LMFDB - Embedded newform 8007.2.a.g.1.13

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			1.13
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)

$f(q)$	$=$	$q-1.84393 q^{2} -1.00000 q^{3} +1.40007 q^{4} +2.87244 q^{5} +1.84393 q^{6} -1.74244 q^{7} +1.10623 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.84393 q^{2} -1.00000 q^{3} +1.40007 q^{4} +2.87244 q^{5} +1.84393 q^{6} -1.74244 q^{7} +1.10623 q^{8} +1.00000 q^{9} -5.29656 q^{10} -6.38626 q^{11} -1.40007 q^{12} +4.06957 q^{13} +3.21293 q^{14} -2.87244 q^{15} -4.83995 q^{16} -1.00000 q^{17} -1.84393 q^{18} -6.09433 q^{19} +4.02161 q^{20} +1.74244 q^{21} +11.7758 q^{22} -8.30391 q^{23} -1.10623 q^{24} +3.25089 q^{25} -7.50400 q^{26} -1.00000 q^{27} -2.43954 q^{28} -3.49057 q^{29} +5.29656 q^{30} -4.29002 q^{31} +6.71205 q^{32} +6.38626 q^{33} +1.84393 q^{34} -5.00505 q^{35} +1.40007 q^{36} -7.30902 q^{37} +11.2375 q^{38} -4.06957 q^{39} +3.17758 q^{40} +6.07531 q^{41} -3.21293 q^{42} -0.766371 q^{43} -8.94120 q^{44} +2.87244 q^{45} +15.3118 q^{46} -5.74712 q^{47} +4.83995 q^{48} -3.96390 q^{49} -5.99441 q^{50} +1.00000 q^{51} +5.69768 q^{52} -12.5814 q^{53} +1.84393 q^{54} -18.3441 q^{55} -1.92754 q^{56} +6.09433 q^{57} +6.43635 q^{58} -12.0709 q^{59} -4.02161 q^{60} +10.8757 q^{61} +7.91049 q^{62} -1.74244 q^{63} -2.69664 q^{64} +11.6896 q^{65} -11.7758 q^{66} -11.7712 q^{67} -1.40007 q^{68} +8.30391 q^{69} +9.22895 q^{70} +8.95117 q^{71} +1.10623 q^{72} -2.35685 q^{73} +13.4773 q^{74} -3.25089 q^{75} -8.53248 q^{76} +11.1277 q^{77} +7.50400 q^{78} +9.35621 q^{79} -13.9024 q^{80} +1.00000 q^{81} -11.2024 q^{82} +13.8585 q^{83} +2.43954 q^{84} -2.87244 q^{85} +1.41313 q^{86} +3.49057 q^{87} -7.06468 q^{88} -4.68455 q^{89} -5.29656 q^{90} -7.09099 q^{91} -11.6260 q^{92} +4.29002 q^{93} +10.5973 q^{94} -17.5056 q^{95} -6.71205 q^{96} -1.63896 q^{97} +7.30914 q^{98} -6.38626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.84393	−1.30385	−0.651927	−	0.758282i	$-0.726039\pi$
$2$	−1.84393	−1.30385	−0.651927	+	0.758282i	$0.726039\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.40007	0.700034
$5$	2.87244	1.28459	0.642296	−	0.766456i	$-0.277982\pi$
$5$	2.87244	1.28459	0.642296	+	0.766456i	$0.277982\pi$
$6$	1.84393	0.752780
$7$	−1.74244	−0.658581	−0.329290	−	0.944229i	$-0.606809\pi$
$7$	−1.74244	−0.658581	−0.329290	+	0.944229i	$0.606809\pi$
$8$	1.10623	0.391111
$9$	1.00000	0.333333
$10$	−5.29656	−1.67492
$11$	−6.38626	−1.92553	−0.962765	−	0.270339i	$-0.912864\pi$
$11$	−6.38626	−1.92553	−0.962765	+	0.270339i	$0.912864\pi$
$12$	−1.40007	−0.404165
$13$	4.06957	1.12870	0.564348	−	0.825537i	$-0.309127\pi$
$13$	4.06957	1.12870	0.564348	+	0.825537i	$0.309127\pi$
$14$	3.21293	0.858693
$15$	−2.87244	−0.741660
$16$	−4.83995	−1.20999
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.84393	−0.434618
$19$	−6.09433	−1.39813	−0.699067	−	0.715056i	$-0.746401\pi$
$19$	−6.09433	−1.39813	−0.699067	+	0.715056i	$0.746401\pi$
$20$	4.02161	0.899259
$21$	1.74244	0.380232
$22$	11.7758	2.51061
$23$	−8.30391	−1.73148	−0.865742	−	0.500490i	$-0.833153\pi$
$23$	−8.30391	−1.73148	−0.865742	+	0.500490i	$0.833153\pi$
$24$	−1.10623	−0.225808
$25$	3.25089	0.650178
$26$	−7.50400	−1.47166
$27$	−1.00000	−0.192450
$28$	−2.43954	−0.461029
$29$	−3.49057	−0.648182	−0.324091	−	0.946026i	$-0.605058\pi$
$29$	−3.49057	−0.648182	−0.324091	+	0.946026i	$0.605058\pi$
$30$	5.29656	0.967016
$31$	−4.29002	−0.770511	−0.385256	−	0.922810i	$-0.625887\pi$
$31$	−4.29002	−0.770511	−0.385256	+	0.922810i	$0.625887\pi$
$32$	6.71205	1.18653
$33$	6.38626	1.11171
$34$	1.84393	0.316231
$35$	−5.00505	−0.846008
$36$	1.40007	0.233345
$37$	−7.30902	−1.20159	−0.600797	−	0.799401i	$-0.705150\pi$
$37$	−7.30902	−1.20159	−0.600797	+	0.799401i	$0.705150\pi$
$38$	11.2375	1.82296
$39$	−4.06957	−0.651653
$40$	3.17758	0.502419
$41$	6.07531	0.948804	0.474402	−	0.880308i	$-0.342664\pi$
$41$	6.07531	0.948804	0.474402	+	0.880308i	$0.342664\pi$
$42$	−3.21293	−0.495767
$43$	−0.766371	−0.116870	−0.0584352	−	0.998291i	$-0.518611\pi$
$43$	−0.766371	−0.116870	−0.0584352	+	0.998291i	$0.518611\pi$
$44$	−8.94120	−1.34794
$45$	2.87244	0.428198
$46$	15.3118	2.25760
$47$	−5.74712	−0.838304	−0.419152	−	0.907916i	$-0.637672\pi$
$47$	−5.74712	−0.838304	−0.419152	+	0.907916i	$0.637672\pi$
$48$	4.83995	0.698586
$49$	−3.96390	−0.566271
$50$	−5.99441	−0.847737
$51$	1.00000	0.140028
$52$	5.69768	0.790126
$53$	−12.5814	−1.72819	−0.864096	−	0.503326i	$-0.832109\pi$
$53$	−12.5814	−1.72819	−0.864096	+	0.503326i	$0.832109\pi$
$54$	1.84393	0.250927
$55$	−18.3441	−2.47352
$56$	−1.92754	−0.257578
$57$	6.09433	0.807213
$58$	6.43635	0.845134
$59$	−12.0709	−1.57150	−0.785748	−	0.618546i	$-0.787722\pi$
$59$	−12.0709	−1.57150	−0.785748	+	0.618546i	$0.787722\pi$
$60$	−4.02161	−0.519187
$61$	10.8757	1.39249	0.696245	−	0.717804i	$-0.254853\pi$
$61$	10.8757	1.39249	0.696245	+	0.717804i	$0.254853\pi$
$62$	7.91049	1.00463
$63$	−1.74244	−0.219527
$64$	−2.69664	−0.337080
$65$	11.6896	1.44992
$66$	−11.7758	−1.44950
$67$	−11.7712	−1.43808	−0.719042	−	0.694967i	$-0.755419\pi$
$67$	−11.7712	−1.43808	−0.719042	+	0.694967i	$0.755419\pi$
$68$	−1.40007	−0.169783
$69$	8.30391	0.999673
$70$	9.22895	1.10307
$71$	8.95117	1.06231	0.531154	−	0.847275i	$-0.321759\pi$
$71$	8.95117	1.06231	0.531154	+	0.847275i	$0.321759\pi$
$72$	1.10623	0.130370
$73$	−2.35685	−0.275848	−0.137924	−	0.990443i	$-0.544043\pi$
$73$	−2.35685	−0.275848	−0.137924	+	0.990443i	$0.544043\pi$
$74$	13.4773	1.56670
