LMFDB - Embedded newform 4017.2.a.l.1.7

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			1.7
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)

$f(q)$	$=$	$q-1.79771 q^{2} +1.00000 q^{3} +1.23177 q^{4} +3.18677 q^{5} -1.79771 q^{6} +1.45324 q^{7} +1.38105 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.79771 q^{2} +1.00000 q^{3} +1.23177 q^{4} +3.18677 q^{5} -1.79771 q^{6} +1.45324 q^{7} +1.38105 q^{8} +1.00000 q^{9} -5.72890 q^{10} +5.12383 q^{11} +1.23177 q^{12} -1.00000 q^{13} -2.61251 q^{14} +3.18677 q^{15} -4.94628 q^{16} +2.85787 q^{17} -1.79771 q^{18} -5.56476 q^{19} +3.92538 q^{20} +1.45324 q^{21} -9.21117 q^{22} -4.19986 q^{23} +1.38105 q^{24} +5.15551 q^{25} +1.79771 q^{26} +1.00000 q^{27} +1.79006 q^{28} -0.718906 q^{29} -5.72890 q^{30} +1.30600 q^{31} +6.12989 q^{32} +5.12383 q^{33} -5.13763 q^{34} +4.63115 q^{35} +1.23177 q^{36} +3.88333 q^{37} +10.0038 q^{38} -1.00000 q^{39} +4.40109 q^{40} +2.77115 q^{41} -2.61251 q^{42} -0.802749 q^{43} +6.31139 q^{44} +3.18677 q^{45} +7.55015 q^{46} +7.70068 q^{47} -4.94628 q^{48} -4.88809 q^{49} -9.26813 q^{50} +2.85787 q^{51} -1.23177 q^{52} -0.798985 q^{53} -1.79771 q^{54} +16.3285 q^{55} +2.00700 q^{56} -5.56476 q^{57} +1.29239 q^{58} +7.71339 q^{59} +3.92538 q^{60} +3.87437 q^{61} -2.34782 q^{62} +1.45324 q^{63} -1.12723 q^{64} -3.18677 q^{65} -9.21117 q^{66} +1.20956 q^{67} +3.52025 q^{68} -4.19986 q^{69} -8.32548 q^{70} +14.6798 q^{71} +1.38105 q^{72} +4.93639 q^{73} -6.98112 q^{74} +5.15551 q^{75} -6.85452 q^{76} +7.44616 q^{77} +1.79771 q^{78} -0.0933822 q^{79} -15.7627 q^{80} +1.00000 q^{81} -4.98174 q^{82} -12.4528 q^{83} +1.79006 q^{84} +9.10738 q^{85} +1.44311 q^{86} -0.718906 q^{87} +7.07627 q^{88} -6.21854 q^{89} -5.72890 q^{90} -1.45324 q^{91} -5.17328 q^{92} +1.30600 q^{93} -13.8436 q^{94} -17.7336 q^{95} +6.12989 q^{96} +7.38889 q^{97} +8.78738 q^{98} +5.12383 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.79771	−1.27118	−0.635588	−	0.772029i	$-0.719242\pi$
$2$	−1.79771	−1.27118	−0.635588	+	0.772029i	$0.719242\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.23177	0.615887
$5$	3.18677	1.42517	0.712584	−	0.701587i	$-0.247525\pi$
$5$	3.18677	1.42517	0.712584	+	0.701587i	$0.247525\pi$
$6$	−1.79771	−0.733913
$7$	1.45324	0.549274	0.274637	−	0.961548i	$-0.411442\pi$
$7$	1.45324	0.549274	0.274637	+	0.961548i	$0.411442\pi$
$8$	1.38105	0.488275
$9$	1.00000	0.333333
$10$	−5.72890	−1.81164
$11$	5.12383	1.54489	0.772446	−	0.635080i	$-0.219033\pi$
$11$	5.12383	1.54489	0.772446	+	0.635080i	$0.219033\pi$
$12$	1.23177	0.355582
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.61251	−0.698223
$15$	3.18677	0.822821
$16$	−4.94628	−1.23657
$17$	2.85787	0.693135	0.346568	−	0.938025i	$-0.387347\pi$
$17$	2.85787	0.693135	0.346568	+	0.938025i	$0.387347\pi$
$18$	−1.79771	−0.423725
$19$	−5.56476	−1.27664	−0.638321	−	0.769770i	$-0.720371\pi$
$19$	−5.56476	−1.27664	−0.638321	+	0.769770i	$0.720371\pi$
$20$	3.92538	0.877741
$21$	1.45324	0.317123
$22$	−9.21117	−1.96383
$23$	−4.19986	−0.875732	−0.437866	−	0.899040i	$-0.644266\pi$
$23$	−4.19986	−0.875732	−0.437866	+	0.899040i	$0.644266\pi$
$24$	1.38105	0.281906
$25$	5.15551	1.03110
$26$	1.79771	0.352561
$27$	1.00000	0.192450
$28$	1.79006	0.338290
$29$	−0.718906	−0.133497	−0.0667487	−	0.997770i	$-0.521263\pi$
$29$	−0.718906	−0.133497	−0.0667487	+	0.997770i	$0.521263\pi$
$30$	−5.72890	−1.04595
$31$	1.30600	0.234565	0.117282	−	0.993099i	$-0.462582\pi$
$31$	1.30600	0.234565	0.117282	+	0.993099i	$0.462582\pi$
$32$	6.12989	1.08362
$33$	5.12383	0.891944
$34$	−5.13763	−0.881096
$35$	4.63115	0.782807
$36$	1.23177	0.205296
$37$	3.88333	0.638416	0.319208	−	0.947685i	$-0.396583\pi$
$37$	3.88333	0.638416	0.319208	+	0.947685i	$0.396583\pi$
$38$	10.0038	1.62284
$39$	−1.00000	−0.160128
$40$	4.40109	0.695874
$41$	2.77115	0.432781	0.216391	−	0.976307i	$-0.430571\pi$
$41$	2.77115	0.432781	0.216391	+	0.976307i	$0.430571\pi$
$42$	−2.61251	−0.403119
$43$	−0.802749	−0.122418	−0.0612090	−	0.998125i	$-0.519496\pi$
$43$	−0.802749	−0.122418	−0.0612090	+	0.998125i	$0.519496\pi$
$44$	6.31139	0.951478
$45$	3.18677	0.475056
$46$	7.55015	1.11321
$47$	7.70068	1.12326	0.561630	−	0.827388i	$-0.310174\pi$
$47$	7.70068	1.12326	0.561630	+	0.827388i	$0.310174\pi$
$48$	−4.94628	−0.713934
$49$	−4.88809	−0.698298
$50$	−9.26813	−1.31071
$51$	2.85787	0.400182
$52$	−1.23177	−0.170816
$53$	−0.798985	−0.109749	−0.0548745	−	0.998493i	$-0.517476\pi$
$53$	−0.798985	−0.109749	−0.0548745	+	0.998493i	$0.517476\pi$
$54$	−1.79771	−0.244638
$55$	16.3285	2.20173
$56$	2.00700	0.268197
$57$	−5.56476	−0.737070
$58$	1.29239	0.169699
$59$	7.71339	1.00420	0.502099	−	0.864810i	$-0.332561\pi$
$59$	7.71339	1.00420	0.502099	+	0.864810i	$0.332561\pi$
$60$	3.92538	0.506764
$61$	3.87437	0.496062	0.248031	−	0.968752i	$-0.420216\pi$
$61$	3.87437	0.496062	0.248031	+	0.968752i	$0.420216\pi$
$62$	−2.34782	−0.298173
$63$	1.45324	0.183091
$64$	−1.12723	−0.140903
$65$	−3.18677	−0.395270
$66$	−9.21117	−1.13382
$67$	1.20956	0.147771	0.0738854	−	0.997267i	$-0.476460\pi$
$67$	1.20956	0.147771	0.0738854	+	0.997267i	$0.476460\pi$
$68$	3.52025	0.426893
$69$	−4.19986	−0.505604
$70$	−8.32548	−0.995085
$71$	14.6798	1.74217	0.871084	−	0.491135i	$-0.163418\pi$
$71$	14.6798	1.74217	0.871084	+	0.491135i	$0.163418\pi$
$72$	1.38105	0.162758
$73$	4.93639	0.577760	0.288880	−	0.957365i	$-0.406717\pi$
$73$	4.93639	0.577760	0.288880	+	0.957365i	$0.406717\pi$
$74$	−6.98112	−0.811539
$75$	5.15551	0.595307
$76$	−6.85452	−0.786267
