LMFDB - Embedded newform 4031.2.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, 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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$1$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.50584 q^{2} -0.996538 q^{3} +0.267567 q^{4} +0.533194 q^{5} +1.50063 q^{6} +3.56628 q^{7} +2.60877 q^{8} -2.00691 q^{9} +O(q^{10})$	\(q-1.50584 q^{2} -0.996538 q^{3} +0.267567 q^{4} +0.533194 q^{5} +1.50063 q^{6} +3.56628 q^{7} +2.60877 q^{8} -2.00691 q^{9} -0.802908 q^{10} -1.85590 q^{11} -0.266641 q^{12} -0.546756 q^{13} -5.37026 q^{14} -0.531348 q^{15} -4.46354 q^{16} +3.22596 q^{17} +3.02210 q^{18} +0.447533 q^{19} +0.142665 q^{20} -3.55393 q^{21} +2.79470 q^{22} +4.54791 q^{23} -2.59974 q^{24} -4.71570 q^{25} +0.823330 q^{26} +4.98958 q^{27} +0.954220 q^{28} -1.00000 q^{29} +0.800128 q^{30} -1.38386 q^{31} +1.50385 q^{32} +1.84948 q^{33} -4.85779 q^{34} +1.90152 q^{35} -0.536984 q^{36} -1.42959 q^{37} -0.673915 q^{38} +0.544863 q^{39} +1.39098 q^{40} -4.79477 q^{41} +5.35167 q^{42} -1.84240 q^{43} -0.496579 q^{44} -1.07007 q^{45} -6.84844 q^{46} -11.9403 q^{47} +4.44809 q^{48} +5.71835 q^{49} +7.10112 q^{50} -3.21479 q^{51} -0.146294 q^{52} -8.51261 q^{53} -7.51353 q^{54} -0.989557 q^{55} +9.30362 q^{56} -0.445983 q^{57} +1.50584 q^{58} +0.183189 q^{59} -0.142171 q^{60} +10.1235 q^{61} +2.08387 q^{62} -7.15721 q^{63} +6.66252 q^{64} -0.291527 q^{65} -2.78502 q^{66} -0.991572 q^{67} +0.863161 q^{68} -4.53216 q^{69} -2.86339 q^{70} +6.65460 q^{71} -5.23558 q^{72} +5.08255 q^{73} +2.15273 q^{74} +4.69938 q^{75} +0.119745 q^{76} -6.61867 q^{77} -0.820479 q^{78} -16.2374 q^{79} -2.37994 q^{80} +1.04844 q^{81} +7.22018 q^{82} -17.4016 q^{83} -0.950916 q^{84} +1.72006 q^{85} +2.77437 q^{86} +0.996538 q^{87} -4.84163 q^{88} +8.28978 q^{89} +1.61137 q^{90} -1.94988 q^{91} +1.21687 q^{92} +1.37906 q^{93} +17.9802 q^{94} +0.238622 q^{95} -1.49865 q^{96} -12.3705 q^{97} -8.61094 q^{98} +3.72463 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * 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 $

$2$	−1.50584	−1.06479	−0.532396	−	0.846495i	$-0.678708\pi$
$2$	−1.50584	−1.06479	−0.532396	+	0.846495i	$0.678708\pi$
$3$	−0.996538	−0.575351	−0.287676	−	0.957728i	$-0.592883\pi$
$3$	−0.996538	−0.575351	−0.287676	+	0.957728i	$0.592883\pi$
$4$	0.267567	0.133784
$5$	0.533194	0.238452	0.119226	−	0.992867i	$-0.461959\pi$
$5$	0.533194	0.238452	0.119226	+	0.992867i	$0.461959\pi$
$6$	1.50063	0.612630
$7$	3.56628	1.34793	0.673963	−	0.738765i	$-0.264591\pi$
$7$	3.56628	1.34793	0.673963	+	0.738765i	$0.264591\pi$
$8$	2.60877	0.922341
$9$	−2.00691	−0.668971
$10$	−0.802908	−0.253902
$11$	−1.85590	−0.559576	−0.279788	−	0.960062i	$-0.590264\pi$
$11$	−1.85590	−0.559576	−0.279788	+	0.960062i	$0.590264\pi$
$12$	−0.266641	−0.0769726
$13$	−0.546756	−0.151643	−0.0758214	−	0.997121i	$-0.524158\pi$
$13$	−0.546756	−0.151643	−0.0758214	+	0.997121i	$0.524158\pi$
$14$	−5.37026	−1.43526
$15$	−0.531348	−0.137194
$16$	−4.46354	−1.11589
$17$	3.22596	0.782410	0.391205	−	0.920304i	$-0.372058\pi$
$17$	3.22596	0.782410	0.391205	+	0.920304i	$0.372058\pi$
$18$	3.02210	0.712315
$19$	0.447533	0.102671	0.0513355	−	0.998681i	$-0.483652\pi$
$19$	0.447533	0.102671	0.0513355	+	0.998681i	$0.483652\pi$
$20$	0.142665	0.0319010
$21$	−3.55393	−0.775531
$22$	2.79470	0.595832
$23$	4.54791	0.948305	0.474152	−	0.880443i	$-0.342755\pi$
$23$	4.54791	0.948305	0.474152	+	0.880443i	$0.342755\pi$
$24$	−2.59974	−0.530670
$25$	−4.71570	−0.943141
$26$	0.823330	0.161468
$27$	4.98958	0.960245
$28$	0.954220	0.180331
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0.800128	0.146083
$31$	−1.38386	−0.248548	−0.124274	−	0.992248i	$-0.539660\pi$
$31$	−1.38386	−0.248548	−0.124274	+	0.992248i	$0.539660\pi$
$32$	1.50385	0.265846
$33$	1.84948	0.321953
$34$	−4.85779	−0.833104
$35$	1.90152	0.321416
$36$	−0.536984	−0.0894974
$37$	−1.42959	−0.235022	−0.117511	−	0.993072i	$-0.537492\pi$
$37$	−1.42959	−0.235022	−0.117511	+	0.993072i	$0.537492\pi$
$38$	−0.673915	−0.109323
$39$	0.544863	0.0872479
$40$	1.39098	0.219934
$41$	−4.79477	−0.748817	−0.374409	−	0.927264i	$-0.622154\pi$
$41$	−4.79477	−0.748817	−0.374409	+	0.927264i	$0.622154\pi$
$42$	5.35167	0.825780
$43$	−1.84240	−0.280963	−0.140482	−	0.990083i	$-0.544865\pi$
$43$	−1.84240	−0.280963	−0.140482	+	0.990083i	$0.544865\pi$
$44$	−0.496579	−0.0748621
$45$	−1.07007	−0.159517
$46$	−6.84844	−1.00975
$47$	−11.9403	−1.74167	−0.870835	−	0.491576i	$-0.836421\pi$
$47$	−11.9403	−1.74167	−0.870835	+	0.491576i	$0.836421\pi$
$48$	4.44809	0.642026
$49$	5.71835	0.816907
$50$	7.10112	1.00425
$51$	−3.21479	−0.450160
$52$	−0.146294	−0.0202873
$53$	−8.51261	−1.16930	−0.584649	−	0.811287i	$-0.698768\pi$
$53$	−8.51261	−1.16930	−0.584649	+	0.811287i	$0.698768\pi$
$54$	−7.51353	−1.02246
$55$	−0.989557	−0.133432
$56$	9.30362	1.24325
$57$	−0.445983	−0.0590719
$58$	1.50584	0.197727
$59$	0.183189	0.0238492	0.0119246	−	0.999929i	$-0.496204\pi$
$59$	0.183189	0.0238492	0.0119246	+	0.999929i	$0.496204\pi$
$60$	−0.142171	−0.0183543
$61$	10.1235	1.29619	0.648093	−	0.761562i	$-0.275567\pi$
$61$	10.1235	1.29619	0.648093	+	0.761562i	$0.275567\pi$
$62$	2.08387	0.264652
$63$	−7.15721	−0.901724
$64$	6.66252	0.832815
$65$	−0.291527	−0.0361595
$66$	−2.78502	−0.342813
$67$	−0.991572	−0.121140	−0.0605699	−	0.998164i	$-0.519292\pi$
$67$	−0.991572	−0.121140	−0.0605699	+	0.998164i	$0.519292\pi$
$68$	0.863161	0.104674
$69$	−4.53216	−0.545608
$70$	−2.86339	−0.342241
$71$	6.65460	0.789755	0.394878	−	0.918734i	$-0.370787\pi$
