LMFDB - Embedded newform 8013.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.85225 q^{2} -1.00000 q^{3} +1.43083 q^{4} +2.49048 q^{5} +1.85225 q^{6} -3.91286 q^{7} +1.05424 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.85225 q^{2} -1.00000 q^{3} +1.43083 q^{4} +2.49048 q^{5} +1.85225 q^{6} -3.91286 q^{7} +1.05424 q^{8} +1.00000 q^{9} -4.61299 q^{10} +5.91321 q^{11} -1.43083 q^{12} +2.98776 q^{13} +7.24759 q^{14} -2.49048 q^{15} -4.81438 q^{16} +2.46047 q^{17} -1.85225 q^{18} +2.62873 q^{19} +3.56345 q^{20} +3.91286 q^{21} -10.9527 q^{22} -8.65037 q^{23} -1.05424 q^{24} +1.20247 q^{25} -5.53409 q^{26} -1.00000 q^{27} -5.59864 q^{28} -7.81222 q^{29} +4.61299 q^{30} -0.209636 q^{31} +6.80896 q^{32} -5.91321 q^{33} -4.55741 q^{34} -9.74488 q^{35} +1.43083 q^{36} +8.96487 q^{37} -4.86906 q^{38} -2.98776 q^{39} +2.62557 q^{40} -8.67498 q^{41} -7.24759 q^{42} +4.28725 q^{43} +8.46081 q^{44} +2.49048 q^{45} +16.0227 q^{46} -3.94683 q^{47} +4.81438 q^{48} +8.31044 q^{49} -2.22728 q^{50} -2.46047 q^{51} +4.27498 q^{52} +10.8105 q^{53} +1.85225 q^{54} +14.7267 q^{55} -4.12510 q^{56} -2.62873 q^{57} +14.4702 q^{58} +12.9279 q^{59} -3.56345 q^{60} -6.38568 q^{61} +0.388298 q^{62} -3.91286 q^{63} -2.98313 q^{64} +7.44095 q^{65} +10.9527 q^{66} +11.7044 q^{67} +3.52052 q^{68} +8.65037 q^{69} +18.0499 q^{70} +8.36506 q^{71} +1.05424 q^{72} +0.929329 q^{73} -16.6052 q^{74} -1.20247 q^{75} +3.76127 q^{76} -23.1375 q^{77} +5.53409 q^{78} +2.58329 q^{79} -11.9901 q^{80} +1.00000 q^{81} +16.0682 q^{82} +15.0663 q^{83} +5.59864 q^{84} +6.12775 q^{85} -7.94106 q^{86} +7.81222 q^{87} +6.23396 q^{88} -12.3834 q^{89} -4.61299 q^{90} -11.6907 q^{91} -12.3772 q^{92} +0.209636 q^{93} +7.31051 q^{94} +6.54679 q^{95} -6.80896 q^{96} -1.11990 q^{97} -15.3930 q^{98} +5.91321 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9}+O(q^{10}) $ 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9} - 3 q^{10} + 55 q^{11} - 109 q^{12} - 8 q^{13} + 27 q^{14} - 16 q^{15} + 111 q^{16} + 28 q^{17} + 15 q^{18} + q^{19} + 54 q^{20} - 35 q^{21} + 20 q^{22} + 62 q^{23} - 48 q^{24} + 102 q^{25} + 21 q^{26} - 106 q^{27} + 79 q^{28} + 36 q^{29} + 3 q^{30} + q^{31} + 111 q^{32} - 55 q^{33} - 27 q^{34} + 72 q^{35} + 109 q^{36} + 31 q^{37} + 43 q^{38} + 8 q^{39} - 13 q^{40} + 35 q^{41} - 27 q^{42} + 98 q^{43} + 121 q^{44} + 16 q^{45} + 8 q^{46} + 75 q^{47} - 111 q^{48} + 49 q^{49} + 83 q^{50} - 28 q^{51} - 18 q^{52} + 60 q^{53} - 15 q^{54} + 14 q^{55} + 85 q^{56} - q^{57} + 65 q^{58} + 77 q^{59} - 54 q^{60} - 55 q^{61} + 83 q^{62} + 35 q^{63} + 122 q^{64} + 86 q^{65} - 20 q^{66} + 121 q^{67} + 80 q^{68} - 62 q^{69} - 11 q^{70} + 79 q^{71} + 48 q^{72} - 29 q^{73} + 91 q^{74} - 102 q^{75} - 10 q^{76} + 87 q^{77} - 21 q^{78} + 15 q^{79} + 108 q^{80} + 106 q^{81} + 21 q^{82} + 196 q^{83} - 79 q^{84} - 5 q^{85} + 65 q^{86} - 36 q^{87} + 84 q^{88} + 34 q^{89} - 3 q^{90} + 17 q^{91} + 162 q^{92} - q^{93} - 35 q^{94} + 113 q^{95} - 111 q^{96} - 63 q^{97} + 112 q^{98} + 55 q^{99}+O(q^{100}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9 - 3 * q^10 + 55 * q^11 - 109 * q^12 - 8 * q^13 + 27 * q^14 - 16 * q^15 + 111 * q^16 + 28 * q^17 + 15 * q^18 + q^19 + 54 * q^20 - 35 * q^21 + 20 * q^22 + 62 * q^23 - 48 * q^24 + 102 * q^25 + 21 * q^26 - 106 * q^27 + 79 * q^28 + 36 * q^29 + 3 * q^30 + q^31 + 111 * q^32 - 55 * q^33 - 27 * q^34 + 72 * q^35 + 109 * q^36 + 31 * q^37 + 43 * q^38 + 8 * q^39 - 13 * q^40 + 35 * q^41 - 27 * q^42 + 98 * q^43 + 121 * q^44 + 16 * q^45 + 8 * q^46 + 75 * q^47 - 111 * q^48 + 49 * q^49 + 83 * q^50 - 28 * q^51 - 18 * q^52 + 60 * q^53 - 15 * q^54 + 14 * q^55 + 85 * q^56 - q^57 + 65 * q^58 + 77 * q^59 - 54 * q^60 - 55 * q^61 + 83 * q^62 + 35 * q^63 + 122 * q^64 + 86 * q^65 - 20 * q^66 + 121 * q^67 + 80 * q^68 - 62 * q^69 - 11 * q^70 + 79 * q^71 + 48 * q^72 - 29 * q^73 + 91 * q^74 - 102 * q^75 - 10 * q^76 + 87 * q^77 - 21 * q^78 + 15 * q^79 + 108 * q^80 + 106 * q^81 + 21 * q^82 + 196 * q^83 - 79 * q^84 - 5 * q^85 + 65 * q^86 - 36 * q^87 + 84 * q^88 + 34 * q^89 - 3 * q^90 + 17 * q^91 + 162 * q^92 - q^93 - 35 * q^94 + 113 * q^95 - 111 * q^96 - 63 * q^97 + 112 * q^98 + 55 * 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 $

$2$	−1.85225	−1.30974	−0.654869	−	0.755742i	$-0.727276\pi$
$2$	−1.85225	−1.30974	−0.654869	+	0.755742i	$0.727276\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.43083	0.715416
$5$	2.49048	1.11377	0.556887	−	0.830588i	$-0.311995\pi$
$5$	2.49048	1.11377	0.556887	+	0.830588i	$0.311995\pi$
$6$	1.85225	0.756178
$7$	−3.91286	−1.47892	−0.739460	−	0.673200i	$-0.764919\pi$
$7$	−3.91286	−1.47892	−0.739460	+	0.673200i	$0.764919\pi$
$8$	1.05424	0.372731
$9$	1.00000	0.333333
$10$	−4.61299	−1.45875
$11$	5.91321	1.78290	0.891450	−	0.453119i	$-0.149689\pi$
$11$	5.91321	1.78290	0.891450	+	0.453119i	$0.149689\pi$
$12$	−1.43083	−0.413045
$13$	2.98776	0.828656	0.414328	−	0.910128i	$-0.364017\pi$
$13$	2.98776	0.828656	0.414328	+	0.910128i	$0.364017\pi$
$14$	7.24759	1.93700
$15$	−2.49048	−0.643038
$16$	−4.81438	−1.20360
$17$	2.46047	0.596752	0.298376	−	0.954448i	$-0.403555\pi$
$17$	2.46047	0.596752	0.298376	+	0.954448i	$0.403555\pi$
$18$	−1.85225	−0.436580
$19$	2.62873	0.603072	0.301536	−	0.953455i	$-0.402501\pi$
$19$	2.62873	0.603072	0.301536	+	0.953455i	$0.402501\pi$
$20$	3.56345	0.796812
$21$	3.91286	0.853855
$22$	−10.9527	−2.33513
$23$	−8.65037	−1.80373	−0.901864	−	0.432020i	$-0.857801\pi$
$23$	−8.65037	−1.80373	−0.901864	+	0.432020i	$0.857801\pi$
$24$	−1.05424	−0.215196
$25$	1.20247	0.240495
$26$	−5.53409	−1.08532
$27$	−1.00000	−0.192450
$28$	−5.59864	−1.05804
$29$	−7.81222	−1.45069	−0.725346	−	0.688384i	$-0.758320\pi$
$29$	−7.81222	−1.45069	−0.725346	+	0.688384i	$0.758320\pi$
$30$	4.61299	0.842212
$31$	−0.209636	−0.0376517	−0.0188259	−	0.999823i	$-0.505993\pi$
$31$	−0.209636	−0.0376517	−0.0188259	+	0.999823i	$0.505993\pi$
$32$	6.80896	1.20367
$33$	−5.91321	−1.02936
$34$	−4.55741	−0.781590
$35$	−9.74488	−1.64718
$36$	1.43083	0.238472
$37$	8.96487	1.47382	0.736908	−	0.675993i	$-0.236285\pi$
