LMFDB - Embedded newform 4031.2.a.c.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.10281 q^{2} -1.04272 q^{3} +2.42182 q^{4} +3.50696 q^{5} +2.19264 q^{6} -3.91864 q^{7} -0.887016 q^{8} -1.91274 q^{9} +O(q^{10})$	\(q-2.10281 q^{2} -1.04272 q^{3} +2.42182 q^{4} +3.50696 q^{5} +2.19264 q^{6} -3.91864 q^{7} -0.887016 q^{8} -1.91274 q^{9} -7.37448 q^{10} -0.686935 q^{11} -2.52528 q^{12} -0.0835199 q^{13} +8.24017 q^{14} -3.65677 q^{15} -2.97842 q^{16} -6.13443 q^{17} +4.02213 q^{18} -2.60752 q^{19} +8.49323 q^{20} +4.08604 q^{21} +1.44450 q^{22} +6.11523 q^{23} +0.924909 q^{24} +7.29875 q^{25} +0.175627 q^{26} +5.12260 q^{27} -9.49026 q^{28} -1.00000 q^{29} +7.68951 q^{30} +8.22281 q^{31} +8.03709 q^{32} +0.716281 q^{33} +12.8996 q^{34} -13.7425 q^{35} -4.63231 q^{36} +3.10413 q^{37} +5.48312 q^{38} +0.0870878 q^{39} -3.11073 q^{40} +2.48308 q^{41} -8.59219 q^{42} +3.60914 q^{43} -1.66364 q^{44} -6.70789 q^{45} -12.8592 q^{46} +4.95268 q^{47} +3.10565 q^{48} +8.35576 q^{49} -15.3479 q^{50} +6.39649 q^{51} -0.202271 q^{52} +2.09829 q^{53} -10.7719 q^{54} -2.40905 q^{55} +3.47590 q^{56} +2.71891 q^{57} +2.10281 q^{58} +0.107135 q^{59} -8.85606 q^{60} +5.60696 q^{61} -17.2910 q^{62} +7.49533 q^{63} -10.9437 q^{64} -0.292901 q^{65} -1.50620 q^{66} +4.35469 q^{67} -14.8565 q^{68} -6.37647 q^{69} +28.8979 q^{70} -13.1621 q^{71} +1.69663 q^{72} -6.23169 q^{73} -6.52740 q^{74} -7.61055 q^{75} -6.31495 q^{76} +2.69185 q^{77} -0.183129 q^{78} +7.29203 q^{79} -10.4452 q^{80} +0.396773 q^{81} -5.22146 q^{82} +0.984862 q^{83} +9.89568 q^{84} -21.5132 q^{85} -7.58935 q^{86} +1.04272 q^{87} +0.609323 q^{88} -12.9439 q^{89} +14.1054 q^{90} +0.327285 q^{91} +14.8100 q^{92} -8.57408 q^{93} -10.4146 q^{94} -9.14446 q^{95} -8.38043 q^{96} -10.0691 q^{97} -17.5706 q^{98} +1.31393 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.10281	−1.48691	−0.743457	−	0.668784i	$-0.766815\pi$
$2$	−2.10281	−1.48691	−0.743457	+	0.668784i	$0.766815\pi$
$3$	−1.04272	−0.602014	−0.301007	−	0.953622i	$-0.597323\pi$
$3$	−1.04272	−0.602014	−0.301007	+	0.953622i	$0.597323\pi$
$4$	2.42182	1.21091
$5$	3.50696	1.56836	0.784180	−	0.620534i	$-0.213084\pi$
$5$	3.50696	1.56836	0.784180	+	0.620534i	$0.213084\pi$
$6$	2.19264	0.895143
$7$	−3.91864	−1.48111	−0.740554	−	0.671997i	$-0.765437\pi$
$7$	−3.91864	−1.48111	−0.740554	+	0.671997i	$0.765437\pi$
$8$	−0.887016	−0.313608
$9$	−1.91274	−0.637579
$10$	−7.37448	−2.33201
$11$	−0.686935	−0.207119	−0.103559	−	0.994623i	$-0.533023\pi$
$11$	−0.686935	−0.207119	−0.103559	+	0.994623i	$0.533023\pi$
$12$	−2.52528	−0.728986
$13$	−0.0835199	−0.0231643	−0.0115821	−	0.999933i	$-0.503687\pi$
$13$	−0.0835199	−0.0231643	−0.0115821	+	0.999933i	$0.503687\pi$
$14$	8.24017	2.20228
$15$	−3.65677	−0.944174
$16$	−2.97842	−0.744604
$17$	−6.13443	−1.48782	−0.743909	−	0.668281i	$-0.767030\pi$
$17$	−6.13443	−1.48782	−0.743909	+	0.668281i	$0.767030\pi$
$18$	4.02213	0.948025
$19$	−2.60752	−0.598206	−0.299103	−	0.954221i	$-0.596687\pi$
$19$	−2.60752	−0.598206	−0.299103	+	0.954221i	$0.596687\pi$
$20$	8.49323	1.89914
$21$	4.08604	0.891648
$22$	1.44450	0.307968
$23$	6.11523	1.27511	0.637557	−	0.770403i	$-0.279945\pi$
$23$	6.11523	1.27511	0.637557	+	0.770403i	$0.279945\pi$
$24$	0.924909	0.188796
$25$	7.29875	1.45975
$26$	0.175627	0.0344433
$27$	5.12260	0.985846
$28$	−9.49026	−1.79349
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	7.68951	1.40391
$31$	8.22281	1.47686	0.738430	−	0.674330i	$-0.235567\pi$
$31$	8.22281	1.47686	0.738430	+	0.674330i	$0.235567\pi$
$32$	8.03709	1.42077
$33$	0.716281	0.124688
$34$	12.8996	2.21226
$35$	−13.7425	−2.32291
$36$	−4.63231	−0.772052
$37$	3.10413	0.510315	0.255158	−	0.966899i	$-0.417873\pi$
$37$	3.10413	0.510315	0.255158	+	0.966899i	$0.417873\pi$
$38$	5.48312	0.889480
$39$	0.0870878	0.0139452
$40$	−3.11073	−0.491849
$41$	2.48308	0.387792	0.193896	−	0.981022i	$-0.437888\pi$
$41$	2.48308	0.387792	0.193896	+	0.981022i	$0.437888\pi$
$42$	−8.59219	−1.32580
$43$	3.60914	0.550389	0.275194	−	0.961389i	$-0.411258\pi$
$43$	3.60914	0.550389	0.275194	+	0.961389i	$0.411258\pi$
$44$	−1.66364	−0.250803
$45$	−6.70789	−0.999953
$46$	−12.8592	−1.89598
$47$	4.95268	0.722422	0.361211	−	0.932484i	$-0.382363\pi$
$47$	4.95268	0.722422	0.361211	+	0.932484i	$0.382363\pi$
$48$	3.10565	0.448262
$49$	8.35576	1.19368
$50$	−15.3479	−2.17052
$51$	6.39649	0.895688
$52$	−0.202271	−0.0280499
$53$	2.09829	0.288222	0.144111	−	0.989562i	$-0.453968\pi$
$53$	2.09829	0.288222	0.144111	+	0.989562i	$0.453968\pi$
$54$	−10.7719	−1.46587
$55$	−2.40905	−0.324837
$56$	3.47590	0.464487
$57$	2.71891	0.360128
$58$	2.10281	0.276113
$59$	0.107135	0.0139479	0.00697393	−	0.999976i	$-0.497780\pi$
$59$	0.107135	0.0139479	0.00697393	+	0.999976i	$0.497780\pi$
$60$	−8.85606	−1.14331
$61$	5.60696	0.717898	0.358949	−	0.933357i	$-0.383135\pi$
$61$	5.60696	0.717898	0.358949	+	0.933357i	$0.383135\pi$
$62$	−17.2910	−2.19596
$63$	7.49533	0.944323
$64$	−10.9437	−1.36796
$65$	−0.292901	−0.0363299
$66$	−1.50620	−0.185401
$67$	4.35469	0.532010	0.266005	−	0.963972i	$-0.414296\pi$
$67$	4.35469	0.532010	0.266005	+	0.963972i	$0.414296\pi$
$68$	−14.8565	−1.80162
$69$	−6.37647	−0.767637
$70$	28.8979	3.45396
$71$	−13.1621	−1.56205	−0.781027	−	0.624497i	$-0.785304\pi$
$71$	−13.1621	−1.56205	−0.781027	+	0.624497i	$0.785304\pi$
$72$	1.69663	0.199950
$73$	−6.23169	−0.729364	−0.364682	−	0.931132i	$-0.618822\pi$
$73$	−6.23169	−0.729364	−0.364682	+	0.931132i	$0.618822\pi$
$74$	−6.52740	−0.758795
$75$	−7.61055	−0.878791
