LMFDB - Embedded newform 4017.2.a.g.1.2

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:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-2.42509 q^{2} -1.00000 q^{3} +3.88107 q^{4} -0.736887 q^{5} +2.42509 q^{6} -2.40625 q^{7} -4.56178 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.42509 q^{2} -1.00000 q^{3} +3.88107 q^{4} -0.736887 q^{5} +2.42509 q^{6} -2.40625 q^{7} -4.56178 q^{8} +1.00000 q^{9} +1.78702 q^{10} -1.03214 q^{11} -3.88107 q^{12} -1.00000 q^{13} +5.83538 q^{14} +0.736887 q^{15} +3.30058 q^{16} -2.49183 q^{17} -2.42509 q^{18} +0.457503 q^{19} -2.85991 q^{20} +2.40625 q^{21} +2.50303 q^{22} +7.34494 q^{23} +4.56178 q^{24} -4.45700 q^{25} +2.42509 q^{26} -1.00000 q^{27} -9.33883 q^{28} +4.43011 q^{29} -1.78702 q^{30} -10.0926 q^{31} +1.11933 q^{32} +1.03214 q^{33} +6.04292 q^{34} +1.77313 q^{35} +3.88107 q^{36} -7.33903 q^{37} -1.10949 q^{38} +1.00000 q^{39} +3.36151 q^{40} -9.29467 q^{41} -5.83538 q^{42} +6.10317 q^{43} -4.00580 q^{44} -0.736887 q^{45} -17.8122 q^{46} +7.85456 q^{47} -3.30058 q^{48} -1.20996 q^{49} +10.8086 q^{50} +2.49183 q^{51} -3.88107 q^{52} +2.17459 q^{53} +2.42509 q^{54} +0.760567 q^{55} +10.9768 q^{56} -0.457503 q^{57} -10.7434 q^{58} -9.65000 q^{59} +2.85991 q^{60} +7.37742 q^{61} +24.4756 q^{62} -2.40625 q^{63} -9.31566 q^{64} +0.736887 q^{65} -2.50303 q^{66} -2.66784 q^{67} -9.67098 q^{68} -7.34494 q^{69} -4.30001 q^{70} -15.6595 q^{71} -4.56178 q^{72} +2.29765 q^{73} +17.7978 q^{74} +4.45700 q^{75} +1.77560 q^{76} +2.48358 q^{77} -2.42509 q^{78} -15.5068 q^{79} -2.43216 q^{80} +1.00000 q^{81} +22.5404 q^{82} +9.92650 q^{83} +9.33883 q^{84} +1.83620 q^{85} -14.8007 q^{86} -4.43011 q^{87} +4.70837 q^{88} +17.7002 q^{89} +1.78702 q^{90} +2.40625 q^{91} +28.5063 q^{92} +10.0926 q^{93} -19.0480 q^{94} -0.337128 q^{95} -1.11933 q^{96} -5.44562 q^{97} +2.93426 q^{98} -1.03214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.42509	−1.71480	−0.857400	−	0.514651i	$-0.827921\pi$
$2$	−2.42509	−1.71480	−0.857400	+	0.514651i	$0.827921\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.88107	1.94054
$5$	−0.736887	−0.329546	−0.164773	−	0.986332i	$-0.552689\pi$
$5$	−0.736887	−0.329546	−0.164773	+	0.986332i	$0.552689\pi$
$6$	2.42509	0.990040
$7$	−2.40625	−0.909477	−0.454739	−	0.890625i	$-0.650267\pi$
$7$	−2.40625	−0.909477	−0.454739	+	0.890625i	$0.650267\pi$
$8$	−4.56178	−1.61283
$9$	1.00000	0.333333
$10$	1.78702	0.565105
$11$	−1.03214	−0.311201	−0.155600	−	0.987820i	$-0.549731\pi$
$11$	−1.03214	−0.311201	−0.155600	+	0.987820i	$0.549731\pi$
$12$	−3.88107	−1.12037
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	5.83538	1.55957
$15$	0.736887	0.190263
$16$	3.30058	0.825146
$17$	−2.49183	−0.604358	−0.302179	−	0.953251i	$-0.597714\pi$
$17$	−2.49183	−0.604358	−0.302179	+	0.953251i	$0.597714\pi$
$18$	−2.42509	−0.571600
$19$	0.457503	0.104958	0.0524792	−	0.998622i	$-0.483288\pi$
$19$	0.457503	0.104958	0.0524792	+	0.998622i	$0.483288\pi$
$20$	−2.85991	−0.639496
$21$	2.40625	0.525087
$22$	2.50303	0.533647
$23$	7.34494	1.53153	0.765763	−	0.643123i	$-0.222361\pi$
$23$	7.34494	1.53153	0.765763	+	0.643123i	$0.222361\pi$
$24$	4.56178	0.931169
$25$	−4.45700	−0.891400
$26$	2.42509	0.475600
$27$	−1.00000	−0.192450
$28$	−9.33883	−1.76487
$29$	4.43011	0.822652	0.411326	−	0.911488i	$-0.365066\pi$
$29$	4.43011	0.822652	0.411326	+	0.911488i	$0.365066\pi$
$30$	−1.78702	−0.326263
$31$	−10.0926	−1.81269	−0.906347	−	0.422535i	$-0.861140\pi$
$31$	−10.0926	−1.81269	−0.906347	+	0.422535i	$0.861140\pi$
$32$	1.11933	0.197872
$33$	1.03214	0.179672
$34$	6.04292	1.03635
$35$	1.77313	0.299714
$36$	3.88107	0.646846
$37$	−7.33903	−1.20653	−0.603265	−	0.797541i	$-0.706134\pi$
$37$	−7.33903	−1.20653	−0.603265	+	0.797541i	$0.706134\pi$
$38$	−1.10949	−0.179983
$39$	1.00000	0.160128
$40$	3.36151	0.531502
$41$	−9.29467	−1.45158	−0.725792	−	0.687914i	$-0.758527\pi$
$41$	−9.29467	−1.45158	−0.725792	+	0.687914i	$0.758527\pi$
$42$	−5.83538	−0.900419
$43$	6.10317	0.930724	0.465362	−	0.885120i	$-0.345924\pi$
$43$	6.10317	0.930724	0.465362	+	0.885120i	$0.345924\pi$
$44$	−4.00580	−0.603896
$45$	−0.736887	−0.109849
$46$	−17.8122	−2.62626
$47$	7.85456	1.14570	0.572852	−	0.819659i	$-0.305837\pi$
$47$	7.85456	1.14570	0.572852	+	0.819659i	$0.305837\pi$
$48$	−3.30058	−0.476398
$49$	−1.20996	−0.172851
$50$	10.8086	1.52857
$51$	2.49183	0.348926
$52$	−3.88107	−0.538208
$53$	2.17459	0.298703	0.149352	−	0.988784i	$-0.452281\pi$
$53$	2.17459	0.298703	0.149352	+	0.988784i	$0.452281\pi$
$54$	2.42509	0.330013
$55$	0.760567	0.102555
$56$	10.9768	1.46683
$57$	−0.457503	−0.0605978
$58$	−10.7434	−1.41068
$59$	−9.65000	−1.25632	−0.628161	−	0.778083i	$-0.716192\pi$
$59$	−9.65000	−1.25632	−0.628161	+	0.778083i	$0.716192\pi$
$60$	2.85991	0.369213
$61$	7.37742	0.944582	0.472291	−	0.881443i	$-0.343427\pi$
$61$	7.37742	0.944582	0.472291	+	0.881443i	$0.343427\pi$
$62$	24.4756	3.10840
$63$	−2.40625	−0.303159
$64$	−9.31566	−1.16446
$65$	0.736887	0.0913995
$66$	−2.50303	−0.308101
$67$	−2.66784	−0.325928	−0.162964	−	0.986632i	$-0.552105\pi$
$67$	−2.66784	−0.325928	−0.162964	+	0.986632i	$0.552105\pi$
$68$	−9.67098	−1.17278
$69$	−7.34494	−0.884227
$70$	−4.30001	−0.513950
$71$	−15.6595	−1.85844	−0.929218	−	0.369533i	$-0.879518\pi$
$71$	−15.6595	−1.85844	−0.929218	+	0.369533i	$0.879518\pi$
$72$	−4.56178	−0.537610
$73$	2.29765	0.268920	0.134460	−	0.990919i	$-0.457070\pi$
$73$	2.29765	0.268920	0.134460	+	0.990919i	$0.457070\pi$
$74$	17.7978	2.06896
$75$	4.45700	0.514650