$37$	8.96487	1.47382	0.736908	+	0.675993i	$0.236285\pi$
$38$	−4.86906	−0.789866
$39$	−2.98776	−0.478425
$40$	2.62557	0.415139
$41$	−8.67498	−1.35480	−0.677402	−	0.735613i	$-0.736894\pi$
$41$	−8.67498	−1.35480	−0.677402	+	0.735613i	$0.736894\pi$
$42$	−7.24759	−1.11833
$43$	4.28725	0.653799	0.326900	−	0.945059i	$-0.393996\pi$
$43$	4.28725	0.653799	0.326900	+	0.945059i	$0.393996\pi$
$44$	8.46081	1.27551
$45$	2.49048	0.371258
$46$	16.0227	2.36241
$47$	−3.94683	−0.575704	−0.287852	−	0.957675i	$-0.592941\pi$
$47$	−3.94683	−0.575704	−0.287852	+	0.957675i	$0.592941\pi$
$48$	4.81438	0.694897
$49$	8.31044	1.18721
$50$	−2.22728	−0.314985
$51$	−2.46047	−0.344535
$52$	4.27498	0.592834
$53$	10.8105	1.48493	0.742467	−	0.669882i	$-0.233656\pi$
$53$	10.8105	1.48493	0.742467	+	0.669882i	$0.233656\pi$
$54$	1.85225	0.252059
$55$	14.7267	1.98575
$56$	−4.12510	−0.551240
$57$	−2.62873	−0.348184
$58$	14.4702	1.90003
$59$	12.9279	1.68306	0.841531	−	0.540208i	$-0.181655\pi$
$59$	12.9279	1.68306	0.841531	+	0.540208i	$0.181655\pi$
$60$	−3.56345	−0.460040
$61$	−6.38568	−0.817602	−0.408801	−	0.912623i	$-0.634053\pi$
$61$	−6.38568	−0.817602	−0.408801	+	0.912623i	$0.634053\pi$
$62$	0.388298	0.0493139
$63$	−3.91286	−0.492974
$64$	−2.98313	−0.372891
$65$	7.44095	0.922937
$66$	10.9527	1.34819
$67$	11.7044	1.42992	0.714960	−	0.699165i	$-0.246445\pi$
$67$	11.7044	1.42992	0.714960	+	0.699165i	$0.246445\pi$
$68$	3.52052	0.426926
$69$	8.65037	1.04138
$70$	18.0499	2.15738
$71$	8.36506	0.992749	0.496375	−	0.868108i	$-0.334664\pi$
$71$	8.36506	0.992749	0.496375	+	0.868108i	$0.334664\pi$
$72$	1.05424	0.124244
$73$	0.929329	0.108770	0.0543849	−	0.998520i	$-0.482680\pi$
$73$	0.929329	0.108770	0.0543849	+	0.998520i	$0.482680\pi$
$74$	−16.6052	−1.93031
$75$	−1.20247	−0.138850
$76$	3.76127	0.431447
$77$	−23.1375	−2.63677
$78$	5.53409	0.626612
$79$	2.58329	0.290643	0.145322	−	0.989384i	$-0.453578\pi$
$79$	2.58329	0.290643	0.145322	+	0.989384i	$0.453578\pi$
$80$	−11.9901	−1.34054
$81$	1.00000	0.111111
$82$	16.0682	1.77444
$83$	15.0663	1.65374	0.826871	−	0.562392i	$-0.190119\pi$
$83$	15.0663	1.65374	0.826871	+	0.562392i	$0.190119\pi$
$84$	5.59864	0.610861
$85$	6.12775	0.664648
$86$	−7.94106	−0.856306
$87$	7.81222	0.837557
$88$	6.23396	0.664543
$89$	−12.3834	−1.31264	−0.656321	−	0.754481i	$-0.727888\pi$
$89$	−12.3834	−1.31264	−0.656321	+	0.754481i	$0.727888\pi$
$90$	−4.61299	−0.486251
$91$	−11.6907	−1.22552
$92$	−12.3772	−1.29041
$93$	0.209636	0.0217382
$94$	7.31051	0.754022
$95$	6.54679	0.671686
$96$	−6.80896	−0.694936
$97$	−1.11990	−0.113709	−0.0568545	−	0.998382i	$-0.518107\pi$
$97$	−1.11990	−0.113709	−0.0568545	+	0.998382i	$0.518107\pi$
$98$	−15.3930	−1.55493
$99$	5.91321	0.594300
$100$	1.72054	0.172054
$101$	1.29987	0.129342	0.0646711	−	0.997907i	$-0.479400\pi$
$101$	1.29987	0.129342	0.0646711	+	0.997907i	$0.479400\pi$
$102$	4.55741	0.451251
$103$	−12.0219	−1.18455	−0.592275	−	0.805736i	$-0.701770\pi$
$103$	−12.0219	−1.18455	−0.592275	+	0.805736i	$0.701770\pi$
$104$	3.14983	0.308866
$105$	9.74488	0.951003
$106$	−20.0237	−1.94488
$107$	12.2729	1.18647	0.593233	−	0.805031i	$-0.297851\pi$
$107$	12.2729	1.18647	0.593233	+	0.805031i	$0.297851\pi$
$108$	−1.43083	−0.137682
$109$	−13.5005	−1.29312	−0.646559	−	0.762864i	$-0.723793\pi$
$109$	−13.5005	−1.29312	−0.646559	+	0.762864i	$0.723793\pi$
$110$	−27.2776	−2.60081
$111$	−8.96487	−0.850908
$112$	18.8380	1.78002
$113$	7.00437	0.658915	0.329458	−	0.944170i	$-0.393134\pi$
$113$	7.00437	0.658915	0.329458	+	0.944170i	$0.393134\pi$
$114$	4.86906	0.456030
$115$	−21.5436	−2.00895
$116$	−11.1780	−1.03785
$117$	2.98776	0.276219
$118$	−23.9456	−2.20437
$119$	−9.62748	−0.882549
$120$	−2.62557	−0.239680
$121$	23.9661	2.17873
$122$	11.8279	1.07085
$123$	8.67498	0.782197
$124$	−0.299954	−0.0269366
$125$	−9.45765	−0.845918
$126$	7.24759	0.645667
$127$	0.296749	0.0263322	0.0131661	−	0.999913i	$-0.495809\pi$
$127$	0.296749	0.0263322	0.0131661	+	0.999913i	$0.495809\pi$
$128$	−8.09242	−0.715276
$129$	−4.28725	−0.377471
$130$	−13.7825	−1.20881
$131$	−6.06777	−0.530143	−0.265072	−	0.964229i	$-0.585396\pi$
$131$	−6.06777	−0.530143	−0.265072	+	0.964229i	$0.585396\pi$
$132$	−8.46081	−0.736419
$133$	−10.2858	−0.891895
$134$	−21.6795	−1.87282
$135$	−2.49048	−0.214346
$136$	2.59394	0.222428
$137$	−9.36427	−0.800044	−0.400022	−	0.916506i	$-0.630997\pi$
$137$	−9.36427	−0.800044	−0.400022	+	0.916506i	$0.630997\pi$
$138$	−16.0227	−1.36394
$139$	12.8425	1.08929	0.544644	−	0.838667i	$-0.316665\pi$
$139$	12.8425	1.08929	0.544644	+	0.838667i	$0.316665\pi$
$140$	−13.9433	−1.17842
$141$	3.94683	0.332383
$142$	−15.4942	−1.30024
$143$	17.6673	1.47741
$144$	−4.81438	−0.401199
$145$	−19.4561	−1.61574
$146$	−1.72135	−0.142460
$147$	−8.31044	−0.685434
$148$	12.8272	1.05439
$149$	−8.85744	−0.725629	−0.362815	−	0.931861i	$-0.618184\pi$
$149$	−8.85744	−0.725629	−0.362815	+	0.931861i	$0.618184\pi$
$150$	2.22728	0.181857
$151$	16.6968	1.35877	0.679384	−	0.733783i	$-0.262247\pi$
$151$	16.6968	1.35877	0.679384	+	0.733783i	$0.262247\pi$
$152$	2.77132	0.224784
$153$	2.46047	0.198917
$154$	42.8565	3.45348
$155$	−0.522093	−0.0419355
$156$	−4.27498	−0.342273
$157$	−13.6014	−1.08551	−0.542755	−	0.839891i	$-0.682619\pi$
$157$	−13.6014	−1.08551	−0.542755	+	0.839891i	$0.682619\pi$
$158$	−4.78491	−0.380667
$159$	−10.8105	−0.857327
$160$	16.9576	1.34061
$161$	33.8477	2.66757
$162$	−1.85225	−0.145527
$163$	21.1855	1.65938	0.829689	−	0.558226i	$-0.188518\pi$
$163$	21.1855	1.65938	0.829689	+	0.558226i	$0.188518\pi$
$164$	−12.4124	−0.969249
$165$	−14.7267	−1.14647
$166$	−27.9066	−2.16597
$167$	−6.74008	−0.521563	−0.260782	−	0.965398i	$-0.583980\pi$
$167$	−6.74008	−0.521563	−0.260782	+	0.965398i	$0.583980\pi$
$168$	4.12510	0.318259
$169$	−4.07327	−0.313328
$170$	−11.3501	−0.870515
$171$	2.62873	0.201024
$172$	6.13433	0.467738
$173$	1.54401	0.117389	0.0586945	−	0.998276i	$-0.481306\pi$
$173$	1.54401	0.117389	0.0586945	+	0.998276i	$0.481306\pi$
$174$	−14.4702	−1.09698
$175$	−4.70510	−0.355672
$176$	−28.4685	−2.14589
$177$	−12.9279	−0.971717
$178$	22.9372	1.71922
