LMFDB - Embedded newform 4031.2.a.b.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:	$59$
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)

$f(q)$	$=$	$q-1.45467 q^{2} +0.452328 q^{3} +0.116052 q^{4} -2.57197 q^{5} -0.657986 q^{6} +3.66955 q^{7} +2.74051 q^{8} -2.79540 q^{9} +O(q^{10})$	\(q-1.45467 q^{2} +0.452328 q^{3} +0.116052 q^{4} -2.57197 q^{5} -0.657986 q^{6} +3.66955 q^{7} +2.74051 q^{8} -2.79540 q^{9} +3.74136 q^{10} -2.93433 q^{11} +0.0524935 q^{12} +2.49330 q^{13} -5.33797 q^{14} -1.16338 q^{15} -4.21864 q^{16} +6.40808 q^{17} +4.06637 q^{18} -3.49802 q^{19} -0.298482 q^{20} +1.65984 q^{21} +4.26846 q^{22} +1.44313 q^{23} +1.23961 q^{24} +1.61505 q^{25} -3.62692 q^{26} -2.62142 q^{27} +0.425858 q^{28} +1.00000 q^{29} +1.69232 q^{30} -8.88131 q^{31} +0.655674 q^{32} -1.32728 q^{33} -9.32162 q^{34} -9.43800 q^{35} -0.324411 q^{36} -2.73580 q^{37} +5.08845 q^{38} +1.12779 q^{39} -7.04853 q^{40} +0.584181 q^{41} -2.41452 q^{42} +0.583716 q^{43} -0.340534 q^{44} +7.18969 q^{45} -2.09928 q^{46} +4.41166 q^{47} -1.90821 q^{48} +6.46563 q^{49} -2.34935 q^{50} +2.89856 q^{51} +0.289352 q^{52} +0.988874 q^{53} +3.81329 q^{54} +7.54701 q^{55} +10.0565 q^{56} -1.58225 q^{57} -1.45467 q^{58} +6.69320 q^{59} -0.135012 q^{60} +5.80854 q^{61} +12.9193 q^{62} -10.2579 q^{63} +7.48348 q^{64} -6.41271 q^{65} +1.93075 q^{66} +5.16481 q^{67} +0.743669 q^{68} +0.652770 q^{69} +13.7291 q^{70} +3.81808 q^{71} -7.66083 q^{72} -15.3088 q^{73} +3.97968 q^{74} +0.730531 q^{75} -0.405951 q^{76} -10.7677 q^{77} -1.64056 q^{78} -3.65727 q^{79} +10.8502 q^{80} +7.20045 q^{81} -0.849787 q^{82} +11.4971 q^{83} +0.192628 q^{84} -16.4814 q^{85} -0.849112 q^{86} +0.452328 q^{87} -8.04157 q^{88} -15.4764 q^{89} -10.4586 q^{90} +9.14931 q^{91} +0.167478 q^{92} -4.01727 q^{93} -6.41749 q^{94} +8.99682 q^{95} +0.296580 q^{96} +7.82262 q^{97} -9.40533 q^{98} +8.20261 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9} - 18 q^{10} - 27 q^{11} - 8 q^{12} - 22 q^{13} - 24 q^{14} - 18 q^{15} + 5 q^{16} - 23 q^{17} + q^{18} - 32 q^{19} - 14 q^{20} - 36 q^{21} - 6 q^{22} - 3 q^{23} - 18 q^{24} - 8 q^{25} - q^{26} - 12 q^{27} - 9 q^{28} + 59 q^{29} - 18 q^{30} - 32 q^{31} - 39 q^{32} - 12 q^{33} - 18 q^{34} - 9 q^{35} + 10 q^{36} - 44 q^{37} + 5 q^{38} - 27 q^{39} - 68 q^{40} - 44 q^{41} - 25 q^{42} - 40 q^{43} - 56 q^{44} - 39 q^{45} - 40 q^{46} - 20 q^{47} - 9 q^{48} - 39 q^{49} - 21 q^{50} - 28 q^{51} - 49 q^{52} - 31 q^{53} - 32 q^{54} - 32 q^{55} - 48 q^{56} - 58 q^{57} - 5 q^{58} + 6 q^{59} - 44 q^{60} - 88 q^{61} + 35 q^{62} - 22 q^{63} - 10 q^{64} - 43 