LMFDB - Embedded newform 8043.2.a.r.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17399 q^{2} -1.00000 q^{3} +2.72624 q^{4} -2.42046 q^{5} +2.17399 q^{6} -1.00000 q^{7} -1.57885 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.17399 q^{2} -1.00000 q^{3} +2.72624 q^{4} -2.42046 q^{5} +2.17399 q^{6} -1.00000 q^{7} -1.57885 q^{8} +1.00000 q^{9} +5.26206 q^{10} -1.69655 q^{11} -2.72624 q^{12} -2.67257 q^{13} +2.17399 q^{14} +2.42046 q^{15} -2.02008 q^{16} +5.10047 q^{17} -2.17399 q^{18} +7.18888 q^{19} -6.59877 q^{20} +1.00000 q^{21} +3.68828 q^{22} -4.22978 q^{23} +1.57885 q^{24} +0.858628 q^{25} +5.81014 q^{26} -1.00000 q^{27} -2.72624 q^{28} +3.57872 q^{29} -5.26206 q^{30} -7.01954 q^{31} +7.54934 q^{32} +1.69655 q^{33} -11.0884 q^{34} +2.42046 q^{35} +2.72624 q^{36} -6.50056 q^{37} -15.6286 q^{38} +2.67257 q^{39} +3.82154 q^{40} +9.15363 q^{41} -2.17399 q^{42} -6.02229 q^{43} -4.62520 q^{44} -2.42046 q^{45} +9.19550 q^{46} -5.97178 q^{47} +2.02008 q^{48} +1.00000 q^{49} -1.86665 q^{50} -5.10047 q^{51} -7.28607 q^{52} -2.88579 q^{53} +2.17399 q^{54} +4.10642 q^{55} +1.57885 q^{56} -7.18888 q^{57} -7.78011 q^{58} +1.67522 q^{59} +6.59877 q^{60} -1.74614 q^{61} +15.2604 q^{62} -1.00000 q^{63} -12.3720 q^{64} +6.46884 q^{65} -3.68828 q^{66} +0.417689 q^{67} +13.9051 q^{68} +4.22978 q^{69} -5.26206 q^{70} +5.51631 q^{71} -1.57885 q^{72} -12.1558 q^{73} +14.1322 q^{74} -0.858628 q^{75} +19.5986 q^{76} +1.69655 q^{77} -5.81014 q^{78} +2.28179 q^{79} +4.88952 q^{80} +1.00000 q^{81} -19.8999 q^{82} +13.3984 q^{83} +2.72624 q^{84} -12.3455 q^{85} +13.0924 q^{86} -3.57872 q^{87} +2.67859 q^{88} +5.63874 q^{89} +5.26206 q^{90} +2.67257 q^{91} -11.5314 q^{92} +7.01954 q^{93} +12.9826 q^{94} -17.4004 q^{95} -7.54934 q^{96} +1.50043 q^{97} -2.17399 q^{98} -1.69655 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9} - 10 q^{10} + 31 q^{11} - 45 q^{12} - 32 q^{13} - 3 q^{14} + 9 q^{15} + 43 q^{16} - 36 q^{17} + 3 q^{18} - 13 q^{19} - 19 q^{20} + 46 q^{21} - 13 q^{22} + 24 q^{23} - 6 q^{24} + 35 q^{25} - 11 q^{26} - 46 q^{27} - 45 q^{28} + 11 q^{29} + 10 q^{30} - 23 q^{31} + 5 q^{32} - 31 q^{33} - 35 q^{34} + 9 q^{35} + 45 q^{36} - 37 q^{37} - 32 q^{38} + 32 q^{39} - 28 q^{40} - 27 q^{41} + 3 q^{42} - 7 q^{43} + 46 q^{44} - 9 q^{45} + 16 q^{46} - 18 q^{47} - 43 q^{48} + 46 q^{49} + 10 q^{50} + 36 q^{51} - 62 q^{52} - 62 q^{53} - 3 q^{54} - 28 q^{55} - 6 q^{56} + 13 q^{57} - 36 q^{58} - 3 q^{59} + 19 q^{60} - 31 q^{61} - 41 q^{62} - 46 q^{63} + 42 q^{64} + 2 q^{65} + 13 q^{66} - 9 q^{67} - 70 q^{68} - 24 q^{69} + 10 q^{70} + 77 q^{71} + 6 q^{72} - 38 q^{73} + 14 q^{74} - 35 q^{75} - 41 q^{76} - 31 q^{77} + 11 q^{78} + 8 q^{79} - 59 q^{80} + 46 q^{81} - 53 q^{82} - 38 q^{83} + 45 q^{84} - 26 q^{85} + 37 q^{86} - 11 q^{87} - 26 q^{88} - 39 q^{89} - 10 q^{90} + 32 q^{91} + 2 q^{92} + 23 q^{93} - 55 q^{94} + 35 q^{95} - 5 q^{96} - 61 q^{97} + 3 q^{98} + 31 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9 - 10 * q^10 + 31 * q^11 - 45 * q^12 - 32 * q^13 - 3 * q^14 + 9 * q^15 + 43 * q^16 - 36 * q^17 + 3 * q^18 - 13 * q^19 - 19 * q^20 + 46 * q^21 - 13 * q^22 + 24 * q^23 - 6 * q^24 + 35 * q^25 - 11 * q^26 - 46 * q^27 - 45 * q^28 + 11 * q^29 + 10 * q^30 - 23 * q^31 + 5 * q^32 - 31 * q^33 - 35 * q^34 + 9 * q^35 + 45 * q^36 - 37 * q^37 - 32 * q^38 + 32 * q^39 - 28 * q^40 - 27 * q^41 + 3 * q^42 - 7 * q^43 + 46 * q^44 - 9 * q^45 + 16 * q^46 - 18 * q^47 - 43 * q^48 + 46 * q^49 + 10 * q^50 + 36 * q^51 - 62 * q^52 - 62 * q^53 - 3 * q^54 - 28 * q^55 - 6 * q^56 + 13 * q^57 - 36 * q^58 - 3 * q^59 + 19 * q^60 - 31 * q^61 - 41 * q^62 - 46 * q^63 + 42 * q^64 + 2 * q^65 + 13 * q^66 - 9 * q^67 - 70 * q^68 - 24 * q^69 + 10 * q^70 + 77 * q^71 + 6 * q^72 - 38 * q^73 + 14 * q^74 - 35 * q^75 - 41 * q^76 - 31 * q^77 + 11 * q^78 + 8 * q^79 - 59 * q^80 + 46 * q^81 - 53 * q^82 - 38 * q^83 + 45 * q^84 - 26 * q^85 + 37 * q^86 - 11 * q^87 - 26 * q^88 - 39 * q^89 - 10 * q^90 + 32 * q^91 + 2 * q^92 + 23 * q^93 - 55 * q^94 + 35 * q^95 - 5 * q^96 - 61 * q^97 + 3 * q^98 + 31 * 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 $

$2$	−2.17399	−1.53725	−0.768623	−	0.639703i	$-0.779058\pi$
$2$	−2.17399	−1.53725	−0.768623	+	0.639703i	$0.779058\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.72624	1.36312
$5$	−2.42046	−1.08246	−0.541231	−	0.840874i	$-0.682042\pi$
$5$	−2.42046	−1.08246	−0.541231	+	0.840874i	$0.682042\pi$
$6$	2.17399	0.887529
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.57885	−0.558208
$9$	1.00000	0.333333
$10$	5.26206	1.66401
$11$	−1.69655	−0.511528	−0.255764	−	0.966739i	$-0.582327\pi$
$11$	−1.69655	−0.511528	−0.255764	+	0.966739i	$0.582327\pi$
$12$	−2.72624	−0.786999
$13$	−2.67257	−0.741237	−0.370618	−	0.928785i	$-0.620854\pi$
$13$	−2.67257	−0.741237	−0.370618	+	0.928785i	$0.620854\pi$
$14$	2.17399	0.581024
$15$	2.42046	0.624960
$16$	−2.02008	−0.505020
$17$	5.10047	1.23705	0.618523	−	0.785767i	$-0.287731\pi$
$17$	5.10047	1.23705	0.618523	+	0.785767i	$0.287731\pi$
$18$	−2.17399	−0.512415
$19$	7.18888	1.64924	0.824621	−	0.565686i	$-0.191388\pi$
$19$	7.18888	1.64924	0.824621	+	0.565686i	$0.191388\pi$
$20$	−6.59877	−1.47553
$21$	1.00000	0.218218
$22$	3.68828	0.786344
$23$	−4.22978	−0.881969	−0.440985	−	0.897515i	$-0.645371\pi$
$23$	−4.22978	−0.881969	−0.440985	+	0.897515i	$0.645371\pi$
$24$	1.57885	0.322281
$25$	0.858628	0.171726
$26$	5.81014	1.13946
$27$	−1.00000	−0.192450
$28$	−2.72624	−0.515212
$29$	3.57872	0.664551	0.332276	−	0.943182i	$-0.392184\pi$
$29$	3.57872	0.664551	0.332276	+	0.943182i	$0.392184\pi$
$30$	−5.26206	−0.960717
$31$	−7.01954	−1.26075	−0.630374	−	0.776292i	$-0.717098\pi$
$31$	−7.01954	−1.26075	−0.630374	+	0.776292i	$0.717098\pi$
$32$	7.54934	1.33455
$33$	1.69655	0.295331
$34$	−11.0884	−1.90164
$35$	2.42046	0.409132
$36$	2.72624	0.454374
$37$	−6.50056	−1.06869	−0.534343	−	0.845268i	$-0.679441\pi$
$37$	−6.50056	−1.06869	−0.534343	+	0.845268i	$0.679441\pi$
$38$	−15.6286	−2.53529
$39$	2.67257	0.427953
$40$	3.82154	0.604239
$41$	9.15363	1.42956	0.714778	−	0.699351i	$-0.246528\pi$