$179$	−10.1934	−0.761889	−0.380945	−	0.924598i	$-0.624401\pi$
$179$	−10.1934	−0.761889	−0.380945	+	0.924598i	$0.624401\pi$
$180$	3.56345	0.265604
$181$	6.83648	0.508152	0.254076	−	0.967184i	$-0.418229\pi$
$181$	6.83648	0.508152	0.254076	+	0.967184i	$0.418229\pi$
$182$	21.6541	1.60511
$183$	6.38568	0.472043
$184$	−9.11960	−0.672306
$185$	22.3268	1.64150
$186$	−0.388298	−0.0284714
$187$	14.5493	1.06395
$188$	−5.64724	−0.411868
$189$	3.91286	0.284618
$190$	−12.1263	−0.879734
$191$	−19.7891	−1.43189	−0.715946	−	0.698156i	$-0.754004\pi$
$191$	−19.7891	−1.43189	−0.715946	+	0.698156i	$0.754004\pi$
$192$	2.98313	0.215289
$193$	−12.3860	−0.891562	−0.445781	−	0.895142i	$-0.647074\pi$
$193$	−12.3860	−0.891562	−0.445781	+	0.895142i	$0.647074\pi$
$194$	2.07434	0.148929
$195$	−7.44095	−0.532858
$196$	11.8908	0.849346
$197$	11.1486	0.794303	0.397152	−	0.917753i	$-0.369999\pi$
$197$	11.1486	0.794303	0.397152	+	0.917753i	$0.369999\pi$
$198$	−10.9527	−0.778378
$199$	−5.68847	−0.403245	−0.201622	−	0.979463i	$-0.564621\pi$
$199$	−5.68847	−0.403245	−0.201622	+	0.979463i	$0.564621\pi$
$200$	1.26770	0.0896399
$201$	−11.7044	−0.825565
$202$	−2.40769	−0.169405
$203$	30.5681	2.14546
$204$	−3.52052	−0.246486
$205$	−21.6048	−1.50895
$206$	22.2675	1.55145
$207$	−8.65037	−0.601243
$208$	−14.3842	−0.997368
$209$	15.5442	1.07522
$210$	−18.0499	−1.24556
$211$	8.55114	0.588685	0.294342	−	0.955700i	$-0.404899\pi$
$211$	8.55114	0.588685	0.294342	+	0.955700i	$0.404899\pi$
$212$	15.4680	1.06235
$213$	−8.36506	−0.573164
$214$	−22.7325	−1.55396
$215$	10.6773	0.728185
$216$	−1.05424	−0.0717322
$217$	0.820275	0.0556839
$218$	25.0064	1.69365
$219$	−0.929329	−0.0627982
$220$	21.0714	1.42064
$221$	7.35131	0.494503
$222$	16.6052	1.11447
$223$	17.6842	1.18422	0.592110	−	0.805857i	$-0.298295\pi$
$223$	17.6842	1.18422	0.592110	+	0.805857i	$0.298295\pi$
$224$	−26.6425	−1.78013
$225$	1.20247	0.0801649
$226$	−12.9738	−0.863007
$227$	23.4680	1.55763	0.778813	−	0.627257i	$-0.215822\pi$
$227$	23.4680	1.55763	0.778813	+	0.627257i	$0.215822\pi$
$228$	−3.76127	−0.249096
$229$	−18.1457	−1.19910	−0.599551	−	0.800337i	$-0.704654\pi$
$229$	−18.1457	−1.19910	−0.599551	+	0.800337i	$0.704654\pi$
$230$	39.9041	2.63120
$231$	23.1375	1.52234
$232$	−8.23597	−0.540718
$233$	11.1363	0.729561	0.364781	−	0.931093i	$-0.381144\pi$
$233$	11.1363	0.729561	0.364781	+	0.931093i	$0.381144\pi$
$234$	−5.53409	−0.361774
$235$	−9.82948	−0.641205
$236$	18.4976	1.20409
$237$	−2.58329	−0.167803
$238$	17.8325	1.15591
$239$	15.8678	1.02641	0.513203	−	0.858267i	$-0.328459\pi$
$239$	15.8678	1.02641	0.513203	+	0.858267i	$0.328459\pi$
$240$	11.9901	0.773958
$241$	−13.8177	−0.890075	−0.445037	−	0.895512i	$-0.646810\pi$
$241$	−13.8177	−0.890075	−0.445037	+	0.895512i	$0.646810\pi$
$242$	−44.3912	−2.85357
$243$	−1.00000	−0.0641500
$244$	−9.13683	−0.584925
$245$	20.6970	1.32228
$246$	−16.0682	−1.02447
$247$	7.85402	0.499739
$248$	−0.221007	−0.0140340
$249$	−15.0663	−0.954788
$250$	17.5179	1.10793
$251$	13.4244	0.847342	0.423671	−	0.905816i	$-0.360741\pi$
$251$	13.4244	0.847342	0.423671	+	0.905816i	$0.360741\pi$
$252$	−5.59864	−0.352681
$253$	−51.1515	−3.21587
$254$	−0.549654	−0.0344883
$255$	−6.12775	−0.383735
$256$	20.9554	1.30972
$257$	−16.1562	−1.00780	−0.503898	−	0.863763i	$-0.668101\pi$
$257$	−16.1562	−1.00780	−0.503898	+	0.863763i	$0.668101\pi$
$258$	7.94106	0.494389
$259$	−35.0782	−2.17966
$260$	10.6467	0.660283
$261$	−7.81222	−0.483564
$262$	11.2390	0.694349
$263$	−1.36466	−0.0841485	−0.0420742	−	0.999114i	$-0.513397\pi$
$263$	−1.36466	−0.0841485	−0.0420742	+	0.999114i	$0.513397\pi$
$264$	−6.23396	−0.383674
$265$	26.9233	1.65388
$266$	19.0519	1.16815
$267$	12.3834	0.757855
$268$	16.7470	1.02299
$269$	8.30379	0.506291	0.253145	−	0.967428i	$-0.418535\pi$
$269$	8.30379	0.506291	0.253145	+	0.967428i	$0.418535\pi$
$270$	4.61299	0.280737
$271$	−3.48129	−0.211473	−0.105737	−	0.994394i	$-0.533720\pi$
$271$	−3.48129	−0.211473	−0.105737	+	0.994394i	$0.533720\pi$
$272$	−11.8457	−0.718249
$273$	11.6907	0.707553
$274$	17.3450	1.04785
$275$	7.11048	0.428778
$276$	12.3772	0.745021
$277$	3.22535	0.193793	0.0968964	−	0.995294i	$-0.469108\pi$
$277$	3.22535	0.193793	0.0968964	+	0.995294i	$0.469108\pi$
$278$	−23.7876	−1.42668
$279$	−0.209636	−0.0125506
$280$	−10.2735	−0.613957
$281$	12.4805	0.744523	0.372261	−	0.928128i	$-0.378583\pi$
$281$	12.4805	0.744523	0.372261	+	0.928128i	$0.378583\pi$
$282$	−7.31051	−0.435335
$283$	18.9924	1.12898	0.564492	−	0.825439i	$-0.309072\pi$
$283$	18.9924	1.12898	0.564492	+	0.825439i	$0.309072\pi$
$284$	11.9690	0.710228
$285$	−6.54679	−0.387798
$286$	−32.7242	−1.93502
$287$	33.9440	2.00365
$288$	6.80896	0.401222
$289$	−10.9461	−0.643887
$290$	36.0376	2.11620
$291$	1.11990	0.0656500
$292$	1.32971	0.0778156
$293$	−5.91700	−0.345675	−0.172837	−	0.984950i	$-0.555293\pi$
$293$	−5.91700	−0.345675	−0.172837	+	0.984950i	$0.555293\pi$
$294$	15.3930	0.897739
$295$	32.1965	1.87455
$296$	9.45115	0.549337
$297$	−5.91321	−0.343119
$298$	16.4062	0.950385
$299$	−25.8453	−1.49467
$300$	−1.72054	−0.0993352
$301$	−16.7754	−0.966917
$302$	−30.9267	−1.77963
$303$	−1.29987	−0.0746758
$304$	−12.6557	−0.725855
$305$	−15.9034	−0.910625
$306$	−4.55741	−0.260530
$307$	8.84352	0.504727	0.252363	−	0.967633i	$-0.418792\pi$
$307$	8.84352	0.504727	0.252363	+	0.967633i	$0.418792\pi$
$308$	−33.1059	−1.88638
$309$	12.0219	0.683901
$310$	0.967047	0.0549246
$311$	−25.5235	−1.44731	−0.723654	−	0.690163i	$-0.757539\pi$
$311$	−25.5235	−1.44731	−0.723654	+	0.690163i	$0.757539\pi$
$312$	−3.14983	−0.178324
$313$	15.6131	0.882506	0.441253	−	0.897383i	$-0.354534\pi$
$313$	15.6131	0.882506	0.441253	+	0.897383i	$0.354534\pi$
$314$	25.1932	1.42173
$315$	−9.74488	−0.549062
$316$	3.69626	0.207931
$317$	1.14161	0.0641193	0.0320597	−	0.999486i	$-0.489793\pi$
$317$	1.14161	0.0641193	0.0320597	+	0.999486i	$0.489793\pi$
$318$	20.0237	1.12287
$319$	−46.1953	−2.58644
$320$	−7.42941	−0.415317
$321$	−12.2729	−0.685006
$322$	−62.6944	−3.49382
$323$	6.46792	0.359885
$324$	1.43083	0.0794906
$325$	3.59271	0.199287
$326$	−39.2409	−2.17335
