	14.5983	1.41127	0.705635	−	0.708575i	$-0.250662\pi$
$107$	14.5983	1.41127	0.705635	+	0.708575i	$0.250662\pi$
$108$	−0.672658	−0.0647265
$109$	10.2634	0.983059	0.491529	−	0.870861i	$-0.336438\pi$
$109$	10.2634	0.983059	0.491529	+	0.870861i	$0.336438\pi$
$110$	−2.48504	−0.236940
$111$	7.01206	0.665555
$112$	−1.79846	−0.169939
$113$	−7.14302	−0.671959	−0.335980	−	0.941869i	$-0.609067\pi$
$113$	−7.14302	−0.671959	−0.335980	+	0.941869i	$0.609067\pi$
$114$	3.78878	0.354852
$115$	1.32409	0.123472
$116$	−6.09957	−0.566331
$117$	−3.28811	−0.303986
$118$	−5.52301	−0.508434
$119$	−0.816661	−0.0748632
$120$	−2.61360	−0.238588
$121$	−4.54233	−0.412939
$122$	5.62639	0.509389
$123$	−7.71623	−0.695749
$124$	−1.13009	−0.101485
$125$	−7.87646	−0.704492
$126$	0.940878	0.0838201
$127$	6.09236	0.540609	0.270305	−	0.962775i	$-0.412876\pi$
$127$	6.09236	0.540609	0.270305	+	0.962775i	$0.412876\pi$
$128$	2.63855	0.233217
$129$	−0.842345	−0.0741644
$130$	−3.21545	−0.282014
$131$	17.6987	1.54635	0.773173	−	0.634196i	$-0.218669\pi$
$131$	17.6987	1.54635	0.773173	+	0.634196i	$0.218669\pi$
$132$	1.70935	0.148780
$133$	2.68565	0.232875
$134$	15.3986	1.33024
$135$	0.848798	0.0730529
$136$	3.07918	0.264037
$137$	14.1517	1.20906	0.604530	−	0.796582i	$-0.293361\pi$
$137$	14.1517	1.20906	0.604530	+	0.796582i	$0.293361\pi$
$138$	1.79724	0.152991
$139$	−12.1793	−1.03304	−0.516518	−	0.856276i	$-0.672772\pi$
$139$	−12.1793	−1.03304	−0.516518	+	0.856276i	$0.672772\pi$
$140$	−0.466273	−0.0394073
$141$	4.62097	0.389155
$142$	−5.72507	−0.480437
$143$	8.35572	0.698741
$144$	−2.20222	−0.183518
$145$	7.69680	0.639184
$146$	14.4252	1.19383
$147$	−6.33306	−0.522342
$148$	−4.71672	−0.387712
$149$	18.4362	1.51035	0.755175	−	0.655523i	$-0.227552\pi$
$149$	18.4362	1.51035	0.755175	+	0.655523i	$0.227552\pi$
$150$	−4.93047	−0.402572
$151$	2.32660	0.189336	0.0946682	−	0.995509i	$-0.469821\pi$
$151$	2.32660	0.189336	0.0946682	+	0.995509i	$0.469821\pi$
$152$	−10.1261	−0.821336
$153$	−1.00000	−0.0808452
$154$	−2.39095	−0.192669
$155$	1.42601	0.114540
$156$	2.21177	0.177083
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	10.1749	0.809471
$159$	9.47955	0.751777
$160$	3.07365	0.242993
$161$	1.27396	0.100402
$162$	1.15210	0.0905178
$163$	1.17175	0.0917788	0.0458894	−	0.998947i	$-0.485388\pi$
$163$	1.17175	0.0917788	0.0458894	+	0.998947i	$0.485388\pi$
$164$	5.19038	0.405301
$165$	−2.15696	−0.167919
$166$	9.66168	0.749892
$167$	−19.7748	−1.53022	−0.765110	−	0.643900i	$-0.777315\pi$
$167$	−19.7748	−1.53022	−0.765110	+	0.643900i	$0.777315\pi$
$168$	−2.51465	−0.194009
$169$	−2.18834	−0.168334
$170$	−0.977904	−0.0750018
$171$	3.28857	0.251484
$172$	0.566610	0.0432036
$173$	−2.96615	−0.225512	−0.112756	−	0.993623i	$-0.535968\pi$
$173$	−2.96615	−0.225512	−0.112756	+	0.993623i	$0.535968\pi$
$174$	10.4471	0.791995
$175$	−3.49494	−0.264192
$176$	5.59626	0.421834
$177$	−4.79385	−0.360328
$178$	−11.5304	−0.864244
$179$	19.7181	1.47380	0.736899	−	0.676002i	$-0.236289\pi$
$179$	19.7181	1.47380	0.736899	+	0.676002i	$0.236289\pi$
$180$	−0.570951	−0.0425562
$181$	−11.1957	−0.832169	−0.416085	−	0.909326i	$-0.636598\pi$
$181$	−11.1957	−0.832169	−0.416085	+	0.909326i	$0.636598\pi$
$182$	−3.09371	−0.229321
$183$	4.88358	0.361005
$184$	−4.80340	−0.354112
$185$	5.95183	0.437587
$186$	1.93557	0.141923
$187$	2.54119	0.185831
$188$	−3.10833	−0.226698
$189$	0.816661	0.0594034
$190$	3.21591	0.233307
$191$	8.47459	0.613200	0.306600	−	0.951838i	$-0.400809\pi$
$191$	8.47459	0.613200	0.306600	+	0.951838i	$0.400809\pi$
$192$	8.57640	0.618948
$193$	−6.33388	−0.455923	−0.227961	−	0.973670i	$-0.573206\pi$
$193$	−6.33388	−0.455923	−0.227961	+	0.973670i	$0.573206\pi$
$194$	−12.4304	−0.892451
$195$	−2.79094	−0.199864
$196$	4.25998	0.304285
$197$	21.4555	1.52864	0.764321	−	0.644836i	$-0.223074\pi$
$197$	21.4555	1.52864	0.764321	+	0.644836i	$0.223074\pi$
$198$	−2.92772	−0.208064
$199$	18.9588	1.34396	0.671978	−	0.740571i	$-0.265445\pi$
$199$	18.9588	1.34396	0.671978	+	0.740571i	$0.265445\pi$
$200$	13.1775	0.931788
$201$	13.3656	0.942739
$202$	10.0284	0.705595
$203$	7.40538	0.519756
$204$	0.672658	0.0470955
$205$	−6.54952	−0.457438
$206$	−0.505580	−0.0352255
$207$	1.55996	0.108425
$208$	7.24113	0.502082
$209$	−8.35690	−0.578059
$210$	0.798616	0.0551097
$211$	−6.68585	−0.460273	−0.230136	−	0.973158i	$-0.573917\pi$
$211$	−6.68585	−0.460273	−0.230136	+	0.973158i	$0.573917\pi$
$212$	−6.37649	−0.437939
$213$	−4.96923	−0.340486
$214$	16.8187	1.14971
$215$	−0.714981	−0.0487613
$216$	−3.07918	−0.209512
$217$	1.37202	0.0931385
$218$	11.8245	0.800859
$219$	12.5207	0.846071
$220$	1.45090	0.0978194
$221$	3.28811	0.221182
$222$	8.07862	0.542201