q^{65} - 31 q^{66} - 45 q^{67} - 29 q^{68} - 60 q^{69} - 14 q^{70} - 20 q^{71} - 4 q^{72} - 90 q^{73} - 25 q^{74} + 15 q^{75} - 64 q^{76} - 39 q^{77} - 28 q^{78} - 120 q^{79} + 24 q^{80} - 77 q^{81} - 71 q^{82} - 33 q^{83} - 14 q^{84} - 71 q^{85} - 61 q^{86} - 6 q^{87} - 34 q^{88} - 78 q^{89} - 88 q^{90} - 28 q^{91} - 31 q^{92} - 36 q^{93} - 4 q^{94} - 12 q^{95} - 29 q^{96} - 48 q^{97} - 4 q^{98} - 43 q^{99}+O(q^{100}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9 - 18 * q^10 - 27 * q^11 - 8 * q^12 - 22 * q^13 - 24 * q^14 - 18 * q^15 + 5 * q^16 - 23 * q^17 + q^18 - 32 * q^19 - 14 * q^20 - 36 * q^21 - 6 * q^22 - 3 * q^23 - 18 * q^24 - 8 * q^25 - q^26 - 12 * q^27 - 9 * q^28 + 59 * q^29 - 18 * q^30 - 32 * q^31 - 39 * q^32 - 12 * q^33 - 18 * q^34 - 9 * q^35 + 10 * q^36 - 44 * q^37 + 5 * q^38 - 27 * q^39 - 68 * q^40 - 44 * q^41 - 25 * q^42 - 40 * q^43 - 56 * q^44 - 39 * q^45 - 40 * q^46 - 20 * q^47 - 9 * q^48 - 39 * q^49 - 21 * q^50 - 28 * q^51 - 49 * q^52 - 31 * q^53 - 32 * q^54 - 32 * q^55 - 48 * q^56 - 58 * q^57 - 5 * q^58 + 6 * q^59 - 44 * q^60 - 88 * q^61 + 35 * q^62 - 22 * q^63 - 10 * q^64 - 43 * q^65 - 31 * q^66 - 45 * q^67 - 29 * q^68 - 60 * q^69 - 14 * q^70 - 20 * q^71 - 4 * q^72 - 90 * q^73 - 25 * q^74 + 15 * q^75 - 64 * q^76 - 39 * q^77 - 28 * q^78 - 120 * q^79 + 24 * q^80 - 77 * q^81 - 71 * q^82 - 33 * q^83 - 14 * q^84 - 71 * q^85 - 61 * q^86 - 6 * q^87 - 34 * q^88 - 78 * q^89 - 88 * q^90 - 28 * q^91 - 31 * q^92 - 36 * q^93 - 4 * q^94 - 12 * q^95 - 29 * q^96 - 48 * q^97 - 4 * q^98 - 43 * 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 $

$2$	−1.45467	−1.02860	−0.514302	−	0.857609i	$-0.671949\pi$
$2$	−1.45467	−1.02860	−0.514302	+	0.857609i	$0.671949\pi$
$3$	0.452328	0.261152	0.130576	−	0.991438i	$-0.458317\pi$
$3$	0.452328	0.261152	0.130576	+	0.991438i	$0.458317\pi$
$4$	0.116052	0.0580258
$5$	−2.57197	−1.15022	−0.575111	−	0.818076i	$-0.695041\pi$
$5$	−2.57197	−1.15022	−0.575111	+	0.818076i	$0.695041\pi$
$6$	−0.657986	−0.268622
$7$	3.66955	1.38696	0.693481	−	0.720475i	$-0.256076\pi$
$7$	3.66955	1.38696	0.693481	+	0.720475i	$0.256076\pi$
$8$	2.74051	0.968918
$9$	−2.79540	−0.931800
$10$	3.74136	1.18312
$11$	−2.93433	−0.884733	−0.442366	−	0.896834i	$-0.645861\pi$
$11$	−2.93433	−0.884733	−0.442366	+	0.896834i	$0.645861\pi$
$12$	0.0524935	0.0151536
$13$	2.49330	0.691518	0.345759	−	0.938323i	$-0.387621\pi$
$13$	2.49330	0.691518	0.345759	+	0.938323i	$0.387621\pi$
$14$	−5.33797	−1.42663
$15$	−1.16338	−0.300382
$16$	−4.21864	−1.05466
$17$	6.40808	1.55419	0.777094	−	0.629384i	$-0.216693\pi$
$17$	6.40808	1.55419	0.777094	+	0.629384i	$0.216693\pi$