$76$	−6.31495	−0.724374
$77$	2.69185	0.306765
$78$	−0.183129	−0.0207353
$79$	7.29203	0.820417	0.410209	−	0.911992i	$-0.365456\pi$
$79$	7.29203	0.820417	0.410209	+	0.911992i	$0.365456\pi$
$80$	−10.4452	−1.16781
$81$	0.396773	0.0440858
$82$	−5.22146	−0.576614
$83$	0.984862	0.108103	0.0540513	−	0.998538i	$-0.482787\pi$
$83$	0.984862	0.108103	0.0540513	+	0.998538i	$0.482787\pi$
$84$	9.89568	1.07971
$85$	−21.5132	−2.33343
$86$	−7.58935	−0.818381
$87$	1.04272	0.111791
$88$	0.609323	0.0649541
$89$	−12.9439	−1.37205	−0.686026	−	0.727577i	$-0.740646\pi$
$89$	−12.9439	−1.37205	−0.686026	+	0.727577i	$0.740646\pi$
$90$	14.1054	1.48684
$91$	0.327285	0.0343088
$92$	14.8100	1.54405
$93$	−8.57408	−0.889091
$94$	−10.4146	−1.07418
$95$	−9.14446	−0.938202
$96$	−8.38043	−0.855324
$97$	−10.0691	−1.02236	−0.511179	−	0.859475i	$-0.670791\pi$
$97$	−10.0691	−1.02236	−0.511179	+	0.859475i	$0.670791\pi$
$98$	−17.5706	−1.77490
$99$	1.31393	0.132055
$100$	17.6763	1.76763
$101$	−7.28969	−0.725351	−0.362675	−	0.931916i	$-0.618137\pi$
$101$	−7.28969	−0.725351	−0.362675	+	0.931916i	$0.618137\pi$
$102$	−13.4506	−1.33181
$103$	0.147878	0.0145708	0.00728542	−	0.999973i	$-0.497681\pi$
$103$	0.147878	0.0145708	0.00728542	+	0.999973i	$0.497681\pi$
$104$	0.0740836	0.00726449
$105$	14.3296	1.39842
$106$	−4.41231	−0.428562
$107$	−0.866579	−0.0837754	−0.0418877	−	0.999122i	$-0.513337\pi$
$107$	−0.866579	−0.0837754	−0.0418877	+	0.999122i	$0.513337\pi$
$108$	12.4060	1.19377
$109$	−1.24876	−0.119610	−0.0598048	−	0.998210i	$-0.519048\pi$
$109$	−1.24876	−0.119610	−0.0598048	+	0.998210i	$0.519048\pi$
$110$	5.06579	0.483004
$111$	−3.23673	−0.307217
$112$	11.6714	1.10284
$113$	−8.99068	−0.845772	−0.422886	−	0.906183i	$-0.638983\pi$
$113$	−8.99068	−0.845772	−0.422886	+	0.906183i	$0.638983\pi$
$114$	−5.71736	−0.535480
$115$	21.4459	1.99984
$116$	−2.42182	−0.224861
$117$	0.159752	0.0147690
$118$	−0.225286	−0.0207392
$119$	24.0386	2.20362
$120$	3.24362	0.296100
$121$	−10.5281	−0.957102
$122$	−11.7904	−1.06745
$123$	−2.58916	−0.233456
$124$	19.9142	1.78835
$125$	8.06163	0.721054
$126$	−15.7613	−1.40413
$127$	3.40450	0.302101	0.151050	−	0.988526i	$-0.451734\pi$
$127$	3.40450	0.302101	0.151050	+	0.988526i	$0.451734\pi$
$128$	6.93830	0.613265
$129$	−3.76332	−0.331342
$130$	0.615916	0.0540194
$131$	−3.71368	−0.324465	−0.162233	−	0.986753i	$-0.551870\pi$
$131$	−3.71368	−0.324465	−0.162233	+	0.986753i	$0.551870\pi$
$132$	1.73471	0.150987
$133$	10.2179	0.886007
$134$	−9.15710	−0.791053
$135$	17.9648	1.54616
$136$	5.44134	0.466591
$137$	19.8097	1.69245	0.846227	−	0.532823i	$-0.178869\pi$
$137$	19.8097	1.69245	0.846227	+	0.532823i	$0.178869\pi$
$138$	13.4085	1.14141
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	−33.2819	−2.81284
$141$	−5.16425	−0.434908
$142$	27.6774	2.32264
$143$	0.0573728	0.00479776
$144$	5.69693	0.474744
$145$	−3.50696	−0.291237
$146$	13.1041	1.08450
$147$	−8.71271	−0.718612
$148$	7.51765	0.617947
$149$	−5.54235	−0.454047	−0.227023	−	0.973889i	$-0.572899\pi$
$149$	−5.54235	−0.454047	−0.227023	+	0.973889i	$0.572899\pi$
$150$	16.0036	1.30669
$151$	−9.93145	−0.808210	−0.404105	−	0.914713i	$-0.632417\pi$
$151$	−9.93145	−0.808210	−0.404105	+	0.914713i	$0.632417\pi$
$152$	2.31291	0.187602
$153$	11.7336	0.948602
$154$	−5.66047	−0.456133
$155$	28.8370	2.31625
$156$	0.210911	0.0168864
$157$	−8.23938	−0.657574	−0.328787	−	0.944404i	$-0.606640\pi$
$157$	−8.23938	−0.657574	−0.328787	+	0.944404i	$0.606640\pi$
$158$	−15.3338	−1.21989
$159$	−2.18793	−0.173514
$160$	28.1857	2.22828
$161$	−23.9634	−1.88858
$162$	−0.834339	−0.0655518
$163$	5.27298	0.413012	0.206506	−	0.978445i	$-0.433791\pi$
$163$	5.27298	0.413012	0.206506	+	0.978445i	$0.433791\pi$
$164$	6.01359	0.469582
$165$	2.51197	0.195556
$166$	−2.07098	−0.160739
$167$	−7.03096	−0.544072	−0.272036	−	0.962287i	$-0.587697\pi$
$167$	−7.03096	−0.544072	−0.272036	+	0.962287i	$0.587697\pi$
$168$	−3.62439	−0.279628
$169$	−12.9930	−0.999463
$170$	45.2382	3.46961
$171$	4.98750	0.381403
$172$	8.74070	0.666472
$173$	−12.9429	−0.984028	−0.492014	−	0.870587i	$-0.663739\pi$
$173$	−12.9429	−0.984028	−0.492014	+	0.870587i	$0.663739\pi$
$174$	−2.19264	−0.166224
$175$	−28.6012	−2.16205
$176$	2.04598	0.154222
$177$	−0.111712	−0.00839680
$178$	27.2186	2.04012
$179$	−8.23835	−0.615763	−0.307882	−	0.951425i	$-0.599620\pi$
$179$	−8.23835	−0.615763	−0.307882	+	0.951425i	$0.599620\pi$
$180$	−16.2453	−1.21085
$181$	−2.63754	−0.196047	−0.0980234	−	0.995184i	$-0.531252\pi$
$181$	−2.63754	−0.196047	−0.0980234	+	0.995184i	$0.531252\pi$
$182$	−0.688219	−0.0510142
$183$	−5.84649	−0.432185
$184$	−5.42431	−0.399886
$185$	10.8860	0.800358
$186$	18.0297	1.32200
$187$	4.21396	0.308155
$188$	11.9945	0.874790
$189$	−20.0737	−1.46014
$190$	19.2291	1.39502
$191$	−9.09683	−0.658223	−0.329112	−	0.944291i	$-0.606749\pi$
$191$	−9.09683	−0.658223	−0.329112	+	0.944291i	$0.606749\pi$
$192$	11.4112	0.823530
$193$	4.90942	0.353388	0.176694	−	0.984266i	$-0.443460\pi$
$193$	4.90942	0.353388	0.176694	+	0.984266i	$0.443460\pi$
$194$	21.1733	1.52016
$195$	0.305413	0.0218711
$196$	20.2362	1.44544
$197$	−10.4899	−0.747376	−0.373688	−	0.927554i	$-0.621907\pi$
$197$	−10.4899	−0.747376	−0.373688	+	0.927554i	$0.621907\pi$
$198$	−2.76294	−0.196354
$199$	−6.71681	−0.476142	−0.238071	−	0.971248i	$-0.576515\pi$
$199$	−6.71681	−0.476142	−0.238071	+	0.971248i	$0.576515\pi$
$200$	−6.47411	−0.457789
$201$	−4.54072	−0.320277
$202$	15.3288	1.07853
$203$	3.91864	0.275035
$204$	15.4912	1.08460
$205$	8.70806	0.608198
$206$	−0.310960	−0.0216656
