LMFDB - Embedded newform 8031.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$1$
Dimension:	$102$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63837 q^{2} -1.00000 q^{3} +4.96099 q^{4} -0.827443 q^{5} +2.63837 q^{6} +4.06107 q^{7} -7.81219 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.63837 q^{2} -1.00000 q^{3} +4.96099 q^{4} -0.827443 q^{5} +2.63837 q^{6} +4.06107 q^{7} -7.81219 q^{8} +1.00000 q^{9} +2.18310 q^{10} +1.88646 q^{11} -4.96099 q^{12} -5.96092 q^{13} -10.7146 q^{14} +0.827443 q^{15} +10.6894 q^{16} +0.243176 q^{17} -2.63837 q^{18} -3.37914 q^{19} -4.10494 q^{20} -4.06107 q^{21} -4.97718 q^{22} -7.39214 q^{23} +7.81219 q^{24} -4.31534 q^{25} +15.7271 q^{26} -1.00000 q^{27} +20.1470 q^{28} -7.38646 q^{29} -2.18310 q^{30} +4.99040 q^{31} -12.5783 q^{32} -1.88646 q^{33} -0.641588 q^{34} -3.36031 q^{35} +4.96099 q^{36} +8.85570 q^{37} +8.91541 q^{38} +5.96092 q^{39} +6.46414 q^{40} +6.50441 q^{41} +10.7146 q^{42} +11.5715 q^{43} +9.35871 q^{44} -0.827443 q^{45} +19.5032 q^{46} +0.239644 q^{47} -10.6894 q^{48} +9.49233 q^{49} +11.3855 q^{50} -0.243176 q^{51} -29.5721 q^{52} +4.82029 q^{53} +2.63837 q^{54} -1.56094 q^{55} -31.7259 q^{56} +3.37914 q^{57} +19.4882 q^{58} -10.1189 q^{59} +4.10494 q^{60} -1.06763 q^{61} -13.1665 q^{62} +4.06107 q^{63} +11.8074 q^{64} +4.93232 q^{65} +4.97718 q^{66} +15.0631 q^{67} +1.20639 q^{68} +7.39214 q^{69} +8.86573 q^{70} +8.20112 q^{71} -7.81219 q^{72} -8.32080 q^{73} -23.3646 q^{74} +4.31534 q^{75} -16.7639 q^{76} +7.66105 q^{77} -15.7271 q^{78} -2.51617 q^{79} -8.84491 q^{80} +1.00000 q^{81} -17.1610 q^{82} -7.69428 q^{83} -20.1470 q^{84} -0.201214 q^{85} -30.5300 q^{86} +7.38646 q^{87} -14.7374 q^{88} -16.3693 q^{89} +2.18310 q^{90} -24.2077 q^{91} -36.6723 q^{92} -4.99040 q^{93} -0.632268 q^{94} +2.79604 q^{95} +12.5783 q^{96} +12.3581 q^{97} -25.0443 q^{98} +1.88646 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 102 q^{3} + 96 q^{4} - 20 q^{5} + 6 q^{6} + 12 q^{7} - 21 q^{8} + 102 q^{9}+O(q^{10}) $ 102 * q - 6 * q^2 - 102 * q^3 + 96 * q^4 - 20 * q^5 + 6 * q^6 + 12 * q^7 - 21 * q^8 + 102 * q^9	\( 102 q - 6 q^{2} - 102 q^{3} + 96 q^{4} - 20 q^{5} + 6 q^{6} + 12 q^{7} - 21 q^{8} + 102 q^{9} - 16 q^{10} - 28 q^{11} - 96 q^{12} - 2 q^{13} - 41 q^{14} + 20 q^{15} + 88 q^{16} - 77 q^{17} - 6 q^{18} + 10 q^{19} - 50 q^{20} - 12 q^{21} + 24 q^{22} - 29 q^{23} + 21 q^{24} + 74 q^{25} - 45 q^{26} - 102 q^{27} + 19 q^{28} - 68 q^{29} + 16 q^{30} - 29 q^{31} - 48 q^{32} + 28 q^{33} - 19 q^{34} - 49 q^{35} + 96 q^{36} + 4 q^{37} - 44 q^{38} + 2 q^{39} - 41 q^{40} - 122 q^{41} + 41 q^{42} + 85 q^{43} - 86 q^{44} - 20 q^{45} - 28 q^{46} - 39 q^{47} - 88 q^{48} + 24 q^{49} - 37 q^{50} + 77 q^{51} + 8 q^{52} - 37 q^{53} + 6 q^{54} - 13 q^{55} - 130 q^{56} - 10 q^{57} + 17 q^{58} - 58 q^{59} + 50 q^{60} - 114 q^{61} - 64 q^{62} + 12 q^{63} + 47 q^{64} - 92 q^{65} - 24 q^{66} + 121 q^{67} - 138 q^{68} + 29 q^{69} - 2 q^{70} - 67 q^{71} - 21 q^{72} - 72 q^{73} - 111 q^{74} - 74 q^{75} - 17 q^{76} - 57 q^{77} + 45 q^{78} - 24 q^{79} - 97 q^{80} + 102 q^{81} - q^{82} - 78 q^{83} - 19 q^{84} - 24 q^{85} - 80 q^{86} + 68 q^{87} + 54 q^{88} - 176 q^{89} - 16 q^{90} - 3 q^{91} - 82 q^{92} + 29 q^{93} - 41 q^{94} - 90 q^{95} + 48 q^{96} - 77 q^{97} - 48 q^{98} - 28 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 102 * q^3 + 96 * q^4 - 20 * q^5 + 6 * q^6 + 12 * q^7 - 21 * q^8 + 102 * q^9 - 16 * q^10 - 28 * q^11 - 96 * q^12 - 2 * q^13 - 41 * q^14 + 20 * q^15 + 88 * q^16 - 77 * q^17 - 6 * q^18 + 10 * q^19 - 50 * q^20 - 12 * q^21 + 24 * q^22 - 29 * q^23 + 21 * q^24 + 74 * q^25 - 45 * q^26 - 102 * q^27 + 19 * q^28 - 68 * q^29 + 16 * q^30 - 29 * q^31 - 48 * q^32 + 28 * q^33 - 19 * q^34 - 49 * q^35 + 96 * q^36 + 4 * q^37 - 44 * q^38 + 2 * q^39 - 41 * q^40 - 122 * q^41 + 41 * q^42 + 85 * q^43 - 86 * q^44 - 20 * q^45 - 28 * q^46 - 39 * q^47 - 88 * q^48 + 24 * q^49 - 37 * q^50 + 77 * q^51 + 8 * q^52 - 37 * q^53 + 6 * q^54 - 13 * q^55 - 130 * q^56 - 10 * q^57 + 17 * q^58 - 58 * q^59 + 50 * q^60 - 114 * q^61 - 64 * q^62 + 12 * q^63 + 47 * q^64 - 92 * q^65 - 24 * q^66 + 121 * q^67 - 138 * q^68 + 29 * q^69 - 2 * q^70 - 67 * q^71 - 21 * q^72 - 72 * q^73 - 111 * q^74 - 74 * q^75 - 17 * q^76 - 57 * q^77 + 45 * q^78 - 24 * q^79 - 97 * q^80 + 102 * q^81 - q^82 - 78 * q^83 - 19 * q^84 - 24 * q^85 - 80 * q^86 + 68 * q^87 + 54 * q^88 - 176 * q^89 - 16 * q^90 - 3 * q^91 - 82 * q^92 + 29 * q^93 - 41 * q^94 - 90 * q^95 + 48 * q^96 - 77 * q^97 - 48 * q^98 - 28 * 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 $

$2$	−2.63837	−1.86561	−0.932804	−	0.360383i	$-0.882646\pi$
$2$	−2.63837	−1.86561	−0.932804	+	0.360383i	$0.882646\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.96099	2.48050
$5$	−0.827443	−0.370044	−0.185022	−	0.982734i	$-0.559236\pi$
$5$	−0.827443	−0.370044	−0.185022	+	0.982734i	$0.559236\pi$
$6$	2.63837	1.07711
$7$	4.06107	1.53494	0.767471	−	0.641084i	$-0.221515\pi$
$7$	4.06107	1.53494	0.767471	+	0.641084i	$0.221515\pi$
$8$	−7.81219	−2.76203
$9$	1.00000	0.333333
$10$	2.18310	0.690357
$11$	1.88646	0.568789	0.284395	−	0.958707i	$-0.408207\pi$
$11$	1.88646	0.568789	0.284395	+	0.958707i	$0.408207\pi$
$12$	−4.96099	−1.43211
$13$	−5.96092	−1.65326	−0.826631	−	0.562745i	$-0.809745\pi$
$13$	−5.96092	−1.65326	−0.826631	+	0.562745i	$0.809745\pi$
$14$	−10.7146	−2.86360
$15$	0.827443	0.213645
$16$	10.6894	2.67236
$17$	0.243176	0.0589789	0.0294894	−	0.999565i	$-0.490612\pi$
$17$	0.243176	0.0589789	0.0294894	+	0.999565i	$0.490612\pi$
$18$	−2.63837	−0.621870
$19$	−3.37914	−0.775227	−0.387614	−	0.921822i	$-0.626700\pi$
$19$	−3.37914	−0.775227	−0.387614	+	0.921822i	$0.626700\pi$
$20$	−4.10494	−0.917892
$21$	−4.06107	−0.886199
$22$	−4.97718	−1.06114
$23$	−7.39214	−1.54137	−0.770684	−	0.637218i	$-0.780085\pi$
$23$	−7.39214	−1.54137	−0.770684	+	0.637218i	$0.780085\pi$
$24$	7.81219	1.59466
$25$	−4.31534	−0.863068
$26$	15.7271	3.08434
$27$	−1.00000	−0.192450
$28$	20.1470	3.80742
$29$	−7.38646	−1.37163	−0.685816	−	0.727775i	$-0.740554\pi$
$29$	−7.38646	−1.37163	−0.685816	+	0.727775i	$0.740554\pi$
$30$	−2.18310	−0.398578
$31$	4.99040	0.896303	0.448151	−	0.893958i	$-0.352083\pi$