$41$	9.15363	1.42956	0.714778	+	0.699351i	$0.246528\pi$
$42$	−2.17399	−0.335454
$43$	−6.02229	−0.918390	−0.459195	−	0.888335i	$-0.651862\pi$
$43$	−6.02229	−0.918390	−0.459195	+	0.888335i	$0.651862\pi$
$44$	−4.62520	−0.697275
$45$	−2.42046	−0.360821
$46$	9.19550	1.35580
$47$	−5.97178	−0.871073	−0.435537	−	0.900171i	$-0.643441\pi$
$47$	−5.97178	−0.871073	−0.435537	+	0.900171i	$0.643441\pi$
$48$	2.02008	0.291573
$49$	1.00000	0.142857
$50$	−1.86665	−0.263984
$51$	−5.10047	−0.714209
$52$	−7.28607	−1.01040
$53$	−2.88579	−0.396394	−0.198197	−	0.980162i	$-0.563509\pi$
$53$	−2.88579	−0.396394	−0.198197	+	0.980162i	$0.563509\pi$
$54$	2.17399	0.295843
$55$	4.10642	0.553710
$56$	1.57885	0.210983
$57$	−7.18888	−0.952190
$58$	−7.78011	−1.02158
$59$	1.67522	0.218096	0.109048	−	0.994037i	$-0.465220\pi$
$59$	1.67522	0.218096	0.109048	+	0.994037i	$0.465220\pi$
$60$	6.59877	0.851897
$61$	−1.74614	−0.223570	−0.111785	−	0.993732i	$-0.535657\pi$
$61$	−1.74614	−0.223570	−0.111785	+	0.993732i	$0.535657\pi$
$62$	15.2604	1.93808
$63$	−1.00000	−0.125988
$64$	−12.3720	−1.54651
$65$	6.46884	0.802361
$66$	−3.68828	−0.453996
$67$	0.417689	0.0510289	0.0255144	−	0.999674i	$-0.491878\pi$
$67$	0.417689	0.0510289	0.0255144	+	0.999674i	$0.491878\pi$
$68$	13.9051	1.68625
$69$	4.22978	0.509205
$70$	−5.26206	−0.628937
$71$	5.51631	0.654665	0.327333	−	0.944909i	$-0.393850\pi$
$71$	5.51631	0.654665	0.327333	+	0.944909i	$0.393850\pi$
$72$	−1.57885	−0.186069
$73$	−12.1558	−1.42273	−0.711364	−	0.702824i	$-0.751922\pi$
$73$	−12.1558	−1.42273	−0.711364	+	0.702824i	$0.751922\pi$
$74$	14.1322	1.64283
$75$	−0.858628	−0.0991458
$76$	19.5986	2.24812
$77$	1.69655	0.193339
$78$	−5.81014	−0.657869
$79$	2.28179	0.256721	0.128361	−	0.991728i	$-0.459029\pi$
$79$	2.28179	0.256721	0.128361	+	0.991728i	$0.459029\pi$
$80$	4.88952	0.546665
$81$	1.00000	0.111111
$82$	−19.8999	−2.19758
$83$	13.3984	1.47067	0.735333	−	0.677706i	$-0.237026\pi$
$83$	13.3984	1.47067	0.735333	+	0.677706i	$0.237026\pi$
$84$	2.72624	0.297458
$85$	−12.3455	−1.33906
$86$	13.0924	1.41179
$87$	−3.57872	−0.383679
$88$	2.67859	0.285539
$89$	5.63874	0.597705	0.298853	−	0.954299i	$-0.403396\pi$
$89$	5.63874	0.597705	0.298853	+	0.954299i	$0.403396\pi$
$90$	5.26206	0.554670
$91$	2.67257	0.280161
$92$	−11.5314	−1.20223
$93$	7.01954	0.727893
$94$	12.9826	1.33905
$95$	−17.4004	−1.78524
$96$	−7.54934	−0.770501
$97$	1.50043	0.152346	0.0761728	−	0.997095i	$-0.475730\pi$
$97$	1.50043	0.152346	0.0761728	+	0.997095i	$0.475730\pi$
$98$	−2.17399	−0.219606
$99$	−1.69655	−0.170509
$100$	2.34083	0.234083
$101$	−5.94679	−0.591727	−0.295864	−	0.955230i	$-0.595607\pi$
$101$	−5.94679	−0.591727	−0.295864	+	0.955230i	$0.595607\pi$
$102$	11.0884	1.09791
$103$	10.0262	0.987910	0.493955	−	0.869487i	$-0.335551\pi$
$103$	10.0262	0.987910	0.493955	+	0.869487i	$0.335551\pi$
$104$	4.21958	0.413764
$105$	−2.42046	−0.236213
$106$	6.27368	0.609354
$107$	11.3022	1.09263	0.546314	−	0.837580i	$-0.316030\pi$
$107$	11.3022	1.09263	0.546314	+	0.837580i	$0.316030\pi$
$108$	−2.72624	−0.262333
$109$	6.33375	0.606663	0.303332	−	0.952885i	$-0.401901\pi$
$109$	6.33375	0.606663	0.303332	+	0.952885i	$0.401901\pi$
$110$	−8.92734	−0.851188
$111$	6.50056	0.617006
$112$	2.02008	0.190880
$113$	13.3528	1.25612	0.628062	−	0.778164i	$-0.283849\pi$
$113$	13.3528	1.25612	0.628062	+	0.778164i	$0.283849\pi$
$114$	15.6286	1.46375
$115$	10.2380	0.954699
$116$	9.75646	0.905864
$117$	−2.67257	−0.247079
$118$	−3.64193	−0.335266
$119$	−5.10047	−0.467560
$120$	−3.82154	−0.348858
$121$	−8.12173	−0.738339
$122$	3.79610	0.343682
$123$	−9.15363	−0.825355
$124$	−19.1370	−1.71855
$125$	10.0240	0.896576
$126$	2.17399	0.193675
$127$	−6.29917	−0.558961	−0.279481	−	0.960151i	$-0.590162\pi$
$127$	−6.29917	−0.558961	−0.279481	+	0.960151i	$0.590162\pi$
$128$	11.7981	1.04281
$129$	6.02229	0.530233
$130$	−14.0632	−1.23343
$131$	−17.5302	−1.53162	−0.765808	−	0.643069i	$-0.777661\pi$
$131$	−17.5302	−1.53162	−0.765808	+	0.643069i	$0.777661\pi$
$132$	4.62520	0.402572
$133$	−7.18888	−0.623355
$134$	−0.908054	−0.0784439
$135$	2.42046	0.208320
$136$	−8.05288	−0.690529
$137$	−4.64857	−0.397154	−0.198577	−	0.980085i	$-0.563632\pi$
$137$	−4.64857	−0.397154	−0.198577	+	0.980085i	$0.563632\pi$
$138$	−9.19550	−0.782773
$139$	15.5021	1.31487	0.657436	−	0.753511i	$-0.271641\pi$
$139$	15.5021	1.31487	0.657436	+	0.753511i	$0.271641\pi$
$140$	6.59877	0.557698
$141$	5.97178	0.502914
$142$	−11.9924	−1.00638
$143$	4.53414	0.379163
$144$	−2.02008	−0.168340
$145$	−8.66214	−0.719352
$146$	26.4266	2.18708
$147$	−1.00000	−0.0824786
$148$	−17.7221	−1.45675
$149$	−5.55611	−0.455174	−0.227587	−	0.973758i	$-0.573084\pi$
$149$	−5.55611	−0.455174	−0.227587	+	0.973758i	$0.573084\pi$
$150$	1.86665	0.152411
$151$	7.08098	0.576242	0.288121	−	0.957594i	$-0.406969\pi$
$151$	7.08098	0.576242	0.288121	+	0.957594i	$0.406969\pi$
$152$	−11.3502	−0.920620
$153$	5.10047	0.412349
$154$	−3.68828	−0.297210
$155$	16.9905	1.36471
$156$	7.28607	0.583353
$157$	−17.1582	−1.36937	−0.684685	−	0.728839i	$-0.740060\pi$
$157$	−17.1582	−1.36937	−0.684685	+	0.728839i	$0.740060\pi$
$158$	−4.96059	−0.394643
$159$	2.88579	0.228858
$160$	−18.2729	−1.44460
$161$	4.22978	0.333353
$162$	−2.17399	−0.170805
$163$	17.9917	1.40922	0.704610	−	0.709595i	$-0.251122\pi$
$163$	17.9917	1.40922	0.704610	+	0.709595i	$0.251122\pi$
$164$	24.9550	1.94866
$165$	−4.10642	−0.319685
$166$	−29.1280	−2.26077
$167$	−21.8013	−1.68704	−0.843519	−	0.537099i	$-0.819520\pi$
$167$	−21.8013	−1.68704	−0.843519	+	0.537099i	$0.819520\pi$
$168$	−1.57885	−0.121811
$169$	−5.85738	−0.450568
$170$	26.8390	2.05846
$171$	7.18888	0.549747
$172$	−16.4182	−1.25188
$173$	6.69397	0.508933	0.254467	−	0.967082i	$-0.418100\pi$
$173$	6.69397	0.508933	0.254467	+	0.967082i	$0.418100\pi$
$174$	7.78011	0.589808
$175$	−0.858628	−0.0649062
$176$	3.42716	0.258332
$177$	−1.67522	−0.125918
$178$	−12.2586	−0.918819
$179$	22.5204	1.68326	0.841628	−	0.540057i	$-0.181597\pi$
$179$	22.5204	1.68326	0.841628	+	0.540057i	$0.181597\pi$
$180$	−6.59877	−0.491843