$223$	−17.1114	−1.14586	−0.572932	−	0.819603i	$-0.694194\pi$
$223$	−17.1114	−1.14586	−0.572932	+	0.819603i	$0.694194\pi$
$224$	2.95727	0.197591
$225$	−4.27954	−0.285303
$226$	−8.22950	−0.547418
$227$	−24.0915	−1.59901	−0.799506	−	0.600658i	$-0.794905\pi$
$227$	−24.0915	−1.59901	−0.799506	+	0.600658i	$0.794905\pi$
$228$	−2.21208	−0.146499
$229$	15.1902	1.00380	0.501899	−	0.864926i	$-0.332635\pi$
$229$	15.1902	1.00380	0.501899	+	0.864926i	$0.332635\pi$
$230$	1.52549	0.100588
$231$	−2.07529	−0.136544
$232$	−27.9216	−1.83314
$233$	13.8508	0.907398	0.453699	−	0.891155i	$-0.350104\pi$
$233$	13.8508	0.907398	0.453699	+	0.891155i	$0.350104\pi$
$234$	−3.78824	−0.247645
$235$	3.92227	0.255861
$236$	3.22462	0.209905
$237$	8.83158	0.573673
$238$	−0.940878	−0.0609881
$239$	−9.37876	−0.606662	−0.303331	−	0.952885i	$-0.598099\pi$
$239$	−9.37876	−0.606662	−0.303331	+	0.952885i	$0.598099\pi$
$240$	−1.86924	−0.120659
$241$	−9.20155	−0.592724	−0.296362	−	0.955076i	$-0.595773\pi$
$241$	−9.20155	−0.592724	−0.296362	+	0.955076i	$0.595773\pi$
$242$	−5.23324	−0.336405
$243$	1.00000	0.0641500
$244$	−3.28498	−0.210299
$245$	−5.37550	−0.343428
$246$	−8.88989	−0.566799
$247$	−10.8132	−0.688027
$248$	−5.17311	−0.328493
$249$	8.38612	0.531449
$250$	−9.07450	−0.573922
$251$	−19.1374	−1.20794	−0.603972	−	0.797005i	$-0.706416\pi$
$251$	−19.1374	−1.20794	−0.603972	+	0.797005i	$0.706416\pi$
$252$	−0.549334	−0.0346048
$253$	−3.96417	−0.249225
$254$	7.01903	0.440413
$255$	−0.848798	−0.0531538
$256$	−14.1129	−0.882057
$257$	−6.22606	−0.388371	−0.194185	−	0.980965i	$-0.562206\pi$
$257$	−6.22606	−0.388371	−0.194185	+	0.980965i	$0.562206\pi$
$258$	−0.970469	−0.0604188
$259$	5.72648	0.355826
$260$	1.87735	0.116428
$261$	9.06787	0.561287
$262$	20.3908	1.25975
$263$	−6.32240	−0.389856	−0.194928	−	0.980818i	$-0.562447\pi$
$263$	−6.32240	−0.389856	−0.194928	+	0.980818i	$0.562447\pi$
$264$	7.82479	0.481582
$265$	8.04623	0.494276
$266$	3.09415	0.189714
$267$	−10.0082	−0.612490
$268$	−8.99049	−0.549182
$269$	5.00378	0.305086	0.152543	−	0.988297i	$-0.451254\pi$
$269$	5.00378	0.305086	0.152543	+	0.988297i	$0.451254\pi$
$270$	0.977904	0.0595133
$271$	15.9307	0.967720	0.483860	−	0.875146i	$-0.339234\pi$
$271$	15.9307	0.967720	0.483860	+	0.875146i	$0.339234\pi$
$272$	2.20222	0.133529
$273$	−2.68527	−0.162520
$274$	16.3042	0.984973
$275$	10.8751	0.655796
$276$	−1.04932	−0.0631617
$277$	20.7935	1.24936	0.624680	−	0.780881i	$-0.285229\pi$
$277$	20.7935	1.24936	0.624680	+	0.780881i	$0.285229\pi$
$278$	−14.0318	−0.841573
$279$	1.68003	0.100581
$280$	−2.13443	−0.127556
$281$	17.1088	1.02063	0.510313	−	0.859988i	$-0.329529\pi$
$281$	17.1088	1.02063	0.510313	+	0.859988i	$0.329529\pi$
$282$	5.32383	0.317029
$283$	−2.30491	−0.137013	−0.0685064	−	0.997651i	$-0.521823\pi$
$283$	−2.30491	−0.137013	−0.0685064	+	0.997651i	$0.521823\pi$
$284$	3.34259	0.198346
$285$	2.79134	0.165345
$286$	9.62666	0.569236
$287$	−6.30155	−0.371968
$288$	3.62118	0.213380
$289$	1.00000	0.0588235
$290$	8.86750	0.520718
$291$	−10.7893	−0.632481
$292$	−8.42215	−0.492869
$293$	−27.2428	−1.59154	−0.795771	−	0.605597i	$-0.792934\pi$
$293$	−27.2428	−1.59154	−0.795771	+	0.605597i	$0.792934\pi$
$294$	−7.29635	−0.425531
$295$	−4.06901	−0.236907
$296$	−21.5914	−1.25497
$297$	−2.54119	−0.147455
$298$	21.2404	1.23042
$299$	−5.12933	−0.296637
$300$	2.87867	0.166200
$301$	−0.687911	−0.0396505
$302$	2.68049	0.154245
$303$	8.70442	0.500056
$304$	−7.24215	−0.415366
$305$	4.14518	0.237352
$306$	−1.15210	−0.0658614
$307$	11.7733	0.671936	0.335968	−	0.941873i	$-0.390937\pi$
$307$	11.7733	0.671936	0.335968	+	0.941873i	$0.390937\pi$
$308$	1.39596	0.0795424
$309$	−0.438833	−0.0249643
$310$	1.64291	0.0933109
$311$	−3.74289	−0.212240	−0.106120	−	0.994353i	$-0.533843\pi$
$311$	−3.74289	−0.212240	−0.106120	+	0.994353i	$0.533843\pi$
$312$	10.1247	0.573197
$313$	−11.3257	−0.640167	−0.320084	−	0.947389i	$-0.603711\pi$
$313$	−11.3257	−0.640167	−0.320084	+	0.947389i	$0.603711\pi$
$314$	−1.15210	−0.0650170
$315$	0.693181	0.0390563
$316$	−5.94063	−0.334187
$317$	−0.383982	−0.0215666	−0.0107833	−	0.999942i	$-0.503432\pi$
$317$	−0.383982	−0.0215666	−0.0107833	+	0.999942i	$0.503432\pi$
$318$	10.9214	0.612443
$319$	−23.0432	−1.29017
$320$	7.27964	0.406944
$321$	14.5983	0.814797
$322$	1.46774	0.0817937
$323$	−3.28857	−0.182981
$324$	−0.672658	−0.0373699
$325$	14.0716	0.780552
$326$	1.34998	0.0747685
$327$	10.2634	0.567569
$328$	23.7596	1.31191
$329$	3.77376	0.208054
$330$	−2.48504	−0.136797
$331$	−6.06232	−0.333215	−0.166607	−	0.986023i	$-0.553281\pi$
$331$	−6.06232	−0.333215	−0.166607	+	0.986023i	$0.553281\pi$
$332$	−5.64099	−0.309590
$333$	7.01206	0.384259
$334$	−22.7826	−1.24661
