LMFDB - Embedded newform 8007.2.a.g.1.7

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			1.7
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36108 q^{2} -1.00000 q^{3} +3.57471 q^{4} +4.34691 q^{5} +2.36108 q^{6} -0.239132 q^{7} -3.71802 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.36108 q^{2} -1.00000 q^{3} +3.57471 q^{4} +4.34691 q^{5} +2.36108 q^{6} -0.239132 q^{7} -3.71802 q^{8} +1.00000 q^{9} -10.2634 q^{10} -4.29376 q^{11} -3.57471 q^{12} -2.72772 q^{13} +0.564611 q^{14} -4.34691 q^{15} +1.62912 q^{16} -1.00000 q^{17} -2.36108 q^{18} -0.558873 q^{19} +15.5389 q^{20} +0.239132 q^{21} +10.1379 q^{22} +2.65463 q^{23} +3.71802 q^{24} +13.8956 q^{25} +6.44036 q^{26} -1.00000 q^{27} -0.854829 q^{28} +5.97258 q^{29} +10.2634 q^{30} +4.82570 q^{31} +3.58954 q^{32} +4.29376 q^{33} +2.36108 q^{34} -1.03949 q^{35} +3.57471 q^{36} +10.0820 q^{37} +1.31954 q^{38} +2.72772 q^{39} -16.1619 q^{40} +3.97167 q^{41} -0.564611 q^{42} -7.12244 q^{43} -15.3489 q^{44} +4.34691 q^{45} -6.26780 q^{46} -2.80084 q^{47} -1.62912 q^{48} -6.94282 q^{49} -32.8086 q^{50} +1.00000 q^{51} -9.75079 q^{52} +1.71862 q^{53} +2.36108 q^{54} -18.6646 q^{55} +0.889098 q^{56} +0.558873 q^{57} -14.1017 q^{58} -2.11577 q^{59} -15.5389 q^{60} -1.44266 q^{61} -11.3939 q^{62} -0.239132 q^{63} -11.7334 q^{64} -11.8571 q^{65} -10.1379 q^{66} +10.5560 q^{67} -3.57471 q^{68} -2.65463 q^{69} +2.45431 q^{70} +15.0221 q^{71} -3.71802 q^{72} +13.2860 q^{73} -23.8045 q^{74} -13.8956 q^{75} -1.99781 q^{76} +1.02678 q^{77} -6.44036 q^{78} -17.3773 q^{79} +7.08164 q^{80} +1.00000 q^{81} -9.37745 q^{82} -15.7988 q^{83} +0.854829 q^{84} -4.34691 q^{85} +16.8167 q^{86} -5.97258 q^{87} +15.9643 q^{88} -3.58085 q^{89} -10.2634 q^{90} +0.652286 q^{91} +9.48953 q^{92} -4.82570 q^{93} +6.61302 q^{94} -2.42937 q^{95} -3.58954 q^{96} +9.93045 q^{97} +16.3926 q^{98} -4.29376 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) $ 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.36108	−1.66954	−0.834769	−	0.550601i	$-0.814399\pi$
$2$	−2.36108	−1.66954	−0.834769	+	0.550601i	$0.814399\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.57471	1.78735
$5$	4.34691	1.94400	0.971998	−	0.234991i	$-0.0755060\pi$
$5$	4.34691	1.94400	0.971998	+	0.234991i	$0.0755060\pi$
$6$	2.36108	0.963908
$7$	−0.239132	−0.0903835	−0.0451918	−	0.998978i	$-0.514390\pi$
$7$	−0.239132	−0.0903835	−0.0451918	+	0.998978i	$0.514390\pi$
$8$	−3.71802	−1.31452
$9$	1.00000	0.333333
$10$	−10.2634	−3.24557
$11$	−4.29376	−1.29462	−0.647309	−	0.762228i	$-0.724106\pi$
$11$	−4.29376	−1.29462	−0.647309	+	0.762228i	$0.724106\pi$
$12$	−3.57471	−1.03193
$13$	−2.72772	−0.756533	−0.378266	−	0.925697i	$-0.623480\pi$
$13$	−2.72772	−0.756533	−0.378266	+	0.925697i	$0.623480\pi$
$14$	0.564611	0.150899
$15$	−4.34691	−1.12237
$16$	1.62912	0.407281
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.36108	−0.556512
$19$	−0.558873	−0.128214	−0.0641071	−	0.997943i	$-0.520420\pi$
$19$	−0.558873	−0.128214	−0.0641071	+	0.997943i	$0.520420\pi$
$20$	15.5389	3.47461
$21$	0.239132	0.0521830
$22$	10.1379	2.16141
$23$	2.65463	0.553529	0.276764	−	0.960938i	$-0.410738\pi$
$23$	2.65463	0.553529	0.276764	+	0.960938i	$0.410738\pi$
$24$	3.71802	0.758937
$25$	13.8956	2.77912
$26$	6.44036	1.26306
$27$	−1.00000	−0.192450
$28$	−0.854829	−0.161547
$29$	5.97258	1.10908	0.554540	−	0.832157i	$-0.312894\pi$
$29$	5.97258	1.10908	0.554540	+	0.832157i	$0.312894\pi$
$30$	10.2634	1.87383
$31$	4.82570	0.866721	0.433361	−	0.901221i	$-0.357328\pi$
$31$	4.82570	0.866721	0.433361	+	0.901221i	$0.357328\pi$
$32$	3.58954	0.634547
$33$	4.29376	0.747448
$34$	2.36108	0.404922
$35$	−1.03949	−0.175705
$36$	3.57471	0.595785
$37$	10.0820	1.65747	0.828737	−	0.559638i	$-0.189060\pi$
$37$	10.0820	1.65747	0.828737	+	0.559638i	$0.189060\pi$
$38$	1.31954	0.214058
$39$	2.72772	0.436784
$40$	−16.1619	−2.55541
$41$	3.97167	0.620271	0.310136	−	0.950692i	$-0.399626\pi$
$41$	3.97167	0.620271	0.310136	+	0.950692i	$0.399626\pi$
$42$	−0.564611	−0.0871214
$43$	−7.12244	−1.08616	−0.543081	−	0.839680i	$-0.682742\pi$
$43$	−7.12244	−1.08616	−0.543081	+	0.839680i	$0.682742\pi$
$44$	−15.3489	−2.31394
$45$	4.34691	0.647998
$46$	−6.26780	−0.924137
$47$	−2.80084	−0.408545	−0.204273	−	0.978914i	$-0.565483\pi$
$47$	−2.80084	−0.408545	−0.204273	+	0.978914i	$0.565483\pi$
$48$	−1.62912	−0.235144
$49$	−6.94282	−0.991831
$50$	−32.8086	−4.63984
$51$	1.00000	0.140028
$52$	−9.75079	−1.35219
$53$	1.71862	0.236070	0.118035	−	0.993009i	$-0.462340\pi$
$53$	1.71862	0.236070	0.118035	+	0.993009i	$0.462340\pi$
$54$	2.36108	0.321303
$55$	−18.6646	−2.51673
$56$	0.889098	0.118811
$57$	0.558873	0.0740245
$58$	−14.1017	−1.85165
$59$	−2.11577	−0.275449	−0.137725	−	0.990471i	$-0.543979\pi$
$59$	−2.11577	−0.275449	−0.137725	+	0.990471i	$0.543979\pi$
$60$	−15.5389	−2.00607
$61$	−1.44266	−0.184714	−0.0923569	−	0.995726i	$-0.529440\pi$
$61$	−1.44266	−0.184714	−0.0923569	+	0.995726i	$0.529440\pi$
$62$	−11.3939	−1.44702
$63$	−0.239132	−0.0301278
$64$	−11.7334	−1.46668
$65$	−11.8571	−1.47070
$66$	−10.1379	−1.24789
$67$	10.5560	1.28963	0.644813	−	0.764340i	$-0.276935\pi$
$67$	10.5560	1.28963	0.644813	+	0.764340i	$0.276935\pi$
$68$	−3.57471	−0.433497
$69$	−2.65463	−0.319580
$70$	2.45431	0.293346
$71$	15.0221	1.78280	0.891401	−	0.453216i	$-0.149724\pi$
$71$	15.0221	1.78280	0.891401	+	0.453216i	$0.149724\pi$
$72$	−3.71802	−0.438172
$73$	13.2860	1.55501	0.777507	−	0.628874i	$-0.216484\pi$
$73$	13.2860	1.55501	0.777507	+	0.628874i	$0.216484\pi$