$77$	7.44616	0.848569
$78$	1.79771	0.203551
$79$	−0.0933822	−0.0105063	−0.00525316	−	0.999986i	$-0.501672\pi$
$79$	−0.0933822	−0.0105063	−0.00525316	+	0.999986i	$0.501672\pi$
$80$	−15.7627	−1.76232
$81$	1.00000	0.111111
$82$	−4.98174	−0.550141
$83$	−12.4528	−1.36688	−0.683439	−	0.730008i	$-0.739516\pi$
$83$	−12.4528	−1.36688	−0.683439	+	0.730008i	$0.739516\pi$
$84$	1.79006	0.195312
$85$	9.10738	0.987834
$86$	1.44311	0.155615
$87$	−0.718906	−0.0770748
$88$	7.07627	0.754333
$89$	−6.21854	−0.659164	−0.329582	−	0.944127i	$-0.606908\pi$
$89$	−6.21854	−0.659164	−0.329582	+	0.944127i	$0.606908\pi$
$90$	−5.72890	−0.603879
$91$	−1.45324	−0.152341
$92$	−5.17328	−0.539352
$93$	1.30600	0.135426
$94$	−13.8436	−1.42786
$95$	−17.7336	−1.81943
$96$	6.12989	0.625630
$97$	7.38889	0.750228	0.375114	−	0.926979i	$-0.377604\pi$
$97$	7.38889	0.750228	0.375114	+	0.926979i	$0.377604\pi$
$98$	8.78738	0.887660
$99$	5.12383	0.514964
$100$	6.35042	0.635042
$101$	−10.2148	−1.01641	−0.508206	−	0.861236i	$-0.669691\pi$
$101$	−10.2148	−1.01641	−0.508206	+	0.861236i	$0.669691\pi$
$102$	−5.13763	−0.508701
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.38105	−0.135423
$105$	4.63115	0.451954
$106$	1.43635	0.139510
$107$	5.52181	0.533814	0.266907	−	0.963722i	$-0.413998\pi$
$107$	5.52181	0.533814	0.266907	+	0.963722i	$0.413998\pi$
$108$	1.23177	0.118527
$109$	12.9933	1.24453	0.622267	−	0.782805i	$-0.286212\pi$
$109$	12.9933	1.24453	0.622267	+	0.782805i	$0.286212\pi$
$110$	−29.3539	−2.79878
$111$	3.88333	0.368590
$112$	−7.18814	−0.679216
$113$	−2.79516	−0.262946	−0.131473	−	0.991320i	$-0.541971\pi$
$113$	−2.79516	−0.262946	−0.131473	+	0.991320i	$0.541971\pi$
$114$	10.0038	0.936945
$115$	−13.3840	−1.24806
$116$	−0.885529	−0.0822193
$117$	−1.00000	−0.0924500
$118$	−13.8665	−1.27651
$119$	4.15318	0.380721
$120$	4.40109	0.401763
$121$	15.2536	1.38669
$122$	−6.96501	−0.630582
$123$	2.77115	0.249866
$124$	1.60870	0.144465
$125$	0.495568	0.0443249
$126$	−2.61251	−0.232741
$127$	−16.1489	−1.43298	−0.716492	−	0.697596i	$-0.754253\pi$
$127$	−16.1489	−1.43298	−0.716492	+	0.697596i	$0.754253\pi$
$128$	−10.2334	−0.904509
$129$	−0.802749	−0.0706781
$130$	5.72890	0.502458
$131$	−1.67417	−0.146273	−0.0731366	−	0.997322i	$-0.523301\pi$
$131$	−1.67417	−0.146273	−0.0731366	+	0.997322i	$0.523301\pi$
$132$	6.31139	0.549336
$133$	−8.08694	−0.701226
$134$	−2.17443	−0.187843
$135$	3.18677	0.274274
$136$	3.94687	0.338441
$137$	22.6307	1.93347	0.966737	−	0.255771i	$-0.0823292\pi$
$137$	22.6307	1.93347	0.966737	+	0.255771i	$0.0823292\pi$
$138$	7.55015	0.642712
$139$	9.95746	0.844581	0.422290	−	0.906461i	$-0.361226\pi$
$139$	9.95746	0.844581	0.422290	+	0.906461i	$0.361226\pi$
$140$	5.70452	0.482120
$141$	7.70068	0.648515
$142$	−26.3900	−2.21460
$143$	−5.12383	−0.428476
$144$	−4.94628	−0.412190
$145$	−2.29099	−0.190256
$146$	−8.87421	−0.734435
$147$	−4.88809	−0.403163
$148$	4.78339	0.393192
$149$	−11.5279	−0.944403	−0.472201	−	0.881491i	$-0.656540\pi$
$149$	−11.5279	−0.944403	−0.472201	+	0.881491i	$0.656540\pi$
$150$	−9.26813	−0.756739
$151$	23.1033	1.88012	0.940059	−	0.341012i	$-0.110770\pi$
$151$	23.1033	1.88012	0.940059	+	0.341012i	$0.110770\pi$
$152$	−7.68522	−0.623353
$153$	2.85787	0.231045
$154$	−13.3861	−1.07868
$155$	4.16193	0.334294
$156$	−1.23177	−0.0986208
$157$	−11.3030	−0.902076	−0.451038	−	0.892505i	$-0.648946\pi$
$157$	−11.3030	−0.902076	−0.451038	+	0.892505i	$0.648946\pi$
$158$	0.167874	0.0133554
$159$	−0.798985	−0.0633637
$160$	19.5346	1.54434
$161$	−6.10342	−0.481017
$162$	−1.79771	−0.141242
$163$	14.0694	1.10200	0.550999	−	0.834506i	$-0.314247\pi$
$163$	14.0694	1.10200	0.550999	+	0.834506i	$0.314247\pi$
$164$	3.41343	0.266544
$165$	16.3285	1.27117
$166$	22.3866	1.73754
$167$	12.9452	1.00173	0.500865	−	0.865525i	$-0.333015\pi$
$167$	12.9452	1.00173	0.500865	+	0.865525i	$0.333015\pi$
$168$	2.00700	0.154844
$169$	1.00000	0.0769231
$170$	−16.3725	−1.25571
$171$	−5.56476	−0.425548
$172$	−0.988805	−0.0753957
$173$	−23.2103	−1.76464	−0.882322	−	0.470646i	$-0.844021\pi$
$173$	−23.2103	−1.76464	−0.882322	+	0.470646i	$0.844021\pi$
$174$	1.29239	0.0979756
$175$	7.49220	0.566357
$176$	−25.3439	−1.91037
$177$	7.71339	0.579774
$178$	11.1792	0.837913
$179$	1.72114	0.128644	0.0643219	−	0.997929i	$-0.479512\pi$
$179$	1.72114	0.128644	0.0643219	+	0.997929i	$0.479512\pi$
$180$	3.92538	0.292580
$181$	−0.453129	−0.0336808	−0.0168404	−	0.999858i	$-0.505361\pi$
$181$	−0.453129	−0.0336808	−0.0168404	+	0.999858i	$0.505361\pi$
$182$	2.61251	0.193652
$183$	3.87437	0.286402
$184$	−5.80023	−0.427599
$185$	12.3753	0.909850
$186$	−2.34782	−0.172150
$187$	14.6432	1.07082
$188$	9.48550	0.691801
$189$	1.45324	0.105708
$190$	31.8799	2.31281
$191$	−6.27856	−0.454300	−0.227150	−	0.973860i	$-0.572941\pi$
$191$	−6.27856	−0.454300	−0.227150	+	0.973860i	$0.572941\pi$
$192$	−1.12723	−0.0813506
$193$	−19.5882	−1.40999	−0.704994	−	0.709213i	$-0.749050\pi$
$193$	−19.5882	−1.40999	−0.704994	+	0.709213i	$0.749050\pi$
$194$	−13.2831	−0.953671
$195$	−3.18677	−0.228209
$196$	−6.02102	−0.430073
$197$	−5.43189	−0.387006	−0.193503	−	0.981100i	$-0.561985\pi$
$197$	−5.43189	−0.387006	−0.193503	+	0.981100i	$0.561985\pi$
$198$	−9.21117	−0.654609
$199$	2.23775	0.158630	0.0793149	−	0.996850i	$-0.474727\pi$
$199$	2.23775	0.158630	0.0793149	+	0.996850i	$0.474727\pi$
$200$	7.12002	0.503462
$201$	1.20956	0.0853155
$202$	18.3633	1.29204
$203$	−1.04474	−0.0733266
$204$	3.52025	0.246467
$205$	8.83103	0.616786
$206$	1.79771	0.125253
