LMFDB - Embedded newform 4017.2.a.l.1.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.86788 q^{2} +1.00000 q^{3} +1.48899 q^{4} +2.45231 q^{5} +1.86788 q^{6} +3.90874 q^{7} -0.954515 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.86788 q^{2} +1.00000 q^{3} +1.48899 q^{4} +2.45231 q^{5} +1.86788 q^{6} +3.90874 q^{7} -0.954515 q^{8} +1.00000 q^{9} +4.58063 q^{10} +0.862252 q^{11} +1.48899 q^{12} -1.00000 q^{13} +7.30107 q^{14} +2.45231 q^{15} -4.76089 q^{16} -6.68966 q^{17} +1.86788 q^{18} +4.14678 q^{19} +3.65146 q^{20} +3.90874 q^{21} +1.61059 q^{22} +7.60551 q^{23} -0.954515 q^{24} +1.01383 q^{25} -1.86788 q^{26} +1.00000 q^{27} +5.82006 q^{28} +1.65365 q^{29} +4.58063 q^{30} +2.43165 q^{31} -6.98376 q^{32} +0.862252 q^{33} -12.4955 q^{34} +9.58544 q^{35} +1.48899 q^{36} +2.03996 q^{37} +7.74570 q^{38} -1.00000 q^{39} -2.34077 q^{40} +6.43167 q^{41} +7.30107 q^{42} -10.6645 q^{43} +1.28388 q^{44} +2.45231 q^{45} +14.2062 q^{46} +0.232910 q^{47} -4.76089 q^{48} +8.27824 q^{49} +1.89371 q^{50} -6.68966 q^{51} -1.48899 q^{52} +2.07945 q^{53} +1.86788 q^{54} +2.11451 q^{55} -3.73095 q^{56} +4.14678 q^{57} +3.08882 q^{58} -1.45521 q^{59} +3.65146 q^{60} +6.32063 q^{61} +4.54204 q^{62} +3.90874 q^{63} -3.52306 q^{64} -2.45231 q^{65} +1.61059 q^{66} -0.649897 q^{67} -9.96082 q^{68} +7.60551 q^{69} +17.9045 q^{70} -13.1811 q^{71} -0.954515 q^{72} -8.96605 q^{73} +3.81040 q^{74} +1.01383 q^{75} +6.17450 q^{76} +3.37032 q^{77} -1.86788 q^{78} +12.1102 q^{79} -11.6752 q^{80} +1.00000 q^{81} +12.0136 q^{82} -12.4874 q^{83} +5.82006 q^{84} -16.4051 q^{85} -19.9200 q^{86} +1.65365 q^{87} -0.823033 q^{88} +4.11544 q^{89} +4.58063 q^{90} -3.90874 q^{91} +11.3245 q^{92} +2.43165 q^{93} +0.435049 q^{94} +10.1692 q^{95} -6.98376 q^{96} +11.7071 q^{97} +15.4628 q^{98} +0.862252 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.86788	1.32079	0.660396	−	0.750917i	$-0.270388\pi$
$2$	1.86788	1.32079	0.660396	+	0.750917i	$0.270388\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.48899	0.744493
$5$	2.45231	1.09671	0.548353	−	0.836247i	$-0.315255\pi$
$5$	2.45231	1.09671	0.548353	+	0.836247i	$0.315255\pi$
$6$	1.86788	0.762560
$7$	3.90874	1.47736	0.738682	−	0.674054i	$-0.235448\pi$
$7$	3.90874	1.47736	0.738682	+	0.674054i	$0.235448\pi$
$8$	−0.954515	−0.337472
$9$	1.00000	0.333333
$10$	4.58063	1.44852
$11$	0.862252	0.259979	0.129989	−	0.991515i	$-0.458506\pi$
$11$	0.862252	0.259979	0.129989	+	0.991515i	$0.458506\pi$
$12$	1.48899	0.429833
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	7.30107	1.95129
$15$	2.45231	0.633184
$16$	−4.76089	−1.19022
$17$	−6.68966	−1.62248	−0.811241	−	0.584712i	$-0.801208\pi$
$17$	−6.68966	−1.62248	−0.811241	+	0.584712i	$0.801208\pi$
$18$	1.86788	0.440264
$19$	4.14678	0.951337	0.475669	−	0.879625i	$-0.342206\pi$
$19$	4.14678	0.951337	0.475669	+	0.879625i	$0.342206\pi$
$20$	3.65146	0.816490
$21$	3.90874	0.852957
$22$	1.61059	0.343378
$23$	7.60551	1.58586	0.792930	−	0.609313i	$-0.208555\pi$
$23$	7.60551	1.58586	0.792930	+	0.609313i	$0.208555\pi$
$24$	−0.954515	−0.194839
$25$	1.01383	0.202766
$26$	−1.86788	−0.366322
$27$	1.00000	0.192450
$28$	5.82006	1.09989
$29$	1.65365	0.307075	0.153537	−	0.988143i	$-0.450933\pi$
$29$	1.65365	0.307075	0.153537	+	0.988143i	$0.450933\pi$
$30$	4.58063	0.836305
$31$	2.43165	0.436738	0.218369	−	0.975866i	$-0.429926\pi$
$31$	2.43165	0.436738	0.218369	+	0.975866i	$0.429926\pi$
$32$	−6.98376	−1.23457
$33$	0.862252	0.150099
$34$	−12.4955	−2.14296
$35$	9.58544	1.62024
$36$	1.48899	0.248164
$37$	2.03996	0.335367	0.167683	−	0.985841i	$-0.446371\pi$
$37$	2.03996	0.335367	0.167683	+	0.985841i	$0.446371\pi$
$38$	7.74570	1.25652
$39$	−1.00000	−0.160128
$40$	−2.34077	−0.370108
$41$	6.43167	1.00446	0.502229	−	0.864734i	$-0.332513\pi$
$41$	6.43167	1.00446	0.502229	+	0.864734i	$0.332513\pi$
$42$	7.30107	1.12658
$43$	−10.6645	−1.62632	−0.813160	−	0.582040i	$-0.802255\pi$
$43$	−10.6645	−1.62632	−0.813160	+	0.582040i	$0.802255\pi$
$44$	1.28388	0.193552
$45$	2.45231	0.365569
$46$	14.2062	2.09459
$47$	0.232910	0.0339734	0.0169867	−	0.999856i	$-0.494593\pi$
$47$	0.232910	0.0339734	0.0169867	+	0.999856i	$0.494593\pi$
$48$	−4.76089	−0.687176
$49$	8.27824	1.18261
$50$	1.89371	0.267811
$51$	−6.68966	−0.936740
$52$	−1.48899	−0.206485
$53$	2.07945	0.285634	0.142817	−	0.989749i	$-0.454384\pi$
$53$	2.07945	0.285634	0.142817	+	0.989749i	$0.454384\pi$
$54$	1.86788	0.254187
$55$	2.11451	0.285121
$56$	−3.73095	−0.498569
$57$	4.14678	0.549255
$58$	3.08882	0.405582
$59$	−1.45521	−0.189452	−0.0947262	−	0.995503i	$-0.530198\pi$
$59$	−1.45521	−0.189452	−0.0947262	+	0.995503i	$0.530198\pi$
$60$	3.65146	0.471401
$61$	6.32063	0.809274	0.404637	−	0.914477i	$-0.367398\pi$
$61$	6.32063	0.809274	0.404637	+	0.914477i	$0.367398\pi$
$62$	4.54204	0.576840
$63$	3.90874	0.492455
$64$	−3.52306	−0.440382
$65$	−2.45231	−0.304172
$66$	1.61059	0.198249
$67$	−0.649897	−0.0793975	−0.0396988	−	0.999212i	$-0.512640\pi$
$67$	−0.649897	−0.0793975	−0.0396988	+	0.999212i	$0.512640\pi$
$68$	−9.96082	−1.20793
$69$	7.60551	0.915596
$70$	17.9045	2.13999
$71$	−13.1811	−1.56431	−0.782153	−	0.623086i	$-0.785878\pi$
$71$	−13.1811	−1.56431	−0.782153	+	0.623086i	$0.785878\pi$
$72$	−0.954515	−0.112491
$73$	−8.96605	−1.04940	−0.524699	−	0.851288i	$-0.675822\pi$
$73$	−8.96605	−1.04940	−0.524699	+	0.851288i	$0.675822\pi$
$74$	3.81040	0.442950
$75$	1.01383	0.117067
$76$	6.17450	0.708264
$77$	3.37032	0.384084
$78$	−1.86788	−0.211496