$74$	−23.8045	−2.76722
$75$	−13.8956	−1.60452
$76$	−1.99781	−0.229164
$77$	1.02678	0.117012
$78$	−6.44036	−0.729228
$79$	−17.3773	−1.95510	−0.977549	−	0.210709i	$-0.932423\pi$
$79$	−17.3773	−1.95510	−0.977549	+	0.210709i	$0.932423\pi$
$80$	7.08164	0.791752
$81$	1.00000	0.111111
$82$	−9.37745	−1.03557
$83$	−15.7988	−1.73414	−0.867072	−	0.498182i	$-0.834001\pi$
$83$	−15.7988	−1.73414	−0.867072	+	0.498182i	$0.834001\pi$
$84$	0.854829	0.0932694
$85$	−4.34691	−0.471488
$86$	16.8167	1.81339
$87$	−5.97258	−0.640327
$88$	15.9643	1.70180
$89$	−3.58085	−0.379569	−0.189785	−	0.981826i	$-0.560779\pi$
$89$	−3.58085	−0.379569	−0.189785	+	0.981826i	$0.560779\pi$
$90$	−10.2634	−1.08186
$91$	0.652286	0.0683781
$92$	9.48953	0.989352
$93$	−4.82570	−0.500402
$94$	6.61302	0.682081
$95$	−2.42937	−0.249248
$96$	−3.58954	−0.366356
$97$	9.93045	1.00828	0.504142	−	0.863621i	$-0.331809\pi$
$97$	9.93045	1.00828	0.504142	+	0.863621i	$0.331809\pi$
$98$	16.3926	1.65590
$99$	−4.29376	−0.431539
$100$	49.6727	4.96727
$101$	13.2773	1.32114	0.660570	−	0.750764i	$-0.270315\pi$
$101$	13.2773	1.32114	0.660570	+	0.750764i	$0.270315\pi$
$102$	−2.36108	−0.233782
$103$	5.88732	0.580095	0.290047	−	0.957012i	$-0.406329\pi$
$103$	5.88732	0.580095	0.290047	+	0.957012i	$0.406329\pi$
$104$	10.1417	0.994475
$105$	1.03949	0.101443
$106$	−4.05780	−0.394128
$107$	−8.75477	−0.846356	−0.423178	−	0.906047i	$-0.639085\pi$
$107$	−8.75477	−0.846356	−0.423178	+	0.906047i	$0.639085\pi$
$108$	−3.57471	−0.343976
$109$	−18.7043	−1.79154	−0.895771	−	0.444515i	$-0.853376\pi$
$109$	−18.7043	−1.79154	−0.895771	+	0.444515i	$0.853376\pi$
$110$	44.0686	4.20177
$111$	−10.0820	−0.956944
$112$	−0.389576	−0.0368115
$113$	−17.0792	−1.60668	−0.803340	−	0.595521i	$-0.796946\pi$
$113$	−17.0792	−1.60668	−0.803340	+	0.595521i	$0.796946\pi$
$114$	−1.31954	−0.123587
$115$	11.5394	1.07606
$116$	21.3502	1.98232
$117$	−2.72772	−0.252178
$118$	4.99549	0.459873
$119$	0.239132	0.0219212
$120$	16.1619	1.47537
$121$	7.43637	0.676034
$122$	3.40624	0.308387
$123$	−3.97167	−0.358114
$124$	17.2505	1.54914
$125$	38.6683	3.45860
$126$	0.564611	0.0502996
$127$	5.59833	0.496772	0.248386	−	0.968661i	$-0.420100\pi$
$127$	5.59833	0.496772	0.248386	+	0.968661i	$0.420100\pi$
$128$	20.5245	1.81413
$129$	7.12244	0.627096
$130$	27.9957	2.45538
$131$	−0.225417	−0.0196948	−0.00984741	−	0.999952i	$-0.503135\pi$
$131$	−0.225417	−0.0196948	−0.00984741	+	0.999952i	$0.503135\pi$
$132$	15.3489	1.33595
$133$	0.133645	0.0115885
$134$	−24.9237	−2.15308
$135$	−4.34691	−0.374122
$136$	3.71802	0.318817
$137$	12.1855	1.04108	0.520540	−	0.853838i	$-0.325731\pi$
$137$	12.1855	1.04108	0.520540	+	0.853838i	$0.325731\pi$
$138$	6.26780	0.533551
$139$	12.2898	1.04241	0.521204	−	0.853432i	$-0.325483\pi$
$139$	12.2898	1.04241	0.521204	+	0.853432i	$0.325483\pi$
$140$	−3.71586	−0.314047
$141$	2.80084	0.235874
$142$	−35.4685	−2.97645
$143$	11.7122	0.979420
$144$	1.62912	0.135760
$145$	25.9622	2.15605
$146$	−31.3694	−2.59615
$147$	6.94282	0.572634
$148$	36.0403	2.96249
$149$	−6.45616	−0.528910	−0.264455	−	0.964398i	$-0.585192\pi$
$149$	−6.45616	−0.528910	−0.264455	+	0.964398i	$0.585192\pi$
$150$	32.8086	2.67881
$151$	−6.83320	−0.556078	−0.278039	−	0.960570i	$-0.589684\pi$
$151$	−6.83320	−0.556078	−0.278039	+	0.960570i	$0.589684\pi$
$152$	2.07790	0.168540
$153$	−1.00000	−0.0808452
$154$	−2.42430	−0.195356
$155$	20.9769	1.68490
$156$	9.75079	0.780688
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	41.0292	3.26411
$159$	−1.71862	−0.136295
$160$	15.6034	1.23356
$161$	−0.634808	−0.0500299
$162$	−2.36108	−0.185504
$163$	10.9751	0.859633	0.429816	−	0.902916i	$-0.358578\pi$
$163$	10.9751	0.859633	0.429816	+	0.902916i	$0.358578\pi$
$164$	14.1976	1.10864
$165$	18.6646	1.45303
$166$	37.3023	2.89522
$167$	−18.9833	−1.46897	−0.734487	−	0.678623i	$-0.762577\pi$
$167$	−18.9833	−1.46897	−0.734487	+	0.678623i	$0.762577\pi$
$168$	−0.889098	−0.0685954
$169$	−5.55956	−0.427658
$170$	10.2634	0.787167
$171$	−0.558873	−0.0427381
$172$	−25.4607	−1.94136
$173$	−8.69719	−0.661235	−0.330617	−	0.943765i	$-0.607257\pi$
$173$	−8.69719	−0.661235	−0.330617	+	0.943765i	$0.607257\pi$
$174$	14.1017	1.06905
$175$	−3.32288	−0.251186
$176$	−6.99506	−0.527273
$177$	2.11577	0.159031
$178$	8.45467	0.633705
$179$	−13.0370	−0.974434	−0.487217	−	0.873281i	$-0.661988\pi$
$179$	−13.0370	−0.974434	−0.487217	+	0.873281i	$0.661988\pi$
$180$	15.5389	1.15820
$181$	5.90900	0.439212	0.219606	−	0.975589i	$-0.429523\pi$
$181$	5.90900	0.439212	0.219606	+	0.975589i	$0.429523\pi$
$182$	−1.54010	−0.114160
$183$	1.44266	0.106645
$184$	−9.86996	−0.727623
$185$	43.8256	3.22212
$186$	11.3939	0.835439
$187$	4.29376	0.313991
$188$	−10.0122	−0.730215
$189$	0.239132	0.0173943
$190$	5.73594	0.416129
$191$	−19.2275	−1.39125	−0.695627	−	0.718403i	$-0.744873\pi$
$191$	−19.2275	−1.39125	−0.695627	+	0.718403i	$0.744873\pi$
$192$	11.7334	0.846788
$193$	2.61911	0.188528	0.0942640	−	0.995547i	$-0.469950\pi$
$193$	2.61911	0.188528	0.0942640	+	0.995547i	$0.469950\pi$
$194$	−23.4466	−1.68337
$195$	11.8571	0.849107
$196$	−24.8185	−1.77275
$197$	−18.7336	−1.33471	−0.667356	−	0.744739i	$-0.732574\pi$
$197$	−18.7336	−1.33471	−0.667356	+	0.744739i	$0.732574\pi$
$198$	10.1379	0.720471
$199$	−5.84406	−0.414275	−0.207137	−	0.978312i	$-0.566415\pi$
$199$	−5.84406	−0.414275	−0.207137	+	0.978312i	$0.566415\pi$
$200$	−51.6640	−3.65320
$201$	−10.5560	−0.744566
$202$	−31.3488	−2.20569
$203$	−1.42824	−0.100243
$204$	3.57471	0.250280