$207$	−4.19986	−0.291911
$208$	4.94628	0.342963
$209$	−28.5129	−1.97228
$210$	−8.32548	−0.574512
$211$	−14.6599	−1.00923	−0.504616	−	0.863344i	$-0.668366\pi$
$211$	−14.6599	−1.00923	−0.504616	+	0.863344i	$0.668366\pi$
$212$	−0.984169	−0.0675930
$213$	14.6798	1.00584
$214$	−9.92664	−0.678571
$215$	−2.55818	−0.174466
$216$	1.38105	0.0939687
$217$	1.89794	0.128840
$218$	−23.3582	−1.58202
$219$	4.93639	0.333570
$220$	20.1130	1.35602
$221$	−2.85787	−0.192241
$222$	−6.98112	−0.468542
$223$	−22.9212	−1.53491	−0.767457	−	0.641100i	$-0.778478\pi$
$223$	−22.9212	−1.53491	−0.767457	+	0.641100i	$0.778478\pi$
$224$	8.90821	0.595205
$225$	5.15551	0.343701
$226$	5.02489	0.334251
$227$	−5.33919	−0.354375	−0.177187	−	0.984177i	$-0.556700\pi$
$227$	−5.33919	−0.354375	−0.177187	+	0.984177i	$0.556700\pi$
$228$	−6.85452	−0.453952
$229$	15.3828	1.01652	0.508261	−	0.861203i	$-0.330288\pi$
$229$	15.3828	1.01652	0.508261	+	0.861203i	$0.330288\pi$
$230$	24.0606	1.58651
$231$	7.44616	0.489921
$232$	−0.992846	−0.0651835
$233$	9.50076	0.622416	0.311208	−	0.950342i	$-0.399266\pi$
$233$	9.50076	0.622416	0.311208	+	0.950342i	$0.399266\pi$
$234$	1.79771	0.117520
$235$	24.5403	1.60083
$236$	9.50114	0.618472
$237$	−0.0933822	−0.00606583
$238$	−7.46622	−0.483963
$239$	−11.5186	−0.745074	−0.372537	−	0.928017i	$-0.621512\pi$
$239$	−11.5186	−0.745074	−0.372537	+	0.928017i	$0.621512\pi$
$240$	−15.7627	−1.01748
$241$	−3.48715	−0.224627	−0.112314	−	0.993673i	$-0.535826\pi$
$241$	−3.48715	−0.224627	−0.112314	+	0.993673i	$0.535826\pi$
$242$	−27.4216	−1.76273
$243$	1.00000	0.0641500
$244$	4.77235	0.305518
$245$	−15.5772	−0.995192
$246$	−4.98174	−0.317624
$247$	5.56476	0.354077
$248$	1.80366	0.114532
$249$	−12.4528	−0.789167
$250$	−0.890889	−0.0563447
$251$	−12.3424	−0.779042	−0.389521	−	0.921017i	$-0.627360\pi$
$251$	−12.3424	−0.779042	−0.389521	+	0.921017i	$0.627360\pi$
$252$	1.79006	0.112763
$253$	−21.5194	−1.35291
$254$	29.0311	1.82157
$255$	9.10738	0.570326
$256$	20.6511	1.29069
$257$	0.603901	0.0376703	0.0188351	−	0.999823i	$-0.494004\pi$
$257$	0.603901	0.0376703	0.0188351	+	0.999823i	$0.494004\pi$
$258$	1.44311	0.0898443
$259$	5.64342	0.350665
$260$	−3.92538	−0.243442
$261$	−0.718906	−0.0444992
$262$	3.00968	0.185939
$263$	18.3018	1.12854	0.564268	−	0.825592i	$-0.309159\pi$
$263$	18.3018	1.12854	0.564268	+	0.825592i	$0.309159\pi$
$264$	7.07627	0.435514
$265$	−2.54618	−0.156411
$266$	14.5380	0.891382
$267$	−6.21854	−0.380568
$268$	1.48990	0.0910100
$269$	−24.1391	−1.47179	−0.735894	−	0.677097i	$-0.763238\pi$
$269$	−24.1391	−1.47179	−0.735894	+	0.677097i	$0.763238\pi$
$270$	−5.72890	−0.348650
$271$	−8.43510	−0.512396	−0.256198	−	0.966624i	$-0.582470\pi$
$271$	−8.43510	−0.512396	−0.256198	+	0.966624i	$0.582470\pi$
$272$	−14.1358	−0.857111
$273$	−1.45324	−0.0879542
$274$	−40.6836	−2.45779
$275$	26.4159	1.59294
$276$	−5.17328	−0.311395
$277$	−5.24035	−0.314862	−0.157431	−	0.987530i	$-0.550321\pi$
$277$	−5.24035	−0.314862	−0.157431	+	0.987530i	$0.550321\pi$
$278$	−17.9007	−1.07361
$279$	1.30600	0.0781883
$280$	6.39585	0.382225
$281$	−27.1682	−1.62072	−0.810360	−	0.585933i	$-0.800728\pi$
$281$	−27.1682	−1.62072	−0.810360	+	0.585933i	$0.800728\pi$
$282$	−13.8436	−0.824376
$283$	31.8213	1.89158	0.945791	−	0.324775i	$-0.105289\pi$
$283$	31.8213	1.89158	0.945791	+	0.324775i	$0.105289\pi$
$284$	18.0821	1.07298
$285$	−17.7336	−1.05045
$286$	9.21117	0.544668
$287$	4.02716	0.237715
$288$	6.12989	0.361207
$289$	−8.83258	−0.519563
$290$	4.11854	0.241849
$291$	7.38889	0.433144
$292$	6.08051	0.355835
$293$	10.9236	0.638165	0.319082	−	0.947727i	$-0.396625\pi$
$293$	10.9236	0.638165	0.319082	+	0.947727i	$0.396625\pi$
$294$	8.78738	0.512491
$295$	24.5808	1.43115
$296$	5.36308	0.311723
$297$	5.12383	0.297315
$298$	20.7239	1.20050
$299$	4.19986	0.242884
$300$	6.35042	0.366641
$301$	−1.16659	−0.0672410
$302$	−41.5331	−2.38996
$303$	−10.2148	−0.586826
$304$	27.5249	1.57866
$305$	12.3467	0.706972
$306$	−5.13763	−0.293699
$307$	−6.25733	−0.357125	−0.178562	−	0.983929i	$-0.557145\pi$
$307$	−6.25733	−0.357125	−0.178562	+	0.983929i	$0.557145\pi$
$308$	9.17198	0.522622
$309$	−1.00000	−0.0568880
$310$	−7.48195	−0.424946
$311$	15.4254	0.874696	0.437348	−	0.899292i	$-0.355918\pi$
$311$	15.4254	0.874696	0.437348	+	0.899292i	$0.355918\pi$
$312$	−1.38105	−0.0781867
$313$	28.7825	1.62688	0.813442	−	0.581646i	$-0.197591\pi$
$313$	28.7825	1.62688	0.813442	+	0.581646i	$0.197591\pi$
$314$	20.3195	1.14670
$315$	4.63115	0.260936
$316$	−0.115026	−0.00647070
$317$	10.6111	0.595981	0.297990	−	0.954569i	$-0.403684\pi$
$317$	10.6111	0.595981	0.297990	+	0.954569i	$0.403684\pi$
$318$	1.43635	0.0805463
$319$	−3.68355	−0.206239
$320$	−3.59221	−0.200811
$321$	5.52181	0.308198
$322$	10.9722	0.611457
$323$	−15.9034	−0.884886
$324$	1.23177	0.0684318
$325$	−5.15551	−0.285976
$326$	−25.2927	−1.40083
$327$	12.9933	0.718531
$328$	3.82711	0.211317
$329$	11.1910	0.616977
$330$	−29.3539	−1.61588
$331$	−33.5823	−1.84585	−0.922925	−	0.384981i	$-0.874208\pi$
$331$	−33.5823	−1.84585	−0.922925	+	0.384981i	$0.874208\pi$
$332$	−15.3391	−0.841842
$333$	3.88333	0.212805
$334$	−23.2718	−1.27337
$335$	3.85458	0.210598
$336$	−7.18814	−0.392145
$337$	34.2918	1.86799	0.933997	−	0.357280i	$-0.116296\pi$
$337$	34.2918	1.86799	0.933997	+	0.357280i	$0.116296\pi$
$338$	−1.79771	−0.0977827
$339$	−2.79516	−0.151812
$340$	11.2182	0.608394
$341$	6.69173	0.362377
$342$	10.0038	0.540946
$343$	−17.2763	−0.932831
$344$	−1.10864	−0.0597738
$345$	−13.3840	−0.720571
$346$	41.7254	2.24317