$181$	6.28105	0.466867	0.233433	−	0.972373i	$-0.425004\pi$
$181$	6.28105	0.466867	0.233433	+	0.972373i	$0.425004\pi$
$182$	−5.81014	−0.430676
$183$	1.74614	0.129078
$184$	6.67818	0.492322
$185$	15.7343	1.15681
$186$	−15.2604	−1.11895
$187$	−8.65319	−0.632784
$188$	−16.2805	−1.18738
$189$	1.00000	0.0727393
$190$	37.8283	2.74436
$191$	−4.69391	−0.339640	−0.169820	−	0.985475i	$-0.554319\pi$
$191$	−4.69391	−0.339640	−0.169820	+	0.985475i	$0.554319\pi$
$192$	12.3720	0.892876
$193$	11.7562	0.846227	0.423114	−	0.906077i	$-0.360937\pi$
$193$	11.7562	0.846227	0.423114	+	0.906077i	$0.360937\pi$
$194$	−3.26192	−0.234192
$195$	−6.46884	−0.463244
$196$	2.72624	0.194732
$197$	−14.0875	−1.00369	−0.501847	−	0.864957i	$-0.667346\pi$
$197$	−14.0875	−1.00369	−0.501847	+	0.864957i	$0.667346\pi$
$198$	3.68828	0.262115
$199$	2.80321	0.198714	0.0993572	−	0.995052i	$-0.468321\pi$
$199$	2.80321	0.198714	0.0993572	+	0.995052i	$0.468321\pi$
$200$	−1.35565	−0.0958586
$201$	−0.417689	−0.0294615
$202$	12.9283	0.909630
$203$	−3.57872	−0.251177
$204$	−13.9051	−0.973554
$205$	−22.1560	−1.54744
$206$	−21.7969	−1.51866
$207$	−4.22978	−0.293990
$208$	5.39880	0.374339
$209$	−12.1963	−0.843634
$210$	5.26206	0.363117
$211$	20.0390	1.37954	0.689770	−	0.724029i	$-0.257712\pi$
$211$	20.0390	1.37954	0.689770	+	0.724029i	$0.257712\pi$
$212$	−7.86737	−0.540333
$213$	−5.51631	−0.377971
$214$	−24.5710	−1.67964
$215$	14.5767	0.994123
$216$	1.57885	0.107427
$217$	7.01954	0.476518
$218$	−13.7695	−0.932590
$219$	12.1558	0.821412
$220$	11.1951	0.754775
$221$	−13.6314	−0.916944
$222$	−14.1322	−0.948489
$223$	17.8225	1.19348	0.596741	−	0.802434i	$-0.296462\pi$
$223$	17.8225	1.19348	0.596741	+	0.802434i	$0.296462\pi$
$224$	−7.54934	−0.504411
$225$	0.858628	0.0572419
$226$	−29.0288	−1.93097
$227$	1.12224	0.0744857	0.0372428	−	0.999306i	$-0.488142\pi$
$227$	1.12224	0.0744857	0.0372428	+	0.999306i	$0.488142\pi$
$228$	−19.5986	−1.29795
$229$	−16.0844	−1.06289	−0.531444	−	0.847093i	$-0.678351\pi$
$229$	−16.0844	−1.06289	−0.531444	+	0.847093i	$0.678351\pi$
$230$	−22.2573	−1.46761
$231$	−1.69655	−0.111625
$232$	−5.65026	−0.370958
$233$	16.5679	1.08540	0.542699	−	0.839927i	$-0.317402\pi$
$233$	16.5679	1.08540	0.542699	+	0.839927i	$0.317402\pi$
$234$	5.81014	0.379821
$235$	14.4544	0.942904
$236$	4.56707	0.297291
$237$	−2.28179	−0.148218
$238$	11.0884	0.718754
$239$	15.4365	0.998507	0.499254	−	0.866456i	$-0.333608\pi$
$239$	15.4365	0.998507	0.499254	+	0.866456i	$0.333608\pi$
$240$	−4.88952	−0.315617
$241$	−5.14373	−0.331337	−0.165668	−	0.986181i	$-0.552978\pi$
$241$	−5.14373	−0.331337	−0.165668	+	0.986181i	$0.552978\pi$
$242$	17.6566	1.13501
$243$	−1.00000	−0.0641500
$244$	−4.76041	−0.304754
$245$	−2.42046	−0.154638
$246$	19.8999	1.26877
$247$	−19.2128	−1.22248
$248$	11.0828	0.703759
$249$	−13.3984	−0.849090
$250$	−21.7922	−1.37826
$251$	2.83962	0.179235	0.0896175	−	0.995976i	$-0.471436\pi$
$251$	2.83962	0.179235	0.0896175	+	0.995976i	$0.471436\pi$
$252$	−2.72624	−0.171737
$253$	7.17601	0.451152
$254$	13.6944	0.859260
$255$	12.3455	0.773105
$256$	−0.904812	−0.0565508
$257$	25.2198	1.57317	0.786583	−	0.617484i	$-0.211848\pi$
$257$	25.2198	1.57317	0.786583	+	0.617484i	$0.211848\pi$
$258$	−13.0924	−0.815098
$259$	6.50056	0.403925
$260$	17.6357	1.09372
$261$	3.57872	0.221517
$262$	38.1104	2.35447
$263$	−24.5459	−1.51356	−0.756782	−	0.653667i	$-0.773230\pi$
$263$	−24.5459	−1.51356	−0.756782	+	0.653667i	$0.773230\pi$
$264$	−2.67859	−0.164856
$265$	6.98494	0.429081
$266$	15.6286	0.958249
$267$	−5.63874	−0.345085
$268$	1.13872	0.0695586
$269$	−9.36047	−0.570718	−0.285359	−	0.958421i	$-0.592113\pi$
$269$	−9.36047	−0.570718	−0.285359	+	0.958421i	$0.592113\pi$
$270$	−5.26206	−0.320239
$271$	9.35743	0.568423	0.284212	−	0.958762i	$-0.408268\pi$
$271$	9.35743	0.568423	0.284212	+	0.958762i	$0.408268\pi$
$272$	−10.3034	−0.624733
$273$	−2.67257	−0.161751
$274$	10.1059	0.610523
$275$	−1.45670	−0.0878425
$276$	11.5314	0.694109
$277$	−3.94540	−0.237056	−0.118528	−	0.992951i	$-0.537818\pi$
$277$	−3.94540	−0.237056	−0.118528	+	0.992951i	$0.537818\pi$
$278$	−33.7015	−2.02128
$279$	−7.01954	−0.420249
$280$	−3.82154	−0.228381
$281$	25.6525	1.53030	0.765151	−	0.643851i	$-0.222664\pi$
$281$	25.6525	1.53030	0.765151	+	0.643851i	$0.222664\pi$
$282$	−12.9826	−0.773102
$283$	10.4001	0.618225	0.309112	−	0.951026i	$-0.399968\pi$
$283$	10.4001	0.618225	0.309112	+	0.951026i	$0.399968\pi$
$284$	15.0388	0.892389
$285$	17.4004	1.03071
$286$	−9.85718	−0.582867
$287$	−9.15363	−0.540322
$288$	7.54934	0.444849
$289$	9.01482	0.530284
$290$	18.8314	1.10582
$291$	−1.50043	−0.0879567
$292$	−33.1397	−1.93935
$293$	27.4652	1.60453	0.802266	−	0.596966i	$-0.203627\pi$
$293$	27.4652	1.60453	0.802266	+	0.596966i	$0.203627\pi$
$294$	2.17399	0.126790
$295$	−4.05481	−0.236080
$296$	10.2634	0.596548
$297$	1.69655	0.0984436
$298$	12.0789	0.699714
$299$	11.3044	0.653748
$300$	−2.34083	−0.135148
$301$	6.02229	0.347119
$302$	−15.3940	−0.885825
$303$	5.94679	0.341634
$304$	−14.5221	−0.832900
$305$	4.22646	0.242007
$306$	−11.0884	−0.633881
$307$	−14.7549	−0.842108	−0.421054	−	0.907035i	$-0.638340\pi$
$307$	−14.7549	−0.842108	−0.421054	+	0.907035i	$0.638340\pi$
$308$	4.62520	0.263545
$309$	−10.0262	−0.570370
$310$	−36.9373	−2.09790
$311$	8.65983	0.491054	0.245527	−	0.969390i	$-0.421039\pi$
$311$	8.65983	0.491054	0.245527	+	0.969390i	$0.421039\pi$
$312$	−4.21958	−0.238887
$313$	−17.9591	−1.01511	−0.507554	−	0.861620i	$-0.669450\pi$
$313$	−17.9591	−1.01511	−0.507554	+	0.861620i	$0.669450\pi$
$314$	37.3017	2.10506
$315$	2.42046	0.136377
$316$	6.22071	0.349942
$317$	−16.6379	−0.934478	−0.467239	−	0.884131i	$-0.654751\pi$
$317$	−16.6379	−0.934478	−0.467239	+	0.884131i	$0.654751\pi$
$318$	−6.27368	−0.351811
$319$	−6.07146	−0.339937
$320$	29.9461	1.67404
$321$	−11.3022	−0.630830
$322$	−9.19550	−0.512445
$323$	36.6667	2.04019
$324$	2.72624	0.151458
$325$	−2.29474	−0.127289
$326$	−39.1139	−2.16632
$327$	−6.33375	−0.350257
$328$	−14.4522	−0.797990
$329$	5.97178	0.329235
$330$	8.92734	0.491434
