LMFDB - Embedded newform 4017.2.a.k.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.135928 q^{2} +1.00000 q^{3} -1.98152 q^{4} -2.49648 q^{5} +0.135928 q^{6} +4.30504 q^{7} -0.541201 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.135928 q^{2} +1.00000 q^{3} -1.98152 q^{4} -2.49648 q^{5} +0.135928 q^{6} +4.30504 q^{7} -0.541201 q^{8} +1.00000 q^{9} -0.339342 q^{10} -2.90992 q^{11} -1.98152 q^{12} +1.00000 q^{13} +0.585177 q^{14} -2.49648 q^{15} +3.88948 q^{16} -5.61400 q^{17} +0.135928 q^{18} +0.831416 q^{19} +4.94683 q^{20} +4.30504 q^{21} -0.395540 q^{22} -2.62085 q^{23} -0.541201 q^{24} +1.23239 q^{25} +0.135928 q^{26} +1.00000 q^{27} -8.53054 q^{28} +2.69096 q^{29} -0.339342 q^{30} +9.48891 q^{31} +1.61109 q^{32} -2.90992 q^{33} -0.763101 q^{34} -10.7474 q^{35} -1.98152 q^{36} -6.20417 q^{37} +0.113013 q^{38} +1.00000 q^{39} +1.35110 q^{40} +5.58567 q^{41} +0.585177 q^{42} +6.82261 q^{43} +5.76607 q^{44} -2.49648 q^{45} -0.356247 q^{46} +2.19415 q^{47} +3.88948 q^{48} +11.5334 q^{49} +0.167517 q^{50} -5.61400 q^{51} -1.98152 q^{52} -1.92548 q^{53} +0.135928 q^{54} +7.26454 q^{55} -2.32990 q^{56} +0.831416 q^{57} +0.365777 q^{58} -11.3329 q^{59} +4.94683 q^{60} -0.867932 q^{61} +1.28981 q^{62} +4.30504 q^{63} -7.55997 q^{64} -2.49648 q^{65} -0.395540 q^{66} +2.40485 q^{67} +11.1243 q^{68} -2.62085 q^{69} -1.46088 q^{70} -1.33609 q^{71} -0.541201 q^{72} +2.25129 q^{73} -0.843321 q^{74} +1.23239 q^{75} -1.64747 q^{76} -12.5273 q^{77} +0.135928 q^{78} +12.0108 q^{79} -9.71000 q^{80} +1.00000 q^{81} +0.759251 q^{82} -8.53021 q^{83} -8.53054 q^{84} +14.0152 q^{85} +0.927385 q^{86} +2.69096 q^{87} +1.57485 q^{88} +2.42516 q^{89} -0.339342 q^{90} +4.30504 q^{91} +5.19327 q^{92} +9.48891 q^{93} +0.298248 q^{94} -2.07561 q^{95} +1.61109 q^{96} +7.67026 q^{97} +1.56771 q^{98} -2.90992 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.135928	0.0961158	0.0480579	−	0.998845i	$-0.484697\pi$
$2$	0.135928	0.0961158	0.0480579	+	0.998845i	$0.484697\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.98152	−0.990762
$5$	−2.49648	−1.11646	−0.558229	−	0.829687i	$-0.688519\pi$
$5$	−2.49648	−1.11646	−0.558229	+	0.829687i	$0.688519\pi$
$6$	0.135928	0.0554925
$7$	4.30504	1.62715	0.813577	−	0.581458i	$-0.197517\pi$
$7$	4.30504	1.62715	0.813577	+	0.581458i	$0.197517\pi$
$8$	−0.541201	−0.191344
$9$	1.00000	0.333333
$10$	−0.339342	−0.107309
$11$	−2.90992	−0.877374	−0.438687	−	0.898640i	$-0.644556\pi$
$11$	−2.90992	−0.877374	−0.438687	+	0.898640i	$0.644556\pi$
$12$	−1.98152	−0.572017
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.585177	0.156395
$15$	−2.49648	−0.644587
$16$	3.88948	0.972371
$17$	−5.61400	−1.36160	−0.680798	−	0.732471i	$-0.738367\pi$
$17$	−5.61400	−1.36160	−0.680798	+	0.732471i	$0.738367\pi$
$18$	0.135928	0.0320386
$19$	0.831416	0.190740	0.0953699	−	0.995442i	$-0.469597\pi$
$19$	0.831416	0.190740	0.0953699	+	0.995442i	$0.469597\pi$
$20$	4.94683	1.10614
$21$	4.30504	0.939438
$22$	−0.395540	−0.0843295
$23$	−2.62085	−0.546485	−0.273242	−	0.961945i	$-0.588096\pi$
$23$	−2.62085	−0.546485	−0.273242	+	0.961945i	$0.588096\pi$
$24$	−0.541201	−0.110472
$25$	1.23239	0.246478
$26$	0.135928	0.0266577
$27$	1.00000	0.192450
$28$	−8.53054	−1.61212
$29$	2.69096	0.499698	0.249849	−	0.968285i	$-0.419619\pi$
$29$	2.69096	0.499698	0.249849	+	0.968285i	$0.419619\pi$
$30$	−0.339342	−0.0619550
$31$	9.48891	1.70426	0.852130	−	0.523331i	$-0.175311\pi$
$31$	9.48891	1.70426	0.852130	+	0.523331i	$0.175311\pi$
$32$	1.61109	0.284804
$33$	−2.90992	−0.506552
$34$	−0.763101	−0.130871
$35$	−10.7474	−1.81665
$36$	−1.98152	−0.330254
$37$	−6.20417	−1.01996	−0.509979	−	0.860187i	$-0.670347\pi$
$37$	−6.20417	−1.01996	−0.509979	+	0.860187i	$0.670347\pi$
$38$	0.113013	0.0183331
$39$	1.00000	0.160128
$40$	1.35110	0.213627
$41$	5.58567	0.872335	0.436168	−	0.899865i	$-0.356335\pi$
$41$	5.58567	0.872335	0.436168	+	0.899865i	$0.356335\pi$
$42$	0.585177	0.0902948
$43$	6.82261	1.04044	0.520219	−	0.854033i	$-0.325850\pi$
$43$	6.82261	1.04044	0.520219	+	0.854033i	$0.325850\pi$
$44$	5.76607	0.869268
$45$	−2.49648	−0.372153
$46$	−0.356247	−0.0525258
$47$	2.19415	0.320050	0.160025	−	0.987113i	$-0.448842\pi$
$47$	2.19415	0.320050	0.160025	+	0.987113i	$0.448842\pi$
$48$	3.88948	0.561398
$49$	11.5334	1.64763
$50$	0.167517	0.0236905
$51$	−5.61400	−0.786118
$52$	−1.98152	−0.274788
$53$	−1.92548	−0.264484	−0.132242	−	0.991217i	$-0.542218\pi$
$53$	−1.92548	−0.264484	−0.132242	+	0.991217i	$0.542218\pi$
$54$	0.135928	0.0184975
$55$	7.26454	0.979551
$56$	−2.32990	−0.311345
$57$	0.831416	0.110124
$58$	0.365777	0.0480289
$59$	−11.3329	−1.47541	−0.737707	−	0.675121i	$-0.764091\pi$
$59$	−11.3329	−1.47541	−0.737707	+	0.675121i	$0.764091\pi$
$60$	4.94683	0.638632
$61$	−0.867932	−0.111127	−0.0555636	−	0.998455i	$-0.517696\pi$
$61$	−0.867932	−0.111127	−0.0555636	+	0.998455i	$0.517696\pi$
$62$	1.28981	0.163806
$63$	4.30504	0.542384
$64$	−7.55997	−0.944996
$65$	−2.49648	−0.309650
$66$	−0.395540	−0.0486876
$67$	2.40485	0.293799	0.146900	−	0.989151i	$-0.453071\pi$
$67$	2.40485	0.293799	0.146900	+	0.989151i	$0.453071\pi$
$68$	11.1243	1.34902
$69$	−2.62085	−0.315513
$70$	−1.46088	−0.174609
$71$	−1.33609	−0.158564	−0.0792822	−	0.996852i	$-0.525263\pi$
$71$	−1.33609	−0.158564	−0.0792822	+	0.996852i	$0.525263\pi$
$72$	−0.541201	−0.0637812
$73$	2.25129	0.263494	0.131747	−	0.991283i	$-0.457941\pi$
$73$	2.25129	0.263494	0.131747	+	0.991283i	$0.457941\pi$
$74$	−0.843321	−0.0980341
$75$	1.23239	0.142304
$76$	−1.64747	−0.188978
$77$	−12.5273	−1.42762