$76$	1.77560	0.203676
$77$	2.48358	0.283030
$78$	−2.42509	−0.274588
$79$	−15.5068	−1.74465	−0.872327	−	0.488924i	$-0.837390\pi$
$79$	−15.5068	−1.74465	−0.872327	+	0.488924i	$0.837390\pi$
$80$	−2.43216	−0.271923
$81$	1.00000	0.111111
$82$	22.5404	2.48918
$83$	9.92650	1.08958	0.544788	−	0.838574i	$-0.316610\pi$
$83$	9.92650	1.08958	0.544788	+	0.838574i	$0.316610\pi$
$84$	9.33883	1.01895
$85$	1.83620	0.199164
$86$	−14.8007	−1.59600
$87$	−4.43011	−0.474958
$88$	4.70837	0.501914
$89$	17.7002	1.87622	0.938109	−	0.346340i	$-0.112576\pi$
$89$	17.7002	1.87622	0.938109	+	0.346340i	$0.112576\pi$
$90$	1.78702	0.188368
$91$	2.40625	0.252244
$92$	28.5063	2.97198
$93$	10.0926	1.04656
$94$	−19.0480	−1.96465
$95$	−0.337128	−0.0345886
$96$	−1.11933	−0.114242
$97$	−5.44562	−0.552919	−0.276460	−	0.961026i	$-0.589161\pi$
$97$	−5.44562	−0.552919	−0.276460	+	0.961026i	$0.589161\pi$
$98$	2.93426	0.296405
$99$	−1.03214	−0.103734
$100$	−17.2979	−1.72979
$101$	−5.00434	−0.497951	−0.248975	−	0.968510i	$-0.580094\pi$
$101$	−5.00434	−0.497951	−0.248975	+	0.968510i	$0.580094\pi$
$102$	−6.04292	−0.598339
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	4.56178	0.447319
$105$	−1.77313	−0.173040
$106$	−5.27359	−0.512216
$107$	0.832788	0.0805086	0.0402543	−	0.999189i	$-0.487183\pi$
$107$	0.832788	0.0805086	0.0402543	+	0.999189i	$0.487183\pi$
$108$	−3.88107	−0.373456
$109$	3.59843	0.344667	0.172333	−	0.985039i	$-0.444869\pi$
$109$	3.59843	0.344667	0.172333	+	0.985039i	$0.444869\pi$
$110$	−1.84445	−0.175861
$111$	7.33903	0.696590
$112$	−7.94203	−0.750451
$113$	6.39659	0.601741	0.300870	−	0.953665i	$-0.402723\pi$
$113$	6.39659	0.601741	0.300870	+	0.953665i	$0.402723\pi$
$114$	1.10949	0.103913
$115$	−5.41239	−0.504708
$116$	17.1936	1.59639
$117$	−1.00000	−0.0924500
$118$	23.4021	2.15434
$119$	5.99597	0.549650
$120$	−3.36151	−0.306863
$121$	−9.93470	−0.903154
$122$	−17.8909	−1.61977
$123$	9.29467	0.838072
$124$	−39.1703	−3.51760
$125$	6.96874	0.623303
$126$	5.83538	0.519857
$127$	−2.96803	−0.263370	−0.131685	−	0.991292i	$-0.542039\pi$
$127$	−2.96803	−0.263370	−0.131685	+	0.991292i	$0.542039\pi$
$128$	20.3527	1.79894
$129$	−6.10317	−0.537354
$130$	−1.78702	−0.156732
$131$	−6.59312	−0.576043	−0.288022	−	0.957624i	$-0.592998\pi$
$131$	−6.59312	−0.576043	−0.288022	+	0.957624i	$0.592998\pi$
$132$	4.00580	0.348660
$133$	−1.10087	−0.0954573
$134$	6.46975	0.558901
$135$	0.736887	0.0634211
$136$	11.3672	0.974728
$137$	−13.5821	−1.16039	−0.580197	−	0.814476i	$-0.697024\pi$
$137$	−13.5821	−1.16039	−0.580197	+	0.814476i	$0.697024\pi$
$138$	17.8122	1.51627
$139$	−0.100655	−0.00853747	−0.00426873	−	0.999991i	$-0.501359\pi$
$139$	−0.100655	−0.00853747	−0.00426873	+	0.999991i	$0.501359\pi$
$140$	6.88166	0.581607
$141$	−7.85456	−0.661473
$142$	37.9756	3.18684
$143$	1.03214	0.0863116
$144$	3.30058	0.275049
$145$	−3.26449	−0.271101
$146$	−5.57202	−0.461144
$147$	1.20996	0.0997957
$148$	−28.4833	−2.34132
$149$	7.87718	0.645323	0.322662	−	0.946514i	$-0.395422\pi$
$149$	7.87718	0.645323	0.322662	+	0.946514i	$0.395422\pi$
$150$	−10.8086	−0.882521
$151$	0.103266	0.00840365	0.00420183	−	0.999991i	$-0.498663\pi$
$151$	0.103266	0.00840365	0.00420183	+	0.999991i	$0.498663\pi$
$152$	−2.08703	−0.169280
$153$	−2.49183	−0.201453
$154$	−6.02291	−0.485340
$155$	7.43714	0.597365
$156$	3.88107	0.310735
$157$	6.88898	0.549800	0.274900	−	0.961473i	$-0.411355\pi$
$157$	6.88898	0.549800	0.274900	+	0.961473i	$0.411355\pi$
$158$	37.6055	2.99173
$159$	−2.17459	−0.172457
$160$	−0.824823	−0.0652080
$161$	−17.6738	−1.39289
$162$	−2.42509	−0.190533
$163$	8.76839	0.686793	0.343397	−	0.939190i	$-0.388422\pi$
$163$	8.76839	0.686793	0.343397	+	0.939190i	$0.388422\pi$
$164$	−36.0733	−2.81685
$165$	−0.760567	−0.0592101
$166$	−24.0727	−1.86840
$167$	−13.9402	−1.07873	−0.539364	−	0.842072i	$-0.681335\pi$
$167$	−13.9402	−1.07873	−0.539364	+	0.842072i	$0.681335\pi$
$168$	−10.9768	−0.846877
$169$	1.00000	0.0769231
$170$	−4.45295	−0.341526
$171$	0.457503	0.0349861
$172$	23.6868	1.80610
$173$	−22.7134	−1.72687	−0.863434	−	0.504462i	$-0.831691\pi$
$173$	−22.7134	−1.72687	−0.863434	+	0.504462i	$0.831691\pi$
$174$	10.7434	0.814458
$175$	10.7247	0.810708
$176$	−3.40665	−0.256786
$177$	9.65000	0.725338
$178$	−42.9246	−3.21734
$179$	−0.201038	−0.0150263	−0.00751313	−	0.999972i	$-0.502392\pi$
$179$	−0.201038	−0.0150263	−0.00751313	+	0.999972i	$0.502392\pi$
$180$	−2.85991	−0.213165
$181$	−17.3415	−1.28899	−0.644493	−	0.764610i	$-0.722931\pi$
$181$	−17.3415	−1.28899	−0.644493	+	0.764610i	$0.722931\pi$
$182$	−5.83538	−0.432547
$183$	−7.37742	−0.545355
$184$	−33.5060	−2.47009
$185$	5.40804	0.397607
$186$	−24.4756	−1.79464
$187$	2.57191	0.188077
$188$	30.4841	2.22328
$189$	2.40625	0.175029
$190$	0.817567	0.0593125
$191$	−17.2577	−1.24872	−0.624360	−	0.781137i	$-0.714640\pi$
$191$	−17.2577	−1.24872	−0.624360	+	0.781137i	$0.714640\pi$
$192$	9.31566	0.672300
$193$	−11.3979	−0.820437	−0.410219	−	0.911987i	$-0.634548\pi$
$193$	−11.3979	−0.820437	−0.410219	+	0.911987i	$0.634548\pi$
$194$	13.2061	0.948145
$195$	−0.736887	−0.0527696
$196$	−4.69594	−0.335424
$197$	27.4912	1.95866	0.979332	−	0.202259i	$-0.0648281\pi$
$197$	27.4912	1.95866	0.979332	+	0.202259i	$0.0648281\pi$
$198$	2.50303	0.177882
$199$	7.57034	0.536647	0.268324	−	0.963329i	$-0.413530\pi$
$199$	7.57034	0.536647	0.268324	+	0.963329i	$0.413530\pi$
$200$	20.3318	1.43768
$201$	2.66784	0.188175
$202$	12.1360	0.853885
$203$	−10.6600	−0.748183
$204$	9.67098	0.677104
$205$	6.84912	0.478363