$71$	6.65460	0.789755	0.394878	+	0.918734i	$0.370787\pi$
$72$	−5.23558	−0.617019
$73$	5.08255	0.594867	0.297434	−	0.954742i	$-0.403869\pi$
$73$	5.08255	0.594867	0.297434	+	0.954742i	$0.403869\pi$
$74$	2.15273	0.250250
$75$	4.69938	0.542637
$76$	0.119745	0.0137357
$77$	−6.61867	−0.754267
$78$	−0.820479	−0.0929009
$79$	−16.2374	−1.82685	−0.913427	−	0.407002i	$-0.866574\pi$
$79$	−16.2374	−1.82685	−0.913427	+	0.407002i	$0.866574\pi$
$80$	−2.37994	−0.266085
$81$	1.04844	0.116493
$82$	7.22018	0.797335
$83$	−17.4016	−1.91007	−0.955035	−	0.296494i	$-0.904183\pi$
$83$	−17.4016	−1.91007	−0.955035	+	0.296494i	$0.904183\pi$
$84$	−0.950916	−0.103753
$85$	1.72006	0.186567
$86$	2.77437	0.299168
$87$	0.996538	0.106840
$88$	−4.84163	−0.516120
$89$	8.28978	0.878715	0.439358	−	0.898312i	$-0.355206\pi$
$89$	8.28978	0.878715	0.439358	+	0.898312i	$0.355206\pi$
$90$	1.61137	0.169853
$91$	−1.94988	−0.204403
$92$	1.21687	0.126868
$93$	1.37906	0.143002
$94$	17.9802	1.85452
$95$	0.238622	0.0244821
$96$	−1.49865	−0.152955
$97$	−12.3705	−1.25604	−0.628019	−	0.778198i	$-0.716134\pi$
$97$	−12.3705	−1.25604	−0.628019	+	0.778198i	$0.716134\pi$
$98$	−8.61094	−0.869837
$99$	3.72463	0.374340
$100$	−1.26177	−0.126177
$101$	9.80623	0.975756	0.487878	−	0.872912i	$-0.337771\pi$
$101$	9.80623	0.975756	0.487878	+	0.872912i	$0.337771\pi$
$102$	4.84097	0.479328
$103$	−6.58895	−0.649229	−0.324614	−	0.945846i	$-0.605235\pi$
$103$	−6.58895	−0.649229	−0.324614	+	0.945846i	$0.605235\pi$
$104$	−1.42636	−0.139866
$105$	−1.89494	−0.184927
$106$	12.8187	1.24506
$107$	1.77285	0.171387	0.0856937	−	0.996322i	$-0.472689\pi$
$107$	1.77285	0.171387	0.0856937	+	0.996322i	$0.472689\pi$
$108$	1.33505	0.128465
$109$	10.6745	1.02243	0.511216	−	0.859452i	$-0.329195\pi$
$109$	10.6745	1.02243	0.511216	+	0.859452i	$0.329195\pi$
$110$	1.49012	0.142077
$111$	1.42464	0.135220
$112$	−15.9182	−1.50413
$113$	6.62343	0.623080	0.311540	−	0.950233i	$-0.399155\pi$
$113$	6.62343	0.623080	0.311540	+	0.950233i	$0.399155\pi$
$114$	0.671581	0.0628994
$115$	2.42492	0.226125
$116$	−0.267567	−0.0248430
$117$	1.09729	0.101445
$118$	−0.275854	−0.0253945
$119$	11.5047	1.05463
$120$	−1.38617	−0.126539
$121$	−7.55563	−0.686875
$122$	−15.2445	−1.38017
$123$	4.77817	0.430833
$124$	−0.370275	−0.0332517
$125$	−5.18036	−0.463345
$126$	10.7776	0.960149
$127$	12.0085	1.06558	0.532792	−	0.846246i	$-0.321143\pi$
$127$	12.0085	1.06558	0.532792	+	0.846246i	$0.321143\pi$
$128$	−13.0404	−1.15262
$129$	1.83602	0.161653
$130$	0.438995	0.0385024
$131$	10.4677	0.914565	0.457282	−	0.889322i	$-0.348823\pi$
$131$	10.4677	0.914565	0.457282	+	0.889322i	$0.348823\pi$
$132$	0.494860	0.0430720
$133$	1.59603	0.138393
$134$	1.49315	0.128989
$135$	2.66041	0.228972
$136$	8.41579	0.721648
$137$	6.77339	0.578690	0.289345	−	0.957225i	$-0.406563\pi$
$137$	6.77339	0.578690	0.289345	+	0.957225i	$0.406563\pi$
$138$	6.82473	0.580960
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	0.508785	0.0430002
$141$	11.8989	1.00207
$142$	−10.0208	−0.840926
$143$	1.01473	0.0848557
$144$	8.95794	0.746495
$145$	−0.533194	−0.0442794
$146$	−7.65353	−0.633410
$147$	−5.69855	−0.470008
$148$	−0.382511	−0.0314422
$149$	10.9634	0.898158	0.449079	−	0.893492i	$-0.351752\pi$
$149$	10.9634	0.898158	0.449079	+	0.893492i	$0.351752\pi$
$150$	−7.07653	−0.577796
$151$	9.24888	0.752663	0.376331	−	0.926485i	$-0.377185\pi$
$151$	9.24888	0.752663	0.376331	+	0.926485i	$0.377185\pi$
$152$	1.16751	0.0946977
$153$	−6.47422	−0.523409
$154$	9.96668	0.803138
$155$	−0.737864	−0.0592667
$156$	0.145788	0.0116723
$157$	6.64000	0.529930	0.264965	−	0.964258i	$-0.414640\pi$
$157$	6.64000	0.529930	0.264965	+	0.964258i	$0.414640\pi$
$158$	24.4511	1.94522
$159$	8.48314	0.672757
$160$	0.801846	0.0633915
$161$	16.2191	1.27825
$162$	−1.57878	−0.124041
$163$	−9.30139	−0.728541	−0.364271	−	0.931293i	$-0.618682\pi$
$163$	−9.30139	−0.728541	−0.364271	+	0.931293i	$0.618682\pi$
$164$	−1.28292	−0.100180
$165$	0.986131	0.0767702
$166$	26.2040	2.03383
$167$	0.921978	0.0713448	0.0356724	−	0.999364i	$-0.488643\pi$
$167$	0.921978	0.0713448	0.0356724	+	0.999364i	$0.488643\pi$
$168$	−9.27140	−0.715304
$169$	−12.7011	−0.977004
$170$	−2.59015	−0.198655
$171$	−0.898159	−0.0686840
$172$	−0.492966	−0.0375883
$173$	−4.11889	−0.313153	−0.156577	−	0.987666i	$-0.550046\pi$
$173$	−4.11889	−0.313153	−0.156577	+	0.987666i	$0.550046\pi$
$174$	−1.50063	−0.113763
$175$	−16.8175	−1.27128
$176$	8.28390	0.624422
$177$	−0.182555	−0.0137217
$178$	−12.4831	−0.935649
$179$	−1.50370	−0.112392	−0.0561958	−	0.998420i	$-0.517897\pi$
$179$	−1.50370	−0.112392	−0.0561958	+	0.998420i	$0.517897\pi$
$180$	−0.286317	−0.0213408
$181$	−12.0879	−0.898485	−0.449242	−	0.893410i	$-0.648306\pi$
$181$	−12.0879	−0.898485	−0.449242	+	0.893410i	$0.648306\pi$
$182$	2.93622	0.217647
$183$	−10.0885	−0.745762
$184$	11.8645	0.874660
$185$	−0.762247	−0.0560415
$186$	−2.07666	−0.152268
$187$	−5.98706	−0.437817
$188$	−3.19483	−0.233007
$189$	17.7942	1.29434
$190$	−0.359328	−0.0260684
$191$	−9.73818	−0.704630	−0.352315	−	0.935881i	$-0.614605\pi$
$191$	−9.73818	−0.704630	−0.352315	+	0.935881i	$0.614605\pi$
$192$	−6.63945	−0.479161
$193$	−2.99921	−0.215888	−0.107944	−	0.994157i	$-0.534427\pi$
$193$	−2.99921	−0.215888	−0.107944	+	0.994157i	$0.534427\pi$
$194$	18.6281	1.33742
$195$	0.290518	0.0208044
$196$	1.53004	0.109289
$197$	−6.66612	−0.474941	−0.237471	−	0.971395i	$-0.576318\pi$
$197$	−6.66612	−0.474941	−0.237471	+	0.971395i	$0.576318\pi$
$198$	−5.60872	−0.398594
$199$	5.54858	0.393329	0.196664	−	0.980471i	$-0.436989\pi$
$199$	5.54858	0.393329	0.196664	+	0.980471i	$0.436989\pi$