$78$	0.135928	0.0153908
$79$	12.0108	1.35132	0.675658	−	0.737215i	$-0.263859\pi$
$79$	12.0108	1.35132	0.675658	+	0.737215i	$0.263859\pi$
$80$	−9.71000	−1.08561
$81$	1.00000	0.111111
$82$	0.759251	0.0838452
$83$	−8.53021	−0.936312	−0.468156	−	0.883646i	$-0.655082\pi$
$83$	−8.53021	−0.936312	−0.468156	+	0.883646i	$0.655082\pi$
$84$	−8.53054	−0.930759
$85$	14.0152	1.52016
$86$	0.927385	0.100002
$87$	2.69096	0.288501
$88$	1.57485	0.167880
$89$	2.42516	0.257067	0.128533	−	0.991705i	$-0.458973\pi$
$89$	2.42516	0.257067	0.128533	+	0.991705i	$0.458973\pi$
$90$	−0.339342	−0.0357697
$91$	4.30504	0.451291
$92$	5.19327	0.541436
$93$	9.48891	0.983954
$94$	0.298248	0.0307619
$95$	−2.07561	−0.212953
$96$	1.61109	0.164432
$97$	7.67026	0.778797	0.389398	−	0.921069i	$-0.372683\pi$
$97$	7.67026	0.778797	0.389398	+	0.921069i	$0.372683\pi$
$98$	1.56771	0.158363
$99$	−2.90992	−0.292458
$100$	−2.44201	−0.244201
$101$	9.80569	0.975702	0.487851	−	0.872927i	$-0.337781\pi$
$101$	9.80569	0.975702	0.487851	+	0.872927i	$0.337781\pi$
$102$	−0.763101	−0.0755583
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−0.541201	−0.0530692
$105$	−10.7474	−1.04884
$106$	−0.261726	−0.0254211
$107$	7.33504	0.709105	0.354552	−	0.935036i	$-0.384633\pi$
$107$	7.33504	0.709105	0.354552	+	0.935036i	$0.384633\pi$
$108$	−1.98152	−0.190672
$109$	−6.81001	−0.652281	−0.326141	−	0.945321i	$-0.605748\pi$
$109$	−6.81001	−0.652281	−0.326141	+	0.945321i	$0.605748\pi$
$110$	0.987457	0.0941503
$111$	−6.20417	−0.588873
$112$	16.7444	1.58220
$113$	14.9644	1.40773	0.703864	−	0.710334i	$-0.251456\pi$
$113$	14.9644	1.40773	0.703864	+	0.710334i	$0.251456\pi$
$114$	0.113013	0.0105846
$115$	6.54288	0.610127
$116$	−5.33219	−0.495082
$117$	1.00000	0.0924500
$118$	−1.54046	−0.141811
$119$	−24.1685	−2.21553
$120$	1.35110	0.123338
$121$	−2.53237	−0.230215
$122$	−0.117976	−0.0106811
$123$	5.58567	0.503643
$124$	−18.8025	−1.68851
$125$	9.40574	0.841275
$126$	0.585177	0.0521317
$127$	8.10037	0.718792	0.359396	−	0.933185i	$-0.382983\pi$
$127$	8.10037	0.718792	0.359396	+	0.933185i	$0.382983\pi$
$128$	−4.24980	−0.375633
$129$	6.82261	0.600697
$130$	−0.339342	−0.0297622
$131$	17.5390	1.53239	0.766196	−	0.642607i	$-0.222147\pi$
$131$	17.5390	1.53239	0.766196	+	0.642607i	$0.222147\pi$
$132$	5.76607	0.501872
$133$	3.57928	0.310363
$134$	0.326887	0.0282388
$135$	−2.49648	−0.214862
$136$	3.03831	0.260533
$137$	12.2658	1.04794	0.523971	−	0.851736i	$-0.324450\pi$
$137$	12.2658	1.04794	0.523971	+	0.851736i	$0.324450\pi$
$138$	−0.356247	−0.0303258
$139$	11.5843	0.982568	0.491284	−	0.871000i	$-0.336528\pi$
$139$	11.5843	0.982568	0.491284	+	0.871000i	$0.336528\pi$
$140$	21.2963	1.79987
$141$	2.19415	0.184781
$142$	−0.181612	−0.0152405
$143$	−2.90992	−0.243340
$144$	3.88948	0.324124
$145$	−6.71791	−0.557892
$146$	0.306014	0.0253259
$147$	11.5334	0.951259
$148$	12.2937	1.01054
$149$	−0.482700	−0.0395444	−0.0197722	−	0.999805i	$-0.506294\pi$
$149$	−0.482700	−0.0395444	−0.0197722	+	0.999805i	$0.506294\pi$
$150$	0.167517	0.0136777
$151$	−0.843984	−0.0686824	−0.0343412	−	0.999410i	$-0.510933\pi$
$151$	−0.843984	−0.0686824	−0.0343412	+	0.999410i	$0.510933\pi$
$152$	−0.449963	−0.0364968
$153$	−5.61400	−0.453865
$154$	−1.70282	−0.137217
$155$	−23.6888	−1.90273
$156$	−1.98152	−0.158649
$157$	−17.5861	−1.40353	−0.701763	−	0.712411i	$-0.747603\pi$
$157$	−17.5861	−1.40353	−0.701763	+	0.712411i	$0.747603\pi$
$158$	1.63260	0.129883
$159$	−1.92548	−0.152700
$160$	−4.02206	−0.317971
$161$	−11.2829	−0.889214
$162$	0.135928	0.0106795
$163$	−2.93231	−0.229677	−0.114838	−	0.993384i	$-0.536635\pi$
$163$	−2.93231	−0.229677	−0.114838	+	0.993384i	$0.536635\pi$
$164$	−11.0681	−0.864277
$165$	7.26454	0.565544
$166$	−1.15950	−0.0899944
$167$	4.92856	0.381383	0.190692	−	0.981650i	$-0.438927\pi$
$167$	4.92856	0.381383	0.190692	+	0.981650i	$0.438927\pi$
$168$	−2.32990	−0.179755
$169$	1.00000	0.0769231
$170$	1.90506	0.146112
$171$	0.831416	0.0635799
$172$	−13.5192	−1.03083
$173$	13.7726	1.04711	0.523556	−	0.851991i	$-0.324605\pi$
$173$	13.7726	1.04711	0.523556	+	0.851991i	$0.324605\pi$
$174$	0.365777	0.0277295
$175$	5.30550	0.401058
$176$	−11.3181	−0.853132
$177$	−11.3329	−0.851831
$178$	0.329648	0.0247082
$179$	−0.808458	−0.0604270	−0.0302135	−	0.999543i	$-0.509619\pi$
$179$	−0.808458	−0.0604270	−0.0302135	+	0.999543i	$0.509619\pi$
$180$	4.94683	0.368715
$181$	−9.74803	−0.724565	−0.362283	−	0.932068i	$-0.618002\pi$
$181$	−9.74803	−0.724565	−0.362283	+	0.932068i	$0.618002\pi$
$182$	0.585177	0.0433762
$183$	−0.867932	−0.0641594
$184$	1.41841	0.104566
$185$	15.4886	1.13874
$186$	1.28981	0.0945735
$187$	16.3363	1.19463
$188$	−4.34777	−0.317094
$189$	4.30504	0.313146
$190$	−0.282134	−0.0204681
$191$	−2.35262	−0.170230	−0.0851149	−	0.996371i	$-0.527126\pi$
$191$	−2.35262	−0.170230	−0.0851149	+	0.996371i	$0.527126\pi$
$192$	−7.55997	−0.545594
$193$	2.14849	0.154652	0.0773258	−	0.997006i	$-0.475362\pi$
$193$	2.14849	0.154652	0.0773258	+	0.997006i	$0.475362\pi$
$194$	1.04261	0.0748547
$195$	−2.49648	−0.178776
$196$	−22.8537	−1.63241
$197$	12.0987	0.861998	0.430999	−	0.902352i	$-0.358161\pi$
$197$	12.0987	0.861998	0.430999	+	0.902352i	$0.358161\pi$
$198$	−0.395540	−0.0281098
$199$	−5.30838	−0.376301	−0.188150	−	0.982140i	$-0.560249\pi$
$199$	−5.30838	−0.376301	−0.188150	+	0.982140i	$0.560249\pi$
$200$	−0.666973	−0.0471621
$201$	2.40485	0.169625
$202$	1.33287	0.0937804
$203$	11.5847	0.813085
$204$	11.1243	0.778855
$205$	−13.9445	−0.973926
$206$	0.135928	0.00947057
$207$	−2.62085	−0.182162
$208$	3.88948	0.269687