$31$	4.99040	0.896303	0.448151	+	0.893958i	$0.352083\pi$
$32$	−12.5783	−2.22356
$33$	−1.88646	−0.328391
$34$	−0.641588	−0.110031
$35$	−3.36031	−0.567996
$36$	4.96099	0.826832
$37$	8.85570	1.45587	0.727934	−	0.685647i	$-0.240481\pi$
$37$	8.85570	1.45587	0.727934	+	0.685647i	$0.240481\pi$
$38$	8.91541	1.44627
$39$	5.96092	0.954511
$40$	6.46414	1.02207
$41$	6.50441	1.01582	0.507909	−	0.861411i	$-0.330419\pi$
$41$	6.50441	1.01582	0.507909	+	0.861411i	$0.330419\pi$
$42$	10.7146	1.65330
$43$	11.5715	1.76464	0.882322	−	0.470646i	$-0.155979\pi$
$43$	11.5715	1.76464	0.882322	+	0.470646i	$0.155979\pi$
$44$	9.35871	1.41088
$45$	−0.827443	−0.123348
$46$	19.5032	2.87559
$47$	0.239644	0.0349556	0.0174778	−	0.999847i	$-0.494436\pi$
$47$	0.239644	0.0349556	0.0174778	+	0.999847i	$0.494436\pi$
$48$	−10.6894	−1.54289
$49$	9.49233	1.35605
$50$	11.3855	1.61015
$51$	−0.243176	−0.0340515
$52$	−29.5721	−4.10091
$53$	4.82029	0.662118	0.331059	−	0.943610i	$-0.392594\pi$
$53$	4.82029	0.662118	0.331059	+	0.943610i	$0.392594\pi$
$54$	2.63837	0.359037
$55$	−1.56094	−0.210477
$56$	−31.7259	−4.23955
$57$	3.37914	0.447578
$58$	19.4882	2.55893
$59$	−10.1189	−1.31737	−0.658687	−	0.752417i	$-0.728888\pi$
$59$	−10.1189	−1.31737	−0.658687	+	0.752417i	$0.728888\pi$
$60$	4.10494	0.529945
$61$	−1.06763	−0.136697	−0.0683483	−	0.997662i	$-0.521773\pi$
$61$	−1.06763	−0.136697	−0.0683483	+	0.997662i	$0.521773\pi$
$62$	−13.1665	−1.67215
$63$	4.06107	0.511647
$64$	11.8074	1.47592
$65$	4.93232	0.611779
$66$	4.97718	0.612648
$67$	15.0631	1.84026	0.920128	−	0.391618i	$-0.128085\pi$
$67$	15.0631	1.84026	0.920128	+	0.391618i	$0.128085\pi$
$68$	1.20639	0.146297
$69$	7.39214	0.889909
$70$	8.86573	1.05966
$71$	8.20112	0.973294	0.486647	−	0.873599i	$-0.338220\pi$
$71$	8.20112	0.973294	0.486647	+	0.873599i	$0.338220\pi$
$72$	−7.81219	−0.920675
$73$	−8.32080	−0.973876	−0.486938	−	0.873436i	$-0.661886\pi$
$73$	−8.32080	−0.973876	−0.486938	+	0.873436i	$0.661886\pi$
$74$	−23.3646	−2.71608
$75$	4.31534	0.498292
$76$	−16.7639	−1.92295
$77$	7.66105	0.873058
$78$	−15.7271	−1.78074
$79$	−2.51617	−0.283092	−0.141546	−	0.989932i	$-0.545207\pi$
$79$	−2.51617	−0.283092	−0.141546	+	0.989932i	$0.545207\pi$
$80$	−8.84491	−0.988891
$81$	1.00000	0.111111
$82$	−17.1610	−1.89512
$83$	−7.69428	−0.844557	−0.422278	−	0.906466i	$-0.638770\pi$
$83$	−7.69428	−0.844557	−0.422278	+	0.906466i	$0.638770\pi$
$84$	−20.1470	−2.19821
$85$	−0.201214	−0.0218248
$86$	−30.5300	−3.29213
$87$	7.38646	0.791912
$88$	−14.7374	−1.57101
$89$	−16.3693	−1.73515	−0.867573	−	0.497309i	$-0.834321\pi$
$89$	−16.3693	−1.73515	−0.867573	+	0.497309i	$0.834321\pi$
$90$	2.18310	0.230119
$91$	−24.2077	−2.53766
$92$	−36.6723	−3.82336
$93$	−4.99040	−0.517481
$94$	−0.632268	−0.0652135
$95$	2.79604	0.286868
$96$	12.5783	1.28377
$97$	12.3581	1.25478	0.627390	−	0.778705i	$-0.284123\pi$
$97$	12.3581	1.25478	0.627390	+	0.778705i	$0.284123\pi$
$98$	−25.0443	−2.52985
$99$	1.88646	0.189596
$100$	−21.4084	−2.14084
$101$	8.60943	0.856671	0.428335	−	0.903620i	$-0.359100\pi$
$101$	8.60943	0.856671	0.428335	+	0.903620i	$0.359100\pi$
$102$	0.641588	0.0635267
$103$	7.83562	0.772066	0.386033	−	0.922485i	$-0.373845\pi$
$103$	7.83562	0.772066	0.386033	+	0.922485i	$0.373845\pi$
$104$	46.5678	4.56635
$105$	3.36031	0.327932
$106$	−12.7177	−1.23525
$107$	14.5580	1.40737	0.703687	−	0.710510i	$-0.251536\pi$
$107$	14.5580	1.40737	0.703687	+	0.710510i	$0.251536\pi$
$108$	−4.96099	−0.477372
$109$	−1.68998	−0.161871	−0.0809355	−	0.996719i	$-0.525791\pi$
$109$	−1.68998	−0.161871	−0.0809355	+	0.996719i	$0.525791\pi$
$110$	4.11833	0.392667
$111$	−8.85570	−0.840546
$112$	43.4107	4.10192
$113$	13.1550	1.23752	0.618761	−	0.785579i	$-0.287635\pi$
$113$	13.1550	1.23752	0.618761	+	0.785579i	$0.287635\pi$
$114$	−8.91541	−0.835005
$115$	6.11657	0.570374
$116$	−36.6442	−3.40233
$117$	−5.96092	−0.551087
$118$	26.6975	2.45770
$119$	0.987556	0.0905291
$120$	−6.46414	−0.590093
$121$	−7.44127	−0.676479
$122$	2.81681	0.255022
$123$	−6.50441	−0.586483
$124$	24.7573	2.22327
$125$	7.70791	0.689417
$126$	−10.7146	−0.954534
$127$	7.07813	0.628083	0.314041	−	0.949409i	$-0.398317\pi$
$127$	7.07813	0.628083	0.314041	+	0.949409i	$0.398317\pi$
$128$	−5.99560	−0.529941
$129$	−11.5715	−1.01882
$130$	−13.0133	−1.14134
$131$	−6.16966	−0.539046	−0.269523	−	0.962994i	$-0.586866\pi$
$131$	−6.16966	−0.539046	−0.269523	+	0.962994i	$0.586866\pi$
$132$	−9.35871	−0.814571
$133$	−13.7229	−1.18993
$134$	−39.7421	−3.43320
$135$	0.827443	0.0712150
$136$	−1.89974	−0.162901
$137$	−4.44335	−0.379621	−0.189810	−	0.981821i	$-0.560787\pi$
$137$	−4.44335	−0.379621	−0.189810	+	0.981821i	$0.560787\pi$
$138$	−19.5032	−1.66022
$139$	−10.0794	−0.854923	−0.427462	−	0.904034i	$-0.640592\pi$
$139$	−10.0794	−0.854923	−0.427462	+	0.904034i	$0.640592\pi$
$140$	−16.6705	−1.40891
$141$	−0.239644	−0.0201816
$142$	−21.6376	−1.81579
$143$	−11.2450	−0.940357
$144$	10.6894	0.890787
$145$	6.11188	0.507564
$146$	21.9534	1.81687
$147$	−9.49233	−0.782914
$148$	43.9331	3.61128
$149$	−3.15306	−0.258308	−0.129154	−	0.991625i	$-0.541226\pi$
$149$	−3.15306	−0.258308	−0.129154	+	0.991625i	$0.541226\pi$
$150$	−11.3855	−0.929618
$151$	−19.2254	−1.56454	−0.782270	−	0.622940i	$-0.785938\pi$
$151$	−19.2254	−1.56454	−0.782270	+	0.622940i	$0.785938\pi$
$152$	26.3984	2.14120
$153$	0.243176	0.0196596
$154$	−20.2127	−1.62878
$155$	−4.12927	−0.331671
$156$	29.5721	2.36766
$157$	16.1182	1.28638	0.643188	−	0.765708i	$-0.277611\pi$
$157$	16.1182	1.28638	0.643188	+	0.765708i	$0.277611\pi$
$158$	6.63860	0.528138
$159$	−4.82029	−0.382274
$160$	10.4079	0.822813
$161$	−30.0200	−2.36591
$162$	−2.63837	−0.207290
$163$	−6.25081	−0.489601	−0.244800	−	0.969573i	$-0.578722\pi$
$163$	−6.25081	−0.489601	−0.244800	+	0.969573i	$0.578722\pi$
$164$	32.2683	2.51973
$165$	1.56094	0.121519
$166$	20.3003	1.57561
$167$	−16.2848	−1.26016	−0.630078	−	0.776532i	$-0.716977\pi$
$167$	−16.2848	−1.26016	−0.630078	+	0.776532i	$0.716977\pi$
$168$	31.7259	2.44770
$169$	22.5326	1.73327
$170$	0.530878	0.0407165
$171$	−3.37914	−0.258409
$172$	57.4063	4.37719
$173$	5.23258	0.397825	0.198913	−	0.980017i	$-0.436259\pi$