$79$	12.1102	1.36251	0.681253	−	0.732049i	$-0.261436\pi$
$79$	12.1102	1.36251	0.681253	+	0.732049i	$0.261436\pi$
$80$	−11.6752	−1.30533
$81$	1.00000	0.111111
$82$	12.0136	1.32668
$83$	−12.4874	−1.37067	−0.685337	−	0.728226i	$-0.740345\pi$
$83$	−12.4874	−1.37067	−0.685337	+	0.728226i	$0.740345\pi$
$84$	5.82006	0.635020
$85$	−16.4051	−1.77939
$86$	−19.9200	−2.14803
$87$	1.65365	0.177290
$88$	−0.823033	−0.0877356
$89$	4.11544	0.436236	0.218118	−	0.975922i	$-0.430008\pi$
$89$	4.11544	0.436236	0.218118	+	0.975922i	$0.430008\pi$
$90$	4.58063	0.482841
$91$	−3.90874	−0.409747
$92$	11.3245	1.18066
$93$	2.43165	0.252151
$94$	0.435049	0.0448718
$95$	10.1692	1.04334
$96$	−6.98376	−0.712777
$97$	11.7071	1.18868	0.594338	−	0.804215i	$-0.297414\pi$
$97$	11.7071	1.18868	0.594338	+	0.804215i	$0.297414\pi$
$98$	15.4628	1.56198
$99$	0.862252	0.0866596
$100$	1.50957	0.150957
$101$	−3.26052	−0.324434	−0.162217	−	0.986755i	$-0.551864\pi$
$101$	−3.26052	−0.324434	−0.162217	+	0.986755i	$0.551864\pi$
$102$	−12.4955	−1.23724
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	0.954515	0.0935979
$105$	9.58544	0.935443
$106$	3.88416	0.377263
$107$	4.25192	0.411048	0.205524	−	0.978652i	$-0.434110\pi$
$107$	4.25192	0.411048	0.205524	+	0.978652i	$0.434110\pi$
$108$	1.48899	0.143278
$109$	10.8915	1.04322	0.521609	−	0.853185i	$-0.325332\pi$
$109$	10.8915	1.04322	0.521609	+	0.853185i	$0.325332\pi$
$110$	3.94966	0.376585
$111$	2.03996	0.193624
$112$	−18.6091	−1.75839
$113$	−18.5826	−1.74811	−0.874053	−	0.485830i	$-0.838517\pi$
$113$	−18.5826	−1.74811	−0.874053	+	0.485830i	$0.838517\pi$
$114$	7.74570	0.725452
$115$	18.6511	1.73922
$116$	2.46226	0.228615
$117$	−1.00000	−0.0924500
$118$	−2.71816	−0.250227
$119$	−26.1482	−2.39700
$120$	−2.34077	−0.213682
$121$	−10.2565	−0.932411
$122$	11.8062	1.06888
$123$	6.43167	0.579925
$124$	3.62070	0.325148
$125$	−9.77533	−0.874332
$126$	7.30107	0.650431
$127$	−14.8659	−1.31914	−0.659568	−	0.751645i	$-0.729261\pi$
$127$	−14.8659	−1.31914	−0.659568	+	0.751645i	$0.729261\pi$
$128$	7.38686	0.652912
$129$	−10.6645	−0.938957
$130$	−4.58063	−0.401748
$131$	4.27364	0.373389	0.186695	−	0.982418i	$-0.440223\pi$
$131$	4.27364	0.373389	0.186695	+	0.982418i	$0.440223\pi$
$132$	1.28388	0.111748
$133$	16.2087	1.40547
$134$	−1.21393	−0.104868
$135$	2.45231	0.211061
$136$	6.38538	0.547542
$137$	20.1351	1.72026	0.860130	−	0.510074i	$-0.170382\pi$
$137$	20.1351	1.72026	0.860130	+	0.510074i	$0.170382\pi$
$138$	14.2062	1.20931
$139$	−16.1855	−1.37283	−0.686416	−	0.727209i	$-0.740817\pi$
$139$	−16.1855	−1.37283	−0.686416	+	0.727209i	$0.740817\pi$
$140$	14.2726	1.20625
$141$	0.232910	0.0196146
$142$	−24.6207	−2.06612
$143$	−0.862252	−0.0721052
$144$	−4.76089	−0.396741
$145$	4.05526	0.336771
$146$	−16.7475	−1.38604
$147$	8.27824	0.682778
$148$	3.03747	0.249678
$149$	−15.4432	−1.26516	−0.632579	−	0.774496i	$-0.718004\pi$
$149$	−15.4432	−1.26516	−0.632579	+	0.774496i	$0.718004\pi$
$150$	1.89371	0.154621
$151$	−19.2969	−1.57036	−0.785181	−	0.619266i	$-0.787430\pi$
$151$	−19.2969	−1.57036	−0.785181	+	0.619266i	$0.787430\pi$
$152$	−3.95816	−0.321050
$153$	−6.68966	−0.540827
$154$	6.29536	0.507295
$155$	5.96317	0.478973
$156$	−1.48899	−0.119214
$157$	−12.7357	−1.01642	−0.508211	−	0.861233i	$-0.669693\pi$
$157$	−12.7357	−1.01642	−0.508211	+	0.861233i	$0.669693\pi$
$158$	22.6205	1.79959
$159$	2.07945	0.164911
$160$	−17.1263	−1.35396
$161$	29.7280	2.34289
$162$	1.86788	0.146755
$163$	18.8058	1.47298	0.736492	−	0.676447i	$-0.236481\pi$
$163$	18.8058	1.47298	0.736492	+	0.676447i	$0.236481\pi$
$164$	9.57667	0.747812
$165$	2.11451	0.164614
$166$	−23.3251	−1.81038
$167$	−3.72142	−0.287972	−0.143986	−	0.989580i	$-0.545992\pi$
$167$	−3.72142	−0.287972	−0.143986	+	0.989580i	$0.545992\pi$
$168$	−3.73095	−0.287849
$169$	1.00000	0.0769231
$170$	−30.6429	−2.35020
$171$	4.14678	0.317112
$172$	−15.8793	−1.21078
$173$	−10.8829	−0.827409	−0.413705	−	0.910411i	$-0.635765\pi$
$173$	−10.8829	−0.827409	−0.413705	+	0.910411i	$0.635765\pi$
$174$	3.08882	0.234163
$175$	3.96279	0.299559
$176$	−4.10509	−0.309433
$177$	−1.45521	−0.109380
$178$	7.68717	0.576177
$179$	−20.3407	−1.52033	−0.760167	−	0.649728i	$-0.774883\pi$
$179$	−20.3407	−1.52033	−0.760167	+	0.649728i	$0.774883\pi$
$180$	3.65146	0.272163
$181$	5.20691	0.387027	0.193513	−	0.981098i	$-0.438012\pi$
$181$	5.20691	0.387027	0.193513	+	0.981098i	$0.438012\pi$
$182$	−7.30107	−0.541191
$183$	6.32063	0.467234
$184$	−7.25957	−0.535183
$185$	5.00261	0.367799
$186$	4.54204	0.333039
$187$	−5.76818	−0.421811
$188$	0.346800	0.0252930
$189$	3.90874	0.284319
$190$	18.9949	1.37803
$191$	−7.98086	−0.577475	−0.288737	−	0.957408i	$-0.593235\pi$
$191$	−7.98086	−0.577475	−0.288737	+	0.957408i	$0.593235\pi$
$192$	−3.52306	−0.254255
$193$	13.4773	0.970118	0.485059	−	0.874481i	$-0.338798\pi$
$193$	13.4773	0.970118	0.485059	+	0.874481i	$0.338798\pi$
$194$	21.8675	1.56999
$195$	−2.45231	−0.175614
$196$	12.3262	0.880441
$197$	4.56602	0.325316	0.162658	−	0.986683i	$-0.447993\pi$
$197$	4.56602	0.325316	0.162658	+	0.986683i	$0.447993\pi$
$198$	1.61059	0.114459
$199$	−13.9199	−0.986758	−0.493379	−	0.869814i	$-0.664238\pi$
$199$	−13.9199	−0.986758	−0.493379	+	0.869814i	$0.664238\pi$
$200$	−0.967713	−0.0684277
$201$	−0.649897	−0.0458402
$202$	−6.09027	−0.428510
$203$	6.46368	0.453662
$204$	−9.96082	−0.697397
$205$	15.7725	1.10160
$206$	−1.86788	−0.130142
$207$	7.60551	0.528620
$208$	4.76089	0.330109
$209$	3.57557	0.247328
$210$	17.9045	1.23553