$206$	−2.42509	−0.168964
$207$	7.34494	0.510509
$208$	−3.30058	−0.228854
$209$	−0.472206	−0.0326631
$210$	4.30001	0.296729
$211$	6.51166	0.448281	0.224141	−	0.974557i	$-0.428042\pi$
$211$	6.51166	0.448281	0.224141	+	0.974557i	$0.428042\pi$
$212$	8.43976	0.579645
$213$	15.6595	1.07297
$214$	−2.01959	−0.138056
$215$	−4.49734	−0.306716
$216$	4.56178	0.310390
$217$	24.2854	1.64860
$218$	−8.72651	−0.591034
$219$	−2.29765	−0.155261
$220$	2.95182	0.199011
$221$	2.49183	0.167619
$222$	−17.7978	−1.19451
$223$	4.59451	0.307671	0.153835	−	0.988096i	$-0.450837\pi$
$223$	4.59451	0.307671	0.153835	+	0.988096i	$0.450837\pi$
$224$	−2.69340	−0.179960
$225$	−4.45700	−0.297133
$226$	−15.5123	−1.03186
$227$	−6.31995	−0.419470	−0.209735	−	0.977758i	$-0.567260\pi$
$227$	−6.31995	−0.419470	−0.209735	+	0.977758i	$0.567260\pi$
$228$	−1.77560	−0.117592
$229$	2.77737	0.183534	0.0917670	−	0.995781i	$-0.470748\pi$
$229$	2.77737	0.183534	0.0917670	+	0.995781i	$0.470748\pi$
$230$	13.1255	0.865473
$231$	−2.48358	−0.163407
$232$	−20.2092	−1.32680
$233$	12.6057	0.825830	0.412915	−	0.910770i	$-0.364511\pi$
$233$	12.6057	0.825830	0.412915	+	0.910770i	$0.364511\pi$
$234$	2.42509	0.158533
$235$	−5.78792	−0.377562
$236$	−37.4524	−2.43794
$237$	15.5068	1.00728
$238$	−14.5408	−0.942539
$239$	8.80126	0.569306	0.284653	−	0.958631i	$-0.408122\pi$
$239$	8.80126	0.569306	0.284653	+	0.958631i	$0.408122\pi$
$240$	2.43216	0.156995
$241$	−11.1193	−0.716258	−0.358129	−	0.933672i	$-0.616585\pi$
$241$	−11.1193	−0.716258	−0.358129	+	0.933672i	$0.616585\pi$
$242$	24.0926	1.54873
$243$	−1.00000	−0.0641500
$244$	28.6323	1.83300
$245$	0.891602	0.0569624
$246$	−22.5404	−1.43713
$247$	−0.457503	−0.0291102
$248$	46.0404	2.92357
$249$	−9.92650	−0.629067
$250$	−16.8998	−1.06884
$251$	−14.2098	−0.896917	−0.448458	−	0.893804i	$-0.648027\pi$
$251$	−14.2098	−0.896917	−0.448458	+	0.893804i	$0.648027\pi$
$252$	−9.33883	−0.588291
$253$	−7.58098	−0.476612
$254$	7.19776	0.451627
$255$	−1.83620	−0.114987
$256$	−30.7258	−1.92036
$257$	17.9852	1.12188	0.560942	−	0.827855i	$-0.310439\pi$
$257$	17.9852	1.12188	0.560942	+	0.827855i	$0.310439\pi$
$258$	14.8007	0.921454
$259$	17.6596	1.09731
$260$	2.85991	0.177364
$261$	4.43011	0.274217
$262$	15.9889	0.987799
$263$	−17.5106	−1.07975	−0.539876	−	0.841745i	$-0.681529\pi$
$263$	−17.5106	−1.07975	−0.539876	+	0.841745i	$0.681529\pi$
$264$	−4.70837	−0.289780
$265$	−1.60243	−0.0984364
$266$	2.66971	0.163690
$267$	−17.7002	−1.08323
$268$	−10.3541	−0.632475
$269$	20.0866	1.22470	0.612350	−	0.790587i	$-0.290224\pi$
$269$	20.0866	1.22470	0.612350	+	0.790587i	$0.290224\pi$
$270$	−1.78702	−0.108754
$271$	9.58458	0.582222	0.291111	−	0.956689i	$-0.405975\pi$
$271$	9.58458	0.582222	0.291111	+	0.956689i	$0.405975\pi$
$272$	−8.22450	−0.498684
$273$	−2.40625	−0.145633
$274$	32.9378	1.98984
$275$	4.60023	0.277404
$276$	−28.5063	−1.71588
$277$	−7.60414	−0.456889	−0.228444	−	0.973557i	$-0.573364\pi$
$277$	−7.60414	−0.456889	−0.228444	+	0.973557i	$0.573364\pi$
$278$	0.244098	0.0146400
$279$	−10.0926	−0.604231
$280$	−8.08864	−0.483389
$281$	−17.2223	−1.02740	−0.513698	−	0.857971i	$-0.671725\pi$
$281$	−17.2223	−1.02740	−0.513698	+	0.857971i	$0.671725\pi$
$282$	19.0480	1.13429
$283$	21.8076	1.29633	0.648165	−	0.761500i	$-0.275537\pi$
$283$	21.8076	1.29633	0.648165	+	0.761500i	$0.275537\pi$
$284$	−60.7755	−3.60636
$285$	0.337128	0.0199697
$286$	−2.50303	−0.148007
$287$	22.3653	1.32018
$288$	1.11933	0.0659574
$289$	−10.7908	−0.634751
$290$	7.91670	0.464884
$291$	5.44562	0.319228
$292$	8.91736	0.521849
$293$	5.54431	0.323902	0.161951	−	0.986799i	$-0.448221\pi$
$293$	5.54431	0.323902	0.161951	+	0.986799i	$0.448221\pi$
$294$	−2.93426	−0.171130
$295$	7.11096	0.414016
$296$	33.4790	1.94593
$297$	1.03214	0.0598906
$298$	−19.1029	−1.10660
$299$	−7.34494	−0.424769
$300$	17.2979	0.998697
$301$	−14.6857	−0.846472
$302$	−0.250429	−0.0144106
$303$	5.00434	0.287492
$304$	1.51003	0.0866060
$305$	−5.43632	−0.311283
$306$	6.04292	0.345451
$307$	−20.1990	−1.15282	−0.576409	−	0.817161i	$-0.695546\pi$
$307$	−20.1990	−1.15282	−0.576409	+	0.817161i	$0.695546\pi$
$308$	9.63895	0.549230
$309$	−1.00000	−0.0568880
$310$	−18.0357	−1.02436
$311$	32.8801	1.86446	0.932230	−	0.361867i	$-0.117861\pi$
$311$	32.8801	1.86446	0.932230	+	0.361867i	$0.117861\pi$
$312$	−4.56178	−0.258260
$313$	25.4786	1.44013	0.720067	−	0.693904i	$-0.244111\pi$
$313$	25.4786	1.44013	0.720067	+	0.693904i	$0.244111\pi$
$314$	−16.7064	−0.942797
$315$	1.77313	0.0999048
$316$	−60.1831	−3.38556
$317$	−33.6684	−1.89100	−0.945502	−	0.325617i	$-0.894428\pi$
$317$	−33.6684	−1.89100	−0.945502	+	0.325617i	$0.894428\pi$
$318$	5.27359	0.295728
$319$	−4.57248	−0.256010
$320$	6.86458	0.383742
$321$	−0.832788	−0.0464817
$322$	42.8605	2.38852
$323$	−1.14002	−0.0634325
$324$	3.88107	0.215615
$325$	4.45700	0.247230
$326$	−21.2642	−1.17771
$327$	−3.59843	−0.198993
$328$	42.4002	2.34116
$329$	−18.9000	−1.04199
$330$	1.84445	0.101533
$331$	6.72901	0.369860	0.184930	−	0.982752i	$-0.440794\pi$
$331$	6.72901	0.369860	0.184930	+	0.982752i	$0.440794\pi$
$332$	38.5255	2.11436
$333$	−7.33903	−0.402177
$334$	33.8064	1.84980
$335$	1.96589	0.107408
$336$	7.94203	0.433273
$337$	19.6151	1.06850	0.534250	−	0.845327i	$-0.320594\pi$
$337$	19.6151	1.06850	0.534250	+	0.845327i	$0.320594\pi$
$338$	−2.42509	−0.131908
$339$	−6.39659	−0.347415
$340$	7.12642	0.386484
$341$	10.4170	0.564111
$342$	−1.10949	−0.0599942
$343$	19.7552	1.06668
$344$	−27.8413	−1.50110
$345$	5.41239	0.291393