$173$	5.23258	0.397825	0.198913	+	0.980017i	$0.436259\pi$
$174$	−19.4882	−1.47740
$175$	−17.5249	−1.32476
$176$	20.1652	1.52001
$177$	10.1189	0.760586
$178$	43.1884	3.23710
$179$	2.14408	0.160256	0.0801281	−	0.996785i	$-0.474467\pi$
$179$	2.14408	0.160256	0.0801281	+	0.996785i	$0.474467\pi$
$180$	−4.10494	−0.305964
$181$	−7.41618	−0.551240	−0.275620	−	0.961267i	$-0.588883\pi$
$181$	−7.41618	−0.551240	−0.275620	+	0.961267i	$0.588883\pi$
$182$	63.8690	4.73428
$183$	1.06763	0.0789218
$184$	57.7488	4.25730
$185$	−7.32759	−0.538735
$186$	13.1665	0.965416
$187$	0.458742	0.0335465
$188$	1.18887	0.0867073
$189$	−4.06107	−0.295400
$190$	−7.37699	−0.535183
$191$	−16.7886	−1.21478	−0.607390	−	0.794404i	$-0.707784\pi$
$191$	−16.7886	−1.21478	−0.607390	+	0.794404i	$0.707784\pi$
$192$	−11.8074	−0.852126
$193$	11.4871	0.826860	0.413430	−	0.910536i	$-0.364331\pi$
$193$	11.4871	0.826860	0.413430	+	0.910536i	$0.364331\pi$
$194$	−32.6054	−2.34093
$195$	−4.93232	−0.353211
$196$	47.0914	3.36367
$197$	−23.2148	−1.65399	−0.826993	−	0.562212i	$-0.809951\pi$
$197$	−23.2148	−1.65399	−0.826993	+	0.562212i	$0.809951\pi$
$198$	−4.97718	−0.353713
$199$	−21.1585	−1.49989	−0.749944	−	0.661501i	$-0.769920\pi$
$199$	−21.1585	−1.49989	−0.749944	+	0.661501i	$0.769920\pi$
$200$	33.7122	2.38381
$201$	−15.0631	−1.06247
$202$	−22.7149	−1.59821
$203$	−29.9970	−2.10537
$204$	−1.20639	−0.0844645
$205$	−5.38203	−0.375897
$206$	−20.6733	−1.44037
$207$	−7.39214	−0.513789
$208$	−63.7190	−4.41811
$209$	−6.37461	−0.440941
$210$	−8.86573	−0.611794
$211$	4.29296	0.295540	0.147770	−	0.989022i	$-0.452791\pi$
$211$	4.29296	0.295540	0.147770	+	0.989022i	$0.452791\pi$
$212$	23.9134	1.64238
$213$	−8.20112	−0.561931
$214$	−38.4093	−2.62561
$215$	−9.57479	−0.652996
$216$	7.81219	0.531552
$217$	20.2664	1.37577
$218$	4.45880	0.301988
$219$	8.32080	0.562268
$220$	−7.74380	−0.522087
$221$	−1.44955	−0.0975075
$222$	23.3646	1.56813
$223$	−9.66959	−0.647523	−0.323762	−	0.946139i	$-0.604948\pi$
$223$	−9.66959	−0.647523	−0.323762	+	0.946139i	$0.604948\pi$
$224$	−51.0816	−3.41303
$225$	−4.31534	−0.287689
$226$	−34.7079	−2.30873
$227$	16.2892	1.08115	0.540575	−	0.841296i	$-0.318207\pi$
$227$	16.2892	1.08115	0.540575	+	0.841296i	$0.318207\pi$
$228$	16.7639	1.11021
$229$	8.28068	0.547203	0.273601	−	0.961843i	$-0.411785\pi$
$229$	8.28068	0.547203	0.273601	+	0.961843i	$0.411785\pi$
$230$	−16.1378	−1.06409
$231$	−7.66105	−0.504060
$232$	57.7044	3.78848
$233$	−12.7656	−0.836304	−0.418152	−	0.908377i	$-0.637322\pi$
$233$	−12.7656	−0.836304	−0.418152	+	0.908377i	$0.637322\pi$
$234$	15.7271	1.02811
$235$	−0.198291	−0.0129351
$236$	−50.2000	−3.26774
$237$	2.51617	0.163443
$238$	−2.60554	−0.168892
$239$	−9.05736	−0.585872	−0.292936	−	0.956132i	$-0.594632\pi$
$239$	−9.05736	−0.585872	−0.292936	+	0.956132i	$0.594632\pi$
$240$	8.84491	0.570937
$241$	18.2228	1.17383	0.586916	−	0.809648i	$-0.300342\pi$
$241$	18.2228	1.17383	0.586916	+	0.809648i	$0.300342\pi$
$242$	19.6328	1.26205
$243$	−1.00000	−0.0641500
$244$	−5.29652	−0.339075
$245$	−7.85436	−0.501797
$246$	17.1610	1.09415
$247$	20.1428	1.28165
$248$	−38.9860	−2.47561
$249$	7.69428	0.487605
$250$	−20.3363	−1.28618
$251$	−5.59605	−0.353219	−0.176610	−	0.984281i	$-0.556513\pi$
$251$	−5.59605	−0.353219	−0.176610	+	0.984281i	$0.556513\pi$
$252$	20.1470	1.26914
$253$	−13.9450	−0.876713
$254$	−18.6747	−1.17176
$255$	0.201214	0.0126005
$256$	−7.79619	−0.487262
$257$	−6.26550	−0.390831	−0.195416	−	0.980721i	$-0.562606\pi$
$257$	−6.26550	−0.390831	−0.195416	+	0.980721i	$0.562606\pi$
$258$	30.5300	1.90072
$259$	35.9637	2.23467
$260$	24.4692	1.51752
$261$	−7.38646	−0.457211
$262$	16.2778	1.00565
$263$	−1.97108	−0.121542	−0.0607710	−	0.998152i	$-0.519356\pi$
$263$	−1.97108	−0.121542	−0.0607710	+	0.998152i	$0.519356\pi$
$264$	14.7374	0.907023
$265$	−3.98852	−0.245013
$266$	36.2061	2.21994
$267$	16.3693	1.00179
$268$	74.7281	4.56475
$269$	28.0222	1.70855	0.854273	−	0.519825i	$-0.174003\pi$
$269$	28.0222	1.70855	0.854273	+	0.519825i	$0.174003\pi$
$270$	−2.18310	−0.132859
$271$	−11.8594	−0.720404	−0.360202	−	0.932874i	$-0.617292\pi$
$271$	−11.8594	−0.720404	−0.360202	+	0.932874i	$0.617292\pi$
$272$	2.59942	0.157613
$273$	24.2077	1.46512
$274$	11.7232	0.708224
$275$	−8.14071	−0.490903
$276$	36.6723	2.20742
$277$	32.6523	1.96189	0.980943	−	0.194296i	$-0.0622422\pi$
$277$	32.6523	1.96189	0.980943	+	0.194296i	$0.0622422\pi$
$278$	26.5932	1.59495
$279$	4.99040	0.298768
$280$	26.2514	1.56882
$281$	−26.5588	−1.58436	−0.792182	−	0.610284i	$-0.791055\pi$
$281$	−26.5588	−1.58436	−0.792182	+	0.610284i	$0.791055\pi$
$282$	0.632268	0.0376510
$283$	−15.8232	−0.940594	−0.470297	−	0.882508i	$-0.655853\pi$
$283$	−15.8232	−0.940594	−0.470297	+	0.882508i	$0.655853\pi$
$284$	40.6857	2.41425
$285$	−2.79604	−0.165623
$286$	29.6686	1.75434
$287$	26.4149	1.55922
$288$	−12.5783	−0.741186
$289$	−16.9409	−0.996521
$290$	−16.1254	−0.946915
$291$	−12.3581	−0.724447
$292$	−41.2794	−2.41570
$293$	−25.7679	−1.50538	−0.752688	−	0.658378i	$-0.771243\pi$
$293$	−25.7679	−1.50538	−0.752688	+	0.658378i	$0.771243\pi$
$294$	25.0443	1.46061
$295$	8.37285	0.487486
$296$	−69.1824	−4.02115
$297$	−1.88646	−0.109464
$298$	8.31893	0.481903
$299$	44.0640	2.54828
$300$	21.4084	1.23601
$301$	46.9929	2.70863
$302$	50.7236	2.91882
$303$	−8.60943	−0.494599
$304$	−36.1211	−2.07169
$305$	0.883406	0.0505837
$306$	−0.641588	−0.0366772
$307$	−18.7290	−1.06892	−0.534461	−	0.845193i	$-0.679485\pi$
$307$	−18.7290	−1.06892	−0.534461	+	0.845193i	$0.679485\pi$
$308$	38.0064	2.16562
$309$	−7.83562	−0.445753
$310$	10.8945	0.618769
$311$	4.23513	0.240152	0.120076	−	0.992765i	$-0.461686\pi$
$311$	4.23513	0.240152	0.120076	+	0.992765i	$0.461686\pi$
$312$	−46.5678	−2.63638
$313$	−9.80629	−0.554284	−0.277142	−	0.960829i	$-0.589387\pi$
$313$	−9.80629	−0.554284	−0.277142	+	0.960829i	$0.589387\pi$
$314$	−42.5259	−2.39987
$315$	−3.36031	−0.189332
$316$	−12.4827	−0.702208
$317$	29.5952	1.66223	0.831115	−	0.556101i	$-0.187703\pi$
$317$	29.5952	1.66223	0.831115	+	0.556101i	$0.187703\pi$
$318$	12.7177	0.713173
$319$	−13.9343	−0.780169
$320$	−9.76995	−0.546157
$321$	−14.5580	−0.812548
$322$	79.2039	4.41386
