LMFDB - Embedded newform 4017.2.a.l.1.19

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			1.19
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)

$f(q)$	$=$	$q+0.934190 q^{2} +1.00000 q^{3} -1.12729 q^{4} -1.38248 q^{5} +0.934190 q^{6} -2.39473 q^{7} -2.92148 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.934190 q^{2} +1.00000 q^{3} -1.12729 q^{4} -1.38248 q^{5} +0.934190 q^{6} -2.39473 q^{7} -2.92148 q^{8} +1.00000 q^{9} -1.29149 q^{10} -2.56391 q^{11} -1.12729 q^{12} -1.00000 q^{13} -2.23713 q^{14} -1.38248 q^{15} -0.474643 q^{16} -1.77090 q^{17} +0.934190 q^{18} +7.23485 q^{19} +1.55845 q^{20} -2.39473 q^{21} -2.39518 q^{22} -2.69394 q^{23} -2.92148 q^{24} -3.08876 q^{25} -0.934190 q^{26} +1.00000 q^{27} +2.69955 q^{28} -2.04037 q^{29} -1.29149 q^{30} +6.73910 q^{31} +5.39956 q^{32} -2.56391 q^{33} -1.65435 q^{34} +3.31065 q^{35} -1.12729 q^{36} +1.26273 q^{37} +6.75873 q^{38} -1.00000 q^{39} +4.03888 q^{40} -4.70667 q^{41} -2.23713 q^{42} +4.91059 q^{43} +2.89027 q^{44} -1.38248 q^{45} -2.51665 q^{46} -3.37827 q^{47} -0.474643 q^{48} -1.26529 q^{49} -2.88549 q^{50} -1.77090 q^{51} +1.12729 q^{52} +10.5208 q^{53} +0.934190 q^{54} +3.54454 q^{55} +6.99615 q^{56} +7.23485 q^{57} -1.90609 q^{58} +3.50926 q^{59} +1.55845 q^{60} +3.05665 q^{61} +6.29560 q^{62} -2.39473 q^{63} +5.99350 q^{64} +1.38248 q^{65} -2.39518 q^{66} +12.1419 q^{67} +1.99631 q^{68} -2.69394 q^{69} +3.09277 q^{70} -5.69575 q^{71} -2.92148 q^{72} +4.34859 q^{73} +1.17963 q^{74} -3.08876 q^{75} -8.15576 q^{76} +6.13986 q^{77} -0.934190 q^{78} +6.70890 q^{79} +0.656182 q^{80} +1.00000 q^{81} -4.39693 q^{82} -17.6252 q^{83} +2.69955 q^{84} +2.44822 q^{85} +4.58742 q^{86} -2.04037 q^{87} +7.49042 q^{88} +5.32743 q^{89} -1.29149 q^{90} +2.39473 q^{91} +3.03685 q^{92} +6.73910 q^{93} -3.15595 q^{94} -10.0020 q^{95} +5.39956 q^{96} +9.59962 q^{97} -1.18202 q^{98} -2.56391 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * 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 $

$2$	0.934190	0.660572	0.330286	−	0.943881i	$-0.392855\pi$
$2$	0.934190	0.660572	0.330286	+	0.943881i	$0.392855\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.12729	−0.563644
$5$	−1.38248	−0.618262	−0.309131	−	0.951020i	$-0.600038\pi$
$5$	−1.38248	−0.618262	−0.309131	+	0.951020i	$0.600038\pi$
$6$	0.934190	0.381382
$7$	−2.39473	−0.905121	−0.452561	−	0.891734i	$-0.649489\pi$
$7$	−2.39473	−0.905121	−0.452561	+	0.891734i	$0.649489\pi$
$8$	−2.92148	−1.03290
$9$	1.00000	0.333333
$10$	−1.29149	−0.408406
$11$	−2.56391	−0.773048	−0.386524	−	0.922279i	$-0.626324\pi$
$11$	−2.56391	−0.773048	−0.386524	+	0.922279i	$0.626324\pi$
$12$	−1.12729	−0.325420
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.23713	−0.597898
$15$	−1.38248	−0.356954
$16$	−0.474643	−0.118661
$17$	−1.77090	−0.429505	−0.214753	−	0.976668i	$-0.568895\pi$
$17$	−1.77090	−0.429505	−0.214753	+	0.976668i	$0.568895\pi$
$18$	0.934190	0.220191
$19$	7.23485	1.65979	0.829894	−	0.557921i	$-0.188401\pi$
$19$	7.23485	1.65979	0.829894	+	0.557921i	$0.188401\pi$
$20$	1.55845	0.348480
$21$	−2.39473	−0.522572
$22$	−2.39518	−0.510654
$23$	−2.69394	−0.561725	−0.280863	−	0.959748i	$-0.590621\pi$
$23$	−2.69394	−0.561725	−0.280863	+	0.959748i	$0.590621\pi$
$24$	−2.92148	−0.596345
$25$	−3.08876	−0.617753
$26$	−0.934190	−0.183210
$27$	1.00000	0.192450
$28$	2.69955	0.510166
$29$	−2.04037	−0.378887	−0.189444	−	0.981892i	$-0.560668\pi$
$29$	−2.04037	−0.378887	−0.189444	+	0.981892i	$0.560668\pi$
$30$	−1.29149	−0.235794
$31$	6.73910	1.21038	0.605189	−	0.796082i	$-0.293097\pi$
$31$	6.73910	1.21038	0.605189	+	0.796082i	$0.293097\pi$
$32$	5.39956	0.954516
$33$	−2.56391	−0.446319
$34$	−1.65435	−0.283719
$35$	3.31065	0.559602
$36$	−1.12729	−0.187881
$37$	1.26273	0.207591	0.103796	−	0.994599i	$-0.466901\pi$
$37$	1.26273	0.207591	0.103796	+	0.994599i	$0.466901\pi$
$38$	6.75873	1.09641
$39$	−1.00000	−0.160128
$40$	4.03888	0.638602
$41$	−4.70667	−0.735059	−0.367529	−	0.930012i	$-0.619796\pi$
$41$	−4.70667	−0.735059	−0.367529	+	0.930012i	$0.619796\pi$
$42$	−2.23713	−0.345196
$43$	4.91059	0.748858	0.374429	−	0.927256i	$-0.377839\pi$
$43$	4.91059	0.748858	0.374429	+	0.927256i	$0.377839\pi$
$44$	2.89027	0.435724
$45$	−1.38248	−0.206087
$46$	−2.51665	−0.371060
$47$	−3.37827	−0.492772	−0.246386	−	0.969172i	$-0.579243\pi$
$47$	−3.37827	−0.492772	−0.246386	+	0.969172i	$0.579243\pi$
$48$	−0.474643	−0.0685088
$49$	−1.26529	−0.180756
$50$	−2.88549	−0.408070
$51$	−1.77090	−0.247975
$52$	1.12729	0.156327
$53$	10.5208	1.44514	0.722569	−	0.691299i	$-0.242961\pi$
$53$	10.5208	1.44514	0.722569	+	0.691299i	$0.242961\pi$
$54$	0.934190	0.127127
$55$	3.54454	0.477946
$56$	6.99615	0.934900
$57$	7.23485	0.958279
$58$	−1.90609	−0.250282
$59$	3.50926	0.456866	0.228433	−	0.973560i	$-0.426640\pi$
$59$	3.50926	0.456866	0.228433	+	0.973560i	$0.426640\pi$
$60$	1.55845	0.201195
$61$	3.05665	0.391364	0.195682	−	0.980667i	$-0.437308\pi$
$61$	3.05665	0.391364	0.195682	+	0.980667i	$0.437308\pi$
$62$	6.29560	0.799542
$63$	−2.39473	−0.301707
$64$	5.99350	0.749188
$65$	1.38248	0.171475
$66$	−2.39518	−0.294826
$67$	12.1419	1.48337	0.741686	−	0.670747i	$-0.234026\pi$
$67$	12.1419	1.48337	0.741686	+	0.670747i	$0.234026\pi$
$68$	1.99631	0.242088
$69$	−2.69394	−0.324312
$70$	3.09277	0.369657
$71$	−5.69575	−0.675961	−0.337980	−	0.941153i	$-0.609744\pi$
$71$	−5.69575	−0.675961	−0.337980	+	0.941153i	$0.609744\pi$
$72$	−2.92148	−0.344300
$73$	4.34859	0.508964	0.254482	−	0.967077i	$-0.418095\pi$