$205$	17.2645	1.20580
$206$	−13.9004	−0.968490
$207$	2.65463	0.184510
$208$	−4.44379	−0.308121
$209$	2.39967	0.165988
$210$	−2.45431	−0.169364
$211$	8.18565	0.563523	0.281762	−	0.959484i	$-0.409081\pi$
$211$	8.18565	0.563523	0.281762	+	0.959484i	$0.409081\pi$
$212$	6.14356	0.421941
$213$	−15.0221	−1.02930
$214$	20.6707	1.41302
$215$	−30.9606	−2.11149
$216$	3.71802	0.252979
$217$	−1.15398	−0.0783373
$218$	44.1623	2.99105
$219$	−13.2860	−0.897788
$220$	−66.7204	−4.49829
$221$	2.72772	0.183486
$222$	23.8045	1.59765
$223$	8.53078	0.571263	0.285632	−	0.958339i	$-0.407797\pi$
$223$	8.53078	0.571263	0.285632	+	0.958339i	$0.407797\pi$
$224$	−0.858375	−0.0573526
$225$	13.8956	0.926372
$226$	40.3255	2.68241
$227$	20.5611	1.36469	0.682345	−	0.731030i	$-0.260960\pi$
$227$	20.5611	1.36469	0.682345	+	0.731030i	$0.260960\pi$
$228$	1.99781	0.132308
$229$	21.5999	1.42736	0.713679	−	0.700472i	$-0.247027\pi$
$229$	21.5999	1.42736	0.713679	+	0.700472i	$0.247027\pi$
$230$	−27.2455	−1.79652
$231$	−1.02678	−0.0675570
$232$	−22.2061	−1.45790
$233$	−14.9035	−0.976362	−0.488181	−	0.872742i	$-0.662339\pi$
$233$	−14.9035	−0.976362	−0.488181	+	0.872742i	$0.662339\pi$
$234$	6.44036	0.421020
$235$	−12.1750	−0.794210
$236$	−7.56324	−0.492325
$237$	17.3773	1.12878
$238$	−0.564611	−0.0365983
$239$	29.1491	1.88550	0.942750	−	0.333500i	$-0.108230\pi$
$239$	29.1491	1.88550	0.942750	+	0.333500i	$0.108230\pi$
$240$	−7.08164	−0.457118
$241$	23.2353	1.49672	0.748358	−	0.663295i	$-0.230842\pi$
$241$	23.2353	1.49672	0.748358	+	0.663295i	$0.230842\pi$
$242$	−17.5579	−1.12866
$243$	−1.00000	−0.0641500
$244$	−5.15709	−0.330149
$245$	−30.1798	−1.92811
$246$	9.37745	0.597884
$247$	1.52445	0.0969983
$248$	−17.9420	−1.13932
$249$	15.7988	1.00121
$250$	−91.2990	−5.77425
$251$	−21.3881	−1.35000	−0.675002	−	0.737816i	$-0.735857\pi$
$251$	−21.3881	−1.35000	−0.675002	+	0.737816i	$0.735857\pi$
$252$	−0.854829	−0.0538491
$253$	−11.3983	−0.716608
$254$	−13.2181	−0.829379
$255$	4.34691	0.272214
$256$	−24.9932	−1.56208
$257$	−17.8369	−1.11264	−0.556319	−	0.830969i	$-0.687787\pi$
$257$	−17.8369	−1.11264	−0.556319	+	0.830969i	$0.687787\pi$
$258$	−16.8167	−1.04696
$259$	−2.41094	−0.149808
$260$	−42.3858	−2.62865
$261$	5.97258	0.369693
$262$	0.532229	0.0328812
$263$	30.6048	1.88718	0.943588	−	0.331122i	$-0.107427\pi$
$263$	30.6048	1.88718	0.943588	+	0.331122i	$0.107427\pi$
$264$	−15.9643	−0.982533
$265$	7.47067	0.458920
$266$	−0.315546	−0.0193474
$267$	3.58085	0.219144
$268$	37.7348	2.30502
$269$	−4.17373	−0.254477	−0.127238	−	0.991872i	$-0.540611\pi$
$269$	−4.17373	−0.254477	−0.127238	+	0.991872i	$0.540611\pi$
$270$	10.2634	0.624611
$271$	8.22291	0.499506	0.249753	−	0.968310i	$-0.419651\pi$
$271$	8.22291	0.499506	0.249753	+	0.968310i	$0.419651\pi$
$272$	−1.62912	−0.0987801
$273$	−0.652286	−0.0394781
$274$	−28.7710	−1.73812
$275$	−59.6643	−3.59789
$276$	−9.48953	−0.571203
$277$	2.24584	0.134940	0.0674698	−	0.997721i	$-0.478507\pi$
$277$	2.24584	0.134940	0.0674698	+	0.997721i	$0.478507\pi$
$278$	−29.0173	−1.74034
$279$	4.82570	0.288907
$280$	3.86482	0.230967
$281$	26.9942	1.61034	0.805169	−	0.593046i	$-0.202075\pi$
$281$	26.9942	1.61034	0.805169	+	0.593046i	$0.202075\pi$
$282$	−6.61302	−0.393800
$283$	−11.0508	−0.656902	−0.328451	−	0.944521i	$-0.606527\pi$
$283$	−11.0508	−0.656902	−0.328451	+	0.944521i	$0.606527\pi$
$284$	53.6998	3.18650
$285$	2.42937	0.143903
$286$	−27.6534	−1.63518
$287$	−0.949756	−0.0560623
$288$	3.58954	0.211516
$289$	1.00000	0.0588235
$290$	−61.2989	−3.59960
$291$	−9.93045	−0.582133
$292$	47.4937	2.77936
$293$	12.5607	0.733806	0.366903	−	0.930259i	$-0.380418\pi$
$293$	12.5607	0.733806	0.366903	+	0.930259i	$0.380418\pi$
$294$	−16.3926	−0.956033
$295$	−9.19703	−0.535472
$296$	−37.4851	−2.17878
$297$	4.29376	0.249149
$298$	15.2435	0.883034
$299$	−7.24108	−0.418763
$300$	−49.6727	−2.86785
$301$	1.70321	0.0981712
$302$	16.1337	0.928392
$303$	−13.2773	−0.762761
$304$	−0.910472	−0.0522192
$305$	−6.27111	−0.359083
$306$	2.36108	0.134974
$307$	25.1925	1.43781	0.718906	−	0.695107i	$-0.244643\pi$
$307$	25.1925	1.43781	0.718906	+	0.695107i	$0.244643\pi$
$308$	3.67043	0.209142
$309$	−5.88732	−0.334918
$310$	−49.5281	−2.81301
$311$	−24.5619	−1.39278	−0.696390	−	0.717663i	$-0.745212\pi$
$311$	−24.5619	−1.39278	−0.696390	+	0.717663i	$0.745212\pi$
$312$	−10.1417	−0.574160
$313$	13.1599	0.743843	0.371921	−	0.928264i	$-0.378699\pi$
$313$	13.1599	0.743843	0.371921	+	0.928264i	$0.378699\pi$
$314$	−2.36108	−0.133244
$315$	−1.03949	−0.0585684
$316$	−62.1187	−3.49445
$317$	12.5489	0.704815	0.352408	−	0.935847i	$-0.385363\pi$
$317$	12.5489	0.704815	0.352408	+	0.935847i	$0.385363\pi$
$318$	4.05780	0.227550
$319$	−25.6448	−1.43583
$320$	−51.0042	−2.85122
$321$	8.75477	0.488644
$322$	1.49883	0.0835268
$323$	0.558873	0.0310965
$324$	3.57471	0.198595
$325$	−37.9032	−2.10249
$326$	−25.9130	−1.43519
$327$	18.7043	1.03435
$328$	−14.7667	−0.815357
$329$	0.669773	0.0369258
$330$	−44.0686	−2.42590
$331$	23.8446	1.31062	0.655310	−	0.755360i	$-0.272538\pi$
$331$	23.8446	1.31062	0.655310	+	0.755360i	$0.272538\pi$
$332$	−56.4761	−3.09953
$333$	10.0820	0.552492
$334$	44.8212	2.45250
$335$	45.8861	2.50703
$336$	0.389576	0.0212531
$337$	−5.79654	−0.315758	−0.157879	−	0.987458i	$-0.550466\pi$
$337$	−5.79654	−0.315758	−0.157879	+	0.987458i	$0.550466\pi$
$338$	13.1266	0.713991
$339$	17.0792	0.927617
$340$	−15.5389	−0.842716
$341$	−20.7204	−1.12207
$342$	1.31954	0.0713528
$343$	3.33418	0.180029
$344$	26.4814	1.42778