$211$	−4.76634	−0.328128	−0.164064	−	0.986450i	$-0.552460\pi$
$211$	−4.76634	−0.328128	−0.164064	+	0.986450i	$0.552460\pi$
$212$	3.09627	0.212653
$213$	−13.1811	−0.903153
$214$	7.94208	0.542910
$215$	−26.1527	−1.78360
$216$	−0.954515	−0.0649465
$217$	9.50470	0.645221
$218$	20.3441	1.37787
$219$	−8.96605	−0.605870
$220$	3.14848	0.212270
$221$	6.68966	0.449996
$222$	3.81040	0.255737
$223$	2.74509	0.183825	0.0919124	−	0.995767i	$-0.470702\pi$
$223$	2.74509	0.183825	0.0919124	+	0.995767i	$0.470702\pi$
$224$	−27.2977	−1.82390
$225$	1.01383	0.0675885
$226$	−34.7102	−2.30889
$227$	17.3206	1.14961	0.574804	−	0.818291i	$-0.305078\pi$
$227$	17.3206	1.14961	0.574804	+	0.818291i	$0.305078\pi$
$228$	6.17450	0.408916
$229$	6.66675	0.440551	0.220276	−	0.975438i	$-0.429304\pi$
$229$	6.66675	0.440551	0.220276	+	0.975438i	$0.429304\pi$
$230$	34.8380	2.29715
$231$	3.37032	0.221751
$232$	−1.57843	−0.103629
$233$	−8.96727	−0.587465	−0.293733	−	0.955888i	$-0.594898\pi$
$233$	−8.96727	−0.587465	−0.293733	+	0.955888i	$0.594898\pi$
$234$	−1.86788	−0.122107
$235$	0.571168	0.0372589
$236$	−2.16679	−0.141046
$237$	12.1102	0.786643
$238$	−48.8417	−3.16594
$239$	23.5551	1.52365	0.761826	−	0.647782i	$-0.224303\pi$
$239$	23.5551	1.52365	0.761826	+	0.647782i	$0.224303\pi$
$240$	−11.6752	−0.753630
$241$	20.6327	1.32907	0.664535	−	0.747257i	$-0.268630\pi$
$241$	20.6327	1.32907	0.664535	+	0.747257i	$0.268630\pi$
$242$	−19.1580	−1.23152
$243$	1.00000	0.0641500
$244$	9.41133	0.602498
$245$	20.3008	1.29697
$246$	12.0136	0.765960
$247$	−4.14678	−0.263853
$248$	−2.32105	−0.147387
$249$	−12.4874	−0.791359
$250$	−18.2592	−1.15481
$251$	−20.6705	−1.30471	−0.652355	−	0.757913i	$-0.726219\pi$
$251$	−20.6705	−1.30471	−0.652355	+	0.757913i	$0.726219\pi$
$252$	5.82006	0.366629
$253$	6.55787	0.412290
$254$	−27.7678	−1.74230
$255$	−16.4051	−1.02733
$256$	20.8439	1.30274
$257$	−5.10456	−0.318414	−0.159207	−	0.987245i	$-0.550894\pi$
$257$	−5.10456	−0.318414	−0.159207	+	0.987245i	$0.550894\pi$
$258$	−19.9200	−1.24017
$259$	7.97366	0.495459
$260$	−3.65146	−0.226454
$261$	1.65365	0.102358
$262$	7.98265	0.493170
$263$	−11.9455	−0.736589	−0.368294	−	0.929709i	$-0.620058\pi$
$263$	−11.9455	−0.736589	−0.368294	+	0.929709i	$0.620058\pi$
$264$	−0.823033	−0.0506542
$265$	5.09945	0.313257
$266$	30.2759	1.85634
$267$	4.11544	0.251861
$268$	−0.967687	−0.0591109
$269$	4.91421	0.299624	0.149812	−	0.988714i	$-0.452133\pi$
$269$	4.91421	0.299624	0.149812	+	0.988714i	$0.452133\pi$
$270$	4.58063	0.278768
$271$	−4.40919	−0.267839	−0.133920	−	0.990992i	$-0.542756\pi$
$271$	−4.40919	−0.267839	−0.133920	+	0.990992i	$0.542756\pi$
$272$	31.8488	1.93112
$273$	−3.90874	−0.236568
$274$	37.6101	2.27211
$275$	0.874175	0.0527148
$276$	11.3245	0.681655
$277$	28.7978	1.73029	0.865147	−	0.501518i	$-0.167225\pi$
$277$	28.7978	1.73029	0.865147	+	0.501518i	$0.167225\pi$
$278$	−30.2325	−1.81323
$279$	2.43165	0.145579
$280$	−9.14944	−0.546784
$281$	20.7089	1.23539	0.617694	−	0.786419i	$-0.288067\pi$
$281$	20.7089	1.23539	0.617694	+	0.786419i	$0.288067\pi$
$282$	0.435049	0.0259068
$283$	−1.13845	−0.0676738	−0.0338369	−	0.999427i	$-0.510773\pi$
$283$	−1.13845	−0.0676738	−0.0338369	+	0.999427i	$0.510773\pi$
$284$	−19.6264	−1.16461
$285$	10.1692	0.602371
$286$	−1.61059	−0.0952360
$287$	25.1397	1.48395
$288$	−6.98376	−0.411522
$289$	27.7516	1.63245
$290$	7.57475	0.444805
$291$	11.7071	0.686282
$292$	−13.3503	−0.781269
$293$	−14.2845	−0.834508	−0.417254	−	0.908790i	$-0.637007\pi$
$293$	−14.2845	−0.834508	−0.417254	+	0.908790i	$0.637007\pi$
$294$	15.4628	0.901808
$295$	−3.56863	−0.207774
$296$	−1.94717	−0.113177
$297$	0.862252	0.0500330
$298$	−28.8461	−1.67101
$299$	−7.60551	−0.439838
$300$	1.50957	0.0871553
$301$	−41.6847	−2.40267
$302$	−36.0444	−2.07412
$303$	−3.26052	−0.187312
$304$	−19.7424	−1.13230
$305$	15.5001	0.887536
$306$	−12.4955	−0.714321
$307$	8.24457	0.470542	0.235271	−	0.971930i	$-0.424402\pi$
$307$	8.24457	0.470542	0.235271	+	0.971930i	$0.424402\pi$
$308$	5.01836	0.285947
$309$	−1.00000	−0.0568880
$310$	11.1385	0.632624
$311$	1.89729	0.107585	0.0537926	−	0.998552i	$-0.482869\pi$
$311$	1.89729	0.107585	0.0537926	+	0.998552i	$0.482869\pi$
$312$	0.954515	0.0540387
$313$	17.9934	1.01705	0.508523	−	0.861048i	$-0.330192\pi$
$313$	17.9934	1.01705	0.508523	+	0.861048i	$0.330192\pi$
$314$	−23.7889	−1.34248
$315$	9.58544	0.540078
$316$	18.0319	1.01438
$317$	3.89982	0.219036	0.109518	−	0.993985i	$-0.465069\pi$
$317$	3.89982	0.219036	0.109518	+	0.993985i	$0.465069\pi$
$318$	3.88416	0.217813
$319$	1.42586	0.0798330
$320$	−8.63964	−0.482970
$321$	4.25192	0.237319
$322$	55.5284	3.09447
$323$	−27.7406	−1.54353
$324$	1.48899	0.0827214
$325$	−1.01383	−0.0562370
$326$	35.1270	1.94551
$327$	10.8915	0.602302
$328$	−6.13913	−0.338977
$329$	0.910384	0.0501911
$330$	3.94966	0.217422
$331$	7.89973	0.434209	0.217104	−	0.976148i	$-0.430339\pi$
$331$	7.89973	0.434209	0.217104	+	0.976148i	$0.430339\pi$
$332$	−18.5936	−1.02046
$333$	2.03996	0.111789
$334$	−6.95117	−0.380351
$335$	−1.59375	−0.0870758
$336$	−18.6091	−1.01521
$337$	−14.0389	−0.764747	−0.382374	−	0.924008i	$-0.624893\pi$
$337$	−14.0389	−0.764747	−0.382374	+	0.924008i	$0.624893\pi$
$338$	1.86788	0.101599
$339$	−18.5826	−1.00927
$340$	−24.4270	−1.32474
$341$	2.09670	0.113543
$342$	7.74570	0.418840
$343$	4.99630	0.269775
$344$	10.1794	0.548837
$345$	18.6511	1.00414
$346$	−20.3279	−1.09284
$347$	−17.0063	−0.912947	−0.456474	−	0.889737i	$-0.650888\pi$
$347$	−17.0063	−0.912947	−0.456474	+	0.889737i	$0.650888\pi$