$200$	−12.3022	−0.869897
$201$	0.988138	0.0696979
$202$	−14.7666	−1.03898
$203$	−3.56628	−0.250304
$204$	−0.860173	−0.0602241
$205$	−2.55654	−0.178557
$206$	9.92194	0.691294
$207$	−9.12726	−0.634388
$208$	2.44047	0.169216
$209$	−0.830577	−0.0574522
$210$	2.85348	0.196909
$211$	−24.1942	−1.66560	−0.832798	−	0.553576i	$-0.813263\pi$
$211$	−24.1942	−1.66560	−0.832798	+	0.553576i	$0.813263\pi$
$212$	−2.27770	−0.156433
$213$	−6.63156	−0.454387
$214$	−2.66963	−0.182492
$215$	−0.982357	−0.0669962
$216$	13.0167	0.885673
$217$	−4.93522	−0.335024
$218$	−16.0741	−1.08868
$219$	−5.06495	−0.342258
$220$	−0.264773	−0.0178510
$221$	−1.76381	−0.118647
$222$	−2.14528	−0.143982
$223$	9.44158	0.632255	0.316128	−	0.948717i	$-0.397617\pi$
$223$	9.44158	0.632255	0.316128	+	0.948717i	$0.397617\pi$
$224$	5.36316	0.358341
$225$	9.46401	0.630934
$226$	−9.97386	−0.663451
$227$	21.5271	1.42881	0.714403	−	0.699734i	$-0.246698\pi$
$227$	21.5271	1.42881	0.714403	+	0.699734i	$0.246698\pi$
$228$	−0.119331	−0.00790286
$229$	−23.9008	−1.57941	−0.789703	−	0.613489i	$-0.789766\pi$
$229$	−23.9008	−1.57941	−0.789703	+	0.613489i	$0.789766\pi$
$230$	−3.65155	−0.240776
$231$	6.59575	0.433969
$232$	−2.60877	−0.171274
$233$	6.52276	0.427320	0.213660	−	0.976908i	$-0.431461\pi$
$233$	6.52276	0.427320	0.213660	+	0.976908i	$0.431461\pi$
$234$	−1.65235	−0.108018
$235$	−6.36649	−0.415304
$236$	0.0490155	0.00319063
$237$	16.1812	1.05108
$238$	−17.3242	−1.12296
$239$	−25.0050	−1.61744	−0.808721	−	0.588193i	$-0.799840\pi$
$239$	−25.0050	−1.61744	−0.808721	+	0.588193i	$0.799840\pi$
$240$	2.37170	0.153092
$241$	15.4575	0.995707	0.497854	−	0.867261i	$-0.334122\pi$
$241$	15.4575	0.995707	0.497854	+	0.867261i	$0.334122\pi$
$242$	11.3776	0.731380
$243$	−16.0135	−1.02727
$244$	2.70873	0.173408
$245$	3.04899	0.194793
$246$	−7.19518	−0.458748
$247$	−0.244691	−0.0155693
$248$	−3.61017	−0.229246
$249$	17.3413	1.09896
$250$	7.80081	0.493367
$251$	4.60415	0.290612	0.145306	−	0.989387i	$-0.453583\pi$
$251$	4.60415	0.290612	0.145306	+	0.989387i	$0.453583\pi$
$252$	−1.91504	−0.120636
$253$	−8.44048	−0.530648
$254$	−18.0830	−1.13463
$255$	−1.71411	−0.107342
$256$	6.31181	0.394488
$257$	−20.0195	−1.24879	−0.624393	−	0.781111i	$-0.714653\pi$
$257$	−20.0195	−1.24879	−0.624393	+	0.781111i	$0.714653\pi$
$258$	−2.76476	−0.172127
$259$	−5.09830	−0.316793
$260$	−0.0780032	−0.00483755
$261$	2.00691	0.124225
$262$	−15.7627	−0.973822
$263$	6.83942	0.421737	0.210868	−	0.977514i	$-0.432371\pi$
$263$	6.83942	0.421737	0.210868	+	0.977514i	$0.432371\pi$
$264$	4.82487	0.296950
$265$	−4.53888	−0.278821
$266$	−2.40337	−0.147360
$267$	−8.26108	−0.505570
$268$	−0.265312	−0.0162065
$269$	23.4324	1.42870	0.714350	−	0.699789i	$-0.246723\pi$
$269$	23.4324	1.42870	0.714350	+	0.699789i	$0.246723\pi$
$270$	−4.00617	−0.243808
$271$	−20.0439	−1.21758	−0.608790	−	0.793331i	$-0.708345\pi$
$271$	−20.0439	−1.21758	−0.608790	+	0.793331i	$0.708345\pi$
$272$	−14.3992	−0.873080
$273$	1.94313	0.117604
$274$	−10.1997	−0.616185
$275$	8.75189	0.527759
$276$	−1.21266	−0.0729935
$277$	−11.0581	−0.664419	−0.332210	−	0.943206i	$-0.607794\pi$
$277$	−11.0581	−0.664419	−0.332210	+	0.943206i	$0.607794\pi$
$278$	1.50584	0.0903145
$279$	2.77728	0.166271
$280$	4.96064	0.296455
$281$	−28.0077	−1.67080	−0.835399	−	0.549643i	$-0.814764\pi$
$281$	−28.0077	−1.67080	−0.835399	+	0.549643i	$0.814764\pi$
$282$	−17.9180	−1.06700
$283$	−15.7444	−0.935908	−0.467954	−	0.883753i	$-0.655009\pi$
$283$	−15.7444	−0.935908	−0.467954	+	0.883753i	$0.655009\pi$
$284$	1.78055	0.105656
$285$	−0.237796	−0.0140858
$286$	−1.52802	−0.0903537
$287$	−17.0995	−1.00935
$288$	−3.01810	−0.177843
$289$	−6.59320	−0.387835
$290$	0.802908	0.0471484
$291$	12.3277	0.722663
$292$	1.35992	0.0795836
$293$	11.1312	0.650290	0.325145	−	0.945664i	$-0.394587\pi$
$293$	11.1312	0.650290	0.325145	+	0.945664i	$0.394587\pi$
$294$	8.58113	0.500462
$295$	0.0976754	0.00568688
$296$	−3.72947	−0.216771
$297$	−9.26017	−0.537329
$298$	−16.5092	−0.956352
$299$	−2.48660	−0.143804
$300$	1.25740	0.0725960
$301$	−6.57051	−0.378718
$302$	−13.9274	−0.801430
$303$	−9.77227	−0.561402
$304$	−1.99758	−0.114569
$305$	5.39781	0.309078
$306$	9.74916	0.557322
$307$	−15.5498	−0.887474	−0.443737	−	0.896157i	$-0.646348\pi$
$307$	−15.5498	−0.887474	−0.443737	+	0.896157i	$0.646348\pi$
$308$	−1.77094	−0.100909
$309$	6.56614	0.373535
$310$	1.11111	0.0631067
$311$	−6.43317	−0.364792	−0.182396	−	0.983225i	$-0.558385\pi$
$311$	−6.43317	−0.364792	−0.182396	+	0.983225i	$0.558385\pi$
$312$	1.42142	0.0804723
$313$	−29.9163	−1.69097	−0.845484	−	0.534001i	$-0.820688\pi$
$313$	−29.9163	−1.69097	−0.845484	+	0.534001i	$0.820688\pi$
$314$	−9.99880	−0.564265
$315$	−3.81618	−0.215018
$316$	−4.34461	−0.244403
$317$	−6.34686	−0.356475	−0.178238	−	0.983987i	$-0.557040\pi$
$317$	−6.34686	−0.356475	−0.178238	+	0.983987i	$0.557040\pi$
$318$	−12.7743	−0.716347
$319$	1.85590	0.103911
$320$	3.55242	0.198586
$321$	−1.76671	−0.0986080
$322$	−24.4235	−1.36107
$323$	1.44372	0.0803308
$324$	0.280528	0.0155849
$325$	2.57834	0.143021
$326$	14.0064	0.775745
$327$	−10.6375	−0.588258
$328$	−12.5085	−0.690665
$329$	−42.5824	−2.34764
$330$	−1.48496	−0.0817443
$331$	5.15247	0.283205	0.141603	−	0.989924i	$-0.454774\pi$
$331$	5.15247	0.283205	0.141603	+	0.989924i	$0.454774\pi$
$332$	−4.65609	−0.255536
$333$	2.86905	0.157223
$334$	−1.38836	−0.0759674
$335$	−0.528700	−0.0288860
$336$	15.8631	0.865404
$337$	11.7453	0.639809	0.319905	−	0.947450i	$-0.396349\pi$
$337$	11.7453	0.639809	0.319905	+	0.947450i	$0.396349\pi$
$338$	19.1258	1.04031
$339$	−6.60050	−0.358490