$75$	−3.25089	−0.375380
$76$	−8.53248	−0.978742
$77$	11.1277	1.26812
$78$	7.50400	0.849661
$79$	9.35621	1.05266	0.526328	−	0.850282i	$-0.323568\pi$
$79$	9.35621	1.05266	0.526328	+	0.850282i	$0.323568\pi$
$80$	−13.9024	−1.55434
$81$	1.00000	0.111111
$82$	−11.2024	−1.23710
$83$	13.8585	1.52117	0.760585	−	0.649238i	$-0.224912\pi$
$83$	13.8585	1.52117	0.760585	+	0.649238i	$0.224912\pi$
$84$	2.43954	0.266175
$85$	−2.87244	−0.311559
$86$	1.41313	0.152382
$87$	3.49057	0.374228
$88$	−7.06468	−0.753097
$89$	−4.68455	−0.496562	−0.248281	−	0.968688i	$-0.579866\pi$
$89$	−4.68455	−0.496562	−0.248281	+	0.968688i	$0.579866\pi$
$90$	−5.29656	−0.558307
$91$	−7.09099	−0.743338
$92$	−11.6260	−1.21210
$93$	4.29002	0.444855
$94$	10.5973	1.09303
$95$	−17.5056	−1.79603
$96$	−6.71205	−0.685045
$97$	−1.63896	−0.166411	−0.0832056	−	0.996532i	$-0.526516\pi$
$97$	−1.63896	−0.166411	−0.0832056	+	0.996532i	$0.526516\pi$
$98$	7.30914	0.738335
$99$	−6.38626	−0.641843
$100$	4.55147	0.455147
$101$	−6.70134	−0.666808	−0.333404	−	0.942784i	$-0.608197\pi$
$101$	−6.70134	−0.666808	−0.333404	+	0.942784i	$0.608197\pi$
$102$	−1.84393	−0.182576
$103$	7.08223	0.697833	0.348917	−	0.937154i	$-0.386550\pi$
$103$	7.08223	0.697833	0.348917	+	0.937154i	$0.386550\pi$
$104$	4.50189	0.441446
$105$	5.00505	0.488443
$106$	23.1993	2.25331
$107$	13.0973	1.26616	0.633080	−	0.774086i	$-0.281790\pi$
$107$	13.0973	1.26616	0.633080	+	0.774086i	$0.281790\pi$
$108$	−1.40007	−0.134722
$109$	−3.34572	−0.320462	−0.160231	−	0.987080i	$-0.551224\pi$
$109$	−3.34572	−0.320462	−0.160231	+	0.987080i	$0.551224\pi$
$110$	33.8252	3.22511
$111$	7.30902	0.693741
$112$	8.43332	0.796874
$113$	11.0536	1.03983	0.519916	−	0.854217i	$-0.325963\pi$
$113$	11.0536	1.03983	0.519916	+	0.854217i	$0.325963\pi$
$114$	−11.2375	−1.05249
$115$	−23.8524	−2.22425
$116$	−4.88703	−0.453750
$117$	4.06957	0.376232
$118$	22.2579	2.04900
$119$	1.74244	0.159729
$120$	−3.17758	−0.290072
$121$	29.7843	2.70767
$122$	−20.0540	−1.81560
$123$	−6.07531	−0.547792
$124$	−6.00633	−0.539384
$125$	−5.02421	−0.449379
$126$	3.21293	0.286231
$127$	16.6414	1.47668	0.738342	−	0.674427i	$-0.235609\pi$
$127$	16.6414	1.47668	0.738342	+	0.674427i	$0.235609\pi$
$128$	−8.45169	−0.747031
$129$	0.766371	0.0674752
$130$	−21.5548	−1.89048
$131$	14.6603	1.28087	0.640436	−	0.768011i	$-0.278754\pi$
$131$	14.6603	1.28087	0.640436	+	0.768011i	$0.278754\pi$
$132$	8.94120	0.778232
$133$	10.6190	0.920785
$134$	21.7053	1.87505
$135$	−2.87244	−0.247220
$136$	−1.10623	−0.0948585
$137$	18.7892	1.60527	0.802634	−	0.596472i	$-0.203431\pi$
$137$	18.7892	1.60527	0.802634	+	0.596472i	$0.203431\pi$
$138$	−15.3118	−1.30343
$139$	14.7231	1.24880	0.624399	−	0.781106i	$-0.285344\pi$
$139$	14.7231	1.24880	0.624399	+	0.781106i	$0.285344\pi$
$140$	−7.00741	−0.592234
$141$	5.74712	0.483995
$142$	−16.5053	−1.38509
$143$	−25.9894	−2.17334
$144$	−4.83995	−0.403329
$145$	−10.0264	−0.832650
$146$	4.34585	0.359665
$147$	3.96390	0.326937
$148$	−10.2331	−0.841158
$149$	6.73151	0.551467	0.275733	−	0.961234i	$-0.411079\pi$
$149$	6.73151	0.551467	0.275733	+	0.961234i	$0.411079\pi$
$150$	5.99441	0.489441
$151$	7.59344	0.617946	0.308973	−	0.951071i	$-0.400015\pi$
$151$	7.59344	0.617946	0.308973	+	0.951071i	$0.400015\pi$
$152$	−6.74173	−0.546827
$153$	−1.00000	−0.0808452
$154$	−20.5186	−1.65344
$155$	−12.3228	−0.989793
$156$	−5.69768	−0.456180
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−17.2522	−1.37251
$159$	12.5814	0.997773
$160$	19.2799	1.52421
$161$	14.4691	1.14032
$162$	−1.84393	−0.144873
$163$	−22.5844	−1.76895	−0.884475	−	0.466587i	$-0.845483\pi$
$163$	−22.5844	−1.76895	−0.884475	+	0.466587i	$0.845483\pi$
$164$	8.50585	0.664195
$165$	18.3441	1.42809
$166$	−25.5541	−1.98338
$167$	−12.0242	−0.930461	−0.465231	−	0.885190i	$-0.654029\pi$
$167$	−12.0242	−0.930461	−0.465231	+	0.885190i	$0.654029\pi$
$168$	1.92754	0.148713
$169$	3.56143	0.273956
$170$	5.29656	0.406228
$171$	−6.09433	−0.466045
$172$	−1.07297	−0.0818133
$173$	−2.15505	−0.163846	−0.0819228	−	0.996639i	$-0.526106\pi$
$173$	−2.15505	−0.163846	−0.0819228	+	0.996639i	$0.526106\pi$
$174$	−6.43635	−0.487939
$175$	−5.66448	−0.428195
$176$	30.9092	2.32987
$177$	12.0709	0.907304
$178$	8.63797	0.647444
$179$	12.8703	0.961974	0.480987	−	0.876728i	$-0.340278\pi$
$179$	12.8703	0.961974	0.480987	+	0.876728i	$0.340278\pi$
$180$	4.02161	0.299753
$181$	−15.4372	−1.14744	−0.573719	−	0.819052i	$-0.694500\pi$
$181$	−15.4372	−1.14744	−0.573719	+	0.819052i	$0.694500\pi$
$182$	13.0753	0.969204
$183$	−10.8757	−0.803955
$184$	−9.18603	−0.677203
$185$	−20.9947	−1.54356
$186$	−7.91049	−0.580025
$187$	6.38626	0.467010
$188$	−8.04636	−0.586841
$189$	1.74244	0.126744
$190$	32.2790	2.34176
$191$	8.39748	0.607620	0.303810	−	0.952733i	$-0.401741\pi$
$191$	8.39748	0.607620	0.303810	+	0.952733i	$0.401741\pi$
$192$	2.69664	0.194613
$193$	6.68955	0.481524	0.240762	−	0.970584i	$-0.422603\pi$
$193$	6.68955	0.481524	0.240762	+	0.970584i	$0.422603\pi$
$194$	3.02212	0.216976
$195$	−11.6896	−0.837109
$196$	−5.54973	−0.396409
$197$	−10.0098	−0.713169	−0.356584	−	0.934263i	$-0.616059\pi$
$197$	−10.0098	−0.713169	−0.356584	+	0.934263i	$0.616059\pi$
$198$	11.7758	0.836870
$199$	18.0143	1.27700	0.638499	−	0.769623i	$-0.279556\pi$
$199$	18.0143	1.27700	0.638499	+	0.769623i	$0.279556\pi$
$200$	3.59623	0.254292
$201$	11.7712	0.830278
$202$	12.3568	0.869420
$203$	6.08211	0.426880
$204$	1.40007	0.0980244
$205$	17.4509	1.21883
$206$	−13.0591	−0.909872