$348$	2.46226	0.131991
$349$	−18.3097	−0.980096	−0.490048	−	0.871696i	$-0.663021\pi$
$349$	−18.3097	−0.980096	−0.490048	+	0.871696i	$0.663021\pi$
$350$	7.40202	0.395655
$351$	−1.00000	−0.0533761
$352$	−6.02176	−0.320961
$353$	9.27766	0.493800	0.246900	−	0.969041i	$-0.420588\pi$
$353$	9.27766	0.493800	0.246900	+	0.969041i	$0.420588\pi$
$354$	−2.71816	−0.144469
$355$	−32.3241	−1.71558
$356$	6.12784	0.324775
$357$	−26.1482	−1.38391
$358$	−37.9940	−2.00805
$359$	−4.75209	−0.250806	−0.125403	−	0.992106i	$-0.540022\pi$
$359$	−4.75209	−0.250806	−0.125403	+	0.992106i	$0.540022\pi$
$360$	−2.34077	−0.123369
$361$	−1.80419	−0.0949574
$362$	9.72590	0.511182
$363$	−10.2565	−0.538328
$364$	−5.82006	−0.305054
$365$	−21.9875	−1.15088
$366$	11.8062	0.617120
$367$	−2.60964	−0.136222	−0.0681110	−	0.997678i	$-0.521697\pi$
$367$	−2.60964	−0.136222	−0.0681110	+	0.997678i	$0.521697\pi$
$368$	−36.2090	−1.88753
$369$	6.43167	0.334820
$370$	9.34429	0.485786
$371$	8.12802	0.421986
$372$	3.62070	0.187724
$373$	−17.4404	−0.903031	−0.451516	−	0.892263i	$-0.649116\pi$
$373$	−17.4404	−0.903031	−0.451516	+	0.892263i	$0.649116\pi$
$374$	−10.7743	−0.557125
$375$	−9.77533	−0.504796
$376$	−0.222316	−0.0114651
$377$	−1.65365	−0.0851673
$378$	7.30107	0.375526
$379$	1.61484	0.0829489	0.0414745	−	0.999140i	$-0.486794\pi$
$379$	1.61484	0.0829489	0.0414745	+	0.999140i	$0.486794\pi$
$380$	15.1418	0.776758
$381$	−14.8659	−0.761603
$382$	−14.9073	−0.762724
$383$	18.2900	0.934575	0.467288	−	0.884105i	$-0.345231\pi$
$383$	18.2900	0.934575	0.467288	+	0.884105i	$0.345231\pi$
$384$	7.38686	0.376959
$385$	8.26507	0.421227
$386$	25.1740	1.28132
$387$	−10.6645	−0.542107
$388$	17.4317	0.884961
$389$	−1.10090	−0.0558177	−0.0279088	−	0.999610i	$-0.508885\pi$
$389$	−1.10090	−0.0558177	−0.0279088	+	0.999610i	$0.508885\pi$
$390$	−4.58063	−0.231949
$391$	−50.8783	−2.57303
$392$	−7.90170	−0.399096
$393$	4.27364	0.215576
$394$	8.52880	0.429675
$395$	29.6980	1.49427
$396$	1.28388	0.0645175
$397$	14.3048	0.717940	0.358970	−	0.933349i	$-0.383128\pi$
$397$	14.3048	0.717940	0.358970	+	0.933349i	$0.383128\pi$
$398$	−26.0008	−1.30330
$399$	16.2087	0.811450
$400$	−4.82672	−0.241336
$401$	19.1997	0.958788	0.479394	−	0.877600i	$-0.340857\pi$
$401$	19.1997	0.958788	0.479394	+	0.877600i	$0.340857\pi$
$402$	−1.21393	−0.0605454
$403$	−2.43165	−0.121129
$404$	−4.85487	−0.241539
$405$	2.45231	0.121856
$406$	12.0734	0.599193
$407$	1.75896	0.0871883
$408$	6.38538	0.316124
$409$	−25.5773	−1.26472	−0.632358	−	0.774677i	$-0.717913\pi$
$409$	−25.5773	−1.26472	−0.632358	+	0.774677i	$0.717913\pi$
$410$	29.4611	1.45498
$411$	20.1351	0.993193
$412$	−1.48899	−0.0733571
$413$	−5.68804	−0.279890
$414$	14.2062	0.698197
$415$	−30.6231	−1.50323
$416$	6.98376	0.342407
$417$	−16.1855	−0.792605
$418$	6.67875	0.326668
$419$	12.4773	0.609556	0.304778	−	0.952423i	$-0.401418\pi$
$419$	12.4773	0.609556	0.304778	+	0.952423i	$0.401418\pi$
$420$	14.2726	0.696431
$421$	−36.7608	−1.79161	−0.895806	−	0.444445i	$-0.853401\pi$
$421$	−36.7608	−1.79161	−0.895806	+	0.444445i	$0.853401\pi$
$422$	−8.90296	−0.433389
$423$	0.232910	0.0113245
$424$	−1.98486	−0.0963935
$425$	−6.78217	−0.328983
$426$	−24.6207	−1.19288
$427$	24.7057	1.19559
$428$	6.33104	0.306023
$429$	−0.862252	−0.0416299
$430$	−48.8501	−2.35576
$431$	19.9656	0.961709	0.480854	−	0.876801i	$-0.340327\pi$
$431$	19.9656	0.961709	0.480854	+	0.876801i	$0.340327\pi$
$432$	−4.76089	−0.229059
$433$	8.95934	0.430559	0.215279	−	0.976553i	$-0.430934\pi$
$433$	8.95934	0.430559	0.215279	+	0.976553i	$0.430934\pi$
$434$	17.7537	0.852203
$435$	4.05526	0.194435
$436$	16.2173	0.776668
$437$	31.5384	1.50869
$438$	−16.7475	−0.800228
$439$	−18.5586	−0.885755	−0.442877	−	0.896582i	$-0.646042\pi$
$439$	−18.5586	−0.885755	−0.442877	+	0.896582i	$0.646042\pi$
$440$	−2.01833	−0.0962202
$441$	8.27824	0.394202
$442$	12.4955	0.594351
$443$	9.58415	0.455357	0.227678	−	0.973736i	$-0.426887\pi$
$443$	9.58415	0.455357	0.227678	+	0.973736i	$0.426887\pi$
$444$	3.03747	0.144152
$445$	10.0923	0.478423
$446$	5.12751	0.242794
$447$	−15.4432	−0.730440
$448$	−13.7707	−0.650605
$449$	−38.7241	−1.82750	−0.913752	−	0.406272i	$-0.866829\pi$
$449$	−38.7241	−1.82750	−0.913752	+	0.406272i	$0.866829\pi$
$450$	1.89371	0.0892704
$451$	5.54573	0.261138
$452$	−27.6693	−1.30145
$453$	−19.2969	−0.906649
$454$	32.3528	1.51839
$455$	−9.58544	−0.449372
$456$	−3.95816	−0.185358
$457$	10.3537	0.484323	0.242162	−	0.970236i	$-0.422144\pi$
$457$	10.3537	0.484323	0.242162	+	0.970236i	$0.422144\pi$
$458$	12.4527	0.581877
$459$	−6.68966	−0.312247
$460$	27.7712	1.29484
$461$	9.93528	0.462732	0.231366	−	0.972867i	$-0.425681\pi$
$461$	9.93528	0.462732	0.231366	+	0.972867i	$0.425681\pi$
$462$	6.29536	0.292887
$463$	38.3620	1.78283	0.891417	−	0.453185i	$-0.149712\pi$
$463$	38.3620	1.78283	0.891417	+	0.453185i	$0.149712\pi$
$464$	−7.87285	−0.365488
$465$	5.96317	0.276535
$466$	−16.7498	−0.775920
$467$	−13.2794	−0.614499	−0.307250	−	0.951629i	$-0.599409\pi$
$467$	−13.2794	−0.614499	−0.307250	+	0.951629i	$0.599409\pi$
$468$	−1.48899	−0.0688284
$469$	−2.54028	−0.117299
$470$	1.06687	0.0492112
$471$	−12.7357	−0.586832
$472$	1.38902	0.0639348
$473$	−9.19549	−0.422809
$474$	22.6205	1.03899
$475$	4.20412	0.192898
$476$	−38.9342	−1.78455
$477$	2.07945	0.0952113
$478$	43.9981	2.01243
$479$	−12.6613	−0.578509	−0.289255	−	0.957252i	$-0.593407\pi$
$479$	−12.6613	−0.578509	−0.289255	+	0.957252i	$0.593407\pi$
$480$	−17.1263	−0.781707