$331$	−26.1879	−1.43942	−0.719709	−	0.694275i	$-0.755725\pi$
$331$	−26.1879	−1.43942	−0.719709	+	0.694275i	$0.755725\pi$
$332$	36.5273	2.00470
$333$	−6.50056	−0.356228
$334$	47.3960	2.59339
$335$	−1.01100	−0.0552369
$336$	−2.02008	−0.110204
$337$	−19.2586	−1.04908	−0.524541	−	0.851385i	$-0.675763\pi$
$337$	−19.2586	−1.04908	−0.524541	+	0.851385i	$0.675763\pi$
$338$	12.7339	0.692633
$339$	−13.3528	−0.725223
$340$	−33.6568	−1.82530
$341$	11.9090	0.644908
$342$	−15.6286	−0.845096
$343$	−1.00000	−0.0539949
$344$	9.50829	0.512653
$345$	−10.2380	−0.551196
$346$	−14.5526	−0.782355
$347$	1.12777	0.0605419	0.0302710	−	0.999542i	$-0.490363\pi$
$347$	1.12777	0.0605419	0.0302710	+	0.999542i	$0.490363\pi$
$348$	−9.75646	−0.523001
$349$	6.88294	0.368435	0.184218	−	0.982885i	$-0.441025\pi$
$349$	6.88294	0.368435	0.184218	+	0.982885i	$0.441025\pi$
$350$	1.86665	0.0997767
$351$	2.67257	0.142651
$352$	−12.8078	−0.682658
$353$	−11.0071	−0.585847	−0.292924	−	0.956136i	$-0.594628\pi$
$353$	−11.0071	−0.585847	−0.292924	+	0.956136i	$0.594628\pi$
$354$	3.64193	0.193566
$355$	−13.3520	−0.708651
$356$	15.3726	0.814745
$357$	5.10047	0.269946
$358$	−48.9593	−2.58758
$359$	−11.3761	−0.600408	−0.300204	−	0.953875i	$-0.597055\pi$
$359$	−11.3761	−0.600408	−0.300204	+	0.953875i	$0.597055\pi$
$360$	3.82154	0.201413
$361$	32.6800	1.72000
$362$	−13.6550	−0.717688
$363$	8.12173	0.426280
$364$	7.28607	0.381894
$365$	29.4226	1.54005
$366$	−3.79610	−0.198425
$367$	13.0909	0.683338	0.341669	−	0.939820i	$-0.389008\pi$
$367$	13.0909	0.683338	0.341669	+	0.939820i	$0.389008\pi$
$368$	8.54448	0.445412
$369$	9.15363	0.476519
$370$	−34.2063	−1.77830
$371$	2.88579	0.149823
$372$	19.1370	0.992207
$373$	14.8836	0.770646	0.385323	−	0.922782i	$-0.374090\pi$
$373$	14.8836	0.770646	0.385323	+	0.922782i	$0.374090\pi$
$374$	18.8120	0.972744
$375$	−10.0240	−0.517638
$376$	9.42854	0.486240
$377$	−9.56436	−0.492590
$378$	−2.17399	−0.111818
$379$	−21.0799	−1.08280	−0.541401	−	0.840765i	$-0.682106\pi$
$379$	−21.0799	−1.08280	−0.541401	+	0.840765i	$0.682106\pi$
$380$	−47.4377	−2.43350
$381$	6.29917	0.322716
$382$	10.2045	0.522109
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	−11.7981	−0.602068
$385$	−4.10642	−0.209283
$386$	−25.5578	−1.30086
$387$	−6.02229	−0.306130
$388$	4.09054	0.207666
$389$	8.57328	0.434683	0.217341	−	0.976096i	$-0.430262\pi$
$389$	8.57328	0.434683	0.217341	+	0.976096i	$0.430262\pi$
$390$	14.0632	0.712119
$391$	−21.5739	−1.09104
$392$	−1.57885	−0.0797440
$393$	17.5302	0.884279
$394$	30.6261	1.54292
$395$	−5.52297	−0.277891
$396$	−4.62520	−0.232425
$397$	−1.94990	−0.0978627	−0.0489314	−	0.998802i	$-0.515582\pi$
$397$	−1.94990	−0.0978627	−0.0489314	+	0.998802i	$0.515582\pi$
$398$	−6.09416	−0.305473
$399$	7.18888	0.359894
$400$	−1.73450	−0.0867249
$401$	21.6336	1.08033	0.540165	−	0.841559i	$-0.318362\pi$
$401$	21.6336	1.08033	0.540165	+	0.841559i	$0.318362\pi$
$402$	0.908054	0.0452896
$403$	18.7602	0.934512
$404$	−16.2124	−0.806597
$405$	−2.42046	−0.120274
$406$	7.78011	0.386120
$407$	11.0285	0.546663
$408$	8.05288	0.398677
$409$	−6.71318	−0.331946	−0.165973	−	0.986130i	$-0.553076\pi$
$409$	−6.71318	−0.331946	−0.165973	+	0.986130i	$0.553076\pi$
$410$	48.1670	2.37880
$411$	4.64857	0.229297
$412$	27.3339	1.34664
$413$	−1.67522	−0.0824324
$414$	9.19550	0.451934
$415$	−32.4303	−1.59194
$416$	−20.1761	−0.989216
$417$	−15.5021	−0.759141
$418$	26.5146	1.29687
$419$	5.56649	0.271941	0.135971	−	0.990713i	$-0.456585\pi$
$419$	5.56649	0.271941	0.135971	+	0.990713i	$0.456585\pi$
$420$	−6.59877	−0.321987
$421$	−21.0677	−1.02677	−0.513387	−	0.858157i	$-0.671610\pi$
$421$	−21.0677	−1.02677	−0.513387	+	0.858157i	$0.671610\pi$
$422$	−43.5646	−2.12069
$423$	−5.97178	−0.290358
$424$	4.55623	0.221270
$425$	4.37941	0.212433
$426$	11.9924	0.581034
$427$	1.74614	0.0845017
$428$	30.8127	1.48939
$429$	−4.53414	−0.218910
$430$	−31.6897	−1.52821
$431$	11.4858	0.553253	0.276626	−	0.960978i	$-0.410784\pi$
$431$	11.4858	0.553253	0.276626	+	0.960978i	$0.410784\pi$
$432$	2.02008	0.0971911
$433$	21.4929	1.03288	0.516441	−	0.856323i	$-0.327257\pi$
$433$	21.4929	1.03288	0.516441	+	0.856323i	$0.327257\pi$
$434$	−15.2604	−0.732524
$435$	8.66214	0.415318
$436$	17.2674	0.826956
$437$	−30.4073	−1.45458
$438$	−26.4266	−1.26271
$439$	14.7821	0.705512	0.352756	−	0.935715i	$-0.385245\pi$
$439$	14.7821	0.705512	0.352756	+	0.935715i	$0.385245\pi$
$440$	−6.48343	−0.309085
$441$	1.00000	0.0476190
$442$	29.6345	1.40957
$443$	−32.5288	−1.54549	−0.772745	−	0.634717i	$-0.781117\pi$
$443$	−32.5288	−1.54549	−0.772745	+	0.634717i	$0.781117\pi$
$444$	17.7221	0.841054
$445$	−13.6483	−0.646993
$446$	−38.7460	−1.83468
$447$	5.55611	0.262795
$448$	12.3720	0.584524
$449$	7.02401	0.331484	0.165742	−	0.986169i	$-0.446998\pi$
$449$	7.02401	0.331484	0.165742	+	0.986169i	$0.446998\pi$
$450$	−1.86665	−0.0879948
$451$	−15.5296	−0.731258
$452$	36.4029	1.71225
$453$	−7.08098	−0.332693
$454$	−2.43974	−0.114503
$455$	−6.46884	−0.303264
$456$	11.3502	0.531520
$457$	−41.2616	−1.93014	−0.965069	−	0.261996i	$-0.915619\pi$
$457$	−41.2616	−1.93014	−0.965069	+	0.261996i	$0.915619\pi$
$458$	34.9674	1.63392
$459$	−5.10047	−0.238070
$460$	27.9113	1.30137
$461$	−16.3044	−0.759370	−0.379685	−	0.925116i	$-0.623968\pi$
$461$	−16.3044	−0.759370	−0.379685	+	0.925116i	$0.623968\pi$
$462$	3.68828	0.171594
$463$	18.1224	0.842220	0.421110	−	0.907010i	$-0.361641\pi$
$463$	18.1224	0.842220	0.421110	+	0.907010i	$0.361641\pi$
$464$	−7.22930	−0.335612
$465$	−16.9905	−0.787917
$466$	−36.0185	−1.66852
$467$	4.96596	0.229797	0.114899	−	0.993377i	$-0.463346\pi$
$467$	4.96596	0.229797	0.114899	+	0.993377i	$0.463346\pi$
$468$	−7.28607	−0.336799
$469$	−0.417689	−0.0192871
$470$	−31.4239	−1.44947
$471$	17.1582	0.790606
$472$	−2.64493	−0.121743
$473$	10.2171	0.469782
$474$	4.96059	0.227847
$475$	6.17257	0.283217
$476$	−13.9051	−0.637341
$477$	−2.88579	−0.132131
$478$	−33.5589	−1.53495
$479$	16.4395	0.751139	0.375570	−	0.926794i	$-0.377447\pi$
$479$	16.4395	0.751139	0.375570	+	0.926794i	$0.377447\pi$