$207$	−11.6968	−0.812986
$208$	0.248757	0.0172482
$209$	1.79120	0.123900
$210$	−30.1324	−2.07934
$211$	−10.4311	−0.718108	−0.359054	−	0.933317i	$-0.616901\pi$
$211$	−10.4311	−0.718108	−0.359054	+	0.933317i	$0.616901\pi$
$212$	5.08169	0.349012
$213$	13.7244	0.940379
$214$	1.82225	0.124567
$215$	12.6571	0.863207
$216$	−4.54383	−0.309169
$217$	−32.2222	−2.18739
$218$	2.62591	0.177849
$219$	6.49790	0.439087
$220$	−5.83430	−0.393349
$221$	0.512347	0.0344642
$222$	6.80625	0.456805
$223$	18.0043	1.20566	0.602828	−	0.797871i	$-0.294040\pi$
$223$	18.0043	1.20566	0.602828	+	0.797871i	$0.294040\pi$
$224$	−31.4945	−2.10431
$225$	−13.9606	−0.930706
$226$	18.9057	1.25759
$227$	23.4123	1.55393	0.776963	−	0.629546i	$-0.216759\pi$
$227$	23.4123	1.55393	0.776963	+	0.629546i	$0.216759\pi$
$228$	6.58472	0.436084
$229$	16.6858	1.10263	0.551314	−	0.834298i	$-0.314127\pi$
$229$	16.6858	1.10263	0.551314	+	0.834298i	$0.314127\pi$
$230$	−45.0967	−2.97359
$231$	−2.80685	−0.184677
$232$	0.887016	0.0582355
$233$	−3.34132	−0.218897	−0.109449	−	0.993992i	$-0.534909\pi$
$233$	−3.34132	−0.218897	−0.109449	+	0.993992i	$0.534909\pi$
$234$	−0.335928	−0.0219603
$235$	17.3688	1.13302
$236$	0.259463	0.0168896
$237$	−7.60354	−0.493903
$238$	−50.5488	−3.27659
$239$	18.0675	1.16869	0.584344	−	0.811506i	$-0.301352\pi$
$239$	18.0675	1.16869	0.584344	+	0.811506i	$0.301352\pi$
$240$	10.8914	0.703036
$241$	−17.7528	−1.14356	−0.571779	−	0.820407i	$-0.693747\pi$
$241$	−17.7528	−1.14356	−0.571779	+	0.820407i	$0.693747\pi$
$242$	22.1387	1.42313
$243$	−15.7815	−1.01239
$244$	13.5791	0.869311
$245$	29.3033	1.87212
$246$	5.44451	0.347130
$247$	0.217780	0.0138570
$248$	−7.29377	−0.463155
$249$	−1.02693	−0.0650793
$250$	−16.9521	−1.07215
$251$	9.22426	0.582230	0.291115	−	0.956688i	$-0.405974\pi$
$251$	9.22426	0.582230	0.291115	+	0.956688i	$0.405974\pi$
$252$	18.1524	1.14349
$253$	−4.20077	−0.264100
$254$	−7.15903	−0.449198
$255$	22.4322	1.40476
$256$	7.29737	0.456086
$257$	−5.31611	−0.331610	−0.165805	−	0.986159i	$-0.553022\pi$
$257$	−5.31611	−0.331610	−0.165805	+	0.986159i	$0.553022\pi$
$258$	7.91356	0.492677
$259$	−12.1640	−0.755832
$260$	−0.709354	−0.0439923
$261$	1.91274	0.118395
$262$	7.80917	0.482452
$263$	−0.378874	−0.0233624	−0.0116812	−	0.999932i	$-0.503718\pi$
$263$	−0.378874	−0.0233624	−0.0116812	+	0.999932i	$0.503718\pi$
$264$	−0.635353	−0.0391033
$265$	7.35862	0.452036
$266$	−21.4864	−1.31742
$267$	13.4969	0.825994
$268$	10.5463	0.644217
$269$	19.8767	1.21190	0.605952	−	0.795501i	$-0.292792\pi$
$269$	19.8767	1.21190	0.605952	+	0.795501i	$0.292792\pi$
$270$	−37.7765	−2.29901
$271$	−15.6441	−0.950311	−0.475155	−	0.879902i	$-0.657608\pi$
$271$	−15.6441	−0.950311	−0.475155	+	0.879902i	$0.657608\pi$
$272$	18.2709	1.10784
$273$	−0.341266	−0.0206544
$274$	−41.6560	−2.51653
$275$	−5.01377	−0.302342
$276$	−15.4427	−0.929541
$277$	11.8379	0.711271	0.355635	−	0.934625i	$-0.384264\pi$
$277$	11.8379	0.711271	0.355635	+	0.934625i	$0.384264\pi$
$278$	2.10281	0.126118
$279$	−15.7281	−0.941615
$280$	12.1898	0.728482
$281$	−25.6727	−1.53150	−0.765752	−	0.643136i	$-0.777633\pi$
$281$	−25.6727	−1.53150	−0.765752	+	0.643136i	$0.777633\pi$
$282$	10.8595	0.646671
$283$	−13.2895	−0.789979	−0.394989	−	0.918686i	$-0.629252\pi$
$283$	−13.2895	−0.789979	−0.394989	+	0.918686i	$0.629252\pi$
$284$	−31.8763	−1.89151
$285$	9.53510	0.564811
$286$	−0.120644	−0.00713385
$287$	−9.73031	−0.574362
$288$	−15.3728	−0.905853
$289$	20.6313	1.21360
$290$	7.37448	0.433044
$291$	10.4992	0.615474
$292$	−15.0920	−0.883195
$293$	1.18986	0.0695124	0.0347562	−	0.999396i	$-0.488935\pi$
$293$	1.18986	0.0695124	0.0347562	+	0.999396i	$0.488935\pi$
$294$	18.3212	1.06851
$295$	0.375720	0.0218752
$296$	−2.75341	−0.160039
$297$	−3.51890	−0.204187
$298$	11.6545	0.675128
$299$	−0.510744	−0.0295371
$300$	−18.4314	−1.06414
$301$	−14.1429	−0.815185
$302$	20.8840	1.20174
$303$	7.60109	0.436671
$304$	7.76628	0.445427
$305$	19.6634	1.12592
$306$	−24.6735	−1.41049
$307$	7.28607	0.415838	0.207919	−	0.978146i	$-0.433331\pi$
$307$	7.28607	0.415838	0.207919	+	0.978146i	$0.433331\pi$
$308$	6.51920	0.371466
$309$	−0.154195	−0.00877185
$310$	−60.6389	−3.44406
$311$	−2.83001	−0.160475	−0.0802375	−	0.996776i	$-0.525568\pi$
$311$	−2.83001	−0.160475	−0.0802375	+	0.996776i	$0.525568\pi$
$312$	−0.0772484	−0.00437333
$313$	−22.1222	−1.25042	−0.625211	−	0.780456i	$-0.714987\pi$
$313$	−22.1222	−1.25042	−0.625211	+	0.780456i	$0.714987\pi$
$314$	17.3259	0.977756
$315$	26.2858	1.48104
$316$	17.6600	0.993453
$317$	3.17373	0.178254	0.0891272	−	0.996020i	$-0.471592\pi$
$317$	3.17373	0.178254	0.0891272	+	0.996020i	$0.471592\pi$
$318$	4.60080	0.258000
$319$	0.686935	0.0384610
$320$	−38.3790	−2.14545
$321$	0.903599	0.0504340
$322$	50.3906	2.80816
$323$	15.9956	0.890021
$324$	0.960913	0.0533841
$325$	−0.609591	−0.0338141
$326$	−11.0881	−0.614113
$327$	1.30211	0.0720067
$328$	−2.20253	−0.121615
$329$	−19.4078	−1.06999
$330$	−5.28220	−0.290775
$331$	−36.1564	−1.98734	−0.993668	−	0.112358i	$-0.964160\pi$
$331$	−36.1564	−1.98734	−0.993668	+	0.112358i	$0.964160\pi$
$332$	2.38516	0.130903
$333$	−5.93738	−0.325366
$334$	14.7848	0.808988
$335$	15.2717	0.834383
$336$	−12.1699	−0.663925
$337$	−17.4664	−0.951455	−0.475728	−	0.879593i	$-0.657815\pi$
$337$	−17.4664	−0.951455	−0.475728	+	0.879593i	$0.657815\pi$
$338$	27.3219	1.48612
$339$	9.37475	0.509167
$340$	−52.1012	−2.82558
$341$	−5.64854	−0.305886
$342$	−10.4878	−0.567114
$343$	−5.31273	−0.286860
$344$	−3.20137	−0.172606
$345$	−22.3620	−1.20393