$207$	−8.30391	−0.577161
$208$	−19.6965	−1.36571
$209$	38.9200	2.69215
$210$	−9.22895	−0.636858
$211$	11.3747	0.783070	0.391535	−	0.920163i	$-0.371944\pi$
$211$	11.3747	0.783070	0.391535	+	0.920163i	$0.371944\pi$
$212$	−17.6149	−1.20979
$213$	−8.95117	−0.613324
$214$	−24.1504	−1.65089
$215$	−2.20135	−0.150131
$216$	−1.10623	−0.0752694
$217$	7.47511	0.507444
$218$	6.16927	0.417836
$219$	2.35685	0.159261
$220$	−25.6830	−1.73155
$221$	−4.06957	−0.273749
$222$	−13.4773	−0.904537
$223$	−6.20725	−0.415668	−0.207834	−	0.978164i	$-0.566641\pi$
$223$	−6.20725	−0.415668	−0.207834	+	0.978164i	$0.566641\pi$
$224$	−11.6953	−0.781428
$225$	3.25089	0.216726
$226$	−20.3820	−1.35579
$227$	1.84375	0.122374	0.0611870	−	0.998126i	$-0.480511\pi$
$227$	1.84375	0.122374	0.0611870	+	0.998126i	$0.480511\pi$
$228$	8.53248	0.565077
$229$	23.4872	1.55208	0.776039	−	0.630684i	$-0.217226\pi$
$229$	23.4872	1.55208	0.776039	+	0.630684i	$0.217226\pi$
$230$	43.9822	2.90010
$231$	−11.1277	−0.732148
$232$	−3.86137	−0.253511
$233$	2.97745	0.195059	0.0975296	−	0.995233i	$-0.468906\pi$
$233$	2.97745	0.195059	0.0975296	+	0.995233i	$0.468906\pi$
$234$	−7.50400	−0.490552
$235$	−16.5082	−1.07688
$236$	−16.9001	−1.10010
$237$	−9.35621	−0.607751
$238$	−3.21293	−0.208264
$239$	−12.8232	−0.829466	−0.414733	−	0.909943i	$-0.636125\pi$
$239$	−12.8232	−0.829466	−0.414733	+	0.909943i	$0.636125\pi$
$240$	13.9024	0.897398
$241$	1.75410	0.112991	0.0564957	−	0.998403i	$-0.482007\pi$
$241$	1.75410	0.112991	0.0564957	+	0.998403i	$0.482007\pi$
$242$	−54.9202	−3.53040
$243$	−1.00000	−0.0641500
$244$	15.2267	0.974791
$245$	−11.3861	−0.727428
$246$	11.2024	0.714241
$247$	−24.8013	−1.57807
$248$	−4.74575	−0.301356
$249$	−13.8585	−0.878248
$250$	9.26427	0.585924
$251$	−27.3628	−1.72712	−0.863562	−	0.504243i	$-0.831772\pi$
$251$	−27.3628	−1.72712	−0.863562	+	0.504243i	$0.831772\pi$
$252$	−2.43954	−0.153676
$253$	53.0309	3.33403
$254$	−30.6855	−1.92538
$255$	2.87244	0.179879
$256$	20.9776	1.31110
$257$	30.5389	1.90496	0.952482	−	0.304596i	$-0.0985215\pi$
$257$	30.5389	1.90496	0.952482	+	0.304596i	$0.0985215\pi$
$258$	−1.41313	−0.0879778
$259$	12.7355	0.791347
$260$	16.3662	1.01499
$261$	−3.49057	−0.216061
$262$	−27.0325	−1.67007
$263$	6.00881	0.370519	0.185260	−	0.982690i	$-0.440687\pi$
$263$	6.00881	0.370519	0.185260	+	0.982690i	$0.440687\pi$
$264$	7.06468	0.434801
$265$	−36.1394	−2.22002
$266$	−19.5807	−1.20057
$267$	4.68455	0.286690
$268$	−16.4805	−1.00671
$269$	−6.01468	−0.366722	−0.183361	−	0.983046i	$-0.558698\pi$
$269$	−6.01468	−0.366722	−0.183361	+	0.983046i	$0.558698\pi$
$270$	5.29656	0.322339
$271$	−24.3492	−1.47911	−0.739553	−	0.673098i	$-0.764963\pi$
$271$	−24.3492	−1.47911	−0.739553	+	0.673098i	$0.764963\pi$
$272$	4.83995	0.293465
$273$	7.09099	0.429166
$274$	−34.6459	−2.09303
$275$	−20.7610	−1.25194
$276$	11.6260	0.699805
$277$	−0.321627	−0.0193247	−0.00966235	−	0.999953i	$-0.503076\pi$
$277$	−0.321627	−0.0193247	−0.00966235	+	0.999953i	$0.503076\pi$
$278$	−27.1483	−1.62825
$279$	−4.29002	−0.256837
$280$	−5.53674	−0.330883
$281$	3.42570	0.204360	0.102180	−	0.994766i	$-0.467418\pi$
$281$	3.42570	0.204360	0.102180	+	0.994766i	$0.467418\pi$
$282$	−10.5973	−0.631058
$283$	22.1038	1.31394	0.656968	−	0.753919i	$-0.271839\pi$
$283$	22.1038	1.31394	0.656968	+	0.753919i	$0.271839\pi$
$284$	12.5322	0.743652
$285$	17.5056	1.03694
$286$	47.9225	2.83372
$287$	−10.5859	−0.624864
$288$	6.71205	0.395511
$289$	1.00000	0.0588235
$290$	18.4880	1.08565
$291$	1.63896	0.0960775
$292$	−3.29975	−0.193103
$293$	−32.9636	−1.92575	−0.962877	−	0.269940i	$-0.912996\pi$
$293$	−32.9636	−1.92575	−0.962877	+	0.269940i	$0.912996\pi$
$294$	−7.30914	−0.426278
$295$	−34.6729	−2.01873
$296$	−8.08546	−0.469958
$297$	6.38626	0.370568
$298$	−12.4124	−0.719032
$299$	−33.7934	−1.95432
$300$	−4.55147	−0.262779
$301$	1.33536	0.0769686
$302$	−14.0018	−0.805711
$303$	6.70134	0.384982
$304$	29.4962	1.69172
$305$	31.2398	1.78878
$306$	1.84393	0.105410
$307$	31.1103	1.77556	0.887778	−	0.460272i	$-0.152248\pi$
$307$	31.1103	1.77556	0.887778	+	0.460272i	$0.152248\pi$
$308$	15.5795	0.887725
$309$	−7.08223	−0.402894
$310$	22.7224	1.29054
$311$	−2.37507	−0.134678	−0.0673388	−	0.997730i	$-0.521451\pi$
$311$	−2.37507	−0.134678	−0.0673388	+	0.997730i	$0.521451\pi$
$312$	−4.50189	−0.254869
$313$	15.5403	0.878389	0.439195	−	0.898392i	$-0.355264\pi$
$313$	15.5403	0.878389	0.439195	+	0.898392i	$0.355264\pi$
$314$	−1.84393	−0.104059
$315$	−5.00505	−0.282003
$316$	13.0993	0.736895
$317$	11.6488	0.654261	0.327130	−	0.944979i	$-0.393918\pi$
$317$	11.6488	0.654261	0.327130	+	0.944979i	$0.393918\pi$
$318$	−23.1993	−1.30095
$319$	22.2917	1.24809
$320$	−7.74592	−0.433010
$321$	−13.0973	−0.731018
$322$	−26.6799	−1.48681
$323$	6.09433	0.339097
$324$	1.40007	0.0777816
$325$	13.2297	0.733854
$326$	41.6441	2.30645
$327$	3.34572	0.185019
$328$	6.72069	0.371088
$329$	10.0140	0.552091
$330$	−33.8252	−1.86202
$331$	25.0357	1.37609	0.688044	−	0.725669i	$-0.258470\pi$
$331$	25.0357	1.37609	0.688044	+	0.725669i	$0.258470\pi$
$332$	19.4029	1.06487
$333$	−7.30902	−0.400532
$334$	22.1718	1.21319
$335$	−33.8121	−1.84735
$336$	−8.43332	−0.460075
$337$	23.8472	1.29904	0.649519	−	0.760346i	$-0.274970\pi$
$337$	23.8472	1.29904	0.649519	+	0.760346i	$0.274970\pi$
$338$	−6.56702	−0.357199
$339$	−11.0536	−0.600348
$340$	−4.02161	−0.218102
$341$	27.3972	1.48364
$342$	11.2375	0.607654
$343$	19.1039	1.03152
$344$	−0.847783	−0.0457094
$345$	23.8524	1.28417