$335$	11.3447	0.619828
$336$	−1.79846	−0.0981143
$337$	0.0344369	0.00187590	0.000937949	−	1.00000i	$-0.499701\pi$
$337$	0.0344369	0.00187590	0.000937949		1.00000i	$0.499701\pi$
$338$	−2.52119	−0.137135
$339$	−7.14302	−0.387956
$340$	0.570951	0.0309642
$341$	−4.26928	−0.231195
$342$	3.78878	0.204874
$343$	−10.8886	−0.587929
$344$	2.59373	0.139845
$345$	1.32409	0.0712868
$346$	−3.41731	−0.183716
$347$	−28.8366	−1.54803	−0.774015	−	0.633168i	$-0.781754\pi$
$347$	−28.8366	−1.54803	−0.774015	+	0.633168i	$0.781754\pi$
$348$	−6.09957	−0.326972
$349$	9.11100	0.487701	0.243850	−	0.969813i	$-0.421589\pi$
$349$	9.11100	0.487701	0.243850	+	0.969813i	$0.421589\pi$
$350$	−4.02653	−0.215227
$351$	−3.28811	−0.175506
$352$	−9.20211	−0.490474
$353$	−17.7644	−0.945504	−0.472752	−	0.881195i	$-0.656739\pi$
$353$	−17.7644	−0.945504	−0.472752	+	0.881195i	$0.656739\pi$
$354$	−5.52301	−0.293544
$355$	−4.21788	−0.223862
$356$	6.73207	0.356799
$357$	−0.816661	−0.0432223
$358$	22.7173	1.20065
$359$	30.1519	1.59136	0.795678	−	0.605719i	$-0.207115\pi$
$359$	30.1519	1.59136	0.795678	+	0.605719i	$0.207115\pi$
$360$	−2.61360	−0.137749
$361$	−8.18528	−0.430804
$362$	−12.8986	−0.677935
$363$	−4.54233	−0.238411
$364$	1.80627	0.0946742
$365$	10.6276	0.556272
$366$	5.62639	0.294096
$367$	30.3544	1.58449	0.792245	−	0.610204i	$-0.208912\pi$
$367$	30.3544	1.58449	0.792245	+	0.610204i	$0.208912\pi$
$368$	−3.43538	−0.179081
$369$	−7.71623	−0.401691
$370$	6.85712	0.356485
$371$	7.74158	0.401923
$372$	−1.13009	−0.0585922
$373$	−7.21230	−0.373439	−0.186719	−	0.982413i	$-0.559785\pi$
$373$	−7.21230	−0.373439	−0.186719	+	0.982413i	$0.559785\pi$
$374$	2.92772	0.151389
$375$	−7.87646	−0.406739
$376$	−14.2288	−0.733793
$377$	−29.8162	−1.53561
$378$	0.940878	0.0483936
$379$	27.8212	1.42908	0.714540	−	0.699594i	$-0.246636\pi$
$379$	27.8212	1.42908	0.714540	+	0.699594i	$0.246636\pi$
$380$	−1.87761	−0.0963196
$381$	6.09236	0.312121
$382$	9.76360	0.499549
$383$	0.935866	0.0478205	0.0239102	−	0.999714i	$-0.492388\pi$
$383$	0.935866	0.0478205	0.0239102	+	0.999714i	$0.492388\pi$
$384$	2.63855	0.134648
$385$	−1.76151	−0.0897747
$386$	−7.29729	−0.371422
$387$	−0.842345	−0.0428188
$388$	7.25751	0.368445
$389$	32.5169	1.64867	0.824335	−	0.566102i	$-0.191549\pi$
$389$	32.5169	1.64867	0.824335	+	0.566102i	$0.191549\pi$
$390$	−3.21545	−0.162821
$391$	−1.55996	−0.0788907
$392$	19.5006	0.984931
$393$	17.6987	0.892783
$394$	24.7190	1.24532
$395$	7.49623	0.377176
$396$	1.70935	0.0858983
$397$	−5.91652	−0.296941	−0.148471	−	0.988917i	$-0.547435\pi$
$397$	−5.91652	−0.296941	−0.148471	+	0.988917i	$0.547435\pi$
$398$	21.8425	1.09487
$399$	2.68565	0.134451
$400$	9.42447	0.471224
$401$	−5.48820	−0.274068	−0.137034	−	0.990566i	$-0.543757\pi$
$401$	−5.48820	−0.274068	−0.137034	+	0.990566i	$0.543757\pi$
$402$	15.3986	0.768012
$403$	−5.52412	−0.275176
$404$	−5.85510	−0.291302
$405$	0.848798	0.0421771
$406$	8.53176	0.423424
$407$	−17.8190	−0.883255
$408$	3.07918	0.152442
$409$	25.0694	1.23960	0.619800	−	0.784760i	$-0.287214\pi$
$409$	25.0694	1.23960	0.619800	+	0.784760i	$0.287214\pi$
$410$	−7.54573	−0.372657
$411$	14.1517	0.698051
$412$	0.295184	0.0145427
$413$	−3.91495	−0.192642
$414$	1.79724	0.0883294
$415$	7.11813	0.349415
$416$	−11.9068	−0.583780
$417$	−12.1793	−0.596423
$418$	−9.62802	−0.470922
$419$	4.38901	0.214417	0.107208	−	0.994237i	$-0.465809\pi$
$419$	4.38901	0.214417	0.107208	+	0.994237i	$0.465809\pi$
$420$	−0.466273	−0.0227518
$421$	1.83598	0.0894801	0.0447400	−	0.998999i	$-0.485754\pi$
$421$	1.83598	0.0894801	0.0447400	+	0.998999i	$0.485754\pi$
$422$	−7.70279	−0.374966
$423$	4.62097	0.224679
$424$	−29.1892	−1.41755
$425$	4.27954	0.207588
$426$	−5.72507	−0.277381
$427$	3.98823	0.193004
$428$	−9.81966	−0.474651
$429$	8.35572	0.403418
$430$	−0.823732	−0.0397239
$431$	19.7037	0.949092	0.474546	−	0.880231i	$-0.342612\pi$
$431$	19.7037	0.949092	0.474546	+	0.880231i	$0.342612\pi$
$432$	−2.20222	−0.105954
$433$	−35.0335	−1.68360	−0.841800	−	0.539789i	$-0.818504\pi$
$433$	−35.0335	−1.68360	−0.841800	+	0.539789i	$0.818504\pi$
$434$	1.58070	0.0758762
$435$	7.69680	0.369033
$436$	−6.90378	−0.330631
$437$	5.13005	0.245404
$438$	14.4252	0.689261
$439$	4.18461	0.199720	0.0998602	−	0.995001i	$-0.468160\pi$
$439$	4.18461	0.199720	0.0998602	+	0.995001i	$0.468160\pi$
$440$	6.64167	0.316629
$441$	−6.33306	−0.301574
$442$	3.78824	0.180188
$443$	23.1923	1.10190	0.550949	−	0.834539i	$-0.314266\pi$
$443$	23.1923	1.10190	0.550949	+	0.834539i	$0.314266\pi$
$444$	−4.71672	−0.223845
$445$	−8.49492	−0.402698
$446$	−19.7141	−0.933490
$447$	18.4362	0.872001
$448$	7.00401	0.330909
$449$	−41.1844	−1.94361	−0.971807	−	0.235779i	$-0.924236\pi$