$340$	0.460233	0.0249596
$341$	2.56830	0.139081
$342$	1.35249	0.0731342
$343$	−4.57073	−0.246796
$344$	−4.80640	−0.259144
$345$	−2.41652	−0.130101
$346$	6.20240	0.333443
$347$	−11.9719	−0.642687	−0.321344	−	0.946963i	$-0.604134\pi$
$347$	−11.9719	−0.642687	−0.321344	+	0.946963i	$0.604134\pi$
$348$	0.266641	0.0142935
$349$	−31.8967	−1.70739	−0.853695	−	0.520774i	$-0.825643\pi$
$349$	−31.8967	−1.70739	−0.853695	+	0.520774i	$0.825643\pi$
$350$	25.3246	1.35365
$351$	−2.72808	−0.145614
$352$	−2.79100	−0.148761
$353$	−4.04102	−0.215082	−0.107541	−	0.994201i	$-0.534298\pi$
$353$	−4.04102	−0.215082	−0.107541	+	0.994201i	$0.534298\pi$
$354$	0.274899	0.0146107
$355$	3.54819	0.188319
$356$	2.21808	0.117558
$357$	−11.4648	−0.606783
$358$	2.26433	0.119674
$359$	9.42565	0.497467	0.248733	−	0.968572i	$-0.419986\pi$
$359$	9.42565	0.497467	0.248733	+	0.968572i	$0.419986\pi$
$360$	−2.79158	−0.147129
$361$	−18.7997	−0.989459
$362$	18.2025	0.956700
$363$	7.52947	0.395194
$364$	−0.521726	−0.0273459
$365$	2.70999	0.141847
$366$	15.1917	0.794082
$367$	−8.95622	−0.467511	−0.233756	−	0.972295i	$-0.575102\pi$
$367$	−8.95622	−0.467511	−0.233756	+	0.972295i	$0.575102\pi$
$368$	−20.2998	−1.05820
$369$	9.62268	0.500937
$370$	1.14783	0.0596726
$371$	−30.3584	−1.57613
$372$	0.368993	0.0191314
$373$	−20.5670	−1.06492	−0.532459	−	0.846456i	$-0.678732\pi$
$373$	−20.5670	−1.06492	−0.532459	+	0.846456i	$0.678732\pi$
$374$	9.01559	0.466185
$375$	5.16242	0.266586
$376$	−31.1495	−1.60641
$377$	0.546756	0.0281594
$378$	−26.7953	−1.37820
$379$	8.03308	0.412632	0.206316	−	0.978485i	$-0.433853\pi$
$379$	8.03308	0.412632	0.206316	+	0.978485i	$0.433853\pi$
$380$	0.0638475	0.00327531
$381$	−11.9670	−0.613086
$382$	14.6642	0.750285
$383$	2.22058	0.113466	0.0567332	−	0.998389i	$-0.481932\pi$
$383$	2.22058	0.113466	0.0567332	+	0.998389i	$0.481932\pi$
$384$	12.9953	0.663162
$385$	−3.52904	−0.179856
$386$	4.51634	0.229876
$387$	3.69754	0.187956
$388$	−3.30995	−0.168037
$389$	19.2054	0.973752	0.486876	−	0.873471i	$-0.338136\pi$
$389$	19.2054	0.973752	0.486876	+	0.873471i	$0.338136\pi$
$390$	−0.437475	−0.0221524
$391$	14.6714	0.741963
$392$	14.9179	0.753467
$393$	−10.4314	−0.526196
$394$	10.0381	0.505714
$395$	−8.65771	−0.435617
$396$	0.996591	0.0500806
$397$	−9.61856	−0.482742	−0.241371	−	0.970433i	$-0.577597\pi$
$397$	−9.61856	−0.482742	−0.241371	+	0.970433i	$0.577597\pi$
$398$	−8.35530	−0.418813
$399$	−1.59050	−0.0796246
$400$	21.0487	1.05244
$401$	19.9900	0.998253	0.499126	−	0.866529i	$-0.333654\pi$
$401$	19.9900	0.998253	0.499126	+	0.866529i	$0.333654\pi$
$402$	−1.48798	−0.0742138
$403$	0.756632	0.0376905
$404$	2.62383	0.130540
$405$	0.559021	0.0277780
$406$	5.37026	0.266522
$407$	2.65317	0.131513
$408$	−8.38666	−0.415201
$409$	−14.6149	−0.722659	−0.361329	−	0.932438i	$-0.617677\pi$
$409$	−14.6149	−0.722659	−0.361329	+	0.932438i	$0.617677\pi$
$410$	3.84976	0.190126
$411$	−6.74994	−0.332950
$412$	−1.76299	−0.0868562
$413$	0.653304	0.0321470
$414$	13.7442	0.675492
$415$	−9.27841	−0.455459
$416$	−0.822241	−0.0403137
$417$	0.996538	0.0488007
$418$	1.25072	0.0611747
$419$	4.76640	0.232854	0.116427	−	0.993199i	$-0.462856\pi$
$419$	4.76640	0.232854	0.116427	+	0.993199i	$0.462856\pi$
$420$	−0.507023	−0.0247402
$421$	−20.7279	−1.01022	−0.505108	−	0.863056i	$-0.668547\pi$
$421$	−20.7279	−1.01022	−0.505108	+	0.863056i	$0.668547\pi$
$422$	36.4327	1.77352
$423$	23.9631	1.16513
$424$	−22.2075	−1.07849
$425$	−15.2127	−0.737922
$426$	9.98609	0.483828
$427$	36.1033	1.74716
$428$	0.474356	0.0229288
$429$	−1.01121	−0.0488218
$430$	1.47928	0.0713371
$431$	25.5315	1.22981	0.614903	−	0.788602i	$-0.289195\pi$
$431$	25.5315	1.22981	0.614903	+	0.788602i	$0.289195\pi$
$432$	−22.2712	−1.07152
$433$	−4.93800	−0.237305	−0.118652	−	0.992936i	$-0.537857\pi$
$433$	−4.93800	−0.237305	−0.118652	+	0.992936i	$0.537857\pi$
$434$	7.43167	0.356732
$435$	0.531348	0.0254762
$436$	2.85615	0.136785
$437$	2.03534	0.0973634
$438$	7.62703	0.364433
$439$	−31.7313	−1.51445	−0.757226	−	0.653153i	$-0.773446\pi$
$439$	−31.7313	−1.51445	−0.757226	+	0.653153i	$0.773446\pi$
$440$	−2.58153	−0.123070
$441$	−11.4762	−0.546487
$442$	2.65603	0.126334
$443$	−6.75497	−0.320938	−0.160469	−	0.987041i	$-0.551301\pi$
$443$	−6.75497	−0.320938	−0.160469	+	0.987041i	$0.551301\pi$
$444$	0.381186	0.0180903
$445$	4.42006	0.209531
$446$	−14.2176	−0.673221
$447$	−10.9255	−0.516756
$448$	23.7604	1.12257
$449$	−28.5970	−1.34958	−0.674788	−	0.738012i	$-0.735765\pi$
$449$	−28.5970	−1.34958	−0.674788	+	0.738012i	$0.735765\pi$
$450$	−14.2513	−0.671814
$451$	8.89862	0.419020
$452$	1.77221	0.0833579
$453$	−9.21685	−0.433046
$454$	−32.4165	−1.52138
$455$	−1.03967	−0.0487404
$456$	−1.16347	−0.0544845
$457$	21.6677	1.01357	0.506786	−	0.862072i	$-0.330833\pi$
$457$	21.6677	1.01357	0.506786	+	0.862072i	$0.330833\pi$
$458$	35.9908	1.68174
$459$	16.0962	0.751305
$460$	0.648829	0.0302518
$461$	−20.0139	−0.932141	−0.466070	−	0.884748i	$-0.654331\pi$
$461$	−20.0139	−0.932141	−0.466070	+	0.884748i	$0.654331\pi$
$462$	−9.93217	−0.462087
$463$	15.5175	0.721159	0.360579	−	0.932729i	$-0.382579\pi$
$463$	15.5175	0.721159	0.360579	+	0.932729i	$0.382579\pi$
$464$	4.46354	0.207215
$465$	0.735309	0.0340992
$466$	−9.82226	−0.455008
$467$	18.2714	0.845499	0.422750	−	0.906246i	$-0.361065\pi$
$467$	18.2714	0.845499	0.422750	+	0.906246i	$0.361065\pi$
$468$	0.293600	0.0135716
$469$	−3.53622	−0.163288
$470$	9.58694	0.442213
$471$	−6.61701	−0.304896
$472$	0.477899	0.0219971
$473$	3.41931	0.157220
$474$	−24.3664	−1.11919
$475$	−2.11043	−0.0968333
$476$	3.07827	0.141092