$346$	3.97376	0.213631
$347$	−30.6975	−1.64793	−0.823964	−	0.566641i	$-0.808242\pi$
$347$	−30.6975	−1.64793	−0.823964	+	0.566641i	$0.808242\pi$
$348$	4.88703	0.261972
$349$	−11.7481	−0.628859	−0.314430	−	0.949281i	$-0.601813\pi$
$349$	−11.7481	−0.628859	−0.314430	+	0.949281i	$0.601813\pi$
$350$	10.4449	0.558303
$351$	−4.06957	−0.217218
$352$	−42.8649	−2.28471
$353$	−28.6255	−1.52358	−0.761790	−	0.647824i	$-0.775679\pi$
$353$	−28.6255	−1.52358	−0.761790	+	0.647824i	$0.775679\pi$
$354$	−22.2579	−1.18299
$355$	25.7117	1.36463
$356$	−6.55869	−0.347610
$357$	−1.74244	−0.0922197
$358$	−23.7320	−1.25427
$359$	3.06994	0.162025	0.0810126	−	0.996713i	$-0.474185\pi$
$359$	3.06994	0.162025	0.0810126	+	0.996713i	$0.474185\pi$
$360$	3.17758	0.167473
$361$	18.1408	0.954781
$362$	28.4651	1.49609
$363$	−29.7843	−1.56327
$364$	−9.92787	−0.520362
$365$	−6.76989	−0.354352
$366$	20.0540	1.04824
$367$	−10.2859	−0.536921	−0.268461	−	0.963291i	$-0.586515\pi$
$367$	−10.2859	−0.536921	−0.268461	+	0.963291i	$0.586515\pi$
$368$	40.1905	2.09507
$369$	6.07531	0.316268
$370$	38.7127	2.01258
$371$	21.9224	1.13815
$372$	6.00633	0.311414
$373$	−19.8035	−1.02539	−0.512694	−	0.858571i	$-0.671353\pi$
$373$	−19.8035	−1.02539	−0.512694	+	0.858571i	$0.671353\pi$
$374$	−11.7758	−0.608912
$375$	5.02421	0.259449
$376$	−6.35764	−0.327870
$377$	−14.2051	−0.731601
$378$	−3.21293	−0.165256
$379$	−14.7351	−0.756892	−0.378446	−	0.925623i	$-0.623541\pi$
$379$	−14.7351	−0.756892	−0.378446	+	0.925623i	$0.623541\pi$
$380$	−24.5090	−1.25728
$381$	−16.6414	−0.852564
$382$	−15.4843	−0.792248
$383$	−33.1654	−1.69467	−0.847337	−	0.531055i	$-0.821796\pi$
$383$	−33.1654	−1.69467	−0.847337	+	0.531055i	$0.821796\pi$
$384$	8.45169	0.431299
$385$	31.9636	1.62901
$386$	−12.3350	−0.627837
$387$	−0.766371	−0.0389568
$388$	−2.29466	−0.116493
$389$	−17.0589	−0.864922	−0.432461	−	0.901653i	$-0.642355\pi$
$389$	−17.0589	−0.864922	−0.432461	+	0.901653i	$0.642355\pi$
$390$	21.5548	1.09147
$391$	8.30391	0.419947
$392$	−4.38499	−0.221475
$393$	−14.6603	−0.739512
$394$	18.4573	0.929868
$395$	26.8751	1.35223
$396$	−8.94120	−0.449312
$397$	10.7867	0.541370	0.270685	−	0.962668i	$-0.412750\pi$
$397$	10.7867	0.541370	0.270685	+	0.962668i	$0.412750\pi$
$398$	−33.2170	−1.66502
$399$	−10.6190	−0.531615
$400$	−15.7341	−0.786707
$401$	−37.9872	−1.89699	−0.948495	−	0.316793i	$-0.897394\pi$
$401$	−37.9872	−1.89699	−0.948495	+	0.316793i	$0.897394\pi$
$402$	−21.7053	−1.08256
$403$	−17.4586	−0.869673
$404$	−9.38233	−0.466788
$405$	2.87244	0.142733
$406$	−11.2150	−0.556589
$407$	46.6773	2.31371
$408$	1.10623	0.0547666
$409$	−19.9989	−0.988880	−0.494440	−	0.869212i	$-0.664627\pi$
$409$	−19.9989	−0.988880	−0.494440	+	0.869212i	$0.664627\pi$
$410$	−32.1783	−1.58917
$411$	−18.7892	−0.926802
$412$	9.91561	0.488507
$413$	21.0328	1.03496
$414$	15.3118	0.752534
$415$	39.8077	1.95408
$416$	27.3152	1.33924
$417$	−14.7231	−0.720993
$418$	−71.7656	−3.51017
$419$	−32.3690	−1.58133	−0.790665	−	0.612249i	$-0.790265\pi$
$419$	−32.3690	−1.58133	−0.790665	+	0.612249i	$0.790265\pi$
$420$	7.00741	0.341927
$421$	−23.9798	−1.16870	−0.584351	−	0.811501i	$-0.698651\pi$
$421$	−23.9798	−1.16870	−0.584351	+	0.811501i	$0.698651\pi$
$422$	−20.9742	−1.02101
$423$	−5.74712	−0.279435
$424$	−13.9180	−0.675916
$425$	−3.25089	−0.157691
$426$	16.5053	0.799685
$427$	−18.9503	−0.917068
$428$	18.3371	0.886356
$429$	25.9894	1.25478
$430$	4.05913	0.195749
$431$	7.52381	0.362409	0.181205	−	0.983445i	$-0.442000\pi$
$431$	7.52381	0.362409	0.181205	+	0.983445i	$0.442000\pi$
$432$	4.83995	0.232862
$433$	37.5045	1.80235	0.901177	−	0.433452i	$-0.142705\pi$
$433$	37.5045	1.80235	0.901177	+	0.433452i	$0.142705\pi$
$434$	−13.7836	−0.661632
$435$	10.0264	0.480731
$436$	−4.68424	−0.224334
$437$	50.6067	2.42085
$438$	−4.34585	−0.207653
$439$	8.11706	0.387406	0.193703	−	0.981060i	$-0.437950\pi$
$439$	8.11706	0.387406	0.193703	+	0.981060i	$0.437950\pi$
$440$	−20.2928	−0.967423
$441$	−3.96390	−0.188757
$442$	7.50400	0.356929
$443$	−5.87092	−0.278936	−0.139468	−	0.990227i	$-0.544539\pi$
$443$	−5.87092	−0.278936	−0.139468	+	0.990227i	$0.544539\pi$
$444$	10.2331	0.485643
$445$	−13.4561	−0.637879
$446$	11.4457	0.541971
$447$	−6.73151	−0.318390
$448$	4.69873	0.221994
$449$	−38.4946	−1.81667	−0.908337	−	0.418239i	$-0.862647\pi$
$449$	−38.4946	−1.81667	−0.908337	+	0.418239i	$0.862647\pi$
$450$	−5.99441	−0.282579
$451$	−38.7985	−1.82695
$452$	15.4758	0.727918
$453$	−7.59344	−0.356771
$454$	−3.39974	−0.159558
$455$	−20.3684	−0.954886
$456$	6.74173	0.315710
$457$	15.8746	0.742585	0.371292	−	0.928516i	$-0.378915\pi$
$457$	15.8746	0.742585	0.371292	+	0.928516i	$0.378915\pi$
$458$	−43.3087	−2.02368
$459$	1.00000	0.0466760
$460$	−33.3950	−1.55705
$461$	−7.16872	−0.333880	−0.166940	−	0.985967i	$-0.553389\pi$
$461$	−7.16872	−0.333880	−0.166940	+	0.985967i	$0.553389\pi$
$462$	20.5186	0.954613
$463$	−19.7678	−0.918686	−0.459343	−	0.888259i	$-0.651915\pi$
$463$	−19.7678	−0.918686	−0.459343	+	0.888259i	$0.651915\pi$
$464$	16.8942	0.784291
$465$	12.3228	0.571457
$466$	−5.49020	−0.254329
$467$	−3.37582	−0.156214	−0.0781071	−	0.996945i	$-0.524888\pi$
$467$	−3.37582	−0.156214	−0.0781071	+	0.996945i	$0.524888\pi$
$468$	5.69768	0.263375
$469$	20.5107	0.947094
$470$	30.4400	1.40409
$471$	−1.00000	−0.0460776
$472$	−13.3532	−0.614630
$473$	4.89425	0.225038
$474$	17.2522	0.792418
$475$	−19.8120	−0.909036
$476$	2.43954	0.111816
$477$	−12.5814	−0.576064
$478$	23.6451	1.08150