$209$	−2.41935	−0.167350
$210$	−1.46088	−0.100810
$211$	13.9172	0.958097	0.479048	−	0.877788i	$-0.340982\pi$
$211$	13.9172	0.958097	0.479048	+	0.877788i	$0.340982\pi$
$212$	3.81537	0.262041
$213$	−1.33609	−0.0915472
$214$	0.997039	0.0681562
$215$	−17.0325	−1.16161
$216$	−0.541201	−0.0368241
$217$	40.8502	2.77309
$218$	−0.925673	−0.0626945
$219$	2.25129	0.152128
$220$	−14.3949	−0.970502
$221$	−5.61400	−0.377639
$222$	−0.843321	−0.0566000
$223$	16.9746	1.13671	0.568353	−	0.822785i	$-0.307581\pi$
$223$	16.9746	1.13671	0.568353	+	0.822785i	$0.307581\pi$
$224$	6.93583	0.463419
$225$	1.23239	0.0821595
$226$	2.03408	0.135305
$227$	22.5372	1.49585	0.747923	−	0.663785i	$-0.231051\pi$
$227$	22.5372	1.49585	0.747923	+	0.663785i	$0.231051\pi$
$228$	−1.64747	−0.109106
$229$	26.5272	1.75297	0.876484	−	0.481430i	$-0.159883\pi$
$229$	26.5272	1.75297	0.876484	+	0.481430i	$0.159883\pi$
$230$	0.889363	0.0586428
$231$	−12.5273	−0.824238
$232$	−1.45635	−0.0956140
$233$	20.9424	1.37198	0.685990	−	0.727611i	$-0.259369\pi$
$233$	20.9424	1.37198	0.685990	+	0.727611i	$0.259369\pi$
$234$	0.135928	0.00888591
$235$	−5.47766	−0.357323
$236$	22.4563	1.46178
$237$	12.0108	0.780183
$238$	−3.28519	−0.212947
$239$	17.3165	1.12011	0.560056	−	0.828455i	$-0.310780\pi$
$239$	17.3165	1.12011	0.560056	+	0.828455i	$0.310780\pi$
$240$	−9.71000	−0.626778
$241$	11.1901	0.720815	0.360408	−	0.932795i	$-0.382638\pi$
$241$	11.1901	0.720815	0.360408	+	0.932795i	$0.382638\pi$
$242$	−0.344220	−0.0221273
$243$	1.00000	0.0641500
$244$	1.71983	0.110101
$245$	−28.7929	−1.83951
$246$	0.759251	0.0484080
$247$	0.831416	0.0529017
$248$	−5.13541	−0.326099
$249$	−8.53021	−0.540580
$250$	1.27851	0.0808598
$251$	−12.0103	−0.758084	−0.379042	−	0.925380i	$-0.623746\pi$
$251$	−12.0103	−0.758084	−0.379042	+	0.925380i	$0.623746\pi$
$252$	−8.53054	−0.537374
$253$	7.62646	0.479471
$254$	1.10107	0.0690872
$255$	14.0152	0.877667
$256$	14.5423	0.908892
$257$	10.1814	0.635101	0.317550	−	0.948241i	$-0.397140\pi$
$257$	10.1814	0.635101	0.317550	+	0.948241i	$0.397140\pi$
$258$	0.927385	0.0577365
$259$	−26.7092	−1.65963
$260$	4.94683	0.306789
$261$	2.69096	0.166566
$262$	2.38405	0.147287
$263$	17.9972	1.10975	0.554876	−	0.831933i	$-0.312766\pi$
$263$	17.9972	1.10975	0.554876	+	0.831933i	$0.312766\pi$
$264$	1.57485	0.0969255
$265$	4.80690	0.295286
$266$	0.486525	0.0298308
$267$	2.42516	0.148418
$268$	−4.76527	−0.291085
$269$	7.47922	0.456016	0.228008	−	0.973659i	$-0.426779\pi$
$269$	7.47922	0.456016	0.228008	+	0.973659i	$0.426779\pi$
$270$	−0.339342	−0.0206517
$271$	−22.7181	−1.38003	−0.690014	−	0.723796i	$-0.742396\pi$
$271$	−22.7181	−1.38003	−0.690014	+	0.723796i	$0.742396\pi$
$272$	−21.8356	−1.32398
$273$	4.30504	0.260553
$274$	1.66727	0.100724
$275$	−3.58616	−0.216254
$276$	5.19327	0.312598
$277$	−17.2436	−1.03607	−0.518033	−	0.855361i	$-0.673336\pi$
$277$	−17.2436	−1.03607	−0.518033	+	0.855361i	$0.673336\pi$
$278$	1.57463	0.0944403
$279$	9.48891	0.568086
$280$	5.81653	0.347604
$281$	28.0998	1.67630	0.838148	−	0.545443i	$-0.183639\pi$
$281$	28.0998	1.67630	0.838148	+	0.545443i	$0.183639\pi$
$282$	0.298248	0.0177604
$283$	−11.7119	−0.696199	−0.348099	−	0.937458i	$-0.613173\pi$
$283$	−11.7119	−0.696199	−0.348099	+	0.937458i	$0.613173\pi$
$284$	2.64749	0.157100
$285$	−2.07561	−0.122948
$286$	−0.395540	−0.0233888
$287$	24.0466	1.41942
$288$	1.61109	0.0949346
$289$	14.5170	0.853943
$290$	−0.913153	−0.0536222
$291$	7.67026	0.449639
$292$	−4.46099	−0.261060
$293$	−9.05938	−0.529255	−0.264627	−	0.964351i	$-0.585249\pi$
$293$	−9.05938	−0.529255	−0.264627	+	0.964351i	$0.585249\pi$
$294$	1.56771	0.0914310
$295$	28.2922	1.64724
$296$	3.35770	0.195163
$297$	−2.90992	−0.168851
$298$	−0.0656126	−0.00380084
$299$	−2.62085	−0.151568
$300$	−2.44201	−0.140990
$301$	29.3716	1.69295
$302$	−0.114721	−0.00660147
$303$	9.80569	0.563322
$304$	3.23378	0.185470
$305$	2.16677	0.124069
$306$	−0.763101	−0.0436236
$307$	26.1478	1.49233	0.746166	−	0.665759i	$-0.231892\pi$
$307$	26.1478	1.49233	0.746166	+	0.665759i	$0.231892\pi$
$308$	24.8232	1.41443
$309$	1.00000	0.0568880
$310$	−3.21998	−0.182883
$311$	−3.50561	−0.198785	−0.0993925	−	0.995048i	$-0.531690\pi$
$311$	−3.50561	−0.198785	−0.0993925	+	0.995048i	$0.531690\pi$
$312$	−0.541201	−0.0306395
$313$	21.6368	1.22298	0.611491	−	0.791251i	$-0.290570\pi$
$313$	21.6368	1.22298	0.611491	+	0.791251i	$0.290570\pi$
$314$	−2.39045	−0.134901
$315$	−10.7474	−0.605550
$316$	−23.7996	−1.33883
$317$	−30.6237	−1.72000	−0.860000	−	0.510294i	$-0.829537\pi$
$317$	−30.6237	−1.72000	−0.860000	+	0.510294i	$0.829537\pi$
$318$	−0.261726	−0.0146769
$319$	−7.83046	−0.438422
$320$	18.8733	1.05505
$321$	7.33504	0.409402
$322$	−1.53366	−0.0854675
$323$	−4.66757	−0.259711
$324$	−1.98152	−0.110085
$325$	1.23239	0.0683608
$326$	−0.398584	−0.0220755
$327$	−6.81001	−0.376595
$328$	−3.02297	−0.166916
$329$	9.44593	0.520771
$330$	0.987457	0.0543577
$331$	−21.1463	−1.16231	−0.581153	−	0.813795i	$-0.697398\pi$
$331$	−21.1463	−1.16231	−0.581153	+	0.813795i	$0.697398\pi$
$332$	16.9028	0.927663
$333$	−6.20417	−0.339986
$334$	0.669930	0.0366569
$335$	−6.00365	−0.328015
$336$	16.7444	0.913481
$337$	−24.5561	−1.33766	−0.668829	−	0.743416i	$-0.733204\pi$
$337$	−24.5561	−1.33766	−0.668829	+	0.743416i	$0.733204\pi$
$338$	0.135928	0.00739352
$339$	14.9644	0.812753
$340$	−27.7715	−1.50612
$341$	−27.6120	−1.49527
$342$	0.113013	0.00611104
$343$	19.5165	1.05379
$344$	−3.69241	−0.199081
$345$	6.54288	0.352257
$346$	1.87209	0.100644
$347$	−9.75327	−0.523583	−0.261791	−	0.965124i	$-0.584313\pi$