$347$	−18.1013	−0.971730	−0.485865	−	0.874034i	$-0.661495\pi$
$347$	−18.1013	−0.971730	−0.485865	+	0.874034i	$0.661495\pi$
$348$	−0.885529	−0.0474693
$349$	−0.929395	−0.0497493	−0.0248747	−	0.999691i	$-0.507919\pi$
$349$	−0.929395	−0.0497493	−0.0248747	+	0.999691i	$0.507919\pi$
$350$	−13.4688	−0.719939
$351$	−1.00000	−0.0533761
$352$	31.4085	1.67408
$353$	−29.3288	−1.56101	−0.780506	−	0.625148i	$-0.785038\pi$
$353$	−29.3288	−1.56101	−0.780506	+	0.625148i	$0.785038\pi$
$354$	−13.8665	−0.736994
$355$	46.7810	2.48288
$356$	−7.65983	−0.405970
$357$	4.15318	0.219809
$358$	−3.09411	−0.163529
$359$	20.4536	1.07950	0.539749	−	0.841826i	$-0.318519\pi$
$359$	20.4536	1.07950	0.539749	+	0.841826i	$0.318519\pi$
$360$	4.40109	0.231958
$361$	11.9665	0.629817
$362$	0.814596	0.0428142
$363$	15.2536	0.800606
$364$	−1.79006	−0.0938248
$365$	15.7311	0.823405
$366$	−6.96501	−0.364067
$367$	8.00533	0.417875	0.208937	−	0.977929i	$-0.432999\pi$
$367$	8.00533	0.417875	0.208937	+	0.977929i	$0.432999\pi$
$368$	20.7737	1.08290
$369$	2.77115	0.144260
$370$	−22.2472	−1.15658
$371$	−1.16112	−0.0602823
$372$	1.60870	0.0834071
$373$	−2.00647	−0.103891	−0.0519455	−	0.998650i	$-0.516542\pi$
$373$	−2.00647	−0.103891	−0.0519455	+	0.998650i	$0.516542\pi$
$374$	−26.3243	−1.36120
$375$	0.495568	0.0255910
$376$	10.6350	0.548460
$377$	0.718906	0.0370255
$378$	−2.61251	−0.134373
$379$	−6.22584	−0.319800	−0.159900	−	0.987133i	$-0.551117\pi$
$379$	−6.22584	−0.319800	−0.159900	+	0.987133i	$0.551117\pi$
$380$	−21.8438	−1.12056
$381$	−16.1489	−0.827333
$382$	11.2870	0.577496
$383$	−13.0387	−0.666244	−0.333122	−	0.942884i	$-0.608102\pi$
$383$	−13.0387	−0.666244	−0.333122	+	0.942884i	$0.608102\pi$
$384$	−10.2334	−0.522219
$385$	23.7292	1.20935
$386$	35.2139	1.79234
$387$	−0.802749	−0.0408060
$388$	9.10143	0.462055
$389$	36.2528	1.83809	0.919045	−	0.394153i	$-0.128962\pi$
$389$	36.2528	1.83809	0.919045	+	0.394153i	$0.128962\pi$
$390$	5.72890	0.290094
$391$	−12.0027	−0.607001
$392$	−6.75070	−0.340962
$393$	−1.67417	−0.0844508
$394$	9.76499	0.491953
$395$	−0.297588	−0.0149733
$396$	6.31139	0.317159
$397$	−5.35171	−0.268595	−0.134297	−	0.990941i	$-0.542878\pi$
$397$	−5.35171	−0.268595	−0.134297	+	0.990941i	$0.542878\pi$
$398$	−4.02283	−0.201646
$399$	−8.08694	−0.404853
$400$	−25.5006	−1.27503
$401$	−29.2862	−1.46248	−0.731241	−	0.682119i	$-0.761058\pi$
$401$	−29.2862	−1.46248	−0.731241	+	0.682119i	$0.761058\pi$
$402$	−2.17443	−0.108451
$403$	−1.30600	−0.0650566
$404$	−12.5823	−0.625994
$405$	3.18677	0.158352
$406$	1.87815	0.0932110
$407$	19.8975	0.986284
$408$	3.94687	0.195399
$409$	11.1534	0.551499	0.275750	−	0.961229i	$-0.411074\pi$
$409$	11.1534	0.551499	0.275750	+	0.961229i	$0.411074\pi$
$410$	−15.8757	−0.784043
$411$	22.6307	1.11629
$412$	−1.23177	−0.0606851
$413$	11.2094	0.551579
$414$	7.55015	0.371070
$415$	−39.6844	−1.94803
$416$	−6.12989	−0.300543
$417$	9.95746	0.487619
$418$	51.2579	2.50711
$419$	6.90916	0.337534	0.168767	−	0.985656i	$-0.446021\pi$
$419$	6.90916	0.337534	0.168767	+	0.985656i	$0.446021\pi$
$420$	5.70452	0.278352
$421$	−14.8349	−0.723010	−0.361505	−	0.932370i	$-0.617737\pi$
$421$	−14.8349	−0.723010	−0.361505	+	0.932370i	$0.617737\pi$
$422$	26.3544	1.28291
$423$	7.70068	0.374420
$424$	−1.10344	−0.0535878
$425$	14.7338	0.714693
$426$	−26.3900	−1.27860
$427$	5.63040	0.272474
$428$	6.80162	0.328769
$429$	−5.12383	−0.247381
$430$	4.59887	0.221777
$431$	31.0280	1.49456	0.747282	−	0.664507i	$-0.231358\pi$
$431$	31.0280	1.49456	0.747282	+	0.664507i	$0.231358\pi$
$432$	−4.94628	−0.237978
$433$	−5.33361	−0.256317	−0.128159	−	0.991754i	$-0.540907\pi$
$433$	−5.33361	−0.256317	−0.128159	+	0.991754i	$0.540907\pi$
$434$	−3.41194	−0.163779
$435$	−2.29099	−0.109844
$436$	16.0048	0.766491
$437$	23.3712	1.11800
$438$	−8.87421	−0.424026
$439$	11.0935	0.529462	0.264731	−	0.964322i	$-0.414717\pi$
$439$	11.0935	0.529462	0.264731	+	0.964322i	$0.414717\pi$
$440$	22.5504	1.07505
$441$	−4.88809	−0.232766
$442$	5.13763	0.244372
$443$	0.462623	0.0219799	0.0109899	−	0.999940i	$-0.496502\pi$
$443$	0.462623	0.0219799	0.0109899	+	0.999940i	$0.496502\pi$
$444$	4.78339	0.227009
$445$	−19.8171	−0.939419
$446$	41.2057	1.95115
$447$	−11.5279	−0.545251
$448$	−1.63813	−0.0773945
$449$	−23.0357	−1.08712	−0.543561	−	0.839370i	$-0.682924\pi$
$449$	−23.0357	−1.08712	−0.543561	+	0.839370i	$0.682924\pi$
$450$	−9.26813	−0.436904
$451$	14.1989	0.668601
$452$	−3.44300	−0.161945
$453$	23.1033	1.08549
$454$	9.59834	0.450472
$455$	−4.63115	−0.217112
$456$	−7.68522	−0.359893
$457$	3.76060	0.175913	0.0879566	−	0.996124i	$-0.471966\pi$
$457$	3.76060	0.175913	0.0879566	+	0.996124i	$0.471966\pi$
$458$	−27.6538	−1.29218
$459$	2.85787	0.133394
$460$	−16.4861	−0.768666
$461$	23.9492	1.11543	0.557713	−	0.830034i	$-0.311679\pi$
$461$	23.9492	1.11543	0.557713	+	0.830034i	$0.311679\pi$
$462$	−13.3861	−0.622776
$463$	−19.7737	−0.918963	−0.459481	−	0.888187i	$-0.651965\pi$
$463$	−19.7737	−0.918963	−0.459481	+	0.888187i	$0.651965\pi$
$464$	3.55591	0.165079
$465$	4.16193	0.193005
$466$	−17.0796	−0.791199
$467$	0.386829	0.0179003	0.00895015	−	0.999960i	$-0.497151\pi$
$467$	0.386829	0.0179003	0.00895015	+	0.999960i	$0.497151\pi$
$468$	−1.23177	−0.0569387
$469$	1.75778	0.0811666
$470$	−44.1164	−2.03494
$471$	−11.3030	−0.520814
$472$	10.6526	0.490325
$473$	−4.11315	−0.189123
$474$	0.167874	0.00771073
$475$	−28.6891	−1.31635
$476$	5.11577	0.234481
$477$	−0.798985	−0.0365830
$478$	20.7071	0.947120
$479$	4.20034	0.191918	0.0959592	−	0.995385i	$-0.469408\pi$