$73$	4.34859	0.508964	0.254482	+	0.967077i	$0.418095\pi$
$74$	1.17963	0.137129
$75$	−3.08876	−0.356660
$76$	−8.15576	−0.935530
$77$	6.13986	0.699702
$78$	−0.934190	−0.105776
$79$	6.70890	0.754810	0.377405	−	0.926048i	$-0.376816\pi$
$79$	6.70890	0.754810	0.377405	+	0.926048i	$0.376816\pi$
$80$	0.656182	0.0733634
$81$	1.00000	0.111111
$82$	−4.39693	−0.485559
$83$	−17.6252	−1.93461	−0.967306	−	0.253610i	$-0.918382\pi$
$83$	−17.6252	−1.93461	−0.967306	+	0.253610i	$0.918382\pi$
$84$	2.69955	0.294545
$85$	2.44822	0.265547
$86$	4.58742	0.494675
$87$	−2.04037	−0.218751
$88$	7.49042	0.798481
$89$	5.32743	0.564707	0.282353	−	0.959310i	$-0.408885\pi$
$89$	5.32743	0.564707	0.282353	+	0.959310i	$0.408885\pi$
$90$	−1.29149	−0.136135
$91$	2.39473	0.251035
$92$	3.03685	0.316613
$93$	6.73910	0.698812
$94$	−3.15595	−0.325511
$95$	−10.0020	−1.02618
$96$	5.39956	0.551090
$97$	9.59962	0.974693	0.487347	−	0.873209i	$-0.337965\pi$
$97$	9.59962	0.974693	0.487347	+	0.873209i	$0.337965\pi$
$98$	−1.18202	−0.119402
$99$	−2.56391	−0.257683
$100$	3.48193	0.348193
$101$	13.1079	1.30429	0.652144	−	0.758095i	$-0.273870\pi$
$101$	13.1079	1.30429	0.652144	+	0.758095i	$0.273870\pi$
$102$	−1.65435	−0.163805
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	2.92148	0.286475
$105$	3.31065	0.323086
$106$	9.82839	0.954618
$107$	14.0676	1.35997	0.679984	−	0.733226i	$-0.261986\pi$
$107$	14.0676	1.35997	0.679984	+	0.733226i	$0.261986\pi$
$108$	−1.12729	−0.108473
$109$	11.4657	1.09822	0.549109	−	0.835751i	$-0.314967\pi$
$109$	11.4657	1.09822	0.549109	+	0.835751i	$0.314967\pi$
$110$	3.31127	0.315718
$111$	1.26273	0.119853
$112$	1.13664	0.107402
$113$	12.1117	1.13937	0.569687	−	0.821862i	$-0.307065\pi$
$113$	12.1117	1.13937	0.569687	+	0.821862i	$0.307065\pi$
$114$	6.75873	0.633013
$115$	3.72430	0.347293
$116$	2.30009	0.213558
$117$	−1.00000	−0.0924500
$118$	3.27831	0.301793
$119$	4.24081	0.388754
$120$	4.03888	0.368697
$121$	−4.42637	−0.402397
$122$	2.85549	0.258524
$123$	−4.70667	−0.424386
$124$	−7.59691	−0.682223
$125$	11.1825	1.00019
$126$	−2.23713	−0.199299
$127$	−16.5615	−1.46959	−0.734796	−	0.678289i	$-0.762722\pi$
$127$	−16.5615	−1.46959	−0.734796	+	0.678289i	$0.762722\pi$
$128$	−5.20005	−0.459624
$129$	4.91059	0.432353
$130$	1.29149	0.113272
$131$	3.03641	0.265293	0.132646	−	0.991163i	$-0.457653\pi$
$131$	3.03641	0.265293	0.132646	+	0.991163i	$0.457653\pi$
$132$	2.89027	0.251565
$133$	−17.3255	−1.50231
$134$	11.3429	0.979874
$135$	−1.38248	−0.118985
$136$	5.17364	0.443636
$137$	−10.2368	−0.874592	−0.437296	−	0.899318i	$-0.644064\pi$
$137$	−10.2368	−0.874592	−0.437296	+	0.899318i	$0.644064\pi$
$138$	−2.51665	−0.214232
$139$	−12.5441	−1.06398	−0.531989	−	0.846751i	$-0.678555\pi$
$139$	−12.5441	−1.06398	−0.531989	+	0.846751i	$0.678555\pi$
$140$	−3.73206	−0.315416
$141$	−3.37827	−0.284502
$142$	−5.32091	−0.446521
$143$	2.56391	0.214405
$144$	−0.474643	−0.0395536
$145$	2.82076	0.234251
$146$	4.06241	0.336208
$147$	−1.26529	−0.104359
$148$	−1.42346	−0.117008
$149$	18.6466	1.52759	0.763796	−	0.645457i	$-0.223333\pi$
$149$	18.6466	1.52759	0.763796	+	0.645457i	$0.223333\pi$
$150$	−2.88549	−0.235599
$151$	0.568007	0.0462237	0.0231119	−	0.999733i	$-0.492643\pi$
$151$	0.568007	0.0462237	0.0231119	+	0.999733i	$0.492643\pi$
$152$	−21.1365	−1.71440
$153$	−1.77090	−0.143168
$154$	5.73580	0.462204
$155$	−9.31664	−0.748331
$156$	1.12729	0.0902553
$157$	14.6542	1.16953	0.584767	−	0.811201i	$-0.301186\pi$
$157$	14.6542	1.16953	0.584767	+	0.811201i	$0.301186\pi$
$158$	6.26739	0.498607
$159$	10.5208	0.834351
$160$	−7.46475	−0.590141
$161$	6.45125	0.508429
$162$	0.934190	0.0733969
$163$	7.38204	0.578206	0.289103	−	0.957298i	$-0.406643\pi$
$163$	7.38204	0.578206	0.289103	+	0.957298i	$0.406643\pi$
$164$	5.30578	0.414312
$165$	3.54454	0.275942
$166$	−16.4653	−1.27795
$167$	−1.99341	−0.154254	−0.0771272	−	0.997021i	$-0.524575\pi$
$167$	−1.99341	−0.154254	−0.0771272	+	0.997021i	$0.524575\pi$
$168$	6.99615	0.539765
$169$	1.00000	0.0769231
$170$	2.28710	0.175413
$171$	7.23485	0.553263
$172$	−5.53565	−0.422089
$173$	1.98780	0.151129	0.0755647	−	0.997141i	$-0.475924\pi$
$173$	1.98780	0.151129	0.0755647	+	0.997141i	$0.475924\pi$
$174$	−1.90609	−0.144501
$175$	7.39674	0.559141
$176$	1.21694	0.0917304
$177$	3.50926	0.263772
$178$	4.97683	0.373030
$179$	−11.9166	−0.890691	−0.445345	−	0.895359i	$-0.646919\pi$
$179$	−11.9166	−0.890691	−0.445345	+	0.895359i	$0.646919\pi$
$180$	1.55845	0.116160
$181$	19.8888	1.47832	0.739162	−	0.673528i	$-0.235222\pi$
$181$	19.8888	1.47832	0.739162	+	0.673528i	$0.235222\pi$
$182$	2.23713	0.165827
$183$	3.05665	0.225954
$184$	7.87030	0.580206
$185$	−1.74569	−0.128346
$186$	6.29560	0.461616
$187$	4.54042	0.332028
$188$	3.80829	0.277748
$189$	−2.39473	−0.174191
$190$	−9.34377	−0.677868
$191$	−8.36470	−0.605248	−0.302624	−	0.953110i	$-0.597863\pi$
$191$	−8.36470	−0.605248	−0.302624	+	0.953110i	$0.597863\pi$
$192$	5.99350	0.432544
$193$	−12.6507	−0.910618	−0.455309	−	0.890334i	$-0.650471\pi$
$193$	−12.6507	−0.910618	−0.455309	+	0.890334i	$0.650471\pi$
$194$	8.96787	0.643855
$195$	1.38248	0.0990011
$196$	1.42635	0.101882
$197$	12.7588	0.909028	0.454514	−	0.890740i	$-0.349813\pi$
$197$	12.7588	0.909028	0.454514	+	0.890740i	$0.349813\pi$
$198$	−2.39518	−0.170218
$199$	−1.79291	−0.127096	−0.0635479	−	0.997979i	$-0.520242\pi$
$199$	−1.79291	−0.127096	−0.0635479	+	0.997979i	$0.520242\pi$
$200$	9.02377	0.638077
$201$	12.1419	0.856425
$202$	12.2453	0.861577
$203$	4.88612	0.342939
$204$	1.99631	0.139770
$205$	6.50686	0.454459