$477$	17.0841	0.782226
$478$	37.6537	1.72224
$479$	18.2613	0.834378	0.417189	−	0.908820i	$-0.363015\pi$
$479$	18.2613	0.834378	0.417189	+	0.908820i	$0.363015\pi$
$480$	−0.799070	−0.0364724
$481$	0.781635	0.0356395
$482$	−23.2766	−1.06022
$483$	−16.1630	−0.735440
$484$	−2.02164	−0.0918927
$485$	−6.59590	−0.299505
$486$	24.1139	1.09383
$487$	−28.7130	−1.30111	−0.650555	−	0.759459i	$-0.725464\pi$
$487$	−28.7130	−1.30111	−0.650555	+	0.759459i	$0.725464\pi$
$488$	26.4100	1.19552
$489$	9.26919	0.419167
$490$	−4.59131	−0.207414
$491$	−7.83568	−0.353619	−0.176810	−	0.984245i	$-0.556578\pi$
$491$	−7.83568	−0.353619	−0.176810	+	0.984245i	$0.556578\pi$
$492$	1.27848	0.0576384
$493$	−3.22596	−0.145290
$494$	0.368467	0.0165781
$495$	1.98595	0.0892620
$496$	6.17690	0.277351
$497$	23.7322	1.06453
$498$	−26.1133	−1.17017
$499$	32.7557	1.46635	0.733174	−	0.680042i	$-0.238038\pi$
$499$	32.7557	1.46635	0.733174	+	0.680042i	$0.238038\pi$
$500$	−1.38610	−0.0619881
$501$	−0.918786	−0.0410483
$502$	−6.93314	−0.309441
$503$	31.2587	1.39375	0.696877	−	0.717190i	$-0.254572\pi$
$503$	31.2587	1.39375	0.696877	+	0.717190i	$0.254572\pi$
$504$	−18.6715	−0.831697
$505$	5.22862	0.232671
$506$	12.7100	0.565030
$507$	12.6571	0.562121
$508$	3.21309	0.142558
$509$	−13.7101	−0.607690	−0.303845	−	0.952721i	$-0.598271\pi$
$509$	−13.7101	−0.607690	−0.303845	+	0.952721i	$0.598271\pi$
$510$	2.58118	0.114296
$511$	18.1258	0.801838
$512$	16.5762	0.732573
$513$	2.23300	0.0985893
$514$	30.1463	1.32970
$515$	−3.51319	−0.154810
$516$	0.491259	0.0216265
$517$	22.1600	0.974596
$518$	7.67725	0.337319
$519$	4.10462	0.180173
$520$	−0.760529	−0.0333514
$521$	−35.4471	−1.55296	−0.776482	−	0.630139i	$-0.782998\pi$
$521$	−35.4471	−1.55296	−0.776482	+	0.630139i	$0.782998\pi$
$522$	−3.02210	−0.132274
$523$	−23.7853	−1.04006	−0.520030	−	0.854148i	$-0.674079\pi$
$523$	−23.7853	−1.04006	−0.520030	+	0.854148i	$0.674079\pi$
$524$	2.80081	0.122354
$525$	16.7593	0.731435
$526$	−10.2991	−0.449062
$527$	−4.46426	−0.194466
$528$	−8.25522	−0.359262
$529$	−2.31653	−0.100719
$530$	6.83484	0.296887
$531$	−0.367645	−0.0159544
$532$	0.427045	0.0185147
$533$	2.62157	0.113553
$534$	12.4399	0.538327
$535$	0.945271	0.0408676
$536$	−2.58679	−0.111732
$537$	1.49849	0.0646646
$538$	−35.2856	−1.52127
$539$	−10.6127	−0.457121
$540$	0.711840	0.0306327
$541$	12.1302	0.521517	0.260758	−	0.965404i	$-0.416027\pi$
$541$	12.1302	0.521517	0.260758	+	0.965404i	$0.416027\pi$
$542$	30.1830	1.29647
$543$	12.0460	0.516944
$544$	4.85137	0.208001
$545$	5.69158	0.243801
$546$	−2.92606	−0.125224
$547$	22.5418	0.963818	0.481909	−	0.876221i	$-0.339943\pi$
$547$	22.5418	0.963818	0.481909	+	0.876221i	$0.339943\pi$
$548$	1.81234	0.0774193
$549$	−20.3170	−0.867110
$550$	−13.1790	−0.561954
$551$	−0.447533	−0.0190655
$552$	−11.8234	−0.503237
$553$	−57.9073	−2.46247
$554$	16.6518	0.707469
$555$	0.759608	0.0322436
$556$	−0.267567	−0.0113474
$557$	30.5722	1.29539	0.647693	−	0.761901i	$-0.275734\pi$
$557$	30.5722	1.29539	0.647693	+	0.761901i	$0.275734\pi$
$558$	−4.18215	−0.177044
$559$	1.00734	0.0426061
$560$	−8.48752	−0.358663
$561$	5.96633	0.251899
$562$	42.1752	1.77905
$563$	−5.87437	−0.247575	−0.123788	−	0.992309i	$-0.539504\pi$
$563$	−5.87437	−0.247575	−0.123788	+	0.992309i	$0.539504\pi$
$564$	3.18377	0.134061
$565$	3.53158	0.148575
$566$	23.7086	0.996548
$567$	3.73902	0.157024
$568$	17.3603	0.728424
$569$	−16.8377	−0.705875	−0.352938	−	0.935647i	$-0.614817\pi$
$569$	−16.8377	−0.705875	−0.352938	+	0.935647i	$0.614817\pi$
$570$	0.358083	0.0149985
$571$	18.3488	0.767874	0.383937	−	0.923359i	$-0.374568\pi$
$571$	18.3488	0.767874	0.383937	+	0.923359i	$0.374568\pi$
$572$	0.271508	0.0113523
$573$	9.70446	0.405410
$574$	25.7492	1.07475
$575$	−21.4466	−0.894385
$576$	−13.3711	−0.557129
$577$	−2.79171	−0.116220	−0.0581102	−	0.998310i	$-0.518507\pi$
$577$	−2.79171	−0.116220	−0.0581102	+	0.998310i	$0.518507\pi$
$578$	9.92833	0.412964
$579$	2.98882	0.124211
$580$	−0.142665	−0.00592386
$581$	−62.0588	−2.57463
$582$	−18.5636	−0.769487
$583$	15.7986	0.654310
$584$	13.2592	0.548670
$585$	0.585070	0.0241897
$586$	−16.7618	−0.692425
$587$	19.3686	0.799427	0.399713	−	0.916640i	$-0.369110\pi$
$587$	19.3686	0.799427	0.399713	+	0.916640i	$0.369110\pi$
$588$	−1.52475	−0.0628795
$589$	−0.619321	−0.0255187
$590$	−0.147084	−0.00605535
$591$	6.64304	0.273258
$592$	6.38102	0.262258
$593$	13.0609	0.536346	0.268173	−	0.963371i	$-0.413580\pi$
$593$	13.0609	0.536346	0.268173	+	0.963371i	$0.413580\pi$
$594$	13.9444	0.572145
$595$	6.13422	0.251479
$596$	2.93345	0.120159
$597$	−5.52937	−0.226302
$598$	3.74443	0.153121
$599$	−23.6567	−0.966586	−0.483293	−	0.875459i	$-0.660559\pi$
$599$	−23.6567	−0.966586	−0.483293	+	0.875459i	$0.660559\pi$
$600$	12.2596	0.500496
$601$	6.94308	0.283214	0.141607	−	0.989923i	$-0.454773\pi$
$601$	6.94308	0.283214	0.141607	+	0.989923i	$0.454773\pi$
$602$	9.89417	0.403256
$603$	1.99000	0.0810390
$604$	2.47470	0.100694
$605$	−4.02862	−0.163787
$606$	14.7155	0.597777
$607$	−6.80474	−0.276196	−0.138098	−	0.990419i	$-0.544099\pi$
$607$	−6.80474	−0.276196	−0.138098	+	0.990419i	$0.544099\pi$
$608$	0.673023	0.0272947
$609$	3.55393	0.144013
$610$	−8.12826	−0.329104
$611$	6.52842	0.264112
$612$	−1.73229	−0.0700236
$613$	−31.3901	−1.26784	−0.633918	−	0.773400i	$-0.718554\pi$
$613$	−31.3901	−1.26784	−0.633918	+	0.773400i	$0.718554\pi$
$614$	23.4156	0.944976
$615$	2.54769	0.102733
$616$	−17.2666	−0.695691
$617$	−13.9366	−0.561068	−0.280534	−	0.959844i	$-0.590512\pi$
$617$	−13.9366	−0.561068	−0.280534	+	0.959844i	$0.590512\pi$
$618$	−9.88758	−0.397737