$479$	4.20034	0.191918	0.0959592	+	0.995385i	$0.469408\pi$
$480$	19.5346	0.891627
$481$	−3.88333	−0.177065
$482$	6.26890	0.285541
$483$	−6.10342	−0.277715
$484$	18.7890	0.854044
$485$	23.5467	1.06920
$486$	−1.79771	−0.0815459
$487$	3.31360	0.150154	0.0750768	−	0.997178i	$-0.476080\pi$
$487$	3.31360	0.150154	0.0750768	+	0.997178i	$0.476080\pi$
$488$	5.35071	0.242215
$489$	14.0694	0.636239
$490$	28.0034	1.26506
$491$	−14.3423	−0.647258	−0.323629	−	0.946184i	$-0.604903\pi$
$491$	−14.3423	−0.647258	−0.323629	+	0.946184i	$0.604903\pi$
$492$	3.41343	0.153889
$493$	−2.05454	−0.0925318
$494$	−10.0038	−0.450094
$495$	16.3285	0.733910
$496$	−6.45985	−0.290056
$497$	21.3332	0.956927
$498$	22.3866	1.00317
$499$	6.75159	0.302243	0.151121	−	0.988515i	$-0.451712\pi$
$499$	6.75159	0.302243	0.151121	+	0.988515i	$0.451712\pi$
$500$	0.610427	0.0272991
$501$	12.9452	0.578349
$502$	22.1880	0.990300
$503$	9.10272	0.405870	0.202935	−	0.979192i	$-0.434952\pi$
$503$	9.10272	0.405870	0.202935	+	0.979192i	$0.434952\pi$
$504$	2.00700	0.0893990
$505$	−32.5523	−1.44856
$506$	38.6857	1.71979
$507$	1.00000	0.0444116
$508$	−19.8918	−0.882555
$509$	19.4774	0.863321	0.431661	−	0.902036i	$-0.357928\pi$
$509$	19.4774	0.863321	0.431661	+	0.902036i	$0.357928\pi$
$510$	−16.3725	−0.724984
$511$	7.17376	0.317349
$512$	−16.6580	−0.736188
$513$	−5.56476	−0.245690
$514$	−1.08564	−0.0478855
$515$	−3.18677	−0.140426
$516$	−0.988805	−0.0435297
$517$	39.4570	1.73532
$518$	−10.1453	−0.445757
$519$	−23.2103	−1.01882
$520$	−4.40109	−0.193001
$521$	11.4545	0.501832	0.250916	−	0.968009i	$-0.419268\pi$
$521$	11.4545	0.501832	0.250916	+	0.968009i	$0.419268\pi$
$522$	1.29239	0.0565662
$523$	−22.0381	−0.963660	−0.481830	−	0.876265i	$-0.660028\pi$
$523$	−22.0381	−0.963660	−0.481830	+	0.876265i	$0.660028\pi$
$524$	−2.06220	−0.0900877
$525$	7.49220	0.326986
$526$	−32.9013	−1.43457
$527$	3.73238	0.162585
$528$	−25.3439	−1.10295
$529$	−5.36114	−0.233093
$530$	4.57731	0.198826
$531$	7.71339	0.334733
$532$	−9.96127	−0.431876
$533$	−2.77115	−0.120032
$534$	11.1792	0.483769
$535$	17.5968	0.760774
$536$	1.67046	0.0721528
$537$	1.72114	0.0742726
$538$	43.3952	1.87090
$539$	−25.0457	−1.07880
$540$	3.92538	0.168921
$541$	−33.8854	−1.45685	−0.728423	−	0.685127i	$-0.759747\pi$
$541$	−33.8854	−1.45685	−0.728423	+	0.685127i	$0.759747\pi$
$542$	15.1639	0.651345
$543$	−0.453129	−0.0194456
$544$	17.5184	0.751097
$545$	41.4067	1.77367
$546$	2.61251	0.111805
$547$	45.3984	1.94109	0.970547	−	0.240912i	$-0.0774464\pi$
$547$	45.3984	1.94109	0.970547	+	0.240912i	$0.0774464\pi$
$548$	27.8759	1.19080
$549$	3.87437	0.165354
$550$	−47.4883	−2.02491
$551$	4.00054	0.170429
$552$	−5.80023	−0.246874
$553$	−0.135707	−0.00577085
$554$	9.42064	0.400245
$555$	12.3753	0.525302
$556$	12.2653	0.520166
$557$	−22.7961	−0.965904	−0.482952	−	0.875647i	$-0.660435\pi$
$557$	−22.7961	−0.965904	−0.482952	+	0.875647i	$0.660435\pi$
$558$	−2.34782	−0.0993910
$559$	0.802749	0.0339527
$560$	−22.9070	−0.967996
$561$	14.6432	0.618238
$562$	48.8407	2.06022
$563$	−44.5928	−1.87936	−0.939681	−	0.342051i	$-0.888878\pi$
$563$	−44.5928	−1.87936	−0.939681	+	0.342051i	$0.888878\pi$
$564$	9.48550	0.399411
$565$	−8.90752	−0.374742
$566$	−57.2057	−2.40453
$567$	1.45324	0.0610304
$568$	20.2735	0.850658
$569$	14.2600	0.597811	0.298905	−	0.954283i	$-0.403379\pi$
$569$	14.2600	0.597811	0.298905	+	0.954283i	$0.403379\pi$
$570$	31.8799	1.33530
$571$	13.9201	0.582537	0.291268	−	0.956641i	$-0.405923\pi$
$571$	13.9201	0.582537	0.291268	+	0.956641i	$0.405923\pi$
$572$	−6.31139	−0.263893
$573$	−6.27856	−0.262291
$574$	−7.23967	−0.302178
$575$	−21.6524	−0.902969
$576$	−1.12723	−0.0469678
$577$	19.9195	0.829258	0.414629	−	0.909991i	$-0.363911\pi$
$577$	19.9195	0.829258	0.414629	+	0.909991i	$0.363911\pi$
$578$	15.8784	0.660456
$579$	−19.5882	−0.814057
$580$	−2.82198	−0.117176
$581$	−18.0970	−0.750790
$582$	−13.2831	−0.550602
$583$	−4.09386	−0.169550
$584$	6.81740	0.282106
$585$	−3.18677	−0.131757
$586$	−19.6375	−0.811219
$587$	−10.7590	−0.444070	−0.222035	−	0.975039i	$-0.571270\pi$
$587$	−10.7590	−0.444070	−0.222035	+	0.975039i	$0.571270\pi$
$588$	−6.02102	−0.248303
$589$	−7.26758	−0.299455
$590$	−44.1892	−1.81924
$591$	−5.43189	−0.223438
$592$	−19.2081	−0.789447
$593$	9.40307	0.386138	0.193069	−	0.981185i	$-0.438156\pi$
$593$	9.40307	0.386138	0.193069	+	0.981185i	$0.438156\pi$
$594$	−9.21117	−0.377939
$595$	13.2352	0.542591
$596$	−14.1998	−0.581645
$597$	2.23775	0.0915850
$598$	−7.55015	−0.308749
$599$	−4.26583	−0.174297	−0.0871485	−	0.996195i	$-0.527775\pi$
$599$	−4.26583	−0.174297	−0.0871485	+	0.996195i	$0.527775\pi$
$600$	7.12002	0.290674
$601$	−23.3819	−0.953768	−0.476884	−	0.878966i	$-0.658234\pi$
$601$	−23.3819	−0.953768	−0.476884	+	0.878966i	$0.658234\pi$
$602$	2.09719	0.0854752
$603$	1.20956	0.0492569
$604$	28.4580	1.15794
$605$	48.6097	1.97627
$606$	18.3633	0.745958
$607$	3.13425	0.127215	0.0636075	−	0.997975i	$-0.479739\pi$
$607$	3.13425	0.127215	0.0636075	+	0.997975i	$0.479739\pi$
$608$	−34.1114	−1.38340
$609$	−1.04474	−0.0423352
$610$	−22.1959	−0.898685
$611$	−7.70068	−0.311536
$612$	3.52025	0.142298
$613$	42.5646	1.71917	0.859584	−	0.510994i	$-0.170723\pi$
$613$	42.5646	1.71917	0.859584	+	0.510994i	$0.170723\pi$
$614$	11.2489	0.453968
$615$	8.83103	0.356102
$616$	10.2835	0.414335
$617$	4.91808	0.197994	0.0989972	−	0.995088i	$-0.468437\pi$
$617$	4.91808	0.197994	0.0989972	+	0.995088i	$0.468437\pi$
$618$	1.79771	0.0723146