$206$	−0.934190	−0.0650881
$207$	−2.69394	−0.187242
$208$	0.474643	0.0329106
$209$	−18.5495	−1.28310
$210$	3.09277	0.213422
$211$	4.44865	0.306258	0.153129	−	0.988206i	$-0.451065\pi$
$211$	4.44865	0.306258	0.153129	+	0.988206i	$0.451065\pi$
$212$	−11.8599	−0.814544
$213$	−5.69575	−0.390266
$214$	13.1418	0.898358
$215$	−6.78877	−0.462990
$216$	−2.92148	−0.198782
$217$	−16.1383	−1.09554
$218$	10.7112	0.725452
$219$	4.34859	0.293851
$220$	−3.99572	−0.269391
$221$	1.77090	0.119123
$222$	1.17963	0.0791715
$223$	−12.5291	−0.839007	−0.419504	−	0.907754i	$-0.637796\pi$
$223$	−12.5291	−0.839007	−0.419504	+	0.907754i	$0.637796\pi$
$224$	−12.9305	−0.863953
$225$	−3.08876	−0.205918
$226$	11.3146	0.752638
$227$	−10.7617	−0.714280	−0.357140	−	0.934051i	$-0.616248\pi$
$227$	−10.7617	−0.714280	−0.357140	+	0.934051i	$0.616248\pi$
$228$	−8.15576	−0.540129
$229$	−20.7330	−1.37007	−0.685036	−	0.728509i	$-0.740214\pi$
$229$	−20.7330	−1.37007	−0.685036	+	0.728509i	$0.740214\pi$
$230$	3.47921	0.229412
$231$	6.13986	0.403973
$232$	5.96090	0.391352
$233$	−19.5886	−1.28329	−0.641647	−	0.767000i	$-0.721748\pi$
$233$	−19.5886	−1.28329	−0.641647	+	0.767000i	$0.721748\pi$
$234$	−0.934190	−0.0610699
$235$	4.67038	0.304662
$236$	−3.95595	−0.257510
$237$	6.70890	0.435790
$238$	3.96172	0.256800
$239$	−13.4737	−0.871540	−0.435770	−	0.900058i	$-0.643524\pi$
$239$	−13.4737	−0.871540	−0.435770	+	0.900058i	$0.643524\pi$
$240$	0.656182	0.0423564
$241$	−15.2392	−0.981641	−0.490820	−	0.871261i	$-0.663303\pi$
$241$	−15.2392	−0.981641	−0.490820	+	0.871261i	$0.663303\pi$
$242$	−4.13507	−0.265813
$243$	1.00000	0.0641500
$244$	−3.44573	−0.220590
$245$	1.74923	0.111754
$246$	−4.39693	−0.280338
$247$	−7.23485	−0.460342
$248$	−19.6882	−1.25020
$249$	−17.6252	−1.11695
$250$	10.4466	0.660701
$251$	−0.0121631	−0.000767726 0	−0.000383863	−	1.00000i	$-0.500122\pi$
$251$	−0.0121631	−0.000767726 0	−0.000383863		1.00000i	$0.500122\pi$
$252$	2.69955	0.170055
$253$	6.90702	0.434240
$254$	−15.4715	−0.970771
$255$	2.44822	0.153313
$256$	−16.8448	−1.05280
$257$	30.9937	1.93333	0.966666	−	0.256040i	$-0.0824178\pi$
$257$	30.9937	1.93333	0.966666	+	0.256040i	$0.0824178\pi$
$258$	4.58742	0.285601
$259$	−3.02389	−0.187895
$260$	−1.55845	−0.0966509
$261$	−2.04037	−0.126296
$262$	2.83659	0.175245
$263$	30.6481	1.88984	0.944922	−	0.327295i	$-0.106137\pi$
$263$	30.6481	1.88984	0.944922	+	0.327295i	$0.106137\pi$
$264$	7.49042	0.461003
$265$	−14.5447	−0.893473
$266$	−16.1853	−0.992384
$267$	5.32743	0.326034
$268$	−13.6875	−0.836094
$269$	−5.02738	−0.306525	−0.153262	−	0.988186i	$-0.548978\pi$
$269$	−5.02738	−0.306525	−0.153262	+	0.988186i	$0.548978\pi$
$270$	−1.29149	−0.0785979
$271$	25.0545	1.52196	0.760978	−	0.648778i	$-0.224720\pi$
$271$	25.0545	1.52196	0.760978	+	0.648778i	$0.224720\pi$
$272$	0.840543	0.0509654
$273$	2.39473	0.144935
$274$	−9.56315	−0.577731
$275$	7.91931	0.477552
$276$	3.03685	0.182797
$277$	21.0664	1.26576	0.632878	−	0.774252i	$-0.281874\pi$
$277$	21.0664	1.26576	0.632878	+	0.774252i	$0.281874\pi$
$278$	−11.7186	−0.702834
$279$	6.73910	0.403460
$280$	−9.67200	−0.578013
$281$	−14.0435	−0.837763	−0.418882	−	0.908041i	$-0.637578\pi$
$281$	−14.0435	−0.837763	−0.418882	+	0.908041i	$0.637578\pi$
$282$	−3.15595	−0.187934
$283$	−1.91548	−0.113863	−0.0569317	−	0.998378i	$-0.518132\pi$
$283$	−1.91548	−0.113863	−0.0569317	+	0.998378i	$0.518132\pi$
$284$	6.42075	0.381001
$285$	−10.0020	−0.592467
$286$	2.39518	0.141630
$287$	11.2712	0.665317
$288$	5.39956	0.318172
$289$	−13.8639	−0.815525
$290$	2.63513	0.154740
$291$	9.59962	0.562740
$292$	−4.90212	−0.286875
$293$	1.64026	0.0958252	0.0479126	−	0.998852i	$-0.484743\pi$
$293$	1.64026	0.0958252	0.0479126	+	0.998852i	$0.484743\pi$
$294$	−1.18202	−0.0689369
$295$	−4.85146	−0.282463
$296$	−3.68904	−0.214421
$297$	−2.56391	−0.148773
$298$	17.4195	1.00909
$299$	2.69394	0.155795
$300$	3.48193	0.201029
$301$	−11.7595	−0.677807
$302$	0.530626	0.0305341
$303$	13.1079	0.753031
$304$	−3.43397	−0.196952
$305$	−4.22574	−0.241965
$306$	−1.65435	−0.0945731
$307$	−16.1802	−0.923451	−0.461726	−	0.887023i	$-0.652770\pi$
$307$	−16.1802	−0.923451	−0.461726	+	0.887023i	$0.652770\pi$
$308$	−6.92139	−0.394383
$309$	−1.00000	−0.0568880
$310$	−8.70351	−0.494326
$311$	15.3931	0.872860	0.436430	−	0.899738i	$-0.356243\pi$
$311$	15.3931	0.872860	0.436430	+	0.899738i	$0.356243\pi$
$312$	2.92148	0.165396
$313$	11.4136	0.645132	0.322566	−	0.946547i	$-0.395455\pi$
$313$	11.4136	0.645132	0.322566	+	0.946547i	$0.395455\pi$
$314$	13.6898	0.772562
$315$	3.31065	0.186534
$316$	−7.56287	−0.425445
$317$	−22.2899	−1.25193	−0.625963	−	0.779853i	$-0.715294\pi$
$317$	−22.2899	−1.25193	−0.625963	+	0.779853i	$0.715294\pi$
$318$	9.82839	0.551149
$319$	5.23132	0.292898
$320$	−8.28586	−0.463194
$321$	14.0676	0.785178
$322$	6.02669	0.335854
$323$	−12.8122	−0.712888
$324$	−1.12729	−0.0626271
$325$	3.08876	0.171334
$326$	6.89623	0.381947
$327$	11.4657	0.634056
$328$	13.7505	0.759242
$329$	8.09004	0.446018
$330$	3.31127	0.182280
$331$	−11.1134	−0.610850	−0.305425	−	0.952216i	$-0.598798\pi$
$331$	−11.1134	−0.610850	−0.305425	+	0.952216i	$0.598798\pi$
$332$	19.8686	1.09043
$333$	1.26273	0.0691971
$334$	−1.86222	−0.101896
$335$	−16.7859	−0.917112
$336$	1.13664	0.0620088
$337$	−18.5035	−1.00795	−0.503976	−	0.863718i	$-0.668130\pi$
$337$	−18.5035	−1.00795	−0.503976	+	0.863718i	$0.668130\pi$
$338$	0.934190	0.0508132
$339$	12.1117	0.657817
$340$	−2.75985	−0.149674
$341$	−17.2784	−0.935680
$342$	6.75873	0.365470
$343$	19.7931	1.06873