$480$	18.2729	0.834039
$481$	17.3732	0.792149
$482$	11.1824	0.509346
$483$	−4.22978	−0.192461
$484$	−22.1418	−1.00645
$485$	−3.63173	−0.164908
$486$	2.17399	0.0986143
$487$	31.8777	1.44452	0.722258	−	0.691624i	$-0.243104\pi$
$487$	31.8777	1.44452	0.722258	+	0.691624i	$0.243104\pi$
$488$	2.75689	0.124799
$489$	−17.9917	−0.813613
$490$	5.26206	0.237716
$491$	−33.1710	−1.49699	−0.748494	−	0.663142i	$-0.769223\pi$
$491$	−33.1710	−1.49699	−0.748494	+	0.663142i	$0.769223\pi$
$492$	−24.9550	−1.12506
$493$	18.2531	0.822081
$494$	41.7684	1.87925
$495$	4.10642	0.184570
$496$	14.1800	0.636703
$497$	−5.51631	−0.247440
$498$	29.1280	1.30526
$499$	41.5783	1.86130	0.930651	−	0.365908i	$-0.119241\pi$
$499$	41.5783	1.86130	0.930651	+	0.365908i	$0.119241\pi$
$500$	27.3279	1.22214
$501$	21.8013	0.974012
$502$	−6.17331	−0.275528
$503$	−16.4866	−0.735101	−0.367551	−	0.930003i	$-0.619804\pi$
$503$	−16.4866	−0.735101	−0.367551	+	0.930003i	$0.619804\pi$
$504$	1.57885	0.0703276
$505$	14.3940	0.640523
$506$	−15.6006	−0.693531
$507$	5.85738	0.260135
$508$	−17.1731	−0.761932
$509$	−6.40104	−0.283721	−0.141860	−	0.989887i	$-0.545308\pi$
$509$	−6.40104	−0.283721	−0.141860	+	0.989887i	$0.545308\pi$
$510$	−26.8390	−1.18845
$511$	12.1558	0.537740
$512$	−21.6291	−0.955879
$513$	−7.18888	−0.317397
$514$	−54.8276	−2.41834
$515$	−24.2680	−1.06938
$516$	16.4182	0.722772
$517$	10.1314	0.445578
$518$	−14.1322	−0.620932
$519$	−6.69397	−0.293833
$520$	−10.2133	−0.447884
$521$	11.8295	0.518258	0.259129	−	0.965843i	$-0.416564\pi$
$521$	11.8295	0.518258	0.259129	+	0.965843i	$0.416564\pi$
$522$	−7.78011	−0.340526
$523$	−20.9881	−0.917746	−0.458873	−	0.888502i	$-0.651747\pi$
$523$	−20.9881	−0.917746	−0.458873	+	0.888502i	$0.651747\pi$
$524$	−47.7915	−2.08778
$525$	0.858628	0.0374736
$526$	53.3626	2.32672
$527$	−35.8030	−1.55960
$528$	−3.42716	−0.149148
$529$	−5.10900	−0.222131
$530$	−15.1852	−0.659603
$531$	1.67522	0.0726985
$532$	−19.5986	−0.849709
$533$	−24.4637	−1.05964
$534$	12.2586	0.530480
$535$	−27.3566	−1.18273
$536$	−0.659469	−0.0284847
$537$	−22.5204	−0.971829
$538$	20.3496	0.877333
$539$	−1.69655	−0.0730754
$540$	6.59877	0.283966
$541$	−21.1221	−0.908111	−0.454055	−	0.890973i	$-0.650023\pi$
$541$	−21.1221	−0.908111	−0.454055	+	0.890973i	$0.650023\pi$
$542$	−20.3430	−0.873806
$543$	−6.28105	−0.269546
$544$	38.5052	1.65090
$545$	−15.3306	−0.656691
$546$	5.81014	0.248651
$547$	5.57773	0.238487	0.119243	−	0.992865i	$-0.461953\pi$
$547$	5.57773	0.238487	0.119243	+	0.992865i	$0.461953\pi$
$548$	−12.6731	−0.541369
$549$	−1.74614	−0.0745235
$550$	3.16686	0.135035
$551$	25.7270	1.09601
$552$	−6.67818	−0.284242
$553$	−2.28179	−0.0970314
$554$	8.57727	0.364413
$555$	−15.7343	−0.667886
$556$	42.2625	1.79233
$557$	15.8760	0.672686	0.336343	−	0.941740i	$-0.390810\pi$
$557$	15.8760	0.672686	0.336343	+	0.941740i	$0.390810\pi$
$558$	15.2604	0.646026
$559$	16.0950	0.680745
$560$	−4.88952	−0.206620
$561$	8.65319	0.365338
$562$	−55.7684	−2.35245
$563$	−8.84676	−0.372846	−0.186423	−	0.982470i	$-0.559690\pi$
$563$	−8.84676	−0.372846	−0.186423	+	0.982470i	$0.559690\pi$
$564$	16.2805	0.685534
$565$	−32.3199	−1.35971
$566$	−22.6098	−0.950363
$567$	−1.00000	−0.0419961
$568$	−8.70942	−0.365439
$569$	−19.9748	−0.837388	−0.418694	−	0.908127i	$-0.637512\pi$
$569$	−19.9748	−0.837388	−0.418694	+	0.908127i	$0.637512\pi$
$570$	−37.8283	−1.58445
$571$	−20.3583	−0.851968	−0.425984	−	0.904731i	$-0.640072\pi$
$571$	−20.3583	−0.851968	−0.425984	+	0.904731i	$0.640072\pi$
$572$	12.3612	0.516846
$573$	4.69391	0.196091
$574$	19.8999	0.830607
$575$	−3.63180	−0.151457
$576$	−12.3720	−0.515502
$577$	18.8973	0.786705	0.393353	−	0.919388i	$-0.371315\pi$
$577$	18.8973	0.786705	0.393353	+	0.919388i	$0.371315\pi$
$578$	−19.5982	−0.815176
$579$	−11.7562	−0.488569
$580$	−23.6151	−0.980564
$581$	−13.3984	−0.555860
$582$	3.26192	0.135211
$583$	4.89588	0.202766
$584$	19.1922	0.794178
$585$	6.46884	0.267454
$586$	−59.7091	−2.46656
$587$	5.34957	0.220800	0.110400	−	0.993887i	$-0.464787\pi$
$587$	5.34957	0.220800	0.110400	+	0.993887i	$0.464787\pi$
$588$	−2.72624	−0.112428
$589$	−50.4626	−2.07928
$590$	8.81514	0.362913
$591$	14.0875	0.579483
$592$	13.1316	0.539707
$593$	−23.6831	−0.972548	−0.486274	−	0.873806i	$-0.661644\pi$
$593$	−23.6831	−0.972548	−0.486274	+	0.873806i	$0.661644\pi$
$594$	−3.68828	−0.151332
$595$	12.3455	0.506116
$596$	−15.1473	−0.620458
$597$	−2.80321	−0.114728
$598$	−24.5756	−1.00497
$599$	47.8308	1.95431	0.977156	−	0.212523i	$-0.0681681\pi$
$599$	47.8308	1.95431	0.977156	+	0.212523i	$0.0681681\pi$
$600$	1.35565	0.0553440
$601$	−20.9563	−0.854827	−0.427413	−	0.904056i	$-0.640575\pi$
$601$	−20.9563	−0.854827	−0.427413	+	0.904056i	$0.640575\pi$
$602$	−13.0924	−0.533607
$603$	0.417689	0.0170096
$604$	19.3045	0.785488
$605$	19.6583	0.799224
$606$	−12.9283	−0.525175
$607$	−36.3200	−1.47418	−0.737092	−	0.675793i	$-0.763801\pi$
$607$	−36.3200	−1.47418	−0.737092	+	0.675793i	$0.763801\pi$
$608$	54.2713	2.20099
$609$	3.57872	0.145017
$610$	−9.18830	−0.372023
$611$	15.9600	0.645672
$612$	13.9051	0.562082
$613$	27.0434	1.09227	0.546137	−	0.837696i	$-0.316098\pi$
$613$	27.0434	1.09227	0.546137	+	0.837696i	$0.316098\pi$
$614$	32.0771	1.29453
$615$	22.1560	0.893416
$616$	−2.67859	−0.107924
$617$	13.4219	0.540344	0.270172	−	0.962812i	$-0.412919\pi$
$617$	13.4219	0.540344	0.270172	+	0.962812i	$0.412919\pi$
$618$	21.7969	0.876799
$619$	−32.3621	−1.30074	−0.650371	−	0.759617i	$-0.725386\pi$
$619$	−32.3621	−1.30074	−0.650371	+	0.759617i	$0.725386\pi$
$620$	46.3203	1.86027
$621$	4.22978	0.169735
$622$	−18.8264	−0.754870
$623$	−5.63874	−0.225911
$624$	−5.39880	−0.216125
$625$	−28.5559	−1.14224
$626$	39.0430	1.56047
$627$	12.1963	0.487072
$628$	−46.7773	−1.86662
$629$	−33.1559	−1.32201
$630$	−5.26206	−0.209646
$631$	−44.8463	−1.78530	−0.892651	−	0.450749i	$-0.851157\pi$
$631$	−44.8463	−1.78530	−0.892651	+	0.450749i	$0.851157\pi$
$632$	−3.60260	−0.143304
$633$	−20.0390	−0.796478
$634$	36.1707	1.43652
$635$	15.2469	0.605055
$636$	7.86737	0.311961
$637$	−2.67257	−0.105891