$347$	−9.75327	−0.523583	−0.261791	+	0.965124i	$0.584313\pi$
$348$	−5.33219	−0.285835
$349$	−25.8502	−1.38373	−0.691865	−	0.722027i	$-0.743210\pi$
$349$	−25.8502	−1.38373	−0.691865	+	0.722027i	$0.743210\pi$
$350$	0.721168	0.0385480
$351$	1.00000	0.0533761
$352$	−4.68815	−0.249879
$353$	2.55097	0.135774	0.0678871	−	0.997693i	$-0.478374\pi$
$353$	2.55097	0.135774	0.0678871	+	0.997693i	$0.478374\pi$
$354$	−1.54046	−0.0818744
$355$	3.33551	0.177031
$356$	−4.80552	−0.254692
$357$	−24.1685	−1.27913
$358$	−0.109892	−0.00580799
$359$	−23.1260	−1.22054	−0.610271	−	0.792193i	$-0.708939\pi$
$359$	−23.1260	−1.22054	−0.610271	+	0.792193i	$0.708939\pi$
$360$	1.35110	0.0712090
$361$	−18.3087	−0.963618
$362$	−1.32503	−0.0696421
$363$	−2.53237	−0.132915
$364$	−8.53054	−0.447122
$365$	−5.62030	−0.294180
$366$	−0.117976	−0.00616673
$367$	−33.3234	−1.73946	−0.869732	−	0.493524i	$-0.835709\pi$
$367$	−33.3234	−1.73946	−0.869732	+	0.493524i	$0.835709\pi$
$368$	−10.1937	−0.531385
$369$	5.58567	0.290778
$370$	2.10533	0.109451
$371$	−8.28925	−0.430357
$372$	−18.8025	−0.974864
$373$	32.7721	1.69688	0.848438	−	0.529295i	$-0.177543\pi$
$373$	32.7721	1.69688	0.848438	+	0.529295i	$0.177543\pi$
$374$	2.22056	0.114823
$375$	9.40574	0.485710
$376$	−1.18748	−0.0612396
$377$	2.69096	0.138591
$378$	0.585177	0.0300983
$379$	−1.84875	−0.0949640	−0.0474820	−	0.998872i	$-0.515120\pi$
$379$	−1.84875	−0.0949640	−0.0474820	+	0.998872i	$0.515120\pi$
$380$	4.11287	0.210986
$381$	8.10037	0.414995
$382$	−0.319788	−0.0163618
$383$	23.0895	1.17982	0.589910	−	0.807469i	$-0.299163\pi$
$383$	23.0895	1.17982	0.589910	+	0.807469i	$0.299163\pi$
$384$	−4.24980	−0.216872
$385$	31.2742	1.59388
$386$	0.292040	0.0148645
$387$	6.82261	0.346813
$388$	−15.1988	−0.771602
$389$	−13.1466	−0.666558	−0.333279	−	0.942828i	$-0.608155\pi$
$389$	−13.1466	−0.666558	−0.333279	+	0.942828i	$0.608155\pi$
$390$	−0.339342	−0.0171832
$391$	14.7134	0.744091
$392$	−6.24189	−0.315263
$393$	17.5390	0.884727
$394$	1.64456	0.0828516
$395$	−29.9846	−1.50869
$396$	5.76607	0.289756
$397$	−9.09202	−0.456315	−0.228158	−	0.973624i	$-0.573270\pi$
$397$	−9.09202	−0.456315	−0.228158	+	0.973624i	$0.573270\pi$
$398$	−0.721558	−0.0361684
$399$	3.57928	0.179188
$400$	4.79337	0.239668
$401$	−4.38332	−0.218892	−0.109446	−	0.993993i	$-0.534908\pi$
$401$	−4.38332	−0.218892	−0.109446	+	0.993993i	$0.534908\pi$
$402$	0.326887	0.0163037
$403$	9.48891	0.472676
$404$	−19.4302	−0.966689
$405$	−2.49648	−0.124051
$406$	1.57469	0.0781503
$407$	18.0536	0.894885
$408$	3.03831	0.150419
$409$	16.1722	0.799666	0.399833	−	0.916588i	$-0.369068\pi$
$409$	16.1722	0.799666	0.399833	+	0.916588i	$0.369068\pi$
$410$	−1.89545	−0.0936096
$411$	12.2658	0.605030
$412$	−1.98152	−0.0976227
$413$	−48.7885	−2.40072
$414$	−0.356247	−0.0175086
$415$	21.2955	1.04535
$416$	1.61109	0.0789904
$417$	11.5843	0.567286
$418$	−0.328858	−0.0160850
$419$	−32.9844	−1.61139	−0.805696	−	0.592329i	$-0.798209\pi$
$419$	−32.9844	−1.61139	−0.805696	+	0.592329i	$0.798209\pi$
$420$	21.2963	1.03915
$421$	0.790537	0.0385284	0.0192642	−	0.999814i	$-0.493868\pi$
$421$	0.790537	0.0385284	0.0192642	+	0.999814i	$0.493868\pi$
$422$	1.89174	0.0920882
$423$	2.19415	0.106683
$424$	1.04207	0.0506074
$425$	−6.91865	−0.335604
$426$	−0.181612	−0.00879914
$427$	−3.73648	−0.180821
$428$	−14.5345	−0.702554
$429$	−2.90992	−0.140492
$430$	−2.31519	−0.111649
$431$	6.47653	0.311964	0.155982	−	0.987760i	$-0.450146\pi$
$431$	6.47653	0.311964	0.155982	+	0.987760i	$0.450146\pi$
$432$	3.88948	0.187133
$433$	7.69361	0.369731	0.184866	−	0.982764i	$-0.440815\pi$
$433$	7.69361	0.369731	0.184866	+	0.982764i	$0.440815\pi$
$434$	5.55269	0.266538
$435$	−6.71791	−0.322099
$436$	13.4942	0.646255
$437$	−2.17901	−0.104236
$438$	0.306014	0.0146219
$439$	−15.7550	−0.751945	−0.375972	−	0.926631i	$-0.622691\pi$
$439$	−15.7550	−0.751945	−0.375972	+	0.926631i	$0.622691\pi$
$440$	−3.93158	−0.187431
$441$	11.5334	0.549209
$442$	−0.763101	−0.0362970
$443$	−4.58235	−0.217714	−0.108857	−	0.994057i	$-0.534719\pi$
$443$	−4.58235	−0.217714	−0.108857	+	0.994057i	$0.534719\pi$
$444$	12.2937	0.583433
$445$	−6.05436	−0.287004
$446$	2.30733	0.109255
$447$	−0.482700	−0.0228309
$448$	−32.5460	−1.53765
$449$	3.96109	0.186935	0.0934677	−	0.995622i	$-0.470205\pi$
$449$	3.96109	0.186935	0.0934677	+	0.995622i	$0.470205\pi$
$450$	0.167517	0.00789682
$451$	−16.2539	−0.765364
$452$	−29.6522	−1.39472
$453$	−0.843984	−0.0396538
$454$	3.06344	0.143774
$455$	−10.7474	−0.503848
$456$	−0.449963	−0.0210715
$457$	−17.9315	−0.838800	−0.419400	−	0.907801i	$-0.637760\pi$
$457$	−17.9315	−0.838800	−0.419400	+	0.907801i	$0.637760\pi$
$458$	3.60580	0.168488
$459$	−5.61400	−0.262039
$460$	−12.9649	−0.604490
$461$	27.9628	1.30236	0.651179	−	0.758924i	$-0.274275\pi$
$461$	27.9628	1.30236	0.651179	+	0.758924i	$0.274275\pi$
$462$	−1.70282	−0.0792223
$463$	−32.2700	−1.49971	−0.749857	−	0.661600i	$-0.769878\pi$
$463$	−32.2700	−1.49971	−0.749857	+	0.661600i	$0.769878\pi$
$464$	10.4664	0.485892
$465$	−23.6888	−1.09854
$466$	2.84666	0.131869
$467$	11.1883	0.517734	0.258867	−	0.965913i	$-0.416651\pi$
$467$	11.1883	0.517734	0.258867	+	0.965913i	$0.416651\pi$
$468$	−1.98152	−0.0915960
$469$	10.3530	0.478057
$470$	−0.744568	−0.0343444
$471$	−17.5861	−0.810326
$472$	6.13337	0.282311
$473$	−19.8532	−0.912853
$474$	1.63260	0.0749879
$475$	1.02463	0.0470133
$476$	47.8905	2.19506
$477$	−1.92548	−0.0881615
$478$	2.35380	0.107660
$479$	1.63471	0.0746918	0.0373459	−	0.999302i	$-0.488110\pi$
$479$	1.63471	0.0746918	0.0373459	+	0.999302i	$0.488110\pi$