$344$	−14.3462	−0.773495
$345$	3.72430	0.200510
$346$	1.85698	0.0998319
$347$	12.2660	0.658474	0.329237	−	0.944247i	$-0.393208\pi$
$347$	12.2660	0.658474	0.329237	+	0.944247i	$0.393208\pi$
$348$	2.30009	0.123298
$349$	33.2275	1.77863	0.889314	−	0.457297i	$-0.151182\pi$
$349$	33.2275	1.77863	0.889314	+	0.457297i	$0.151182\pi$
$350$	6.90996	0.369353
$351$	−1.00000	−0.0533761
$352$	−13.8440	−0.737886
$353$	5.56818	0.296364	0.148182	−	0.988960i	$-0.452658\pi$
$353$	5.56818	0.296364	0.148182	+	0.988960i	$0.452658\pi$
$354$	3.27831	0.174240
$355$	7.87423	0.417921
$356$	−6.00555	−0.318294
$357$	4.24081	0.224447
$358$	−11.1324	−0.588366
$359$	−11.7873	−0.622112	−0.311056	−	0.950392i	$-0.600683\pi$
$359$	−11.7873	−0.622112	−0.311056	+	0.950392i	$0.600683\pi$
$360$	4.03888	0.212867
$361$	33.3431	1.75490
$362$	18.5799	0.976540
$363$	−4.42637	−0.232324
$364$	−2.69955	−0.141495
$365$	−6.01182	−0.314673
$366$	2.85549	0.149259
$367$	14.7017	0.767423	0.383711	−	0.923453i	$-0.374646\pi$
$367$	14.7017	0.767423	0.383711	+	0.923453i	$0.374646\pi$
$368$	1.27866	0.0666547
$369$	−4.70667	−0.245020
$370$	−1.63081	−0.0847817
$371$	−25.1943	−1.30802
$372$	−7.59691	−0.393882
$373$	−10.1126	−0.523609	−0.261805	−	0.965121i	$-0.584318\pi$
$373$	−10.1126	−0.523609	−0.261805	+	0.965121i	$0.584318\pi$
$374$	4.24161	0.219329
$375$	11.1825	0.577462
$376$	9.86957	0.508984
$377$	2.04037	0.105084
$378$	−2.23713	−0.115065
$379$	−15.7543	−0.809244	−0.404622	−	0.914484i	$-0.632597\pi$
$379$	−15.7543	−0.809244	−0.404622	+	0.914484i	$0.632597\pi$
$380$	11.2751	0.578403
$381$	−16.5615	−0.848469
$382$	−7.81422	−0.399810
$383$	18.3837	0.939362	0.469681	−	0.882836i	$-0.344369\pi$
$383$	18.3837	0.939362	0.469681	+	0.882836i	$0.344369\pi$
$384$	−5.20005	−0.265364
$385$	−8.48820	−0.432599
$386$	−11.8182	−0.601529
$387$	4.91059	0.249619
$388$	−10.8215	−0.549380
$389$	−18.7055	−0.948409	−0.474205	−	0.880415i	$-0.657264\pi$
$389$	−18.7055	−0.948409	−0.474205	+	0.880415i	$0.657264\pi$
$390$	1.29149	0.0653974
$391$	4.77069	0.241264
$392$	3.69652	0.186703
$393$	3.03641	0.153167
$394$	11.9192	0.600479
$395$	−9.27489	−0.466670
$396$	2.89027	0.145241
$397$	22.9606	1.15236	0.576180	−	0.817323i	$-0.304543\pi$
$397$	22.9606	1.15236	0.576180	+	0.817323i	$0.304543\pi$
$398$	−1.67491	−0.0839559
$399$	−17.3255	−0.867359
$400$	1.46606	0.0733030
$401$	−28.5121	−1.42383	−0.711913	−	0.702268i	$-0.752171\pi$
$401$	−28.5121	−1.42383	−0.711913	+	0.702268i	$0.752171\pi$
$402$	11.3429	0.565731
$403$	−6.73910	−0.335699
$404$	−14.7764	−0.735155
$405$	−1.38248	−0.0686957
$406$	4.56457	0.226536
$407$	−3.23752	−0.160478
$408$	5.17364	0.256133
$409$	−19.4987	−0.964147	−0.482073	−	0.876131i	$-0.660116\pi$
$409$	−19.4987	−0.964147	−0.482073	+	0.876131i	$0.660116\pi$
$410$	6.07864	0.300203
$411$	−10.2368	−0.504946
$412$	1.12729	0.0555375
$413$	−8.40371	−0.413519
$414$	−2.51665	−0.123687
$415$	24.3663	1.19610
$416$	−5.39956	−0.264735
$417$	−12.5441	−0.614288
$418$	−17.3288	−0.847577
$419$	7.27154	0.355238	0.177619	−	0.984099i	$-0.443161\pi$
$419$	7.27154	0.355238	0.177619	+	0.984099i	$0.443161\pi$
$420$	−3.73206	−0.182106
$421$	10.3110	0.502527	0.251264	−	0.967919i	$-0.419154\pi$
$421$	10.3110	0.502527	0.251264	+	0.967919i	$0.419154\pi$
$422$	4.15589	0.202305
$423$	−3.37827	−0.164257
$424$	−30.7362	−1.49268
$425$	5.46988	0.265328
$426$	−5.32091	−0.257799
$427$	−7.31984	−0.354232
$428$	−15.8583	−0.766539
$429$	2.56391	0.123787
$430$	−6.34200	−0.305838
$431$	−34.9595	−1.68394	−0.841969	−	0.539525i	$-0.818604\pi$
$431$	−34.9595	−1.68394	−0.841969	+	0.539525i	$0.818604\pi$
$432$	−0.474643	−0.0228363
$433$	27.6291	1.32777	0.663885	−	0.747834i	$-0.268906\pi$
$433$	27.6291	1.32777	0.663885	+	0.747834i	$0.268906\pi$
$434$	−15.0762	−0.723683
$435$	2.82076	0.135245
$436$	−12.9252	−0.619004
$437$	−19.4902	−0.932345
$438$	4.06241	0.194110
$439$	5.53050	0.263956	0.131978	−	0.991253i	$-0.457867\pi$
$439$	5.53050	0.263956	0.131978	+	0.991253i	$0.457867\pi$
$440$	−10.3553	−0.493670
$441$	−1.26529	−0.0602519
$442$	1.65435	0.0786896
$443$	19.2302	0.913656	0.456828	−	0.889555i	$-0.348985\pi$
$443$	19.2302	0.913656	0.456828	+	0.889555i	$0.348985\pi$
$444$	−1.42346	−0.0675544
$445$	−7.36504	−0.349136
$446$	−11.7045	−0.554225
$447$	18.6466	0.881956
$448$	−14.3528	−0.678105
$449$	24.5125	1.15681	0.578407	−	0.815748i	$-0.303674\pi$
$449$	24.5125	1.15681	0.578407	+	0.815748i	$0.303674\pi$
$450$	−2.88549	−0.136023
$451$	12.0675	0.568235
$452$	−13.6534	−0.642201
$453$	0.568007	0.0266873
$454$	−10.0535	−0.471834
$455$	−3.31065	−0.155206
$456$	−21.1365	−0.989807
$457$	−27.9069	−1.30543	−0.652714	−	0.757605i	$-0.726370\pi$
$457$	−27.9069	−1.30543	−0.652714	+	0.757605i	$0.726370\pi$
$458$	−19.3685	−0.905032
$459$	−1.77090	−0.0826583
$460$	−4.19837	−0.195750
$461$	15.0473	0.700825	0.350412	−	0.936596i	$-0.386041\pi$
$461$	15.0473	0.700825	0.350412	+	0.936596i	$0.386041\pi$
$462$	5.73580	0.266853
$463$	27.6030	1.28282	0.641409	−	0.767199i	$-0.278350\pi$
$463$	27.6030	1.28282	0.641409	+	0.767199i	$0.278350\pi$
$464$	0.968447	0.0449590
$465$	−9.31664	−0.432049
$466$	−18.2995	−0.847708
$467$	39.5800	1.83155	0.915773	−	0.401696i	$-0.131579\pi$
$467$	39.5800	1.83155	0.915773	+	0.401696i	$0.131579\pi$
$468$	1.12729	0.0521089
$469$	−29.0766	−1.34263
$470$	4.36302	0.201251
$471$	14.6542	0.675231
$472$	−10.2522	−0.471897
$473$	−12.5903	−0.578903
$474$	6.26739	0.287871
$475$	−22.3467	−1.02534
$476$	−4.78062	−0.219119
$477$	10.5208	0.481713
$478$	−12.5870	−0.575715