$449$	−41.1844	−1.94361	−0.971807	+	0.235779i	$0.924236\pi$
$450$	−4.93047	−0.232425
$451$	19.6084	0.923325
$452$	4.80481	0.225999
$453$	2.32660	0.109313
$454$	−27.7560	−1.30265
$455$	−2.27925	−0.106853
$456$	−10.1261	−0.474198
$457$	−37.1597	−1.73826	−0.869129	−	0.494585i	$-0.835320\pi$
$457$	−37.1597	−1.73826	−0.869129	+	0.494585i	$0.835320\pi$
$458$	17.5007	0.817754
$459$	−1.00000	−0.0466760
$460$	−0.890662	−0.0415273
$461$	−12.8136	−0.596790	−0.298395	−	0.954443i	$-0.596451\pi$
$461$	−12.8136	−0.596790	−0.298395	+	0.954443i	$0.596451\pi$
$462$	−2.39095	−0.111237
$463$	6.21885	0.289014	0.144507	−	0.989504i	$-0.453840\pi$
$463$	6.21885	0.289014	0.144507	+	0.989504i	$0.453840\pi$
$464$	−19.9694	−0.927057
$465$	1.42601	0.0661295
$466$	15.9576	0.739221
$467$	−25.4231	−1.17644	−0.588221	−	0.808700i	$-0.700171\pi$
$467$	−25.4231	−1.17644	−0.588221	+	0.808700i	$0.700171\pi$
$468$	2.21177	0.102239
$469$	10.9152	0.504017
$470$	4.51886	0.208439
$471$	−1.00000	−0.0460776
$472$	14.7611	0.679435
$473$	2.14056	0.0984232
$474$	10.1749	0.467348
$475$	−14.0736	−0.645741
$476$	0.549334	0.0251787
$477$	9.47955	0.434039
$478$	−10.8053	−0.494223
$479$	1.01194	0.0462367	0.0231184	−	0.999733i	$-0.492641\pi$
$479$	1.01194	0.0462367	0.0231184	+	0.999733i	$0.492641\pi$
$480$	3.07365	0.140292
$481$	−23.0564	−1.05128
$482$	−10.6011	−0.482869
$483$	1.27396	0.0579672
$484$	3.05544	0.138883
$485$	−9.15795	−0.415841
$486$	1.15210	0.0522605
$487$	−26.2532	−1.18965	−0.594823	−	0.803856i	$-0.702778\pi$
$487$	−26.2532	−1.18965	−0.594823	+	0.803856i	$0.702778\pi$
$488$	−15.0374	−0.680712
$489$	1.17175	0.0529885
$490$	−6.19313	−0.279777
$491$	10.4800	0.472956	0.236478	−	0.971637i	$-0.424007\pi$
$491$	10.4800	0.472956	0.236478	+	0.971637i	$0.424007\pi$
$492$	5.19038	0.234000
$493$	−9.06787	−0.408396
$494$	−12.4579	−0.560508
$495$	−2.15696	−0.0969482
$496$	−3.69979	−0.166126
$497$	−4.05818	−0.182034
$498$	9.66168	0.432950
$499$	32.0518	1.43483	0.717417	−	0.696644i	$-0.245324\pi$
$499$	32.0518	1.43483	0.717417	+	0.696644i	$0.245324\pi$
$500$	5.29816	0.236941
$501$	−19.7748	−0.883473
$502$	−22.0483	−0.984064
$503$	−37.3237	−1.66418	−0.832091	−	0.554639i	$-0.812856\pi$
$503$	−37.3237	−1.66418	−0.832091	+	0.554639i	$0.812856\pi$
$504$	−2.51465	−0.112011
$505$	7.38830	0.328775
$506$	−4.56713	−0.203034
$507$	−2.18834	−0.0971875
$508$	−4.09807	−0.181823
$509$	20.6577	0.915635	0.457818	−	0.889046i	$-0.348631\pi$
$509$	20.6577	0.915635	0.457818	+	0.889046i	$0.348631\pi$
$510$	−0.977904	−0.0433023
$511$	10.2252	0.452335
$512$	−21.5366	−0.951794
$513$	3.28857	0.145194
$514$	−7.17306	−0.316390
$515$	−0.372480	−0.0164134
$516$	0.566610	0.0249436
$517$	−11.7428	−0.516446
$518$	6.59750	0.289877
$519$	−2.96615	−0.130199
$520$	8.59381	0.376863
$521$	−41.2093	−1.80541	−0.902707	−	0.430256i	$-0.858423\pi$
$521$	−41.2093	−1.80541	−0.902707	+	0.430256i	$0.858423\pi$
$522$	10.4471	0.457258
$523$	−2.72237	−0.119041	−0.0595205	−	0.998227i	$-0.518957\pi$
$523$	−2.72237	−0.119041	−0.0595205	+	0.998227i	$0.518957\pi$
$524$	−11.9052	−0.520080
$525$	−3.49494	−0.152531
$526$	−7.28406	−0.317600
$527$	−1.68003	−0.0731833
$528$	5.59626	0.243546
$529$	−20.5665	−0.894196
$530$	9.27008	0.402667
$531$	−4.79385	−0.208035
$532$	−1.80652	−0.0783228
$533$	25.3718	1.09897
$534$	−11.5304	−0.498971
$535$	12.3910	0.535710
$536$	−41.1551	−1.77763
$537$	19.7181	0.850898
$538$	5.76487	0.248541
$539$	16.0935	0.693198
$540$	−0.570951	−0.0245698
$541$	30.8816	1.32771	0.663853	−	0.747863i	$-0.268920\pi$
$541$	30.8816	1.32771	0.663853	+	0.747863i	$0.268920\pi$
$542$	18.3538	0.788363
$543$	−11.1957	−0.480453
$544$	−3.62118	−0.155257
$545$	8.71159	0.373163
$546$	−3.09371	−0.132399
$547$	40.7903	1.74407	0.872033	−	0.489447i	$-0.162801\pi$
$547$	40.7903	1.74407	0.872033	+	0.489447i	$0.162801\pi$
$548$	−9.51924	−0.406642
$549$	4.88358	0.208426
$550$	12.5293	0.534251
$551$	29.8204	1.27039
$552$	−4.80340	−0.204446
$553$	7.21241	0.306703
$554$	23.9563	1.01780
$555$	5.95183	0.252641
$556$	8.19251	0.347440
$557$	23.2054	0.983242	0.491621	−	0.870809i	$-0.336404\pi$
$557$	23.2054	0.983242	0.491621	+	0.870809i	$0.336404\pi$
$558$	1.93557	0.0819392
$559$	2.76972	0.117147
$560$	−1.52653	−0.0645078
$561$	2.54119	0.107289
$562$	19.7111	0.831464
$563$	7.01938	0.295832	0.147916	−	0.989000i	$-0.452744\pi$
$563$	7.01938	0.295832	0.147916	+	0.989000i	$0.452744\pi$
$564$	−3.10833	−0.130884
$565$	−6.06299	−0.255072
$566$	−2.65550	−0.111619
$567$	0.816661	0.0342966
$568$	15.3012	0.642022
$569$	19.1273	0.801857	0.400928	−	0.916109i	$-0.368688\pi$
$569$	19.1273	0.801857	0.400928	+	0.916109i	$0.368688\pi$
$570$	3.21591	0.134700