$480$	−4.02206	−0.183581
$481$	−6.20417	−0.282886
$482$	1.52105	0.0692817
$483$	−11.2829	−0.513388
$484$	5.01795	0.228088
$485$	−19.1486	−0.869494
$486$	0.135928	0.00616583
$487$	−7.48395	−0.339130	−0.169565	−	0.985519i	$-0.554236\pi$
$487$	−7.48395	−0.339130	−0.169565	+	0.985519i	$0.554236\pi$
$488$	0.469726	0.0212635
$489$	−2.93231	−0.132604
$490$	−3.91376	−0.176806
$491$	−9.02167	−0.407142	−0.203571	−	0.979060i	$-0.565255\pi$
$491$	−9.02167	−0.407142	−0.203571	+	0.979060i	$0.565255\pi$
$492$	−11.0681	−0.498990
$493$	−15.1070	−0.680387
$494$	0.113013	0.00508469
$495$	7.26454	0.326517
$496$	36.9070	1.65717
$497$	−5.75192	−0.258009
$498$	−1.15950	−0.0519583
$499$	10.0853	0.451478	0.225739	−	0.974188i	$-0.427520\pi$
$499$	10.0853	0.451478	0.225739	+	0.974188i	$0.427520\pi$
$500$	−18.6377	−0.833503
$501$	4.92856	0.220192
$502$	−1.63254	−0.0728638
$503$	−40.0463	−1.78558	−0.892788	−	0.450477i	$-0.851254\pi$
$503$	−40.0463	−1.78558	−0.892788	+	0.450477i	$0.851254\pi$
$504$	−2.32990	−0.103782
$505$	−24.4797	−1.08933
$506$	1.03665	0.0460847
$507$	1.00000	0.0444116
$508$	−16.0511	−0.712151
$509$	1.15776	0.0513169	0.0256585	−	0.999671i	$-0.491832\pi$
$509$	1.15776	0.0513169	0.0256585	+	0.999671i	$0.491832\pi$
$510$	1.90506	0.0843577
$511$	9.69192	0.428745
$512$	10.4763	0.462992
$513$	0.831416	0.0367079
$514$	1.38395	0.0610432
$515$	−2.49648	−0.110008
$516$	−13.5192	−0.595148
$517$	−6.38481	−0.280804
$518$	−3.63054	−0.159517
$519$	13.7726	0.604550
$520$	1.35110	0.0592495
$521$	30.0627	1.31707	0.658534	−	0.752551i	$-0.271177\pi$
$521$	30.0627	1.31707	0.658534	+	0.752551i	$0.271177\pi$
$522$	0.365777	0.0160096
$523$	12.7031	0.555468	0.277734	−	0.960658i	$-0.410417\pi$
$523$	12.7031	0.555468	0.277734	+	0.960658i	$0.410417\pi$
$524$	−34.7540	−1.51824
$525$	5.30550	0.231551
$526$	2.44632	0.106665
$527$	−53.2708	−2.32051
$528$	−11.3181	−0.492556
$529$	−16.1312	−0.701355
$530$	0.653394	0.0283816
$531$	−11.3329	−0.491805
$532$	−7.09243	−0.307496
$533$	5.58567	0.241942
$534$	0.329648	0.0142653
$535$	−18.3117	−0.791686
$536$	−1.30151	−0.0562166
$537$	−0.808458	−0.0348875
$538$	1.01664	0.0438303
$539$	−33.5613	−1.44559
$540$	4.94683	0.212877
$541$	15.2024	0.653601	0.326800	−	0.945093i	$-0.394030\pi$
$541$	15.2024	0.653601	0.326800	+	0.945093i	$0.394030\pi$
$542$	−3.08804	−0.132642
$543$	−9.74803	−0.418328
$544$	−9.04468	−0.387788
$545$	17.0010	0.728244
$546$	0.585177	0.0250433
$547$	−30.4068	−1.30010	−0.650050	−	0.759892i	$-0.725252\pi$
$547$	−30.4068	−1.30010	−0.650050	+	0.759892i	$0.725252\pi$
$548$	−24.3051	−1.03826
$549$	−0.867932	−0.0370424
$550$	−0.487461	−0.0207854
$551$	2.23730	0.0953123
$552$	1.41841	0.0603714
$553$	51.7069	2.19880
$554$	−2.34389	−0.0995823
$555$	15.4886	0.657452
$556$	−22.9546	−0.973490
$557$	8.41199	0.356428	0.178214	−	0.983992i	$-0.442968\pi$
$557$	8.41199	0.356428	0.178214	+	0.983992i	$0.442968\pi$
$558$	1.28981	0.0546021
$559$	6.82261	0.288566
$560$	−41.8020	−1.76646
$561$	16.3363	0.689719
$562$	3.81956	0.161118
$563$	1.42925	0.0602356	0.0301178	−	0.999546i	$-0.490412\pi$
$563$	1.42925	0.0602356	0.0301178	+	0.999546i	$0.490412\pi$
$564$	−4.34777	−0.183074
$565$	−37.3582	−1.57167
$566$	−1.59197	−0.0669157
$567$	4.30504	0.180795
$568$	0.723093	0.0303403
$569$	−4.37393	−0.183365	−0.0916823	−	0.995788i	$-0.529224\pi$
$569$	−4.37393	−0.183365	−0.0916823	+	0.995788i	$0.529224\pi$
$570$	−0.282134	−0.0118173
$571$	−44.8605	−1.87735	−0.938676	−	0.344800i	$-0.887947\pi$
$571$	−44.8605	−1.87735	−0.938676	+	0.344800i	$0.887947\pi$
$572$	5.76607	0.241092
$573$	−2.35262	−0.0982822
$574$	3.26861	0.136429
$575$	−3.22991	−0.134697
$576$	−7.55997	−0.314999
$577$	−19.3224	−0.804402	−0.402201	−	0.915551i	$-0.631755\pi$
$577$	−19.3224	−0.804402	−0.402201	+	0.915551i	$0.631755\pi$
$578$	1.97327	0.0820774
$579$	2.14849	0.0892881
$580$	13.3117	0.552738
$581$	−36.7229	−1.52352
$582$	1.04261	0.0432174
$583$	5.60298	0.232052
$584$	−1.21840	−0.0504179
$585$	−2.49648	−0.103217
$586$	−1.23143	−0.0508697
$587$	−8.78525	−0.362606	−0.181303	−	0.983427i	$-0.558031\pi$
$587$	−8.78525	−0.362606	−0.181303	+	0.983427i	$0.558031\pi$
$588$	−22.8537	−0.942471
$589$	7.88923	0.325070
$590$	3.84571	0.158326
$591$	12.0987	0.497675
$592$	−24.1310	−0.991778
$593$	40.9274	1.68069	0.840343	−	0.542056i	$-0.182354\pi$
$593$	40.9274	1.68069	0.840343	+	0.542056i	$0.182354\pi$
$594$	−0.395540	−0.0162292
$595$	60.3361	2.47354
$596$	0.956482	0.0391790
$597$	−5.30838	−0.217257
$598$	−0.356247	−0.0145680
$599$	−6.98483	−0.285392	−0.142696	−	0.989767i	$-0.545577\pi$
$599$	−6.98483	−0.285392	−0.142696	+	0.989767i	$0.545577\pi$
$600$	−0.666973	−0.0272290
$601$	−35.3577	−1.44227	−0.721134	−	0.692795i	$-0.756379\pi$
$601$	−35.3577	−1.44227	−0.721134	+	0.692795i	$0.756379\pi$
$602$	3.99243	0.162719
$603$	2.40485	0.0979331
$604$	1.67237	0.0680479
$605$	6.32200	0.257026
$606$	1.33287	0.0541441
$607$	−5.44607	−0.221049	−0.110525	−	0.993873i	$-0.535253\pi$
$607$	−5.44607	−0.221049	−0.110525	+	0.993873i	$0.535253\pi$
$608$	1.33949	0.0543234
$609$	11.5847	0.469435
$610$	0.294525	0.0119250
$611$	2.19415	0.0887660
$612$	11.1243	0.449672
$613$	30.6536	1.23809	0.619043	−	0.785357i	$-0.287521\pi$
$613$	30.6536	1.23809	0.619043	+	0.785357i	$0.287521\pi$
$614$	3.55422	0.143437
$615$	−13.9445	−0.562296
$616$	6.77981	0.273166
$617$	1.31634	0.0529939	0.0264969	−	0.999649i	$-0.491565\pi$
$617$	1.31634	0.0529939	0.0264969	+	0.999649i	$0.491565\pi$
$618$	0.135928	0.00546784
$619$	−4.70010	−0.188913	−0.0944564	−	0.995529i	$-0.530111\pi$