$479$	−6.42258	−0.293455	−0.146727	−	0.989177i	$-0.546874\pi$
$479$	−6.42258	−0.293455	−0.146727	+	0.989177i	$0.546874\pi$
$480$	−7.46475	−0.340718
$481$	−1.26273	−0.0575755
$482$	−14.2363	−0.648445
$483$	6.45125	0.293542
$484$	4.98980	0.226809
$485$	−13.2712	−0.602616
$486$	0.934190	0.0423757
$487$	21.0390	0.953367	0.476683	−	0.879075i	$-0.341839\pi$
$487$	21.0390	0.953367	0.476683	+	0.879075i	$0.341839\pi$
$488$	−8.92995	−0.404240
$489$	7.38204	0.333828
$490$	1.63412	0.0738218
$491$	20.8417	0.940574	0.470287	−	0.882514i	$-0.344150\pi$
$491$	20.8417	0.940574	0.470287	+	0.882514i	$0.344150\pi$
$492$	5.30578	0.239203
$493$	3.61328	0.162734
$494$	−6.75873	−0.304089
$495$	3.54454	0.159315
$496$	−3.19867	−0.143624
$497$	13.6397	0.611826
$498$	−16.4653	−0.737826
$499$	4.94644	0.221433	0.110716	−	0.993852i	$-0.464685\pi$
$499$	4.94644	0.221433	0.110716	+	0.993852i	$0.464685\pi$
$500$	−12.6059	−0.563754
$501$	−1.99341	−0.0890589
$502$	−0.0113626	−0.000507138 0
$503$	−11.3073	−0.504170	−0.252085	−	0.967705i	$-0.581116\pi$
$503$	−11.3073	−0.504170	−0.252085	+	0.967705i	$0.581116\pi$
$504$	6.99615	0.311633
$505$	−18.1214	−0.806392
$506$	6.45247	0.286847
$507$	1.00000	0.0444116
$508$	18.6695	0.828327
$509$	−37.7028	−1.67115	−0.835574	−	0.549378i	$-0.814865\pi$
$509$	−37.7028	−1.67115	−0.835574	+	0.549378i	$0.814865\pi$
$510$	2.28710	0.101275
$511$	−10.4137	−0.460674
$512$	−5.33618	−0.235828
$513$	7.23485	0.319426
$514$	28.9540	1.27711
$515$	1.38248	0.0609191
$516$	−5.53565	−0.243693
$517$	8.66159	0.380936
$518$	−2.82489	−0.124118
$519$	1.98780	0.0872546
$520$	−4.03888	−0.177116
$521$	−5.96257	−0.261225	−0.130613	−	0.991433i	$-0.541694\pi$
$521$	−5.96257	−0.261225	−0.130613	+	0.991433i	$0.541694\pi$
$522$	−1.90609	−0.0834274
$523$	27.5586	1.20505	0.602526	−	0.798099i	$-0.294161\pi$
$523$	27.5586	1.20505	0.602526	+	0.798099i	$0.294161\pi$
$524$	−3.42292	−0.149531
$525$	7.39674	0.322820
$526$	28.6312	1.24838
$527$	−11.9342	−0.519864
$528$	1.21694	0.0529606
$529$	−15.7427	−0.684465
$530$	−13.5875	−0.590204
$531$	3.50926	0.152289
$532$	19.5308	0.846768
$533$	4.70667	0.203869
$534$	4.97683	0.215369
$535$	−19.4481	−0.840817
$536$	−35.4724	−1.53218
$537$	−11.9166	−0.514240
$538$	−4.69653	−0.202482
$539$	3.24409	0.139733
$540$	1.55845	0.0670649
$541$	−19.2860	−0.829171	−0.414586	−	0.910010i	$-0.636073\pi$
$541$	−19.2860	−0.829171	−0.414586	+	0.910010i	$0.636073\pi$
$542$	23.4057	1.00536
$543$	19.8888	0.853511
$544$	−9.56205	−0.409970
$545$	−15.8511	−0.678985
$546$	2.23713	0.0957403
$547$	−30.2735	−1.29440	−0.647200	−	0.762320i	$-0.724060\pi$
$547$	−30.2735	−1.29440	−0.647200	+	0.762320i	$0.724060\pi$
$548$	11.5399	0.492959
$549$	3.05665	0.130455
$550$	7.39814	0.315458
$551$	−14.7618	−0.628872
$552$	7.87030	0.334982
$553$	−16.0660	−0.683195
$554$	19.6800	0.836123
$555$	−1.74569	−0.0741005
$556$	14.1408	0.599705
$557$	−27.5541	−1.16750	−0.583752	−	0.811932i	$-0.698416\pi$
$557$	−27.5541	−1.16750	−0.583752	+	0.811932i	$0.698416\pi$
$558$	6.29560	0.266514
$559$	−4.91059	−0.207696
$560$	−1.57138	−0.0664027
$561$	4.54042	0.191696
$562$	−13.1193	−0.553403
$563$	36.6735	1.54560	0.772801	−	0.634648i	$-0.218855\pi$
$563$	36.6735	1.54560	0.772801	+	0.634648i	$0.218855\pi$
$564$	3.80829	0.160358
$565$	−16.7441	−0.704431
$566$	−1.78942	−0.0752150
$567$	−2.39473	−0.100569
$568$	16.6400	0.698200
$569$	7.04805	0.295470	0.147735	−	0.989027i	$-0.452802\pi$
$569$	7.04805	0.295470	0.147735	+	0.989027i	$0.452802\pi$
$570$	−9.34377	−0.391367
$571$	26.8512	1.12369	0.561844	−	0.827243i	$-0.310092\pi$
$571$	26.8512	1.12369	0.561844	+	0.827243i	$0.310092\pi$
$572$	−2.89027	−0.120848
$573$	−8.36470	−0.349440
$574$	10.5294	0.439490
$575$	8.32094	0.347007
$576$	5.99350	0.249729
$577$	−36.6186	−1.52445	−0.762227	−	0.647310i	$-0.775894\pi$
$577$	−36.6186	−1.52445	−0.762227	+	0.647310i	$0.775894\pi$
$578$	−12.9515	−0.538713
$579$	−12.6507	−0.525745
$580$	−3.17981	−0.132034
$581$	42.2074	1.75106
$582$	8.96787	0.371730
$583$	−26.9743	−1.11716
$584$	−12.7043	−0.525709
$585$	1.38248	0.0571583
$586$	1.53232	0.0632995
$587$	−19.7164	−0.813784	−0.406892	−	0.913476i	$-0.633387\pi$
$587$	−19.7164	−0.813784	−0.406892	+	0.913476i	$0.633387\pi$
$588$	1.42635	0.0588216
$589$	48.7564	2.00897
$590$	−4.53219	−0.186587
$591$	12.7588	0.524828
$592$	−0.599346	−0.0246329
$593$	−20.5971	−0.845823	−0.422911	−	0.906171i	$-0.638992\pi$
$593$	−20.5971	−0.845823	−0.422911	+	0.906171i	$0.638992\pi$
$594$	−2.39518	−0.0982754
$595$	−5.86281	−0.240352
$596$	−21.0202	−0.861019
$597$	−1.79291	−0.0733787
$598$	2.51665	0.102914
$599$	−30.8256	−1.25950	−0.629751	−	0.776797i	$-0.716843\pi$
$599$	−30.8256	−1.25950	−0.629751	+	0.776797i	$0.716843\pi$
$600$	9.02377	0.368394
$601$	12.9987	0.530227	0.265114	−	0.964217i	$-0.414590\pi$
$601$	12.9987	0.530227	0.265114	+	0.964217i	$0.414590\pi$
$602$	−10.9856	−0.447740
$603$	12.1419	0.494457
$604$	−0.640307	−0.0260537
$605$	6.11935	0.248787
$606$	12.2453	0.497432
$607$	−3.77187	−0.153095	−0.0765477	−	0.997066i	$-0.524390\pi$
$607$	−3.77187	−0.153095	−0.0765477	+	0.997066i	$0.524390\pi$
$608$	39.0650	1.58429
$609$	4.88612	0.197996
$610$	−3.94765	−0.159836
$611$	3.37827	0.136670
$612$	1.99631	0.0806961
$613$	9.25743	0.373904	0.186952	−	0.982369i	$-0.440139\pi$
$613$	9.25743	0.373904	0.186952	+	0.982369i	$0.440139\pi$
$614$	−15.1154	−0.610006
$615$	6.50686	0.262382
$616$	−17.9375	−0.722722
$617$	14.6992	0.591767	0.295884	−	0.955224i	$-0.404386\pi$
$617$	14.6992	0.591767	0.295884	+	0.955224i	$0.404386\pi$
$618$	−0.934190	−0.0375786