$323$	−0.821725	−0.0457220
$324$	4.96099	0.275611
$325$	25.7234	1.42688
$326$	16.4919	0.913404
$327$	1.68998	0.0934563
$328$	−50.8137	−2.80572
$329$	0.973211	0.0536549
$330$	−4.11833	−0.226707
$331$	−10.7653	−0.591715	−0.295857	−	0.955232i	$-0.595605\pi$
$331$	−10.7653	−0.591715	−0.295857	+	0.955232i	$0.595605\pi$
$332$	−38.1712	−2.09492
$333$	8.85570	0.485290
$334$	42.9653	2.35096
$335$	−12.4639	−0.680975
$336$	−43.4107	−2.36825
$337$	−33.8666	−1.84483	−0.922416	−	0.386197i	$-0.873789\pi$
$337$	−33.8666	−1.84483	−0.922416	+	0.386197i	$0.873789\pi$
$338$	−59.4492	−3.23361
$339$	−13.1550	−0.714484
$340$	−0.998223	−0.0541362
$341$	9.41419	0.509807
$342$	8.91541	0.482090
$343$	10.1215	0.546511
$344$	−90.3991	−4.87399
$345$	−6.11657	−0.329305
$346$	−13.8055	−0.742187
$347$	0.721891	0.0387531	0.0193766	−	0.999812i	$-0.493832\pi$
$347$	0.721891	0.0387531	0.0193766	+	0.999812i	$0.493832\pi$
$348$	36.6442	1.96433
$349$	6.06212	0.324498	0.162249	−	0.986750i	$-0.448125\pi$
$349$	6.06212	0.324498	0.162249	+	0.986750i	$0.448125\pi$
$350$	46.2372	2.47148
$351$	5.96092	0.318170
$352$	−23.7285	−1.26473
$353$	−4.28017	−0.227810	−0.113905	−	0.993492i	$-0.536336\pi$
$353$	−4.28017	−0.227810	−0.113905	+	0.993492i	$0.536336\pi$
$354$	−26.6975	−1.41896
$355$	−6.78596	−0.360161
$356$	−81.2082	−4.30402
$357$	−0.987556	−0.0522670
$358$	−5.65688	−0.298975
$359$	17.8955	0.944489	0.472245	−	0.881468i	$-0.343444\pi$
$359$	17.8955	0.944489	0.472245	+	0.881468i	$0.343444\pi$
$360$	6.46414	0.340690
$361$	−7.58144	−0.399023
$362$	19.5666	1.02840
$363$	7.44127	0.390565
$364$	−120.094	−6.29466
$365$	6.88499	0.360377
$366$	−2.81681	−0.147237
$367$	−34.9517	−1.82446	−0.912231	−	0.409675i	$-0.865642\pi$
$367$	−34.9517	−1.82446	−0.912231	+	0.409675i	$0.865642\pi$
$368$	−79.0179	−4.11909
$369$	6.50441	0.338606
$370$	19.3329	1.00507
$371$	19.5756	1.01631
$372$	−24.7573	−1.28361
$373$	−1.75391	−0.0908140	−0.0454070	−	0.998969i	$-0.514458\pi$
$373$	−1.75391	−0.0908140	−0.0454070	+	0.998969i	$0.514458\pi$
$374$	−1.21033	−0.0625847
$375$	−7.70791	−0.398035
$376$	−1.87214	−0.0965483
$377$	44.0301	2.26767
$378$	10.7146	0.551100
$379$	10.3311	0.530672	0.265336	−	0.964156i	$-0.414517\pi$
$379$	10.3311	0.530672	0.265336	+	0.964156i	$0.414517\pi$
$380$	13.8711	0.711575
$381$	−7.07813	−0.362624
$382$	44.2945	2.26631
$383$	8.77749	0.448509	0.224254	−	0.974531i	$-0.428005\pi$
$383$	8.77749	0.448509	0.224254	+	0.974531i	$0.428005\pi$
$384$	5.99560	0.305962
$385$	−6.33909	−0.323070
$386$	−30.3072	−1.54260
$387$	11.5715	0.588215
$388$	61.3087	3.11248
$389$	−11.0917	−0.562370	−0.281185	−	0.959654i	$-0.590727\pi$
$389$	−11.0917	−0.562370	−0.281185	+	0.959654i	$0.590727\pi$
$390$	13.0133	0.658953
$391$	−1.79759	−0.0909081
$392$	−74.1558	−3.74544
$393$	6.16966	0.311218
$394$	61.2492	3.08569
$395$	2.08199	0.104756
$396$	9.35871	0.470293
$397$	−17.4436	−0.875471	−0.437736	−	0.899104i	$-0.644219\pi$
$397$	−17.4436	−0.875471	−0.437736	+	0.899104i	$0.644219\pi$
$398$	55.8240	2.79820
$399$	13.7229	0.687006
$400$	−46.1286	−2.30643
$401$	−4.41147	−0.220298	−0.110149	−	0.993915i	$-0.535133\pi$
$401$	−4.41147	−0.220298	−0.110149	+	0.993915i	$0.535133\pi$
$402$	39.7421	1.98216
$403$	−29.7474	−1.48182
$404$	42.7113	2.12497
$405$	−0.827443	−0.0411160
$406$	79.1431	3.92781
$407$	16.7059	0.828082
$408$	1.89974	0.0940510
$409$	−3.61264	−0.178633	−0.0893167	−	0.996003i	$-0.528468\pi$
$409$	−3.61264	−0.178633	−0.0893167	+	0.996003i	$0.528468\pi$
$410$	14.1998	0.701277
$411$	4.44335	0.219174
$412$	38.8724	1.91511
$413$	−41.0938	−2.02209
$414$	19.5032	0.958530
$415$	6.36658	0.312523
$416$	74.9785	3.67612
$417$	10.0794	0.493590
$418$	16.8186	0.822623
$419$	34.5013	1.68550	0.842750	−	0.538305i	$-0.180935\pi$
$419$	34.5013	1.68550	0.842750	+	0.538305i	$0.180935\pi$
$420$	16.6705	0.813435
$421$	−10.4342	−0.508532	−0.254266	−	0.967134i	$-0.581834\pi$
$421$	−10.4342	−0.508532	−0.254266	+	0.967134i	$0.581834\pi$
$422$	−11.3264	−0.551361
$423$	0.239644	0.0116519
$424$	−37.6570	−1.82879
$425$	−1.04939	−0.0509028
$426$	21.6376	1.04834
$427$	−4.33574	−0.209821
$428$	72.2221	3.49098
$429$	11.2450	0.542915
$430$	25.2618	1.21823
$431$	−6.61003	−0.318394	−0.159197	−	0.987247i	$-0.550890\pi$
$431$	−6.61003	−0.318394	−0.159197	+	0.987247i	$0.550890\pi$
$432$	−10.6894	−0.514296
$433$	−21.7588	−1.04566	−0.522832	−	0.852436i	$-0.675124\pi$
$433$	−21.7588	−1.04566	−0.522832	+	0.852436i	$0.675124\pi$
$434$	−53.4702	−2.56665
$435$	−6.11188	−0.293042
$436$	−8.38399	−0.401520
$437$	24.9791	1.19491
$438$	−21.9534	−1.04897
$439$	−22.8684	−1.09145	−0.545724	−	0.837965i	$-0.683745\pi$
$439$	−22.8684	−1.09145	−0.545724	+	0.837965i	$0.683745\pi$
$440$	12.1943	0.581342
$441$	9.49233	0.452016
$442$	3.82446	0.181911
$443$	17.9159	0.851212	0.425606	−	0.904909i	$-0.360061\pi$
$443$	17.9159	0.851212	0.425606	+	0.904909i	$0.360061\pi$
$444$	−43.9331	−2.08497
$445$	13.5447	0.642080
$446$	25.5119	1.20803
$447$	3.15306	0.149134
$448$	47.9507	2.26546
$449$	−40.2259	−1.89838	−0.949189	−	0.314707i	$-0.898094\pi$
$449$	−40.2259	−1.89838	−0.949189	+	0.314707i	$0.898094\pi$
$450$	11.3855	0.536715
$451$	12.2703	0.577786
$452$	65.2621	3.06967
$453$	19.2254	0.903287
$454$	−42.9768	−2.01700
$455$	20.0305	0.939046
$456$	−26.3984	−1.23622
$457$	−10.4753	−0.490012	−0.245006	−	0.969522i	$-0.578790\pi$
$457$	−10.4753	−0.490012	−0.245006	+	0.969522i	$0.578790\pi$
$458$	−21.8475	−1.02087
$459$	−0.243176	−0.0113505
$460$	30.3443	1.41481
$461$	3.67127	0.170988	0.0854941	−	0.996339i	$-0.472753\pi$
$461$	3.67127	0.170988	0.0854941	+	0.996339i	$0.472753\pi$
$462$	20.2127	0.940379
$463$	2.65603	0.123436	0.0617181	−	0.998094i	$-0.480342\pi$
$463$	2.65603	0.123436	0.0617181	+	0.998094i	$0.480342\pi$
$464$	−78.9572	−3.66550
$465$	4.12927	0.191490
$466$	33.6804	1.56022
$467$	−2.15594	−0.0997651	−0.0498825	−	0.998755i	$-0.515885\pi$
$467$	−2.15594	−0.0997651	−0.0498825	+	0.998755i	$0.515885\pi$
$468$	−29.5721	−1.36697
$469$	61.1725	2.82469
$470$	0.523166	0.0241319
$471$	−16.1182	−0.742690
$472$	79.0510	3.63862
$473$	21.8293	1.00371
$474$	−6.63860	−0.304921
$475$	14.5821	0.669073
$476$	4.89926	0.224557
$477$	4.82029	0.220706