$345$	−11.5394	−0.621262
$346$	20.5348	1.10396
$347$	−9.82793	−0.527591	−0.263795	−	0.964579i	$-0.584974\pi$
$347$	−9.82793	−0.527591	−0.263795	+	0.964579i	$0.584974\pi$
$348$	−21.3502	−1.14449
$349$	−4.59284	−0.245849	−0.122925	−	0.992416i	$-0.539227\pi$
$349$	−4.59284	−0.245849	−0.122925	+	0.992416i	$0.539227\pi$
$350$	7.84560	0.419365
$351$	2.72772	0.145595
$352$	−15.4126	−0.821495
$353$	27.1082	1.44282	0.721412	−	0.692506i	$-0.243494\pi$
$353$	27.1082	1.44282	0.721412	+	0.692506i	$0.243494\pi$
$354$	−4.99549	−0.265508
$355$	65.2999	3.46576
$356$	−12.8005	−0.678424
$357$	−0.239132	−0.0126562
$358$	30.7815	1.62685
$359$	32.1725	1.69800	0.849000	−	0.528393i	$-0.177205\pi$
$359$	32.1725	1.69800	0.849000	+	0.528393i	$0.177205\pi$
$360$	−16.1619	−0.851805
$361$	−18.6877	−0.983561
$362$	−13.9516	−0.733281
$363$	−7.43637	−0.390308
$364$	2.33173	0.122216
$365$	57.7532	3.02294
$366$	−3.40624	−0.178047
$367$	29.1230	1.52021	0.760103	−	0.649803i	$-0.225148\pi$
$367$	29.1230	1.52021	0.760103	+	0.649803i	$0.225148\pi$
$368$	4.32472	0.225442
$369$	3.97167	0.206757
$370$	−103.476	−5.37945
$371$	−0.410977	−0.0213369
$372$	−17.2505	−0.894395
$373$	3.10973	0.161016	0.0805078	−	0.996754i	$-0.474346\pi$
$373$	3.10973	0.161016	0.0805078	+	0.996754i	$0.474346\pi$
$374$	−10.1379	−0.524219
$375$	−38.6683	−1.99682
$376$	10.4136	0.537040
$377$	−16.2915	−0.839055
$378$	−0.564611	−0.0290405
$379$	−29.7419	−1.52774	−0.763868	−	0.645372i	$-0.776702\pi$
$379$	−29.7419	−1.52774	−0.763868	+	0.645372i	$0.776702\pi$
$380$	−8.68428	−0.445494
$381$	−5.59833	−0.286811
$382$	45.3977	2.32275
$383$	15.7433	0.804443	0.402222	−	0.915542i	$-0.368238\pi$
$383$	15.7433	0.804443	0.402222	+	0.915542i	$0.368238\pi$
$384$	−20.5245	−1.04739
$385$	4.46330	0.227471
$386$	−6.18394	−0.314754
$387$	−7.12244	−0.362054
$388$	35.4984	1.80216
$389$	8.68107	0.440148	0.220074	−	0.975483i	$-0.429370\pi$
$389$	8.68107	0.440148	0.220074	+	0.975483i	$0.429370\pi$
$390$	−27.9957	−1.41762
$391$	−2.65463	−0.134250
$392$	25.8135	1.30378
$393$	0.225417	0.0113708
$394$	44.2315	2.22835
$395$	−75.5374	−3.80070
$396$	−15.3489	−0.771313
$397$	38.9186	1.95327	0.976633	−	0.214914i	$-0.0689470\pi$
$397$	38.9186	1.95327	0.976633	+	0.214914i	$0.0689470\pi$
$398$	13.7983	0.691647
$399$	−0.133645	−0.00669060
$400$	22.6376	1.13188
$401$	−29.3930	−1.46782	−0.733908	−	0.679249i	$-0.762306\pi$
$401$	−29.3930	−1.46782	−0.733908	+	0.679249i	$0.762306\pi$
$402$	24.9237	1.24308
$403$	−13.1631	−0.655703
$404$	47.4625	2.36135
$405$	4.34691	0.215999
$406$	3.37218	0.167359
$407$	−43.2898	−2.14580
$408$	−3.71802	−0.184069
$409$	29.4105	1.45426	0.727128	−	0.686502i	$-0.240855\pi$
$409$	29.4105	1.45426	0.727128	+	0.686502i	$0.240855\pi$
$410$	−40.7629	−2.01314
$411$	−12.1855	−0.601067
$412$	21.0454	1.03683
$413$	0.505948	0.0248961
$414$	−6.26780	−0.308046
$415$	−68.6759	−3.37117
$416$	−9.79125	−0.480055
$417$	−12.2898	−0.601835
$418$	−5.66581	−0.277124
$419$	−2.08284	−0.101753	−0.0508766	−	0.998705i	$-0.516202\pi$
$419$	−2.08284	−0.101753	−0.0508766	+	0.998705i	$0.516202\pi$
$420$	3.71586	0.181315
$421$	33.1287	1.61459	0.807296	−	0.590146i	$-0.200930\pi$
$421$	33.1287	1.61459	0.807296	+	0.590146i	$0.200930\pi$
$422$	−19.3270	−0.940823
$423$	−2.80084	−0.136182
$424$	−6.38985	−0.310318
$425$	−13.8956	−0.674035
$426$	35.4685	1.71846
$427$	0.344987	0.0166951
$428$	−31.2958	−1.51274
$429$	−11.7122	−0.565469
$430$	73.1005	3.52522
$431$	−32.0274	−1.54271	−0.771353	−	0.636407i	$-0.780420\pi$
$431$	−32.0274	−1.54271	−0.771353	+	0.636407i	$0.780420\pi$
$432$	−1.62912	−0.0783812
$433$	11.5441	0.554773	0.277387	−	0.960758i	$-0.410532\pi$
$433$	11.5441	0.554773	0.277387	+	0.960758i	$0.410532\pi$
$434$	2.72464	0.130787
$435$	−25.9622	−1.24479
$436$	−66.8623	−3.20212
$437$	−1.48360	−0.0709703
$438$	31.3694	1.49889
$439$	34.2145	1.63297	0.816486	−	0.577366i	$-0.195919\pi$
$439$	34.2145	1.63297	0.816486	+	0.577366i	$0.195919\pi$
$440$	69.3952	3.30828
$441$	−6.94282	−0.330610
$442$	−6.44036	−0.306337
$443$	14.3421	0.681413	0.340707	−	0.940170i	$-0.389334\pi$
$443$	14.3421	0.681413	0.340707	+	0.940170i	$0.389334\pi$
$444$	−36.0403	−1.71040
$445$	−15.5656	−0.737880
$446$	−20.1419	−0.953745
$447$	6.45616	0.305366
$448$	2.80585	0.132564
$449$	−40.6583	−1.91878	−0.959392	−	0.282076i	$-0.908977\pi$
$449$	−40.6583	−1.91878	−0.959392	+	0.282076i	$0.908977\pi$
$450$	−32.8086	−1.54661
$451$	−17.0534	−0.803014
$452$	−61.0533	−2.87171
$453$	6.83320	0.321052
$454$	−48.5465	−2.27840
$455$	2.83542	0.132927
$456$	−2.07790	−0.0973065
$457$	14.6616	0.685839	0.342919	−	0.939365i	$-0.388584\pi$
$457$	14.6616	0.685839	0.342919	+	0.939365i	$0.388584\pi$
$458$	−50.9990	−2.38303
$459$	1.00000	0.0466760
$460$	41.2501	1.92330
$461$	32.9775	1.53591	0.767957	−	0.640501i	$-0.221273\pi$
$461$	32.9775	1.53591	0.767957	+	0.640501i	$0.221273\pi$
$462$	2.42430	0.112789
$463$	32.8403	1.52622	0.763108	−	0.646270i	$-0.223672\pi$
$463$	32.8403	1.52622	0.763108	+	0.646270i	$0.223672\pi$
$464$	9.73006	0.451707
$465$	−20.9769	−0.972778
$466$	35.1884	1.63007
$467$	42.2274	1.95405	0.977025	−	0.213124i	$-0.0683639\pi$
$467$	42.2274	1.95405	0.977025	+	0.213124i	$0.0683639\pi$
$468$	−9.75079	−0.450731
$469$	−2.52429	−0.116561
$470$	28.7462	1.32596
$471$	−1.00000	−0.0460776
$472$	7.86645	0.362083
$473$	30.5821	1.40616
$474$	−41.0292	−1.88453
$475$	−7.76587	−0.356322
$476$	0.854829	0.0391810
$477$	1.71862	0.0786901
$478$	−68.8235	−3.14791
$479$	−39.5310	−1.80622	−0.903108	−	0.429413i	$-0.858721\pi$