$18$	4.06637	0.958453
$19$	−3.49802	−0.802501	−0.401251	−	0.915968i	$-0.631424\pi$
$19$	−3.49802	−0.802501	−0.401251	+	0.915968i	$0.631424\pi$
$20$	−0.298482	−0.0667426
$21$	1.65984	0.362208
$22$	4.26846	0.910040
$23$	1.44313	0.300914	0.150457	−	0.988617i	$-0.451925\pi$
$23$	1.44313	0.300914	0.150457	+	0.988617i	$0.451925\pi$
$24$	1.23961	0.253035
$25$	1.61505	0.323009
$26$	−3.62692	−0.711298
$27$	−2.62142	−0.504493
$28$	0.425858	0.0804796
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	1.69232	0.308975
$31$	−8.88131	−1.59513	−0.797565	−	0.603232i	$-0.793879\pi$
$31$	−8.88131	−1.59513	−0.797565	+	0.603232i	$0.793879\pi$
$32$	0.655674	0.115908
$33$	−1.32728	−0.231050
$34$	−9.32162	−1.59864
$35$	−9.43800	−1.59531
$36$	−0.324411	−0.0540685
$37$	−2.73580	−0.449763	−0.224882	−	0.974386i	$-0.572200\pi$
$37$	−2.73580	−0.449763	−0.224882	+	0.974386i	$0.572200\pi$
$38$	5.08845	0.825456
$39$	1.12779	0.180591
$40$	−7.04853	−1.11447
$41$	0.584181	0.0912337	0.0456168	−	0.998959i	$-0.485475\pi$
$41$	0.584181	0.0912337	0.0456168	+	0.998959i	$0.485475\pi$
$42$	−2.41452	−0.372568
$43$	0.583716	0.0890159	0.0445079	−	0.999009i	$-0.485828\pi$
$43$	0.583716	0.0890159	0.0445079	+	0.999009i	$0.485828\pi$
$44$	−0.340534	−0.0513374
$45$	7.18969	1.07178
$46$	−2.09928	−0.309521
$47$	4.41166	0.643506	0.321753	−	0.946824i	$-0.395728\pi$
$47$	4.41166	0.643506	0.321753	+	0.946824i	$0.395728\pi$
$48$	−1.90821	−0.275426
$49$	6.46563	0.923662
$50$	−2.34935	−0.332248
$51$	2.89856	0.405879
$52$	0.289352	0.0401259
$53$	0.988874	0.135832	0.0679162	−	0.997691i	$-0.478365\pi$
$53$	0.988874	0.135832	0.0679162	+	0.997691i	$0.478365\pi$
$54$	3.81329	0.518924
$55$	7.54701	1.01764
$56$	10.0565	1.34385
$57$	−1.58225	−0.209575
$58$	−1.45467	−0.191007
$59$	6.69320	0.871380	0.435690	−	0.900097i	$-0.356504\pi$
$59$	6.69320	0.871380	0.435690	+	0.900097i	$0.356504\pi$
$60$	−0.135012	−0.0174299
$61$	5.80854	0.743708	0.371854	−	0.928291i	$-0.378722\pi$
$61$	5.80854	0.743708	0.371854	+	0.928291i	$0.378722\pi$
$62$	12.9193	1.64076
$63$	−10.2579	−1.29237
$64$	7.48348	0.935436
$65$	−6.41271	−0.795399
$66$	1.93075	0.237659
$67$	5.16481	0.630982	0.315491	−	0.948929i	$-0.397831\pi$
$67$	5.16481	0.630982	0.315491	+	0.948929i	$0.397831\pi$
$68$	0.743669	0.0901831
$69$	0.652770	0.0785843
$70$	13.7291	1.64094
$71$	3.81808	0.453123	0.226561	−	0.973997i	$-0.427252\pi$
$71$	3.81808	0.453123	0.226561	+	0.973997i	$0.427252\pi$
$72$	−7.66083	−0.902838
$73$	−15.3088	−1.79176	−0.895880	−	0.444295i	$-0.853454\pi$
$73$	−15.3088	−1.79176	−0.895880	+	0.444295i	$0.853454\pi$
$74$	3.97968	0.462628