$346$	55.0821	2.96123
$347$	24.7115	1.32658	0.663292	−	0.748361i	$-0.269159\pi$
$347$	24.7115	1.32658	0.663292	+	0.748361i	$0.269159\pi$
$348$	−17.1936	−0.921674
$349$	−15.7216	−0.841558	−0.420779	−	0.907163i	$-0.638243\pi$
$349$	−15.7216	−0.841558	−0.420779	+	0.907163i	$0.638243\pi$
$350$	−26.0083	−1.39020
$351$	1.00000	0.0533761
$352$	−1.15531	−0.0615780
$353$	2.30377	0.122617	0.0613087	−	0.998119i	$-0.480473\pi$
$353$	2.30377	0.122617	0.0613087	+	0.998119i	$0.480473\pi$
$354$	−23.4021	−1.24381
$355$	11.5392	0.612439
$356$	68.6958	3.64087
$357$	−5.99597	−0.317341
$358$	0.487535	0.0257670
$359$	34.5813	1.82513	0.912565	−	0.408932i	$-0.134099\pi$
$359$	34.5813	1.82513	0.912565	+	0.408932i	$0.134099\pi$
$360$	3.36151	0.177167
$361$	−18.7907	−0.988984
$362$	42.0548	2.21035
$363$	9.93470	0.521436
$364$	9.33883	0.489488
$365$	−1.69311	−0.0886215
$366$	17.8909	0.935174
$367$	7.60757	0.397112	0.198556	−	0.980090i	$-0.436375\pi$
$367$	7.60757	0.397112	0.198556	+	0.980090i	$0.436375\pi$
$368$	24.2426	1.26373
$369$	−9.29467	−0.483861
$370$	−13.1150	−0.681816
$371$	−5.23262	−0.271664
$372$	39.1703	2.03089
$373$	−0.770957	−0.0399186	−0.0199593	−	0.999801i	$-0.506354\pi$
$373$	−0.770957	−0.0399186	−0.0199593	+	0.999801i	$0.506354\pi$
$374$	−6.23712	−0.322514
$375$	−6.96874	−0.359864
$376$	−35.8307	−1.84783
$377$	−4.43011	−0.228163
$378$	−5.83538	−0.300140
$379$	27.9793	1.43720	0.718600	−	0.695423i	$-0.244783\pi$
$379$	27.9793	1.43720	0.718600	+	0.695423i	$0.244783\pi$
$380$	−1.30842	−0.0671205
$381$	2.96803	0.152057
$382$	41.8514	2.14130
$383$	9.98764	0.510345	0.255172	−	0.966896i	$-0.417868\pi$
$383$	9.98764	0.510345	0.255172	+	0.966896i	$0.417868\pi$
$384$	−20.3527	−1.03862
$385$	−1.83012	−0.0932713
$386$	27.6409	1.40689
$387$	6.10317	0.310241
$388$	−21.1349	−1.07296
$389$	6.00321	0.304375	0.152188	−	0.988352i	$-0.451368\pi$
$389$	6.00321	0.304375	0.152188	+	0.988352i	$0.451368\pi$
$390$	1.78702	0.0904892
$391$	−18.3024	−0.925590
$392$	5.51956	0.278780
$393$	6.59312	0.332579
$394$	−66.6686	−3.35872
$395$	11.4268	0.574943
$396$	−4.00580	−0.201299
$397$	−28.1271	−1.41166	−0.705830	−	0.708381i	$-0.749426\pi$
$397$	−28.1271	−1.41166	−0.705830	+	0.708381i	$0.749426\pi$
$398$	−18.3588	−0.920242
$399$	1.10087	0.0551123
$400$	−14.7107	−0.735534
$401$	30.8661	1.54138	0.770689	−	0.637211i	$-0.219912\pi$
$401$	30.8661	1.54138	0.770689	+	0.637211i	$0.219912\pi$
$402$	−6.46975	−0.322682
$403$	10.0926	0.502751
$404$	−19.4222	−0.966291
$405$	−0.736887	−0.0366162
$406$	25.8514	1.28298
$407$	7.57488	0.375473
$408$	−11.3672	−0.562759
$409$	−36.5462	−1.80709	−0.903547	−	0.428488i	$-0.859046\pi$
$409$	−36.5462	−1.80709	−0.903547	+	0.428488i	$0.859046\pi$
$410$	−16.6098	−0.820297
$411$	13.5821	0.669954
$412$	3.88107	0.191207
$413$	23.2203	1.14260
$414$	−17.8122	−0.875420
$415$	−7.31471	−0.359065
$416$	−1.11933	−0.0548799
$417$	0.100655	0.00492911
$418$	1.14514	0.0560107
$419$	28.4145	1.38814	0.694068	−	0.719909i	$-0.255816\pi$
$419$	28.4145	1.38814	0.694068	+	0.719909i	$0.255816\pi$
$420$	−6.88166	−0.335791
$421$	23.7971	1.15980	0.579899	−	0.814688i	$-0.303092\pi$
$421$	23.7971	1.15980	0.579899	+	0.814688i	$0.303092\pi$
$422$	−15.7914	−0.768713
$423$	7.85456	0.381902
$424$	−9.92001	−0.481758
$425$	11.1061	0.538725
$426$	−37.9756	−1.83992
$427$	−17.7519	−0.859076
$428$	3.23211	0.156230
$429$	−1.03214	−0.0498320
$430$	10.9065	0.525957
$431$	30.5617	1.47210	0.736052	−	0.676925i	$-0.236688\pi$
$431$	30.5617	1.47210	0.736052	+	0.676925i	$0.236688\pi$
$432$	−3.30058	−0.158799
$433$	29.3458	1.41027	0.705135	−	0.709073i	$-0.250887\pi$
$433$	29.3458	1.41027	0.705135	+	0.709073i	$0.250887\pi$
$434$	−58.8944	−2.82702
$435$	3.26449	0.156520
$436$	13.9658	0.668838
$437$	3.36033	0.160747
$438$	5.57202	0.266242
$439$	17.6177	0.840847	0.420423	−	0.907328i	$-0.361882\pi$
$439$	17.6177	0.840847	0.420423	+	0.907328i	$0.361882\pi$
$440$	−3.46954	−0.165404
$441$	−1.20996	−0.0576171
$442$	−6.04292	−0.287433
$443$	29.4659	1.39996	0.699982	−	0.714160i	$-0.253191\pi$
$443$	29.4659	1.39996	0.699982	+	0.714160i	$0.253191\pi$
$444$	28.4833	1.35176
$445$	−13.0430	−0.618300
$446$	−11.1421	−0.527594
$447$	−7.87718	−0.372578
$448$	22.4158	1.05905
$449$	0.647454	0.0305553	0.0152776	−	0.999883i	$-0.495137\pi$
$449$	0.647454	0.0305553	0.0152776	+	0.999883i	$0.495137\pi$
$450$	10.8086	0.509524
$451$	9.59337	0.451734
$452$	24.8256	1.16770
$453$	−0.103266	−0.00485185
$454$	15.3265	0.719306
$455$	−1.77313	−0.0831258
$456$	2.08703	0.0977340
$457$	−24.7721	−1.15879	−0.579395	−	0.815047i	$-0.696711\pi$
$457$	−24.7721	−1.15879	−0.579395	+	0.815047i	$0.696711\pi$
$458$	−6.73539	−0.314724
$459$	2.49183	0.116309
$460$	−21.0059	−0.979404
$461$	−14.9311	−0.695413	−0.347706	−	0.937604i	$-0.613039\pi$
$461$	−14.9311	−0.695413	−0.347706	+	0.937604i	$0.613039\pi$
$462$	6.02291	0.280211
$463$	8.71352	0.404951	0.202476	−	0.979287i	$-0.435101\pi$
$463$	8.71352	0.404951	0.202476	+	0.979287i	$0.435101\pi$
$464$	14.6220	0.678807
$465$	−7.43714	−0.344889
$466$	−30.5701	−1.41613
$467$	31.8123	1.47210	0.736050	−	0.676928i	$-0.236689\pi$
$467$	31.8123	1.47210	0.736050	+	0.676928i	$0.236689\pi$
$468$	−3.88107	−0.179403
$469$	6.41948	0.296424
$470$	14.0362	0.647443
$471$	−6.88898	−0.317427
$472$	44.0211	2.02624
$473$	−6.29930	−0.289642
$474$	−37.6055	−1.72728
$475$	−2.03909	−0.0935599
$476$	23.2708	1.06662
$477$	2.17459	0.0995678
$478$	−21.3439	−0.976246
$479$	34.0736	1.55686	0.778431	−	0.627730i	$-0.216016\pi$