$619$	−40.0631	−1.61027	−0.805136	−	0.593091i	$-0.797908\pi$
$619$	−40.0631	−1.61027	−0.805136	+	0.593091i	$0.797908\pi$
$620$	−0.197428	−0.00792892
$621$	22.6921	0.910604
$622$	9.68735	0.388427
$623$	29.5637	1.18444
$624$	−2.43202	−0.0973587
$625$	20.8164	0.832655
$626$	45.0492	1.80053
$627$	0.827702	0.0330552
$628$	1.77665	0.0708959
$629$	−4.61178	−0.183884
$630$	5.74658	0.228949
$631$	27.7324	1.10401	0.552004	−	0.833841i	$-0.313863\pi$
$631$	27.7324	1.10401	0.552004	+	0.833841i	$0.313863\pi$
$632$	−42.3598	−1.68498
$633$	24.1104	0.958303
$634$	9.55738	0.379572
$635$	6.40288	0.254091
$636$	2.26981	0.0900039
$637$	−3.12654	−0.123878
$638$	−2.79470	−0.110643
$639$	−13.3552	−0.528323
$640$	−6.95308	−0.274845
$641$	4.78975	0.189184	0.0945918	−	0.995516i	$-0.469845\pi$
$641$	4.78975	0.189184	0.0945918	+	0.995516i	$0.469845\pi$
$642$	2.66039	0.104997
$643$	17.0621	0.672863	0.336432	−	0.941708i	$-0.390780\pi$
$643$	17.0621	0.672863	0.336432	+	0.941708i	$0.390780\pi$
$644$	4.33971	0.171008
$645$	0.978956	0.0385463
$646$	−2.17402	−0.0855357
$647$	−41.9943	−1.65097	−0.825483	−	0.564427i	$-0.809097\pi$
$647$	−41.9943	−1.65097	−0.825483	+	0.564427i	$0.809097\pi$
$648$	2.73514	0.107446
$649$	−0.339981	−0.0133454
$650$	−3.88258	−0.152287
$651$	4.91813	0.192757
$652$	−2.48875	−0.0974670
$653$	−23.4678	−0.918366	−0.459183	−	0.888342i	$-0.651858\pi$
$653$	−23.4678	−0.918366	−0.459183	+	0.888342i	$0.651858\pi$
$654$	16.0185	0.626372
$655$	5.58130	0.218080
$656$	21.4017	0.835594
$657$	−10.2002	−0.397949
$658$	64.1224	2.49975
$659$	43.8175	1.70689	0.853445	−	0.521184i	$-0.174509\pi$
$659$	43.8175	1.70689	0.853445	+	0.521184i	$0.174509\pi$
$660$	0.263856	0.0102706
$661$	29.4636	1.14600	0.573000	−	0.819555i	$-0.305780\pi$
$661$	29.4636	1.14600	0.573000	+	0.819555i	$0.305780\pi$
$662$	−7.75881	−0.301555
$663$	1.75770	0.0682636
$664$	−45.3967	−1.76174
$665$	0.850993	0.0330001
$666$	−4.32035	−0.167410
$667$	−4.54791	−0.176096
$668$	0.246691	0.00954477
$669$	−9.40889	−0.363769
$670$	0.796140	0.0307576
$671$	−18.7883	−0.725314
$672$	−5.34459	−0.206172
$673$	−35.7137	−1.37666	−0.688330	−	0.725397i	$-0.741656\pi$
$673$	−35.7137	−1.37666	−0.688330	+	0.725397i	$0.741656\pi$
$674$	−17.6866	−0.681264
$675$	−23.5294	−0.905646
$676$	−3.39839	−0.130707
$677$	8.09211	0.311005	0.155502	−	0.987836i	$-0.450300\pi$
$677$	8.09211	0.311005	0.155502	+	0.987836i	$0.450300\pi$
$678$	9.93932	0.381717
$679$	−44.1168	−1.69305
$680$	4.48725	0.172078
$681$	−21.4526	−0.822066
$682$	−3.86746	−0.148093
$683$	−41.2516	−1.57845	−0.789224	−	0.614105i	$-0.789517\pi$
$683$	−41.2516	−1.57845	−0.789224	+	0.614105i	$0.789517\pi$
$684$	−0.240318	−0.00918879
$685$	3.61153	0.137990
$686$	6.88281	0.262787
$687$	23.8180	0.908714
$688$	8.22363	0.313523
$689$	4.65432	0.177316
$690$	3.63891	0.138531
$691$	3.20874	0.122066	0.0610331	−	0.998136i	$-0.480560\pi$
$691$	3.20874	0.122066	0.0610331	+	0.998136i	$0.480560\pi$
$692$	−1.10208	−0.0418948
$693$	13.2831	0.504583
$694$	18.0279	0.684329
$695$	−0.533194	−0.0202252
$696$	2.59974	0.0985429
$697$	−15.4677	−0.585882
$698$	48.0314	1.81802
$699$	−6.50018	−0.245859
$700$	−4.49982	−0.170077
$701$	−16.7741	−0.633549	−0.316774	−	0.948501i	$-0.602600\pi$
$701$	−16.7741	−0.633549	−0.316774	+	0.948501i	$0.602600\pi$
$702$	4.10807	0.155049
$703$	−0.639787	−0.0241300
$704$	−12.3650	−0.466023
$705$	6.34445	0.238946
$706$	6.08515	0.229017
$707$	34.9717	1.31525
$708$	−0.0488457	−0.00183574
$709$	−20.2346	−0.759927	−0.379963	−	0.925001i	$-0.624063\pi$
$709$	−20.2346	−0.759927	−0.379963	+	0.925001i	$0.624063\pi$
$710$	−5.34303	−0.200520
$711$	32.5871	1.22211
$712$	21.6262	0.810475
$713$	−6.29365	−0.235699
$714$	17.2643	0.646098
$715$	0.541046	0.0202340
$716$	−0.402340	−0.0150362
$717$	24.9185	0.930597
$718$	−14.1936	−0.529699
$719$	−49.3467	−1.84032	−0.920160	−	0.391542i	$-0.871942\pi$
$719$	−49.3467	−1.84032	−0.920160	+	0.391542i	$0.871942\pi$
$720$	4.77632	0.178003
$721$	−23.4980	−0.875113
$722$	28.3094	1.05357
$723$	−15.4040	−0.572882
$724$	−3.23432	−0.120203
$725$	4.71570	0.175137
$726$	−11.3382	−0.420800
$727$	−21.3409	−0.791492	−0.395746	−	0.918360i	$-0.629514\pi$
$727$	−21.3409	−0.791492	−0.395746	+	0.918360i	$0.629514\pi$
$728$	−5.08681	−0.188530
$729$	12.8128	0.474547
$730$	−4.08082	−0.151038
$731$	−5.94350	−0.219828
$732$	−2.69935	−0.0997708
$733$	−10.8299	−0.400010	−0.200005	−	0.979795i	$-0.564096\pi$
$733$	−10.8299	−0.400010	−0.200005	+	0.979795i	$0.564096\pi$
$734$	13.4867	0.497802
$735$	−3.03843	−0.112074
$736$	6.83939	0.252103
$737$	1.84026	0.0677869
$738$	−14.4903	−0.533394
$739$	20.4680	0.752926	0.376463	−	0.926432i	$-0.377140\pi$
$739$	20.4680	0.752926	0.376463	+	0.926432i	$0.377140\pi$
$740$	−0.203952	−0.00749744
$741$	0.243844	0.00895784
$742$	45.7150	1.67825
$743$	−7.06376	−0.259144	−0.129572	−	0.991570i	$-0.541360\pi$
$743$	−7.06376	−0.259144	−0.129572	+	0.991570i	$0.541360\pi$
$744$	3.59767	0.131897
$745$	5.84563	0.214167
$746$	30.9707	1.13392
$747$	34.9234	1.27778
$748$	−1.60194	−0.0585728
$749$	6.32246	0.231018
$750$	−7.77380	−0.283859
$751$	−2.76001	−0.100714	−0.0503571	−	0.998731i	$-0.516036\pi$
$751$	−2.76001	−0.100714	−0.0503571	+	0.998731i	$0.516036\pi$
$752$	53.2960	1.94350
$753$	−4.58821	−0.167204
$754$	−0.823330	−0.0299839
$755$	4.93145	0.179474
$756$	4.76116	0.173162
$757$	28.6303	1.04059	0.520293	−	0.853988i	$-0.325823\pi$
$757$	28.6303	1.04059	0.520293	+	0.853988i	$0.325823\pi$
$758$	−12.0966	−0.439367
$759$	8.41125	0.305309
$760$	0.622511	0.0225808
$761$	−12.7362	−0.461685	−0.230843	−	0.972991i	$-0.574148\pi$