$75$	0.730531	0.0843544
$76$	−0.405951	−0.0465658
$77$	−10.7677	−1.22709
$78$	−1.64056	−0.185757
$79$	−3.65727	−0.411475	−0.205738	−	0.978607i	$-0.565959\pi$
$79$	−3.65727	−0.411475	−0.205738	+	0.978607i	$0.565959\pi$
$80$	10.8502	1.21309
$81$	7.20045	0.800050
$82$	−0.849787	−0.0938433
$83$	11.4971	1.26197	0.630985	−	0.775795i	$-0.282651\pi$
$83$	11.4971	1.26197	0.630985	+	0.775795i	$0.282651\pi$
$84$	0.192628	0.0210174
$85$	−16.4814	−1.78766
$86$	−0.849112	−0.0915621
$87$	0.452328	0.0484947
$88$	−8.04157	−0.857234
$89$	−15.4764	−1.64050	−0.820249	−	0.572007i	$-0.806165\pi$
$89$	−15.4764	−1.64050	−0.820249	+	0.572007i	$0.806165\pi$
$90$	−10.4586	−1.10243
$91$	9.14931	0.959109
$92$	0.167478	0.0174608
$93$	−4.01727	−0.416571
$94$	−6.41749	−0.661913
$95$	8.99682	0.923054
$96$	0.296580	0.0302696
$97$	7.82262	0.794267	0.397133	−	0.917761i	$-0.370005\pi$
$97$	7.82262	0.794267	0.397133	+	0.917761i	$0.370005\pi$
$98$	−9.40533	−0.950082
$99$	8.20261	0.824394
$100$	0.187429	0.0187429
$101$	−2.34504	−0.233340	−0.116670	−	0.993171i	$-0.537222\pi$
$101$	−2.34504	−0.233340	−0.116670	+	0.993171i	$0.537222\pi$
$102$	−4.21643	−0.417489
$103$	1.76883	0.174288	0.0871440	−	0.996196i	$-0.472226\pi$
$103$	1.76883	0.174288	0.0871440	+	0.996196i	$0.472226\pi$
$104$	6.83293	0.670024
$105$	−4.26907	−0.416619
$106$	−1.43848	−0.139718
$107$	−17.7276	−1.71380	−0.856898	−	0.515487i	$-0.827611\pi$
$107$	−17.7276	−1.71380	−0.856898	+	0.515487i	$0.827611\pi$
$108$	−0.304221	−0.0292736
$109$	−7.06227	−0.676443	−0.338221	−	0.941067i	$-0.609825\pi$
$109$	−7.06227	−0.676443	−0.338221	+	0.941067i	$0.609825\pi$
$110$	−10.9784	−1.04675
$111$	−1.23748	−0.117457
$112$	−15.4805	−1.46277
$113$	10.3893	0.977345	0.488672	−	0.872467i	$-0.337481\pi$
$113$	10.3893	0.977345	0.488672	+	0.872467i	$0.337481\pi$
$114$	2.30165	0.215569
$115$	−3.71170	−0.346118
$116$	0.116052	0.0107751
$117$	−6.96978	−0.644356
$118$	−9.73636	−0.896305
$119$	23.5148	2.15560
$120$	−3.18825	−0.291046
$121$	−2.38973	−0.217248
$122$	−8.44949	−0.764981
$123$	0.264241	0.0238259
$124$	−1.03069	−0.0925588
$125$	8.70601	0.778689
$126$	14.9218	1.32934
$127$	−3.76685	−0.334254	−0.167127	−	0.985935i	$-0.553449\pi$
$127$	−3.76685	−0.334254	−0.167127	+	0.985935i	$0.553449\pi$
$128$	−12.1973	−1.07810
$129$	0.264031	0.0232467
$130$	9.32835	0.818150
$131$	2.62936	0.229728	0.114864	−	0.993381i	$-0.463357\pi$
$131$	2.62936	0.229728	0.114864	+	0.993381i	$0.463357\pi$
$132$	−0.154033	−0.0134068
$133$	−12.8362	−1.11304
$134$	−7.51307	−0.649030
$135$	6.74223	0.580279
$136$	17.5614	1.50588
$137$	−9.29355	−0.794002	−0.397001	−	0.917818i	$-0.629949\pi$