$479$	−39.5310	−1.80622	−0.903108	+	0.429413i	$0.858721\pi$
$480$	−15.6034	−0.712194
$481$	−27.5009	−1.25393
$482$	−54.8604	−2.49882
$483$	0.634808	0.0288848
$484$	26.5829	1.20831
$485$	43.1667	1.96010
$486$	2.36108	0.107101
$487$	18.4553	0.836287	0.418144	−	0.908381i	$-0.362681\pi$
$487$	18.4553	0.836287	0.418144	+	0.908381i	$0.362681\pi$
$488$	5.36384	0.242809
$489$	−10.9751	−0.496309
$490$	71.2569	3.21906
$491$	−28.6553	−1.29320	−0.646599	−	0.762830i	$-0.723809\pi$
$491$	−28.6553	−1.29320	−0.646599	+	0.762830i	$0.723809\pi$
$492$	−14.1976	−0.640076
$493$	−5.97258	−0.268991
$494$	−3.59934	−0.161942
$495$	−18.6646	−0.838910
$496$	7.86165	0.352999
$497$	−3.59228	−0.161136
$498$	−37.3023	−1.67156
$499$	12.2309	0.547531	0.273766	−	0.961796i	$-0.411731\pi$
$499$	12.2309	0.547531	0.273766	+	0.961796i	$0.411731\pi$
$500$	138.228	6.18174
$501$	18.9833	0.848112
$502$	50.4990	2.25388
$503$	−2.53088	−0.112846	−0.0564231	−	0.998407i	$-0.517970\pi$
$503$	−2.53088	−0.112846	−0.0564231	+	0.998407i	$0.517970\pi$
$504$	0.889098	0.0396036
$505$	57.7152	2.56829
$506$	26.9124	1.19640
$507$	5.55956	0.246909
$508$	20.0124	0.887907
$509$	−1.71224	−0.0758938	−0.0379469	−	0.999280i	$-0.512082\pi$
$509$	−1.71224	−0.0758938	−0.0379469	+	0.999280i	$0.512082\pi$
$510$	−10.2634	−0.454471
$511$	−3.17712	−0.140548
$512$	17.9620	0.793816
$513$	0.558873	0.0246748
$514$	42.1145	1.85759
$515$	25.5916	1.12770
$516$	25.4607	1.12084
$517$	12.0262	0.528910
$518$	5.69242	0.250111
$519$	8.69719	0.381764
$520$	44.0850	1.93325
$521$	−1.78373	−0.0781465	−0.0390733	−	0.999236i	$-0.512441\pi$
$521$	−1.78373	−0.0781465	−0.0390733	+	0.999236i	$0.512441\pi$
$522$	−14.1017	−0.617217
$523$	−20.9715	−0.917020	−0.458510	−	0.888689i	$-0.651617\pi$
$523$	−20.9715	−0.917020	−0.458510	+	0.888689i	$0.651617\pi$
$524$	−0.805802	−0.0352016
$525$	3.32288	0.145023
$526$	−72.2606	−3.15071
$527$	−4.82570	−0.210211
$528$	6.99506	0.304421
$529$	−15.9529	−0.693606
$530$	−17.6389	−0.766183
$531$	−2.11577	−0.0918164
$532$	0.477740	0.0207127
$533$	−10.8336	−0.469256
$534$	−8.45467	−0.365869
$535$	−38.0562	−1.64531
$536$	−39.2475	−1.69524
$537$	13.0370	0.562590
$538$	9.85451	0.424858
$539$	29.8108	1.28404
$540$	−15.5389	−0.668689
$541$	−36.2603	−1.55895	−0.779476	−	0.626433i	$-0.784514\pi$
$541$	−36.2603	−1.55895	−0.779476	+	0.626433i	$0.784514\pi$
$542$	−19.4150	−0.833944
$543$	−5.90900	−0.253579
$544$	−3.58954	−0.153900
$545$	−81.3056	−3.48275
$546$	1.54010	0.0659102
$547$	15.5266	0.663869	0.331935	−	0.943302i	$-0.392299\pi$
$547$	15.5266	0.663869	0.331935	+	0.943302i	$0.392299\pi$
$548$	43.5597	1.86078
$549$	−1.44266	−0.0615713
$550$	140.872	6.00682
$551$	−3.33791	−0.142200
$552$	9.86996	0.420093
$553$	4.15547	0.176709
$554$	−5.30262	−0.225287
$555$	−43.8256	−1.86029
$556$	43.9325	1.86315
$557$	−15.5911	−0.660615	−0.330307	−	0.943873i	$-0.607152\pi$
$557$	−15.5911	−0.660615	−0.330307	+	0.943873i	$0.607152\pi$
$558$	−11.3939	−0.482341
$559$	19.4280	0.821718
$560$	−1.69345	−0.0715613
$561$	−4.29376	−0.181283
$562$	−63.7355	−2.68852
$563$	−10.2620	−0.432492	−0.216246	−	0.976339i	$-0.569381\pi$
$563$	−10.2620	−0.432492	−0.216246	+	0.976339i	$0.569381\pi$
$564$	10.0122	0.421590
$565$	−74.2418	−3.12338
$566$	26.0918	1.09672
$567$	−0.239132	−0.0100426
$568$	−55.8526	−2.34352
$569$	−19.4921	−0.817152	−0.408576	−	0.912724i	$-0.633975\pi$
$569$	−19.4921	−0.817152	−0.408576	+	0.912724i	$0.633975\pi$
$570$	−5.73594	−0.240252
$571$	27.7876	1.16287	0.581437	−	0.813592i	$-0.302491\pi$
$571$	27.7876	1.16287	0.581437	+	0.813592i	$0.302491\pi$
$572$	41.8676	1.75057
$573$	19.2275	0.803240
$574$	2.24245	0.0935981
$575$	36.8877	1.53832
$576$	−11.7334	−0.488893
$577$	17.4527	0.726565	0.363283	−	0.931679i	$-0.381656\pi$
$577$	17.4527	0.726565	0.363283	+	0.931679i	$0.381656\pi$
$578$	−2.36108	−0.0982081
$579$	−2.61911	−0.108847
$580$	92.8074	3.85362
$581$	3.77801	0.156738
$582$	23.4466	0.971893
$583$	−7.37933	−0.305621
$584$	−49.3977	−2.04409
$585$	−11.8571	−0.490232
$586$	−29.6569	−1.22512
$587$	−8.29956	−0.342559	−0.171280	−	0.985222i	$-0.554790\pi$
$587$	−8.29956	−0.342559	−0.171280	+	0.985222i	$0.554790\pi$
$588$	24.8185	1.02350
$589$	−2.69695	−0.111126
$590$	21.7149	0.893990
$591$	18.7336	0.770597
$592$	16.4249	0.675057
$593$	−13.1422	−0.539686	−0.269843	−	0.962904i	$-0.586972\pi$
$593$	−13.1422	−0.539686	−0.269843	+	0.962904i	$0.586972\pi$
$594$	−10.1379	−0.415964
$595$	1.03949	0.0426148
$596$	−23.0789	−0.945349
$597$	5.84406	0.239182
$598$	17.0968	0.699140
$599$	4.90358	0.200355	0.100177	−	0.994970i	$-0.468059\pi$
$599$	4.90358	0.200355	0.100177	+	0.994970i	$0.468059\pi$
$600$	51.6640	2.10917
$601$	−18.4545	−0.752776	−0.376388	−	0.926462i	$-0.622834\pi$
$601$	−18.4545	−0.752776	−0.376388	+	0.926462i	$0.622834\pi$
$602$	−4.02141	−0.163901
$603$	10.5560	0.429875
$604$	−24.4267	−0.993908
$605$	32.3252	1.31421
$606$	31.3488	1.27346
$607$	4.69772	0.190675	0.0953373	−	0.995445i	$-0.469607\pi$
$607$	4.69772	0.190675	0.0953373	+	0.995445i	$0.469607\pi$
$608$	−2.00610	−0.0813579
$609$	1.42824	0.0578751
$610$	14.8066	0.599502
$611$	7.63991	0.309078
$612$	−3.57471	−0.144499
$613$	36.5863	1.47771	0.738853	−	0.673867i	$-0.235368\pi$
$613$	36.5863	1.47771	0.738853	+	0.673867i	$0.235368\pi$
$614$	−59.4816	−2.40048
$615$	−17.2645	−0.696172
$616$	−3.81757	−0.153814
$617$	48.5686	1.95530	0.977649	−	0.210243i	$-0.0674256\pi$
$617$	48.5686	1.95530	0.977649	+	0.210243i	$0.0674256\pi$
$618$	13.9004	0.559158