$481$	−2.03996	−0.0930141
$482$	38.5395	1.75542
$483$	29.7280	1.35267
$484$	−15.2718	−0.694173
$485$	28.7094	1.30363
$486$	1.86788	0.0847289
$487$	−0.0590074	−0.00267388	−0.00133694	−	0.999999i	$-0.500426\pi$
$487$	−0.0590074	−0.00267388	−0.00133694	+	0.999999i	$0.500426\pi$
$488$	−6.03313	−0.273107
$489$	18.8058	0.850427
$490$	37.9195	1.71303
$491$	−2.16340	−0.0976329	−0.0488165	−	0.998808i	$-0.515545\pi$
$491$	−2.16340	−0.0976329	−0.0488165	+	0.998808i	$0.515545\pi$
$492$	9.57667	0.431750
$493$	−11.0624	−0.498224
$494$	−7.74570	−0.348496
$495$	2.11451	0.0950402
$496$	−11.5768	−0.519815
$497$	−51.5214	−2.31105
$498$	−23.3251	−1.04522
$499$	38.5001	1.72350	0.861751	−	0.507332i	$-0.169368\pi$
$499$	38.5001	1.72350	0.861751	+	0.507332i	$0.169368\pi$
$500$	−14.5553	−0.650934
$501$	−3.72142	−0.166261
$502$	−38.6101	−1.72325
$503$	38.1225	1.69980	0.849900	−	0.526944i	$-0.176662\pi$
$503$	38.1225	1.69980	0.849900	+	0.526944i	$0.176662\pi$
$504$	−3.73095	−0.166190
$505$	−7.99581	−0.355809
$506$	12.2493	0.544549
$507$	1.00000	0.0444116
$508$	−22.1351	−0.982087
$509$	−11.3998	−0.505289	−0.252644	−	0.967559i	$-0.581300\pi$
$509$	−11.3998	−0.505289	−0.252644	+	0.967559i	$0.581300\pi$
$510$	−30.6429	−1.35689
$511$	−35.0460	−1.55034
$512$	24.1603	1.06774
$513$	4.14678	0.183085
$514$	−9.53472	−0.420558
$515$	−2.45231	−0.108062
$516$	−15.8793	−0.699047
$517$	0.200827	0.00883237
$518$	14.8939	0.654399
$519$	−10.8829	−0.477705
$520$	2.34077	0.102649
$521$	−24.8621	−1.08923	−0.544614	−	0.838687i	$-0.683324\pi$
$521$	−24.8621	−1.08923	−0.544614	+	0.838687i	$0.683324\pi$
$522$	3.08882	0.135194
$523$	3.65341	0.159752	0.0798761	−	0.996805i	$-0.474548\pi$
$523$	3.65341	0.159752	0.0798761	+	0.996805i	$0.474548\pi$
$524$	6.36338	0.277986
$525$	3.96279	0.172950
$526$	−22.3127	−0.972881
$527$	−16.2669	−0.708599
$528$	−4.10509	−0.178651
$529$	34.8438	1.51495
$530$	9.52518	0.413747
$531$	−1.45521	−0.0631508
$532$	24.1345	1.04636
$533$	−6.43167	−0.278587
$534$	7.68717	0.332656
$535$	10.4270	0.450799
$536$	0.620336	0.0267944
$537$	−20.3407	−0.877765
$538$	9.17916	0.395742
$539$	7.13793	0.307452
$540$	3.65146	0.157134
$541$	−33.4194	−1.43681	−0.718406	−	0.695624i	$-0.755128\pi$
$541$	−33.4194	−1.43681	−0.718406	+	0.695624i	$0.755128\pi$
$542$	−8.23584	−0.353760
$543$	5.20691	0.223450
$544$	46.7190	2.00306
$545$	26.7094	1.14410
$546$	−7.30107	−0.312457
$547$	5.59607	0.239271	0.119635	−	0.992818i	$-0.461827\pi$
$547$	5.59607	0.239271	0.119635	+	0.992818i	$0.461827\pi$
$548$	29.9809	1.28072
$549$	6.32063	0.269758
$550$	1.63286	0.0696253
$551$	6.85733	0.292132
$552$	−7.25957	−0.308988
$553$	47.3356	2.01292
$554$	53.7910	2.28536
$555$	5.00261	0.212349
$556$	−24.0999	−1.02206
$557$	−14.5181	−0.615153	−0.307577	−	0.951523i	$-0.599518\pi$
$557$	−14.5181	−0.615153	−0.307577	+	0.951523i	$0.599518\pi$
$558$	4.54204	0.192280
$559$	10.6645	0.451060
$560$	−45.6353	−1.92844
$561$	−5.76818	−0.243533
$562$	38.6817	1.63169
$563$	7.67049	0.323273	0.161636	−	0.986850i	$-0.448323\pi$
$563$	7.67049	0.323273	0.161636	+	0.986850i	$0.448323\pi$
$564$	0.346800	0.0146029
$565$	−45.5704	−1.91716
$566$	−2.12649	−0.0893830
$567$	3.90874	0.164152
$568$	12.5815	0.527909
$569$	18.2443	0.764843	0.382421	−	0.923988i	$-0.375090\pi$
$569$	18.2443	0.764843	0.382421	+	0.923988i	$0.375090\pi$
$570$	18.9949	0.795608
$571$	−15.2995	−0.640263	−0.320131	−	0.947373i	$-0.603727\pi$
$571$	−15.2995	−0.640263	−0.320131	+	0.947373i	$0.603727\pi$
$572$	−1.28388	−0.0536818
$573$	−7.98086	−0.333405
$574$	46.9581	1.95999
$575$	7.71068	0.321558
$576$	−3.52306	−0.146794
$577$	−32.7654	−1.36404	−0.682020	−	0.731334i	$-0.738898\pi$
$577$	−32.7654	−1.36404	−0.682020	+	0.731334i	$0.738898\pi$
$578$	51.8368	2.15612
$579$	13.4773	0.560098
$580$	6.03823	0.250724
$581$	−48.8101	−2.02498
$582$	21.8675	0.906437
$583$	1.79301	0.0742588
$584$	8.55823	0.354142
$585$	−2.45231	−0.101391
$586$	−26.6817	−1.10221
$587$	−0.415537	−0.0171511	−0.00857553	−	0.999963i	$-0.502730\pi$
$587$	−0.415537	−0.0171511	−0.00857553	+	0.999963i	$0.502730\pi$
$588$	12.3262	0.508323
$589$	10.0835	0.415485
$590$	−6.66578	−0.274426
$591$	4.56602	0.187821
$592$	−9.71202	−0.399162
$593$	−17.5147	−0.719244	−0.359622	−	0.933098i	$-0.617094\pi$
$593$	−17.5147	−0.719244	−0.359622	+	0.933098i	$0.617094\pi$
$594$	1.61059	0.0660832
$595$	−64.1234	−2.62880
$596$	−22.9947	−0.941901
$597$	−13.9199	−0.569705
$598$	−14.2062	−0.580935
$599$	−23.2166	−0.948604	−0.474302	−	0.880362i	$-0.657300\pi$
$599$	−23.2166	−0.948604	−0.474302	+	0.880362i	$0.657300\pi$
$600$	−0.967713	−0.0395067
$601$	−13.4495	−0.548617	−0.274308	−	0.961642i	$-0.588449\pi$
$601$	−13.4495	−0.548617	−0.274308	+	0.961642i	$0.588449\pi$
$602$	−77.8622	−3.17343
$603$	−0.649897	−0.0264658
$604$	−28.7329	−1.16912
$605$	−25.1522	−1.02258
$606$	−6.09027	−0.247400
$607$	0.533708	0.0216625	0.0108313	−	0.999941i	$-0.496552\pi$
$607$	0.533708	0.0216625	0.0108313	+	0.999941i	$0.496552\pi$
$608$	−28.9601	−1.17449
$609$	6.46368	0.261922
$610$	28.9525	1.17225
$611$	−0.232910	−0.00942253
$612$	−9.96082	−0.402642
$613$	−3.28728	−0.132772	−0.0663859	−	0.997794i	$-0.521147\pi$
$613$	−3.28728	−0.132772	−0.0663859	+	0.997794i	$0.521147\pi$
$614$	15.3999	0.621489
$615$	15.7725	0.636007
$616$	−3.21702	−0.129617
$617$	−43.5267	−1.75232	−0.876159	−	0.482023i	$-0.839902\pi$
$617$	−43.5267	−1.75232	−0.876159	+	0.482023i	$0.839902\pi$
$618$	−1.86788	−0.0751373
$619$	−7.14779	−0.287294	−0.143647	−	0.989629i	$-0.545883\pi$