$346$	27.2164	1.46316
$347$	−19.8394	−1.06503	−0.532517	−	0.846419i	$-0.678754\pi$
$347$	−19.8394	−1.06503	−0.532517	+	0.846419i	$0.678754\pi$
$348$	2.52528	0.135369
$349$	−27.3702	−1.46509	−0.732547	−	0.680717i	$-0.761668\pi$
$349$	−27.3702	−1.46509	−0.732547	+	0.680717i	$0.761668\pi$
$350$	60.1430	3.21478
$351$	−0.427840	−0.0228364
$352$	−5.52096	−0.294268
$353$	7.01146	0.373182	0.186591	−	0.982438i	$-0.440256\pi$
$353$	7.01146	0.373182	0.186591	+	0.982438i	$0.440256\pi$
$354$	0.234910	0.0124853
$355$	−46.1589	−2.44986
$356$	−31.3479	−1.66143
$357$	−25.0656	−1.32661
$358$	17.3237	0.915587
$359$	−26.2224	−1.38397	−0.691983	−	0.721913i	$-0.743263\pi$
$359$	−26.2224	−1.38397	−0.691983	+	0.721913i	$0.743263\pi$
$360$	5.95001	0.313593
$361$	−12.2008	−0.642150
$362$	5.54626	0.291505
$363$	10.9779	0.576189
$364$	0.792626	0.0415449
$365$	−21.8543	−1.14390
$366$	12.2941	0.642621
$367$	−8.27547	−0.431976	−0.215988	−	0.976396i	$-0.569297\pi$
$367$	−8.27547	−0.431976	−0.215988	+	0.976396i	$0.569297\pi$
$368$	−18.2137	−0.949456
$369$	−4.74948	−0.247248
$370$	−22.8913	−1.19006
$371$	−8.22245	−0.426888
$372$	−20.7649	−1.07661
$373$	−23.9075	−1.23788	−0.618942	−	0.785437i	$-0.712438\pi$
$373$	−23.9075	−1.23788	−0.618942	+	0.785437i	$0.712438\pi$
$374$	−8.86117	−0.458200
$375$	−8.40602	−0.434085
$376$	−4.39311	−0.226557
$377$	0.0835199	0.00430150
$378$	42.2111	2.17111
$379$	−5.46090	−0.280508	−0.140254	−	0.990116i	$-0.544792\pi$
$379$	−5.46090	−0.280508	−0.140254	+	0.990116i	$0.544792\pi$
$380$	−22.1463	−1.13608
$381$	−3.54994	−0.181869
$382$	19.1289	0.978721
$383$	−25.3897	−1.29735	−0.648677	−	0.761064i	$-0.724677\pi$
$383$	−25.3897	−1.29735	−0.648677	+	0.761064i	$0.724677\pi$
$384$	−7.23470	−0.369194
$385$	9.44022	0.481118
$386$	−10.3236	−0.525457
$387$	−6.90334	−0.350916
$388$	−24.3855	−1.23798
$389$	12.6637	0.642076	0.321038	−	0.947066i	$-0.395968\pi$
$389$	12.6637	0.642076	0.321038	+	0.947066i	$0.395968\pi$
$390$	−0.642227	−0.0325204
$391$	−37.5135	−1.89714
$392$	−7.41169	−0.374347
$393$	3.87232	0.195333
$394$	22.0583	1.11128
$395$	25.5728	1.28671
$396$	3.18210	0.159906
$397$	−17.3326	−0.869900	−0.434950	−	0.900455i	$-0.643234\pi$
$397$	−17.3326	−0.869900	−0.434950	+	0.900455i	$0.643234\pi$
$398$	14.1242	0.707982
$399$	−10.6544	−0.533389
$400$	−21.7387	−1.08694
$401$	3.45185	0.172377	0.0861885	−	0.996279i	$-0.472531\pi$
$401$	3.45185	0.172377	0.0861885	+	0.996279i	$0.472531\pi$
$402$	9.54828	0.476225
$403$	−0.686769	−0.0342104
$404$	−17.6543	−0.878336
$405$	1.39146	0.0691424
$406$	−8.24017	−0.408953
$407$	−2.13234	−0.105696
$408$	−5.67379	−0.280895
$409$	27.1946	1.34469	0.672343	−	0.740240i	$-0.265288\pi$
$409$	27.1946	1.34469	0.672343	+	0.740240i	$0.265288\pi$
$410$	−18.3114	−0.904337
$411$	−20.6559	−1.01888
$412$	0.358134	0.0176440
$413$	−0.419826	−0.0206583
$414$	24.5963	1.20884
$415$	3.45387	0.169544
$416$	−0.671257	−0.0329111
$417$	1.04272	0.0510622
$418$	−3.76655	−0.184228
$419$	35.8510	1.75143	0.875717	−	0.482824i	$-0.160389\pi$
$419$	35.8510	1.75143	0.875717	+	0.482824i	$0.160389\pi$
$420$	34.7037	1.69337
$421$	−36.3630	−1.77222	−0.886111	−	0.463473i	$-0.846603\pi$
$421$	−36.3630	−1.77222	−0.886111	+	0.463473i	$0.846603\pi$
$422$	21.9347	1.06776
$423$	−9.47317	−0.460601
$424$	−1.86122	−0.0903887
$425$	−44.7737	−2.17184
$426$	−28.8598	−1.39826
$427$	−21.9717	−1.06328
$428$	−2.09870	−0.101445
$429$	−0.0598237	−0.00288832
$430$	−26.6155	−1.28351
$431$	0.321407	0.0154816	0.00774081	−	0.999970i	$-0.497536\pi$
$431$	0.321407	0.0154816	0.00774081	+	0.999970i	$0.497536\pi$
$432$	−15.2573	−0.734065
$433$	29.1376	1.40027	0.700133	−	0.714012i	$-0.253124\pi$
$433$	29.1376	1.40027	0.700133	+	0.714012i	$0.253124\pi$
$434$	67.7574	3.25246
$435$	3.65677	0.175329
$436$	−3.02428	−0.144837
$437$	−15.9456	−0.762781
$438$	−13.6639	−0.652885
$439$	−18.5092	−0.883395	−0.441697	−	0.897164i	$-0.645624\pi$
$439$	−18.5092	−0.883395	−0.441697	+	0.897164i	$0.645624\pi$
$440$	2.13687	0.101871
$441$	−15.9824	−0.761065
$442$	−1.07737	−0.0512453
$443$	22.5793	1.07277	0.536387	−	0.843972i	$-0.319789\pi$
$443$	22.5793	1.07277	0.536387	+	0.843972i	$0.319789\pi$
$444$	−7.83880	−0.372013
$445$	−45.3937	−2.15187
$446$	−37.8597	−1.79271
$447$	5.77911	0.273343
$448$	42.8843	2.02609
$449$	19.2916	0.910429	0.455215	−	0.890382i	$-0.349563\pi$
$449$	19.2916	0.910429	0.455215	+	0.890382i	$0.349563\pi$
$450$	29.3565	1.38388
$451$	−1.70572	−0.0803191
$452$	−21.7738	−1.02416
$453$	10.3557	0.486554
$454$	−49.2316	−2.31055
$455$	1.14777	0.0538085
$456$	−2.41172	−0.112939
$457$	10.7219	0.501550	0.250775	−	0.968045i	$-0.419315\pi$
$457$	10.7219	0.501550	0.250775	+	0.968045i	$0.419315\pi$
$458$	−35.0871	−1.63951
$459$	−31.4243	−1.46676
$460$	51.9381	2.42163
$461$	−16.9188	−0.787988	−0.393994	−	0.919113i	$-0.628907\pi$
$461$	−16.9188	−0.787988	−0.393994	+	0.919113i	$0.628907\pi$
$462$	5.90228	0.274599
$463$	34.7591	1.61539	0.807697	−	0.589598i	$-0.200714\pi$
$463$	34.7591	1.61539	0.807697	+	0.589598i	$0.200714\pi$
$464$	2.97842	0.138270
$465$	−30.0689	−1.39441
$466$	7.02618	0.325481
$467$	6.99023	0.323469	0.161735	−	0.986834i	$-0.448291\pi$
$467$	6.99023	0.323469	0.161735	+	0.986834i	$0.448291\pi$
$468$	0.386890	0.0178840
$469$	−17.0645	−0.787964
$470$	−36.5234	−1.68470
$471$	8.59136	0.395869
$472$	−0.0950309	−0.00437415
$473$	−2.47925	−0.113996
$474$	15.9888	0.734391
$475$	−19.0316	−0.873231
$476$	58.2174	2.66839
$477$	−4.01348	−0.183765
$478$	−37.9925	−1.73774
$479$	29.5808	1.35158	0.675790	−	0.737095i	$-0.263803\pi$