$479$	−16.2842	−0.744044	−0.372022	−	0.928224i	$-0.621335\pi$
$479$	−16.2842	−0.744044	−0.372022	+	0.928224i	$0.621335\pi$
$480$	−19.2799	−0.880004
$481$	−29.7446	−1.35624
$482$	−3.23443	−0.147324
$483$	−14.4691	−0.658365
$484$	41.7001	1.89546
$485$	−4.70781	−0.213771
$486$	1.84393	0.0836422
$487$	16.4040	0.743337	0.371668	−	0.928366i	$-0.378786\pi$
$487$	16.4040	0.743337	0.371668	+	0.928366i	$0.378786\pi$
$488$	12.0310	0.544619
$489$	22.5844	1.02130
$490$	20.9951	0.948460
$491$	−10.0739	−0.454629	−0.227315	−	0.973821i	$-0.572995\pi$
$491$	−10.0739	−0.454629	−0.227315	+	0.973821i	$0.572995\pi$
$492$	−8.50585	−0.383473
$493$	3.49057	0.157207
$494$	45.7318	2.05757
$495$	−18.3441	−0.824507
$496$	20.7635	0.932308
$497$	−15.5969	−0.699616
$498$	25.5541	1.14511
$499$	−7.05969	−0.316035	−0.158018	−	0.987436i	$-0.550510\pi$
$499$	−7.05969	−0.316035	−0.158018	+	0.987436i	$0.550510\pi$
$500$	−7.03423	−0.314580
$501$	12.0242	0.537202
$502$	50.4550	2.25192
$503$	−1.95177	−0.0870251	−0.0435126	−	0.999053i	$-0.513855\pi$
$503$	−1.95177	−0.0870251	−0.0435126	+	0.999053i	$0.513855\pi$
$504$	−1.92754	−0.0858595
$505$	−19.2492	−0.856576
$506$	−97.7852	−4.34708
$507$	−3.56143	−0.158169
$508$	23.2991	1.03373
$509$	11.5547	0.512154	0.256077	−	0.966656i	$-0.417570\pi$
$509$	11.5547	0.512154	0.256077	+	0.966656i	$0.417570\pi$
$510$	−5.29656	−0.234536
$511$	4.10666	0.181668
$512$	−21.7778	−0.962450
$513$	6.09433	0.269071
$514$	−56.3115	−2.48379
$515$	20.3433	0.896431
$516$	1.07297	0.0472349
$517$	36.7026	1.61418
$518$	−23.4834	−1.03180
$519$	2.15505	0.0945963
$520$	12.9314	0.567079
$521$	17.5320	0.768089	0.384044	−	0.923315i	$-0.374531\pi$
$521$	17.5320	0.768089	0.384044	+	0.923315i	$0.374531\pi$
$522$	6.43635	0.281711
$523$	−8.81713	−0.385546	−0.192773	−	0.981243i	$-0.561748\pi$
$523$	−8.81713	−0.385546	−0.192773	+	0.981243i	$0.561748\pi$
$524$	20.5254	0.896655
$525$	5.66448	0.247218
$526$	−11.0798	−0.483103
$527$	4.29002	0.186876
$528$	−30.9092	−1.34515
$529$	45.9549	1.99804
$530$	66.6384	2.89459
$531$	−12.0709	−0.523832
$532$	14.8673	0.644581
$533$	24.7239	1.07091
$534$	−8.63797	−0.373802
$535$	37.6211	1.62650
$536$	−13.0217	−0.562451
$537$	−12.8703	−0.555396
$538$	11.0906	0.478151
$539$	25.3145	1.09037
$540$	−4.02161	−0.173062
$541$	−11.8970	−0.511493	−0.255747	−	0.966744i	$-0.582321\pi$
$541$	−11.8970	−0.511493	−0.255747	+	0.966744i	$0.582321\pi$
$542$	44.8981	1.92854
$543$	15.4372	0.662474
$544$	−6.71205	−0.287777
$545$	−9.61037	−0.411663
$546$	−13.0753	−0.559570
$547$	−0.931758	−0.0398391	−0.0199195	−	0.999802i	$-0.506341\pi$
$547$	−0.931758	−0.0398391	−0.0199195	+	0.999802i	$0.506341\pi$
$548$	26.3061	1.12374
$549$	10.8757	0.464164
$550$	38.2818	1.63234
$551$	21.2727	0.906246
$552$	9.18603	0.390984
$553$	−16.3026	−0.693259
$554$	0.593057	0.0251966
$555$	20.9947	0.891175
$556$	20.6134	0.874201
$557$	−43.0936	−1.82593	−0.912967	−	0.408033i	$-0.866215\pi$
$557$	−43.0936	−1.82593	−0.912967	+	0.408033i	$0.866215\pi$
$558$	7.91049	0.334878
$559$	−3.11880	−0.131911
$560$	24.2242	1.02366
$561$	−6.38626	−0.269628
$562$	−6.31674	−0.266455
$563$	0.250716	0.0105664	0.00528321	−	0.999986i	$-0.498318\pi$
$563$	0.250716	0.0105664	0.00528321	+	0.999986i	$0.498318\pi$
$564$	8.04636	0.338813
$565$	31.7507	1.33576
$566$	−40.7578	−1.71318
$567$	−1.74244	−0.0731756
$568$	9.90205	0.415481
$569$	36.2795	1.52091	0.760457	−	0.649388i	$-0.224975\pi$
$569$	36.2795	1.52091	0.760457	+	0.649388i	$0.224975\pi$
$570$	−32.2790	−1.35202
$571$	−17.0886	−0.715136	−0.357568	−	0.933887i	$-0.616394\pi$
$571$	−17.0886	−0.715136	−0.357568	+	0.933887i	$0.616394\pi$
$572$	−36.3869	−1.52141
$573$	−8.39748	−0.350810
$574$	19.5196	0.814731
$575$	−26.9951	−1.12577
$576$	−2.69664	−0.112360
$577$	−7.90358	−0.329030	−0.164515	−	0.986375i	$-0.552606\pi$
$577$	−7.90358	−0.329030	−0.164515	+	0.986375i	$0.552606\pi$
$578$	−1.84393	−0.0766973
$579$	−6.68955	−0.278008
$580$	−14.0377	−0.582883
$581$	−24.1477	−1.00181
$582$	−3.02212	−0.125271
$583$	80.3483	3.32769
$584$	−2.60721	−0.107887
$585$	11.6896	0.483305
$586$	60.7825	2.51090
$587$	2.67259	0.110310	0.0551548	−	0.998478i	$-0.482435\pi$
$587$	2.67259	0.110310	0.0551548	+	0.998478i	$0.482435\pi$
$588$	5.54973	0.228867
$589$	26.1448	1.07728
$590$	63.9343	2.63213
$591$	10.0098	0.411748
$592$	35.3752	1.45391
$593$	−14.6989	−0.603610	−0.301805	−	0.953370i	$-0.597589\pi$
$593$	−14.6989	−0.603610	−0.301805	+	0.953370i	$0.597589\pi$
$594$	−11.7758	−0.483167
$595$	5.00505	0.205187
$596$	9.42458	0.386046
$597$	−18.0143	−0.737275
$598$	62.3125	2.54815
$599$	17.1705	0.701567	0.350784	−	0.936457i	$-0.385915\pi$
$599$	17.1705	0.701567	0.350784	+	0.936457i	$0.385915\pi$
$600$	−3.59623	−0.146816
$601$	41.5047	1.69301	0.846505	−	0.532380i	$-0.178702\pi$
$601$	41.5047	1.69301	0.846505	+	0.532380i	$0.178702\pi$
$602$	−2.46230	−0.100356
$603$	−11.7712	−0.479361
$604$	10.6313	0.432583
$605$	85.5536	3.47825
$606$	−12.3568	−0.501960
$607$	44.2334	1.79538	0.897689	−	0.440630i	$-0.145245\pi$
$607$	44.2334	1.79538	0.897689	+	0.440630i	$0.145245\pi$
$608$	−40.9054	−1.65893
$609$	−6.08211	−0.246459
$610$	−57.6039	−2.33231
$611$	−23.3883	−0.946190
$612$	−1.40007	−0.0565944
$613$	−32.0608	−1.29492	−0.647462	−	0.762098i	$-0.724170\pi$
$613$	−32.0608	−1.29492	−0.647462	+	0.762098i	$0.724170\pi$
$614$	−57.3651	−2.31507
$615$	−17.4509	−0.703690
$616$	12.3098	0.495975
$617$	6.55433	0.263867	0.131934	−	0.991259i	$-0.457881\pi$
$617$	6.55433	0.263867	0.131934	+	0.991259i	$0.457881\pi$