$619$	−7.14779	−0.287294	−0.143647	+	0.989629i	$0.545883\pi$
$620$	8.87907	0.356592
$621$	7.60551	0.305199
$622$	3.54391	0.142098
$623$	16.0862	0.644480
$624$	4.76089	0.190588
$625$	−29.0413	−1.16165
$626$	33.6095	1.34331
$627$	3.57557	0.142795
$628$	−18.9633	−0.756719
$629$	−13.6466	−0.544127
$630$	17.9045	0.713332
$631$	−35.8918	−1.42883	−0.714415	−	0.699722i	$-0.753307\pi$
$631$	−35.8918	−1.42883	−0.714415	+	0.699722i	$0.753307\pi$
$632$	−11.5594	−0.459807
$633$	−4.76634	−0.189445
$634$	7.28441	0.289301
$635$	−36.4558	−1.44671
$636$	3.09627	0.122775
$637$	−8.27824	−0.327996
$638$	2.66335	0.105443
$639$	−13.1811	−0.521435
$640$	18.1149	0.716053
$641$	−7.88684	−0.311511	−0.155756	−	0.987796i	$-0.549781\pi$
$641$	−7.88684	−0.311511	−0.155756	+	0.987796i	$0.549781\pi$
$642$	7.94208	0.313449
$643$	39.6930	1.56534	0.782670	−	0.622436i	$-0.213857\pi$
$643$	39.6930	1.56534	0.782670	+	0.622436i	$0.213857\pi$
$644$	44.2645	1.74427
$645$	−26.1527	−1.02976
$646$	−51.8162	−2.03868
$647$	14.3873	0.565624	0.282812	−	0.959175i	$-0.408733\pi$
$647$	14.3873	0.565624	0.282812	+	0.959175i	$0.408733\pi$
$648$	−0.954515	−0.0374969
$649$	−1.25476	−0.0492536
$650$	−1.89371	−0.0742775
$651$	9.50470	0.372518
$652$	28.0016	1.09663
$653$	−38.3875	−1.50222	−0.751109	−	0.660178i	$-0.770481\pi$
$653$	−38.3875	−1.50222	−0.751109	+	0.660178i	$0.770481\pi$
$654$	20.3441	0.795516
$655$	10.4803	0.409498
$656$	−30.6205	−1.19553
$657$	−8.96605	−0.349799
$658$	1.70049	0.0662921
$659$	−43.9831	−1.71334	−0.856670	−	0.515865i	$-0.827471\pi$
$659$	−43.9831	−1.71334	−0.856670	+	0.515865i	$0.827471\pi$
$660$	3.14848	0.122554
$661$	11.5147	0.447869	0.223935	−	0.974604i	$-0.428110\pi$
$661$	11.5147	0.447869	0.223935	+	0.974604i	$0.428110\pi$
$662$	14.7558	0.573499
$663$	6.68966	0.259805
$664$	11.9194	0.462564
$665$	39.7487	1.54139
$666$	3.81040	0.147650
$667$	12.5769	0.486978
$668$	−5.54114	−0.214393
$669$	2.74509	0.106131
$670$	−2.97694	−0.115009
$671$	5.44998	0.210394
$672$	−27.2977	−1.05303
$673$	−9.20425	−0.354798	−0.177399	−	0.984139i	$-0.556768\pi$
$673$	−9.20425	−0.354798	−0.177399	+	0.984139i	$0.556768\pi$
$674$	−26.2230	−1.01007
$675$	1.01383	0.0390222
$676$	1.48899	0.0572687
$677$	−22.1149	−0.849944	−0.424972	−	0.905206i	$-0.639716\pi$
$677$	−22.1149	−0.849944	−0.424972	+	0.905206i	$0.639716\pi$
$678$	−34.7102	−1.33304
$679$	45.7600	1.75611
$680$	15.6589	0.600493
$681$	17.3206	0.663726
$682$	3.91639	0.149966
$683$	−14.8560	−0.568450	−0.284225	−	0.958758i	$-0.591736\pi$
$683$	−14.8560	−0.568450	−0.284225	+	0.958758i	$0.591736\pi$
$684$	6.17450	0.236088
$685$	49.3776	1.88662
$686$	9.33250	0.356317
$687$	6.66675	0.254352
$688$	50.7725	1.93568
$689$	−2.07945	−0.0792206
$690$	34.8380	1.32626
$691$	48.8886	1.85981	0.929906	−	0.367799i	$-0.119888\pi$
$691$	48.8886	1.85981	0.929906	+	0.367799i	$0.119888\pi$
$692$	−16.2044	−0.616000
$693$	3.37032	0.128028
$694$	−31.7658	−1.20581
$695$	−39.6918	−1.50559
$696$	−1.57843	−0.0598303
$697$	−43.0257	−1.62972
$698$	−34.2004	−1.29450
$699$	−8.96727	−0.339173
$700$	5.90053	0.223019
$701$	−49.1844	−1.85767	−0.928835	−	0.370494i	$-0.879188\pi$
$701$	−49.1844	−1.85767	−0.928835	+	0.370494i	$0.879188\pi$
$702$	−1.86788	−0.0704987
$703$	8.45926	0.319047
$704$	−3.03777	−0.114490
$705$	0.571168	0.0215114
$706$	17.3296	0.652207
$707$	−12.7445	−0.479307
$708$	−2.16679	−0.0814329
$709$	27.9586	1.05001	0.525004	−	0.851100i	$-0.324064\pi$
$709$	27.9586	1.05001	0.525004	+	0.851100i	$0.324064\pi$
$710$	−60.3776	−2.26593
$711$	12.1102	0.454168
$712$	−3.92825	−0.147217
$713$	18.4940	0.692605
$714$	−48.8417	−1.82785
$715$	−2.11451	−0.0790782
$716$	−30.2870	−1.13188
$717$	23.5551	0.879681
$718$	−8.87635	−0.331262
$719$	−47.4368	−1.76909	−0.884546	−	0.466452i	$-0.845532\pi$
$719$	−47.4368	−1.76909	−0.884546	+	0.466452i	$0.845532\pi$
$720$	−11.6752	−0.435109
$721$	−3.90874	−0.145569
$722$	−3.37002	−0.125419
$723$	20.6327	0.767339
$724$	7.75302	0.288139
$725$	1.67652	0.0622642
$726$	−19.1580	−0.711019
$727$	−6.00241	−0.222617	−0.111309	−	0.993786i	$-0.535504\pi$
$727$	−6.00241	−0.222617	−0.111309	+	0.993786i	$0.535504\pi$
$728$	3.73095	0.138278
$729$	1.00000	0.0370370
$730$	−41.0702	−1.52007
$731$	71.3419	2.63868
$732$	9.41133	0.347853
$733$	2.89217	0.106825	0.0534124	−	0.998573i	$-0.482990\pi$
$733$	2.89217	0.106825	0.0534124	+	0.998573i	$0.482990\pi$
$734$	−4.87450	−0.179921
$735$	20.3008	0.748807
$736$	−53.1151	−1.95785
$737$	−0.560375	−0.0206417
$738$	12.0136	0.442227
$739$	40.0019	1.47149	0.735747	−	0.677256i	$-0.236831\pi$
$739$	40.0019	1.47149	0.735747	+	0.677256i	$0.236831\pi$
$740$	7.44882	0.273824
$741$	−4.14678	−0.152336
$742$	15.1822	0.557355
$743$	46.4761	1.70504	0.852522	−	0.522691i	$-0.175072\pi$
$743$	46.4761	1.70504	0.852522	+	0.522691i	$0.175072\pi$
$744$	−2.32105	−0.0850938
$745$	−37.8716	−1.38751
$746$	−32.5767	−1.19272
$747$	−12.4874	−0.456891
$748$	−8.58874	−0.314035
$749$	16.6196	0.607268
$750$	−18.2592	−0.666731
$751$	2.57051	0.0937992	0.0468996	−	0.998900i	$-0.485066\pi$
$751$	2.57051	0.0937992	0.0468996	+	0.998900i	$0.485066\pi$
$752$	−1.10886	−0.0404360
$753$	−20.6705	−0.753275
$754$	−3.08882	−0.112488
$755$	−47.3221	−1.72223
$756$	5.82006	0.211673
$757$	24.2939	0.882978	0.441489	−	0.897267i	$-0.354450\pi$
$757$	24.2939	0.882978	0.441489	+	0.897267i	$0.354450\pi$
$758$	3.01634	0.109558
$759$	6.55787	0.238036
$760$	−9.70665	−0.352097
$761$	−34.5319	−1.25178	−0.625891	−	0.779911i	$-0.715264\pi$