$327$	13.5005	0.746582
$328$	−9.14554	−0.504978
$329$	15.4434	0.851421
$330$	27.2776	1.50158
$331$	−13.9309	−0.765712	−0.382856	−	0.923808i	$-0.625059\pi$
$331$	−13.9309	−0.765712	−0.382856	+	0.923808i	$0.625059\pi$
$332$	21.5573	1.18311
$333$	8.96487	0.491272
$334$	12.4843	0.683112
$335$	29.1495	1.59261
$336$	−18.8380	−1.02770
$337$	−11.1789	−0.608953	−0.304477	−	0.952520i	$-0.598482\pi$
$337$	−11.1789	−0.608953	−0.304477	+	0.952520i	$0.598482\pi$
$338$	7.54472	0.410378
$339$	−7.00437	−0.380425
$340$	8.76778	0.475499
$341$	−1.23962	−0.0671293
$342$	−4.86906	−0.263289
$343$	−5.12757	−0.276863
$344$	4.51980	0.243691
$345$	21.5436	1.15987
$346$	−2.85990	−0.153749
$347$	4.20349	0.225655	0.112828	−	0.993615i	$-0.464009\pi$
$347$	4.20349	0.225655	0.112828	+	0.993615i	$0.464009\pi$
$348$	11.1780	0.599202
$349$	2.58836	0.138552	0.0692760	−	0.997598i	$-0.477931\pi$
$349$	2.58836	0.138552	0.0692760	+	0.997598i	$0.477931\pi$
$350$	8.71503	0.465838
$351$	−2.98776	−0.159475
$352$	40.2628	2.14602
$353$	11.9036	0.633563	0.316781	−	0.948499i	$-0.397398\pi$
$353$	11.9036	0.633563	0.316781	+	0.948499i	$0.397398\pi$
$354$	23.9456	1.27270
$355$	20.8330	1.10570
$356$	−17.7186	−0.939085
$357$	9.62748	0.509540
$358$	18.8807	0.997876
$359$	8.72540	0.460509	0.230254	−	0.973130i	$-0.426044\pi$
$359$	8.72540	0.460509	0.230254	+	0.973130i	$0.426044\pi$
$360$	2.62557	0.138380
$361$	−12.0898	−0.636304
$362$	−12.6629	−0.665546
$363$	−23.9661	−1.25789
$364$	−16.7274	−0.876754
$365$	2.31447	0.121145
$366$	−11.8279	−0.618253
$367$	−20.9480	−1.09348	−0.546738	−	0.837304i	$-0.684131\pi$
$367$	−20.9480	−1.09348	−0.546738	+	0.837304i	$0.684131\pi$
$368$	41.6462	2.17096
$369$	−8.67498	−0.451602
$370$	−41.3548	−2.14993
$371$	−42.2999	−2.19610
$372$	0.299954	0.0155519
$373$	−3.86232	−0.199983	−0.0999916	−	0.994988i	$-0.531882\pi$
$373$	−3.86232	−0.199983	−0.0999916	+	0.994988i	$0.531882\pi$
$374$	−26.9489	−1.39350
$375$	9.45765	0.488391
$376$	−4.16092	−0.214583
$377$	−23.3411	−1.20213
$378$	−7.24759	−0.372776
$379$	12.4943	0.641791	0.320895	−	0.947115i	$-0.396016\pi$
$379$	12.4943	0.641791	0.320895	+	0.947115i	$0.396016\pi$
$380$	9.36735	0.480535
$381$	−0.296749	−0.0152029
$382$	36.6544	1.87540
$383$	9.60867	0.490980	0.245490	−	0.969399i	$-0.421051\pi$
$383$	9.60867	0.490980	0.245490	+	0.969399i	$0.421051\pi$
$384$	8.09242	0.412965
$385$	−57.6235	−2.93677
$386$	22.9419	1.16771
$387$	4.28725	0.217933
$388$	−1.60239	−0.0813492
$389$	29.7839	1.51010	0.755052	−	0.655664i	$-0.227611\pi$
$389$	29.7839	1.51010	0.755052	+	0.655664i	$0.227611\pi$
$390$	13.7825	0.697905
$391$	−21.2840	−1.07638
$392$	8.76123	0.442509
$393$	6.06777	0.306078
$394$	−20.6500	−1.04033
$395$	6.43363	0.323711
$396$	8.46081	0.425172
$397$	−13.7587	−0.690531	−0.345266	−	0.938505i	$-0.612211\pi$
$397$	−13.7587	−0.690531	−0.345266	+	0.938505i	$0.612211\pi$
$398$	10.5365	0.528146
$399$	10.2858	0.514936
$400$	−5.78917	−0.289458
$401$	39.3626	1.96568	0.982838	−	0.184471i	$-0.0590573\pi$
$401$	39.3626	1.96568	0.982838	+	0.184471i	$0.0590573\pi$
$402$	21.6795	1.08127
$403$	−0.626342	−0.0312003
$404$	1.85990	0.0925334
$405$	2.49048	0.123753
$406$	−56.6197	−2.80999
$407$	53.0112	2.62767
$408$	−2.59394	−0.128419
$409$	−18.4676	−0.913164	−0.456582	−	0.889681i	$-0.650926\pi$
$409$	−18.4676	−0.913164	−0.456582	+	0.889681i	$0.650926\pi$
$410$	40.0176	1.97633
$411$	9.36427	0.461905
$412$	−17.2013	−0.847446
$413$	−50.5848	−2.48912
$414$	16.0227	0.787471
$415$	37.5223	1.84190
$416$	20.3436	0.997425
$417$	−12.8425	−0.628901
$418$	−28.7918	−1.40825
$419$	−14.8830	−0.727080	−0.363540	−	0.931579i	$-0.618432\pi$
$419$	−14.8830	−0.727080	−0.363540	+	0.931579i	$0.618432\pi$
$420$	13.9433	0.680362
$421$	34.0796	1.66094	0.830468	−	0.557066i	$-0.188073\pi$
$421$	34.0796	1.66094	0.830468	+	0.557066i	$0.188073\pi$
$422$	−15.8389	−0.771023
$423$	−3.94683	−0.191901
$424$	11.3969	0.553481
$425$	2.95865	0.143516
$426$	15.4942	0.750695
$427$	24.9862	1.20917
$428$	17.5604	0.848816
$429$	−17.6673	−0.852984
$430$	−19.7770	−0.953732
$431$	−7.88985	−0.380041	−0.190020	−	0.981780i	$-0.560855\pi$
$431$	−7.88985	−0.380041	−0.190020	+	0.981780i	$0.560855\pi$
$432$	4.81438	0.231632
$433$	−19.4859	−0.936433	−0.468216	−	0.883614i	$-0.655103\pi$
$433$	−19.4859	−0.936433	−0.468216	+	0.883614i	$0.655103\pi$
$434$	−1.51935	−0.0729314
$435$	19.4561	0.932850
$436$	−19.3170	−0.925117
$437$	−22.7395	−1.08778
$438$	1.72135	0.0822493
$439$	−27.7923	−1.32645	−0.663227	−	0.748418i	$-0.730814\pi$
$439$	−27.7923	−1.32645	−0.663227	+	0.748418i	$0.730814\pi$
$440$	15.5255	0.740151
$441$	8.31044	0.395735
$442$	−13.6165	−0.647669
$443$	−21.5371	−1.02326	−0.511630	−	0.859206i	$-0.670958\pi$
$443$	−21.5371	−1.02326	−0.511630	+	0.859206i	$0.670958\pi$
$444$	−12.8272	−0.608753
$445$	−30.8407	−1.46199
$446$	−32.7555	−1.55102
$447$	8.85744	0.418942
$448$	11.6725	0.551476
$449$	29.3966	1.38731	0.693656	−	0.720307i	$-0.255999\pi$
$449$	29.3966	1.38731	0.693656	+	0.720307i	$0.255999\pi$
$450$	−2.22728	−0.104995
$451$	−51.2970	−2.41548
$452$	10.0221	0.471398
$453$	−16.6968	−0.784486
$454$	−43.4686	−2.04008
$455$	−29.1154	−1.36495
$456$	−2.77132	−0.129779
$457$	19.5158	0.912909	0.456454	−	0.889747i	$-0.349119\pi$
$457$	19.5158	0.912909	0.456454	+	0.889747i	$0.349119\pi$
$458$	33.6104	1.57051
$459$	−2.46047	−0.114845
$460$	−30.8252	−1.43723
$461$	−12.2137	−0.568850	−0.284425	−	0.958698i	$-0.591803\pi$
$461$	−12.2137	−0.568850	−0.284425	+	0.958698i	$0.591803\pi$
$462$	−42.8565	−1.99387
$463$	19.0479	0.885229	0.442614	−	0.896712i	$-0.354051\pi$
$463$	19.0479	0.885229	0.442614	+	0.896712i	$0.354051\pi$
$464$	37.6110	1.74605
$465$	0.522093	0.0242115
$466$	−20.6272	−0.955535
$467$	41.3845	1.91505	0.957524	−	0.288354i	$-0.0931081\pi$
$467$	41.3845	1.91505	0.957524	+	0.288354i	$0.0931081\pi$
$468$	4.27498	0.197611
$469$	−45.7976	−2.11474
$470$	18.2067	0.839811
$471$	13.6014	0.626719
$472$	13.6291	0.627330
$473$	25.3514	1.16566
$474$	4.78491	0.219778
$475$	3.16098	0.145036
$476$	−13.7753	−0.631390
$477$	10.8105	0.494978
$478$	−29.3912	−1.34432