$571$	−17.4691	−0.731058	−0.365529	−	0.930800i	$-0.619112\pi$
$571$	−17.4691	−0.731058	−0.365529	+	0.930800i	$0.619112\pi$
$572$	−5.62054	−0.235007
$573$	8.47459	0.354031
$574$	−7.26003	−0.303028
$575$	−6.67592	−0.278405
$576$	8.57640	0.357350
$577$	−5.27757	−0.219708	−0.109854	−	0.993948i	$-0.535038\pi$
$577$	−5.27757	−0.219708	−0.109854	+	0.993948i	$0.535038\pi$
$578$	1.15210	0.0479212
$579$	−6.33388	−0.263227
$580$	−5.17731	−0.214976
$581$	6.84862	0.284129
$582$	−12.4304	−0.515257
$583$	−24.0894	−0.997680
$584$	−38.5535	−1.59536
$585$	−2.79094	−0.115391
$586$	−31.3866	−1.29657
$587$	−11.2432	−0.464058	−0.232029	−	0.972709i	$-0.574536\pi$
$587$	−11.2432	−0.464058	−0.232029	+	0.972709i	$0.574536\pi$
$588$	4.25998	0.175679
$589$	5.52491	0.227650
$590$	−4.68792	−0.192999
$591$	21.4555	0.882562
$592$	−15.4421	−0.634665
$593$	32.9675	1.35381	0.676906	−	0.736069i	$-0.263320\pi$
$593$	32.9675	1.35381	0.676906	+	0.736069i	$0.263320\pi$
$594$	−2.92772	−0.120126
$595$	−0.693181	−0.0284176
$596$	−12.4012	−0.507975
$597$	18.9588	0.775933
$598$	−5.90952	−0.241658
$599$	−11.0246	−0.450452	−0.225226	−	0.974307i	$-0.572312\pi$
$599$	−11.0246	−0.450452	−0.225226	+	0.974307i	$0.572312\pi$
$600$	13.1775	0.537968
$601$	−32.7903	−1.33754	−0.668772	−	0.743467i	$-0.733180\pi$
$601$	−32.7903	−1.33754	−0.668772	+	0.743467i	$0.733180\pi$
$602$	−0.792544	−0.0323017
$603$	13.3656	0.544290
$604$	−1.56501	−0.0636793
$605$	−3.85553	−0.156749
$606$	10.0284	0.407376
$607$	25.0519	1.01683	0.508413	−	0.861113i	$-0.330232\pi$
$607$	25.0519	1.01683	0.508413	+	0.861113i	$0.330232\pi$
$608$	11.9085	0.482954
$609$	7.40538	0.300081
$610$	4.77567	0.193361
$611$	−15.1942	−0.614693
$612$	0.672658	0.0271906
$613$	19.3381	0.781060	0.390530	−	0.920590i	$-0.372292\pi$
$613$	19.3381	0.781060	0.390530	+	0.920590i	$0.372292\pi$
$614$	13.5640	0.547400
$615$	−6.54952	−0.264102
$616$	6.39020	0.257469
$617$	−21.8949	−0.881454	−0.440727	−	0.897641i	$-0.645279\pi$
$617$	−21.8949	−0.881454	−0.440727	+	0.897641i	$0.645279\pi$
$618$	−0.505580	−0.0203374
$619$	−39.1865	−1.57504	−0.787519	−	0.616290i	$-0.788635\pi$
$619$	−39.1865	−1.57504	−0.787519	+	0.616290i	$0.788635\pi$
$620$	−0.959215	−0.0385230
$621$	1.55996	0.0625991
$622$	−4.31219	−0.172903
$623$	−8.17329	−0.327456
$624$	7.24113	0.289877
$625$	14.7122	0.588487
$626$	−13.0484	−0.521519
$627$	−8.35690	−0.333743
$628$	0.672658	0.0268420
$629$	−7.01206	−0.279589
$630$	0.798616	0.0318176
$631$	−39.3988	−1.56844	−0.784221	−	0.620481i	$-0.786937\pi$
$631$	−39.3988	−1.56844	−0.784221	+	0.620481i	$0.786937\pi$
$632$	−27.1940	−1.08172
$633$	−6.68585	−0.265739
$634$	−0.442387	−0.0175694
$635$	5.17119	0.205212
$636$	−6.37649	−0.252844
$637$	20.8238	0.825069
$638$	−26.5482	−1.05105
$639$	−4.96923	−0.196580
$640$	2.23960	0.0885278
$641$	20.6138	0.814198	0.407099	−	0.913384i	$-0.366540\pi$
$641$	20.6138	0.814198	0.407099	+	0.913384i	$0.366540\pi$
$642$	16.8187	0.663783
$643$	24.5472	0.968046	0.484023	−	0.875055i	$-0.339175\pi$
$643$	24.5472	0.968046	0.484023	+	0.875055i	$0.339175\pi$
$644$	−0.856940	−0.0337682
$645$	−0.714981	−0.0281524
$646$	−3.78878	−0.149067
$647$	28.4264	1.11756	0.558778	−	0.829317i	$-0.311270\pi$
$647$	28.4264	1.11756	0.558778	+	0.829317i	$0.311270\pi$
$648$	−3.07918	−0.120962
$649$	12.1821	0.478189
$650$	16.2119	0.635885
$651$	1.37202	0.0537736
$652$	−0.788189	−0.0308679
$653$	48.7147	1.90635	0.953177	−	0.302411i	$-0.0977917\pi$
$653$	48.7147	1.90635	0.953177	+	0.302411i	$0.0977917\pi$
$654$	11.8245	0.462376
$655$	15.0227	0.586984
$656$	16.9928	0.663457
$657$	12.5207	0.488479
$658$	4.34777	0.169494
$659$	34.2648	1.33477	0.667384	−	0.744713i	$-0.267414\pi$
$659$	34.2648	1.33477	0.667384	+	0.744713i	$0.267414\pi$
$660$	1.45090	0.0564761
$661$	−4.09600	−0.159316	−0.0796579	−	0.996822i	$-0.525383\pi$
$661$	−4.09600	−0.159316	−0.0796579	+	0.996822i	$0.525383\pi$
$662$	−6.98441	−0.271457
$663$	3.28811	0.127700
$664$	−25.8224	−1.00210
$665$	2.27958	0.0883982
$666$	8.07862	0.313040
$667$	14.1455	0.547718
$668$	13.3017	0.514657
$669$	−17.1114	−0.661565
$670$	13.0703	0.504950
$671$	−12.4101	−0.479088
$672$	2.95727	0.114079
$673$	−26.0466	−1.00402	−0.502011	−	0.864861i	$-0.667406\pi$
$673$	−26.0466	−1.00402	−0.502011	+	0.864861i	$0.667406\pi$
$674$	0.0396749	0.00152822
$675$	−4.27954	−0.164720
$676$	1.47200	0.0566155
$677$	28.1462	1.08174	0.540872	−	0.841105i	$-0.318094\pi$
$677$	28.1462	1.08174	0.540872	+	0.841105i	$0.318094\pi$
$678$	−8.22950	−0.316052
$679$	−8.81121	−0.338143
$680$	2.61360	0.100227
$681$	−24.0915	−0.923190
$682$	−4.91866	−0.188345
$683$	31.3491	1.19954	0.599771	−	0.800172i	$-0.295258\pi$
$683$	31.3491	1.19954	0.599771	+	0.800172i	$0.295258\pi$