$761$	−34.5319	−1.25178	−0.625891	+	0.779911i	$0.715264\pi$
$762$	−27.7678	−1.00592
$763$	42.5721	1.54121
$764$	−11.8834	−0.429926
$765$	−16.4051	−0.593129
$766$	34.1636	1.23438
$767$	1.45521	0.0525446
$768$	20.8439	0.752140
$769$	−1.79050	−0.0645671	−0.0322835	−	0.999479i	$-0.510278\pi$
$769$	−1.79050	−0.0645671	−0.0322835	+	0.999479i	$0.510278\pi$
$770$	15.4382	0.556354
$771$	−5.10456	−0.183836
$772$	20.0675	0.722246
$773$	51.5160	1.85290	0.926450	−	0.376418i	$-0.122844\pi$
$773$	51.5160	1.85290	0.926450	+	0.376418i	$0.122844\pi$
$774$	−19.9200	−0.716011
$775$	2.46528	0.0885554
$776$	−11.1746	−0.401145
$777$	7.97366	0.286054
$778$	−2.05635	−0.0737236
$779$	26.6708	0.955579
$780$	−3.65146	−0.130743
$781$	−11.3654	−0.406687
$782$	−95.0348	−3.39844
$783$	1.65365	0.0590966
$784$	−39.4118	−1.40756
$785$	−31.2320	−1.11472
$786$	7.98265	0.284732
$787$	−27.5239	−0.981121	−0.490561	−	0.871407i	$-0.663208\pi$
$787$	−27.5239	−0.981121	−0.490561	+	0.871407i	$0.663208\pi$
$788$	6.79874	0.242195
$789$	−11.9455	−0.425270
$790$	55.4724	1.97362
$791$	−72.6346	−2.58259
$792$	−0.823033	−0.0292452
$793$	−6.32063	−0.224452
$794$	26.7198	0.948249
$795$	5.09945	0.180859
$796$	−20.7266	−0.734634
$797$	−13.0629	−0.462711	−0.231355	−	0.972869i	$-0.574316\pi$
$797$	−13.0629	−0.462711	−0.231355	+	0.972869i	$0.574316\pi$
$798$	30.2759	1.07176
$799$	−1.55809	−0.0551213
$800$	−7.08033	−0.250327
$801$	4.11544	0.145412
$802$	35.8628	1.26636
$803$	−7.73100	−0.272821
$804$	−0.967687	−0.0341277
$805$	72.9022	2.56947
$806$	−4.54204	−0.159987
$807$	4.91421	0.172988
$808$	3.11221	0.109487
$809$	38.0519	1.33783	0.668917	−	0.743338i	$-0.266758\pi$
$809$	38.0519	1.33783	0.668917	+	0.743338i	$0.266758\pi$
$810$	4.58063	0.160947
$811$	−13.5806	−0.476880	−0.238440	−	0.971157i	$-0.576636\pi$
$811$	−13.5806	−0.476880	−0.238440	+	0.971157i	$0.576636\pi$
$812$	9.62433	0.337748
$813$	−4.40919	−0.154637
$814$	3.28553	0.115158
$815$	46.1176	1.61543
$816$	31.8488	1.11493
$817$	−44.2234	−1.54718
$818$	−47.7754	−1.67043
$819$	−3.90874	−0.136582
$820$	23.4850	0.820131
$821$	−32.2120	−1.12421	−0.562103	−	0.827067i	$-0.690008\pi$
$821$	−32.2120	−1.12421	−0.562103	+	0.827067i	$0.690008\pi$
$822$	37.6101	1.31180
$823$	16.9992	0.592556	0.296278	−	0.955102i	$-0.404254\pi$
$823$	16.9992	0.592556	0.296278	+	0.955102i	$0.404254\pi$
$824$	0.954515	0.0332521
$825$	0.874175	0.0304349
$826$	−10.6246	−0.369677
$827$	36.2207	1.25952	0.629758	−	0.776792i	$-0.283154\pi$
$827$	36.2207	1.25952	0.629758	+	0.776792i	$0.283154\pi$
$828$	11.3245	0.393554
$829$	−28.0747	−0.975074	−0.487537	−	0.873102i	$-0.662105\pi$
$829$	−28.0747	−0.975074	−0.487537	+	0.873102i	$0.662105\pi$
$830$	−57.2003	−1.98545
$831$	28.7978	0.998986
$832$	3.52306	0.122140
$833$	−55.3786	−1.91876
$834$	−30.2325	−1.04687
$835$	−9.12607	−0.315821
$836$	5.32398	0.184134
$837$	2.43165	0.0840502
$838$	23.3062	0.805098
$839$	−26.7423	−0.923246	−0.461623	−	0.887076i	$-0.652733\pi$
$839$	−26.7423	−0.923246	−0.461623	+	0.887076i	$0.652733\pi$
$840$	−9.14944	−0.315686
$841$	−26.2654	−0.905705
$842$	−68.6649	−2.36635
$843$	20.7089	0.713251
$844$	−7.09701	−0.244289
$845$	2.45231	0.0843621
$846$	0.435049	0.0149573
$847$	−40.0901	−1.37751
$848$	−9.90003	−0.339968
$849$	−1.13845	−0.0390715
$850$	−12.6683	−0.434519
$851$	15.5149	0.531845
$852$	−19.6264	−0.672391
$853$	33.6185	1.15108	0.575538	−	0.817775i	$-0.304793\pi$
$853$	33.6185	1.15108	0.575538	+	0.817775i	$0.304793\pi$
$854$	46.1473	1.57913
$855$	10.1692	0.347779
$856$	−4.05852	−0.138717
$857$	32.2184	1.10056	0.550280	−	0.834980i	$-0.314521\pi$
$857$	32.2184	1.10056	0.550280	+	0.834980i	$0.314521\pi$
$858$	−1.61059	−0.0549845
$859$	45.4786	1.55171	0.775855	−	0.630911i	$-0.217319\pi$
$859$	45.4786	1.55171	0.775855	+	0.630911i	$0.217319\pi$
$860$	−38.9409	−1.32788
$861$	25.1397	0.856760
$862$	37.2934	1.27022
$863$	47.9494	1.63222	0.816108	−	0.577900i	$-0.196127\pi$
$863$	47.9494	1.63222	0.816108	+	0.577900i	$0.196127\pi$
$864$	−6.98376	−0.237592
$865$	−26.6882	−0.907425
$866$	16.7350	0.568679
$867$	27.7516	0.942494
$868$	14.1524	0.480362
$869$	10.4421	0.354223
$870$	7.57475	0.256808
$871$	0.649897	0.0220209
$872$	−10.3961	−0.352057
$873$	11.7071	0.396225
$874$	58.9101	1.99266
$875$	−38.2092	−1.29171
$876$	−13.3503	−0.451066
$877$	26.1496	0.883009	0.441505	−	0.897259i	$-0.354445\pi$
$877$	26.1496	0.883009	0.441505	+	0.897259i	$0.354445\pi$
$878$	−34.6653	−1.16990
$879$	−14.2845	−0.481803
$880$	−10.0670	−0.339357
$881$	−0.748208	−0.0252078	−0.0126039	−	0.999921i	$-0.504012\pi$
$881$	−0.748208	−0.0252078	−0.0126039	+	0.999921i	$0.504012\pi$
$882$	15.4628	0.520659
$883$	4.75982	0.160181	0.0800904	−	0.996788i	$-0.474479\pi$
$883$	4.75982	0.160181	0.0800904	+	0.996788i	$0.474479\pi$
$884$	9.96082	0.335018
$885$	−3.56863	−0.119958
$886$	17.9021	0.601432
$887$	8.00073	0.268638	0.134319	−	0.990938i	$-0.457115\pi$
$887$	8.00073	0.268638	0.134319	+	0.990938i	$0.457115\pi$
$888$	−1.94717	−0.0653427
$889$	−58.1069	−1.94884
$890$	18.8513	0.631898
$891$	0.862252	0.0288865
$892$	4.08740	0.136856
$893$	0.965827	0.0323202
$894$	−28.8461	−0.964759
$895$	−49.8817	−1.66736
$896$	28.8733	0.964589
$897$	−7.60551	−0.253941
$898$	−72.3321	−2.41375
$899$	4.02110	0.134111
$900$	1.50957	0.0503192
$901$	−13.9108	−0.463436
$902$	10.3588	0.344909
$903$	−41.6847	−1.38718
$904$	17.7374	0.589937
$905$	12.7690	0.424455
$906$	−36.0444	−1.19750
$907$	−17.4915	−0.580796	−0.290398	−	0.956906i	$-0.593788\pi$
$907$	−17.4915	−0.580796	−0.290398	+	0.956906i	$0.593788\pi$