$479$	29.5808	1.35158	0.675790	+	0.737095i	$0.263803\pi$
$480$	−29.3898	−1.34145
$481$	−0.259257	−0.0118211
$482$	37.3308	1.70037
$483$	24.9871	1.13695
$484$	−25.4972	−1.15897
$485$	−35.3117	−1.60342
$486$	33.1856	1.50533
$487$	−35.9514	−1.62911	−0.814556	−	0.580085i	$-0.803019\pi$
$487$	−35.9514	−1.62911	−0.814556	+	0.580085i	$0.803019\pi$
$488$	−4.97347	−0.225138
$489$	−5.49824	−0.248639
$490$	−61.6193	−2.78368
$491$	−0.944071	−0.0426053	−0.0213027	−	0.999773i	$-0.506781\pi$
$491$	−0.944071	−0.0426053	−0.0213027	+	0.999773i	$0.506781\pi$
$492$	−6.27048	−0.282695
$493$	6.13443	0.276281
$494$	−0.457950	−0.0206042
$495$	4.60789	0.207109
$496$	−24.4910	−1.09968
$497$	51.5776	2.31357
$498$	2.15945	0.0967673
$499$	17.6273	0.789107	0.394553	−	0.918873i	$-0.370899\pi$
$499$	17.6273	0.789107	0.394553	+	0.918873i	$0.370899\pi$
$500$	19.5238	0.873133
$501$	7.33132	0.327539
$502$	−19.3969	−0.865726
$503$	−9.28633	−0.414057	−0.207028	−	0.978335i	$-0.566379\pi$
$503$	−9.28633	−0.414057	−0.207028	+	0.978335i	$0.566379\pi$
$504$	−6.64848	−0.296147
$505$	−25.5646	−1.13761
$506$	8.83344	0.392694
$507$	13.5481	0.601691
$508$	8.24510	0.365817
$509$	−32.2608	−1.42994	−0.714968	−	0.699157i	$-0.753559\pi$
$509$	−32.2608	−1.42994	−0.714968	+	0.699157i	$0.753559\pi$
$510$	−47.1708	−2.08876
$511$	24.4197	1.08027
$512$	−29.2216	−1.29143
$513$	−13.3573	−0.589739
$514$	11.1788	0.493075
$515$	0.518602	0.0228523
$516$	−9.11410	−0.401226
$517$	−3.40217	−0.149627
$518$	25.5785	1.12386
$519$	13.4958	0.592399
$520$	0.259808	0.0113933
$521$	−6.49922	−0.284736	−0.142368	−	0.989814i	$-0.545472\pi$
$521$	−6.49922	−0.284736	−0.142368	+	0.989814i	$0.545472\pi$
$522$	−4.02213	−0.176044
$523$	−2.79653	−0.122284	−0.0611419	−	0.998129i	$-0.519474\pi$
$523$	−2.79653	−0.122284	−0.0611419	+	0.998129i	$0.519474\pi$
$524$	−8.99387	−0.392899
$525$	29.8230	1.30158
$526$	0.796701	0.0347378
$527$	−50.4423	−2.19730
$528$	−2.13338	−0.0928436
$529$	14.3961	0.625916
$530$	−15.4738	−0.672139
$531$	−0.204922	−0.00889286
$532$	24.7460	1.07288
$533$	−0.207387	−0.00898292
$534$	−28.3814	−1.22818
$535$	−3.03906	−0.131390
$536$	−3.86268	−0.166842
$537$	8.59029	0.370698
$538$	−41.7970	−1.80200
$539$	−5.73987	−0.247234
$540$	43.5075	1.87226
$541$	−13.7229	−0.589996	−0.294998	−	0.955498i	$-0.595319\pi$
$541$	−13.7229	−0.589996	−0.294998	+	0.955498i	$0.595319\pi$
$542$	32.8966	1.41303
$543$	2.75021	0.118023
$544$	−49.3030	−2.11385
$545$	−4.37935	−0.187591
$546$	0.717619	0.0307113
$547$	2.06811	0.0884258	0.0442129	−	0.999022i	$-0.485922\pi$
$547$	2.06811	0.0884258	0.0442129	+	0.999022i	$0.485922\pi$
$548$	47.9755	2.04941
$549$	−10.7246	−0.457717
$550$	10.5430	0.449556
$551$	2.60752	0.111084
$552$	5.65603	0.240737
$553$	−28.5749	−1.21513
$554$	−24.8929	−1.05760
$555$	−11.3511	−0.481827
$556$	−2.42182	−0.102708
$557$	−36.6618	−1.55341	−0.776705	−	0.629864i	$-0.783110\pi$
$557$	−36.6618	−1.55341	−0.776705	+	0.629864i	$0.783110\pi$
$558$	33.0732	1.40010
$559$	−0.301435	−0.0127494
$560$	40.9309	1.72965
$561$	−4.39398	−0.185514
$562$	53.9849	2.27721
$563$	0.432140	0.0182125	0.00910626	−	0.999959i	$-0.497101\pi$
$563$	0.432140	0.0182125	0.00910626	+	0.999959i	$0.497101\pi$
$564$	−12.5069	−0.526636
$565$	−31.5299	−1.32647
$566$	27.9453	1.17463
$567$	−1.55481	−0.0652959
$568$	11.6750	0.489872
$569$	8.64233	0.362305	0.181153	−	0.983455i	$-0.442017\pi$
$569$	8.64233	0.362305	0.181153	+	0.983455i	$0.442017\pi$
$570$	−20.0505	−0.839825
$571$	−8.99945	−0.376615	−0.188308	−	0.982110i	$-0.560300\pi$
$571$	−8.99945	−0.376615	−0.188308	+	0.982110i	$0.560300\pi$
$572$	0.138947	0.00580966
$573$	9.48544	0.396260
$574$	20.4610	0.854027
$575$	44.6336	1.86135
$576$	20.9323	0.872181
$577$	22.2843	0.927709	0.463855	−	0.885911i	$-0.346466\pi$
$577$	22.2843	0.927709	0.463855	+	0.885911i	$0.346466\pi$
$578$	−43.3837	−1.80452
$579$	−5.11914	−0.212744
$580$	−8.49323	−0.352662
$581$	−3.85932	−0.160112
$582$	−22.0778	−0.915156
$583$	−1.44139	−0.0596963
$584$	5.52761	0.228734
$585$	0.560242	0.0231632
$586$	−2.50206	−0.103359
$587$	−29.8291	−1.23118	−0.615590	−	0.788067i	$-0.711082\pi$
$587$	−29.8291	−1.23118	−0.615590	+	0.788067i	$0.711082\pi$
$588$	−21.1006	−0.870176
$589$	−21.4411	−0.883466
$590$	−0.790068	−0.0325266
$591$	10.9380	0.449931
$592$	−9.24539	−0.379983
$593$	17.0650	0.700777	0.350388	−	0.936604i	$-0.386050\pi$
$593$	17.0650	0.700777	0.350388	+	0.936604i	$0.386050\pi$
$594$	7.39959	0.303609
$595$	84.3025	3.45607
$596$	−13.4226	−0.549811
$597$	7.00375	0.286644
$598$	1.07400	0.0439191
$599$	−5.31383	−0.217117	−0.108559	−	0.994090i	$-0.534624\pi$
$599$	−5.31383	−0.217117	−0.108559	+	0.994090i	$0.534624\pi$
$600$	6.75068	0.275595
$601$	−25.0796	−1.02302	−0.511509	−	0.859278i	$-0.670913\pi$
$601$	−25.0796	−1.02302	−0.511509	+	0.859278i	$0.670913\pi$
$602$	29.7399	1.21211
$603$	−8.32937	−0.339198
$604$	−24.0522	−0.978671
$605$	−36.9217	−1.50108
$606$	−15.9837	−0.649293
$607$	47.4201	1.92472	0.962360	−	0.271776i	$-0.0876111\pi$
$607$	47.4201	1.92472	0.962360	+	0.271776i	$0.0876111\pi$
$608$	−20.9569	−0.849913
$609$	−4.08604	−0.165575
$610$	−41.3484	−1.67415
$611$	−0.413647	−0.0167344
$612$	28.4166	1.14867
$613$	28.8690	1.16601	0.583004	−	0.812470i	$-0.301877\pi$
$613$	28.8690	1.16601	0.583004	+	0.812470i	$0.301877\pi$
$614$	−15.3212	−0.618315
$615$	−9.08007	−0.366144
$616$	−2.38772	−0.0962039
$617$	39.7252	1.59928	0.799638	−	0.600483i	$-0.205025\pi$
$617$	39.7252	1.59928	0.799638	+	0.600483i	$0.205025\pi$
$618$	0.324244	0.0130430