$761$	−12.7362	−0.461685	−0.230843	+	0.972991i	$0.574148\pi$
$762$	18.0204	0.652809
$763$	38.0683	1.37816
$764$	−2.60562	−0.0942680
$765$	−3.45201	−0.124808
$766$	−3.34385	−0.120818
$767$	−0.100160	−0.00361656
$768$	−6.28996	−0.226969
$769$	11.1633	0.402560	0.201280	−	0.979534i	$-0.435490\pi$
$769$	11.1633	0.402560	0.201280	+	0.979534i	$0.435490\pi$
$770$	5.31418	0.191510
$771$	19.9502	0.718490
$772$	−0.802490	−0.0288822
$773$	26.1489	0.940512	0.470256	−	0.882530i	$-0.344162\pi$
$773$	26.1489	0.940512	0.470256	+	0.882530i	$0.344162\pi$
$774$	−5.56791	−0.200134
$775$	6.52586	0.234416
$776$	−32.2720	−1.15850
$777$	5.08065	0.182267
$778$	−28.9203	−1.03684
$779$	−2.14582	−0.0768819
$780$	0.0777331	0.00278329
$781$	−12.3503	−0.441928
$782$	−22.0928	−0.790036
$783$	−4.98958	−0.178313
$784$	−25.5241	−0.911575
$785$	3.54041	0.126363
$786$	15.7081	0.560290
$787$	−5.84644	−0.208403	−0.104202	−	0.994556i	$-0.533229\pi$
$787$	−5.84644	−0.208403	−0.104202	+	0.994556i	$0.533229\pi$
$788$	−1.78364	−0.0635394
$789$	−6.81574	−0.242647
$790$	13.0372	0.463842
$791$	23.6210	0.839866
$792$	9.71673	0.345269
$793$	−5.53510	−0.196557
$794$	14.4841	0.514020
$795$	4.52316	0.160420
$796$	1.48462	0.0526210
$797$	−32.1562	−1.13903	−0.569516	−	0.821980i	$-0.692869\pi$
$797$	−32.1562	−1.13903	−0.569516	+	0.821980i	$0.692869\pi$
$798$	2.39505	0.0847837
$799$	−38.5188	−1.36270
$800$	−7.09172	−0.250730
$801$	−16.6369	−0.587835
$802$	−30.1018	−1.06293
$803$	−9.43271	−0.332873
$804$	0.264394	0.00932445
$805$	8.64794	0.304800
$806$	−1.13937	−0.0401326
$807$	−23.3513	−0.822004
$808$	25.5822	0.899980
$809$	−22.5870	−0.794117	−0.397059	−	0.917793i	$-0.629969\pi$
$809$	−22.5870	−0.794117	−0.397059	+	0.917793i	$0.629969\pi$
$810$	−0.841798	−0.0295778
$811$	−3.88764	−0.136513	−0.0682567	−	0.997668i	$-0.521744\pi$
$811$	−3.88764	−0.136513	−0.0682567	+	0.997668i	$0.521744\pi$
$812$	−0.954220	−0.0334866
$813$	19.9745	0.700536
$814$	−3.99526	−0.140034
$815$	−4.95945	−0.173722
$816$	14.3493	0.502327
$817$	−0.824534	−0.0288468
$818$	22.0077	0.769482
$819$	3.91325	0.136740
$820$	−0.684048	−0.0238880
$821$	−12.4384	−0.434104	−0.217052	−	0.976160i	$-0.569644\pi$
$821$	−12.4384	−0.434104	−0.217052	+	0.976160i	$0.569644\pi$
$822$	10.1644	0.354523
$823$	−3.11605	−0.108619	−0.0543094	−	0.998524i	$-0.517296\pi$
$823$	−3.11605	−0.108619	−0.0543094	+	0.998524i	$0.517296\pi$
$824$	−17.1891	−0.598810
$825$	−8.72158	−0.303647
$826$	−0.983774	−0.0342299
$827$	27.9296	0.971206	0.485603	−	0.874179i	$-0.338600\pi$
$827$	27.9296	0.971206	0.485603	+	0.874179i	$0.338600\pi$
$828$	−2.44216	−0.0848708
$829$	1.89086	0.0656724	0.0328362	−	0.999461i	$-0.489546\pi$
$829$	1.89086	0.0656724	0.0328362	+	0.999461i	$0.489546\pi$
$830$	13.9718	0.484970
$831$	11.0199	0.382274
$832$	−3.64277	−0.126290
$833$	18.4471	0.639156
$834$	−1.50063	−0.0519626
$835$	0.491593	0.0170123
$836$	−0.222235	−0.00768617
$837$	−6.90486	−0.238667
$838$	−7.17746	−0.247941
$839$	−11.6256	−0.401360	−0.200680	−	0.979657i	$-0.564315\pi$
$839$	−11.6256	−0.401360	−0.200680	+	0.979657i	$0.564315\pi$
$840$	−4.94346	−0.170566
$841$	1.00000	0.0344828
$842$	31.2130	1.07567
$843$	27.9107	0.961296
$844$	−6.47358	−0.222830
$845$	−6.77213	−0.232968
$846$	−36.0847	−1.24062
$847$	−26.9455	−0.925857
$848$	37.9964	1.30480
$849$	15.6899	0.538476
$850$	22.9079	0.785734
$851$	−6.50163	−0.222873
$852$	−1.77439	−0.0607896
$853$	0.954917	0.0326957	0.0163479	−	0.999866i	$-0.494796\pi$
$853$	0.954917	0.0326957	0.0163479	+	0.999866i	$0.494796\pi$
$854$	−54.3660	−1.86037
$855$	−0.478893	−0.0163778
$856$	4.62495	0.158078
$857$	52.1614	1.78180	0.890900	−	0.454200i	$-0.150075\pi$
$857$	52.1614	1.78180	0.890900	+	0.454200i	$0.150075\pi$
$858$	1.52273	0.0519851
$859$	27.5919	0.941423	0.470712	−	0.882287i	$-0.343997\pi$
$859$	27.5919	0.941423	0.470712	+	0.882287i	$0.343997\pi$
$860$	−0.262847	−0.00896300
$861$	17.0403	0.580731
$862$	−38.4464	−1.30949
$863$	−4.97719	−0.169426	−0.0847128	−	0.996405i	$-0.526997\pi$
$863$	−4.97719	−0.169426	−0.0847128	+	0.996405i	$0.526997\pi$
$864$	7.50359	0.255277
$865$	−2.19617	−0.0746719
$866$	7.43585	0.252681
$867$	6.57037	0.223141
$868$	−1.32050	−0.0448208
$869$	30.1351	1.02226
$870$	−0.800128	−0.0271269
$871$	0.542148	0.0183700
$872$	27.8474	0.943031
$873$	24.8266	0.840253
$874$	−3.06490	−0.103672
$875$	−18.4746	−0.624556
$876$	−1.35522	−0.0457885
$877$	5.00166	0.168894	0.0844470	−	0.996428i	$-0.473088\pi$
$877$	5.00166	0.168894	0.0844470	+	0.996428i	$0.473088\pi$
$878$	47.7824	1.61258
$879$	−11.0926	−0.374145
$880$	4.41693	0.148895
$881$	6.24092	0.210262	0.105131	−	0.994458i	$-0.466474\pi$
$881$	6.24092	0.210262	0.105131	+	0.994458i	$0.466474\pi$
$882$	17.2814	0.581895
$883$	−14.1974	−0.477780	−0.238890	−	0.971047i	$-0.576784\pi$
$883$	−14.1974	−0.477780	−0.238890	+	0.971047i	$0.576784\pi$
$884$	−0.471939	−0.0158730
$885$	−0.0973372	−0.00327196
$886$	10.1719	0.341733
$887$	55.6545	1.86869	0.934347	−	0.356365i	$-0.115984\pi$
$887$	55.6545	1.86869	0.934347	+	0.356365i	$0.115984\pi$
$888$	3.71655	0.124719
$889$	42.8258	1.43633
$890$	−6.65593	−0.223107
$891$	−1.94580	−0.0651866
$892$	2.52626	0.0845854
$893$	−5.34367	−0.178819
$894$	16.4520	0.550238
$895$	−0.801763	−0.0268000
$896$	−46.5058	−1.55365
$897$	2.47799	0.0827376
$898$	43.0626	1.43702
$899$	1.38386	0.0461542
$900$	2.53226	0.0844087
$901$	−27.4613	−0.914869
$902$	−13.3999	−0.446169
$903$	6.54776	0.217896
$904$	17.2790	0.574692
$905$	−6.44519	−0.214245
$906$	13.8791	0.461104
$907$	5.68503	0.188768	0.0943842	−	0.995536i	$-0.469912\pi$