$479$	−4.92301	−0.224938	−0.112469	−	0.993655i	$-0.535876\pi$
$479$	−4.92301	−0.224938	−0.112469	+	0.993655i	$0.535876\pi$
$480$	−16.9576	−0.774003
$481$	26.7849	1.22129
$482$	25.5938	1.16577
$483$	−33.8477	−1.54012
$484$	34.2914	1.55870
$485$	−2.78910	−0.126646
$486$	1.85225	0.0840198
$487$	18.5351	0.839907	0.419953	−	0.907546i	$-0.362046\pi$
$487$	18.5351	0.839907	0.419953	+	0.907546i	$0.362046\pi$
$488$	−6.73206	−0.304746
$489$	−21.1855	−0.958042
$490$	−38.3360	−1.73184
$491$	10.1944	0.460065	0.230032	−	0.973183i	$-0.426117\pi$
$491$	10.1944	0.460065	0.230032	+	0.973183i	$0.426117\pi$
$492$	12.4124	0.559596
$493$	−19.2217	−0.865704
$494$	−14.5476	−0.654528
$495$	14.7267	0.661917
$496$	1.00927	0.0453175
$497$	−32.7313	−1.46820
$498$	27.9066	1.25052
$499$	32.4460	1.45248	0.726242	−	0.687440i	$-0.241265\pi$
$499$	32.4460	1.45248	0.726242	+	0.687440i	$0.241265\pi$
$500$	−13.5323	−0.605183
$501$	6.74008	0.301125
$502$	−24.8654	−1.10980
$503$	30.3907	1.35505	0.677527	−	0.735497i	$-0.263051\pi$
$503$	30.3907	1.35505	0.677527	+	0.735497i	$0.263051\pi$
$504$	−4.12510	−0.183747
$505$	3.23730	0.144058
$506$	94.7454	4.21194
$507$	4.07327	0.180900
$508$	0.424598	0.0188385
$509$	−36.8459	−1.63317	−0.816584	−	0.577227i	$-0.804135\pi$
$509$	−36.8459	−1.63317	−0.816584	+	0.577227i	$0.804135\pi$
$510$	11.3501	0.502592
$511$	−3.63633	−0.160862
$512$	−22.6299	−1.00011
$513$	−2.62873	−0.116061
$514$	29.9254	1.31995
$515$	−29.9402	−1.31932
$516$	−6.13433	−0.270049
$517$	−23.3384	−1.02642
$518$	64.9737	2.85478
$519$	−1.54401	−0.0677746
$520$	7.84458	0.344007
$521$	35.1861	1.54153	0.770766	−	0.637119i	$-0.219874\pi$
$521$	35.1861	1.54153	0.770766	+	0.637119i	$0.219874\pi$
$522$	14.4702	0.633343
$523$	25.5516	1.11729	0.558647	−	0.829405i	$-0.311321\pi$
$523$	25.5516	1.11729	0.558647	+	0.829405i	$0.311321\pi$
$524$	−8.68195	−0.379273
$525$	4.70510	0.205348
$526$	2.52769	0.110213
$527$	−0.515803	−0.0224688
$528$	28.4685	1.23893
$529$	51.8290	2.25343
$530$	−49.8686	−2.16615
$531$	12.9279	0.561021
$532$	−14.7173	−0.638076
$533$	−25.9188	−1.12267
$534$	−22.9372	−0.992592
$535$	30.5654	1.32146
$536$	12.3393	0.532976
$537$	10.1934	0.439877
$538$	−15.3807	−0.663109
$539$	49.1414	2.11667
$540$	−3.56345	−0.153347
$541$	−37.3734	−1.60681	−0.803405	−	0.595433i	$-0.796980\pi$
$541$	−37.3734	−1.60681	−0.803405	+	0.595433i	$0.796980\pi$
$542$	6.44822	0.276975
$543$	−6.83648	−0.293382
$544$	16.7533	0.718290
$545$	−33.6228	−1.44024
$546$	−21.6541	−0.926709
$547$	28.0027	1.19731	0.598655	−	0.801007i	$-0.295702\pi$
$547$	28.0027	1.19731	0.598655	+	0.801007i	$0.295702\pi$
$548$	−13.3987	−0.572364
$549$	−6.38568	−0.272534
$550$	−13.1704	−0.561587
$551$	−20.5362	−0.874871
$552$	9.11960	0.388156
$553$	−10.1081	−0.429838
$554$	−5.97416	−0.253818
$555$	−22.3268	−0.947720
$556$	18.3755	0.779293
$557$	20.4059	0.864625	0.432313	−	0.901724i	$-0.357698\pi$
$557$	20.4059	0.864625	0.432313	+	0.901724i	$0.357698\pi$
$558$	0.388298	0.0164380
$559$	12.8093	0.541775
$560$	46.9156	1.98255
$561$	−14.5493	−0.614272
$562$	−23.1170	−0.975130
$563$	−18.9057	−0.796782	−0.398391	−	0.917216i	$-0.630431\pi$
$563$	−18.9057	−0.796782	−0.398391	+	0.917216i	$0.630431\pi$
$564$	5.64724	0.237792
$565$	17.4442	0.733883
$566$	−35.1788	−1.47867
$567$	−3.91286	−0.164325
$568$	8.81880	0.370029
$569$	−30.6270	−1.28395	−0.641975	−	0.766725i	$-0.721885\pi$
$569$	−30.6270	−1.28395	−0.641975	+	0.766725i	$0.721885\pi$
$570$	12.1263	0.507914
$571$	−10.8008	−0.451999	−0.226000	−	0.974127i	$-0.572565\pi$
$571$	−10.8008	−0.451999	−0.226000	+	0.974127i	$0.572565\pi$
$572$	25.2789	1.05696
$573$	19.7891	0.826703
$574$	−62.8727	−2.62426
$575$	−10.4018	−0.433787
$576$	−2.98313	−0.124297
$577$	−27.7217	−1.15407	−0.577036	−	0.816719i	$-0.695791\pi$
$577$	−27.7217	−1.15407	−0.577036	+	0.816719i	$0.695791\pi$
$578$	20.2749	0.843323
$579$	12.3860	0.514743
$580$	−27.8385	−1.15593
$581$	−58.9523	−2.44575
$582$	−2.07434	−0.0859843
$583$	63.9247	2.64749
$584$	0.979739	0.0405419
$585$	7.44095	0.307646
$586$	10.9598	0.452743
$587$	−34.6998	−1.43221	−0.716107	−	0.697991i	$-0.754078\pi$
$587$	−34.6998	−1.43221	−0.716107	+	0.697991i	$0.754078\pi$
$588$	−11.8908	−0.490370
$589$	−0.551076	−0.0227067
$590$	−59.6360	−2.45517
$591$	−11.1486	−0.458591
$592$	−43.1603	−1.77388
$593$	−18.5212	−0.760573	−0.380286	−	0.924869i	$-0.624175\pi$
$593$	−18.5212	−0.760573	−0.380286	+	0.924869i	$0.624175\pi$
$594$	10.9527	0.449397
$595$	−23.9770	−0.982961
$596$	−12.6735	−0.519127
$597$	5.68847	0.232814
$598$	47.8719	1.95763
$599$	−7.83295	−0.320046	−0.160023	−	0.987113i	$-0.551157\pi$
$599$	−7.83295	−0.320046	−0.160023	+	0.987113i	$0.551157\pi$
$600$	−1.26770	−0.0517536
$601$	3.90045	0.159103	0.0795514	−	0.996831i	$-0.474651\pi$
$601$	3.90045	0.159103	0.0795514	+	0.996831i	$0.474651\pi$
$602$	31.0722	1.26641
$603$	11.7044	0.476640
$604$	23.8903	0.972084
$605$	59.6869	2.42662
$606$	2.40769	0.0978057
$607$	−16.9656	−0.688611	−0.344306	−	0.938858i	$-0.611886\pi$
$607$	−16.9656	−0.688611	−0.344306	+	0.938858i	$0.611886\pi$
$608$	17.8989	0.725897
$609$	−30.5681	−1.23868
$610$	29.4570	1.19268
$611$	−11.7922	−0.477061
$612$	3.52052	0.142309
$613$	15.9006	0.642220	0.321110	−	0.947042i	$-0.395944\pi$
$613$	15.9006	0.642220	0.321110	+	0.947042i	$0.395944\pi$
$614$	−16.3804	−0.661060
$615$	21.6048	0.871191
$616$	−24.3926	−0.982806
$617$	5.72191	0.230356	0.115178	−	0.993345i	$-0.463256\pi$
$617$	5.72191	0.230356	0.115178	+	0.993345i	$0.463256\pi$
$618$	−22.2675	−0.895731
$619$	−10.5838	−0.425398	−0.212699	−	0.977118i	$-0.568225\pi$
$619$	−10.5838	−0.425398	−0.212699	+	0.977118i	$0.568225\pi$
$620$	−0.747027	−0.0300013
$621$	8.65037	0.347128
$622$	47.2760	1.89559
$623$	48.4546	1.94129
$624$	14.3842	0.575831
$625$	−29.5664	−1.18266
$626$	−28.9194	−1.15585
$627$	−15.5442	−0.620777
$628$	−19.4613	−0.776590
$629$	22.0578	0.879503
$630$	18.0499	0.719127
$631$	−46.3825	−1.84646	−0.923228	−	0.384252i	$-0.874459\pi$
$631$	−46.3825	−1.84646	−0.923228	+	0.384252i	$0.874459\pi$
$632$	2.72342	0.108332
$633$	−8.55114	−0.339877
$634$	−2.11455	−0.0839796