$479$	34.0736	1.55686	0.778431	+	0.627730i	$0.216016\pi$
$480$	0.824823	0.0376478
$481$	7.33903	0.334631
$482$	26.9654	1.22824
$483$	17.6738	0.804184
$484$	−38.5573	−1.75260
$485$	4.01281	0.182212
$486$	2.42509	0.110004
$487$	38.4784	1.74362	0.871810	−	0.489844i	$-0.162946\pi$
$487$	38.4784	1.74362	0.871810	+	0.489844i	$0.162946\pi$
$488$	−33.6542	−1.52345
$489$	−8.76839	−0.396520
$490$	−2.16222	−0.0976790
$491$	18.6505	0.841686	0.420843	−	0.907134i	$-0.361734\pi$
$491$	18.6505	0.841686	0.420843	+	0.907134i	$0.361734\pi$
$492$	36.0733	1.62631
$493$	−11.0391	−0.497176
$494$	1.10949	0.0499182
$495$	0.760567	0.0341850
$496$	−33.3116	−1.49574
$497$	37.6806	1.69020
$498$	24.0727	1.07872
$499$	40.2325	1.80105	0.900527	−	0.434800i	$-0.143181\pi$
$499$	40.2325	1.80105	0.900527	+	0.434800i	$0.143181\pi$
$500$	27.0462	1.20954
$501$	13.9402	0.622804
$502$	34.4602	1.53803
$503$	5.68533	0.253497	0.126748	−	0.991935i	$-0.459546\pi$
$503$	5.68533	0.253497	0.126748	+	0.991935i	$0.459546\pi$
$504$	10.9768	0.488944
$505$	3.68763	0.164098
$506$	18.3846	0.817294
$507$	−1.00000	−0.0444116
$508$	−11.5192	−0.511080
$509$	−41.5192	−1.84031	−0.920153	−	0.391559i	$-0.871936\pi$
$509$	−41.5192	−1.84031	−0.920153	+	0.391559i	$0.871936\pi$
$510$	4.45295	0.197180
$511$	−5.52873	−0.244577
$512$	33.8075	1.49409
$513$	−0.457503	−0.0201993
$514$	−43.6157	−1.92381
$515$	−0.736887	−0.0324711
$516$	−23.6868	−1.04275
$517$	−8.10697	−0.356544
$518$	−42.8261	−1.88167
$519$	22.7134	0.997008
$520$	−3.36151	−0.147412
$521$	42.2686	1.85182	0.925910	−	0.377743i	$-0.123300\pi$
$521$	42.2686	1.85182	0.925910	+	0.377743i	$0.123300\pi$
$522$	−10.7434	−0.470228
$523$	43.2537	1.89135	0.945677	−	0.325108i	$-0.105401\pi$
$523$	43.2537	1.89135	0.945677	+	0.325108i	$0.105401\pi$
$524$	−25.5884	−1.11783
$525$	−10.7247	−0.468062
$526$	42.4649	1.85156
$527$	25.1492	1.09552
$528$	3.40665	0.148255
$529$	30.9482	1.34557
$530$	3.88604	0.168799
$531$	−9.65000	−0.418774
$532$	−4.27255	−0.185238
$533$	9.29467	0.402597
$534$	42.9246	1.85753
$535$	−0.613670	−0.0265313
$536$	12.1701	0.525667
$537$	0.201038	0.00867542
$538$	−48.7118	−2.10011
$539$	1.24884	0.0537914
$540$	2.85991	0.123071
$541$	24.2506	1.04261	0.521306	−	0.853370i	$-0.325445\pi$
$541$	24.2506	1.04261	0.521306	+	0.853370i	$0.325445\pi$
$542$	−23.2435	−0.998394
$543$	17.3415	0.744196
$544$	−2.78920	−0.119586
$545$	−2.65163	−0.113583
$546$	5.83538	0.249731
$547$	21.9228	0.937350	0.468675	−	0.883371i	$-0.344731\pi$
$547$	21.9228	0.937350	0.468675	+	0.883371i	$0.344731\pi$
$548$	−52.7130	−2.25179
$549$	7.37742	0.314861
$550$	−11.1560	−0.475693
$551$	2.02679	0.0863442
$552$	33.5060	1.42611
$553$	37.3133	1.58672
$554$	18.4407	0.783472
$555$	−5.40804	−0.229558
$556$	−0.390650	−0.0165673
$557$	−18.3477	−0.777418	−0.388709	−	0.921361i	$-0.627079\pi$
$557$	−18.3477	−0.777418	−0.388709	+	0.921361i	$0.627079\pi$
$558$	24.4756	1.03613
$559$	−6.10317	−0.258136
$560$	5.85237	0.247308
$561$	−2.57191	−0.108586
$562$	41.7656	1.76178
$563$	−27.8999	−1.17584	−0.587920	−	0.808919i	$-0.700053\pi$
$563$	−27.8999	−1.17584	−0.587920	+	0.808919i	$0.700053\pi$
$564$	−30.4841	−1.28361
$565$	−4.71356	−0.198301
$566$	−52.8855	−2.22295
$567$	−2.40625	−0.101053
$568$	71.4349	2.99734
$569$	8.82944	0.370149	0.185075	−	0.982724i	$-0.440747\pi$
$569$	8.82944	0.370149	0.185075	+	0.982724i	$0.440747\pi$
$570$	−0.817567	−0.0342441
$571$	−25.3457	−1.06068	−0.530342	−	0.847784i	$-0.677936\pi$
$571$	−25.3457	−1.06068	−0.530342	+	0.847784i	$0.677936\pi$
$572$	4.00580	0.167491
$573$	17.2577	0.720949
$574$	−54.2380	−2.26385
$575$	−32.7364	−1.36520
$576$	−9.31566	−0.388152
$577$	−8.47434	−0.352791	−0.176396	−	0.984319i	$-0.556444\pi$
$577$	−8.47434	−0.352791	−0.176396	+	0.984319i	$0.556444\pi$
$578$	26.1686	1.08847
$579$	11.3979	0.473680
$580$	−12.6697	−0.526082
$581$	−23.8857	−0.990944
$582$	−13.2061	−0.547412
$583$	−2.24448	−0.0929567
$584$	−10.4814	−0.433723
$585$	0.736887	0.0304665
$586$	−13.4455	−0.555427
$587$	−45.1161	−1.86214	−0.931071	−	0.364838i	$-0.881124\pi$
$587$	−45.1161	−1.86214	−0.931071	+	0.364838i	$0.881124\pi$
$588$	4.69594	0.193657
$589$	−4.61742	−0.190257
$590$	−17.2447	−0.709954
$591$	−27.4912	−1.13084
$592$	−24.2231	−0.995563
$593$	−10.3606	−0.425458	−0.212729	−	0.977111i	$-0.568235\pi$
$593$	−10.3606	−0.425458	−0.212729	+	0.977111i	$0.568235\pi$
$594$	−2.50303	−0.102700
$595$	−4.41835	−0.181135
$596$	30.5719	1.25227
$597$	−7.57034	−0.309833
$598$	17.8122	0.728394
$599$	36.0892	1.47457	0.737283	−	0.675584i	$-0.236108\pi$
$599$	36.0892	1.47457	0.737283	+	0.675584i	$0.236108\pi$
$600$	−20.3318	−0.830043
$601$	−22.6755	−0.924954	−0.462477	−	0.886631i	$-0.653039\pi$
$601$	−22.6755	−0.924954	−0.462477	+	0.886631i	$0.653039\pi$
$602$	35.6143	1.45153
$603$	−2.66784	−0.108643
$604$	0.400782	0.0163076
$605$	7.32074	0.297631
$606$	−12.1360	−0.492991
$607$	5.17000	0.209844	0.104922	−	0.994480i	$-0.466541\pi$
$607$	5.17000	0.209844	0.104922	+	0.994480i	$0.466541\pi$
$608$	0.512099	0.0207684
$609$	10.6600	0.431964
$610$	13.1836	0.533788
$611$	−7.85456	−0.317761
$612$	−9.67098	−0.390926
$613$	13.0350	0.526478	0.263239	−	0.964731i	$-0.415209\pi$
$613$	13.0350	0.526478	0.263239	+	0.964731i	$0.415209\pi$
$614$	48.9845	1.97685
$615$	−6.84912	−0.276183
$616$	−11.3295	−0.456480
$617$	−13.8450	−0.557377	−0.278689	−	0.960381i	$-0.589900\pi$
$617$	−13.8450	−0.557377	−0.278689	+	0.960381i	$0.589900\pi$
$618$	2.42509	0.0975515
$619$	35.6195	1.43167	0.715834	−	0.698271i	$-0.246047\pi$