$907$	5.68503	0.188768	0.0943842	+	0.995536i	$0.469912\pi$
$908$	5.75996	0.191151
$909$	−19.6802	−0.652752
$910$	1.56558	0.0518984
$911$	30.2169	1.00113	0.500565	−	0.865699i	$-0.333126\pi$
$911$	30.2169	1.00113	0.500565	+	0.865699i	$0.333126\pi$
$912$	1.99067	0.0659175
$913$	32.2956	1.06883
$914$	−32.6282	−1.07924
$915$	−5.37912	−0.177828
$916$	−6.39507	−0.211299
$917$	37.3306	1.23277
$918$	−24.2383	−0.799984
$919$	−37.4121	−1.23411	−0.617055	−	0.786920i	$-0.711674\pi$
$919$	−37.4121	−1.23411	−0.617055	+	0.786920i	$0.711674\pi$
$920$	6.32607	0.208564
$921$	15.4960	0.510609
$922$	30.1378	0.992537
$923$	−3.63844	−0.119761
$924$	1.76481	0.0580579
$925$	6.74150	0.221659
$926$	−23.3669	−0.767885
$927$	13.2235	0.434315
$928$	−1.50385	−0.0493664
$929$	−46.3491	−1.52067	−0.760333	−	0.649534i	$-0.774964\pi$
$929$	−46.3491	−1.52067	−0.760333	+	0.649534i	$0.774964\pi$
$930$	−1.10726	−0.0363085
$931$	2.55915	0.0838727
$932$	1.74528	0.0571685
$933$	6.41090	0.209883
$934$	−27.5139	−0.900282
$935$	−3.19227	−0.104398
$936$	2.86259	0.0935666
$937$	0.919669	0.0300443	0.0150221	−	0.999887i	$-0.495218\pi$
$937$	0.919669	0.0300443	0.0150221	+	0.999887i	$0.495218\pi$
$938$	5.32500	0.173867
$939$	29.8127	0.972900
$940$	−1.70347	−0.0555609
$941$	24.4052	0.795586	0.397793	−	0.917475i	$-0.369776\pi$
$941$	24.4052	0.795586	0.397793	+	0.917475i	$0.369776\pi$
$942$	9.96418	0.324651
$943$	−21.8062	−0.710107
$944$	−0.817673	−0.0266130
$945$	9.48778	0.308638
$946$	−5.14896	−0.167407
$947$	11.0230	0.358199	0.179099	−	0.983831i	$-0.442682\pi$
$947$	11.0230	0.358199	0.179099	+	0.983831i	$0.442682\pi$
$948$	4.32957	0.140618
$949$	−2.77891	−0.0902074
$950$	3.17798	0.103107
$951$	6.32488	0.205098
$952$	30.0131	0.972729
$953$	−15.7100	−0.508898	−0.254449	−	0.967086i	$-0.581894\pi$
$953$	−15.7100	−0.508898	−0.254449	+	0.967086i	$0.581894\pi$
$954$	−25.7260	−0.832909
$955$	−5.19234	−0.168020
$956$	−6.69053	−0.216387
$957$	−1.84948	−0.0597851
$958$	−27.4986	−0.888440
$959$	24.1558	0.780032
$960$	−3.54012	−0.114257
$961$	−29.0849	−0.938224
$962$	−1.17702	−0.0379487
$963$	−3.55795	−0.114653
$964$	4.13593	0.133209
$965$	−1.59916	−0.0514788
$966$	24.3389	0.783091
$967$	30.3705	0.976651	0.488325	−	0.872662i	$-0.337608\pi$
$967$	30.3705	0.976651	0.488325	+	0.872662i	$0.337608\pi$
$968$	−19.7109	−0.633533
$969$	−1.43872	−0.0462184
$970$	9.93240	0.318910
$971$	9.66019	0.310010	0.155005	−	0.987914i	$-0.450461\pi$
$971$	9.66019	0.310010	0.155005	+	0.987914i	$0.450461\pi$
$972$	−4.28470	−0.137432
$973$	−3.56628	−0.114330
$974$	43.2373	1.38541
$975$	−2.56941	−0.0822871
$976$	−45.1868	−1.44639
$977$	−58.1945	−1.86181	−0.930904	−	0.365264i	$-0.880979\pi$
$977$	−58.1945	−1.86181	−0.930904	+	0.365264i	$0.880979\pi$
$978$	−13.9580	−0.446326
$979$	−15.3850	−0.491708
$980$	0.815811	0.0260601
$981$	−21.4228	−0.683977
$982$	11.7993	0.376531
$983$	−40.7163	−1.29865	−0.649324	−	0.760512i	$-0.724948\pi$
$983$	−40.7163	−1.29865	−0.649324	+	0.760512i	$0.724948\pi$
$984$	12.4652	0.397375
$985$	−3.55434	−0.113251
$986$	4.85779	0.154704
$987$	42.4349	1.35072
$988$	−0.0654714	−0.00208292
$989$	−8.37906	−0.266439
$990$	−2.99054	−0.0950455
$991$	3.01736	0.0958495	0.0479248	−	0.998851i	$-0.484739\pi$
$991$	3.01736	0.0958495	0.0479248	+	0.998851i	$0.484739\pi$
$992$	−2.08112	−0.0660755
$993$	−5.13463	−0.162942
$994$	−35.7369	−1.13351
$995$	2.95847	0.0937899
$996$	4.63997	0.147023
$997$	−32.4003	−1.02613	−0.513064	−	0.858350i	$-0.671490\pi$
$997$	−32.4003	−1.02613	−0.513064	+	0.858350i	$0.671490\pi$
$998$	−49.3250	−1.56136
$999$	−7.13303	−0.225679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.16	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.16	✓	61	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-1.50584 q^{2} -0.996538 q^{3} +0.267567 q^{4} +0.533194 q^{5} +1.50063 q^{6} +3.56628 q^{7} +2.60877 q^{8} -2.00691 q^{9} +O(q^{10})\)	\(q-1.50584 q^{2} -0.996538 q^{3} +0.267567 q^{4} +0.533194 q^{5} +1.50063 q^{6} +3.56628 q^{7} +2.60877 q^{8} -2.00691 q^{9} -0.802908 q^{10} -1.85590 q^{11} -0.266641 q^{12} -0.546756 q^{13} -5.37026 q^{14} -0.531348 q^{15} -4.46354 q^{16} +3.22596 q^{17} +3.02210 q^{18} +0.447533 q^{19} +0.142665 q^{20} -3.55393 q^{21} +2.79470 q^{22} +4.54791 q^{23} -2.59974 q^{24} -4.71570 q^{25} +0.823330 q^{26} +4.98958 q^{27} +0.954220 q^{28} -1.00000 q^{29} +0.800128 q^{30} -1.38386 q^{31} +1.50385 q^{32} +1.84948 q^{33} -4.85779 q^{34} +1.90152 q^{35} -0.536984 q^{36} -1.42959 q^{37} -0.673915 q^{38} +0.544863 q^{39} +1.39098 q^{40} -4.79477 q^{41} +5.35167 q^{42} -1.84240 q^{43} -0.496579 q^{44} -1.07007 q^{45} -6.84844 q^{46} -11.9403 q^{47} +4.44809 q^{48} +5.71835 q^{49} +7.10112 q^{50} -3.21479 q^{51} -0.146294 q^{52} -8.51261 q^{53} -7.51353 q^{54} -0.989557 q^{55} +9.30362 q^{56} -0.445983 q^{57} +1.50584 q^{58} +0.183189 q^{59} -0.142171 q^{60} +10.1235 q^{61} +2.08387 q^{62} -7.15721 q^{63} +6.66252 q^{64} -0.291527 q^{65} -2.78502 q^{66} -0.991572 q^{67} +0.863161 q^{68} -4.53216 q^{69} -2.86339 q^{70} +6.65460 q^{71} -5.23558 q^{72} +5.08255 q^{73} +2.15273 q^{74} +4.69938 q^{75} +0.119745 q^{76} -6.61867 q^{77} -0.820479 q^{78} -16.2374 q^{79} -2.37994 q^{80} +1.04844 q^{81} +7.22018 q^{82} -17.4016 q^{83} -0.950916 q^{84} +1.72006 q^{85} +2.77437 q^{86} +0.996538 q^{87} -4.84163 q^{88} +8.28978 q^{89} +1.61137 q^{90} -1.94988 q^{91} +1.21687 q^{92} +1.37906 q^{93} +17.9802 q^{94} +0.238622 q^{95} -1.49865 q^{96} -12.3705 q^{97} -8.61094 q^{98} +3.72463 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * q^99

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