$635$	0.739047	0.0293282
$636$	−15.4680	−0.613345
$637$	24.8296	0.983786
$638$	85.5652	3.38756
$639$	8.36506	0.330916
$640$	−20.1540	−0.796656
$641$	−22.8975	−0.904399	−0.452199	−	0.891917i	$-0.649360\pi$
$641$	−22.8975	−0.904399	−0.452199	+	0.891917i	$0.649360\pi$
$642$	22.7325	0.897179
$643$	15.4385	0.608835	0.304417	−	0.952539i	$-0.401538\pi$
$643$	15.4385	0.608835	0.304417	+	0.952539i	$0.401538\pi$
$644$	48.4303	1.90842
$645$	−10.6773	−0.420418
$646$	−11.9802	−0.471355
$647$	14.5981	0.573911	0.286955	−	0.957944i	$-0.407357\pi$
$647$	14.5981	0.573911	0.286955	+	0.957944i	$0.407357\pi$
$648$	1.05424	0.0414146
$649$	76.4451	3.00073
$650$	−6.65459	−0.261014
$651$	−0.820275	−0.0321491
$652$	30.3129	1.18715
$653$	15.1655	0.593473	0.296736	−	0.954959i	$-0.404102\pi$
$653$	15.1655	0.593473	0.296736	+	0.954959i	$0.404102\pi$
$654$	−25.0064	−0.977827
$655$	−15.1116	−0.590460
$656$	41.7647	1.63064
$657$	0.929329	0.0362566
$658$	−28.6050	−1.11514
$659$	−5.98174	−0.233015	−0.116508	−	0.993190i	$-0.537170\pi$
$659$	−5.98174	−0.233015	−0.116508	+	0.993190i	$0.537170\pi$
$660$	−21.0714	−0.820205
$661$	49.2412	1.91526	0.957630	−	0.288001i	$-0.0929907\pi$
$661$	49.2412	1.91526	0.957630	+	0.288001i	$0.0929907\pi$
$662$	25.8035	1.00288
$663$	−7.35131	−0.285501
$664$	15.8835	0.616401
$665$	−25.6166	−0.993371
$666$	−16.6052	−0.643438
$667$	67.5786	2.61665
$668$	−9.64392	−0.373135
$669$	−17.6842	−0.683710
$670$	−53.9922	−2.08590
$671$	−37.7599	−1.45770
$672$	26.6425	1.02776
$673$	43.1726	1.66418	0.832091	−	0.554640i	$-0.187144\pi$
$673$	43.1726	1.66418	0.832091	+	0.554640i	$0.187144\pi$
$674$	20.7061	0.797569
$675$	−1.20247	−0.0462832
$676$	−5.82816	−0.224160
$677$	−2.54184	−0.0976910	−0.0488455	−	0.998806i	$-0.515554\pi$
$677$	−2.54184	−0.0976910	−0.0488455	+	0.998806i	$0.515554\pi$
$678$	12.9738	0.498257
$679$	4.38202	0.168167
$680$	6.46014	0.247735
$681$	−23.4680	−0.899295
$682$	2.29609	0.0879218
$683$	−30.2545	−1.15766	−0.578828	−	0.815450i	$-0.696490\pi$
$683$	−30.2545	−1.15766	−0.578828	+	0.815450i	$0.696490\pi$
$684$	3.76127	0.143816
$685$	−23.3215	−0.891069
$686$	9.49755	0.362618
$687$	18.1457	0.692302
$688$	−20.6405	−0.786910
$689$	32.2992	1.23050
$690$	−39.9041	−1.51912
$691$	−6.00319	−0.228372	−0.114186	−	0.993459i	$-0.536426\pi$
$691$	−6.00319	−0.228372	−0.114186	+	0.993459i	$0.536426\pi$
$692$	2.20922	0.0839820
$693$	−23.1375	−0.878923
$694$	−7.78591	−0.295549
$695$	31.9840	1.21322
$696$	8.23597	0.312184
$697$	−21.3446	−0.808483
$698$	−4.79430	−0.181467
$699$	−11.1363	−0.421212
$700$	−6.73221	−0.254454
$701$	−2.23777	−0.0845193	−0.0422596	−	0.999107i	$-0.513456\pi$
$701$	−2.23777	−0.0845193	−0.0422596	+	0.999107i	$0.513456\pi$
$702$	5.53409	0.208871
$703$	23.5662	0.888816
$704$	−17.6399	−0.664827
$705$	9.82948	0.370200
$706$	−22.0484	−0.829802
$707$	−5.08622	−0.191287
$708$	−18.4976	−0.695181
$709$	−12.1724	−0.457146	−0.228573	−	0.973527i	$-0.573406\pi$
$709$	−12.1724	−0.457146	−0.228573	+	0.973527i	$0.573406\pi$
$710$	−38.5879	−1.44818
$711$	2.58329	0.0968811
$712$	−13.0552	−0.489263
$713$	1.81343	0.0679134
$714$	−17.8325	−0.667364
$715$	43.9999	1.64550
$716$	−14.5850	−0.545068
$717$	−15.8678	−0.592596
$718$	−16.1616	−0.603146
$719$	43.6524	1.62796	0.813979	−	0.580894i	$-0.197297\pi$
$719$	43.6524	1.62796	0.813979	+	0.580894i	$0.197297\pi$
$720$	−11.9901	−0.446845
$721$	47.0399	1.75186
$722$	22.3933	0.833393
$723$	13.8177	0.513885
$724$	9.78185	0.363540
$725$	−9.39398	−0.348884
$726$	44.3912	1.64751
$727$	−30.0526	−1.11459	−0.557295	−	0.830314i	$-0.688161\pi$
$727$	−30.0526	−1.11459	−0.557295	+	0.830314i	$0.688161\pi$
$728$	−12.3248	−0.456789
$729$	1.00000	0.0370370
$730$	−4.28698	−0.158668
$731$	10.5487	0.390156
$732$	9.13683	0.337707
$733$	5.95898	0.220100	0.110050	−	0.993926i	$-0.464899\pi$
$733$	5.95898	0.220100	0.110050	+	0.993926i	$0.464899\pi$
$734$	38.8009	1.43217
$735$	−20.6970	−0.763419
$736$	−58.9000	−2.17108
$737$	69.2106	2.54941
$738$	16.0682	0.591480
$739$	12.9956	0.478052	0.239026	−	0.971013i	$-0.423172\pi$
$739$	12.9956	0.478052	0.239026	+	0.971013i	$0.423172\pi$
$740$	31.9459	1.17435
$741$	−7.85402	−0.288525
$742$	78.3500	2.87632
$743$	−13.4002	−0.491605	−0.245803	−	0.969320i	$-0.579051\pi$
$743$	−13.4002	−0.491605	−0.245803	+	0.969320i	$0.579051\pi$
$744$	0.221007	0.00810252
$745$	−22.0592	−0.808188
$746$	7.15398	0.261926
$747$	15.0663	0.551247
$748$	20.8176	0.761166
$749$	−48.0221	−1.75469
$750$	−17.5179	−0.639665
$751$	21.0577	0.768408	0.384204	−	0.923248i	$-0.374476\pi$
$751$	21.0577	0.768408	0.384204	+	0.923248i	$0.374476\pi$
$752$	19.0015	0.692915
$753$	−13.4244	−0.489213
$754$	43.2335	1.57447
$755$	41.5831	1.51336
$756$	5.59864	0.203620
$757$	43.5502	1.58286	0.791429	−	0.611261i	$-0.209337\pi$
$757$	43.5502	1.58286	0.791429	+	0.611261i	$0.209337\pi$
$758$	−23.1426	−0.840578
$759$	51.1515	1.85668
$760$	6.90191	0.250358
$761$	47.8793	1.73562	0.867812	−	0.496893i	$-0.165526\pi$
$761$	47.8793	1.73562	0.867812	+	0.496893i	$0.165526\pi$
$762$	0.549654	0.0199119
$763$	52.8257	1.91242
$764$	−28.3149	−1.02440
$765$	6.12775	0.221549
$766$	−17.7977	−0.643056
$767$	38.6254	1.39468
$768$	−20.9554	−0.756164
$769$	−44.9145	−1.61966	−0.809830	−	0.586665i	$-0.800441\pi$
$769$	−44.9145	−1.61966	−0.809830	+	0.586665i	$0.800441\pi$
$770$	106.733	3.84640
$771$	16.1562	0.581852
$772$	−17.7222	−0.637837
$773$	31.5190	1.13366	0.566830	−	0.823835i	$-0.308170\pi$
$773$	31.5190	1.13366	0.566830	+	0.823835i	$0.308170\pi$
$774$	−7.94106	−0.285435
$775$	−0.252082	−0.00905504
$776$	−1.18065	−0.0423829
$777$	35.0782	1.25842
$778$	−55.1673	−1.97784
$779$	−22.8042	−0.817045
$780$	−10.6467	−0.381215
$781$	49.4643	1.76997
$782$	39.4233	1.40977
$783$	7.81222	0.279186
$784$	−40.0097	−1.42892
$785$	−33.8739	−1.20901
$786$	−11.2390	−0.400883
$787$	−3.79219	−0.135177	−0.0675885	−	0.997713i	$-0.521531\pi$
$787$	−3.79219	−0.135177	−0.0675885	+	0.997713i	$0.521531\pi$
$788$	15.9517	0.568257
$789$	1.36466	0.0485831
$790$	−11.9167	−0.423977
$791$	−27.4071	−0.974483
$792$	6.23396	0.221514
$793$	−19.0789	−0.677511