$619$	−9.67869	−0.389019	−0.194510	−	0.980901i	$-0.562312\pi$
$619$	−9.67869	−0.389019	−0.194510	+	0.980901i	$0.562312\pi$
$620$	69.8382	2.80477
$621$	31.3259	1.25707
$622$	5.95097	0.238612
$623$	50.7225	2.03216
$624$	−0.259384	−0.0103837
$625$	−8.22197	−0.328879
$626$	46.5189	1.85927
$627$	−1.86772	−0.0745894
$628$	−19.9543	−0.796264
$629$	−19.0421	−0.759257
$630$	−55.2742	−2.20217
$631$	−14.5200	−0.578031	−0.289015	−	0.957324i	$-0.593328\pi$
$631$	−14.5200	−0.578031	−0.289015	+	0.957324i	$0.593328\pi$
$632$	−6.46815	−0.257289
$633$	10.8767	0.432311
$634$	−6.67376	−0.265049
$635$	11.9394	0.473802
$636$	−5.29877	−0.210110
$637$	−0.697872	−0.0276507
$638$	−1.44450	−0.0571882
$639$	25.1756	0.995933
$640$	24.3323	0.961820
$641$	9.89790	0.390944	0.195472	−	0.980709i	$-0.437376\pi$
$641$	9.89790	0.390944	0.195472	+	0.980709i	$0.437376\pi$
$642$	−1.90010	−0.0749909
$643$	15.5904	0.614826	0.307413	−	0.951576i	$-0.400537\pi$
$643$	15.5904	0.614826	0.307413	+	0.951576i	$0.400537\pi$
$644$	−58.0352	−2.28691
$645$	−13.1978	−0.519663
$646$	−33.6359	−1.32338
$647$	42.4093	1.66728	0.833641	−	0.552307i	$-0.186252\pi$
$647$	42.4093	1.66728	0.833641	+	0.552307i	$0.186252\pi$
$648$	−0.351944	−0.0138257
$649$	−0.0735952	−0.00288886
$650$	1.28186	0.0502786
$651$	33.5988	1.31684
$652$	12.7702	0.500121
$653$	27.8273	1.08897	0.544483	−	0.838772i	$-0.316726\pi$
$653$	27.8273	1.08897	0.544483	+	0.838772i	$0.316726\pi$
$654$	−2.73809	−0.107068
$655$	−13.0237	−0.508878
$656$	−7.39565	−0.288752
$657$	11.9196	0.465027
$658$	40.8109	1.59098
$659$	25.8774	1.00804	0.504021	−	0.863691i	$-0.331853\pi$
$659$	25.8774	1.00804	0.504021	+	0.863691i	$0.331853\pi$
$660$	6.08354	0.236801
$661$	−30.2353	−1.17602	−0.588008	−	0.808855i	$-0.700088\pi$
$661$	−30.2353	−1.17602	−0.588008	+	0.808855i	$0.700088\pi$
$662$	76.0302	2.95500
$663$	−0.534234	−0.0207479
$664$	−0.873589	−0.0339018
$665$	35.8339	1.38958
$666$	12.4852	0.483792
$667$	−6.11523	−0.236783
$668$	−17.0277	−0.658823
$669$	−18.7734	−0.725822
$670$	−32.1136	−1.24065
$671$	−3.85162	−0.148690
$672$	32.8399	1.26683
$673$	−2.51537	−0.0969604	−0.0484802	−	0.998824i	$-0.515438\pi$
$673$	−2.51537	−0.0969604	−0.0484802	+	0.998824i	$0.515438\pi$
$674$	36.7286	1.41473
$675$	37.3886	1.43909
$676$	−31.4668	−1.21026
$677$	−2.60433	−0.100093	−0.0500463	−	0.998747i	$-0.515937\pi$
$677$	−2.60433	−0.100093	−0.0500463	+	0.998747i	$0.515937\pi$
$678$	−19.7134	−0.757087
$679$	39.4570	1.51422
$680$	19.0826	0.731783
$681$	−24.4124	−0.935486
$682$	11.8778	0.454825
$683$	19.2096	0.735035	0.367518	−	0.930017i	$-0.380208\pi$
$683$	19.2096	0.735035	0.367518	+	0.930017i	$0.380208\pi$
$684$	12.0788	0.461846
$685$	69.4716	2.65437
$686$	11.1717	0.426537
$687$	−17.3986	−0.663797
$688$	−10.7495	−0.409822
$689$	−0.175249	−0.00667646
$690$	47.0231	1.79014
$691$	−38.0600	−1.44787	−0.723936	−	0.689867i	$-0.757669\pi$
$691$	−38.0600	−1.44787	−0.723936	+	0.689867i	$0.757669\pi$
$692$	−31.3453	−1.19157
$693$	−5.14881	−0.195587
$694$	41.7185	1.58361
$695$	−3.50696	−0.133026
$696$	−0.924909	−0.0350586
$697$	−15.2323	−0.576964
$698$	57.5544	2.17847
$699$	3.48406	0.131779
$700$	−69.2671	−2.61805
$701$	−39.8972	−1.50689	−0.753447	−	0.657508i	$-0.771610\pi$
$701$	−39.8972	−1.50689	−0.753447	+	0.657508i	$0.771610\pi$
$702$	0.899667	0.0339557
$703$	−8.09407	−0.305274
$704$	7.51759	0.283330
$705$	−18.1108	−0.682093
$706$	−14.7438	−0.554890
$707$	28.5657	1.07432
$708$	−0.270547	−0.0101678
$709$	39.0083	1.46499	0.732494	−	0.680773i	$-0.238356\pi$
$709$	39.0083	1.46499	0.732494	+	0.680773i	$0.238356\pi$
$710$	97.0636	3.64273
$711$	−13.9477	−0.523081
$712$	11.4815	0.430286
$713$	50.2844	1.88317
$714$	52.7082	1.97255
$715$	0.201204	0.00752460
$716$	−19.9518	−0.745635
$717$	−18.8393	−0.703567
$718$	55.1409	2.05784
$719$	4.19148	0.156316	0.0781579	−	0.996941i	$-0.475096\pi$
$719$	4.19148	0.156316	0.0781579	+	0.996941i	$0.475096\pi$
$720$	19.9789	0.744569
$721$	−0.579481	−0.0215810
$722$	25.6561	0.954821
$723$	18.5112	0.688438
$724$	−6.38766	−0.237395
$725$	−7.29875	−0.271069
$726$	−23.0844	−0.856743
$727$	20.7800	0.770689	0.385344	−	0.922773i	$-0.374083\pi$
$727$	20.7800	0.770689	0.385344	+	0.922773i	$0.374083\pi$
$728$	−0.290307	−0.0107595
$729$	15.2654	0.565385
$730$	45.9554	1.70089
$731$	−22.1400	−0.818878
$732$	−14.1592	−0.523338
$733$	−12.7192	−0.469794	−0.234897	−	0.972020i	$-0.575475\pi$
$733$	−12.7192	−0.469794	−0.234897	+	0.972020i	$0.575475\pi$
$734$	17.4018	0.642311
$735$	−30.5551	−1.12704
$736$	49.1487	1.81164
$737$	−2.99139	−0.110189
$738$	9.98727	0.367637
$739$	40.3992	1.48611	0.743055	−	0.669231i	$-0.233376\pi$
$739$	40.3992	1.48611	0.743055	+	0.669231i	$0.233376\pi$
$740$	26.3641	0.969163
$741$	−0.227083	−0.00834211
$742$	17.2903	0.634746
$743$	43.4824	1.59521	0.797607	−	0.603178i	$-0.206099\pi$
$743$	43.4824	1.59521	0.797607	+	0.603178i	$0.206099\pi$
$744$	7.60535	0.278826
$745$	−19.4368	−0.712109
$746$	50.2730	1.84063
$747$	−1.88378	−0.0689240
$748$	10.2055	0.373149
$749$	3.39581	0.124080
$750$	17.6763	0.645447
$751$	−13.5066	−0.492864	−0.246432	−	0.969160i	$-0.579258\pi$
$751$	−13.5066	−0.492864	−0.246432	+	0.969160i	$0.579258\pi$
$752$	−14.7511	−0.537919
$753$	−9.61831	−0.350511
$754$	−0.175627	−0.00639595
$755$	−34.8292	−1.26756
$756$	−48.6149	−1.76811
$757$	1.47513	0.0536144	0.0268072	−	0.999641i	$-0.491466\pi$
$757$	1.47513	0.0536144	0.0268072	+	0.999641i	$0.491466\pi$
$758$	11.4833	0.417091
$759$	4.38022	0.158992
$760$	8.11128	0.294227
$761$	22.4140	0.812506	0.406253	−	0.913761i	$-0.366835\pi$