$638$	13.1993	0.522566
$639$	5.51631	0.218222
$640$	−28.5568	−1.12880
$641$	19.2088	0.758704	0.379352	−	0.925252i	$-0.376147\pi$
$641$	19.2088	0.758704	0.379352	+	0.925252i	$0.376147\pi$
$642$	24.5710	0.969740
$643$	−29.7325	−1.17254	−0.586269	−	0.810117i	$-0.699404\pi$
$643$	−29.7325	−1.17254	−0.586269	+	0.810117i	$0.699404\pi$
$644$	11.5314	0.454401
$645$	−14.5767	−0.573957
$646$	−79.7131	−3.13627
$647$	−4.26802	−0.167793	−0.0838965	−	0.996474i	$-0.526737\pi$
$647$	−4.26802	−0.167793	−0.0838965	+	0.996474i	$0.526737\pi$
$648$	−1.57885	−0.0620231
$649$	−2.84210	−0.111562
$650$	4.98875	0.195675
$651$	−7.01954	−0.275118
$652$	49.0498	1.92094
$653$	−13.4897	−0.527894	−0.263947	−	0.964537i	$-0.585024\pi$
$653$	−13.4897	−0.527894	−0.263947	+	0.964537i	$0.585024\pi$
$654$	13.7695	0.538431
$655$	42.4310	1.65792
$656$	−18.4911	−0.721955
$657$	−12.1558	−0.474243
$658$	−12.9826	−0.506114
$659$	31.8191	1.23950	0.619748	−	0.784801i	$-0.287235\pi$
$659$	31.8191	1.23950	0.619748	+	0.784801i	$0.287235\pi$
$660$	−11.1951	−0.435769
$661$	41.3505	1.60835	0.804174	−	0.594394i	$-0.202608\pi$
$661$	41.3505	1.60835	0.804174	+	0.594394i	$0.202608\pi$
$662$	56.9324	2.21274
$663$	13.6314	0.529398
$664$	−21.1541	−0.820938
$665$	17.4004	0.674758
$666$	14.1322	0.547610
$667$	−15.1372	−0.586114
$668$	−59.4358	−2.29964
$669$	−17.8225	−0.689057
$670$	2.19791	0.0849126
$671$	2.96241	0.114363
$672$	7.54934	0.291222
$673$	27.0940	1.04440	0.522198	−	0.852824i	$-0.325112\pi$
$673$	27.0940	1.04440	0.522198	+	0.852824i	$0.325112\pi$
$674$	41.8680	1.61270
$675$	−0.858628	−0.0330486
$676$	−15.9687	−0.614179
$677$	−36.1698	−1.39012	−0.695059	−	0.718953i	$-0.744622\pi$
$677$	−36.1698	−1.39012	−0.695059	+	0.718953i	$0.744622\pi$
$678$	29.0288	1.11485
$679$	−1.50043	−0.0575812
$680$	19.4917	0.747472
$681$	−1.12224	−0.0430043
$682$	−25.8900	−0.991381
$683$	−28.7262	−1.09918	−0.549589	−	0.835435i	$-0.685216\pi$
$683$	−28.7262	−1.09918	−0.549589	+	0.835435i	$0.685216\pi$
$684$	19.5986	0.749373
$685$	11.2517	0.429904
$686$	2.17399	0.0830034
$687$	16.0844	0.613659
$688$	12.1655	0.463805
$689$	7.71247	0.293822
$690$	22.2573	0.847323
$691$	−5.36240	−0.203995	−0.101998	−	0.994785i	$-0.532523\pi$
$691$	−5.36240	−0.203995	−0.101998	+	0.994785i	$0.532523\pi$
$692$	18.2494	0.693738
$693$	1.69655	0.0644465
$694$	−2.45177	−0.0930678
$695$	−37.5222	−1.42330
$696$	5.65026	0.214172
$697$	46.6878	1.76843
$698$	−14.9635	−0.566375
$699$	−16.5679	−0.626655
$700$	−2.34083	−0.0884751
$701$	19.9447	0.753299	0.376650	−	0.926356i	$-0.377076\pi$
$701$	19.9447	0.753299	0.376650	+	0.926356i	$0.377076\pi$
$702$	−5.81014	−0.219290
$703$	−46.7317	−1.76252
$704$	20.9898	0.791081
$705$	−14.4544	−0.544386
$706$	23.9293	0.900590
$707$	5.94679	0.223652
$708$	−4.56707	−0.171641
$709$	−42.5577	−1.59829	−0.799144	−	0.601140i	$-0.794713\pi$
$709$	−42.5577	−1.59829	−0.799144	+	0.601140i	$0.794713\pi$
$710$	29.0272	1.08937
$711$	2.28179	0.0855737
$712$	−8.90272	−0.333644
$713$	29.6911	1.11194
$714$	−11.0884	−0.414973
$715$	−10.9747	−0.410430
$716$	61.3962	2.29448
$717$	−15.4365	−0.576488
$718$	24.7316	0.922975
$719$	−21.3920	−0.797788	−0.398894	−	0.916997i	$-0.630606\pi$
$719$	−21.3920	−0.797788	−0.398894	+	0.916997i	$0.630606\pi$
$720$	4.88952	0.182222
$721$	−10.0262	−0.373395
$722$	−71.0461	−2.64406
$723$	5.14373	0.191298
$724$	17.1237	0.636396
$725$	3.07279	0.114120
$726$	−17.6566	−0.655297
$727$	7.85226	0.291224	0.145612	−	0.989342i	$-0.453485\pi$
$727$	7.85226	0.291224	0.145612	+	0.989342i	$0.453485\pi$
$728$	−4.21958	−0.156388
$729$	1.00000	0.0370370
$730$	−63.9645	−2.36743
$731$	−30.7165	−1.13609
$732$	4.76041	0.175950
$733$	−31.2916	−1.15578	−0.577892	−	0.816113i	$-0.696124\pi$
$733$	−31.2916	−1.15578	−0.577892	+	0.816113i	$0.696124\pi$
$734$	−28.4595	−1.05046
$735$	2.42046	0.0892800
$736$	−31.9320	−1.17703
$737$	−0.708630	−0.0261027
$738$	−19.8999	−0.732526
$739$	2.11881	0.0779418	0.0389709	−	0.999240i	$-0.487592\pi$
$739$	2.11881	0.0779418	0.0389709	+	0.999240i	$0.487592\pi$
$740$	42.8957	1.57688
$741$	19.2128	0.705799
$742$	−6.27368	−0.230314
$743$	−41.9983	−1.54077	−0.770384	−	0.637580i	$-0.779936\pi$
$743$	−41.9983	−1.54077	−0.770384	+	0.637580i	$0.779936\pi$
$744$	−11.0828	−0.406315
$745$	13.4483	0.492709
$746$	−32.3569	−1.18467
$747$	13.3984	0.490222
$748$	−23.5907	−0.862562
$749$	−11.3022	−0.412975
$750$	21.7922	0.795737
$751$	−1.78982	−0.0653116	−0.0326558	−	0.999467i	$-0.510397\pi$
$751$	−1.78982	−0.0653116	−0.0326558	+	0.999467i	$0.510397\pi$
$752$	12.0635	0.439909
$753$	−2.83962	−0.103481
$754$	20.7929	0.757231
$755$	−17.1392	−0.623760
$756$	2.72624	0.0991526
$757$	12.5821	0.457306	0.228653	−	0.973508i	$-0.426568\pi$
$757$	12.5821	0.457306	0.228653	+	0.973508i	$0.426568\pi$
$758$	45.8275	1.66453
$759$	−7.17601	−0.260473
$760$	27.4726	0.996537
$761$	−40.9330	−1.48382	−0.741910	−	0.670500i	$-0.766080\pi$
$761$	−40.9330	−1.48382	−0.741910	+	0.670500i	$0.766080\pi$
$762$	−13.6944	−0.496094
$763$	−6.33375	−0.229297
$764$	−12.7968	−0.462970
$765$	−12.3455	−0.446352
$766$	2.17399	0.0785496
$767$	−4.47715	−0.161661
$768$	0.904812	0.0326496
$769$	−23.5749	−0.850131	−0.425066	−	0.905162i	$-0.639749\pi$
$769$	−23.5749	−0.850131	−0.425066	+	0.905162i	$0.639749\pi$
$770$	8.92734	0.321719
$771$	−25.2198	−0.908268
$772$	32.0502	1.15351
$773$	−1.55930	−0.0560840	−0.0280420	−	0.999607i	$-0.508927\pi$
$773$	−1.55930	−0.0560840	−0.0280420	+	0.999607i	$0.508927\pi$
$774$	13.0924	0.470597
$775$	−6.02718	−0.216503
$776$	−2.36895	−0.0850405
$777$	−6.50056	−0.233206
$778$	−18.6383	−0.668214
$779$	65.8043	2.35768
$780$	−17.6357	−0.631458
$781$	−9.35868	−0.334880
$782$	46.9014	1.67719
$783$	−3.57872	−0.127893
$784$	−2.02008	−0.0721457
$785$	41.5306	1.48229
$786$	−38.1104	−1.35935
$787$	−39.4682	−1.40689	−0.703445	−	0.710750i	$-0.748356\pi$
$787$	−39.4682	−1.40689	−0.703445	+	0.710750i	$0.748356\pi$
$788$	−38.4060	−1.36816
$789$	24.5459	0.873857
$790$	12.0069	0.427187
$791$	−13.3528	−0.474770
$792$	2.67859	0.0951797
$793$	4.66668	0.165719
$794$	4.23907	0.150439