$794$	25.4846	0.904415
$795$	−26.9233	−0.954870
$796$	−8.13924	−0.288488
$797$	5.53761	0.196152	0.0980762	−	0.995179i	$-0.468731\pi$
$797$	5.53761	0.196152	0.0980762	+	0.995179i	$0.468731\pi$
$798$	−19.0519	−0.674432
$799$	−9.71106	−0.343553
$800$	8.18759	0.289475
$801$	−12.3834	−0.437548
$802$	−72.9094	−2.57452
$803$	5.49532	0.193926
$804$	−16.7470	−0.590622
$805$	84.2968	2.97107
$806$	1.16014	0.0408643
$807$	−8.30379	−0.292307
$808$	1.37038	0.0482099
$809$	41.7961	1.46947	0.734736	−	0.678354i	$-0.237306\pi$
$809$	41.7961	1.46947	0.734736	+	0.678354i	$0.237306\pi$
$810$	−4.61299	−0.162084
$811$	40.1566	1.41009	0.705044	−	0.709164i	$-0.250927\pi$
$811$	40.1566	1.41009	0.705044	+	0.709164i	$0.250927\pi$
$812$	43.7378	1.53489
$813$	3.48129	0.122094
$814$	−98.1899	−3.44156
$815$	52.7620	1.84817
$816$	11.8457	0.414681
$817$	11.2700	0.394288
$818$	34.2066	1.19601
$819$	−11.6907	−0.408506
$820$	−30.9129	−1.07952
$821$	33.0001	1.15171	0.575856	−	0.817551i	$-0.304669\pi$
$821$	33.0001	1.15171	0.575856	+	0.817551i	$0.304669\pi$
$822$	−17.3450	−0.604975
$823$	25.5283	0.889860	0.444930	−	0.895565i	$-0.353228\pi$
$823$	25.5283	0.889860	0.444930	+	0.895565i	$0.353228\pi$
$824$	−12.6740	−0.441519
$825$	−7.11048	−0.247555
$826$	93.6957	3.26009
$827$	−37.0350	−1.28783	−0.643916	−	0.765096i	$-0.722692\pi$
$827$	−37.0350	−1.28783	−0.643916	+	0.765096i	$0.722692\pi$
$828$	−12.3772	−0.430138
$829$	35.6638	1.23865	0.619327	−	0.785133i	$-0.287405\pi$
$829$	35.6638	1.23865	0.619327	+	0.785133i	$0.287405\pi$
$830$	−69.5007	−2.41240
$831$	−3.22535	−0.111886
$832$	−8.91288	−0.308998
$833$	20.4476	0.708468
$834$	23.7876	0.823696
$835$	−16.7860	−0.580904
$836$	22.2412	0.769227
$837$	0.209636	0.00724608
$838$	27.5670	0.952285
$839$	−22.2667	−0.768733	−0.384366	−	0.923181i	$-0.625580\pi$
$839$	−22.2667	−0.768733	−0.384366	+	0.923181i	$0.625580\pi$
$840$	10.2735	0.354468
$841$	32.0307	1.10451
$842$	−63.1239	−2.17539
$843$	−12.4805	−0.429850
$844$	12.2352	0.421154
$845$	−10.1444	−0.348977
$846$	7.31051	0.251341
$847$	−93.7758	−3.22217
$848$	−52.0458	−1.78726
$849$	−18.9924	−0.651819
$850$	−5.48017	−0.187968
$851$	−77.5495	−2.65836
$852$	−11.9690	−0.410051
$853$	29.3262	1.00411	0.502055	−	0.864836i	$-0.332578\pi$
$853$	29.3262	1.00411	0.502055	+	0.864836i	$0.332578\pi$
$854$	−46.2808	−1.58370
$855$	6.54679	0.223895
$856$	12.9386	0.442233
$857$	25.8922	0.884460	0.442230	−	0.896902i	$-0.354187\pi$
$857$	25.8922	0.884460	0.442230	+	0.896902i	$0.354187\pi$
$858$	32.7242	1.11719
$859$	−20.5216	−0.700188	−0.350094	−	0.936715i	$-0.613850\pi$
$859$	−20.5216	−0.700188	−0.350094	+	0.936715i	$0.613850\pi$
$860$	15.2774	0.520955
$861$	−33.9440	−1.15681
$862$	14.6140	0.497754
$863$	33.5470	1.14195	0.570976	−	0.820967i	$-0.306565\pi$
$863$	33.5470	1.14195	0.570976	+	0.820967i	$0.306565\pi$
$864$	−6.80896	−0.231645
$865$	3.84533	0.130745
$866$	36.0928	1.22648
$867$	10.9461	0.371748
$868$	1.17368	0.0398371
$869$	15.2756	0.518188
$870$	−36.0376	−1.22179
$871$	34.9700	1.18491
$872$	−14.2329	−0.481985
$873$	−1.11990	−0.0379030
$874$	42.1192	1.42470
$875$	37.0064	1.25105
$876$	−1.32971	−0.0449268
$877$	−2.95337	−0.0997284	−0.0498642	−	0.998756i	$-0.515879\pi$
$877$	−2.95337	−0.0997284	−0.0498642	+	0.998756i	$0.515879\pi$
$878$	51.4783	1.73731
$879$	5.91700	0.199575
$880$	−70.9001	−2.39004
$881$	−7.39409	−0.249113	−0.124557	−	0.992213i	$-0.539751\pi$
$881$	−7.39409	−0.249113	−0.124557	+	0.992213i	$0.539751\pi$
$882$	−15.3930	−0.518310
$883$	−31.6411	−1.06481	−0.532404	−	0.846490i	$-0.678711\pi$
$883$	−31.6411	−1.06481	−0.532404	+	0.846490i	$0.678711\pi$
$884$	10.5185	0.353775
$885$	−32.1965	−1.08227
$886$	39.8921	1.34020
$887$	28.8224	0.967761	0.483881	−	0.875134i	$-0.339227\pi$
$887$	28.8224	0.967761	0.483881	+	0.875134i	$0.339227\pi$
$888$	−9.45115	−0.317160
$889$	−1.16114	−0.0389433
$890$	57.1247	1.91482
$891$	5.91321	0.198100
$892$	25.3031	0.847210
$893$	−10.3751	−0.347191
$894$	−16.4062	−0.548705
$895$	−25.3864	−0.848573
$896$	31.6645	1.05784
$897$	25.8453	0.862948
$898$	−54.4499	−1.81702
$899$	1.63772	0.0546210
$900$	1.72054	0.0573512
$901$	26.5989	0.886138
$902$	95.0149	3.16365
$903$	16.7754	0.558250
$904$	7.38430	0.245598
$905$	17.0261	0.565967
$906$	30.9267	1.02747
$907$	−26.6818	−0.885953	−0.442977	−	0.896533i	$-0.646078\pi$
$907$	−26.6818	−0.885953	−0.442977	+	0.896533i	$0.646078\pi$
$908$	33.5787	1.11435
$909$	1.29987	0.0431141
$910$	53.9290	1.78773
$911$	32.0799	1.06285	0.531427	−	0.847104i	$-0.321656\pi$
$911$	32.0799	1.06285	0.531427	+	0.847104i	$0.321656\pi$
$912$	12.6557	0.419073
$913$	89.0902	2.94846
$914$	−36.1481	−1.19567
$915$	15.9034	0.525750
$916$	−25.9634	−0.857856
$917$	23.7423	0.784040
$918$	4.55741	0.150417
$919$	21.8022	0.719187	0.359594	−	0.933109i	$-0.382915\pi$
$919$	21.8022	0.719187	0.359594	+	0.933109i	$0.382915\pi$
$920$	−22.7121	−0.748797
$921$	−8.84352	−0.291404
$922$	22.6229	0.745044
$923$	24.9928	0.822648
$924$	33.1059	1.08910
$925$	10.7800	0.354445
$926$	−35.2814	−1.15942
$927$	−12.0219	−0.394850
$928$	−53.1931	−1.74615
$929$	−42.4908	−1.39408	−0.697038	−	0.717034i	$-0.745499\pi$
$929$	−42.4908	−1.39408	−0.697038	+	0.717034i	$0.745499\pi$
$930$	−0.967047	−0.0317107
$931$	21.8459	0.715971
$932$	15.9341	0.521940
$933$	25.5235	0.835603
$934$	−76.6545	−2.50821
$935$	36.2347	1.18500
$936$	3.14983	0.102955
$937$	24.2060	0.790775	0.395388	−	0.918514i	$-0.370610\pi$
$937$	24.2060	0.790775	0.395388	+	0.918514i	$0.370610\pi$
$938$	84.8287	2.76976
$939$	−15.6131	−0.509515
$940$	−14.0643	−0.458728
$941$	41.9975	1.36908	0.684540	−	0.728975i	$-0.260003\pi$
$941$	41.9975	1.36908	0.684540	+	0.728975i	$0.260003\pi$
$942$	−25.1932	−0.820838
$943$	75.0419	2.44370
$944$	−62.2396	−2.02573
$945$	9.74488	0.317001
$946$	−46.9571	−1.52671
$947$	1.61823	0.0525855	0.0262928	−	0.999654i	$-0.491630\pi$
$947$	1.61823	0.0525855	0.0262928	+	0.999654i	$0.491630\pi$
$948$	−3.69626	−0.120049
$949$	2.77662	0.0901327
$950$	−5.85492	−0.189959
$951$	−1.14161	−0.0370193
$952$	−10.1497	−0.328954
$953$	47.0812	1.52511	0.762555	−	0.646923i	$-0.223945\pi$