$761$	22.4140	0.812506	0.406253	+	0.913761i	$0.366835\pi$
$762$	7.46486	0.270423
$763$	4.89345	0.177155
$764$	−22.0309	−0.797050
$765$	41.1491	1.48775
$766$	53.3899	1.92905
$767$	−0.00894795	−0.000323092 0
$768$	−7.60911	−0.274570
$769$	−37.8544	−1.36506	−0.682532	−	0.730856i	$-0.739121\pi$
$769$	−37.8544	−1.36506	−0.682532	+	0.730856i	$0.739121\pi$
$770$	−19.8510	−0.715381
$771$	5.54321	0.199634
$772$	11.8897	0.427921
$773$	6.70940	0.241320	0.120660	−	0.992694i	$-0.461499\pi$
$773$	6.70940	0.241320	0.120660	+	0.992694i	$0.461499\pi$
$774$	14.5164	0.521782
$775$	60.0163	2.15585
$776$	8.93141	0.320619
$777$	12.6836	0.455022
$778$	−26.6294	−0.954712
$779$	−6.47468	−0.231980
$780$	0.739657	0.0264840
$781$	9.04151	0.323531
$782$	78.8838	2.82088
$783$	−5.12260	−0.183067
$784$	−24.8869	−0.888819
$785$	−28.8952	−1.03131
$786$	−8.14277	−0.290443
$787$	20.7250	0.738765	0.369382	−	0.929277i	$-0.379569\pi$
$787$	20.7250	0.738765	0.369382	+	0.929277i	$0.379569\pi$
$788$	−25.4047	−0.905006
$789$	0.395059	0.0140645
$790$	−53.7749	−1.91323
$791$	35.2313	1.25268
$792$	−1.16547	−0.0414133
$793$	−0.468293	−0.0166296
$794$	36.4473	1.29347
$795$	−7.67297	−0.272132
$796$	−16.2669	−0.576566
$797$	−2.54925	−0.0902991	−0.0451495	−	0.998980i	$-0.514376\pi$
$797$	−2.54925	−0.0902991	−0.0451495	+	0.998980i	$0.514376\pi$
$798$	22.4043	0.793103
$799$	−30.3819	−1.07483
$800$	58.6607	2.07397
$801$	24.7583	0.874791
$802$	−7.25859	−0.256310
$803$	4.28077	0.151065
$804$	−10.9968	−0.387828
$805$	−84.0387	−2.96197
$806$	1.44415	0.0508679
$807$	−20.7258	−0.729584
$808$	6.46607	0.227476
$809$	43.2595	1.52092	0.760462	−	0.649383i	$-0.224973\pi$
$809$	43.2595	1.52092	0.760462	+	0.649383i	$0.224973\pi$
$810$	−2.92599	−0.102809
$811$	22.8573	0.802630	0.401315	−	0.915940i	$-0.368553\pi$
$811$	22.8573	0.802630	0.401315	+	0.915940i	$0.368553\pi$
$812$	9.49026	0.333043
$813$	16.3124	0.572101
$814$	4.48390	0.157161
$815$	18.4921	0.647751
$816$	−19.0514	−0.666933
$817$	−9.41090	−0.329246
$818$	−57.1852	−1.99943
$819$	−0.626010	−0.0218745
$820$	21.0894	0.736474
$821$	−18.6341	−0.650334	−0.325167	−	0.945657i	$-0.605421\pi$
$821$	−18.6341	−0.650334	−0.325167	+	0.945657i	$0.605421\pi$
$822$	43.4355	1.51499
$823$	−22.0827	−0.769754	−0.384877	−	0.922968i	$-0.625756\pi$
$823$	−22.0827	−0.769754	−0.384877	+	0.922968i	$0.625756\pi$
$824$	−0.131170	−0.00456953
$825$	5.22796	0.182014
$826$	0.882815	0.0307171
$827$	−35.4039	−1.23112	−0.615558	−	0.788092i	$-0.711069\pi$
$827$	−35.4039	−1.23112	−0.615558	+	0.788092i	$0.711069\pi$
$828$	−28.3277	−0.984454
$829$	−51.9060	−1.80277	−0.901385	−	0.433018i	$-0.857449\pi$
$829$	−51.9060	−1.80277	−0.901385	+	0.433018i	$0.857449\pi$
$830$	−7.26284	−0.252097
$831$	−12.3436	−0.428195
$832$	0.914014	0.0316877
$833$	−51.2578	−1.77598
$834$	−2.19264	−0.0759250
$835$	−24.6573	−0.853300
$836$	4.33796	0.150032
$837$	42.1222	1.45596
$838$	−75.3879	−2.60423
$839$	−32.9816	−1.13865	−0.569326	−	0.822112i	$-0.692796\pi$
$839$	−32.9816	−1.13865	−0.569326	+	0.822112i	$0.692796\pi$
$840$	−12.7106	−0.438556
$841$	1.00000	0.0344828
$842$	76.4645	2.63514
$843$	26.7694	0.921987
$844$	−25.2623	−0.869566
$845$	−45.5660	−1.56752
$846$	19.9203	0.684874
$847$	41.2559	1.41757
$848$	−6.24958	−0.214612
$849$	13.8572	0.475578
$850$	94.1507	3.22934
$851$	18.9825	0.650711
$852$	33.2380	1.13872
$853$	−40.7871	−1.39652	−0.698261	−	0.715843i	$-0.746043\pi$
$853$	−40.7871	−1.39652	−0.698261	+	0.715843i	$0.746043\pi$
$854$	46.2023	1.58101
$855$	17.4909	0.598178
$856$	0.768670	0.0262726
$857$	46.5297	1.58942	0.794711	−	0.606987i	$-0.207622\pi$
$857$	46.5297	1.58942	0.794711	+	0.606987i	$0.207622\pi$
$858$	0.125798	0.00429468
$859$	31.4868	1.07432	0.537158	−	0.843481i	$-0.319498\pi$
$859$	31.4868	1.07432	0.537158	+	0.843481i	$0.319498\pi$
$860$	30.6533	1.04527
$861$	10.1460	0.345774
$862$	−0.675859	−0.0230198
$863$	13.7283	0.467316	0.233658	−	0.972319i	$-0.424930\pi$
$863$	13.7283	0.467316	0.233658	+	0.972319i	$0.424930\pi$
$864$	41.1708	1.40066
$865$	−45.3901	−1.54331
$866$	−61.2710	−2.08207
$867$	−21.5126	−0.730606
$868$	−78.0366	−2.64873
$869$	−5.00915	−0.169924
$870$	−7.68951	−0.260699
$871$	−0.363703	−0.0123236
$872$	1.10767	0.0375105
$873$	19.2594	0.651833
$874$	33.5306	1.13419
$875$	−31.5906	−1.06796
$876$	15.7368	0.531696
$877$	8.48767	0.286608	0.143304	−	0.989679i	$-0.454227\pi$
$877$	8.48767	0.286608	0.143304	+	0.989679i	$0.454227\pi$
$878$	38.9213	1.31353
$879$	−1.24069	−0.0418475
$880$	7.17517	0.241875
$881$	34.8625	1.17455	0.587274	−	0.809388i	$-0.300201\pi$
$881$	34.8625	1.17455	0.587274	+	0.809388i	$0.300201\pi$
$882$	33.6079	1.13164
$883$	−30.4512	−1.02476	−0.512382	−	0.858758i	$-0.671237\pi$
$883$	−30.4512	−1.02476	−0.512382	+	0.858758i	$0.671237\pi$
$884$	1.24082	0.0417331
$885$	−0.391770	−0.0131692
$886$	−47.4801	−1.59512
$887$	−22.8188	−0.766180	−0.383090	−	0.923711i	$-0.625140\pi$
$887$	−22.8188	−0.766180	−0.383090	+	0.923711i	$0.625140\pi$
$888$	2.87104	0.0963456
$889$	−13.3410	−0.447444
$890$	95.4546	3.19964
$891$	−0.272557	−0.00913101
$892$	43.6032	1.45994
$893$	−12.9142	−0.432157
$894$	−12.1524	−0.406437
$895$	−28.8916	−0.965738
$896$	−27.1887	−0.908311
$897$	0.532563	0.0177817
$898$	−40.5667	−1.35373
$899$	−8.22281	−0.274246
$900$	−33.8101	−1.12700
$901$	−12.8718	−0.428822
$902$	3.58680	0.119428
$903$	14.7471	0.490753
$904$	7.97488	0.265241
$905$	−9.24974	−0.307472
$906$	−21.7761	−0.723463
$907$	−51.2352	−1.70124	−0.850619	−	0.525783i	$-0.823772\pi$