$478$	23.8967	1.09301
$479$	2.41594	0.110387	0.0551935	−	0.998476i	$-0.482422\pi$
$479$	2.41594	0.110387	0.0551935	+	0.998476i	$0.482422\pi$
$480$	−10.4079	−0.475052
$481$	−52.7881	−2.40693
$482$	−48.0784	−2.18991
$483$	30.0200	1.36596
$484$	−36.9161	−1.67800
$485$	−10.2257	−0.464323
$486$	2.63837	0.119679
$487$	−14.8941	−0.674918	−0.337459	−	0.941340i	$-0.609567\pi$
$487$	−14.8941	−0.674918	−0.337459	+	0.941340i	$0.609567\pi$
$488$	8.34056	0.377559
$489$	6.25081	0.282671
$490$	20.7227	0.936156
$491$	−1.98420	−0.0895456	−0.0447728	−	0.998997i	$-0.514256\pi$
$491$	−1.98420	−0.0895456	−0.0447728	+	0.998997i	$0.514256\pi$
$492$	−32.2683	−1.45477
$493$	−1.79621	−0.0808973
$494$	−53.1440	−2.39106
$495$	−1.56094	−0.0701589
$496$	53.3446	2.39525
$497$	33.3054	1.49395
$498$	−20.3003	−0.909680
$499$	9.75556	0.436719	0.218359	−	0.975868i	$-0.429930\pi$
$499$	9.75556	0.436719	0.218359	+	0.975868i	$0.429930\pi$
$500$	38.2389	1.71009
$501$	16.2848	0.727551
$502$	14.7644	0.658969
$503$	−16.9305	−0.754894	−0.377447	−	0.926031i	$-0.623198\pi$
$503$	−16.9305	−0.754894	−0.377447	+	0.926031i	$0.623198\pi$
$504$	−31.7259	−1.41318
$505$	−7.12382	−0.317006
$506$	36.7920	1.63560
$507$	−22.5326	−1.00071
$508$	35.1145	1.55796
$509$	−4.48525	−0.198805	−0.0994025	−	0.995047i	$-0.531693\pi$
$509$	−4.48525	−0.198805	−0.0994025	+	0.995047i	$0.531693\pi$
$510$	−0.530878	−0.0235077
$511$	−33.7914	−1.49484
$512$	32.5604	1.43898
$513$	3.37914	0.149193
$514$	16.5307	0.729138
$515$	−6.48353	−0.285698
$516$	−57.4063	−2.52717
$517$	0.452078	0.0198824
$518$	−94.8855	−4.16903
$519$	−5.23258	−0.229685
$520$	−38.5322	−1.68975
$521$	18.1359	0.794549	0.397274	−	0.917700i	$-0.369956\pi$
$521$	18.1359	0.794549	0.397274	+	0.917700i	$0.369956\pi$
$522$	19.4882	0.852976
$523$	−14.7684	−0.645777	−0.322889	−	0.946437i	$-0.604654\pi$
$523$	−14.7684	−0.645777	−0.322889	+	0.946437i	$0.604654\pi$
$524$	−30.6076	−1.33710
$525$	17.5249	0.764850
$526$	5.20044	0.226750
$527$	1.21355	0.0528629
$528$	−20.1652	−0.877578
$529$	31.6437	1.37581
$530$	10.5232	0.457097
$531$	−10.1189	−0.439125
$532$	−68.0793	−2.95161
$533$	−38.7723	−1.67941
$534$	−43.1884	−1.86894
$535$	−12.0459	−0.520790
$536$	−117.676	−5.08283
$537$	−2.14408	−0.0925240
$538$	−73.9330	−3.18748
$539$	17.9069	0.771305
$540$	4.10494	0.176648
$541$	33.2609	1.43000	0.714998	−	0.699126i	$-0.246428\pi$
$541$	33.2609	1.43000	0.714998	+	0.699126i	$0.246428\pi$
$542$	31.2894	1.34399
$543$	7.41618	0.318259
$544$	−3.05875	−0.131143
$545$	1.39836	0.0598994
$546$	−63.8690	−2.73334
$547$	−20.6754	−0.884014	−0.442007	−	0.897012i	$-0.645733\pi$
$547$	−20.6754	−0.884014	−0.442007	+	0.897012i	$0.645733\pi$
$548$	−22.0434	−0.941648
$549$	−1.06763	−0.0455655
$550$	21.4782	0.915834
$551$	24.9599	1.06333
$552$	−57.7488	−2.45795
$553$	−10.2184	−0.434529
$554$	−86.1488	−3.66011
$555$	7.32759	0.311039
$556$	−50.0038	−2.12063
$557$	41.4328	1.75556	0.877782	−	0.479060i	$-0.159022\pi$
$557$	41.4328	1.75556	0.877782	+	0.479060i	$0.159022\pi$
$558$	−13.1665	−0.557383
$559$	−68.9771	−2.91742
$560$	−35.9198	−1.51789
$561$	−0.458742	−0.0193681
$562$	70.0719	2.95580
$563$	−9.09415	−0.383273	−0.191636	−	0.981466i	$-0.561379\pi$
$563$	−9.09415	−0.383273	−0.191636	+	0.981466i	$0.561379\pi$
$564$	−1.18887	−0.0500605
$565$	−10.8851	−0.457938
$566$	41.7475	1.75478
$567$	4.06107	0.170549
$568$	−64.0687	−2.68826
$569$	−21.1481	−0.886576	−0.443288	−	0.896379i	$-0.646188\pi$
$569$	−21.1481	−0.886576	−0.443288	+	0.896379i	$0.646188\pi$
$570$	7.37699	0.308988
$571$	24.5179	1.02604	0.513020	−	0.858377i	$-0.328527\pi$
$571$	24.5179	1.02604	0.513020	+	0.858377i	$0.328527\pi$
$572$	−55.7865	−2.33255
$573$	16.7886	0.701354
$574$	−69.6923	−2.90890
$575$	31.8996	1.33030
$576$	11.8074	0.491975
$577$	2.07461	0.0863669	0.0431835	−	0.999067i	$-0.486250\pi$
$577$	2.07461	0.0863669	0.0431835	+	0.999067i	$0.486250\pi$
$578$	44.6963	1.85912
$579$	−11.4871	−0.477388
$580$	30.3210	1.25901
$581$	−31.2470	−1.29635
$582$	32.6054	1.35154
$583$	9.09328	0.376605
$584$	65.0037	2.68987
$585$	4.93232	0.203926
$586$	67.9852	2.80844
$587$	−33.7535	−1.39316	−0.696578	−	0.717481i	$-0.745295\pi$
$587$	−33.7535	−1.39316	−0.696578	+	0.717481i	$0.745295\pi$
$588$	−47.0914	−1.94201
$589$	−16.8632	−0.694838
$590$	−22.0907	−0.909458
$591$	23.2148	0.954930
$592$	94.6626	3.89061
$593$	38.8411	1.59501	0.797506	−	0.603311i	$-0.206152\pi$
$593$	38.8411	1.59501	0.797506	+	0.603311i	$0.206152\pi$
$594$	4.97718	0.204216
$595$	−0.817147	−0.0334997
$596$	−15.6423	−0.640733
$597$	21.1585	0.865961
$598$	−116.257	−4.75410
$599$	−14.1483	−0.578084	−0.289042	−	0.957316i	$-0.593337\pi$
$599$	−14.1483	−0.578084	−0.289042	+	0.957316i	$0.593337\pi$
$600$	−33.7122	−1.37630
$601$	21.1768	0.863821	0.431911	−	0.901916i	$-0.357840\pi$
$601$	21.1768	0.863821	0.431911	+	0.901916i	$0.357840\pi$
$602$	−123.985	−5.05324
$603$	15.0631	0.613419
$604$	−95.3769	−3.88083
$605$	6.15723	0.250327
$606$	22.7149	0.922728
$607$	−15.5618	−0.631635	−0.315818	−	0.948820i	$-0.602279\pi$
$607$	−15.5618	−0.631635	−0.315818	+	0.948820i	$0.602279\pi$
$608$	42.5039	1.72376
$609$	29.9970	1.21554
$610$	−2.33075	−0.0943694
$611$	−1.42850	−0.0577908
$612$	1.20639	0.0487656
$613$	−44.6684	−1.80414	−0.902070	−	0.431589i	$-0.857953\pi$
$613$	−44.6684	−1.80414	−0.902070	+	0.431589i	$0.857953\pi$
$614$	49.4141	1.99419
$615$	5.38203	0.217024
$616$	−59.8496	−2.41141
$617$	−15.2566	−0.614208	−0.307104	−	0.951676i	$-0.599360\pi$
$617$	−15.2566	−0.614208	−0.307104	+	0.951676i	$0.599360\pi$
$618$	20.6733	0.831600
$619$	3.49065	0.140301	0.0701505	−	0.997536i	$-0.477652\pi$
$619$	3.49065	0.140301	0.0701505	+	0.997536i	$0.477652\pi$
$620$	−20.4853	−0.822709
$621$	7.39214	0.296636
$622$	−11.1738	−0.448030
$623$	−66.4771	−2.66335
$624$	63.7190	2.55080
$625$	15.1988	0.607953
$626$	25.8726	1.03408
$627$	6.37461	0.254577
$628$	79.9625	3.19085
$629$	2.15350	0.0858655
$630$	8.86573	0.353219
$631$	−27.2582	−1.08513	−0.542566	−	0.840013i	$-0.682547\pi$
$631$	−27.2582	−1.08513	−0.542566	+	0.840013i	$0.682547\pi$
$632$	19.6568	0.781906
$633$	−4.29296	−0.170630
$634$	−78.0829	−3.10107
$635$	−5.85675	−0.232418
$636$	−23.9134	−0.948229