$618$	13.0591	0.525315
$619$	14.9034	0.599018	0.299509	−	0.954093i	$-0.403177\pi$
$619$	14.9034	0.599018	0.299509	+	0.954093i	$0.403177\pi$
$620$	−17.2528	−0.692889
$621$	8.30391	0.333224
$622$	4.37945	0.175600
$623$	8.16255	0.327026
$624$	19.6965	0.788492
$625$	−30.6862	−1.22745
$626$	−28.6552	−1.14529
$627$	−38.9200	−1.55431
$628$	1.40007	0.0558688
$629$	7.30902	0.291430
$630$	9.22895	0.367690
$631$	−30.5432	−1.21590	−0.607952	−	0.793974i	$-0.708009\pi$
$631$	−30.5432	−1.21590	−0.607952	+	0.793974i	$0.708009\pi$
$632$	10.3501	0.411706
$633$	−11.3747	−0.452106
$634$	−21.4795	−0.853060
$635$	47.8013	1.89694
$636$	17.6149	0.698475
$637$	−16.1314	−0.639149
$638$	−41.1042	−1.62733
$639$	8.95117	0.354103
$640$	−24.2769	−0.959630
$641$	−8.03845	−0.317500	−0.158750	−	0.987319i	$-0.550746\pi$
$641$	−8.03845	−0.317500	−0.158750	+	0.987319i	$0.550746\pi$
$642$	24.1504	0.953141
$643$	5.66131	0.223260	0.111630	−	0.993750i	$-0.464393\pi$
$643$	5.66131	0.223260	0.111630	+	0.993750i	$0.464393\pi$
$644$	20.2577	0.798264
$645$	2.20135	0.0866781
$646$	−11.2375	−0.442133
$647$	35.3551	1.38995	0.694977	−	0.719032i	$-0.255415\pi$
$647$	35.3551	1.38995	0.694977	+	0.719032i	$0.255415\pi$
$648$	1.10623	0.0434568
$649$	77.0879	3.02596
$650$	−24.3947	−0.956838
$651$	−7.47511	−0.292973
$652$	−31.6198	−1.23833
$653$	−31.5659	−1.23527	−0.617635	−	0.786465i	$-0.711909\pi$
$653$	−31.5659	−1.23527	−0.617635	+	0.786465i	$0.711909\pi$
$654$	−6.16927	−0.241237
$655$	42.1107	1.64540
$656$	−29.4042	−1.14804
$657$	−2.35685	−0.0919493
$658$	−18.4651	−0.719845
$659$	20.5937	0.802215	0.401108	−	0.916031i	$-0.368625\pi$
$659$	20.5937	0.802215	0.401108	+	0.916031i	$0.368625\pi$
$660$	25.6830	0.999711
$661$	17.4598	0.679106	0.339553	−	0.940587i	$-0.389724\pi$
$661$	17.4598	0.679106	0.339553	+	0.940587i	$0.389724\pi$
$662$	−46.1640	−1.79422
$663$	4.06957	0.158049
$664$	15.3307	0.594947
$665$	30.5024	1.18283
$666$	13.4773	0.522235
$667$	28.9853	1.12232
$668$	−16.8347	−0.651355
$669$	6.20725	0.239986
$670$	62.3470	2.40868
$671$	−69.4551	−2.68128
$672$	11.6953	0.451158
$673$	0.851723	0.0328315	0.0164158	−	0.999865i	$-0.494774\pi$
$673$	0.851723	0.0328315	0.0164158	+	0.999865i	$0.494774\pi$
$674$	−43.9724	−1.69375
$675$	−3.25089	−0.125127
$676$	4.98625	0.191779
$677$	4.49723	0.172842	0.0864212	−	0.996259i	$-0.472457\pi$
$677$	4.49723	0.172842	0.0864212	+	0.996259i	$0.472457\pi$
$678$	20.3820	0.782766
$679$	2.85579	0.109595
$680$	−3.17758	−0.121854
$681$	−1.84375	−0.0706527
$682$	−50.5185	−1.93445
$683$	25.7454	0.985122	0.492561	−	0.870278i	$-0.336061\pi$
$683$	25.7454	0.985122	0.492561	+	0.870278i	$0.336061\pi$
$684$	−8.53248	−0.326247
$685$	53.9707	2.06212
$686$	−35.2263	−1.34495
$687$	−23.4872	−0.896093
$688$	3.70919	0.141412
$689$	−51.2011	−1.95061
$690$	−43.9822	−1.67437
$691$	13.0508	0.496475	0.248237	−	0.968699i	$-0.420149\pi$
$691$	13.0508	0.496475	0.248237	+	0.968699i	$0.420149\pi$
$692$	−3.01722	−0.114697
$693$	11.1277	0.422706
$694$	56.6040	2.14866
$695$	42.2912	1.60420
$696$	3.86137	0.146365
$697$	−6.07531	−0.230119
$698$	21.6626	0.819940
$699$	−2.97745	−0.112617
$700$	−7.93066	−0.299751
$701$	−17.5580	−0.663158	−0.331579	−	0.943427i	$-0.607581\pi$
$701$	−17.5580	−0.663158	−0.331579	+	0.943427i	$0.607581\pi$
$702$	7.50400	0.283220
$703$	44.5435	1.67999
$704$	17.2214	0.649057
$705$	16.5082	0.621736
$706$	52.7833	1.98653
$707$	11.6767	0.439147
$708$	16.9001	0.635144
$709$	34.6324	1.30065	0.650324	−	0.759657i	$-0.274633\pi$
$709$	34.6324	1.30065	0.650324	+	0.759657i	$0.274633\pi$
$710$	−47.4104	−1.77928
$711$	9.35621	0.350885
$712$	−5.18219	−0.194211
$713$	35.6240	1.33413
$714$	3.21293	0.120241
$715$	−74.6528	−2.79186
$716$	18.0193	0.673415
$717$	12.8232	0.478893
$718$	−5.66074	−0.211257
$719$	7.03284	0.262281	0.131140	−	0.991364i	$-0.458136\pi$
$719$	7.03284	0.262281	0.131140	+	0.991364i	$0.458136\pi$
$720$	−13.9024	−0.518113
$721$	−12.3404	−0.459579
$722$	−33.4504	−1.24489
$723$	−1.75410	−0.0652357
$724$	−21.6132	−0.803246
$725$	−11.3474	−0.421434
$726$	54.9202	2.03828
$727$	18.8703	0.699859	0.349930	−	0.936776i	$-0.386205\pi$
$727$	18.8703	0.699859	0.349930	+	0.936776i	$0.386205\pi$
$728$	−7.84427	−0.290728
$729$	1.00000	0.0370370
$730$	12.4832	0.462023
$731$	0.766371	0.0283453
$732$	−15.2267	−0.562796
$733$	−7.90924	−0.292134	−0.146067	−	0.989275i	$-0.546662\pi$
$733$	−7.90924	−0.292134	−0.146067	+	0.989275i	$0.546662\pi$
$734$	18.9665	0.700067
$735$	11.3861	0.419981
$736$	−55.7362	−2.05446
$737$	75.1741	2.76907
$738$	−11.2024	−0.412367
$739$	27.1490	0.998694	0.499347	−	0.866402i	$-0.333573\pi$
$739$	27.1490	0.998694	0.499347	+	0.866402i	$0.333573\pi$
$740$	−29.3940	−1.08054
$741$	24.8013	0.911099
$742$	−40.4233	−1.48399
$743$	22.2019	0.814510	0.407255	−	0.913314i	$-0.366486\pi$
$743$	22.2019	0.814510	0.407255	+	0.913314i	$0.366486\pi$
$744$	4.74575	0.173988
$745$	19.3358	0.708410
$746$	36.5163	1.33696
$747$	13.8585	0.507057
$748$	8.94120	0.326923
$749$	−22.8212	−0.833869
$750$	−9.26427	−0.338283
$751$	−19.0570	−0.695398	−0.347699	−	0.937606i	$-0.613037\pi$
$751$	−19.0570	−0.695398	−0.347699	+	0.937606i	$0.613037\pi$
$752$	27.8157	1.01434
$753$	27.3628	0.997155
$754$	26.1932	0.953900
$755$	21.8117	0.793808
$756$	2.43954	0.0887251
$757$	33.1730	1.20569	0.602847	−	0.797857i	$-0.294033\pi$
$757$	33.1730	1.20569	0.602847	+	0.797857i	$0.294033\pi$
$758$	27.1705	0.986876
$759$	−53.0309	−1.92490
$760$	−19.3652	−0.702449
$761$	4.57317	0.165777	0.0828886	−	0.996559i	$-0.473585\pi$