$953$	47.0812	1.52511	0.762555	+	0.646923i	$0.223945\pi$
$954$	−20.0237	−0.648292
$955$	−49.2844	−1.59481
$956$	22.7042	0.734307
$957$	46.1953	1.49328
$958$	9.11865	0.294610
$959$	36.6410	1.18320
$960$	7.42941	0.239783
$961$	−30.9561	−0.998582
$962$	−49.6123	−1.59957
$963$	12.2729	0.395489
$964$	−19.7708	−0.636773
$965$	−30.8470	−0.992999
$966$	62.6944	2.01716
$967$	−41.0583	−1.32035	−0.660173	−	0.751113i	$-0.729517\pi$
$967$	−41.0583	−1.32035	−0.660173	+	0.751113i	$0.729517\pi$
$968$	25.2661	0.812082
$969$	−6.46792	−0.207779
$970$	5.16610	0.165874
$971$	−47.0469	−1.50981	−0.754903	−	0.655836i	$-0.772316\pi$
$971$	−47.0469	−1.50981	−0.754903	+	0.655836i	$0.772316\pi$
$972$	−1.43083	−0.0458939
$973$	−50.2509	−1.61097
$974$	−34.3317	−1.10006
$975$	−3.59271	−0.115059
$976$	30.7431	0.984063
$977$	3.44060	0.110074	0.0550372	−	0.998484i	$-0.482472\pi$
$977$	3.44060	0.110074	0.0550372	+	0.998484i	$0.482472\pi$
$978$	39.2409	1.25479
$979$	−73.2259	−2.34031
$980$	29.6139	0.945980
$981$	−13.5005	−0.431039
$982$	−18.8825	−0.602564
$983$	11.5244	0.367573	0.183786	−	0.982966i	$-0.441165\pi$
$983$	11.5244	0.367573	0.183786	+	0.982966i	$0.441165\pi$
$984$	9.14554	0.291549
$985$	27.7653	0.884675
$986$	35.6035	1.13385
$987$	−15.4434	−0.491568
$988$	11.2378	0.357521
$989$	−37.0863	−1.17928
$990$	−27.2776	−0.866938
$991$	3.40748	0.108242	0.0541211	−	0.998534i	$-0.482764\pi$
$991$	3.40748	0.108242	0.0541211	+	0.998534i	$0.482764\pi$
$992$	−1.42740	−0.0453201
$993$	13.9309	0.442084
$994$	60.6265	1.92296
$995$	−14.1670	−0.449124
$996$	−21.5573	−0.683070
$997$	−10.7179	−0.339439	−0.169720	−	0.985492i	$-0.554286\pi$
$997$	−10.7179	−0.339439	−0.169720	+	0.985492i	$0.554286\pi$
$998$	−60.0981	−1.90237
$999$	−8.96487	−0.283636

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.b.1.17	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.b.1.17	✓	106	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.85225 q^{2} -1.00000 q^{3} +1.43083 q^{4} +2.49048 q^{5} +1.85225 q^{6} -3.91286 q^{7} +1.05424 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.85225 q^{2} -1.00000 q^{3} +1.43083 q^{4} +2.49048 q^{5} +1.85225 q^{6} -3.91286 q^{7} +1.05424 q^{8} +1.00000 q^{9} -4.61299 q^{10} +5.91321 q^{11} -1.43083 q^{12} +2.98776 q^{13} +7.24759 q^{14} -2.49048 q^{15} -4.81438 q^{16} +2.46047 q^{17} -1.85225 q^{18} +2.62873 q^{19} +3.56345 q^{20} +3.91286 q^{21} -10.9527 q^{22} -8.65037 q^{23} -1.05424 q^{24} +1.20247 q^{25} -5.53409 q^{26} -1.00000 q^{27} -5.59864 q^{28} -7.81222 q^{29} +4.61299 q^{30} -0.209636 q^{31} +6.80896 q^{32} -5.91321 q^{33} -4.55741 q^{34} -9.74488 q^{35} +1.43083 q^{36} +8.96487 q^{37} -4.86906 q^{38} -2.98776 q^{39} +2.62557 q^{40} -8.67498 q^{41} -7.24759 q^{42} +4.28725 q^{43} +8.46081 q^{44} +2.49048 q^{45} +16.0227 q^{46} -3.94683 q^{47} +4.81438 q^{48} +8.31044 q^{49} -2.22728 q^{50} -2.46047 q^{51} +4.27498 q^{52} +10.8105 q^{53} +1.85225 q^{54} +14.7267 q^{55} -4.12510 q^{56} -2.62873 q^{57} +14.4702 q^{58} +12.9279 q^{59} -3.56345 q^{60} -6.38568 q^{61} +0.388298 q^{62} -3.91286 q^{63} -2.98313 q^{64} +7.44095 q^{65} +10.9527 q^{66} +11.7044 q^{67} +3.52052 q^{68} +8.65037 q^{69} +18.0499 q^{70} +8.36506 q^{71} +1.05424 q^{72} +0.929329 q^{73} -16.6052 q^{74} -1.20247 q^{75} +3.76127 q^{76} -23.1375 q^{77} +5.53409 q^{78} +2.58329 q^{79} -11.9901 q^{80} +1.00000 q^{81} +16.0682 q^{82} +15.0663 q^{83} +5.59864 q^{84} +6.12775 q^{85} -7.94106 q^{86} +7.81222 q^{87} +6.23396 q^{88} -12.3834 q^{89} -4.61299 q^{90} -11.6907 q^{91} -12.3772 q^{92} +0.209636 q^{93} +7.31051 q^{94} +6.54679 q^{95} -6.80896 q^{96} -1.11990 q^{97} -15.3930 q^{98} +5.91321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9}+O(q^{10}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9} - 3 q^{10} + 55 q^{11} - 109 q^{12} - 8 q^{13} + 27 q^{14} - 16 q^{15} + 111 q^{16} + 28 q^{17} + 15 q^{18} + q^{19} + 54 q^{20} - 35 q^{21} + 20 q^{22} + 62 q^{23} - 48 q^{24} + 102 q^{25} + 21 q^{26} - 106 q^{27} + 79 q^{28} + 36 q^{29} + 3 q^{30} + q^{31} + 111 q^{32} - 55 q^{33} - 27 q^{34} + 72 q^{35} + 109 q^{36} + 31 q^{37} + 43 q^{38} + 8 q^{39} - 13 q^{40} + 35 q^{41} - 27 q^{42} + 98 q^{43} + 121 q^{44} + 16 q^{45} + 8 q^{46} + 75 q^{47} - 111 q^{48} + 49 q^{49} + 83 q^{50} - 28 q^{51} - 18 q^{52} + 60 q^{53} - 15 q^{54} + 14 q^{55} + 85 q^{56} - q^{57} + 65 q^{58} + 77 q^{59} - 54 q^{60} - 55 q^{61} + 83 q^{62} + 35 q^{63} + 122 q^{64} + 86 q^{65} - 20 q^{66} + 121 q^{67} + 80 q^{68} - 62 q^{69} - 11 q^{70} + 79 q^{71} + 48 q^{72} - 29 q^{73} + 91 q^{74} - 102 q^{75} - 10 q^{76} + 87 q^{77} - 21 q^{78} + 15 q^{79} + 108 q^{80} + 106 q^{81} + 21 q^{82} + 196 q^{83} - 79 q^{84} - 5 q^{85} + 65 q^{86} - 36 q^{87} + 84 q^{88} + 34 q^{89} - 3 q^{90} + 17 q^{91} + 162 q^{92} - q^{93} - 35 q^{94} + 113 q^{95} - 111 q^{96} - 63 q^{97} + 112 q^{98} + 55 q^{99}+O(q^{100}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9 - 3 * q^10 + 55 * q^11 - 109 * q^12 - 8 * q^13 + 27 * q^14 - 16 * q^15 + 111 * q^16 + 28 * q^17 + 15 * q^18 + q^19 + 54 * q^20 - 35 * q^21 + 20 * q^22 + 62 * q^23 - 48 * q^24 + 102 * q^25 + 21 * q^26 - 106 * q^27 + 79 * q^28 + 36 * q^29 + 3 * q^30 + q^31 + 111 * q^32 - 55 * q^33 - 27 * q^34 + 72 * q^35 + 109 * q^36 + 31 * q^37 + 43 * q^38 + 8 * q^39 - 13 * q^40 + 35 * q^41 - 27 * q^42 + 98 * q^43 + 121 * q^44 + 16 * q^45 + 8 * q^46 + 75 * q^47 - 111 * q^48 + 49 * q^49 + 83 * q^50 - 28 * q^51 - 18 * q^52 + 60 * q^53 - 15 * q^54 + 14 * q^55 + 85 * q^56 - q^57 + 65 * q^58 + 77 * q^59 - 54 * q^60 - 55 * q^61 + 83 * q^62 + 35 * q^63 + 122 * q^64 + 86 * q^65 - 20 * q^66 + 121 * q^67 + 80 * q^68 - 62 * q^69 - 11 * q^70 + 79 * q^71 + 48 * q^72 - 29 * q^73 + 91 * q^74 - 102 * q^75 - 10 * q^76 + 87 * q^77 - 21 * q^78 + 15 * q^79 + 108 * q^80 + 106 * q^81 + 21 * q^82 + 196 * q^83 - 79 * q^84 - 5 * q^85 + 65 * q^86 - 36 * q^87 + 84 * q^88 + 34 * q^89 - 3 * q^90 + 17 * q^91 + 162 * q^92 - q^93 - 35 * q^94 + 113 * q^95 - 111 * q^96 - 63 * q^97 + 112 * q^98 + 55 * q^99

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