$137$	−9.29355	−0.794002	−0.397001	+	0.917818i	$0.629949\pi$
$138$	−0.949562	−0.0808321
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	−1.09530	−0.0925693
$141$	1.99552	0.168053
$142$	−5.55403	−0.466084
$143$	−7.31617	−0.611809
$144$	11.7928	0.982731
$145$	−2.57197	−0.213591
$146$	22.2692	1.84301
$147$	2.92459	0.241216
$148$	−0.317495	−0.0260979
$149$	6.72008	0.550530	0.275265	−	0.961368i	$-0.411234\pi$
$149$	6.72008	0.550530	0.275265	+	0.961368i	$0.411234\pi$
$150$	−1.06268	−0.0867673
$151$	−5.30911	−0.432049	−0.216024	−	0.976388i	$-0.569309\pi$
$151$	−5.30911	−0.432049	−0.216024	+	0.976388i	$0.569309\pi$
$152$	−9.58638	−0.777558
$153$	−17.9132	−1.44819
$154$	15.6634	1.26219
$155$	22.8425	1.83475
$156$	0.130882	0.0104790
$157$	−1.43271	−0.114343	−0.0571713	−	0.998364i	$-0.518208\pi$
$157$	−1.43271	−0.114343	−0.0571713	+	0.998364i	$0.518208\pi$
$158$	5.32010	0.423245
$159$	0.447296	0.0354729
$160$	−1.68638	−0.133320
$161$	5.29566	0.417356
$162$	−10.4743	−0.822935
$163$	0.759060	0.0594541	0.0297271	−	0.999558i	$-0.490536\pi$
$163$	0.759060	0.0594541	0.0297271	+	0.999558i	$0.490536\pi$
$164$	0.0677951	0.00529391
$165$	3.41373	0.265758
$166$	−16.7244	−1.29807
$167$	18.4304	1.42619	0.713095	−	0.701067i	$-0.247293\pi$
$167$	18.4304	1.42619	0.713095	+	0.701067i	$0.247293\pi$
$168$	4.54883	0.350950
$169$	−6.78344	−0.521803
$170$	23.9750	1.83879
$171$	9.77837	0.747770
$172$	0.0677412	0.00516522
$173$	−0.295069	−0.0224337	−0.0112168	−	0.999937i	$-0.503571\pi$
$173$	−0.295069	−0.0224337	−0.0112168	+	0.999937i	$0.503571\pi$
$174$	−0.657986	−0.0498818
$175$	5.92650	0.448001
$176$	12.3789	0.933091
$177$	3.02752	0.227563
$178$	22.5130	1.68742
$179$	10.9862	0.821146	0.410573	−	0.911828i	$-0.365329\pi$
$179$	10.9862	0.821146	0.410573	+	0.911828i	$0.365329\pi$
$180$	0.834376	0.0621907
$181$	−26.3556	−1.95900	−0.979498	−	0.201453i	$-0.935434\pi$
$181$	−26.3556	−1.95900	−0.979498	+	0.201453i	$0.935434\pi$
$182$	−13.3092	−0.986543
$183$	2.62737	0.194221
$184$	3.95493	0.291561
$185$	7.03641	0.517328
$186$	5.84378	0.428487
$187$	−18.8034	−1.37504
$188$	0.511980	0.0373400
$189$	−9.61946	−0.699713
$190$	−13.0874	−0.949457
$191$	−23.0657	−1.66898	−0.834489	−	0.551025i	$-0.814237\pi$
$191$	−23.0657	−1.66898	−0.834489	+	0.551025i	$0.814237\pi$
$192$	3.38499	0.244291
$193$	−16.3362	−1.17591	−0.587953	−	0.808895i	$-0.700066\pi$
$193$	−16.3362	−1.17591	−0.587953	+	0.808895i	$0.700066\pi$
$194$	−11.3793	−0.816986
$195$	−2.90065	−0.207720
$196$	0.750347	0.0535962
$197$	19.7708	1.40861	0.704306	−	0.709896i	$-0.251258\pi$
$197$	19.7708	1.40861	0.704306	+	0.709896i	$0.251258\pi$