$795$	−6.98494	−0.247730
$796$	7.64224	0.270872
$797$	−16.3847	−0.580377	−0.290189	−	0.956969i	$-0.593718\pi$
$797$	−16.3847	−0.580377	−0.290189	+	0.956969i	$0.593718\pi$
$798$	−15.6286	−0.553245
$799$	−30.4589	−1.07756
$800$	6.48208	0.229176
$801$	5.63874	0.199235
$802$	−47.0312	−1.66073
$803$	20.6229	0.727765
$804$	−1.13872	−0.0401597
$805$	−10.2380	−0.360842
$806$	−40.7845	−1.43657
$807$	9.36047	0.329504
$808$	9.38909	0.330307
$809$	20.5305	0.721812	0.360906	−	0.932602i	$-0.382467\pi$
$809$	20.5305	0.721812	0.360906	+	0.932602i	$0.382467\pi$
$810$	5.26206	0.184890
$811$	6.40721	0.224988	0.112494	−	0.993652i	$-0.464116\pi$
$811$	6.40721	0.224988	0.112494	+	0.993652i	$0.464116\pi$
$812$	−9.75646	−0.342385
$813$	−9.35743	−0.328179
$814$	−23.9759	−0.840354
$815$	−43.5482	−1.52543
$816$	10.3034	0.360690
$817$	−43.2935	−1.51465
$818$	14.5944	0.510282
$819$	2.67257	0.0933871
$820$	−60.4027	−2.10935
$821$	18.9557	0.661560	0.330780	−	0.943708i	$-0.392688\pi$
$821$	18.9557	0.661560	0.330780	+	0.943708i	$0.392688\pi$
$822$	−10.1059	−0.352485
$823$	16.8323	0.586736	0.293368	−	0.956000i	$-0.405224\pi$
$823$	16.8323	0.586736	0.293368	+	0.956000i	$0.405224\pi$
$824$	−15.8299	−0.551459
$825$	1.45670	0.0507159
$826$	3.64193	0.126719
$827$	11.2669	0.391787	0.195893	−	0.980625i	$-0.437239\pi$
$827$	11.2669	0.391787	0.195893	+	0.980625i	$0.437239\pi$
$828$	−11.5314	−0.400744
$829$	19.5674	0.679605	0.339803	−	0.940497i	$-0.389640\pi$
$829$	19.5674	0.679605	0.339803	+	0.940497i	$0.389640\pi$
$830$	70.5033	2.44720
$831$	3.94540	0.136864
$832$	33.0651	1.14633
$833$	5.10047	0.176721
$834$	33.7015	1.16699
$835$	52.7693	1.82616
$836$	−33.2500	−1.14998
$837$	7.01954	0.242631
$838$	−12.1015	−0.418040
$839$	29.4510	1.01676	0.508381	−	0.861132i	$-0.330244\pi$
$839$	29.4510	1.01676	0.508381	+	0.861132i	$0.330244\pi$
$840$	3.82154	0.131856
$841$	−16.1928	−0.558372
$842$	45.8009	1.57840
$843$	−25.6525	−0.883520
$844$	54.6311	1.88048
$845$	14.1776	0.487723
$846$	12.9826	0.446351
$847$	8.12173	0.279066
$848$	5.82952	0.200187
$849$	−10.4001	−0.356932
$850$	−9.52080	−0.326561
$851$	27.4959	0.942547
$852$	−15.0388	−0.515221
$853$	7.30226	0.250025	0.125012	−	0.992155i	$-0.460103\pi$
$853$	7.30226	0.250025	0.125012	+	0.992155i	$0.460103\pi$
$854$	−3.79610	−0.129900
$855$	−17.4004	−0.595081
$856$	−17.8445	−0.609914
$857$	−3.15172	−0.107661	−0.0538303	−	0.998550i	$-0.517143\pi$
$857$	−3.15172	−0.107661	−0.0538303	+	0.998550i	$0.517143\pi$
$858$	9.85718	0.336519
$859$	−38.3486	−1.30844	−0.654219	−	0.756305i	$-0.727003\pi$
$859$	−38.3486	−1.30844	−0.654219	+	0.756305i	$0.727003\pi$
$860$	39.7397	1.35511
$861$	9.15363	0.311955
$862$	−24.9701	−0.850485
$863$	3.94878	0.134418	0.0672090	−	0.997739i	$-0.478591\pi$
$863$	3.94878	0.134418	0.0672090	+	0.997739i	$0.478591\pi$
$864$	−7.54934	−0.256834
$865$	−16.2025	−0.550901
$866$	−46.7253	−1.58779
$867$	−9.01482	−0.306159
$868$	19.1370	0.649552
$869$	−3.87116	−0.131320
$870$	−18.8314	−0.638445
$871$	−1.11630	−0.0378245
$872$	−10.0000	−0.338644
$873$	1.50043	0.0507818
$874$	66.1053	2.23605
$875$	−10.0240	−0.338874
$876$	33.1397	1.11969
$877$	−0.287061	−0.00969335	−0.00484667	−	0.999988i	$-0.501543\pi$
$877$	−0.287061	−0.00969335	−0.00484667	+	0.999988i	$0.501543\pi$
$878$	−32.1362	−1.08454
$879$	−27.4652	−0.926377
$880$	−8.29531	−0.279635
$881$	−40.0743	−1.35014	−0.675069	−	0.737754i	$-0.735886\pi$
$881$	−40.0743	−1.35014	−0.675069	+	0.737754i	$0.735886\pi$
$882$	−2.17399	−0.0732021
$883$	−21.3897	−0.719819	−0.359910	−	0.932987i	$-0.617192\pi$
$883$	−21.3897	−0.719819	−0.359910	+	0.932987i	$0.617192\pi$
$884$	−37.1624	−1.24991
$885$	4.05481	0.136301
$886$	70.7173	2.37580
$887$	−48.6653	−1.63402	−0.817011	−	0.576622i	$-0.804371\pi$
$887$	−48.6653	−1.63402	−0.817011	+	0.576622i	$0.804371\pi$
$888$	−10.2634	−0.344417
$889$	6.29917	0.211267
$890$	29.6714	0.994587
$891$	−1.69655	−0.0568365
$892$	48.5885	1.62686
$893$	−42.9304	−1.43661
$894$	−12.0789	−0.403980
$895$	−54.5098	−1.82206
$896$	−11.7981	−0.394146
$897$	−11.3044	−0.377442
$898$	−15.2702	−0.509572
$899$	−25.1210	−0.837831
$900$	2.34083	0.0780277
$901$	−14.7189	−0.490357
$902$	33.7611	1.12412
$903$	−6.02229	−0.200409
$904$	−21.0820	−0.701178
$905$	−15.2030	−0.505366
$906$	15.3940	0.511431
$907$	−20.2869	−0.673614	−0.336807	−	0.941574i	$-0.609347\pi$
$907$	−20.2869	−0.673614	−0.336807	+	0.941574i	$0.609347\pi$
$908$	3.05950	0.101533
$909$	−5.94679	−0.197242
$910$	14.0632	0.466191
$911$	19.6471	0.650939	0.325469	−	0.945553i	$-0.394478\pi$
$911$	19.6471	0.650939	0.325469	+	0.945553i	$0.394478\pi$
$912$	14.5221	0.480875
$913$	−22.7310	−0.752287
$914$	89.7025	2.96709
$915$	−4.22646	−0.139723
$916$	−43.8501	−1.44885
$917$	17.5302	0.578897
$918$	11.0884	0.365971
$919$	−13.2475	−0.436996	−0.218498	−	0.975837i	$-0.570116\pi$
$919$	−13.2475	−0.436996	−0.218498	+	0.975837i	$0.570116\pi$
$920$	−16.1643	−0.532920
$921$	14.7549	0.486191
$922$	35.4456	1.16734
$923$	−14.7427	−0.485262
$924$	−4.62520	−0.152158
$925$	−5.58156	−0.183521
$926$	−39.3980	−1.29470
$927$	10.0262	0.329303
$928$	27.0170	0.886875
$929$	56.9349	1.86797	0.933987	−	0.357306i	$-0.116305\pi$
$929$	56.9349	1.86797	0.933987	+	0.357306i	$0.116305\pi$
$930$	36.9373	1.21122
$931$	7.18888	0.235606
$932$	45.1681	1.47953
$933$	−8.65983	−0.283510
$934$	−10.7960	−0.353254
$935$	20.9447	0.684965
$936$	4.21958	0.137921
$937$	−1.15822	−0.0378375	−0.0189188	−	0.999821i	$-0.506022\pi$
$937$	−1.15822	−0.0378375	−0.0189188	+	0.999821i	$0.506022\pi$
$938$	0.908054	0.0296490
$939$	17.9591	0.586073
$940$	39.4064	1.28529
$941$	−8.78578	−0.286408	−0.143204	−	0.989693i	$-0.545741\pi$
$941$	−8.78578	−0.286408	−0.143204	+	0.989693i	$0.545741\pi$
$942$	−37.3017	−1.21536
$943$	−38.7178	−1.26082
$944$	−3.38409	−0.110143
$945$	−2.42046	−0.0787376
$946$	−22.2119	−0.722171
$947$	−45.1112	−1.46592	−0.732958	−	0.680273i	$-0.761861\pi$
$947$	−45.1112	−1.46592	−0.732958	+	0.680273i	$0.761861\pi$
$948$	−6.22071	−0.202039
$949$	32.4872	1.05458
$950$	−13.4191	−0.435374
$951$	16.6379	0.539521