$637$	−56.5830	−2.24190
$638$	36.7637	1.45549
$639$	8.20112	0.324431
$640$	4.96102	0.196101
$641$	38.1237	1.50580	0.752898	−	0.658138i	$-0.228656\pi$
$641$	38.1237	1.50580	0.752898	+	0.658138i	$0.228656\pi$
$642$	38.4093	1.51590
$643$	−11.8370	−0.466804	−0.233402	−	0.972380i	$-0.574986\pi$
$643$	−11.8370	−0.466804	−0.233402	+	0.972380i	$0.574986\pi$
$644$	−148.929	−5.86863
$645$	9.57479	0.377007
$646$	2.16801	0.0852994
$647$	8.87087	0.348750	0.174375	−	0.984679i	$-0.444210\pi$
$647$	8.87087	0.348750	0.174375	+	0.984679i	$0.444210\pi$
$648$	−7.81219	−0.306892
$649$	−19.0890	−0.749308
$650$	−67.8678	−2.66199
$651$	−20.2664	−0.794303
$652$	−31.0102	−1.21445
$653$	1.65914	0.0649274	0.0324637	−	0.999473i	$-0.489665\pi$
$653$	1.65914	0.0649274	0.0324637	+	0.999473i	$0.489665\pi$
$654$	−4.45880	−0.174353
$655$	5.10504	0.199471
$656$	69.5286	2.71463
$657$	−8.32080	−0.324625
$658$	−2.56769	−0.100099
$659$	−11.7196	−0.456531	−0.228266	−	0.973599i	$-0.573305\pi$
$659$	−11.7196	−0.456531	−0.228266	+	0.973599i	$0.573305\pi$
$660$	7.74380	0.301427
$661$	−20.4153	−0.794063	−0.397032	−	0.917805i	$-0.629960\pi$
$661$	−20.4153	−0.794063	−0.397032	+	0.917805i	$0.629960\pi$
$662$	28.4029	1.10391
$663$	1.44955	0.0562960
$664$	60.1091	2.33269
$665$	11.3549	0.440326
$666$	−23.3646	−0.905360
$667$	54.6018	2.11419
$668$	−80.7887	−3.12581
$669$	9.66959	0.373848
$670$	32.8843	1.27043
$671$	−2.01405	−0.0777515
$672$	51.0816	1.97051
$673$	7.08561	0.273130	0.136565	−	0.990631i	$-0.456394\pi$
$673$	7.08561	0.273130	0.136565	+	0.990631i	$0.456394\pi$
$674$	89.3527	3.44174
$675$	4.31534	0.166097
$676$	111.784	4.29938
$677$	13.4807	0.518106	0.259053	−	0.965863i	$-0.416589\pi$
$677$	13.4807	0.518106	0.259053	+	0.965863i	$0.416589\pi$
$678$	34.7079	1.33295
$679$	50.1874	1.92601
$680$	1.57192	0.0602805
$681$	−16.2892	−0.624202
$682$	−24.8381	−0.951101
$683$	−29.1486	−1.11534	−0.557671	−	0.830062i	$-0.688305\pi$
$683$	−29.1486	−1.11534	−0.557671	+	0.830062i	$0.688305\pi$
$684$	−16.7639	−0.640982
$685$	3.67662	0.140476
$686$	−26.7043	−1.01958
$687$	−8.28068	−0.315928
$688$	123.693	4.71577
$689$	−28.7334	−1.09465
$690$	16.1378	0.614355
$691$	1.11440	0.0423937	0.0211968	−	0.999775i	$-0.493252\pi$
$691$	1.11440	0.0423937	0.0211968	+	0.999775i	$0.493252\pi$
$692$	25.9588	0.986804
$693$	7.66105	0.291019
$694$	−1.90462	−0.0722982
$695$	8.34012	0.316359
$696$	−57.7044	−2.18728
$697$	1.58172	0.0599118
$698$	−15.9941	−0.605386
$699$	12.7656	0.482840
$700$	−86.9409	−3.28606
$701$	−40.6141	−1.53397	−0.766986	−	0.641663i	$-0.778245\pi$
$701$	−40.6141	−1.53397	−0.766986	+	0.641663i	$0.778245\pi$
$702$	−15.7271	−0.593581
$703$	−29.9246	−1.12863
$704$	22.2742	0.839490
$705$	0.198291	0.00746809
$706$	11.2927	0.425005
$707$	34.9636	1.31494
$708$	50.2000	1.88663
$709$	−41.0141	−1.54032	−0.770158	−	0.637853i	$-0.779823\pi$
$709$	−41.0141	−1.54032	−0.770158	+	0.637853i	$0.779823\pi$
$710$	17.9039	0.671920
$711$	−2.51617	−0.0943639
$712$	127.880	4.79252
$713$	−36.8897	−1.38153
$714$	2.60554	0.0975098
$715$	9.30463	0.347973
$716$	10.6368	0.397515
$717$	9.05736	0.338253
$718$	−47.2150	−1.76205
$719$	−53.2903	−1.98739	−0.993696	−	0.112112i	$-0.964238\pi$
$719$	−53.2903	−1.98739	−0.993696	+	0.112112i	$0.964238\pi$
$720$	−8.84491	−0.329630
$721$	31.8210	1.18508
$722$	20.0026	0.744421
$723$	−18.2228	−0.677712
$724$	−36.7916	−1.36735
$725$	31.8751	1.18381
$726$	−19.6328	−0.728642
$727$	−39.6633	−1.47103	−0.735516	−	0.677508i	$-0.763060\pi$
$727$	−39.6633	−1.47103	−0.735516	+	0.677508i	$0.763060\pi$
$728$	189.115	7.00908
$729$	1.00000	0.0370370
$730$	−18.1651	−0.672322
$731$	2.81392	0.104077
$732$	5.29652	0.195765
$733$	−15.3723	−0.567789	−0.283894	−	0.958856i	$-0.591627\pi$
$733$	−15.3723	−0.567789	−0.283894	+	0.958856i	$0.591627\pi$
$734$	92.2154	3.40373
$735$	7.85436	0.289712
$736$	92.9808	3.42732
$737$	28.4160	1.04672
$738$	−17.1610	−0.631707
$739$	7.44280	0.273788	0.136894	−	0.990586i	$-0.456288\pi$
$739$	7.44280	0.273788	0.136894	+	0.990586i	$0.456288\pi$
$740$	−36.3521	−1.33633
$741$	−20.1428	−0.739963
$742$	−51.6475	−1.89604
$743$	7.88168	0.289151	0.144575	−	0.989494i	$-0.453818\pi$
$743$	7.88168	0.289151	0.144575	+	0.989494i	$0.453818\pi$
$744$	38.9860	1.42929
$745$	2.60897	0.0955854
$746$	4.62746	0.169423
$747$	−7.69428	−0.281519
$748$	2.27581	0.0832120
$749$	59.1211	2.16024
$750$	20.3363	0.742577
$751$	36.5220	1.33271	0.666354	−	0.745636i	$-0.267854\pi$
$751$	36.5220	1.33271	0.666354	+	0.745636i	$0.267854\pi$
$752$	2.56166	0.0934141
$753$	5.59605	0.203931
$754$	−116.168	−4.23058
$755$	15.9079	0.578948
$756$	−20.1470	−0.732738
$757$	−37.0377	−1.34616	−0.673079	−	0.739571i	$-0.735029\pi$
$757$	−37.0377	−1.34616	−0.673079	+	0.739571i	$0.735029\pi$
$758$	−27.2572	−0.990027
$759$	13.9450	0.506171
$760$	−21.8432	−0.792337
$761$	−8.87266	−0.321634	−0.160817	−	0.986984i	$-0.551413\pi$
$761$	−8.87266	−0.321634	−0.160817	+	0.986984i	$0.551413\pi$
$762$	18.6747	0.676514
$763$	−6.86315	−0.248463
$764$	−83.2881	−3.01326
$765$	−0.201214	−0.00727492
$766$	−23.1582	−0.836741
$767$	60.3182	2.17796
$768$	7.79619	0.281321
$769$	−18.0361	−0.650397	−0.325198	−	0.945646i	$-0.605431\pi$
$769$	−18.0361	−0.650397	−0.325198	+	0.945646i	$0.605431\pi$
$770$	16.7248	0.602722
$771$	6.26550	0.225647
$772$	56.9874	2.05102
$773$	−37.6071	−1.35263	−0.676317	−	0.736611i	$-0.736425\pi$
$773$	−37.6071	−1.35263	−0.676317	+	0.736611i	$0.736425\pi$
$774$	−30.5300	−1.09738
$775$	−21.5353	−0.773570
$776$	−96.5442	−3.46573
$777$	−35.9637	−1.29019
$778$	29.2639	1.04916
$779$	−21.9793	−0.787490
$780$	−24.4692	−0.876138
$781$	15.4711	0.553599
$782$	4.74271	0.169599
$783$	7.38646	0.263971
$784$	101.468	3.62385
$785$	−13.3369	−0.476015
$786$	−16.2778	−0.580611
$787$	−48.3243	−1.72258	−0.861288	−	0.508117i	$-0.830342\pi$
$787$	−48.3243	−1.72258	−0.861288	+	0.508117i	$0.830342\pi$
$788$	−115.168	−4.10271
$789$	1.97108	0.0701723
$790$	−5.49306	−0.195434
$791$	53.4236	1.89953
$792$	−14.7374	−0.523670
$793$	6.36408	0.225995
$794$	46.0228	1.63329
$795$	3.98852	0.141458
$796$	−104.967	−3.72047
$797$	20.2564	0.717517	0.358758	−	0.933430i	$-0.383200\pi$
$797$	20.2564	0.717517	0.358758	+	0.933430i	$0.383200\pi$