$619$	−4.70010	−0.188913	−0.0944564	+	0.995529i	$0.530111\pi$
$620$	46.9400	1.88516
$621$	−2.62085	−0.105171
$622$	−0.476512	−0.0191064
$623$	10.4404	0.418287
$624$	3.88948	0.155704
$625$	−29.6432	−1.18573
$626$	2.94105	0.117548
$627$	−2.41935	−0.0966196
$628$	34.8473	1.39056
$629$	34.8302	1.38877
$630$	−1.46088	−0.0582029
$631$	27.6240	1.09969	0.549847	−	0.835266i	$-0.314686\pi$
$631$	27.6240	1.09969	0.549847	+	0.835266i	$0.314686\pi$
$632$	−6.50024	−0.258566
$633$	13.9172	0.553158
$634$	−4.16263	−0.165319
$635$	−20.2224	−0.802501
$636$	3.81537	0.151289
$637$	11.5334	0.456970
$638$	−1.06438	−0.0421393
$639$	−1.33609	−0.0528548
$640$	10.6095	0.419378
$641$	−12.5803	−0.496891	−0.248445	−	0.968646i	$-0.579920\pi$
$641$	−12.5803	−0.496891	−0.248445	+	0.968646i	$0.579920\pi$
$642$	0.997039	0.0393500
$643$	−26.9821	−1.06407	−0.532034	−	0.846723i	$-0.678572\pi$
$643$	−26.9821	−1.06407	−0.532034	+	0.846723i	$0.678572\pi$
$644$	22.3573	0.880999
$645$	−17.0325	−0.670653
$646$	−0.634454	−0.0249623
$647$	3.09563	0.121702	0.0608509	−	0.998147i	$-0.480619\pi$
$647$	3.09563	0.121702	0.0608509	+	0.998147i	$0.480619\pi$
$648$	−0.541201	−0.0212604
$649$	32.9777	1.29449
$650$	0.167517	0.00657055
$651$	40.8502	1.60104
$652$	5.81045	0.227555
$653$	−0.0302925	−0.00118544	−0.000592719	−	1.00000i	$-0.500189\pi$
$653$	−0.0302925	−0.00118544	−0.000592719		1.00000i	$0.500189\pi$
$654$	−0.925673	−0.0361967
$655$	−43.7858	−1.71085
$656$	21.7254	0.848233
$657$	2.25129	0.0878313
$658$	1.28397	0.0500543
$659$	−36.6621	−1.42815	−0.714076	−	0.700068i	$-0.753153\pi$
$659$	−36.6621	−1.42815	−0.714076	+	0.700068i	$0.753153\pi$
$660$	−14.3949	−0.560319
$661$	30.6414	1.19181	0.595907	−	0.803054i	$-0.296793\pi$
$661$	30.6414	1.19181	0.595907	+	0.803054i	$0.296793\pi$
$662$	−2.87438	−0.111716
$663$	−5.61400	−0.218030
$664$	4.61656	0.179157
$665$	−8.93559	−0.346507
$666$	−0.843321	−0.0326780
$667$	−7.05258	−0.273077
$668$	−9.76605	−0.377860
$669$	16.9746	0.656278
$670$	−0.816066	−0.0315274
$671$	2.52561	0.0975002
$672$	6.93583	0.267555
$673$	35.2664	1.35942	0.679710	−	0.733481i	$-0.262106\pi$
$673$	35.2664	1.35942	0.679710	+	0.733481i	$0.262106\pi$
$674$	−3.33787	−0.128570
$675$	1.23239	0.0474348
$676$	−1.98152	−0.0762124
$677$	−31.6213	−1.21531	−0.607653	−	0.794203i	$-0.707889\pi$
$677$	−31.6213	−1.21531	−0.607653	+	0.794203i	$0.707889\pi$
$678$	2.03408	0.0781184
$679$	33.0208	1.26722
$680$	−7.58506	−0.290874
$681$	22.5372	0.863627
$682$	−3.75325	−0.143719
$683$	−6.63987	−0.254068	−0.127034	−	0.991898i	$-0.540546\pi$
$683$	−6.63987	−0.254068	−0.127034	+	0.991898i	$0.540546\pi$
$684$	−1.64747	−0.0629926
$685$	−30.6214	−1.16998
$686$	2.65284	0.101286
$687$	26.5272	1.01208
$688$	26.5364	1.01169
$689$	−1.92548	−0.0733548
$690$	0.889363	0.0338575
$691$	10.5529	0.401453	0.200727	−	0.979647i	$-0.435670\pi$
$691$	10.5529	0.401453	0.200727	+	0.979647i	$0.435670\pi$
$692$	−27.2907	−1.03744
$693$	−12.5273	−0.475874
$694$	−1.32574	−0.0503246
$695$	−28.9199	−1.09700
$696$	−1.45635	−0.0552028
$697$	−31.3580	−1.18777
$698$	−3.51377	−0.132998
$699$	20.9424	0.792113
$700$	−10.5130	−0.397353
$701$	13.7772	0.520359	0.260179	−	0.965560i	$-0.416218\pi$
$701$	13.7772	0.520359	0.260179	+	0.965560i	$0.416218\pi$
$702$	0.135928	0.00513028
$703$	−5.15824	−0.194547
$704$	21.9989	0.829115
$705$	−5.47766	−0.206300
$706$	0.346748	0.0130500
$707$	42.2139	1.58762
$708$	22.4563	0.843961
$709$	0.715487	0.0268707	0.0134353	−	0.999910i	$-0.495723\pi$
$709$	0.715487	0.0268707	0.0134353	+	0.999910i	$0.495723\pi$
$710$	0.453390	0.0170154
$711$	12.0108	0.450439
$712$	−1.31250	−0.0491881
$713$	−24.8690	−0.931351
$714$	−3.28519	−0.122945
$715$	7.26454	0.271679
$716$	1.60198	0.0598687
$717$	17.3165	0.646697
$718$	−3.14347	−0.117313
$719$	−23.5405	−0.877911	−0.438955	−	0.898509i	$-0.644651\pi$
$719$	−23.5405	−0.877911	−0.438955	+	0.898509i	$0.644651\pi$
$720$	−9.71000	−0.361870
$721$	4.30504	0.160328
$722$	−2.48868	−0.0926189
$723$	11.1901	0.416163
$724$	19.3159	0.717871
$725$	3.31631	0.123165
$726$	−0.344220	−0.0127752
$727$	1.09443	0.0405900	0.0202950	−	0.999794i	$-0.493539\pi$
$727$	1.09443	0.0405900	0.0202950	+	0.999794i	$0.493539\pi$
$728$	−2.32990	−0.0863517
$729$	1.00000	0.0370370
$730$	−0.763957	−0.0282753
$731$	−38.3021	−1.41666
$732$	1.71983	0.0635666
$733$	−13.5103	−0.499015	−0.249508	−	0.968373i	$-0.580269\pi$
$733$	−13.5103	−0.499015	−0.249508	+	0.968373i	$0.580269\pi$
$734$	−4.52958	−0.167190
$735$	−28.7929	−1.06204
$736$	−4.22243	−0.155641
$737$	−6.99793	−0.257772
$738$	0.759251	0.0279484
$739$	22.6307	0.832483	0.416241	−	0.909254i	$-0.363347\pi$
$739$	22.6307	0.832483	0.416241	+	0.909254i	$0.363347\pi$
$740$	−30.6909	−1.12822
$741$	0.831416	0.0305428
$742$	−1.12674	−0.0413641
$743$	−39.4389	−1.44687	−0.723437	−	0.690391i	$-0.757439\pi$
$743$	−39.4389	−1.44687	−0.723437	+	0.690391i	$0.757439\pi$
$744$	−5.13541	−0.188273
$745$	1.20505	0.0441496
$746$	4.45466	0.163097
$747$	−8.53021	−0.312104
$748$	−32.3708	−1.18359
$749$	31.5776	1.15382
$750$	1.27851	0.0466844
$751$	19.6186	0.715891	0.357946	−	0.933742i	$-0.383477\pi$
$751$	19.6186	0.715891	0.357946	+	0.933742i	$0.383477\pi$
$752$	8.53413	0.311208
$753$	−12.0103	−0.437680
$754$	0.365777	0.0133208
$755$	2.10699	0.0766811
$756$	−8.53054	−0.310253
$757$	52.6094	1.91212	0.956061	−	0.293168i	$-0.0947094\pi$
$757$	52.6094	1.91212	0.956061	+	0.293168i	$0.0947094\pi$
$758$	−0.251298	−0.00912754
$759$	7.62646	0.276823
$760$	1.12332	0.0407472
$761$	−22.6482	−0.820996	−0.410498	−	0.911862i	$-0.634645\pi$