$619$	−28.4862	−1.14496	−0.572479	−	0.819919i	$-0.694018\pi$
$619$	−28.4862	−1.14496	−0.572479	+	0.819919i	$0.694018\pi$
$620$	5.12655	0.205887
$621$	−4.19986	−0.168535
$622$	−27.7305	−1.11189
$623$	−9.03704	−0.362061
$624$	4.94628	0.198010
$625$	−24.1983	−0.967931
$626$	−51.7427	−2.06806
$627$	−28.5129	−1.13869
$628$	−13.9227	−0.555576
$629$	11.0981	0.442509
$630$	−8.32548	−0.331695
$631$	−5.63289	−0.224242	−0.112121	−	0.993695i	$-0.535764\pi$
$631$	−5.63289	−0.224242	−0.112121	+	0.993695i	$0.535764\pi$
$632$	−0.128966	−0.00512998
$633$	−14.6599	−0.582680
$634$	−19.0758	−0.757596
$635$	−51.4628	−2.04224
$636$	−0.984169	−0.0390248
$637$	4.88809	0.193673
$638$	6.62197	0.262166
$639$	14.6798	0.580722
$640$	−32.6114	−1.28908
$641$	45.6077	1.80140	0.900698	−	0.434446i	$-0.143056\pi$
$641$	45.6077	1.80140	0.900698	+	0.434446i	$0.143056\pi$
$642$	−9.92664	−0.391773
$643$	−10.0614	−0.396783	−0.198391	−	0.980123i	$-0.563572\pi$
$643$	−10.0614	−0.396783	−0.198391	+	0.980123i	$0.563572\pi$
$644$	−7.51803	−0.296252
$645$	−2.55818	−0.100728
$646$	28.5897	1.12485
$647$	−16.6977	−0.656454	−0.328227	−	0.944599i	$-0.606451\pi$
$647$	−16.6977	−0.656454	−0.328227	+	0.944599i	$0.606451\pi$
$648$	1.38105	0.0542528
$649$	39.5221	1.55138
$650$	9.26813	0.363526
$651$	1.89794	0.0743860
$652$	17.3303	0.678705
$653$	−23.2663	−0.910481	−0.455240	−	0.890369i	$-0.650447\pi$
$653$	−23.2663	−0.910481	−0.455240	+	0.890369i	$0.650447\pi$
$654$	−23.3582	−0.913379
$655$	−5.33520	−0.208464
$656$	−13.7069	−0.535165
$657$	4.93639	0.192587
$658$	−20.1181	−0.784286
$659$	−15.8026	−0.615581	−0.307791	−	0.951454i	$-0.599590\pi$
$659$	−15.8026	−0.615581	−0.307791	+	0.951454i	$0.599590\pi$
$660$	20.1130	0.782896
$661$	−24.7315	−0.961944	−0.480972	−	0.876736i	$-0.659716\pi$
$661$	−24.7315	−0.961944	−0.480972	+	0.876736i	$0.659716\pi$
$662$	60.3713	2.34640
$663$	−2.85787	−0.110990
$664$	−17.1980	−0.667413
$665$	−25.7712	−0.999365
$666$	−6.98112	−0.270513
$667$	3.01931	0.116908
$668$	15.9456	0.616952
$669$	−22.9212	−0.886184
$670$	−6.92943	−0.267707
$671$	19.8516	0.766363
$672$	8.90821	0.343642
$673$	25.0976	0.967441	0.483721	−	0.875223i	$-0.339285\pi$
$673$	25.0976	0.967441	0.483721	+	0.875223i	$0.339285\pi$
$674$	−61.6469	−2.37455
$675$	5.15551	0.198436
$676$	1.23177	0.0473759
$677$	−22.7803	−0.875518	−0.437759	−	0.899092i	$-0.644228\pi$
$677$	−22.7803	−0.875518	−0.437759	+	0.899092i	$0.644228\pi$
$678$	5.02489	0.192980
$679$	10.7378	0.412080
$680$	12.5778	0.482335
$681$	−5.33919	−0.204598
$682$	−12.0298	−0.460645
$683$	34.5102	1.32050	0.660248	−	0.751047i	$-0.270451\pi$
$683$	34.5102	1.32050	0.660248	+	0.751047i	$0.270451\pi$
$684$	−6.85452	−0.262089
$685$	72.1190	2.75553
$686$	31.0578	1.18579
$687$	15.3828	0.586889
$688$	3.97062	0.151379
$689$	0.798985	0.0304389
$690$	24.0606	0.915971
$691$	16.3735	0.622876	0.311438	−	0.950267i	$-0.399189\pi$
$691$	16.3735	0.622876	0.311438	+	0.950267i	$0.399189\pi$
$692$	−28.5898	−1.08682
$693$	7.44616	0.282856
$694$	32.5410	1.23524
$695$	31.7321	1.20367
$696$	−0.992846	−0.0376337
$697$	7.91960	0.299976
$698$	1.67078	0.0632401
$699$	9.50076	0.359352
$700$	9.22869	0.348812
$701$	−2.08959	−0.0789226	−0.0394613	−	0.999221i	$-0.512564\pi$
$701$	−2.08959	−0.0789226	−0.0394613	+	0.999221i	$0.512564\pi$
$702$	1.79771	0.0678503
$703$	−21.6098	−0.815029
$704$	−5.77571	−0.217680
$705$	24.5403	0.924242
$706$	52.7247	1.98432
$707$	−14.8446	−0.558288
$708$	9.50114	0.357075
$709$	32.0183	1.20247	0.601237	−	0.799071i	$-0.294675\pi$
$709$	32.0183	1.20247	0.601237	+	0.799071i	$0.294675\pi$
$710$	−84.0989	−3.15618
$711$	−0.0933822	−0.00350211
$712$	−8.58812	−0.321854
$713$	−5.48503	−0.205416
$714$	−7.46622	−0.279416
$715$	−16.3285	−0.610650
$716$	2.12005	0.0792300
$717$	−11.5186	−0.430169
$718$	−36.7697	−1.37223
$719$	11.9564	0.445897	0.222948	−	0.974830i	$-0.428432\pi$
$719$	11.9564	0.445897	0.222948	+	0.974830i	$0.428432\pi$
$720$	−15.7627	−0.587440
$721$	−1.45324	−0.0541215
$722$	−21.5124	−0.800607
$723$	−3.48715	−0.129689
$724$	−0.558152	−0.0207436
$725$	−3.70632	−0.137649
$726$	−27.4216	−1.01771
$727$	8.75311	0.324635	0.162317	−	0.986739i	$-0.448103\pi$
$727$	8.75311	0.324635	0.162317	+	0.986739i	$0.448103\pi$
$728$	−2.00700	−0.0743844
$729$	1.00000	0.0370370
$730$	−28.2801	−1.04669
$731$	−2.29415	−0.0848523
$732$	4.77235	0.176391
$733$	13.3018	0.491313	0.245657	−	0.969357i	$-0.420996\pi$
$733$	13.3018	0.491313	0.245657	+	0.969357i	$0.420996\pi$
$734$	−14.3913	−0.531192
$735$	−15.5772	−0.574574
$736$	−25.7447	−0.948963
$737$	6.19756	0.228290
$738$	−4.98174	−0.183380
$739$	−15.4499	−0.568335	−0.284168	−	0.958775i	$-0.591717\pi$
$739$	−15.4499	−0.568335	−0.284168	+	0.958775i	$0.591717\pi$
$740$	15.2436	0.560364
$741$	5.56476	0.204426
$742$	2.08736	0.0766294
$743$	−10.4694	−0.384084	−0.192042	−	0.981387i	$-0.561511\pi$
$743$	−10.4694	−0.384084	−0.192042	+	0.981387i	$0.561511\pi$
$744$	1.80366	0.0661252
$745$	−36.7368	−1.34593
$746$	3.60706	0.132064
$747$	−12.4528	−0.455626
$748$	18.0371	0.659503
$749$	8.02453	0.293210
$750$	−0.890889	−0.0325307
$751$	−30.2576	−1.10412	−0.552059	−	0.833805i	$-0.686158\pi$
$751$	−30.2576	−1.10412	−0.552059	+	0.833805i	$0.686158\pi$
$752$	−38.0897	−1.38899
$753$	−12.3424	−0.449780
$754$	−1.29239	−0.0470659
$755$	73.6248	2.67948
$756$	1.79006	0.0651040
$757$	−25.5494	−0.928609	−0.464305	−	0.885676i	$-0.653696\pi$
$757$	−25.5494	−0.928609	−0.464305	+	0.885676i	$0.653696\pi$
$758$	11.1923	0.406522
$759$	−21.5194	−0.781104
$760$	−24.4910	−0.888383