$684$	−2.21208	−0.0845812
$685$	12.0119	0.458952
$686$	−12.5448	−0.478962
$687$	15.1902	0.579543
$688$	1.85503	0.0707222
$689$	−31.1698	−1.18747
$690$	1.52549	0.0580745
$691$	−14.9819	−0.569940	−0.284970	−	0.958536i	$-0.591984\pi$
$691$	−14.9819	−0.569940	−0.284970	+	0.958536i	$0.591984\pi$
$692$	1.99520	0.0758462
$693$	−2.07529	−0.0788339
$694$	−33.2227	−1.26112
$695$	−10.3378	−0.392134
$696$	−27.9216	−1.05837
$697$	7.71623	0.292273
$698$	10.4968	0.397310
$699$	13.8508	0.523887
$700$	2.35090	0.0888555
$701$	46.8689	1.77022	0.885108	−	0.465386i	$-0.154085\pi$
$701$	46.8689	1.77022	0.885108	+	0.465386i	$0.154085\pi$
$702$	−3.78824	−0.142978
$703$	23.0597	0.869712
$704$	−21.7943	−0.821404
$705$	3.92227	0.147721
$706$	−20.4664	−0.770265
$707$	7.10857	0.267345
$708$	3.22462	0.121189
$709$	−31.4118	−1.17970	−0.589848	−	0.807514i	$-0.700812\pi$
$709$	−31.4118	−1.17970	−0.589848	+	0.807514i	$0.700812\pi$
$710$	−4.85943	−0.182371
$711$	8.83158	0.331210
$712$	30.8169	1.15491
$713$	2.62079	0.0981492
$714$	−0.940878	−0.0352115
$715$	7.09232	0.265238
$716$	−13.2635	−0.495681
$717$	−9.37876	−0.350256
$718$	34.7381	1.29641
$719$	−33.3224	−1.24272	−0.621359	−	0.783526i	$-0.713419\pi$
$719$	−33.3224	−1.24272	−0.621359	+	0.783526i	$0.713419\pi$
$720$	−1.86924	−0.0696624
$721$	−0.358378	−0.0133467
$722$	−9.43029	−0.350959
$723$	−9.20155	−0.342209
$724$	7.53087	0.279882
$725$	−38.8063	−1.44123
$726$	−5.23324	−0.194224
$727$	47.8120	1.77325	0.886625	−	0.462490i	$-0.153044\pi$
$727$	47.8120	1.77325	0.886625	+	0.462490i	$0.153044\pi$
$728$	8.26843	0.306448
$729$	1.00000	0.0370370
$730$	12.2440	0.453173
$731$	0.842345	0.0311553
$732$	−3.28498	−0.121416
$733$	3.78225	0.139701	0.0698503	−	0.997557i	$-0.477748\pi$
$733$	3.78225	0.139701	0.0698503	+	0.997557i	$0.477748\pi$
$734$	34.9715	1.29082
$735$	−5.37550	−0.198278
$736$	5.64890	0.208221
$737$	−33.9647	−1.25110
$738$	−8.88989	−0.327241
$739$	−33.8624	−1.24565	−0.622825	−	0.782361i	$-0.714015\pi$
$739$	−33.8624	−1.24565	−0.622825	+	0.782361i	$0.714015\pi$
$740$	−4.00354	−0.147173
$741$	−10.8132	−0.397233
$742$	8.91910	0.327430
$743$	−25.6536	−0.941140	−0.470570	−	0.882363i	$-0.655952\pi$
$743$	−25.6536	−0.941140	−0.470570	+	0.882363i	$0.655952\pi$
$744$	−5.17311	−0.189656
$745$	15.6486	0.573320
$746$	−8.30931	−0.304226
$747$	8.38612	0.306832
$748$	−1.70935	−0.0625002
$749$	11.9219	0.435615
$750$	−9.07450	−0.331354
$751$	28.8060	1.05115	0.525574	−	0.850748i	$-0.323851\pi$
$751$	28.8060	1.05115	0.525574	+	0.850748i	$0.323851\pi$
$752$	−10.1764	−0.371094
$753$	−19.1374	−0.697407
$754$	−34.3513	−1.25100
$755$	1.97482	0.0718710
$756$	−0.549334	−0.0199791
$757$	9.08986	0.330377	0.165188	−	0.986262i	$-0.447177\pi$
$757$	9.08986	0.330377	0.165188	+	0.986262i	$0.447177\pi$
$758$	32.0529	1.16421
$759$	−3.96417	−0.143890
$760$	−8.59502	−0.311774
$761$	5.26162	0.190734	0.0953669	−	0.995442i	$-0.469598\pi$
$761$	5.26162	0.190734	0.0953669	+	0.995442i	$0.469598\pi$
$762$	7.01903	0.254273
$763$	8.38175	0.303440
$764$	−5.70050	−0.206237
$765$	−0.848798	−0.0306884
$766$	1.07821	0.0389575
$767$	15.7627	0.569158
$768$	−14.1129	−0.509256
$769$	41.0798	1.48137	0.740687	−	0.671850i	$-0.234500\pi$
$769$	41.0798	1.48137	0.740687	+	0.671850i	$0.234500\pi$
$770$	−2.02944	−0.0731359
$771$	−6.22606	−0.224226
$772$	4.26053	0.153340
$773$	49.2520	1.77147	0.885735	−	0.464190i	$-0.153655\pi$
$773$	49.2520	1.77147	0.885735	+	0.464190i	$0.153655\pi$
$774$	−0.970469	−0.0348828
$775$	−7.18976	−0.258264
$776$	33.2222	1.19261
$777$	5.72648	0.205436
$778$	37.4628	1.34311
$779$	−25.3754	−0.909168
$780$	1.87735	0.0672199
$781$	12.6278	0.451858
$782$	−1.79724	−0.0642691
$783$	9.06787	0.324059
$784$	13.9468	0.498099
$785$	−0.848798	−0.0302949
$786$	20.3908	0.727315
$787$	−36.3007	−1.29398	−0.646991	−	0.762498i	$-0.723973\pi$
$787$	−36.3007	−1.29398	−0.646991	+	0.762498i	$0.723973\pi$
$788$	−14.4322	−0.514127
$789$	−6.32240	−0.225083
$790$	8.63643	0.307271
$791$	−5.83343	−0.207413
$792$	7.82479	0.278042
$793$	−16.0577	−0.570227
$794$	−6.81644	−0.241906
$795$	8.04623	0.285370
$796$	−12.7528	−0.452011
$797$	−5.58273	−0.197751	−0.0988753	−	0.995100i	$-0.531524\pi$
$797$	−5.58273	−0.197751	−0.0988753	+	0.995100i	$0.531524\pi$
$798$	3.09415	0.109532
$799$	−4.62097	−0.163478
$800$	−15.4970	−0.547901
$801$	−10.0082	−0.353621
$802$	−6.32297	−0.223272
$803$	−31.8176	−1.12282
$804$	−8.99049	−0.317070
$805$	1.08134	0.0381121
$806$	−6.36436	−0.224175
$807$	5.00378	0.176141
$808$	−26.8025	−0.942908
$809$	37.6307	1.32302	0.661512	−	0.749935i	$-0.269915\pi$
$809$	37.6307	1.32302	0.661512	+	0.749935i	$0.269915\pi$
$810$	0.977904	0.0343600
$811$	54.4384	1.91159	0.955796	−	0.294031i	$-0.0949969\pi$