$907$	−51.2352	−1.70124	−0.850619	+	0.525783i	$0.823772\pi$
$908$	56.7004	1.88167
$909$	13.9433	0.462468
$910$	−2.41355	−0.0800086
$911$	43.8551	1.45298	0.726492	−	0.687175i	$-0.241149\pi$
$911$	43.8551	1.45298	0.726492	+	0.687175i	$0.241149\pi$
$912$	−8.09805	−0.268153
$913$	−0.676537	−0.0223901
$914$	−22.5462	−0.745761
$915$	−20.5034	−0.677821
$916$	40.4100	1.33518
$917$	14.5526	0.480568
$918$	66.0794	2.18094
$919$	−37.0033	−1.22063	−0.610313	−	0.792160i	$-0.708956\pi$
$919$	−37.0033	−1.22063	−0.610313	+	0.792160i	$0.708956\pi$
$920$	−19.0228	−0.627164
$921$	−7.59732	−0.250340
$922$	35.5771	1.17167
$923$	1.09930	0.0361838
$924$	−6.79769	−0.223628
$925$	22.6563	0.744933
$926$	−73.0920	−2.40195
$927$	−0.282851	−0.00929006
$928$	−8.03709	−0.263830
$929$	−47.8652	−1.57041	−0.785203	−	0.619239i	$-0.787441\pi$
$929$	−47.8652	−1.57041	−0.785203	+	0.619239i	$0.787441\pi$
$930$	63.2294	2.07337
$931$	−21.7878	−0.714066
$932$	−8.09209	−0.265065
$933$	2.95090	0.0966082
$934$	−14.6991	−0.480971
$935$	14.7782	0.483298
$936$	−0.141702	−0.00463169
$937$	−10.2772	−0.335741	−0.167870	−	0.985809i	$-0.553689\pi$
$937$	−10.2772	−0.335741	−0.167870	+	0.985809i	$0.553689\pi$
$938$	35.8834	1.17163
$939$	23.0673	0.752771
$940$	42.0642	1.37198
$941$	11.6758	0.380619	0.190309	−	0.981724i	$-0.439051\pi$
$941$	11.6758	0.380619	0.190309	+	0.981724i	$0.439051\pi$
$942$	−18.0660	−0.588623
$943$	15.1846	0.494479
$944$	−0.319094	−0.0103856
$945$	−70.3975	−2.29003
$946$	5.21339	0.169502
$947$	−26.1893	−0.851037	−0.425518	−	0.904950i	$-0.639908\pi$
$947$	−26.1893	−0.851037	−0.425518	+	0.904950i	$0.639908\pi$
$948$	−18.4144	−0.598073
$949$	0.520470	0.0168952
$950$	40.0200	1.29842
$951$	−3.30931	−0.107312
$952$	−21.3227	−0.691072
$953$	−54.0727	−1.75159	−0.875794	−	0.482685i	$-0.839662\pi$
$953$	−54.0727	−1.75159	−0.875794	+	0.482685i	$0.839662\pi$
$954$	8.43959	0.273242
$955$	−31.9022	−1.03233
$956$	43.7563	1.41518
$957$	−0.716281	−0.0231541
$958$	−62.2028	−2.00968
$959$	−77.6270	−2.50671
$960$	40.0185	1.29159
$961$	36.6146	1.18112
$962$	0.545168	0.0175769
$963$	1.65754	0.0534134
$964$	−42.9942	−1.38475
$965$	17.2171	0.554239
$966$	−52.5432	−1.69055
$967$	27.0777	0.870761	0.435381	−	0.900247i	$-0.356614\pi$
$967$	27.0777	0.870761	0.435381	+	0.900247i	$0.356614\pi$
$968$	9.33862	0.300154
$969$	−16.6790	−0.535806
$970$	74.2540	2.38415
$971$	−53.2776	−1.70976	−0.854880	−	0.518825i	$-0.826370\pi$
$971$	−53.2776	−1.70976	−0.854880	+	0.518825i	$0.826370\pi$
$972$	−38.2201	−1.22591
$973$	3.91864	0.125626
$974$	75.5990	2.42235
$975$	0.635633	0.0203565
$976$	−16.6999	−0.534550
$977$	−55.1915	−1.76573	−0.882866	−	0.469625i	$-0.844389\pi$
$977$	−55.1915	−1.76573	−0.882866	+	0.469625i	$0.844389\pi$
$978$	11.5618	0.369705
$979$	8.89163	0.284178
$980$	70.9674	2.26697
$981$	2.38855	0.0762606
$982$	1.98521	0.0633505
$983$	−12.5933	−0.401664	−0.200832	−	0.979626i	$-0.564365\pi$
$983$	−12.5933	−0.401664	−0.200832	+	0.979626i	$0.564365\pi$
$984$	2.29662	0.0732137
$985$	−36.7877	−1.17215
$986$	−12.8996	−0.410806
$987$	20.2369	0.644146
$988$	0.527424	0.0167796
$989$	22.0707	0.701809
$990$	−9.68952	−0.307953
$991$	52.1016	1.65506	0.827532	−	0.561419i	$-0.189744\pi$
$991$	52.1016	1.65506	0.827532	+	0.561419i	$0.189744\pi$
$992$	66.0874	2.09828
$993$	37.7010	1.19640
$994$	−108.458	−3.44008
$995$	−23.5556	−0.746762
$996$	−2.48705	−0.0788053
$997$	20.6417	0.653729	0.326864	−	0.945071i	$-0.394008\pi$
$997$	20.6417	0.653729	0.326864	+	0.945071i	$0.394008\pi$
$998$	−37.0670	−1.17333
$999$	15.9012	0.503092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.9	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.10281 q^{2} -1.04272 q^{3} +2.42182 q^{4} +3.50696 q^{5} +2.19264 q^{6} -3.91864 q^{7} -0.887016 q^{8} -1.91274 q^{9} +O(q^{10})\)	\(q-2.10281 q^{2} -1.04272 q^{3} +2.42182 q^{4} +3.50696 q^{5} +2.19264 q^{6} -3.91864 q^{7} -0.887016 q^{8} -1.91274 q^{9} -7.37448 q^{10} -0.686935 q^{11} -2.52528 q^{12} -0.0835199 q^{13} +8.24017 q^{14} -3.65677 q^{15} -2.97842 q^{16} -6.13443 q^{17} +4.02213 q^{18} -2.60752 q^{19} +8.49323 q^{20} +4.08604 q^{21} +1.44450 q^{22} +6.11523 q^{23} +0.924909 q^{24} +7.29875 q^{25} +0.175627 q^{26} +5.12260 q^{27} -9.49026 q^{28} -1.00000 q^{29} +7.68951 q^{30} +8.22281 q^{31} +8.03709 q^{32} +0.716281 q^{33} +12.8996 q^{34} -13.7425 q^{35} -4.63231 q^{36} +3.10413 q^{37} +5.48312 q^{38} +0.0870878 q^{39} -3.11073 q^{40} +2.48308 q^{41} -8.59219 q^{42} +3.60914 q^{43} -1.66364 q^{44} -6.70789 q^{45} -12.8592 q^{46} +4.95268 q^{47} +3.10565 q^{48} +8.35576 q^{49} -15.3479 q^{50} +6.39649 q^{51} -0.202271 q^{52} +2.09829 q^{53} -10.7719 q^{54} -2.40905 q^{55} +3.47590 q^{56} +2.71891 q^{57} +2.10281 q^{58} +0.107135 q^{59} -8.85606 q^{60} +5.60696 q^{61} -17.2910 q^{62} +7.49533 q^{63} -10.9437 q^{64} -0.292901 q^{65} -1.50620 q^{66} +4.35469 q^{67} -14.8565 q^{68} -6.37647 q^{69} +28.8979 q^{70} -13.1621 q^{71} +1.69663 q^{72} -6.23169 q^{73} -6.52740 q^{74} -7.61055 q^{75} -6.31495 q^{76} +2.69185 q^{77} -0.183129 q^{78} +7.29203 q^{79} -10.4452 q^{80} +0.396773 q^{81} -5.22146 q^{82} +0.984862 q^{83} +9.89568 q^{84} -21.5132 q^{85} -7.58935 q^{86} +1.04272 q^{87} +0.609323 q^{88} -12.9439 q^{89} +14.1054 q^{90} +0.327285 q^{91} +14.8100 q^{92} -8.57408 q^{93} -10.4146 q^{94} -9.14446 q^{95} -8.38043 q^{96} -10.0691 q^{97} -17.5706 q^{98} +1.31393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 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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