$798$	−36.2061	−1.28168
$799$	0.0582756	0.00206164
$800$	54.2798	1.91908
$801$	−16.3693	−0.578382
$802$	11.6391	0.410990
$803$	−15.6969	−0.553930
$804$	−74.7281	−2.63546
$805$	24.8399	0.875490
$806$	78.4846	2.76450
$807$	−28.0222	−0.986429
$808$	−67.2585	−2.36615
$809$	0.751842	0.0264334	0.0132167	−	0.999913i	$-0.495793\pi$
$809$	0.751842	0.0264334	0.0132167	+	0.999913i	$0.495793\pi$
$810$	2.18310	0.0767063
$811$	−43.2284	−1.51796	−0.758978	−	0.651116i	$-0.774301\pi$
$811$	−43.2284	−1.51796	−0.758978	+	0.651116i	$0.774301\pi$
$812$	−148.815	−5.22237
$813$	11.8594	0.415926
$814$	−44.0764	−1.54488
$815$	5.17219	0.181174
$816$	−2.59942	−0.0909979
$817$	−39.1018	−1.36800
$818$	9.53147	0.333260
$819$	−24.2077	−0.845887
$820$	−26.7002	−0.932411
$821$	32.6938	1.14102	0.570511	−	0.821290i	$-0.306745\pi$
$821$	32.6938	1.14102	0.570511	+	0.821290i	$0.306745\pi$
$822$	−11.7232	−0.408893
$823$	−1.53780	−0.0536043	−0.0268021	−	0.999641i	$-0.508532\pi$
$823$	−1.53780	−0.0536043	−0.0268021	+	0.999641i	$0.508532\pi$
$824$	−61.2133	−2.13247
$825$	8.14071	0.283423
$826$	108.421	3.77243
$827$	47.0295	1.63538	0.817688	−	0.575662i	$-0.195256\pi$
$827$	47.0295	1.63538	0.817688	+	0.575662i	$0.195256\pi$
$828$	−36.6723	−1.27445
$829$	43.5422	1.51228	0.756142	−	0.654408i	$-0.227082\pi$
$829$	43.5422	1.51228	0.756142	+	0.654408i	$0.227082\pi$
$830$	−16.7974	−0.583046
$831$	−32.6523	−1.13270
$832$	−70.3830	−2.44009
$833$	2.30831	0.0799781
$834$	−26.5932	−0.920846
$835$	13.4747	0.466313
$836$	−31.6244	−1.09375
$837$	−4.99040	−0.172494
$838$	−91.0273	−3.14448
$839$	−4.74229	−0.163722	−0.0818611	−	0.996644i	$-0.526086\pi$
$839$	−4.74229	−0.163722	−0.0818611	+	0.996644i	$0.526086\pi$
$840$	−26.2514	−0.905758
$841$	25.5598	0.881373
$842$	27.5293	0.948722
$843$	26.5588	0.914733
$844$	21.2973	0.733085
$845$	−18.6444	−0.641387
$846$	−0.632268	−0.0217378
$847$	−30.2196	−1.03836
$848$	51.5262	1.76942
$849$	15.8232	0.543052
$850$	2.76867	0.0949646
$851$	−65.4626	−2.24403
$852$	−40.6857	−1.39387
$853$	37.8746	1.29680	0.648401	−	0.761299i	$-0.275438\pi$
$853$	37.8746	1.29680	0.648401	+	0.761299i	$0.275438\pi$
$854$	11.4393	0.391444
$855$	2.79604	0.0956227
$856$	−113.730	−3.88720
$857$	31.3998	1.07260	0.536298	−	0.844029i	$-0.319822\pi$
$857$	31.3998	1.07260	0.536298	+	0.844029i	$0.319822\pi$
$858$	−29.6686	−1.01287
$859$	−22.0543	−0.752482	−0.376241	−	0.926522i	$-0.622783\pi$
$859$	−22.0543	−0.752482	−0.376241	+	0.926522i	$0.622783\pi$
$860$	−47.5005	−1.61975
$861$	−26.4149	−0.900217
$862$	17.4397	0.593998
$863$	54.1907	1.84467	0.922336	−	0.386389i	$-0.126278\pi$
$863$	54.1907	1.84467	0.922336	+	0.386389i	$0.126278\pi$
$864$	12.5783	0.427924
$865$	−4.32966	−0.147213
$866$	57.4079	1.95080
$867$	16.9409	0.575342
$868$	100.541	3.41260
$869$	−4.74666	−0.161019
$870$	16.1254	0.546702
$871$	−89.7902	−3.04242
$872$	13.2025	0.447092
$873$	12.3581	0.418260
$874$	−65.9040	−2.22923
$875$	31.3024	1.05821
$876$	41.2794	1.39470
$877$	27.6754	0.934532	0.467266	−	0.884117i	$-0.345239\pi$
$877$	27.6754	0.934532	0.467266	+	0.884117i	$0.345239\pi$
$878$	60.3353	2.03622
$879$	25.7679	0.869129
$880$	−16.6856	−0.562470
$881$	15.5584	0.524176	0.262088	−	0.965044i	$-0.415589\pi$
$881$	15.5584	0.524176	0.262088	+	0.965044i	$0.415589\pi$
$882$	−25.0443	−0.843284
$883$	36.5831	1.23112	0.615560	−	0.788090i	$-0.288930\pi$
$883$	36.5831	1.23112	0.615560	+	0.788090i	$0.288930\pi$
$884$	−7.19122	−0.241867
$885$	−8.37285	−0.281450
$886$	−47.2689	−1.58803
$887$	−35.1999	−1.18190	−0.590948	−	0.806710i	$-0.701246\pi$
$887$	−35.1999	−1.18190	−0.590948	+	0.806710i	$0.701246\pi$
$888$	69.1824	2.32161
$889$	28.7448	0.964070
$890$	−35.7359	−1.19787
$891$	1.88646	0.0631988
$892$	−47.9707	−1.60618
$893$	−0.809789	−0.0270985
$894$	−8.31893	−0.278227
$895$	−1.77411	−0.0593018
$896$	−24.3486	−0.813429
$897$	−44.0640	−1.47125
$898$	106.131	3.54163
$899$	−36.8614	−1.22940
$900$	−21.4084	−0.713612
$901$	1.17218	0.0390510
$902$	−32.3736	−1.07792
$903$	−46.9929	−1.56383
$904$	−102.770	−3.41807
$905$	6.13646	0.203983
$906$	−50.7236	−1.68518
$907$	50.2106	1.66722	0.833608	−	0.552356i	$-0.186271\pi$
$907$	50.2106	1.66722	0.833608	+	0.552356i	$0.186271\pi$
$908$	80.8104	2.68179
$909$	8.60943	0.285557
$910$	−52.8479	−1.75189
$911$	31.2916	1.03674	0.518368	−	0.855157i	$-0.326540\pi$
$911$	31.2916	1.03674	0.518368	+	0.855157i	$0.326540\pi$
$912$	36.1211	1.19609
$913$	−14.5149	−0.480375
$914$	27.6376	0.914171
$915$	−0.883406	−0.0292045
$916$	41.0804	1.35733
$917$	−25.0555	−0.827404
$918$	0.641588	0.0211756
$919$	−35.5332	−1.17213	−0.586066	−	0.810264i	$-0.699324\pi$
$919$	−35.5332	−1.17213	−0.586066	+	0.810264i	$0.699324\pi$
$920$	−47.7838	−1.57539
$921$	18.7290	0.617142
$922$	−9.68617	−0.318997
$923$	−48.8862	−1.60911
$924$	−38.0064	−1.25032
$925$	−38.2154	−1.25651
$926$	−7.00759	−0.230284
$927$	7.83562	0.257355
$928$	92.9094	3.04990
$929$	−32.6251	−1.07040	−0.535198	−	0.844727i	$-0.679763\pi$
$929$	−32.6251	−1.07040	−0.535198	+	0.844727i	$0.679763\pi$
$930$	−10.8945	−0.357246
$931$	−32.0759	−1.05124
$932$	−63.3302	−2.07445
$933$	−4.23513	−0.138652
$934$	5.68817	0.186123
$935$	−0.379583	−0.0124137
$936$	46.5678	1.52212
$937$	−40.0757	−1.30922	−0.654609	−	0.755968i	$-0.727167\pi$
$937$	−40.0757	−1.30922	−0.654609	+	0.755968i	$0.727167\pi$
$938$	−161.396	−5.26976
$939$	9.80629	0.320016
$940$	−0.983722	−0.0320855
$941$	−1.38053	−0.0450041	−0.0225020	−	0.999747i	$-0.507163\pi$
$941$	−1.38053	−0.0450041	−0.0225020	+	0.999747i	$0.507163\pi$
$942$	42.5259	1.38557
$943$	−48.0815	−1.56575
$944$	−108.166	−3.52050
$945$	3.36031	0.109311
$946$	−57.5936	−1.87253
$947$	−28.3692	−0.921877	−0.460938	−	0.887432i	$-0.652487\pi$
$947$	−28.3692	−0.921877	−0.460938	+	0.887432i	$0.652487\pi$
$948$	12.4827	0.405420
$949$	49.5996	1.61007
$950$	−38.4730	−1.24823
$951$	−29.5952	−0.959689
$952$	−7.71498	−0.250044
$953$	−30.9010	−1.00098	−0.500491	−	0.865741i	$-0.666847\pi$
$953$	−30.9010	−1.00098	−0.500491	+	0.865741i	$0.666847\pi$
$954$	−12.7177	−0.411751
$955$	13.8916	0.449522
$956$	−44.9335	−1.45325
$957$	13.9343	0.450431
$958$	−6.37413	−0.205939
$959$	−18.0448	−0.582696
$960$	9.76995	0.315324