$811$	54.4384	1.91159	0.955796	+	0.294031i	$0.0949969\pi$
$812$	−4.98129	−0.174809
$813$	15.9307	0.558713
$814$	−20.5293	−0.719553
$815$	0.994582	0.0348387
$816$	2.20222	0.0770930
$817$	−2.77012	−0.0969141
$818$	28.8825	1.00985
$819$	−2.68527	−0.0938310
$820$	4.40559	0.153850
$821$	−37.9441	−1.32426	−0.662129	−	0.749389i	$-0.730347\pi$
$821$	−37.9441	−1.32426	−0.662129	+	0.749389i	$0.730347\pi$
$822$	16.3042	0.568674
$823$	54.2481	1.89097	0.945484	−	0.325667i	$-0.105589\pi$
$823$	54.2481	1.89097	0.945484	+	0.325667i	$0.105589\pi$
$824$	1.35124	0.0470728
$825$	10.8751	0.378624
$826$	−4.51043	−0.156938
$827$	−29.7172	−1.03337	−0.516684	−	0.856176i	$-0.672834\pi$
$827$	−29.7172	−1.03337	−0.516684	+	0.856176i	$0.672834\pi$
$828$	−1.04932	−0.0364664
$829$	−24.8456	−0.862924	−0.431462	−	0.902131i	$-0.642002\pi$
$829$	−24.8456	−0.862924	−0.431462	+	0.902131i	$0.642002\pi$
$830$	8.20082	0.284655
$831$	20.7935	0.721318
$832$	−28.2001	−0.977664
$833$	6.33306	0.219428
$834$	−14.0318	−0.485882
$835$	−16.7848	−0.580862
$836$	5.62134	0.194418
$837$	1.68003	0.0580704
$838$	5.05659	0.174677
$839$	18.3237	0.632603	0.316301	−	0.948659i	$-0.397559\pi$
$839$	18.3237	0.632603	0.316301	+	0.948659i	$0.397559\pi$
$840$	−2.13443	−0.0736447
$841$	53.2263	1.83539
$842$	2.11524	0.0728958
$843$	17.1088	0.589259
$844$	4.49729	0.154803
$845$	−1.85746	−0.0638985
$846$	5.32383	0.183037
$847$	−3.70955	−0.127462
$848$	−20.8760	−0.716885
$849$	−2.30491	−0.0791043
$850$	4.93047	0.169114
$851$	10.9386	0.374969
$852$	3.34259	0.114515
$853$	−28.7910	−0.985787	−0.492893	−	0.870090i	$-0.664061\pi$
$853$	−28.7910	−0.985787	−0.492893	+	0.870090i	$0.664061\pi$
$854$	4.59486	0.157233
$855$	2.79134	0.0954617
$856$	−44.9507	−1.53638
$857$	25.2417	0.862241	0.431121	−	0.902294i	$-0.358118\pi$
$857$	25.2417	0.862241	0.431121	+	0.902294i	$0.358118\pi$
$858$	9.62666	0.328649
$859$	−26.9918	−0.920949	−0.460475	−	0.887673i	$-0.652321\pi$
$859$	−26.9918	−0.920949	−0.460475	+	0.887673i	$0.652321\pi$
$860$	0.480938	0.0163998
$861$	−6.30155	−0.214756
$862$	22.7007	0.773187
$863$	4.32380	0.147184	0.0735919	−	0.997288i	$-0.476554\pi$
$863$	4.32380	0.147184	0.0735919	+	0.997288i	$0.476554\pi$
$864$	3.62118	0.123195
$865$	−2.51766	−0.0856031
$866$	−40.3622	−1.37156
$867$	1.00000	0.0339618
$868$	−0.922897	−0.0313252
$869$	−22.4428	−0.761319
$870$	8.86750	0.300637
$871$	−43.9476	−1.48911
$872$	−31.6029	−1.07021
$873$	−10.7893	−0.365163
$874$	5.91035	0.199921
$875$	−6.43240	−0.217455
$876$	−8.42215	−0.284558
$877$	−39.7348	−1.34175	−0.670875	−	0.741570i	$-0.734081\pi$
$877$	−39.7348	−1.34175	−0.670875	+	0.741570i	$0.734081\pi$
$878$	4.82110	0.162704
$879$	−27.2428	−0.918878
$880$	4.75010	0.160126
$881$	−21.7216	−0.731818	−0.365909	−	0.930651i	$-0.619242\pi$
$881$	−21.7216	−0.731818	−0.365909	+	0.930651i	$0.619242\pi$
$882$	−7.29635	−0.245681
$883$	−23.4351	−0.788656	−0.394328	−	0.918970i	$-0.629023\pi$
$883$	−23.4351	−0.788656	−0.394328	+	0.918970i	$0.629023\pi$
$884$	−2.21177	−0.0743899
$885$	−4.06901	−0.136778
$886$	26.7199	0.897673
$887$	−50.6739	−1.70146	−0.850731	−	0.525601i	$-0.823840\pi$
$887$	−50.6739	−1.70146	−0.850731	+	0.525601i	$0.823840\pi$
$888$	−21.5914	−0.724559
$889$	4.97539	0.166869
$890$	−9.78703	−0.328062
$891$	−2.54119	−0.0851332
$892$	11.5101	0.385387
$893$	15.1964	0.508528
$894$	21.2404	0.710385
$895$	16.7367	0.559445
$896$	2.15480	0.0719869
$897$	−5.12933	−0.171263
$898$	−47.4487	−1.58338
$899$	15.2343	0.508093
$900$	2.87867	0.0959555
$901$	−9.47955	−0.315810
$902$	22.5909	0.752196
$903$	−0.687911	−0.0228922
$904$	21.9946	0.731531
$905$	−9.50288	−0.315887
$906$	2.68049	0.0890533
$907$	−30.5667	−1.01495	−0.507476	−	0.861666i	$-0.669421\pi$
$907$	−30.5667	−1.01495	−0.507476	+	0.861666i	$0.669421\pi$
$908$	16.2054	0.537794
$909$	8.70442	0.288707
$910$	−2.62594	−0.0870490
$911$	19.3859	0.642282	0.321141	−	0.947031i	$-0.395934\pi$
$911$	19.3859	0.642282	0.321141	+	0.947031i	$0.395934\pi$
$912$	−7.24215	−0.239812
$913$	−21.3108	−0.705284
$914$	−42.8118	−1.41609
$915$	4.14518	0.137035
$916$	−10.2178	−0.337606
$917$	14.4539	0.477309
$918$	−1.15210	−0.0380251
$919$	12.1110	0.399505	0.199753	−	0.979846i	$-0.435986\pi$
$919$	12.1110	0.399505	0.199753	+	0.979846i	$0.435986\pi$
$920$	−4.07712	−0.134419
$921$	11.7733	0.387943
$922$	−14.7626	−0.486181
$923$	16.3394	0.537817
$924$	1.39596	0.0459238
$925$	−30.0084	−0.986670
$926$	7.16475	0.235448
$927$	−0.438833	−0.0144132
$928$	32.8364	1.07791
$929$	8.40313	0.275698	0.137849	−	0.990453i	$-0.455981\pi$
$929$	8.40313	0.275698	0.137849	+	0.990453i	$0.455981\pi$
$930$	1.64291	0.0538731
$931$	−20.8268	−0.682569
$932$	−9.31687	−0.305184