$761$	4.57317	0.165777	0.0828886	+	0.996559i	$0.473585\pi$
$762$	30.6855	1.11162
$763$	5.82972	0.211050
$764$	11.7570	0.425355
$765$	−2.87244	−0.103853
$766$	61.1547	2.20961
$767$	−49.1234	−1.77374
$768$	−20.9776	−0.756963
$769$	28.7835	1.03796	0.518979	−	0.854787i	$-0.326312\pi$
$769$	28.7835	1.03796	0.518979	+	0.854787i	$0.326312\pi$
$770$	−58.9385	−2.12400
$771$	−30.5389	−1.09983
$772$	9.36583	0.337083
$773$	40.1050	1.44248	0.721238	−	0.692687i	$-0.243573\pi$
$773$	40.1050	1.44248	0.721238	+	0.692687i	$0.243573\pi$
$774$	1.41313	0.0507940
$775$	−13.9464	−0.500969
$776$	−1.81307	−0.0650853
$777$	−12.7355	−0.456885
$778$	31.4554	1.12773
$779$	−37.0249	−1.32656
$780$	−16.3662	−0.586005
$781$	−57.1645	−2.04551
$782$	−15.3118	−0.547549
$783$	3.49057	0.124743
$784$	19.1851	0.685181
$785$	2.87244	0.102522
$786$	27.0325	0.964216
$787$	15.9291	0.567812	0.283906	−	0.958852i	$-0.408370\pi$
$787$	15.9291	0.567812	0.283906	+	0.958852i	$0.408370\pi$
$788$	−14.0144	−0.499243
$789$	−6.00881	−0.213919
$790$	−49.5558	−1.76311
$791$	−19.2602	−0.684814
$792$	−7.06468	−0.251032
$793$	44.2595	1.57170
$794$	−19.8899	−0.705868
$795$	36.1394	1.28173
$796$	25.2212	0.893942
$797$	−45.8689	−1.62476	−0.812381	−	0.583128i	$-0.801829\pi$
$797$	−45.8689	−1.62476	−0.812381	+	0.583128i	$0.801829\pi$
$798$	19.5807	0.693148
$799$	5.74712	0.203318
$800$	21.8201	0.771458
$801$	−4.68455	−0.165521
$802$	70.0456	2.47340
$803$	15.0514	0.531154
$804$	16.4805	0.581223
$805$	41.5615	1.46485
$806$	32.1923	1.13393
$807$	6.01468	0.211727
$808$	−7.41322	−0.260796
$809$	27.3337	0.961003	0.480502	−	0.876994i	$-0.340455\pi$
$809$	27.3337	0.961003	0.480502	+	0.876994i	$0.340455\pi$
$810$	−5.29656	−0.186102
$811$	33.6663	1.18218	0.591092	−	0.806604i	$-0.298697\pi$
$811$	33.6663	1.18218	0.591092	+	0.806604i	$0.298697\pi$
$812$	8.51536	0.298831
$813$	24.3492	0.853962
$814$	−86.0695	−3.01674
$815$	−64.8724	−2.27238
$816$	−4.83995	−0.169432
$817$	4.67052	0.163401
$818$	36.8765	1.28935
$819$	−7.09099	−0.247779
$820$	24.4325	0.853221
$821$	16.0006	0.558425	0.279213	−	0.960229i	$-0.409927\pi$
$821$	16.0006	0.558425	0.279213	+	0.960229i	$0.409927\pi$
$822$	34.6459	1.20841
$823$	13.6616	0.476214	0.238107	−	0.971239i	$-0.423473\pi$
$823$	13.6616	0.476214	0.238107	+	0.971239i	$0.423473\pi$
$824$	7.83458	0.272931
$825$	20.7610	0.722806
$826$	−38.7830	−1.34943
$827$	41.8606	1.45563	0.727817	−	0.685771i	$-0.240535\pi$
$827$	41.8606	1.45563	0.727817	+	0.685771i	$0.240535\pi$
$828$	−11.6260	−0.404033
$829$	32.7708	1.13818	0.569088	−	0.822277i	$-0.307296\pi$
$829$	32.7708	1.13818	0.569088	+	0.822277i	$0.307296\pi$
$830$	−73.4026	−2.54784
$831$	0.321627	0.0111571
$832$	−10.9742	−0.380461
$833$	3.96390	0.137341
$834$	27.1483	0.940070
$835$	−34.5388	−1.19526
$836$	54.4906	1.88460
$837$	4.29002	0.148285
$838$	59.6861	2.06182
$839$	−3.14118	−0.108446	−0.0542228	−	0.998529i	$-0.517268\pi$
$839$	−3.14118	−0.108446	−0.0542228	+	0.998529i	$0.517268\pi$
$840$	5.53674	0.191036
$841$	−16.8159	−0.579860
$842$	44.2169	1.52382
$843$	−3.42570	−0.117987
$844$	15.9254	0.548176
$845$	10.2300	0.351922
$846$	10.5973	0.364342
$847$	−51.8974	−1.78322
$848$	60.8935	2.09109
$849$	−22.1038	−0.758601
$850$	5.99441	0.205606
$851$	60.6934	2.08054
$852$	−12.5322	−0.429348
$853$	−30.4555	−1.04278	−0.521389	−	0.853319i	$-0.674586\pi$
$853$	−30.4555	−1.04278	−0.521389	+	0.853319i	$0.674586\pi$
$854$	34.9429	1.19572
$855$	−17.5056	−0.598678
$856$	14.4886	0.495210
$857$	32.1949	1.09976	0.549878	−	0.835245i	$-0.314674\pi$
$857$	32.1949	1.09976	0.549878	+	0.835245i	$0.314674\pi$
$858$	−47.9225	−1.63605
$859$	6.01925	0.205374	0.102687	−	0.994714i	$-0.467256\pi$
$859$	6.01925	0.205374	0.102687	+	0.994714i	$0.467256\pi$
$860$	−3.08204	−0.105097
$861$	10.5859	0.360765
$862$	−13.8734	−0.472528
$863$	−46.7530	−1.59149	−0.795745	−	0.605632i	$-0.792920\pi$
$863$	−46.7530	−1.59149	−0.795745	+	0.605632i	$0.792920\pi$
$864$	−6.71205	−0.228348
$865$	−6.19025	−0.210475
$866$	−69.1557	−2.35000
$867$	−1.00000	−0.0339618
$868$	10.4657	0.355228
$869$	−59.7512	−2.02692
$870$	−18.4880	−0.626802
$871$	−47.9039	−1.62316
$872$	−3.70114	−0.125336
$873$	−1.63896	−0.0554704
$874$	−93.3151	−3.15643
$875$	8.75438	0.295952
$876$	3.29975	0.111488
$877$	30.1199	1.01708	0.508539	−	0.861039i	$-0.330186\pi$
$877$	30.1199	1.01708	0.508539	+	0.861039i	$0.330186\pi$
$878$	−14.9673	−0.505121
$879$	32.9636	1.11183
$880$	88.7846	2.99293
$881$	−34.6280	−1.16665	−0.583323	−	0.812240i	$-0.698248\pi$
$881$	−34.6280	−1.16665	−0.583323	+	0.812240i	$0.698248\pi$
$882$	7.30914	0.246112
$883$	2.50462	0.0842870	0.0421435	−	0.999112i	$-0.486581\pi$
$883$	2.50462	0.0842870	0.0421435	+	0.999112i	$0.486581\pi$
$884$	−5.69768	−0.191634
$885$	34.6729	1.16552
$886$	10.8256	0.363692
$887$	−36.8409	−1.23700	−0.618498	−	0.785787i	$-0.712258\pi$
$887$	−36.8409	−1.23700	−0.618498	+	0.785787i	$0.712258\pi$
$888$	8.08546	0.271330
$889$	−28.9966	−0.972515
$890$	24.8120	0.831701
$891$	−6.38626	−0.213948
$892$	−8.69058	−0.290982
$893$	35.0248	1.17206
$894$	12.4124	0.415133
$895$	36.9692	1.23574
$896$	14.7266	0.491980
$897$	33.7934	1.12833
$898$	70.9813	2.36868
$899$	14.9746	0.499431
$900$	4.55147	0.151716
$901$	12.5814	0.419148
$902$	71.5417	2.38208
$903$	−1.33536	−0.0444379
$904$	12.2278	0.406691
$905$	−44.3424	−1.47399
$906$	14.0018	0.465177
$907$	−39.8726	−1.32395	−0.661973	−	0.749528i	$-0.730281\pi$
$907$	−39.8726	−1.32395	−0.661973	+	0.749528i	$0.730281\pi$