$761$	−22.6482	−0.820996	−0.410498	+	0.911862i	$0.634645\pi$
$762$	1.10107	0.0398875
$763$	−29.3174	−1.06136
$764$	4.66178	0.168657
$765$	14.0152	0.506721
$766$	3.13852	0.113399
$767$	−11.3329	−0.409206
$768$	14.5423	0.524749
$769$	−0.459337	−0.0165641	−0.00828205	−	0.999966i	$-0.502636\pi$
$769$	−0.459337	−0.0165641	−0.00828205	+	0.999966i	$0.502636\pi$
$770$	4.25104	0.153197
$771$	10.1814	0.366676
$772$	−4.25728	−0.153223
$773$	−37.4603	−1.34735	−0.673677	−	0.739026i	$-0.735286\pi$
$773$	−37.4603	−1.34735	−0.673677	+	0.739026i	$0.735286\pi$
$774$	0.927385	0.0333342
$775$	11.6941	0.420063
$776$	−4.15116	−0.149018
$777$	−26.7092	−0.958187
$778$	−1.78699	−0.0640667
$779$	4.64401	0.166389
$780$	4.94683	0.177125
$781$	3.88791	0.139120
$782$	1.99997	0.0715189
$783$	2.69096	0.0961669
$784$	44.8590	1.60211
$785$	43.9033	1.56698
$786$	2.38405	0.0850362
$787$	13.9995	0.499027	0.249514	−	0.968371i	$-0.419729\pi$
$787$	13.9995	0.499027	0.249514	+	0.968371i	$0.419729\pi$
$788$	−23.9739	−0.854034
$789$	17.9972	0.640716
$790$	−4.07575	−0.145009
$791$	64.4222	2.29059
$792$	1.57485	0.0559600
$793$	−0.867932	−0.0308212
$794$	−1.23586	−0.0438591
$795$	4.80690	0.170483
$796$	10.5187	0.372824
$797$	31.7790	1.12567	0.562835	−	0.826569i	$-0.309711\pi$
$797$	31.7790	1.12567	0.562835	+	0.826569i	$0.309711\pi$
$798$	0.486525	0.0172228
$799$	−12.3180	−0.435779
$800$	1.98550	0.0701980
$801$	2.42516	0.0856889
$802$	−0.595817	−0.0210390
$803$	−6.55108	−0.231183
$804$	−4.76527	−0.168058
$805$	28.1674	0.992770
$806$	1.28981	0.0454317
$807$	7.47922	0.263281
$808$	−5.30685	−0.186694
$809$	−33.1518	−1.16555	−0.582777	−	0.812632i	$-0.698034\pi$
$809$	−33.1518	−1.16555	−0.582777	+	0.812632i	$0.698034\pi$
$810$	−0.339342	−0.0119232
$811$	−15.6879	−0.550876	−0.275438	−	0.961319i	$-0.588823\pi$
$811$	−15.6879	−0.550876	−0.275438	+	0.961319i	$0.588823\pi$
$812$	−22.9553	−0.805574
$813$	−22.7181	−0.796760
$814$	2.45400	0.0860126
$815$	7.32045	0.256424
$816$	−21.8356	−0.764398
$817$	5.67242	0.198453
$818$	2.19826	0.0768605
$819$	4.30504	0.150430
$820$	27.6313	0.964928
$821$	37.6317	1.31336	0.656678	−	0.754171i	$-0.271961\pi$
$821$	37.6317	1.31336	0.656678	+	0.754171i	$0.271961\pi$
$822$	1.66727	0.0581529
$823$	−4.24928	−0.148120	−0.0740602	−	0.997254i	$-0.523596\pi$
$823$	−4.24928	−0.148120	−0.0740602	+	0.997254i	$0.523596\pi$
$824$	−0.541201	−0.0188536
$825$	−3.58616	−0.124854
$826$	−6.63173	−0.230748
$827$	40.8023	1.41883	0.709417	−	0.704789i	$-0.248958\pi$
$827$	40.8023	1.41883	0.709417	+	0.704789i	$0.248958\pi$
$828$	5.19327	0.180479
$829$	40.8337	1.41821	0.709106	−	0.705102i	$-0.249099\pi$
$829$	40.8337	1.41821	0.709106	+	0.705102i	$0.249099\pi$
$830$	2.89466	0.100475
$831$	−17.2436	−0.598173
$832$	−7.55997	−0.262095
$833$	−64.7485	−2.24340
$834$	1.57463	0.0545251
$835$	−12.3040	−0.425798
$836$	4.79400	0.165804
$837$	9.48891	0.327985
$838$	−4.48351	−0.154880
$839$	−10.8613	−0.374974	−0.187487	−	0.982267i	$-0.560034\pi$
$839$	−10.8613	−0.374974	−0.187487	+	0.982267i	$0.560034\pi$
$840$	5.81653	0.200689
$841$	−21.7588	−0.750302
$842$	0.107456	0.00370319
$843$	28.0998	0.967810
$844$	−27.5772	−0.949246
$845$	−2.49648	−0.0858814
$846$	0.298248	0.0102540
$847$	−10.9020	−0.374596
$848$	−7.48910	−0.257177
$849$	−11.7119	−0.401951
$850$	−0.940440	−0.0322568
$851$	16.2602	0.557392
$852$	2.64749	0.0907015
$853$	−32.8602	−1.12511	−0.562556	−	0.826759i	$-0.690182\pi$
$853$	−32.8602	−1.12511	−0.562556	+	0.826759i	$0.690182\pi$
$854$	−0.507894	−0.0173798
$855$	−2.07561	−0.0709843
$856$	−3.96973	−0.135683
$857$	−42.1660	−1.44036	−0.720181	−	0.693786i	$-0.755941\pi$
$857$	−42.1660	−1.44036	−0.720181	+	0.693786i	$0.755941\pi$
$858$	−0.395540	−0.0135035
$859$	17.1298	0.584462	0.292231	−	0.956348i	$-0.405602\pi$
$859$	17.1298	0.584462	0.292231	+	0.956348i	$0.405602\pi$
$860$	33.7502	1.15087
$861$	24.0466	0.819505
$862$	0.880343	0.0299846
$863$	−47.3726	−1.61258	−0.806292	−	0.591518i	$-0.798529\pi$
$863$	−47.3726	−1.61258	−0.806292	+	0.591518i	$0.798529\pi$
$864$	1.61109	0.0548105
$865$	−34.3830	−1.16906
$866$	1.04578	0.0355370
$867$	14.5170	0.493024
$868$	−80.9456	−2.74747
$869$	−34.9504	−1.18561
$870$	−0.913153	−0.0309588
$871$	2.40485	0.0814853
$872$	3.68559	0.124810
$873$	7.67026	0.259599
$874$	−0.296189	−0.0100188
$875$	40.4921	1.36888
$876$	−4.46099	−0.150723
$877$	−18.4567	−0.623237	−0.311619	−	0.950207i	$-0.600871\pi$
$877$	−18.4567	−0.623237	−0.311619	+	0.950207i	$0.600871\pi$
$878$	−2.14155	−0.0722737
$879$	−9.05938	−0.305565
$880$	28.2553	0.952487
$881$	31.6352	1.06582	0.532909	−	0.846173i	$-0.321099\pi$
$881$	31.6352	1.06582	0.532909	+	0.846173i	$0.321099\pi$
$882$	1.56771	0.0527877
$883$	19.1952	0.645971	0.322986	−	0.946404i	$-0.395313\pi$
$883$	19.1952	0.645971	0.322986	+	0.946404i	$0.395313\pi$
$884$	11.1243	0.374150
$885$	28.2922	0.951033
$886$	−0.622870	−0.0209257
$887$	12.1554	0.408137	0.204069	−	0.978957i	$-0.434583\pi$
$887$	12.1554	0.408137	0.204069	+	0.978957i	$0.434583\pi$
$888$	3.35770	0.112677
$889$	34.8724	1.16958
$890$	−0.822958	−0.0275856
$891$	−2.90992	−0.0974860
$892$	−33.6357	−1.12621
$893$	1.82425	0.0610464
$894$	−0.0656126	−0.00219441
$895$	2.01830	0.0674642
$896$	−18.2956	−0.611212
$897$	−2.62085	−0.0875076
$898$	0.538424	0.0179674
$899$	25.5342	0.851615
$900$	−2.44201	−0.0814005
$901$	10.8096	0.360121
$902$	−2.20936	−0.0735636
$903$	29.3716	0.977426
$904$	−8.09874	−0.269360
$905$	24.3357	0.808947
$906$	−0.114721	−0.00381136
$907$	10.2424	0.340092	0.170046	−	0.985436i	$-0.445608\pi$
$907$	10.2424	0.340092	0.170046	+	0.985436i	$0.445608\pi$