$619$	39.9210	1.60456	0.802281	−	0.596947i	$-0.203620\pi$
$619$	39.9210	1.60456	0.802281	+	0.596947i	$0.203620\pi$
$620$	10.5025	0.421792
$621$	−2.69394	−0.108104
$622$	14.3800	0.576587
$623$	−12.7577	−0.511128
$624$	0.474643	0.0190009
$625$	−0.0157300	−0.000629200 0
$626$	10.6624	0.426156
$627$	−18.5495	−0.740796
$628$	−16.5195	−0.659201
$629$	−2.23616	−0.0891616
$630$	3.09277	0.123219
$631$	−4.36894	−0.173925	−0.0869624	−	0.996212i	$-0.527716\pi$
$631$	−4.36894	−0.173925	−0.0869624	+	0.996212i	$0.527716\pi$
$632$	−19.5999	−0.779644
$633$	4.44865	0.176818
$634$	−20.8230	−0.826988
$635$	22.8958	0.908592
$636$	−11.8599	−0.470277
$637$	1.26529	0.0501326
$638$	4.88705	0.193480
$639$	−5.69575	−0.225320
$640$	7.18894	0.284168
$641$	−32.7802	−1.29474	−0.647370	−	0.762176i	$-0.724131\pi$
$641$	−32.7802	−1.29474	−0.647370	+	0.762176i	$0.724131\pi$
$642$	13.1418	0.518667
$643$	−8.68238	−0.342400	−0.171200	−	0.985236i	$-0.554764\pi$
$643$	−8.68238	−0.342400	−0.171200	+	0.985236i	$0.554764\pi$
$644$	−7.27242	−0.286573
$645$	−6.78877	−0.267307
$646$	−11.9690	−0.470914
$647$	32.7376	1.28705	0.643523	−	0.765426i	$-0.277472\pi$
$647$	32.7376	1.28705	0.643523	+	0.765426i	$0.277472\pi$
$648$	−2.92148	−0.114767
$649$	−8.99742	−0.353179
$650$	2.88549	0.113178
$651$	−16.1383	−0.632510
$652$	−8.32169	−0.325903
$653$	35.1444	1.37531	0.687653	−	0.726039i	$-0.258641\pi$
$653$	35.1444	1.37531	0.687653	+	0.726039i	$0.258641\pi$
$654$	10.7112	0.418840
$655$	−4.19777	−0.164020
$656$	2.23399	0.0872226
$657$	4.34859	0.169655
$658$	7.55764	0.294627
$659$	23.9056	0.931229	0.465615	−	0.884988i	$-0.345833\pi$
$659$	23.9056	0.931229	0.465615	+	0.884988i	$0.345833\pi$
$660$	−3.99572	−0.155533
$661$	42.0725	1.63643	0.818215	−	0.574912i	$-0.194964\pi$
$661$	42.0725	1.63643	0.818215	+	0.574912i	$0.194964\pi$
$662$	−10.3821	−0.403510
$663$	1.77090	0.0687759
$664$	51.4916	1.99826
$665$	23.9520	0.928820
$666$	1.17963	0.0457097
$667$	5.49663	0.212830
$668$	2.24715	0.0869447
$669$	−12.5291	−0.484401
$670$	−15.6812	−0.605819
$671$	−7.83697	−0.302543
$672$	−12.9305	−0.498803
$673$	40.0659	1.54443	0.772213	−	0.635364i	$-0.219150\pi$
$673$	40.0659	1.54443	0.772213	+	0.635364i	$0.219150\pi$
$674$	−17.2858	−0.665825
$675$	−3.08876	−0.118887
$676$	−1.12729	−0.0433573
$677$	2.92889	0.112567	0.0562833	−	0.998415i	$-0.482075\pi$
$677$	2.92889	0.112567	0.0562833	+	0.998415i	$0.482075\pi$
$678$	11.3146	0.434536
$679$	−22.9884	−0.882216
$680$	−7.15243	−0.274283
$681$	−10.7617	−0.412390
$682$	−16.1414	−0.618084
$683$	−15.4044	−0.589433	−0.294717	−	0.955585i	$-0.595225\pi$
$683$	−15.4044	−0.589433	−0.294717	+	0.955585i	$0.595225\pi$
$684$	−8.15576	−0.311843
$685$	14.1522	0.540727
$686$	18.4905	0.705971
$687$	−20.7330	−0.791012
$688$	−2.33078	−0.0888600
$689$	−10.5208	−0.400809
$690$	3.47921	0.132451
$691$	7.76962	0.295570	0.147785	−	0.989019i	$-0.452786\pi$
$691$	7.76962	0.295570	0.147785	+	0.989019i	$0.452786\pi$
$692$	−2.24082	−0.0851833
$693$	6.13986	0.233234
$694$	11.4588	0.434970
$695$	17.3419	0.657816
$696$	5.96090	0.225947
$697$	8.33503	0.315712
$698$	31.0408	1.17491
$699$	−19.5886	−0.740910
$700$	−8.33826	−0.315157
$701$	−1.96375	−0.0741700	−0.0370850	−	0.999312i	$-0.511807\pi$
$701$	−1.96375	−0.0741700	−0.0370850	+	0.999312i	$0.511807\pi$
$702$	−0.934190	−0.0352587
$703$	9.13566	0.344558
$704$	−15.3668	−0.579158
$705$	4.67038	0.175897
$706$	5.20174	0.195770
$707$	−31.3899	−1.18054
$708$	−3.95595	−0.148674
$709$	−11.1603	−0.419132	−0.209566	−	0.977794i	$-0.567205\pi$
$709$	−11.1603	−0.419132	−0.209566	+	0.977794i	$0.567205\pi$
$710$	7.35603	0.276067
$711$	6.70890	0.251603
$712$	−15.5640	−0.583285
$713$	−18.1547	−0.679900
$714$	3.96172	0.148264
$715$	−3.54454	−0.132558
$716$	13.4335	0.502033
$717$	−13.4737	−0.503184
$718$	−11.0116	−0.410950
$719$	44.1147	1.64520	0.822601	−	0.568620i	$-0.192522\pi$
$719$	44.1147	1.64520	0.822601	+	0.568620i	$0.192522\pi$
$720$	0.656182	0.0244545
$721$	2.39473	0.0891842
$722$	31.1488	1.15924
$723$	−15.2392	−0.566751
$724$	−22.4204	−0.833249
$725$	6.30222	0.234058
$726$	−4.13507	−0.153467
$727$	−25.8988	−0.960535	−0.480268	−	0.877122i	$-0.659460\pi$
$727$	−25.8988	−0.960535	−0.480268	+	0.877122i	$0.659460\pi$
$728$	−6.99615	−0.259295
$729$	1.00000	0.0370370
$730$	−5.61618	−0.207864
$731$	−8.69614	−0.321638
$732$	−3.44573	−0.127358
$733$	31.3422	1.15765	0.578825	−	0.815452i	$-0.303511\pi$
$733$	31.3422	1.15765	0.578825	+	0.815452i	$0.303511\pi$
$734$	13.7342	0.506938
$735$	1.74923	0.0645214
$736$	−14.5461	−0.536176
$737$	−31.1308	−1.14672
$738$	−4.39693	−0.161853
$739$	37.2667	1.37088	0.685439	−	0.728130i	$-0.259610\pi$
$739$	37.2667	1.37088	0.685439	+	0.728130i	$0.259610\pi$
$740$	1.96790	0.0723414
$741$	−7.23485	−0.265779
$742$	−23.5363	−0.864045
$743$	23.6862	0.868963	0.434481	−	0.900681i	$-0.356932\pi$
$743$	23.6862	0.868963	0.434481	+	0.900681i	$0.356932\pi$
$744$	−19.6882	−0.721803
$745$	−25.7785	−0.944452
$746$	−9.44707	−0.345882
$747$	−17.6252	−0.644871
$748$	−5.11836	−0.187146
$749$	−33.6881	−1.23094
$750$	10.4466	0.381456
$751$	37.0348	1.35142	0.675709	−	0.737169i	$-0.263838\pi$
$751$	37.0348	1.35142	0.675709	+	0.737169i	$0.263838\pi$
$752$	1.60347	0.0584727
$753$	−0.0121631	−0.000443247 0
$754$	1.90609	0.0694158
$755$	−0.785255	−0.0285784
$756$	2.69955	0.0981816
$757$	36.6476	1.33198	0.665991	−	0.745960i	$-0.268009\pi$
$757$	36.6476	1.33198	0.665991	+	0.745960i	$0.268009\pi$
$758$	−14.7175	−0.534564
$759$	6.90702	0.250709
$760$	29.2207	1.05994