$761$	−11.8925	−0.431101	−0.215551	−	0.976493i	$-0.569155\pi$
$761$	−11.8925	−0.431101	−0.215551	+	0.976493i	$0.569155\pi$
$762$	29.0311	1.05169
$763$	18.8824	0.683589
$764$	−7.73376	−0.279798
$765$	9.10738	0.329278
$766$	23.4398	0.846914
$767$	−7.71339	−0.278514
$768$	20.6511	0.745182
$769$	27.4556	0.990075	0.495037	−	0.868872i	$-0.335154\pi$
$769$	27.4556	0.990075	0.495037	+	0.868872i	$0.335154\pi$
$770$	−42.6583	−1.53730
$771$	0.603901	0.0217489
$772$	−24.1282	−0.868393
$773$	4.24773	0.152780	0.0763902	−	0.997078i	$-0.475661\pi$
$773$	4.24773	0.152780	0.0763902	+	0.997078i	$0.475661\pi$
$774$	1.44311	0.0518716
$775$	6.73310	0.241860
$776$	10.2044	0.366318
$777$	5.64342	0.202457
$778$	−65.1721	−2.33653
$779$	−15.4208	−0.552507
$780$	−3.92538	−0.140551
$781$	75.2166	2.69146
$782$	21.5774	0.771605
$783$	−0.718906	−0.0256916
$784$	24.1779	0.863495
$785$	−36.0200	−1.28561
$786$	3.00968	0.107352
$787$	−25.1939	−0.898067	−0.449034	−	0.893515i	$-0.648232\pi$
$787$	−25.1939	−0.898067	−0.449034	+	0.893515i	$0.648232\pi$
$788$	−6.69086	−0.238352
$789$	18.3018	0.651560
$790$	0.534978	0.0190336
$791$	−4.06204	−0.144429
$792$	7.07627	0.251444
$793$	−3.87437	−0.137583
$794$	9.62085	0.341431
$795$	−2.54618	−0.0903038
$796$	2.75640	0.0976980
$797$	−8.50075	−0.301112	−0.150556	−	0.988601i	$-0.548106\pi$
$797$	−8.50075	−0.301112	−0.150556	+	0.988601i	$0.548106\pi$
$798$	14.5380	0.514639
$799$	22.0076	0.778571
$800$	31.6027	1.11732
$801$	−6.21854	−0.219721
$802$	52.6481	1.85907
$803$	25.2932	0.892577
$804$	1.48990	0.0525447
$805$	−19.4502	−0.685529
$806$	2.34782	0.0826983
$807$	−24.1391	−0.849737
$808$	−14.1072	−0.496289
$809$	−42.7449	−1.50283	−0.751415	−	0.659830i	$-0.770628\pi$
$809$	−42.7449	−1.50283	−0.751415	+	0.659830i	$0.770628\pi$
$810$	−5.72890	−0.201293
$811$	−24.6047	−0.863986	−0.431993	−	0.901877i	$-0.642190\pi$
$811$	−24.6047	−0.863986	−0.431993	+	0.901877i	$0.642190\pi$
$812$	−1.28689	−0.0451609
$813$	−8.43510	−0.295832
$814$	−35.7701	−1.25374
$815$	44.8358	1.57053
$816$	−14.1358	−0.494853
$817$	4.46710	0.156284
$818$	−20.0506	−0.701052
$819$	−1.45324	−0.0507804
$820$	10.8778	0.379870
$821$	−36.1384	−1.26124	−0.630620	−	0.776092i	$-0.717199\pi$
$821$	−36.1384	−1.26124	−0.630620	+	0.776092i	$0.717199\pi$
$822$	−40.6836	−1.41900
$823$	−11.4961	−0.400729	−0.200365	−	0.979721i	$-0.564213\pi$
$823$	−11.4961	−0.400729	−0.200365	+	0.979721i	$0.564213\pi$
$824$	−1.38105	−0.0481112
$825$	26.4159	0.919685
$826$	−20.1513	−0.701154
$827$	3.80992	0.132484	0.0662419	−	0.997804i	$-0.478899\pi$
$827$	3.80992	0.132484	0.0662419	+	0.997804i	$0.478899\pi$
$828$	−5.17328	−0.179784
$829$	−45.3988	−1.57676	−0.788382	−	0.615186i	$-0.789081\pi$
$829$	−45.3988	−1.57676	−0.788382	+	0.615186i	$0.789081\pi$
$830$	71.3411	2.47629
$831$	−5.24035	−0.181786
$832$	1.12723	0.0390796
$833$	−13.9695	−0.484015
$834$	−17.9007	−0.619849
$835$	41.2534	1.42763
$836$	−35.1214	−1.21470
$837$	1.30600	0.0451420
$838$	−12.4207	−0.429065
$839$	51.6401	1.78282	0.891408	−	0.453203i	$-0.149719\pi$
$839$	51.6401	1.78282	0.891408	+	0.453203i	$0.149719\pi$
$840$	6.39585	0.220678
$841$	−28.4832	−0.982178
$842$	26.6690	0.919073
$843$	−27.1682	−0.935723
$844$	−18.0577	−0.621572
$845$	3.18677	0.109628
$846$	−13.8436	−0.475953
$847$	22.1672	0.761673
$848$	3.95201	0.135712
$849$	31.8213	1.09211
$850$	−26.4871	−0.908500
$851$	−16.3095	−0.559082
$852$	18.0821	0.619484
$853$	−58.1628	−1.99146	−0.995728	−	0.0923309i	$-0.970568\pi$
$853$	−58.1628	−1.99146	−0.995728	+	0.0923309i	$0.970568\pi$
$854$	−10.1218	−0.346362
$855$	−17.7336	−0.606476
$856$	7.62591	0.260648
$857$	−37.8322	−1.29232	−0.646161	−	0.763201i	$-0.723627\pi$
$857$	−37.8322	−1.29232	−0.646161	+	0.763201i	$0.723627\pi$
$858$	9.21117	0.314464
$859$	19.0838	0.651131	0.325565	−	0.945520i	$-0.394445\pi$
$859$	19.0838	0.651131	0.325565	+	0.945520i	$0.394445\pi$
$860$	−3.15109	−0.107451
$861$	4.02716	0.137245
$862$	−55.7794	−1.89985
$863$	11.4644	0.390252	0.195126	−	0.980778i	$-0.437488\pi$
$863$	11.4644	0.390252	0.195126	+	0.980778i	$0.437488\pi$
$864$	6.12989	0.208543
$865$	−73.9658	−2.51491
$866$	9.58831	0.325824
$867$	−8.83258	−0.299970
$868$	2.33783	0.0793510
$869$	−0.478474	−0.0162311
$870$	4.11854	0.139632
$871$	−1.20956	−0.0409842
$872$	17.9444	0.607675
$873$	7.38889	0.250076
$874$	−42.0148	−1.42117
$875$	0.720180	0.0243465
$876$	6.08051	0.205441
$877$	−26.7184	−0.902217	−0.451108	−	0.892469i	$-0.648971\pi$
$877$	−26.7184	−0.902217	−0.451108	+	0.892469i	$0.648971\pi$
$878$	−19.9429	−0.673039
$879$	10.9236	0.368444
$880$	−80.7652	−2.72259
$881$	−29.5936	−0.997034	−0.498517	−	0.866880i	$-0.666122\pi$
$881$	−29.5936	−0.997034	−0.498517	+	0.866880i	$0.666122\pi$
$882$	8.78738	0.295887
$883$	11.8256	0.397964	0.198982	−	0.980003i	$-0.436236\pi$
$883$	11.8256	0.397964	0.198982	+	0.980003i	$0.436236\pi$
$884$	−3.52025	−0.118399
$885$	24.5808	0.826274
$886$	−0.831663	−0.0279403
$887$	−51.6099	−1.73289	−0.866446	−	0.499271i	$-0.833601\pi$
$887$	−51.6099	−1.73289	−0.866446	+	0.499271i	$0.833601\pi$
$888$	5.36308	0.179973
$889$	−23.4683	−0.787100
$890$	35.6254	1.19417
$891$	5.12383	0.171655
$892$	−28.2337	−0.945333
$893$	−42.8524	−1.43400
$894$	20.7239	0.693110
$895$	5.48487	0.183339
$896$	−14.8715	−0.496823
$897$	4.19986	0.140229
$898$	41.4116	1.38192
$899$	−0.938892	−0.0313138
$900$	6.35042	0.211681
$901$	−2.28340	−0.0760710
$902$	−25.5256	−0.849909
$903$	−1.16659	−0.0388216
$904$	−3.86025	−0.128390
$905$	−1.44402	−0.0480008
$906$	−41.5331	−1.37984