$908$	2.58138	0.0856660
$909$	−6.70134	−0.222269
$910$	37.5579	1.24503
$911$	−52.5470	−1.74096	−0.870479	−	0.492205i	$-0.836191\pi$
$911$	−52.5470	−1.74096	−0.870479	+	0.492205i	$0.836191\pi$
$912$	−29.4962	−0.976717
$913$	−88.5042	−2.92906
$914$	−29.2717	−0.968222
$915$	−31.2398	−1.03275
$916$	32.8837	1.08651
$917$	−25.5446	−0.843558
$918$	−1.84393	−0.0608587
$919$	−54.9549	−1.81280	−0.906398	−	0.422425i	$-0.861179\pi$
$919$	−54.9549	−1.81280	−0.906398	+	0.422425i	$0.861179\pi$
$920$	−26.3863	−0.869930
$921$	−31.1103	−1.02512
$922$	13.2186	0.435331
$923$	36.4274	1.19902
$924$	−15.5795	−0.512528
$925$	−23.7608	−0.781251
$926$	36.4503	1.19783
$927$	7.08223	0.232611
$928$	−23.4289	−0.769090
$929$	43.1027	1.41415	0.707077	−	0.707137i	$-0.250013\pi$
$929$	43.1027	1.41415	0.707077	+	0.707137i	$0.250013\pi$
$930$	−22.7224	−0.745096
$931$	24.1573	0.791724
$932$	4.16863	0.136548
$933$	2.37507	0.0777562
$934$	6.22476	0.203680
$935$	18.3441	0.599917
$936$	4.50189	0.147149
$937$	12.4661	0.407251	0.203625	−	0.979049i	$-0.434728\pi$
$937$	12.4661	0.407251	0.203625	+	0.979049i	$0.434728\pi$
$938$	−37.8202	−1.23487
$939$	−15.5403	−0.507138
$940$	−23.1127	−0.753852
$941$	−50.2431	−1.63788	−0.818939	−	0.573881i	$-0.805437\pi$
$941$	−50.2431	−1.63788	−0.818939	+	0.573881i	$0.805437\pi$
$942$	1.84393	0.0600784
$943$	−50.4488	−1.64284
$944$	58.4225	1.90149
$945$	5.00505	0.162814
$946$	−9.02463	−0.293416
$947$	40.2429	1.30772	0.653859	−	0.756616i	$-0.273149\pi$
$947$	40.2429	1.30772	0.653859	+	0.756616i	$0.273149\pi$
$948$	−13.0993	−0.425446
$949$	−9.59136	−0.311349
$950$	36.5319	1.18525
$951$	−11.6488	−0.377738
$952$	1.92754	0.0624720
$953$	−28.8519	−0.934606	−0.467303	−	0.884097i	$-0.654774\pi$
$953$	−28.8519	−0.934606	−0.467303	+	0.884097i	$0.654774\pi$
$954$	23.1993	0.751103
$955$	24.1212	0.780544
$956$	−17.9534	−0.580655
$957$	−22.2917	−0.720587
$958$	30.0269	0.970124
$959$	−32.7390	−1.05720
$960$	7.74592	0.249998
$961$	−12.5957	−0.406313
$962$	54.8469	1.76833
$963$	13.0973	0.422054
$964$	2.45586	0.0790979
$965$	19.2153	0.618563
$966$	26.6799	0.858412
$967$	18.9260	0.608621	0.304310	−	0.952573i	$-0.401574\pi$
$967$	18.9260	0.608621	0.304310	+	0.952573i	$0.401574\pi$
$968$	32.9483	1.05900
$969$	−6.09433	−0.195778
$970$	8.68086	0.278725
$971$	5.12362	0.164425	0.0822124	−	0.996615i	$-0.473801\pi$
$971$	5.12362	0.164425	0.0822124	+	0.996615i	$0.473801\pi$
$972$	−1.40007	−0.0449072
$973$	−25.6541	−0.822434
$974$	−30.2478	−0.969202
$975$	−13.2297	−0.423691
$976$	−52.6378	−1.68490
$977$	−23.3811	−0.748029	−0.374014	−	0.927423i	$-0.622019\pi$
$977$	−23.3811	−0.748029	−0.374014	+	0.927423i	$0.622019\pi$
$978$	−41.6441	−1.33163
$979$	29.9168	0.956144
$980$	−15.9413	−0.509225
$981$	−3.34572	−0.106821
$982$	18.5756	0.592770
$983$	25.5210	0.813994	0.406997	−	0.913430i	$-0.366576\pi$
$983$	25.5210	0.813994	0.406997	+	0.913430i	$0.366576\pi$
$984$	−6.72069	−0.214248
$985$	−28.7525	−0.916131
$986$	−6.43635	−0.204975
$987$	−10.0140	−0.318750
$988$	−34.7235	−1.10470
$989$	6.36387	0.202359
$990$	33.8252	1.07504
$991$	−49.6811	−1.57817	−0.789086	−	0.614282i	$-0.789446\pi$
$991$	−49.6811	−1.57817	−0.789086	+	0.614282i	$0.789446\pi$
$992$	−28.7948	−0.914237
$993$	−25.0357	−0.794484
$994$	28.7595	0.912196
$995$	51.7448	1.64042
$996$	−19.4029	−0.614804
$997$	−19.8543	−0.628791	−0.314395	−	0.949292i	$-0.601802\pi$
$997$	−19.8543	−0.628791	−0.314395	+	0.949292i	$0.601802\pi$
$998$	13.0176	0.412064
$999$	7.30902	0.231247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.13	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-1.84393 q^{2} -1.00000 q^{3} +1.40007 q^{4} +2.87244 q^{5} +1.84393 q^{6} -1.74244 q^{7} +1.10623 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.84393 q^{2} -1.00000 q^{3} +1.40007 q^{4} +2.87244 q^{5} +1.84393 q^{6} -1.74244 q^{7} +1.10623 q^{8} +1.00000 q^{9} -5.29656 q^{10} -6.38626 q^{11} -1.40007 q^{12} +4.06957 q^{13} +3.21293 q^{14} -2.87244 q^{15} -4.83995 q^{16} -1.00000 q^{17} -1.84393 q^{18} -6.09433 q^{19} +4.02161 q^{20} +1.74244 q^{21} +11.7758 q^{22} -8.30391 q^{23} -1.10623 q^{24} +3.25089 q^{25} -7.50400 q^{26} -1.00000 q^{27} -2.43954 q^{28} -3.49057 q^{29} +5.29656 q^{30} -4.29002 q^{31} +6.71205 q^{32} +6.38626 q^{33} +1.84393 q^{34} -5.00505 q^{35} +1.40007 q^{36} -7.30902 q^{37} +11.2375 q^{38} -4.06957 q^{39} +3.17758 q^{40} +6.07531 q^{41} -3.21293 q^{42} -0.766371 q^{43} -8.94120 q^{44} +2.87244 q^{45} +15.3118 q^{46} -5.74712 q^{47} +4.83995 q^{48} -3.96390 q^{49} -5.99441 q^{50} +1.00000 q^{51} +5.69768 q^{52} -12.5814 q^{53} +1.84393 q^{54} -18.3441 q^{55} -1.92754 q^{56} +6.09433 q^{57} +6.43635 q^{58} -12.0709 q^{59} -4.02161 q^{60} +10.8757 q^{61} +7.91049 q^{62} -1.74244 q^{63} -2.69664 q^{64} +11.6896 q^{65} -11.7758 q^{66} -11.7712 q^{67} -1.40007 q^{68} +8.30391 q^{69} +9.22895 q^{70} +8.95117 q^{71} +1.10623 q^{72} -2.35685 q^{73} +13.4773 q^{74} -3.25089 q^{75} -8.53248 q^{76} +11.1277 q^{77} +7.50400 q^{78} +9.35621 q^{79} -13.9024 q^{80} +1.00000 q^{81} -11.2024 q^{82} +13.8585 q^{83} +2.43954 q^{84} -2.87244 q^{85} +1.41313 q^{86} +3.49057 q^{87} -7.06468 q^{88} -4.68455 q^{89} -5.29656 q^{90} -7.09099 q^{91} -11.6260 q^{92} +4.29002 q^{93} +10.5973 q^{94} -17.5056 q^{95} -6.71205 q^{96} -1.63896 q^{97} +7.30914 q^{98} -6.38626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 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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