$619$	8.26092	0.332034	0.166017	−	0.986123i	$-0.446909\pi$
$619$	8.26092	0.332034	0.166017	+	0.986123i	$0.446909\pi$
$620$	74.9861	3.01152
$621$	−2.65463	−0.106527
$622$	57.9928	2.32530
$623$	0.856296	0.0343068
$624$	4.44379	0.177894
$625$	98.6094	3.94438
$626$	−31.0717	−1.24187
$627$	−2.39967	−0.0958334
$628$	3.57471	0.142646
$629$	−10.0820	−0.401997
$630$	2.45431	0.0977821
$631$	23.8988	0.951397	0.475698	−	0.879608i	$-0.342195\pi$
$631$	23.8988	0.951397	0.475698	+	0.879608i	$0.342195\pi$
$632$	64.6090	2.57001
$633$	−8.18565	−0.325350
$634$	−29.6289	−1.17672
$635$	24.3354	0.965722
$636$	−6.14356	−0.243608
$637$	18.9380	0.750352
$638$	60.5495	2.39718
$639$	15.0221	0.594267
$640$	89.2182	3.52666
$641$	41.8633	1.65350	0.826750	−	0.562569i	$-0.190187\pi$
$641$	41.8633	1.65350	0.826750	+	0.562569i	$0.190187\pi$
$642$	−20.6707	−0.815809
$643$	20.7153	0.816932	0.408466	−	0.912774i	$-0.366064\pi$
$643$	20.7153	0.816932	0.408466	+	0.912774i	$0.366064\pi$
$644$	−2.26925	−0.0894211
$645$	30.9606	1.21907
$646$	−1.31954	−0.0519168
$647$	−24.2501	−0.953369	−0.476685	−	0.879074i	$-0.658162\pi$
$647$	−24.2501	−0.953369	−0.476685	+	0.879074i	$0.658162\pi$
$648$	−3.71802	−0.146057
$649$	9.08459	0.356601
$650$	89.4926	3.51019
$651$	1.15398	0.0452281
$652$	39.2326	1.53647
$653$	23.9540	0.937393	0.468697	−	0.883359i	$-0.344724\pi$
$653$	23.9540	0.937393	0.468697	+	0.883359i	$0.344724\pi$
$654$	−44.1623	−1.72688
$655$	−0.979868	−0.0382866
$656$	6.47034	0.252625
$657$	13.2860	0.518338
$658$	−1.58139	−0.0616489
$659$	20.9300	0.815317	0.407659	−	0.913134i	$-0.366345\pi$
$659$	20.9300	0.815317	0.407659	+	0.913134i	$0.366345\pi$
$660$	66.7204	2.59709
$661$	−24.2094	−0.941637	−0.470819	−	0.882230i	$-0.656041\pi$
$661$	−24.2094	−0.941637	−0.470819	+	0.882230i	$0.656041\pi$
$662$	−56.2992	−2.18813
$663$	−2.72772	−0.105936
$664$	58.7402	2.27956
$665$	0.580940	0.0225279
$666$	−23.8045	−0.922405
$667$	15.8550	0.613907
$668$	−67.8598	−2.62558
$669$	−8.53078	−0.329819
$670$	−108.341	−4.18558
$671$	6.19444	0.239134
$672$	0.858375	0.0331125
$673$	1.53716	0.0592533	0.0296266	−	0.999561i	$-0.490568\pi$
$673$	1.53716	0.0592533	0.0296266	+	0.999561i	$0.490568\pi$
$674$	13.6861	0.527169
$675$	−13.8956	−0.534841
$676$	−19.8738	−0.764377
$677$	−0.606449	−0.0233077	−0.0116539	−	0.999932i	$-0.503710\pi$
$677$	−0.606449	−0.0233077	−0.0116539	+	0.999932i	$0.503710\pi$
$678$	−40.3255	−1.54869
$679$	−2.37469	−0.0911323
$680$	16.1619	0.619779
$681$	−20.5611	−0.787905
$682$	48.9225	1.87334
$683$	−8.56732	−0.327819	−0.163910	−	0.986475i	$-0.552411\pi$
$683$	−8.56732	−0.327819	−0.163910	+	0.986475i	$0.552411\pi$
$684$	−1.99781	−0.0763881
$685$	52.9693	2.02385
$686$	−7.87227	−0.300565
$687$	−21.5999	−0.824086
$688$	−11.6033	−0.442373
$689$	−4.68790	−0.178595
$690$	27.2455	1.03722
$691$	−0.187920	−0.00714880	−0.00357440	−	0.999994i	$-0.501138\pi$
$691$	−0.187920	−0.00714880	−0.00357440	+	0.999994i	$0.501138\pi$
$692$	−31.0899	−1.18186
$693$	1.02678	0.0390040
$694$	23.2045	0.880833
$695$	53.4227	2.02644
$696$	22.2061	0.841721
$697$	−3.97167	−0.150438
$698$	10.8441	0.410454
$699$	14.9035	0.563703
$700$	−11.8783	−0.448959
$701$	22.0960	0.834555	0.417277	−	0.908779i	$-0.362984\pi$
$701$	22.0960	0.834555	0.417277	+	0.908779i	$0.362984\pi$
$702$	−6.44036	−0.243076
$703$	−5.63457	−0.212512
$704$	50.3806	1.89879
$705$	12.1750	0.458537
$706$	−64.0047	−2.40885
$707$	−3.17503	−0.119409
$708$	7.56324	0.284244
$709$	−15.1413	−0.568642	−0.284321	−	0.958729i	$-0.591768\pi$
$709$	−15.1413	−0.568642	−0.284321	+	0.958729i	$0.591768\pi$
$710$	−154.178	−5.78621
$711$	−17.3773	−0.651699
$712$	13.3136	0.498950
$713$	12.8104	0.479755
$714$	0.564611	0.0211300
$715$	50.9117	1.90399
$716$	−46.6036	−1.74166
$717$	−29.1491	−1.08859
$718$	−75.9619	−2.83487
$719$	51.5149	1.92118	0.960591	−	0.277964i	$-0.0896597\pi$
$719$	51.5149	1.92118	0.960591	+	0.277964i	$0.0896597\pi$
$720$	7.08164	0.263917
$721$	−1.40785	−0.0524310
$722$	44.1231	1.64209
$723$	−23.2353	−0.864130
$724$	21.1229	0.785028
$725$	82.9925	3.08226
$726$	17.5579	0.651634
$727$	34.2647	1.27081	0.635403	−	0.772180i	$-0.280834\pi$
$727$	34.2647	1.27081	0.635403	+	0.772180i	$0.280834\pi$
$728$	−2.42521	−0.0898842
$729$	1.00000	0.0370370
$730$	−136.360	−5.04691
$731$	7.12244	0.263433
$732$	5.15709	0.190612
$733$	48.5082	1.79169	0.895845	−	0.444366i	$-0.146571\pi$
$733$	48.5082	1.79169	0.895845	+	0.444366i	$0.146571\pi$
$734$	−68.7617	−2.53804
$735$	30.1798	1.11320
$736$	9.52890	0.351240
$737$	−45.3251	−1.66957
$738$	−9.37745	−0.345189
$739$	−23.4148	−0.861327	−0.430664	−	0.902512i	$-0.641720\pi$
$739$	−23.4148	−0.861327	−0.430664	+	0.902512i	$0.641720\pi$
$740$	156.664	5.75908
$741$	−1.52445	−0.0560020
$742$	0.970351	0.0356227
$743$	−2.03363	−0.0746066	−0.0373033	−	0.999304i	$-0.511877\pi$
$743$	−2.03363	−0.0746066	−0.0373033	+	0.999304i	$0.511877\pi$
$744$	17.9420	0.657786
$745$	−28.0643	−1.02820
$746$	−7.34232	−0.268821
$747$	−15.7988	−0.578048
$748$	15.3489	0.561213
$749$	2.09355	0.0764966
$750$	91.2990	3.33377
$751$	2.89574	0.105667	0.0528335	−	0.998603i	$-0.483175\pi$
$751$	2.89574	0.105667	0.0528335	+	0.998603i	$0.483175\pi$
$752$	−4.56292	−0.166393
$753$	21.3881	0.779426
$754$	38.4656	1.40083
$755$	−29.7033	−1.08101
$756$	0.854829	0.0310898
$757$	3.24190	0.117829	0.0589145	−	0.998263i	$-0.481236\pi$
$757$	3.24190	0.117829	0.0589145	+	0.998263i	$0.481236\pi$
$758$	70.2230	2.55061
$759$	11.3983	0.413734
$760$	9.03243	0.327641
$761$	18.9431	0.686686	0.343343	−	0.939210i	$-0.388441\pi$