$961$	−6.09589	−0.196642
$962$	139.275	4.49039
$963$	14.5580	0.469125
$964$	90.4030	2.91168
$965$	−9.50492	−0.305974
$966$	−79.2039	−2.54834
$967$	−6.56389	−0.211080	−0.105540	−	0.994415i	$-0.533657\pi$
$967$	−6.56389	−0.211080	−0.105540	+	0.994415i	$0.533657\pi$
$968$	58.1326	1.86845
$969$	0.821725	0.0263976
$970$	26.9791	0.866246
$971$	−7.40148	−0.237525	−0.118762	−	0.992923i	$-0.537893\pi$
$971$	−7.40148	−0.237525	−0.118762	+	0.992923i	$0.537893\pi$
$972$	−4.96099	−0.159124
$973$	−40.9332	−1.31226
$974$	39.2962	1.25913
$975$	−25.7234	−0.823808
$976$	−11.4124	−0.365303
$977$	−27.5908	−0.882707	−0.441354	−	0.897333i	$-0.645502\pi$
$977$	−27.5908	−0.882707	−0.441354	+	0.897333i	$0.645502\pi$
$978$	−16.4919	−0.527354
$979$	−30.8801	−0.986932
$980$	−38.9654	−1.24470
$981$	−1.68998	−0.0539570
$982$	5.23505	0.167057
$983$	−33.6727	−1.07399	−0.536996	−	0.843585i	$-0.680441\pi$
$983$	−33.6727	−1.07399	−0.536996	+	0.843585i	$0.680441\pi$
$984$	50.8137	1.61988
$985$	19.2089	0.612047
$986$	4.73907	0.150923
$987$	−0.973211	−0.0309776
$988$	99.9281	3.17914
$989$	−85.5385	−2.71997
$990$	4.11833	0.130889
$991$	0.783082	0.0248754	0.0124377	−	0.999923i	$-0.496041\pi$
$991$	0.783082	0.0248754	0.0124377	+	0.999923i	$0.496041\pi$
$992$	−62.7710	−1.99298
$993$	10.7653	0.341627
$994$	−87.8718	−2.78713
$995$	17.5075	0.555024
$996$	38.1712	1.20950
$997$	−9.05962	−0.286921	−0.143461	−	0.989656i	$-0.545823\pi$
$997$	−9.05962	−0.286921	−0.143461	+	0.989656i	$0.545823\pi$
$998$	−25.7388	−0.814746
$999$	−8.85570	−0.280182

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.b.1.6	✓	102

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.b.1.6	✓	102	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63837 q^{2} -1.00000 q^{3} +4.96099 q^{4} -0.827443 q^{5} +2.63837 q^{6} +4.06107 q^{7} -7.81219 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.63837 q^{2} -1.00000 q^{3} +4.96099 q^{4} -0.827443 q^{5} +2.63837 q^{6} +4.06107 q^{7} -7.81219 q^{8} +1.00000 q^{9} +2.18310 q^{10} +1.88646 q^{11} -4.96099 q^{12} -5.96092 q^{13} -10.7146 q^{14} +0.827443 q^{15} +10.6894 q^{16} +0.243176 q^{17} -2.63837 q^{18} -3.37914 q^{19} -4.10494 q^{20} -4.06107 q^{21} -4.97718 q^{22} -7.39214 q^{23} +7.81219 q^{24} -4.31534 q^{25} +15.7271 q^{26} -1.00000 q^{27} +20.1470 q^{28} -7.38646 q^{29} -2.18310 q^{30} +4.99040 q^{31} -12.5783 q^{32} -1.88646 q^{33} -0.641588 q^{34} -3.36031 q^{35} +4.96099 q^{36} +8.85570 q^{37} +8.91541 q^{38} +5.96092 q^{39} +6.46414 q^{40} +6.50441 q^{41} +10.7146 q^{42} +11.5715 q^{43} +9.35871 q^{44} -0.827443 q^{45} +19.5032 q^{46} +0.239644 q^{47} -10.6894 q^{48} +9.49233 q^{49} +11.3855 q^{50} -0.243176 q^{51} -29.5721 q^{52} +4.82029 q^{53} +2.63837 q^{54} -1.56094 q^{55} -31.7259 q^{56} +3.37914 q^{57} +19.4882 q^{58} -10.1189 q^{59} +4.10494 q^{60} -1.06763 q^{61} -13.1665 q^{62} +4.06107 q^{63} +11.8074 q^{64} +4.93232 q^{65} +4.97718 q^{66} +15.0631 q^{67} +1.20639 q^{68} +7.39214 q^{69} +8.86573 q^{70} +8.20112 q^{71} -7.81219 q^{72} -8.32080 q^{73} -23.3646 q^{74} +4.31534 q^{75} -16.7639 q^{76} +7.66105 q^{77} -15.7271 q^{78} -2.51617 q^{79} -8.84491 q^{80} +1.00000 q^{81} -17.1610 q^{82} -7.69428 q^{83} -20.1470 q^{84} -0.201214 q^{85} -30.5300 q^{86} +7.38646 q^{87} -14.7374 q^{88} -16.3693 q^{89} +2.18310 q^{90} -24.2077 q^{91} -36.6723 q^{92} -4.99040 q^{93} -0.632268 q^{94} +2.79604 q^{95} +12.5783 q^{96} +12.3581 q^{97} -25.0443 q^{98} +1.88646 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 102 q^{3} + 96 q^{4} - 20 q^{5} + 6 q^{6} + 12 q^{7} - 21 q^{8} + 102 q^{9}+O(q^{10}) \) 102 * q - 6 * q^2 - 102 * q^3 + 96 * q^4 - 20 * q^5 + 6 * q^6 + 12 * q^7 - 21 * q^8 + 102 * q^9	\( 102 q - 6 q^{2} - 102 q^{3} + 96 q^{4} - 20 q^{5} + 6 q^{6} + 12 q^{7} - 21 q^{8} + 102 q^{9} - 16 q^{10} - 28 q^{11} - 96 q^{12} - 2 q^{13} - 41 q^{14} + 20 q^{15} + 88 q^{16} - 77 q^{17} - 6 q^{18} + 10 q^{19} - 50 q^{20} - 12 q^{21} + 24 q^{22} - 29 q^{23} + 21 q^{24} + 74 q^{25} - 45 q^{26} - 102 q^{27} + 19 q^{28} - 68 q^{29} + 16 q^{30} - 29 q^{31} - 48 q^{32} + 28 q^{33} - 19 q^{34} - 49 q^{35} + 96 q^{36} + 4 q^{37} - 44 q^{38} + 2 q^{39} - 41 q^{40} - 122 q^{41} + 41 q^{42} + 85 q^{43} - 86 q^{44} - 20 q^{45} - 28 q^{46} - 39 q^{47} - 88 q^{48} + 24 q^{49} - 37 q^{50} + 77 q^{51} + 8 q^{52} - 37 q^{53} + 6 q^{54} - 13 q^{55} - 130 q^{56} - 10 q^{57} + 17 q^{58} - 58 q^{59} + 50 q^{60} - 114 q^{61} - 64 q^{62} + 12 q^{63} + 47 q^{64} - 92 q^{65} - 24 q^{66} + 121 q^{67} - 138 q^{68} + 29 q^{69} - 2 q^{70} - 67 q^{71} - 21 q^{72} - 72 q^{73} - 111 q^{74} - 74 q^{75} - 17 q^{76} - 57 q^{77} + 45 q^{78} - 24 q^{79} - 97 q^{80} + 102 q^{81} - q^{82} - 78 q^{83} - 19 q^{84} - 24 q^{85} - 80 q^{86} + 68 q^{87} + 54 q^{88} - 176 q^{89} - 16 q^{90} - 3 q^{91} - 82 q^{92} + 29 q^{93} - 41 q^{94} - 90 q^{95} + 48 q^{96} - 77 q^{97} - 48 q^{98} - 28 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 102 * q^3 + 96 * q^4 - 20 * q^5 + 6 * q^6 + 12 * q^7 - 21 * q^8 + 102 * q^9 - 16 * q^10 - 28 * q^11 - 96 * q^12 - 2 * q^13 - 41 * q^14 + 20 * q^15 + 88 * q^16 - 77 * q^17 - 6 * q^18 + 10 * q^19 - 50 * q^20 - 12 * q^21 + 24 * q^22 - 29 * q^23 + 21 * q^24 + 74 * q^25 - 45 * q^26 - 102 * q^27 + 19 * q^28 - 68 * q^29 + 16 * q^30 - 29 * q^31 - 48 * q^32 + 28 * q^33 - 19 * q^34 - 49 * q^35 + 96 * q^36 + 4 * q^37 - 44 * q^38 + 2 * q^39 - 41 * q^40 - 122 * q^41 + 41 * q^42 + 85 * q^43 - 86 * q^44 - 20 * q^45 - 28 * q^46 - 39 * q^47 - 88 * q^48 + 24 * q^49 - 37 * q^50 + 77 * q^51 + 8 * q^52 - 37 * q^53 + 6 * q^54 - 13 * q^55 - 130 * q^56 - 10 * q^57 + 17 * q^58 - 58 * q^59 + 50 * q^60 - 114 * q^61 - 64 * q^62 + 12 * q^63 + 47 * q^64 - 92 * q^65 - 24 * q^66 + 121 * q^67 - 138 * q^68 + 29 * q^69 - 2 * q^70 - 67 * q^71 - 21 * q^72 - 72 * q^73 - 111 * q^74 - 74 * q^75 - 17 * q^76 - 57 * q^77 + 45 * q^78 - 24 * q^79 - 97 * q^80 + 102 * q^81 - q^82 - 78 * q^83 - 19 * q^84 - 24 * q^85 - 80 * q^86 + 68 * q^87 + 54 * q^88 - 176 * q^89 - 16 * q^90 - 3 * q^91 - 82 * q^92 + 29 * q^93 - 41 * q^94 - 90 * q^95 + 48 * q^96 - 77 * q^97 - 48 * q^98 - 28 * q^99

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