$952$	8.05288	0.260995
$953$	−21.0113	−0.680622	−0.340311	−	0.940313i	$-0.610532\pi$
$953$	−21.0113	−0.680622	−0.340311	+	0.940313i	$0.610532\pi$
$954$	6.27368	0.203118
$955$	11.3614	0.367647
$956$	42.0838	1.36109
$957$	6.07146	0.196262
$958$	−35.7393	−1.15468
$959$	4.64857	0.150110
$960$	−29.9461	−0.966505
$961$	18.2740	0.589483
$962$	−37.7692	−1.21773
$963$	11.3022	0.364210
$964$	−14.0231	−0.451653
$965$	−28.4553	−0.916009
$966$	9.19550	0.295860
$967$	21.8759	0.703481	0.351740	−	0.936098i	$-0.385590\pi$
$967$	21.8759	0.703481	0.351740	+	0.936098i	$0.385590\pi$
$968$	12.8230	0.412147
$969$	−36.6667	−1.17790
$970$	7.89536	0.253505
$971$	−32.4250	−1.04057	−0.520284	−	0.853993i	$-0.674174\pi$
$971$	−32.4250	−1.04057	−0.520284	+	0.853993i	$0.674174\pi$
$972$	−2.72624	−0.0874443
$973$	−15.5021	−0.496975
$974$	−69.3019	−2.22057
$975$	2.29474	0.0734906
$976$	3.52734	0.112908
$977$	0.0529477	0.00169395	0.000846974	−	1.00000i	$-0.499730\pi$
$977$	0.0529477	0.00169395	0.000846974		1.00000i	$0.499730\pi$
$978$	39.1139	1.25072
$979$	−9.56638	−0.305743
$980$	−6.59877	−0.210790
$981$	6.33375	0.202221
$982$	72.1136	2.30124
$983$	−30.3893	−0.969270	−0.484635	−	0.874717i	$-0.661047\pi$
$983$	−30.3893	−0.969270	−0.484635	+	0.874717i	$0.661047\pi$
$984$	14.4522	0.460720
$985$	34.0983	1.08646
$986$	−39.6822	−1.26374
$987$	−5.97178	−0.190084
$988$	−52.3787	−1.66639
$989$	25.4729	0.809992
$990$	−8.92734	−0.283729
$991$	−10.1290	−0.321759	−0.160879	−	0.986974i	$-0.551433\pi$
$991$	−10.1290	−0.321759	−0.160879	+	0.986974i	$0.551433\pi$
$992$	−52.9929	−1.68253
$993$	26.1879	0.831049
$994$	11.9924	0.380376
$995$	−6.78507	−0.215101
$996$	−36.5273	−1.15741
$997$	−33.9529	−1.07530	−0.537650	−	0.843168i	$-0.680688\pi$
$997$	−33.9529	−1.07530	−0.537650	+	0.843168i	$0.680688\pi$
$998$	−90.3910	−2.86128
$999$	6.50056	0.205669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.r.1.6	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.r.1.6	✓	46	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.17399 q^{2} -1.00000 q^{3} +2.72624 q^{4} -2.42046 q^{5} +2.17399 q^{6} -1.00000 q^{7} -1.57885 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.17399 q^{2} -1.00000 q^{3} +2.72624 q^{4} -2.42046 q^{5} +2.17399 q^{6} -1.00000 q^{7} -1.57885 q^{8} +1.00000 q^{9} +5.26206 q^{10} -1.69655 q^{11} -2.72624 q^{12} -2.67257 q^{13} +2.17399 q^{14} +2.42046 q^{15} -2.02008 q^{16} +5.10047 q^{17} -2.17399 q^{18} +7.18888 q^{19} -6.59877 q^{20} +1.00000 q^{21} +3.68828 q^{22} -4.22978 q^{23} +1.57885 q^{24} +0.858628 q^{25} +5.81014 q^{26} -1.00000 q^{27} -2.72624 q^{28} +3.57872 q^{29} -5.26206 q^{30} -7.01954 q^{31} +7.54934 q^{32} +1.69655 q^{33} -11.0884 q^{34} +2.42046 q^{35} +2.72624 q^{36} -6.50056 q^{37} -15.6286 q^{38} +2.67257 q^{39} +3.82154 q^{40} +9.15363 q^{41} -2.17399 q^{42} -6.02229 q^{43} -4.62520 q^{44} -2.42046 q^{45} +9.19550 q^{46} -5.97178 q^{47} +2.02008 q^{48} +1.00000 q^{49} -1.86665 q^{50} -5.10047 q^{51} -7.28607 q^{52} -2.88579 q^{53} +2.17399 q^{54} +4.10642 q^{55} +1.57885 q^{56} -7.18888 q^{57} -7.78011 q^{58} +1.67522 q^{59} +6.59877 q^{60} -1.74614 q^{61} +15.2604 q^{62} -1.00000 q^{63} -12.3720 q^{64} +6.46884 q^{65} -3.68828 q^{66} +0.417689 q^{67} +13.9051 q^{68} +4.22978 q^{69} -5.26206 q^{70} +5.51631 q^{71} -1.57885 q^{72} -12.1558 q^{73} +14.1322 q^{74} -0.858628 q^{75} +19.5986 q^{76} +1.69655 q^{77} -5.81014 q^{78} +2.28179 q^{79} +4.88952 q^{80} +1.00000 q^{81} -19.8999 q^{82} +13.3984 q^{83} +2.72624 q^{84} -12.3455 q^{85} +13.0924 q^{86} -3.57872 q^{87} +2.67859 q^{88} +5.63874 q^{89} +5.26206 q^{90} +2.67257 q^{91} -11.5314 q^{92} +7.01954 q^{93} +12.9826 q^{94} -17.4004 q^{95} -7.54934 q^{96} +1.50043 q^{97} -2.17399 q^{98} -1.69655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9} - 10 q^{10} + 31 q^{11} - 45 q^{12} - 32 q^{13} - 3 q^{14} + 9 q^{15} + 43 q^{16} - 36 q^{17} + 3 q^{18} - 13 q^{19} - 19 q^{20} + 46 q^{21} - 13 q^{22} + 24 q^{23} - 6 q^{24} + 35 q^{25} - 11 q^{26} - 46 q^{27} - 45 q^{28} + 11 q^{29} + 10 q^{30} - 23 q^{31} + 5 q^{32} - 31 q^{33} - 35 q^{34} + 9 q^{35} + 45 q^{36} - 37 q^{37} - 32 q^{38} + 32 q^{39} - 28 q^{40} - 27 q^{41} + 3 q^{42} - 7 q^{43} + 46 q^{44} - 9 q^{45} + 16 q^{46} - 18 q^{47} - 43 q^{48} + 46 q^{49} + 10 q^{50} + 36 q^{51} - 62 q^{52} - 62 q^{53} - 3 q^{54} - 28 q^{55} - 6 q^{56} + 13 q^{57} - 36 q^{58} - 3 q^{59} + 19 q^{60} - 31 q^{61} - 41 q^{62} - 46 q^{63} + 42 q^{64} + 2 q^{65} + 13 q^{66} - 9 q^{67} - 70 q^{68} - 24 q^{69} + 10 q^{70} + 77 q^{71} + 6 q^{72} - 38 q^{73} + 14 q^{74} - 35 q^{75} - 41 q^{76} - 31 q^{77} + 11 q^{78} + 8 q^{79} - 59 q^{80} + 46 q^{81} - 53 q^{82} - 38 q^{83} + 45 q^{84} - 26 q^{85} + 37 q^{86} - 11 q^{87} - 26 q^{88} - 39 q^{89} - 10 q^{90} + 32 q^{91} + 2 q^{92} + 23 q^{93} - 55 q^{94} + 35 q^{95} - 5 q^{96} - 61 q^{97} + 3 q^{98} + 31 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9 - 10 * q^10 + 31 * q^11 - 45 * q^12 - 32 * q^13 - 3 * q^14 + 9 * q^15 + 43 * q^16 - 36 * q^17 + 3 * q^18 - 13 * q^19 - 19 * q^20 + 46 * q^21 - 13 * q^22 + 24 * q^23 - 6 * q^24 + 35 * q^25 - 11 * q^26 - 46 * q^27 - 45 * q^28 + 11 * q^29 + 10 * q^30 - 23 * q^31 + 5 * q^32 - 31 * q^33 - 35 * q^34 + 9 * q^35 + 45 * q^36 - 37 * q^37 - 32 * q^38 + 32 * q^39 - 28 * q^40 - 27 * q^41 + 3 * q^42 - 7 * q^43 + 46 * q^44 - 9 * q^45 + 16 * q^46 - 18 * q^47 - 43 * q^48 + 46 * q^49 + 10 * q^50 + 36 * q^51 - 62 * q^52 - 62 * q^53 - 3 * q^54 - 28 * q^55 - 6 * q^56 + 13 * q^57 - 36 * q^58 - 3 * q^59 + 19 * q^60 - 31 * q^61 - 41 * q^62 - 46 * q^63 + 42 * q^64 + 2 * q^65 + 13 * q^66 - 9 * q^67 - 70 * q^68 - 24 * q^69 + 10 * q^70 + 77 * q^71 + 6 * q^72 - 38 * q^73 + 14 * q^74 - 35 * q^75 - 41 * q^76 - 31 * q^77 + 11 * q^78 + 8 * q^79 - 59 * q^80 + 46 * q^81 - 53 * q^82 - 38 * q^83 + 45 * q^84 - 26 * q^85 + 37 * q^86 - 11 * q^87 - 26 * q^88 - 39 * q^89 - 10 * q^90 + 32 * q^91 + 2 * q^92 + 23 * q^93 - 55 * q^94 + 35 * q^95 - 5 * q^96 - 61 * q^97 + 3 * q^98 + 31 * q^99

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