$933$	−3.74289	−0.122537
$934$	−29.2901	−0.958400
$935$	2.15696	0.0705402
$936$	10.1247	0.330935
$937$	−39.7207	−1.29762	−0.648809	−	0.760952i	$-0.724732\pi$
$937$	−39.7207	−1.29762	−0.648809	+	0.760952i	$0.724732\pi$
$938$	12.5754	0.410602
$939$	−11.3257	−0.369601
$940$	−2.63834	−0.0860533
$941$	13.6377	0.444576	0.222288	−	0.974981i	$-0.428647\pi$
$941$	13.6377	0.444576	0.222288	+	0.974981i	$0.428647\pi$
$942$	−1.15210	−0.0375376
$943$	−12.0370	−0.391980
$944$	10.5571	0.343604
$945$	0.693181	0.0225492
$946$	2.46615	0.0801814
$947$	−16.0056	−0.520111	−0.260055	−	0.965594i	$-0.583741\pi$
$947$	−16.0056	−0.520111	−0.260055	+	0.965594i	$0.583741\pi$
$948$	−5.94063	−0.192943
$949$	−41.1695	−1.33642
$950$	−16.2142	−0.526059
$951$	−0.383982	−0.0124515
$952$	2.51465	0.0815001
$953$	−10.1087	−0.327453	−0.163727	−	0.986506i	$-0.552351\pi$
$953$	−10.1087	−0.327453	−0.163727	+	0.986506i	$0.552351\pi$
$954$	10.9214	0.353594
$955$	7.19322	0.232767
$956$	6.30870	0.204038
$957$	−23.0432	−0.744882
$958$	1.16586	0.0376672
$959$	11.5571	0.373199
$960$	7.27964	0.234949
$961$	−28.1775	−0.908951
$962$	−26.5634	−0.856438
$963$	14.5983	0.470423
$964$	6.18949	0.199350
$965$	−5.37619	−0.173066
$966$	1.46774	0.0472236
$967$	20.4886	0.658870	0.329435	−	0.944178i	$-0.393142\pi$
$967$	20.4886	0.658870	0.329435	+	0.944178i	$0.393142\pi$
$968$	13.9867	0.449548
$969$	−3.28857	−0.105644
$970$	−10.5509	−0.338769
$971$	−28.8092	−0.924530	−0.462265	−	0.886742i	$-0.652963\pi$
$971$	−28.8092	−0.924530	−0.462265	+	0.886742i	$0.652963\pi$
$972$	−0.672658	−0.0215755
$973$	−9.94637	−0.318866
$974$	−30.2464	−0.969158
$975$	14.0716	0.450652
$976$	−10.7547	−0.344250
$977$	−32.1986	−1.03012	−0.515062	−	0.857153i	$-0.672231\pi$
$977$	−32.1986	−1.03012	−0.515062	+	0.857153i	$0.672231\pi$
$978$	1.34998	0.0431676
$979$	25.4327	0.812833
$980$	3.61587	0.115505
$981$	10.2634	0.327686
$982$	12.0740	0.385298
$983$	−41.5777	−1.32612	−0.663061	−	0.748565i	$-0.730743\pi$
$983$	−41.5777	−1.32612	−0.663061	+	0.748565i	$0.730743\pi$
$984$	23.7596	0.757430
$985$	18.2114	0.580264
$986$	−10.4471	−0.332704
$987$	3.77376	0.120120
$988$	7.27358	0.231403
$989$	−1.31403	−0.0417836
$990$	−2.48504	−0.0789798
$991$	0.0847971	0.00269367	0.00134683	−	0.999999i	$-0.499571\pi$
$991$	0.0847971	0.00269367	0.00134683	+	0.999999i	$0.499571\pi$
$992$	6.08369	0.193157
$993$	−6.06232	−0.192382
$994$	−4.67544	−0.148296
$995$	16.0922	0.510158
$996$	−5.64099	−0.178742
$997$	−8.21798	−0.260266	−0.130133	−	0.991497i	$-0.541540\pi$
$997$	−8.21798	−0.260266	−0.130133	+	0.991497i	$0.541540\pi$
$998$	36.9269	1.16890
$999$	7.01206	0.221852

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.h.1.36	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.h.1.36	✓	56	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)

\(f(q)\)	\(=\)	\(q+1.15210 q^{2} +1.00000 q^{3} -0.672658 q^{4} +0.848798 q^{5} +1.15210 q^{6} +0.816661 q^{7} -3.07918 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.15210 q^{2} +1.00000 q^{3} -0.672658 q^{4} +0.848798 q^{5} +1.15210 q^{6} +0.816661 q^{7} -3.07918 q^{8} +1.00000 q^{9} +0.977904 q^{10} -2.54119 q^{11} -0.672658 q^{12} -3.28811 q^{13} +0.940878 q^{14} +0.848798 q^{15} -2.20222 q^{16} -1.00000 q^{17} +1.15210 q^{18} +3.28857 q^{19} -0.570951 q^{20} +0.816661 q^{21} -2.92772 q^{22} +1.55996 q^{23} -3.07918 q^{24} -4.27954 q^{25} -3.78824 q^{26} +1.00000 q^{27} -0.549334 q^{28} +9.06787 q^{29} +0.977904 q^{30} +1.68003 q^{31} +3.62118 q^{32} -2.54119 q^{33} -1.15210 q^{34} +0.693181 q^{35} -0.672658 q^{36} +7.01206 q^{37} +3.78878 q^{38} -3.28811 q^{39} -2.61360 q^{40} -7.71623 q^{41} +0.940878 q^{42} -0.842345 q^{43} +1.70935 q^{44} +0.848798 q^{45} +1.79724 q^{46} +4.62097 q^{47} -2.20222 q^{48} -6.33306 q^{49} -4.93047 q^{50} -1.00000 q^{51} +2.21177 q^{52} +9.47955 q^{53} +1.15210 q^{54} -2.15696 q^{55} -2.51465 q^{56} +3.28857 q^{57} +10.4471 q^{58} -4.79385 q^{59} -0.570951 q^{60} +4.88358 q^{61} +1.93557 q^{62} +0.816661 q^{63} +8.57640 q^{64} -2.79094 q^{65} -2.92772 q^{66} +13.3656 q^{67} +0.672658 q^{68} +1.55996 q^{69} +0.798616 q^{70} -4.96923 q^{71} -3.07918 q^{72} +12.5207 q^{73} +8.07862 q^{74} -4.27954 q^{75} -2.21208 q^{76} -2.07529 q^{77} -3.78824 q^{78} +8.83158 q^{79} -1.86924 q^{80} +1.00000 q^{81} -8.88989 q^{82} +8.38612 q^{83} -0.549334 q^{84} -0.848798 q^{85} -0.970469 q^{86} +9.06787 q^{87} +7.82479 q^{88} -10.0082 q^{89} +0.977904 q^{90} -2.68527 q^{91} -1.04932 q^{92} +1.68003 q^{93} +5.32383 q^{94} +2.79134 q^{95} +3.62118 q^{96} -10.7893 q^{97} -7.29635 q^{98} -2.54119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

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