$761$	−11.1708	−0.404940	−0.202470	−	0.979289i	$-0.564897\pi$
$761$	−11.1708	−0.404940	−0.202470	+	0.979289i	$0.564897\pi$
$762$	−15.4715	−0.560475
$763$	−27.4573	−0.994019
$764$	9.42943	0.341145
$765$	2.44822	0.0885155
$766$	17.1739	0.620517
$767$	−3.50926	−0.126712
$768$	−16.8448	−0.607836
$769$	23.7738	0.857304	0.428652	−	0.903470i	$-0.358989\pi$
$769$	23.7738	0.857304	0.428652	+	0.903470i	$0.358989\pi$
$770$	−7.92959	−0.285763
$771$	30.9937	1.11621
$772$	14.2610	0.513265
$773$	40.4150	1.45363	0.726813	−	0.686835i	$-0.241001\pi$
$773$	40.4150	1.45363	0.726813	+	0.686835i	$0.241001\pi$
$774$	4.58742	0.164892
$775$	−20.8155	−0.747714
$776$	−28.0451	−1.00676
$777$	−3.02389	−0.108481
$778$	−17.4745	−0.626493
$779$	−34.0521	−1.22004
$780$	−1.55845	−0.0558014
$781$	14.6034	0.522550
$782$	4.45673	0.159372
$783$	−2.04037	−0.0729169
$784$	0.600561	0.0214486
$785$	−20.2591	−0.723078
$786$	2.83659	0.101178
$787$	37.5125	1.33718	0.668589	−	0.743633i	$-0.266899\pi$
$787$	37.5125	1.33718	0.668589	+	0.743633i	$0.266899\pi$
$788$	−14.3829	−0.512368
$789$	30.6481	1.09110
$790$	−8.66451	−0.308269
$791$	−29.0042	−1.03127
$792$	7.49042	0.266160
$793$	−3.05665	−0.108545
$794$	21.4496	0.761217
$795$	−14.5447	−0.515847
$796$	2.02112	0.0716368
$797$	0.859812	0.0304561	0.0152281	−	0.999884i	$-0.495153\pi$
$797$	0.859812	0.0304561	0.0152281	+	0.999884i	$0.495153\pi$
$798$	−16.1853	−0.572953
$799$	5.98257	0.211648
$800$	−16.6780	−0.589655
$801$	5.32743	0.188236
$802$	−26.6357	−0.940540
$803$	−11.1494	−0.393454
$804$	−13.6875	−0.482719
$805$	−8.91869	−0.314342
$806$	−6.29560	−0.221753
$807$	−5.02738	−0.176972
$808$	−38.2946	−1.34720
$809$	−35.0900	−1.23370	−0.616850	−	0.787081i	$-0.711591\pi$
$809$	−35.0900	−1.23370	−0.616850	+	0.787081i	$0.711591\pi$
$810$	−1.29149	−0.0453785
$811$	41.5735	1.45984	0.729921	−	0.683531i	$-0.239557\pi$
$811$	41.5735	1.45984	0.729921	+	0.683531i	$0.239557\pi$
$812$	−5.50807	−0.193295
$813$	25.0545	0.878701
$814$	−3.02446	−0.106007
$815$	−10.2055	−0.357483
$816$	0.840543	0.0294249
$817$	35.5274	1.24295
$818$	−18.2155	−0.636889
$819$	2.39473	0.0836785
$820$	−7.33511	−0.256153
$821$	−52.5307	−1.83333	−0.916667	−	0.399651i	$-0.869131\pi$
$821$	−52.5307	−1.83333	−0.916667	+	0.399651i	$0.869131\pi$
$822$	−9.56315	−0.333553
$823$	10.1628	0.354253	0.177126	−	0.984188i	$-0.443320\pi$
$823$	10.1628	0.354253	0.177126	+	0.984188i	$0.443320\pi$
$824$	2.92148	0.101775
$825$	7.91931	0.275715
$826$	−7.85066	−0.273159
$827$	−0.181876	−0.00632446	−0.00316223	−	0.999995i	$-0.501007\pi$
$827$	−0.181876	−0.00632446	−0.00316223	+	0.999995i	$0.501007\pi$
$828$	3.03685	0.105538
$829$	−21.2199	−0.736996	−0.368498	−	0.929628i	$-0.620128\pi$
$829$	−21.2199	−0.736996	−0.368498	+	0.929628i	$0.620128\pi$
$830$	22.7628	0.790108
$831$	21.0664	0.730784
$832$	−5.99350	−0.207787
$833$	2.24070	0.0776356
$834$	−11.7186	−0.405781
$835$	2.75584	0.0953696
$836$	20.9106	0.723210
$837$	6.73910	0.232937
$838$	6.79300	0.234660
$839$	46.7356	1.61349	0.806746	−	0.590898i	$-0.201226\pi$
$839$	46.7356	1.61349	0.806746	+	0.590898i	$0.201226\pi$
$840$	−9.67200	−0.333716
$841$	−24.8369	−0.856445
$842$	9.63243	0.331955
$843$	−14.0435	−0.483683
$844$	−5.01492	−0.172621
$845$	−1.38248	−0.0475586
$846$	−3.15595	−0.108504
$847$	10.5999	0.364218
$848$	−4.99361	−0.171481
$849$	−1.91548	−0.0657391
$850$	5.10991	0.175268
$851$	−3.40172	−0.116609
$852$	6.42075	0.219971
$853$	−50.3372	−1.72351	−0.861757	−	0.507322i	$-0.830636\pi$
$853$	−50.3372	−1.72351	−0.861757	+	0.507322i	$0.830636\pi$
$854$	−6.83812	−0.233996
$855$	−10.0020	−0.342061
$856$	−41.0983	−1.40471
$857$	26.0235	0.888947	0.444473	−	0.895792i	$-0.353391\pi$
$857$	26.0235	0.888947	0.444473	+	0.895792i	$0.353391\pi$
$858$	2.39518	0.0817701
$859$	−26.0193	−0.887767	−0.443883	−	0.896085i	$-0.646400\pi$
$859$	−26.0193	−0.887767	−0.443883	+	0.896085i	$0.646400\pi$
$860$	7.65290	0.260962
$861$	11.2712	0.384121
$862$	−32.6588	−1.11236
$863$	−34.6751	−1.18035	−0.590176	−	0.807274i	$-0.700942\pi$
$863$	−34.6751	−1.18035	−0.590176	+	0.807274i	$0.700942\pi$
$864$	5.39956	0.183697
$865$	−2.74808	−0.0934376
$866$	25.8109	0.877089
$867$	−13.8639	−0.470844
$868$	18.1925	0.617494
$869$	−17.2010	−0.583504
$870$	2.63513	0.0893391
$871$	−12.1419	−0.411413
$872$	−33.4969	−1.13435
$873$	9.59962	0.324898
$874$	−18.2076	−0.615881
$875$	−26.7790	−0.905297
$876$	−4.90212	−0.165627
$877$	46.3458	1.56499	0.782494	−	0.622659i	$-0.213947\pi$
$877$	46.3458	1.56499	0.782494	+	0.622659i	$0.213947\pi$
$878$	5.16654	0.174362
$879$	1.64026	0.0553247
$880$	−1.68239	−0.0567134
$881$	−40.9966	−1.38121	−0.690605	−	0.723232i	$-0.742656\pi$
$881$	−40.9966	−1.38121	−0.690605	+	0.723232i	$0.742656\pi$
$882$	−1.18202	−0.0398007
$883$	3.11160	0.104714	0.0523568	−	0.998628i	$-0.483327\pi$
$883$	3.11160	0.104714	0.0523568	+	0.998628i	$0.483327\pi$
$884$	−1.99631	−0.0671432
$885$	−4.85146	−0.163080
$886$	17.9647	0.603536
$887$	−33.6123	−1.12859	−0.564296	−	0.825573i	$-0.690852\pi$
$887$	−33.6123	−1.12859	−0.564296	+	0.825573i	$0.690852\pi$
$888$	−3.68904	−0.123796
$889$	39.6601	1.33016
$890$	−6.88035	−0.230630
$891$	−2.56391	−0.0858942
$892$	14.1239	0.472902
$893$	−24.4413	−0.817897
$894$	17.4195	0.582596
$895$	16.4744	0.550680
$896$	12.4527	0.416015
$897$	2.69394	0.0899480
$898$	22.8993	0.764159
$899$	−13.7503	−0.458597
$900$	3.48193	0.116064
$901$	−18.6312	−0.620694
$902$	11.2733	0.375361
$903$	−11.7595	−0.391332
$904$	−35.3841	−1.17686
$905$	−27.4958	−0.913991
$906$	0.530626	0.0176289
$907$	1.30356	0.0432840	0.0216420	−	0.999766i	$-0.493111\pi$