$908$	25.7901	0.855875
$909$	−3.26052	−0.108145
$910$	−17.9045	−0.593528
$911$	−44.3603	−1.46972	−0.734860	−	0.678218i	$-0.762752\pi$
$911$	−44.3603	−1.46972	−0.734860	+	0.678218i	$0.762752\pi$
$912$	−19.7424	−0.653736
$913$	−10.7673	−0.356346
$914$	19.3394	0.639691
$915$	15.5001	0.512419
$916$	9.92669	0.327987
$917$	16.7045	0.551632
$918$	−12.4955	−0.412413
$919$	27.1265	0.894822	0.447411	−	0.894328i	$-0.352346\pi$
$919$	27.1265	0.894822	0.447411	+	0.894328i	$0.352346\pi$
$920$	−17.8027	−0.586939
$921$	8.24457	0.271668
$922$	18.5579	0.611173
$923$	13.1811	0.433860
$924$	5.01836	0.165092
$925$	2.06817	0.0680009
$926$	71.6557	2.35475
$927$	−1.00000	−0.0328443
$928$	−11.5487	−0.379104
$929$	39.0954	1.28268	0.641339	−	0.767257i	$-0.278379\pi$
$929$	39.0954	1.28268	0.641339	+	0.767257i	$0.278379\pi$
$930$	11.1385	0.365246
$931$	34.3281	1.12506
$932$	−13.3521	−0.437364
$933$	1.89729	0.0621144
$934$	−24.8044	−0.811626
$935$	−14.1454	−0.462603
$936$	0.954515	0.0311993
$937$	7.61398	0.248738	0.124369	−	0.992236i	$-0.460309\pi$
$937$	7.61398	0.248738	0.124369	+	0.992236i	$0.460309\pi$
$938$	−4.74494	−0.154928
$939$	17.9934	0.587192
$940$	0.850461	0.0277390
$941$	49.5109	1.61401	0.807004	−	0.590546i	$-0.201088\pi$
$941$	49.5109	1.61401	0.807004	+	0.590546i	$0.201088\pi$
$942$	−23.7889	−0.775083
$943$	48.9162	1.59293
$944$	6.92811	0.225491
$945$	9.58544	0.311814
$946$	−17.1761	−0.558443
$947$	13.3396	0.433479	0.216739	−	0.976230i	$-0.430458\pi$
$947$	13.3396	0.433479	0.216739	+	0.976230i	$0.430458\pi$
$948$	18.0319	0.585650
$949$	8.96605	0.291050
$950$	7.85281	0.254779
$951$	3.89982	0.126460
$952$	24.9588	0.808919
$953$	22.1692	0.718131	0.359065	−	0.933312i	$-0.383095\pi$
$953$	22.1692	0.718131	0.359065	+	0.933312i	$0.383095\pi$
$954$	3.88416	0.125754
$955$	−19.5715	−0.633320
$956$	35.0732	1.13435
$957$	1.42586	0.0460916
$958$	−23.6498	−0.764091
$959$	78.7030	2.54145
$960$	−8.63964	−0.278843
$961$	−25.0871	−0.809260
$962$	−3.81040	−0.122852
$963$	4.25192	0.137016
$964$	30.7218	0.989483
$965$	33.0506	1.06393
$966$	55.5284	1.78660
$967$	34.1439	1.09799	0.548997	−	0.835824i	$-0.315010\pi$
$967$	34.1439	1.09799	0.548997	+	0.835824i	$0.315010\pi$
$968$	9.79000	0.314662
$969$	−27.7406	−0.891156
$970$	53.6259	1.72182
$971$	21.3041	0.683681	0.341841	−	0.939758i	$-0.388950\pi$
$971$	21.3041	0.683681	0.341841	+	0.939758i	$0.388950\pi$
$972$	1.48899	0.0477592
$973$	−63.2647	−2.02817
$974$	−0.110219	−0.00353164
$975$	−1.01383	−0.0324685
$976$	−30.0918	−0.963216
$977$	46.9917	1.50340	0.751699	−	0.659507i	$-0.229235\pi$
$977$	46.9917	1.50340	0.751699	+	0.659507i	$0.229235\pi$
$978$	35.1270	1.12324
$979$	3.54855	0.113412
$980$	30.2276	0.965586
$981$	10.8915	0.347739
$982$	−4.04098	−0.128953
$983$	8.30587	0.264916	0.132458	−	0.991189i	$-0.457713\pi$
$983$	8.30587	0.264916	0.132458	+	0.991189i	$0.457713\pi$
$984$	−6.13913	−0.195708
$985$	11.1973	0.356776
$986$	−20.6632	−0.658050
$987$	0.910384	0.0289779
$988$	−6.17450	−0.196437
$989$	−81.1090	−2.57912
$990$	3.94966	0.125528
$991$	53.5988	1.70262	0.851312	−	0.524660i	$-0.175808\pi$
$991$	53.5988	1.70262	0.851312	+	0.524660i	$0.175808\pi$
$992$	−16.9821	−0.539182
$993$	7.89973	0.250690
$994$	−96.2359	−3.05242
$995$	−34.1360	−1.08218
$996$	−18.5936	−0.589161
$997$	20.9077	0.662155	0.331077	−	0.943604i	$-0.392588\pi$
$997$	20.9077	0.662155	0.331077	+	0.943604i	$0.392588\pi$
$998$	71.9137	2.27639
$999$	2.03996	0.0645414

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.25	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.25	✓	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+1.86788 q^{2} +1.00000 q^{3} +1.48899 q^{4} +2.45231 q^{5} +1.86788 q^{6} +3.90874 q^{7} -0.954515 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.86788 q^{2} +1.00000 q^{3} +1.48899 q^{4} +2.45231 q^{5} +1.86788 q^{6} +3.90874 q^{7} -0.954515 q^{8} +1.00000 q^{9} +4.58063 q^{10} +0.862252 q^{11} +1.48899 q^{12} -1.00000 q^{13} +7.30107 q^{14} +2.45231 q^{15} -4.76089 q^{16} -6.68966 q^{17} +1.86788 q^{18} +4.14678 q^{19} +3.65146 q^{20} +3.90874 q^{21} +1.61059 q^{22} +7.60551 q^{23} -0.954515 q^{24} +1.01383 q^{25} -1.86788 q^{26} +1.00000 q^{27} +5.82006 q^{28} +1.65365 q^{29} +4.58063 q^{30} +2.43165 q^{31} -6.98376 q^{32} +0.862252 q^{33} -12.4955 q^{34} +9.58544 q^{35} +1.48899 q^{36} +2.03996 q^{37} +7.74570 q^{38} -1.00000 q^{39} -2.34077 q^{40} +6.43167 q^{41} +7.30107 q^{42} -10.6645 q^{43} +1.28388 q^{44} +2.45231 q^{45} +14.2062 q^{46} +0.232910 q^{47} -4.76089 q^{48} +8.27824 q^{49} +1.89371 q^{50} -6.68966 q^{51} -1.48899 q^{52} +2.07945 q^{53} +1.86788 q^{54} +2.11451 q^{55} -3.73095 q^{56} +4.14678 q^{57} +3.08882 q^{58} -1.45521 q^{59} +3.65146 q^{60} +6.32063 q^{61} +4.54204 q^{62} +3.90874 q^{63} -3.52306 q^{64} -2.45231 q^{65} +1.61059 q^{66} -0.649897 q^{67} -9.96082 q^{68} +7.60551 q^{69} +17.9045 q^{70} -13.1811 q^{71} -0.954515 q^{72} -8.96605 q^{73} +3.81040 q^{74} +1.01383 q^{75} +6.17450 q^{76} +3.37032 q^{77} -1.86788 q^{78} +12.1102 q^{79} -11.6752 q^{80} +1.00000 q^{81} +12.0136 q^{82} -12.4874 q^{83} +5.82006 q^{84} -16.4051 q^{85} -19.9200 q^{86} +1.65365 q^{87} -0.823033 q^{88} +4.11544 q^{89} +4.58063 q^{90} -3.90874 q^{91} +11.3245 q^{92} +2.43165 q^{93} +0.435049 q^{94} +10.1692 q^{95} -6.98376 q^{96} +11.7071 q^{97} +15.4628 q^{98} +0.862252 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

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