$619$	35.6195	1.43167	0.715834	+	0.698271i	$0.246047\pi$
$620$	28.8641	1.15921
$621$	−7.34494	−0.294742
$622$	−79.7373	−3.19717
$623$	−42.5911	−1.70638
$624$	3.30058	0.132129
$625$	17.1498	0.685993
$626$	−61.7879	−2.46954
$627$	0.472206	0.0188581
$628$	26.7366	1.06691
$629$	18.2876	0.729176
$630$	−4.30001	−0.171317
$631$	−33.6518	−1.33966	−0.669829	−	0.742515i	$-0.733633\pi$
$631$	−33.6518	−1.33966	−0.669829	+	0.742515i	$0.733633\pi$
$632$	70.7386	2.81383
$633$	−6.51166	−0.258815
$634$	81.6489	3.24269
$635$	2.18710	0.0867926
$636$	−8.43976	−0.334658
$637$	1.20996	0.0479403
$638$	11.0887	0.439005
$639$	−15.6595	−0.619478
$640$	−14.9976	−0.592832
$641$	17.7163	0.699752	0.349876	−	0.936796i	$-0.386224\pi$
$641$	17.7163	0.699752	0.349876	+	0.936796i	$0.386224\pi$
$642$	2.01959	0.0797068
$643$	15.8302	0.624282	0.312141	−	0.950036i	$-0.398954\pi$
$643$	15.8302	0.624282	0.312141	+	0.950036i	$0.398954\pi$
$644$	−68.5932	−2.70295
$645$	4.49734	0.177083
$646$	2.76466	0.108774
$647$	−37.1767	−1.46157	−0.730784	−	0.682608i	$-0.760845\pi$
$647$	−37.1767	−1.46157	−0.730784	+	0.682608i	$0.760845\pi$
$648$	−4.56178	−0.179203
$649$	9.96011	0.390969
$650$	−10.8086	−0.423949
$651$	−24.2854	−0.951821
$652$	34.0308	1.33275
$653$	−33.8815	−1.32589	−0.662944	−	0.748669i	$-0.730693\pi$
$653$	−33.8815	−1.32589	−0.662944	+	0.748669i	$0.730693\pi$
$654$	8.72651	0.341234
$655$	4.85838	0.189833
$656$	−30.6778	−1.19777
$657$	2.29765	0.0896400
$658$	45.8343	1.78681
$659$	−46.8908	−1.82661	−0.913303	−	0.407281i	$-0.866477\pi$
$659$	−46.8908	−1.82661	−0.913303	+	0.407281i	$0.866477\pi$
$660$	−2.95182	−0.114899
$661$	6.14243	0.238913	0.119456	−	0.992839i	$-0.461885\pi$
$661$	6.14243	0.238913	0.119456	+	0.992839i	$0.461885\pi$
$662$	−16.3185	−0.634235
$663$	−2.49183	−0.0967748
$664$	−45.2825	−1.75730
$665$	0.811215	0.0314575
$666$	17.7978	0.689652
$667$	32.5389	1.25991
$668$	−54.1031	−2.09331
$669$	−4.59451	−0.177634
$670$	−4.76747	−0.184183
$671$	−7.61450	−0.293955
$672$	2.69340	0.103900
$673$	5.76050	0.222051	0.111026	−	0.993818i	$-0.464586\pi$
$673$	5.76050	0.222051	0.111026	+	0.993818i	$0.464586\pi$
$674$	−47.5683	−1.83226
$675$	4.45700	0.171550
$676$	3.88107	0.149272
$677$	−17.2905	−0.664529	−0.332264	−	0.943186i	$-0.607813\pi$
$677$	−17.2905	−0.664529	−0.332264	+	0.943186i	$0.607813\pi$
$678$	15.5123	0.595747
$679$	13.1035	0.502867
$680$	−8.37633	−0.321217
$681$	6.31995	0.242181
$682$	−25.2622	−0.967338
$683$	−1.97981	−0.0757554	−0.0378777	−	0.999282i	$-0.512060\pi$
$683$	−1.97981	−0.0757554	−0.0378777	+	0.999282i	$0.512060\pi$
$684$	1.77560	0.0678919
$685$	10.0084	0.382403
$686$	−47.9082	−1.82914
$687$	−2.77737	−0.105963
$688$	20.1440	0.767983
$689$	−2.17459	−0.0828454
$690$	−13.1255	−0.499681
$691$	−38.9826	−1.48297	−0.741485	−	0.670970i	$-0.765878\pi$
$691$	−38.9826	−1.48297	−0.741485	+	0.670970i	$0.765878\pi$
$692$	−88.1524	−3.35105
$693$	2.48358	0.0943433
$694$	−59.9277	−2.27482
$695$	0.0741715	0.00281349
$696$	20.2092	0.766027
$697$	23.1608	0.877277
$698$	38.1263	1.44310
$699$	−12.6057	−0.476793
$700$	41.6232	1.57321
$701$	23.0210	0.869491	0.434746	−	0.900553i	$-0.356838\pi$
$701$	23.0210	0.869491	0.434746	+	0.900553i	$0.356838\pi$
$702$	−2.42509	−0.0915292
$703$	−3.35763	−0.126635
$704$	9.61502	0.362380
$705$	5.78792	0.217986
$706$	−5.58686	−0.210264
$707$	12.0417	0.452875
$708$	37.4524	1.40755
$709$	8.88665	0.333745	0.166873	−	0.985978i	$-0.446633\pi$
$709$	8.88665	0.333745	0.166873	+	0.985978i	$0.446633\pi$
$710$	−27.9837	−1.05021
$711$	−15.5068	−0.581551
$712$	−80.7444	−3.02602
$713$	−74.1299	−2.77619
$714$	14.5408	0.544175
$715$	−0.760567	−0.0284436
$716$	−0.780242	−0.0291590
$717$	−8.80126	−0.328689
$718$	−83.8628	−3.12973
$719$	8.63969	0.322206	0.161103	−	0.986938i	$-0.448495\pi$
$719$	8.63969	0.322206	0.161103	+	0.986938i	$0.448495\pi$
$720$	−2.43216	−0.0906411
$721$	−2.40625	−0.0896135
$722$	45.5692	1.69591
$723$	11.1193	0.413532
$724$	−67.3037	−2.50132
$725$	−19.7450	−0.733311
$726$	−24.0926	−0.894159
$727$	13.1985	0.489506	0.244753	−	0.969585i	$-0.421293\pi$
$727$	13.1985	0.489506	0.244753	+	0.969585i	$0.421293\pi$
$728$	−10.9768	−0.406826
$729$	1.00000	0.0370370
$730$	4.10595	0.151968
$731$	−15.2081	−0.562491
$732$	−28.6323	−1.05828
$733$	3.41978	0.126312	0.0631562	−	0.998004i	$-0.479883\pi$
$733$	3.41978	0.126312	0.0631562	+	0.998004i	$0.479883\pi$
$734$	−18.4491	−0.680967
$735$	−0.891602	−0.0328872
$736$	8.22145	0.303047
$737$	2.75357	0.101429
$738$	22.5404	0.829725
$739$	−7.57987	−0.278830	−0.139415	−	0.990234i	$-0.544522\pi$
$739$	−7.57987	−0.278830	−0.139415	+	0.990234i	$0.544522\pi$
$740$	20.9890	0.771570
$741$	0.457503	0.0168068
$742$	12.6896	0.465849
$743$	8.83628	0.324172	0.162086	−	0.986777i	$-0.448178\pi$
$743$	8.83628	0.324172	0.162086	+	0.986777i	$0.448178\pi$
$744$	−46.0404	−1.68792
$745$	−5.80459	−0.212664
$746$	1.86964	0.0684524
$747$	9.92650	0.363192
$748$	9.98177	0.364970
$749$	−2.00390	−0.0732208
$750$	16.8998	0.617094
$751$	32.8869	1.20006	0.600031	−	0.799977i	$-0.295155\pi$
$751$	32.8869	1.20006	0.600031	+	0.799977i	$0.295155\pi$
$752$	25.9246	0.945373
$753$	14.2098	0.517835
$754$	10.7434	0.391253
$755$	−0.0760952	−0.00276939
$756$	9.33883	0.339650
$757$	−19.2111	−0.698239	−0.349119	−	0.937078i	$-0.613519\pi$
$757$	−19.2111	−0.698239	−0.349119	+	0.937078i	$0.613519\pi$
$758$	−67.8524	−2.46451
$759$	7.58098	0.275172
$760$	1.53790	0.0557856
$761$	9.09738	0.329780	0.164890	−	0.986312i	$-0.447273\pi$