$907$	34.0392	1.13025	0.565127	−	0.825004i	$-0.308827\pi$
$907$	34.0392	1.13025	0.565127	+	0.825004i	$0.308827\pi$
$908$	−6.57667	−0.218255
$909$	−10.2148	−0.338804
$910$	8.32548	0.275987
$911$	28.7046	0.951025	0.475512	−	0.879709i	$-0.342263\pi$
$911$	28.7046	0.951025	0.475512	+	0.879709i	$0.342263\pi$
$912$	27.5249	0.911439
$913$	−63.8062	−2.11168
$914$	−6.76047	−0.223617
$915$	12.3467	0.408170
$916$	18.9481	0.626062
$917$	−2.43298	−0.0803440
$918$	−5.13763	−0.169567
$919$	11.5052	0.379523	0.189761	−	0.981830i	$-0.439229\pi$
$919$	11.5052	0.379523	0.189761	+	0.981830i	$0.439229\pi$
$920$	−18.4840	−0.609399
$921$	−6.25733	−0.206186
$922$	−43.0538	−1.41790
$923$	−14.6798	−0.483190
$924$	9.17198	0.301736
$925$	20.0206	0.658272
$926$	35.5475	1.16816
$927$	−1.00000	−0.0328443
$928$	−4.40682	−0.144661
$929$	17.4847	0.573655	0.286828	−	0.957982i	$-0.407399\pi$
$929$	17.4847	0.573655	0.286828	+	0.957982i	$0.407399\pi$
$930$	−7.48195	−0.245343
$931$	27.2010	0.891478
$932$	11.7028	0.383337
$933$	15.4254	0.505006
$934$	−0.695407	−0.0227544
$935$	46.6646	1.52610
$936$	−1.38105	−0.0451411
$937$	−27.8819	−0.910861	−0.455430	−	0.890271i	$-0.650515\pi$
$937$	−27.8819	−0.910861	−0.455430	+	0.890271i	$0.650515\pi$
$938$	−3.15998	−0.103177
$939$	28.7825	0.939282
$940$	30.2281	0.985932
$941$	−44.0347	−1.43549	−0.717746	−	0.696305i	$-0.754826\pi$
$941$	−44.0347	−1.43549	−0.717746	+	0.696305i	$0.754826\pi$
$942$	20.3195	0.662046
$943$	−11.6385	−0.379001
$944$	−38.1526	−1.24176
$945$	4.63115	0.150651
$946$	7.39426	0.240408
$947$	17.1736	0.558066	0.279033	−	0.960282i	$-0.409986\pi$
$947$	17.1736	0.558066	0.279033	+	0.960282i	$0.409986\pi$
$948$	−0.115026	−0.00373586
$949$	−4.93639	−0.160242
$950$	51.5749	1.67331
$951$	10.6111	0.344090
$952$	5.73575	0.185897
$953$	15.5619	0.504099	0.252049	−	0.967714i	$-0.418895\pi$
$953$	15.5619	0.504099	0.252049	+	0.967714i	$0.418895\pi$
$954$	1.43635	0.0465034
$955$	−20.0083	−0.647454
$956$	−14.1883	−0.458881
$957$	−3.68355	−0.119072
$958$	−7.55100	−0.243962
$959$	32.8879	1.06201
$960$	−3.59221	−0.115938
$961$	−29.2944	−0.944979
$962$	6.98112	0.225080
$963$	5.52181	0.177938
$964$	−4.29538	−0.138345
$965$	−62.4231	−2.00947
$966$	10.9722	0.353025
$967$	22.0080	0.707731	0.353865	−	0.935296i	$-0.384867\pi$
$967$	22.0080	0.707731	0.353865	+	0.935296i	$0.384867\pi$
$968$	21.0660	0.677087
$969$	−15.9034	−0.510889
$970$	−42.3302	−1.35914
$971$	−59.4494	−1.90782	−0.953911	−	0.300091i	$-0.902983\pi$
$971$	−59.4494	−1.90782	−0.953911	+	0.300091i	$0.902983\pi$
$972$	1.23177	0.0395091
$973$	14.4706	0.463906
$974$	−5.95691	−0.190872
$975$	−5.15551	−0.165108
$976$	−19.1637	−0.613416
$977$	33.4345	1.06967	0.534833	−	0.844958i	$-0.320375\pi$
$977$	33.4345	1.06967	0.534833	+	0.844958i	$0.320375\pi$
$978$	−25.2927	−0.808771
$979$	−31.8627	−1.01834
$980$	−19.1876	−0.612925
$981$	12.9933	0.414844
$982$	25.7833	0.822779
$983$	8.78365	0.280155	0.140077	−	0.990141i	$-0.455265\pi$
$983$	8.78365	0.280155	0.140077	+	0.990141i	$0.455265\pi$
$984$	3.82711	0.122004
$985$	−17.3102	−0.551549
$986$	3.69347	0.117624
$987$	11.1910	0.356212
$988$	6.85452	0.218071
$989$	3.37144	0.107205
$990$	−29.3539	−0.932928
$991$	14.8061	0.470330	0.235165	−	0.971955i	$-0.424437\pi$
$991$	14.8061	0.470330	0.235165	+	0.971955i	$0.424437\pi$
$992$	8.00565	0.254180
$993$	−33.5823	−1.06570
$994$	−38.3511	−1.21642
$995$	7.13120	0.226074
$996$	−15.3391	−0.486037
$997$	60.7876	1.92516	0.962581	−	0.270993i	$-0.0873521\pi$
$997$	60.7876	1.92516	0.962581	+	0.270993i	$0.0873521\pi$
$998$	−12.1374	−0.384204
$999$	3.88333	0.122863

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-1.79771 q^{2} +1.00000 q^{3} +1.23177 q^{4} +3.18677 q^{5} -1.79771 q^{6} +1.45324 q^{7} +1.38105 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.79771 q^{2} +1.00000 q^{3} +1.23177 q^{4} +3.18677 q^{5} -1.79771 q^{6} +1.45324 q^{7} +1.38105 q^{8} +1.00000 q^{9} -5.72890 q^{10} +5.12383 q^{11} +1.23177 q^{12} -1.00000 q^{13} -2.61251 q^{14} +3.18677 q^{15} -4.94628 q^{16} +2.85787 q^{17} -1.79771 q^{18} -5.56476 q^{19} +3.92538 q^{20} +1.45324 q^{21} -9.21117 q^{22} -4.19986 q^{23} +1.38105 q^{24} +5.15551 q^{25} +1.79771 q^{26} +1.00000 q^{27} +1.79006 q^{28} -0.718906 q^{29} -5.72890 q^{30} +1.30600 q^{31} +6.12989 q^{32} +5.12383 q^{33} -5.13763 q^{34} +4.63115 q^{35} +1.23177 q^{36} +3.88333 q^{37} +10.0038 q^{38} -1.00000 q^{39} +4.40109 q^{40} +2.77115 q^{41} -2.61251 q^{42} -0.802749 q^{43} +6.31139 q^{44} +3.18677 q^{45} +7.55015 q^{46} +7.70068 q^{47} -4.94628 q^{48} -4.88809 q^{49} -9.26813 q^{50} +2.85787 q^{51} -1.23177 q^{52} -0.798985 q^{53} -1.79771 q^{54} +16.3285 q^{55} +2.00700 q^{56} -5.56476 q^{57} +1.29239 q^{58} +7.71339 q^{59} +3.92538 q^{60} +3.87437 q^{61} -2.34782 q^{62} +1.45324 q^{63} -1.12723 q^{64} -3.18677 q^{65} -9.21117 q^{66} +1.20956 q^{67} +3.52025 q^{68} -4.19986 q^{69} -8.32548 q^{70} +14.6798 q^{71} +1.38105 q^{72} +4.93639 q^{73} -6.98112 q^{74} +5.15551 q^{75} -6.85452 q^{76} +7.44616 q^{77} +1.79771 q^{78} -0.0933822 q^{79} -15.7627 q^{80} +1.00000 q^{81} -4.98174 q^{82} -12.4528 q^{83} +1.79006 q^{84} +9.10738 q^{85} +1.44311 q^{86} -0.718906 q^{87} +7.07627 q^{88} -6.21854 q^{89} -5.72890 q^{90} -1.45324 q^{91} -5.17328 q^{92} +1.30600 q^{93} -13.8436 q^{94} -17.7336 q^{95} +6.12989 q^{96} +7.38889 q^{97} +8.78738 q^{98} +5.12383 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 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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