$908$	−44.6580	−1.48203
$909$	9.80569	0.325234
$910$	−1.46088	−0.0484277
$911$	14.1614	0.469188	0.234594	−	0.972093i	$-0.424624\pi$
$911$	14.1614	0.469188	0.234594	+	0.972093i	$0.424624\pi$
$912$	3.23378	0.107081
$913$	24.8222	0.821496
$914$	−2.43740	−0.0806219
$915$	2.16677	0.0716312
$916$	−52.5643	−1.73677
$917$	75.5063	2.49344
$918$	−0.763101	−0.0251861
$919$	37.4588	1.23565	0.617826	−	0.786315i	$-0.288014\pi$
$919$	37.4588	1.23565	0.617826	+	0.786315i	$0.288014\pi$
$920$	−3.54102	−0.116744
$921$	26.1478	0.861599
$922$	3.80094	0.125177
$923$	−1.33609	−0.0439779
$924$	24.8232	0.816623
$925$	−7.64597	−0.251398
$926$	−4.38640	−0.144146
$927$	1.00000	0.0328443
$928$	4.33538	0.142316
$929$	6.85648	0.224954	0.112477	−	0.993654i	$-0.464122\pi$
$929$	6.85648	0.224954	0.112477	+	0.993654i	$0.464122\pi$
$930$	−3.21998	−0.105587
$931$	9.58905	0.314268
$932$	−41.4978	−1.35930
$933$	−3.50561	−0.114769
$934$	1.52081	0.0497624
$935$	−40.7832	−1.33375
$936$	−0.541201	−0.0176897
$937$	22.8956	0.747966	0.373983	−	0.927436i	$-0.377992\pi$
$937$	22.8956	0.747966	0.373983	+	0.927436i	$0.377992\pi$
$938$	1.40726	0.0459488
$939$	21.6368	0.706089
$940$	10.8541	0.354022
$941$	38.5130	1.25549	0.627744	−	0.778420i	$-0.283979\pi$
$941$	38.5130	1.25549	0.627744	+	0.778420i	$0.283979\pi$
$942$	−2.39045	−0.0778851
$943$	−14.6392	−0.476718
$944$	−44.0790	−1.43465
$945$	−10.7474	−0.349614
$946$	−2.69862	−0.0877396
$947$	1.49683	0.0486403	0.0243202	−	0.999704i	$-0.492258\pi$
$947$	1.49683	0.0486403	0.0243202	+	0.999704i	$0.492258\pi$
$948$	−23.7996	−0.772976
$949$	2.25129	0.0730801
$950$	0.139276	0.00451872
$951$	−30.6237	−0.993042
$952$	13.0800	0.423927
$953$	37.8795	1.22704	0.613518	−	0.789681i	$-0.289754\pi$
$953$	37.8795	1.22704	0.613518	+	0.789681i	$0.289754\pi$
$954$	−0.261726	−0.00847371
$955$	5.87326	0.190054
$956$	−34.3131	−1.10976
$957$	−7.83046	−0.253123
$958$	0.222203	0.00717906
$959$	52.8050	1.70516
$960$	18.8733	0.609133
$961$	59.0395	1.90450
$962$	−0.843321	−0.0271898
$963$	7.33504	0.236368
$964$	−22.1734	−0.714156
$965$	−5.36365	−0.172662
$966$	−1.53366	−0.0493447
$967$	18.3804	0.591074	0.295537	−	0.955331i	$-0.404501\pi$
$967$	18.3804	0.591074	0.295537	+	0.955331i	$0.404501\pi$
$968$	1.37052	0.0440502
$969$	−4.66757	−0.149944
$970$	−2.60284	−0.0835721
$971$	−14.5009	−0.465357	−0.232679	−	0.972554i	$-0.574749\pi$
$971$	−14.5009	−0.465357	−0.232679	+	0.972554i	$0.574749\pi$
$972$	−1.98152	−0.0635574
$973$	49.8709	1.59879
$974$	−1.01728	−0.0325958
$975$	1.23239	0.0394681
$976$	−3.37581	−0.108057
$977$	−46.2146	−1.47853	−0.739267	−	0.673412i	$-0.764828\pi$
$977$	−46.2146	−1.47853	−0.739267	+	0.673412i	$0.764828\pi$
$978$	−0.398584	−0.0127453
$979$	−7.05703	−0.225544
$980$	57.0537	1.82251
$981$	−6.81001	−0.217427
$982$	−1.22630	−0.0391328
$983$	45.4727	1.45035	0.725177	−	0.688562i	$-0.241758\pi$
$983$	45.4727	1.45035	0.725177	+	0.688562i	$0.241758\pi$
$984$	−3.02297	−0.0963689
$985$	−30.2041	−0.962384
$986$	−2.05347	−0.0653959
$987$	9.44593	0.300667
$988$	−1.64747	−0.0524130
$989$	−17.8810	−0.568583
$990$	0.987457	0.0313834
$991$	49.1047	1.55986	0.779932	−	0.625864i	$-0.215254\pi$
$991$	49.1047	1.55986	0.779932	+	0.625864i	$0.215254\pi$
$992$	15.2875	0.485379
$993$	−21.1463	−0.671057
$994$	−0.781848	−0.0247987
$995$	13.2522	0.420124
$996$	16.9028	0.535586
$997$	−6.91870	−0.219118	−0.109559	−	0.993980i	$-0.534944\pi$
$997$	−6.91870	−0.219118	−0.109559	+	0.993980i	$0.534944\pi$
$998$	1.37087	0.0433942
$999$	−6.20417	−0.196291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.16	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.16	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+0.135928 q^{2} +1.00000 q^{3} -1.98152 q^{4} -2.49648 q^{5} +0.135928 q^{6} +4.30504 q^{7} -0.541201 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.135928 q^{2} +1.00000 q^{3} -1.98152 q^{4} -2.49648 q^{5} +0.135928 q^{6} +4.30504 q^{7} -0.541201 q^{8} +1.00000 q^{9} -0.339342 q^{10} -2.90992 q^{11} -1.98152 q^{12} +1.00000 q^{13} +0.585177 q^{14} -2.49648 q^{15} +3.88948 q^{16} -5.61400 q^{17} +0.135928 q^{18} +0.831416 q^{19} +4.94683 q^{20} +4.30504 q^{21} -0.395540 q^{22} -2.62085 q^{23} -0.541201 q^{24} +1.23239 q^{25} +0.135928 q^{26} +1.00000 q^{27} -8.53054 q^{28} +2.69096 q^{29} -0.339342 q^{30} +9.48891 q^{31} +1.61109 q^{32} -2.90992 q^{33} -0.763101 q^{34} -10.7474 q^{35} -1.98152 q^{36} -6.20417 q^{37} +0.113013 q^{38} +1.00000 q^{39} +1.35110 q^{40} +5.58567 q^{41} +0.585177 q^{42} +6.82261 q^{43} +5.76607 q^{44} -2.49648 q^{45} -0.356247 q^{46} +2.19415 q^{47} +3.88948 q^{48} +11.5334 q^{49} +0.167517 q^{50} -5.61400 q^{51} -1.98152 q^{52} -1.92548 q^{53} +0.135928 q^{54} +7.26454 q^{55} -2.32990 q^{56} +0.831416 q^{57} +0.365777 q^{58} -11.3329 q^{59} +4.94683 q^{60} -0.867932 q^{61} +1.28981 q^{62} +4.30504 q^{63} -7.55997 q^{64} -2.49648 q^{65} -0.395540 q^{66} +2.40485 q^{67} +11.1243 q^{68} -2.62085 q^{69} -1.46088 q^{70} -1.33609 q^{71} -0.541201 q^{72} +2.25129 q^{73} -0.843321 q^{74} +1.23239 q^{75} -1.64747 q^{76} -12.5273 q^{77} +0.135928 q^{78} +12.0108 q^{79} -9.71000 q^{80} +1.00000 q^{81} +0.759251 q^{82} -8.53021 q^{83} -8.53054 q^{84} +14.0152 q^{85} +0.927385 q^{86} +2.69096 q^{87} +1.57485 q^{88} +2.42516 q^{89} -0.339342 q^{90} +4.30504 q^{91} +5.19327 q^{92} +9.48891 q^{93} +0.298248 q^{94} -2.07561 q^{95} +1.61109 q^{96} +7.67026 q^{97} +1.56771 q^{98} -2.90992 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

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