$761$	9.09738	0.329780	0.164890	+	0.986312i	$0.447273\pi$
$762$	−7.19776	−0.260747
$763$	−8.65871	−0.313466
$764$	−66.9782	−2.42319
$765$	1.83620	0.0663879
$766$	−24.2210	−0.875139
$767$	9.65000	0.348441
$768$	30.7258	1.10872
$769$	−46.7221	−1.68484	−0.842421	−	0.538820i	$-0.818870\pi$
$769$	−46.7221	−1.68484	−0.842421	+	0.538820i	$0.818870\pi$
$770$	4.43820	0.159942
$771$	−17.9852	−0.647720
$772$	−44.2360	−1.59209
$773$	29.9110	1.07583	0.537913	−	0.843001i	$-0.319213\pi$
$773$	29.9110	1.07583	0.537913	+	0.843001i	$0.319213\pi$
$774$	−14.8007	−0.532002
$775$	44.9829	1.61583
$776$	24.8417	0.891766
$777$	−17.6596	−0.633533
$778$	−14.5583	−0.521942
$779$	−4.25234	−0.152356
$780$	−2.85991	−0.102401
$781$	16.1627	0.578346
$782$	44.3849	1.58720
$783$	−4.43011	−0.158319
$784$	−3.99357	−0.142627
$785$	−5.07639	−0.181184
$786$	−15.9889	−0.570306
$787$	−1.35582	−0.0483296	−0.0241648	−	0.999708i	$-0.507693\pi$
$787$	−1.35582	−0.0483296	−0.0241648	+	0.999708i	$0.507693\pi$
$788$	106.695	3.80086
$789$	17.5106	0.623395
$790$	−27.7110	−0.985912
$791$	−15.3918	−0.547269
$792$	4.70837	0.167305
$793$	−7.37742	−0.261980
$794$	68.2109	2.42071
$795$	1.60243	0.0568323
$796$	29.3810	1.04138
$797$	−18.6259	−0.659765	−0.329882	−	0.944022i	$-0.607009\pi$
$797$	−18.6259	−0.659765	−0.329882	+	0.944022i	$0.607009\pi$
$798$	−2.66971	−0.0945065
$799$	−19.5722	−0.692416
$800$	−4.98887	−0.176383
$801$	17.7002	0.625406
$802$	−74.8531	−2.64315
$803$	−2.37149	−0.0836881
$804$	10.3541	0.365160
$805$	13.0236	0.459020
$806$	−24.4756	−0.862116
$807$	−20.0866	−0.707080
$808$	22.8287	0.803110
$809$	32.1283	1.12957	0.564786	−	0.825237i	$-0.308959\pi$
$809$	32.1283	1.12957	0.564786	+	0.825237i	$0.308959\pi$
$810$	1.78702	0.0627894
$811$	6.79353	0.238553	0.119276	−	0.992861i	$-0.461943\pi$
$811$	6.79353	0.238553	0.119276	+	0.992861i	$0.461943\pi$
$812$	−41.3721	−1.45188
$813$	−9.58458	−0.336146
$814$	−18.3698	−0.643861
$815$	−6.46131	−0.226330
$816$	8.22450	0.287915
$817$	2.79222	0.0976873
$818$	88.6280	3.09880
$819$	2.40625	0.0840812
$820$	26.5819	0.928282
$821$	8.40244	0.293247	0.146624	−	0.989192i	$-0.453159\pi$
$821$	8.40244	0.293247	0.146624	+	0.989192i	$0.453159\pi$
$822$	−32.9378	−1.14884
$823$	11.5273	0.401816	0.200908	−	0.979610i	$-0.435611\pi$
$823$	11.5273	0.401816	0.200908	+	0.979610i	$0.435611\pi$
$824$	−4.56178	−0.158917
$825$	−4.60023	−0.160159
$826$	−56.3114	−1.95932
$827$	−8.48162	−0.294935	−0.147467	−	0.989067i	$-0.547112\pi$
$827$	−8.48162	−0.294935	−0.147467	+	0.989067i	$0.547112\pi$
$828$	28.5063	0.990661
$829$	−9.75661	−0.338861	−0.169431	−	0.985542i	$-0.554193\pi$
$829$	−9.75661	−0.338861	−0.169431	+	0.985542i	$0.554193\pi$
$830$	17.7388	0.615724
$831$	7.60414	0.263785
$832$	9.31566	0.322962
$833$	3.01501	0.104464
$834$	−0.244098	−0.00845243
$835$	10.2724	0.355490
$836$	−1.83266	−0.0633840
$837$	10.0926	0.348853
$838$	−68.9077	−2.38038
$839$	47.5369	1.64115	0.820577	−	0.571535i	$-0.193652\pi$
$839$	47.5369	1.64115	0.820577	+	0.571535i	$0.193652\pi$
$840$	8.08864	0.279085
$841$	−9.37408	−0.323244
$842$	−57.7101	−1.98882
$843$	17.2223	0.593167
$844$	25.2722	0.869907
$845$	−0.736887	−0.0253497
$846$	−19.0480	−0.654885
$847$	23.9054	0.821398
$848$	7.17743	0.246474
$849$	−21.8076	−0.748436
$850$	−26.9333	−0.923805
$851$	−53.9048	−1.84783
$852$	60.7755	2.08213
$853$	−47.9684	−1.64241	−0.821203	−	0.570636i	$-0.806697\pi$
$853$	−47.9684	−1.64241	−0.821203	+	0.570636i	$0.806697\pi$
$854$	43.0501	1.47314
$855$	−0.337128	−0.0115295
$856$	−3.79899	−0.129847
$857$	−14.1371	−0.482915	−0.241457	−	0.970411i	$-0.577625\pi$
$857$	−14.1371	−0.482915	−0.241457	+	0.970411i	$0.577625\pi$
$858$	2.50303	0.0854519
$859$	34.0044	1.16022	0.580108	−	0.814539i	$-0.303010\pi$
$859$	34.0044	1.16022	0.580108	+	0.814539i	$0.303010\pi$
$860$	−17.4545	−0.595194
$861$	−22.3653	−0.762208
$862$	−74.1149	−2.52436
$863$	−29.1658	−0.992814	−0.496407	−	0.868090i	$-0.665348\pi$
$863$	−29.1658	−0.992814	−0.496407	+	0.868090i	$0.665348\pi$
$864$	−1.11933	−0.0380805
$865$	16.7372	0.569082
$866$	−71.1663	−2.41833
$867$	10.7908	0.366474
$868$	94.2536	3.19917
$869$	16.0051	0.542937
$870$	−7.91670	−0.268401
$871$	2.66784	0.0903962
$872$	−16.4152	−0.555889
$873$	−5.44562	−0.184306
$874$	−8.14912	−0.275648
$875$	−16.7685	−0.566880
$876$	−8.91736	−0.301290
$877$	−8.02600	−0.271019	−0.135509	−	0.990776i	$-0.543267\pi$
$877$	−8.02600	−0.271019	−0.135509	+	0.990776i	$0.543267\pi$
$878$	−42.7245	−1.44188
$879$	−5.54431	−0.187005
$880$	2.51032	0.0846227
$881$	−2.46120	−0.0829199	−0.0414599	−	0.999140i	$-0.513201\pi$
$881$	−2.46120	−0.0829199	−0.0414599	+	0.999140i	$0.513201\pi$
$882$	2.93426	0.0988017
$883$	50.1638	1.68815	0.844074	−	0.536227i	$-0.180151\pi$
$883$	50.1638	1.68815	0.844074	+	0.536227i	$0.180151\pi$
$884$	9.67098	0.325270
$885$	−7.11096	−0.239032
$886$	−71.4574	−2.40066
$887$	−54.0941	−1.81630	−0.908151	−	0.418643i	$-0.862506\pi$
$887$	−54.0941	−1.81630	−0.908151	+	0.418643i	$0.862506\pi$
$888$	−33.4790	−1.12348
$889$	7.14183	0.239529
$890$	31.6306	1.06026
$891$	−1.03214	−0.0345779
$892$	17.8316	0.597047
$893$	3.59349	0.120251
$894$	19.1029	0.638896
$895$	0.148142	0.00495184
$896$	−48.9736	−1.63609
$897$	7.34494	0.245240
$898$	−1.57014	−0.0523961
$899$	−44.7116	−1.49122
$900$	−17.2979	−0.576598
$901$	−5.41872	−0.180524
$902$	−23.2648	−0.774633
$903$	14.6857	0.488711
$904$	−29.1798	−0.970506
$905$	12.7787	0.424780
$906$	0.250429	0.00831995
$907$	42.1665	1.40012	0.700058	−	0.714086i	$-0.253157\pi$