$907$	1.30356	0.0432840	0.0216420	+	0.999766i	$0.493111\pi$
$908$	12.1316	0.402600
$909$	13.1079	0.434763
$910$	−3.09277	−0.102524
$911$	29.8713	0.989679	0.494840	−	0.868984i	$-0.335227\pi$
$911$	29.8713	0.989679	0.494840	+	0.868984i	$0.335227\pi$
$912$	−3.43397	−0.113710
$913$	45.1893	1.49555
$914$	−26.0703	−0.862329
$915$	−4.22574	−0.139699
$916$	23.3720	0.772234
$917$	−7.27138	−0.240122
$918$	−1.65435	−0.0546018
$919$	−33.5902	−1.10804	−0.554020	−	0.832503i	$-0.686907\pi$
$919$	−33.5902	−1.10804	−0.554020	+	0.832503i	$0.686907\pi$
$920$	−10.8805	−0.358719
$921$	−16.1802	−0.533155
$922$	14.0571	0.462945
$923$	5.69575	0.187478
$924$	−6.92139	−0.227697
$925$	−3.90027	−0.128240
$926$	25.7864	0.847394
$927$	−1.00000	−0.0328443
$928$	−11.0171	−0.361654
$929$	−48.4443	−1.58941	−0.794703	−	0.606999i	$-0.792373\pi$
$929$	−48.4443	−1.58941	−0.794703	+	0.606999i	$0.792373\pi$
$930$	−8.70351	−0.285399
$931$	−9.15419	−0.300016
$932$	22.0820	0.723321
$933$	15.3931	0.503946
$934$	36.9753	1.20987
$935$	−6.27701	−0.205280
$936$	2.92148	0.0954916
$937$	4.44040	0.145062	0.0725308	−	0.997366i	$-0.476892\pi$
$937$	4.44040	0.145062	0.0725308	+	0.997366i	$0.476892\pi$
$938$	−27.1631	−0.886905
$939$	11.4136	0.372467
$940$	−5.26487	−0.171721
$941$	−25.4123	−0.828418	−0.414209	−	0.910182i	$-0.635942\pi$
$941$	−25.4123	−0.828418	−0.414209	+	0.910182i	$0.635942\pi$
$942$	13.6898	0.446039
$943$	12.6795	0.412901
$944$	−1.66564	−0.0542121
$945$	3.31065	0.107695
$946$	−11.7617	−0.382407
$947$	12.5582	0.408087	0.204043	−	0.978962i	$-0.434592\pi$
$947$	12.5582	0.408087	0.204043	+	0.978962i	$0.434592\pi$
$948$	−7.56287	−0.245631
$949$	−4.34859	−0.141161
$950$	−20.8761	−0.677310
$951$	−22.2899	−0.722800
$952$	−12.3894	−0.401544
$953$	20.5705	0.666345	0.333173	−	0.942866i	$-0.391881\pi$
$953$	20.5705	0.666345	0.333173	+	0.942866i	$0.391881\pi$
$954$	9.82839	0.318206
$955$	11.5640	0.374202
$956$	15.1887	0.491239
$957$	5.23132	0.169105
$958$	−5.99991	−0.193848
$959$	24.5144	0.791612
$960$	−8.28586	−0.267425
$961$	14.4155	0.465016
$962$	−1.17963	−0.0380328
$963$	14.0676	0.453323
$964$	17.1789	0.553296
$965$	17.4893	0.563000
$966$	6.02669	0.193906
$967$	−36.7497	−1.18179	−0.590895	−	0.806748i	$-0.701225\pi$
$967$	−36.7497	−1.18179	−0.590895	+	0.806748i	$0.701225\pi$
$968$	12.9316	0.415636
$969$	−12.8122	−0.411586
$970$	−12.3979	−0.398071
$971$	−2.96311	−0.0950906	−0.0475453	−	0.998869i	$-0.515140\pi$
$971$	−2.96311	−0.0950906	−0.0475453	+	0.998869i	$0.515140\pi$
$972$	−1.12729	−0.0361578
$973$	30.0397	0.963028
$974$	19.6544	0.629768
$975$	3.08876	0.0989196
$976$	−1.45082	−0.0464395
$977$	5.35788	0.171414	0.0857068	−	0.996320i	$-0.472685\pi$
$977$	5.35788	0.171414	0.0857068	+	0.996320i	$0.472685\pi$
$978$	6.89623	0.220517
$979$	−13.6590	−0.436545
$980$	−1.97189	−0.0629897
$981$	11.4657	0.366072
$982$	19.4701	0.621317
$983$	13.0047	0.414785	0.207393	−	0.978258i	$-0.433502\pi$
$983$	13.0047	0.414785	0.207393	+	0.978258i	$0.433502\pi$
$984$	13.7505	0.438349
$985$	−17.6387	−0.562017
$986$	3.37549	0.107498
$987$	8.09004	0.257509
$988$	8.15576	0.259469
$989$	−13.2288	−0.420652
$990$	3.31127	0.105239
$991$	22.7539	0.722803	0.361401	−	0.932410i	$-0.382298\pi$
$991$	22.7539	0.722803	0.361401	+	0.932410i	$0.382298\pi$
$992$	36.3882	1.15533
$993$	−11.1134	−0.352674
$994$	12.7421	0.404156
$995$	2.47865	0.0785784
$996$	19.8686	0.629562
$997$	40.1571	1.27179	0.635894	−	0.771776i	$-0.280631\pi$
$997$	40.1571	1.27179	0.635894	+	0.771776i	$0.280631\pi$
$998$	4.62091	0.146272
$999$	1.26273	0.0399510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.19	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+0.934190 q^{2} +1.00000 q^{3} -1.12729 q^{4} -1.38248 q^{5} +0.934190 q^{6} -2.39473 q^{7} -2.92148 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.934190 q^{2} +1.00000 q^{3} -1.12729 q^{4} -1.38248 q^{5} +0.934190 q^{6} -2.39473 q^{7} -2.92148 q^{8} +1.00000 q^{9} -1.29149 q^{10} -2.56391 q^{11} -1.12729 q^{12} -1.00000 q^{13} -2.23713 q^{14} -1.38248 q^{15} -0.474643 q^{16} -1.77090 q^{17} +0.934190 q^{18} +7.23485 q^{19} +1.55845 q^{20} -2.39473 q^{21} -2.39518 q^{22} -2.69394 q^{23} -2.92148 q^{24} -3.08876 q^{25} -0.934190 q^{26} +1.00000 q^{27} +2.69955 q^{28} -2.04037 q^{29} -1.29149 q^{30} +6.73910 q^{31} +5.39956 q^{32} -2.56391 q^{33} -1.65435 q^{34} +3.31065 q^{35} -1.12729 q^{36} +1.26273 q^{37} +6.75873 q^{38} -1.00000 q^{39} +4.03888 q^{40} -4.70667 q^{41} -2.23713 q^{42} +4.91059 q^{43} +2.89027 q^{44} -1.38248 q^{45} -2.51665 q^{46} -3.37827 q^{47} -0.474643 q^{48} -1.26529 q^{49} -2.88549 q^{50} -1.77090 q^{51} +1.12729 q^{52} +10.5208 q^{53} +0.934190 q^{54} +3.54454 q^{55} +6.99615 q^{56} +7.23485 q^{57} -1.90609 q^{58} +3.50926 q^{59} +1.55845 q^{60} +3.05665 q^{61} +6.29560 q^{62} -2.39473 q^{63} +5.99350 q^{64} +1.38248 q^{65} -2.39518 q^{66} +12.1419 q^{67} +1.99631 q^{68} -2.69394 q^{69} +3.09277 q^{70} -5.69575 q^{71} -2.92148 q^{72} +4.34859 q^{73} +1.17963 q^{74} -3.08876 q^{75} -8.15576 q^{76} +6.13986 q^{77} -0.934190 q^{78} +6.70890 q^{79} +0.656182 q^{80} +1.00000 q^{81} -4.39693 q^{82} -17.6252 q^{83} +2.69955 q^{84} +2.44822 q^{85} +4.58742 q^{86} -2.04037 q^{87} +7.49042 q^{88} +5.32743 q^{89} -1.29149 q^{90} +2.39473 q^{91} +3.03685 q^{92} +6.73910 q^{93} -3.15595 q^{94} -10.0020 q^{95} +5.39956 q^{96} +9.59962 q^{97} -1.18202 q^{98} -2.56391 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

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