$761$	18.9431	0.686686	0.343343	+	0.939210i	$0.388441\pi$
$762$	13.2181	0.478842
$763$	4.47279	0.161926
$764$	−68.7327	−2.48666
$765$	−4.34691	−0.157163
$766$	−37.1711	−1.34305
$767$	5.77121	0.208386
$768$	24.9932	0.901866
$769$	−25.5068	−0.919800	−0.459900	−	0.887971i	$-0.652115\pi$
$769$	−25.5068	−0.919800	−0.459900	+	0.887971i	$0.652115\pi$
$770$	−10.5382	−0.379771
$771$	17.8369	0.642382
$772$	9.36257	0.336966
$773$	−39.6111	−1.42471	−0.712356	−	0.701818i	$-0.752372\pi$
$773$	−39.6111	−1.42471	−0.712356	+	0.701818i	$0.752372\pi$
$774$	16.8167	0.604463
$775$	67.0559	2.40872
$776$	−36.9216	−1.32541
$777$	2.41094	0.0864920
$778$	−20.4967	−0.734843
$779$	−2.21966	−0.0795276
$780$	42.3858	1.51765
$781$	−64.5015	−2.30805
$782$	6.26780	0.224136
$783$	−5.97258	−0.213442
$784$	−11.3107	−0.403953
$785$	4.34691	0.155148
$786$	−0.532229	−0.0189840
$787$	−14.8884	−0.530713	−0.265356	−	0.964150i	$-0.585490\pi$
$787$	−14.8884	−0.530713	−0.265356	+	0.964150i	$0.585490\pi$
$788$	−66.9671	−2.38560
$789$	−30.6048	−1.08956
$790$	178.350	6.34541
$791$	4.08420	0.145217
$792$	15.9643	0.567265
$793$	3.93517	0.139742
$794$	−91.8899	−3.26105
$795$	−7.47067	−0.264957
$796$	−20.8908	−0.740456
$797$	30.4304	1.07790	0.538951	−	0.842337i	$-0.318821\pi$
$797$	30.4304	1.07790	0.538951	+	0.842337i	$0.318821\pi$
$798$	0.315546	0.0111702
$799$	2.80084	0.0990868
$800$	49.8787	1.76348
$801$	−3.58085	−0.126523
$802$	69.3993	2.45057
$803$	−57.0471	−2.01315
$804$	−37.7348	−1.33080
$805$	−2.75945	−0.0972579
$806$	31.0793	1.09472
$807$	4.17373	0.146922
$808$	−49.3652	−1.73666
$809$	16.3888	0.576200	0.288100	−	0.957600i	$-0.406976\pi$
$809$	16.3888	0.576200	0.288100	+	0.957600i	$0.406976\pi$
$810$	−10.2634	−0.360619
$811$	−36.9386	−1.29709	−0.648545	−	0.761176i	$-0.724622\pi$
$811$	−36.9386	−1.29709	−0.648545	+	0.761176i	$0.724622\pi$
$812$	−5.10553	−0.179169
$813$	−8.22291	−0.288390
$814$	102.211	3.58249
$815$	47.7075	1.67112
$816$	1.62912	0.0570307
$817$	3.98054	0.139262
$818$	−69.4406	−2.42793
$819$	0.652286	0.0227927
$820$	61.7155	2.15520
$821$	9.54259	0.333039	0.166519	−	0.986038i	$-0.446747\pi$
$821$	9.54259	0.333039	0.166519	+	0.986038i	$0.446747\pi$
$822$	28.7710	1.00350
$823$	−16.1476	−0.562870	−0.281435	−	0.959580i	$-0.590810\pi$
$823$	−16.1476	−0.562870	−0.281435	+	0.959580i	$0.590810\pi$
$824$	−21.8891	−0.762544
$825$	59.6643	2.07724
$826$	−1.19458	−0.0415649
$827$	−11.8462	−0.411934	−0.205967	−	0.978559i	$-0.566034\pi$
$827$	−11.8462	−0.411934	−0.205967	+	0.978559i	$0.566034\pi$
$828$	9.48953	0.329784
$829$	−24.2450	−0.842063	−0.421031	−	0.907046i	$-0.638332\pi$
$829$	−24.2450	−0.842063	−0.421031	+	0.907046i	$0.638332\pi$
$830$	162.149	5.62829
$831$	−2.24584	−0.0779074
$832$	32.0055	1.10959
$833$	6.94282	0.240554
$834$	29.0173	1.00479
$835$	−82.5187	−2.85568
$836$	8.57811	0.296680
$837$	−4.82570	−0.166801
$838$	4.91775	0.169881
$839$	24.4650	0.844627	0.422314	−	0.906450i	$-0.361218\pi$
$839$	24.4650	0.844627	0.422314	+	0.906450i	$0.361218\pi$
$840$	−3.86482	−0.133349
$841$	6.67167	0.230058
$842$	−78.2195	−2.69562
$843$	−26.9942	−0.929729
$844$	29.2613	1.00722
$845$	−24.1669	−0.831366
$846$	6.61302	0.227360
$847$	−1.77828	−0.0611023
$848$	2.79984	0.0961469
$849$	11.0508	0.379262
$850$	32.8086	1.12533
$851$	26.7641	0.917460
$852$	−53.6998	−1.83972
$853$	19.7630	0.676672	0.338336	−	0.941025i	$-0.390136\pi$
$853$	19.7630	0.676672	0.338336	+	0.941025i	$0.390136\pi$
$854$	−0.814543	−0.0278731
$855$	−2.42937	−0.0830826
$856$	32.5504	1.11255
$857$	14.6229	0.499509	0.249754	−	0.968309i	$-0.419650\pi$
$857$	14.6229	0.499509	0.249754	+	0.968309i	$0.419650\pi$
$858$	27.6534	0.944071
$859$	34.8977	1.19069	0.595347	−	0.803468i	$-0.297014\pi$
$859$	34.8977	1.19069	0.595347	+	0.803468i	$0.297014\pi$
$860$	−110.675	−3.77399
$861$	0.949756	0.0323676
$862$	75.6194	2.57561
$863$	−19.4256	−0.661254	−0.330627	−	0.943761i	$-0.607260\pi$
$863$	−19.4256	−0.661254	−0.330627	+	0.943761i	$0.607260\pi$
$864$	−3.58954	−0.122119
$865$	−37.8059	−1.28544
$866$	−27.2565	−0.926215
$867$	−1.00000	−0.0339618
$868$	−4.12514	−0.140017
$869$	74.6139	2.53110
$870$	61.2989	2.07823
$871$	−28.7939	−0.975644
$872$	69.5427	2.35501
$873$	9.93045	0.336095
$874$	3.50290	0.118487
$875$	−9.24684	−0.312600
$876$	−47.4937	−1.60466
$877$	−30.9996	−1.04678	−0.523391	−	0.852092i	$-0.675333\pi$
$877$	−30.9996	−1.04678	−0.523391	+	0.852092i	$0.675333\pi$
$878$	−80.7833	−2.72631
$879$	−12.5607	−0.423663
$880$	−30.4069	−1.02502
$881$	−30.6950	−1.03414	−0.517070	−	0.855943i	$-0.672977\pi$
$881$	−30.6950	−1.03414	−0.517070	+	0.855943i	$0.672977\pi$
$882$	16.3926	0.551966
$883$	−41.4471	−1.39481	−0.697403	−	0.716679i	$-0.745661\pi$
$883$	−41.4471	−1.39481	−0.697403	+	0.716679i	$0.745661\pi$
$884$	9.75079	0.327955
$885$	9.19703	0.309155
$886$	−33.8628	−1.13764
$887$	−0.357051	−0.0119886	−0.00599429	−	0.999982i	$-0.501908\pi$
$887$	−0.357051	−0.0119886	−0.00599429	+	0.999982i	$0.501908\pi$
$888$	37.4851	1.25792
$889$	−1.33874	−0.0449000
$890$	36.7517	1.23192
$891$	−4.29376	−0.143846
$892$	30.4950	1.02105
$893$	1.56532	0.0523813
$894$	−15.2435	−0.509820
$895$	−56.6708	−1.89430
$896$	−4.90808	−0.163967
$897$	7.24108	0.241773
$898$	95.9976	3.20348
$899$	28.8219	0.961263
$900$	49.6727	1.65576
$901$	−1.71862	−0.0572555
$902$	40.2645	1.34066
$903$	−1.70321	−0.0566792
$904$	63.5009	2.11201
$905$	25.6859	0.853827
$906$	−16.1337	−0.536008
$907$	−11.2127	−0.372311	−0.186155	−	0.982520i	$-0.559603\pi$