$907$	42.1665	1.40012	0.700058	+	0.714086i	$0.253157\pi$
$908$	−24.5282	−0.813996
$909$	−5.00434	−0.165984
$910$	4.30001	0.142544
$911$	26.1470	0.866290	0.433145	−	0.901324i	$-0.357404\pi$
$911$	26.1470	0.866290	0.433145	+	0.901324i	$0.357404\pi$
$912$	−1.51003	−0.0500020
$913$	−10.2455	−0.339077
$914$	60.0746	1.98709
$915$	5.43632	0.179719
$916$	10.7792	0.356154
$917$	15.8647	0.523898
$918$	−6.04292	−0.199446
$919$	−31.1788	−1.02849	−0.514247	−	0.857642i	$-0.671928\pi$
$919$	−31.1788	−1.02849	−0.514247	+	0.857642i	$0.671928\pi$
$920$	24.6901	0.814009
$921$	20.1990	0.665580
$922$	36.2094	1.19249
$923$	15.6595	0.515437
$924$	−9.63895	−0.317098
$925$	32.7101	1.07550
$926$	−21.1311	−0.694410
$927$	1.00000	0.0328443
$928$	4.95878	0.162780
$929$	−15.6646	−0.513940	−0.256970	−	0.966419i	$-0.582724\pi$
$929$	−15.6646	−0.513940	−0.256970	+	0.966419i	$0.582724\pi$
$930$	18.0357	0.591415
$931$	−0.553560	−0.0181422
$932$	48.9238	1.60255
$933$	−32.8801	−1.07645
$934$	−77.1478	−2.52435
$935$	−1.89521	−0.0619799
$936$	4.56178	0.149106
$937$	−49.4591	−1.61576	−0.807880	−	0.589348i	$-0.799385\pi$
$937$	−49.4591	−1.61576	−0.807880	+	0.589348i	$0.799385\pi$
$938$	−15.5678	−0.508308
$939$	−25.4786	−0.831462
$940$	−22.4633	−0.732673
$941$	−12.6849	−0.413516	−0.206758	−	0.978392i	$-0.566291\pi$
$941$	−12.6849	−0.413516	−0.206758	+	0.978392i	$0.566291\pi$
$942$	16.7064	0.544324
$943$	−68.2688	−2.22314
$944$	−31.8506	−1.03665
$945$	−1.77313	−0.0576801
$946$	15.2764	0.496678
$947$	41.5461	1.35007	0.675033	−	0.737788i	$-0.264129\pi$
$947$	41.5461	1.35007	0.675033	+	0.737788i	$0.264129\pi$
$948$	60.1831	1.95466
$949$	−2.29765	−0.0745850
$950$	4.94498	0.160436
$951$	33.6684	1.09177
$952$	−27.3523	−0.886493
$953$	−33.5695	−1.08742	−0.543711	−	0.839272i	$-0.682981\pi$
$953$	−33.5695	−1.08742	−0.543711	+	0.839272i	$0.682981\pi$
$954$	−5.27359	−0.170739
$955$	12.7169	0.411510
$956$	34.1583	1.10476
$957$	4.57248	0.147807
$958$	−82.6316	−2.66971
$959$	32.6818	1.05535
$960$	−6.86458	−0.221553
$961$	70.8615	2.28586
$962$	−17.7978	−0.573825
$963$	0.832788	0.0268362
$964$	−43.1549	−1.38993
$965$	8.39894	0.270372
$966$	−42.8605	−1.37901
$967$	−49.5525	−1.59350	−0.796750	−	0.604309i	$-0.793449\pi$
$967$	−49.5525	−1.59350	−0.796750	+	0.604309i	$0.793449\pi$
$968$	45.3199	1.45664
$969$	1.14002	0.0366228
$970$	−9.73143	−0.312457
$971$	−27.1145	−0.870144	−0.435072	−	0.900396i	$-0.643277\pi$
$971$	−27.1145	−0.870144	−0.435072	+	0.900396i	$0.643277\pi$
$972$	−3.88107	−0.124485
$973$	0.242202	0.00776463
$974$	−93.3136	−2.98996
$975$	−4.45700	−0.142738
$976$	24.3498	0.779418
$977$	31.8008	1.01740	0.508699	−	0.860944i	$-0.330127\pi$
$977$	31.8008	1.01740	0.508699	+	0.860944i	$0.330127\pi$
$978$	21.2642	0.679953
$979$	−18.2690	−0.583880
$980$	3.46037	0.110538
$981$	3.59843	0.114889
$982$	−45.2292	−1.44332
$983$	40.9764	1.30695	0.653473	−	0.756950i	$-0.273311\pi$
$983$	40.9764	1.30695	0.653473	+	0.756950i	$0.273311\pi$
$984$	−42.4002	−1.35167
$985$	−20.2579	−0.645469
$986$	26.7708	0.852558
$987$	18.9000	0.601595
$988$	−1.77560	−0.0564895
$989$	44.8274	1.42543
$990$	−1.84445	−0.0586203
$991$	21.0273	0.667955	0.333977	−	0.942581i	$-0.391609\pi$
$991$	21.0273	0.667955	0.333977	+	0.942581i	$0.391609\pi$
$992$	−11.2971	−0.358682
$993$	−6.72901	−0.213539
$994$	−91.3789	−2.89836
$995$	−5.57848	−0.176850
$996$	−38.5255	−1.22073
$997$	−23.9872	−0.759682	−0.379841	−	0.925052i	$-0.624021\pi$
$997$	−23.9872	−0.759682	−0.379841	+	0.925052i	$0.624021\pi$
$998$	−97.5675	−3.08845
$999$	7.33903	0.232197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.2	✓	24	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)

\(f(q)\)	\(=\)	\(q-2.42509 q^{2} -1.00000 q^{3} +3.88107 q^{4} -0.736887 q^{5} +2.42509 q^{6} -2.40625 q^{7} -4.56178 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.42509 q^{2} -1.00000 q^{3} +3.88107 q^{4} -0.736887 q^{5} +2.42509 q^{6} -2.40625 q^{7} -4.56178 q^{8} +1.00000 q^{9} +1.78702 q^{10} -1.03214 q^{11} -3.88107 q^{12} -1.00000 q^{13} +5.83538 q^{14} +0.736887 q^{15} +3.30058 q^{16} -2.49183 q^{17} -2.42509 q^{18} +0.457503 q^{19} -2.85991 q^{20} +2.40625 q^{21} +2.50303 q^{22} +7.34494 q^{23} +4.56178 q^{24} -4.45700 q^{25} +2.42509 q^{26} -1.00000 q^{27} -9.33883 q^{28} +4.43011 q^{29} -1.78702 q^{30} -10.0926 q^{31} +1.11933 q^{32} +1.03214 q^{33} +6.04292 q^{34} +1.77313 q^{35} +3.88107 q^{36} -7.33903 q^{37} -1.10949 q^{38} +1.00000 q^{39} +3.36151 q^{40} -9.29467 q^{41} -5.83538 q^{42} +6.10317 q^{43} -4.00580 q^{44} -0.736887 q^{45} -17.8122 q^{46} +7.85456 q^{47} -3.30058 q^{48} -1.20996 q^{49} +10.8086 q^{50} +2.49183 q^{51} -3.88107 q^{52} +2.17459 q^{53} +2.42509 q^{54} +0.760567 q^{55} +10.9768 q^{56} -0.457503 q^{57} -10.7434 q^{58} -9.65000 q^{59} +2.85991 q^{60} +7.37742 q^{61} +24.4756 q^{62} -2.40625 q^{63} -9.31566 q^{64} +0.736887 q^{65} -2.50303 q^{66} -2.66784 q^{67} -9.67098 q^{68} -7.34494 q^{69} -4.30001 q^{70} -15.6595 q^{71} -4.56178 q^{72} +2.29765 q^{73} +17.7978 q^{74} +4.45700 q^{75} +1.77560 q^{76} +2.48358 q^{77} -2.42509 q^{78} -15.5068 q^{79} -2.43216 q^{80} +1.00000 q^{81} +22.5404 q^{82} +9.92650 q^{83} +9.33883 q^{84} +1.83620 q^{85} -14.8007 q^{86} -4.43011 q^{87} +4.70837 q^{88} +17.7002 q^{89} +1.78702 q^{90} +2.40625 q^{91} +28.5063 q^{92} +10.0926 q^{93} -19.0480 q^{94} -0.337128 q^{95} -1.11933 q^{96} -5.44562 q^{97} +2.93426 q^{98} -1.03214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

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