$907$	−11.2127	−0.372311	−0.186155	+	0.982520i	$0.559603\pi$
$908$	73.5001	2.43919
$909$	13.2773	0.440380
$910$	−6.69467	−0.221926
$911$	53.7265	1.78004	0.890019	−	0.455923i	$-0.150691\pi$
$911$	53.7265	1.78004	0.890019	+	0.455923i	$0.150691\pi$
$912$	0.910472	0.0301488
$913$	67.8363	2.24505
$914$	−34.6171	−1.14503
$915$	6.27111	0.207317
$916$	77.2132	2.55120
$917$	0.0539046	0.00178009
$918$	−2.36108	−0.0779273
$919$	−11.2400	−0.370773	−0.185386	−	0.982666i	$-0.559354\pi$
$919$	−11.2400	−0.370773	−0.185386	+	0.982666i	$0.559354\pi$
$920$	−42.9038	−1.41450
$921$	−25.1925	−0.830121
$922$	−77.8625	−2.56427
$923$	−40.9762	−1.34875
$924$	−3.67043	−0.120748
$925$	140.096	4.60632
$926$	−77.5386	−2.54808
$927$	5.88732	0.193365
$928$	21.4388	0.703763
$929$	44.8261	1.47070	0.735348	−	0.677689i	$-0.237019\pi$
$929$	44.8261	1.47070	0.735348	+	0.677689i	$0.237019\pi$
$930$	49.5281	1.62409
$931$	3.88015	0.127167
$932$	−53.2758	−1.74511
$933$	24.5619	0.804122
$934$	−99.7023	−3.26236
$935$	18.6646	0.610397
$936$	10.1417	0.331492
$937$	−45.6902	−1.49263	−0.746316	−	0.665592i	$-0.768179\pi$
$937$	−45.6902	−1.49263	−0.746316	+	0.665592i	$0.768179\pi$
$938$	5.96006	0.194603
$939$	−13.1599	−0.429458
$940$	−43.5221	−1.41953
$941$	3.87350	0.126273	0.0631363	−	0.998005i	$-0.479890\pi$
$941$	3.87350	0.126273	0.0631363	+	0.998005i	$0.479890\pi$
$942$	2.36108	0.0769282
$943$	10.5433	0.343338
$944$	−3.44684	−0.112185
$945$	1.03949	0.0338145
$946$	−72.2068	−2.34764
$947$	−2.49828	−0.0811831	−0.0405916	−	0.999176i	$-0.512924\pi$
$947$	−2.49828	−0.0811831	−0.0405916	+	0.999176i	$0.512924\pi$
$948$	62.1187	2.01752
$949$	−36.2406	−1.17642
$950$	18.3358	0.594893
$951$	−12.5489	−0.406925
$952$	−0.889098	−0.0288158
$953$	15.5421	0.503457	0.251729	−	0.967798i	$-0.419001\pi$
$953$	15.5421	0.503457	0.251729	+	0.967798i	$0.419001\pi$
$954$	−4.05780	−0.131376
$955$	−83.5801	−2.70459
$956$	104.200	3.37006
$957$	25.6448	0.828979
$958$	93.3359	3.01555
$959$	−2.91395	−0.0940964
$960$	51.0042	1.64615
$961$	−7.71263	−0.248795
$962$	64.9319	2.09349
$963$	−8.75477	−0.282119
$964$	83.0594	2.67516
$965$	11.3850	0.366498
$966$	−1.49883	−0.0482242
$967$	41.2896	1.32779	0.663893	−	0.747828i	$-0.268903\pi$
$967$	41.2896	1.32779	0.663893	+	0.747828i	$0.268903\pi$
$968$	−27.6486	−0.888658
$969$	−0.558873	−0.0179536
$970$	−101.920	−3.27246
$971$	22.7317	0.729495	0.364747	−	0.931106i	$-0.381155\pi$
$971$	22.7317	0.729495	0.364747	+	0.931106i	$0.381155\pi$
$972$	−3.57471	−0.114659
$973$	−2.93889	−0.0942166
$974$	−43.5744	−1.39621
$975$	37.9032	1.21388
$976$	−2.35027	−0.0752304
$977$	−55.9454	−1.78985	−0.894926	−	0.446215i	$-0.852772\pi$
$977$	−55.9454	−1.78985	−0.894926	+	0.446215i	$0.852772\pi$
$978$	25.9130	0.828607
$979$	15.3753	0.491397
$980$	−107.884	−3.44622
$981$	−18.7043	−0.597181
$982$	67.6576	2.15904
$983$	−4.20101	−0.133992	−0.0669958	−	0.997753i	$-0.521341\pi$
$983$	−4.20101	−0.133992	−0.0669958	+	0.997753i	$0.521341\pi$
$984$	14.7667	0.470747
$985$	−81.4331	−2.59468
$986$	14.1017	0.449091
$987$	−0.669773	−0.0213191
$988$	5.44945	0.173370
$989$	−18.9075	−0.601222
$990$	44.0686	1.40059
$991$	21.1070	0.670485	0.335242	−	0.942132i	$-0.391182\pi$
$991$	21.1070	0.670485	0.335242	+	0.942132i	$0.391182\pi$
$992$	17.3220	0.549975
$993$	−23.8446	−0.756687
$994$	8.48167	0.269022
$995$	−25.4036	−0.805348
$996$	56.4761	1.78951
$997$	−18.4564	−0.584519	−0.292259	−	0.956339i	$-0.594407\pi$
$997$	−18.4564	−0.584519	−0.292259	+	0.956339i	$0.594407\pi$
$998$	−28.8782	−0.914124
$999$	−10.0820	−0.318981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.7	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.36108 q^{2} -1.00000 q^{3} +3.57471 q^{4} +4.34691 q^{5} +2.36108 q^{6} -0.239132 q^{7} -3.71802 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.36108 q^{2} -1.00000 q^{3} +3.57471 q^{4} +4.34691 q^{5} +2.36108 q^{6} -0.239132 q^{7} -3.71802 q^{8} +1.00000 q^{9} -10.2634 q^{10} -4.29376 q^{11} -3.57471 q^{12} -2.72772 q^{13} +0.564611 q^{14} -4.34691 q^{15} +1.62912 q^{16} -1.00000 q^{17} -2.36108 q^{18} -0.558873 q^{19} +15.5389 q^{20} +0.239132 q^{21} +10.1379 q^{22} +2.65463 q^{23} +3.71802 q^{24} +13.8956 q^{25} +6.44036 q^{26} -1.00000 q^{27} -0.854829 q^{28} +5.97258 q^{29} +10.2634 q^{30} +4.82570 q^{31} +3.58954 q^{32} +4.29376 q^{33} +2.36108 q^{34} -1.03949 q^{35} +3.57471 q^{36} +10.0820 q^{37} +1.31954 q^{38} +2.72772 q^{39} -16.1619 q^{40} +3.97167 q^{41} -0.564611 q^{42} -7.12244 q^{43} -15.3489 q^{44} +4.34691 q^{45} -6.26780 q^{46} -2.80084 q^{47} -1.62912 q^{48} -6.94282 q^{49} -32.8086 q^{50} +1.00000 q^{51} -9.75079 q^{52} +1.71862 q^{53} +2.36108 q^{54} -18.6646 q^{55} +0.889098 q^{56} +0.558873 q^{57} -14.1017 q^{58} -2.11577 q^{59} -15.5389 q^{60} -1.44266 q^{61} -11.3939 q^{62} -0.239132 q^{63} -11.7334 q^{64} -11.8571 q^{65} -10.1379 q^{66} +10.5560 q^{67} -3.57471 q^{68} -2.65463 q^{69} +2.45431 q^{70} +15.0221 q^{71} -3.71802 q^{72} +13.2860 q^{73} -23.8045 q^{74} -13.8956 q^{75} -1.99781 q^{76} +1.02678 q^{77} -6.44036 q^{78} -17.3773 q^{79} +7.08164 q^{80} +1.00000 q^{81} -9.37745 q^{82} -15.7988 q^{83} +0.854829 q^{84} -4.34691 q^{85} +16.8167 q^{86} -5.97258 q^{87} +15.9643 q^{88} -3.58085 q^{89} -10.2634 q^{90} +0.652286 q^{91} +9.48953 q^{92} -4.82570 q^{93} +6.61302 q^{94} -2.42937 q^{95} -3.58954 q^{96} +9.93045 q^{97} +16.3926 q^{98} -4.29376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

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