$198$	−11.9321	−0.847975
$199$	−25.5751	−1.81297	−0.906486	−	0.422237i	$-0.861245\pi$
$199$	−25.5751	−1.81297	−0.906486	+	0.422237i	$0.861245\pi$
$200$	4.42606	0.312969
$201$	2.33619	0.164782
$202$	3.41125	0.240015
$203$	3.66955	0.257552
$204$	0.336383	0.0235515
$205$	−1.50250	−0.104939
$206$	−2.57306	−0.179273
$207$	−4.03413	−0.280392
$208$	−10.5183	−0.729315
$209$	10.2643	0.709999
$210$	6.21007	0.428536
$211$	17.9825	1.23797	0.618984	−	0.785404i	$-0.287545\pi$
$211$	17.9825	1.23797	0.618984	+	0.785404i	$0.287545\pi$
$212$	0.114760	0.00788178
$213$	1.72703	0.118334
$214$	25.7878	1.76282
$215$	−1.50130	−0.102388
$216$	−7.18405	−0.488813
$217$	−32.5905	−2.21238
$218$	10.2732	0.695792
$219$	−6.92461	−0.467922
$220$	0.875843	0.0590493
$221$	15.9773	1.07475
$222$	1.80012	0.120816
$223$	−18.3792	−1.23076	−0.615380	−	0.788231i	$-0.710997\pi$
$223$	−18.3792	−1.23076	−0.615380	+	0.788231i	$0.710997\pi$
$224$	2.40603	0.160760
$225$	−4.51470	−0.300980
$226$	−15.1130	−1.00530
$227$	−21.3280	−1.41559	−0.707795	−	0.706418i	$-0.750310\pi$
$227$	−21.3280	−1.41559	−0.707795	+	0.706418i	$0.750310\pi$
$228$	−0.183623	−0.0121607
$229$	12.6990	0.839176	0.419588	−	0.907715i	$-0.362175\pi$
$229$	12.6990	0.839176	0.419588	+	0.907715i	$0.362175\pi$
$230$	5.39928	0.356018
$231$	−4.87052	−0.320457
$232$	2.74051	0.179924
$233$	−13.1917	−0.864217	−0.432108	−	0.901822i	$-0.642230\pi$
$233$	−13.1917	−0.864217	−0.432108	+	0.901822i	$0.642230\pi$
$234$	10.1387	0.662787
$235$	−11.3467	−0.740175
$236$	0.776756	0.0505625
$237$	−1.65429	−0.107457
$238$	−34.2062	−2.21726
$239$	−7.10677	−0.459699	−0.229849	−	0.973226i	$-0.573823\pi$
$239$	−7.10677	−0.459699	−0.229849	+	0.973226i	$0.573823\pi$
$240$	4.90786	0.316801
$241$	−13.3767	−0.861667	−0.430834	−	0.902431i	$-0.641780\pi$
$241$	−13.3767	−0.861667	−0.430834	+	0.902431i	$0.641780\pi$
$242$	3.47625	0.223462
$243$	11.1212	0.713428
$244$	0.674091	0.0431543
$245$	−16.6294	−1.06242
$246$	−0.384383	−0.0245074
$247$	−8.72163	−0.554944
$248$	−24.3394	−1.54555
$249$	5.20046	0.329566
$250$	−12.6643	−0.800963
$251$	−0.947082	−0.0597793	−0.0298896	−	0.999553i	$-0.509516\pi$
$251$	−0.947082	−0.0597793	−0.0298896	+	0.999553i	$0.509516\pi$
$252$	−1.19044	−0.0749909
$253$	−4.23463	−0.266229
$254$	5.47950	0.343815
$255$	−7.45501	−0.466851
$256$	2.77604	0.173503
$257$	−4.15862	−0.259407	−0.129704	−	0.991553i	$-0.541403\pi$
$257$	−4.15862	−0.259407	−0.129704	+	0.991553i	$0.541403\pi$
$258$	−0.384077	−0.0239116
$259$	−10.0392	−0.623804
$260$	−0.744206	−0.0461537
$261$	−2.79540	−0.173031
$262$	−3.82484	−0.236300
$263$	−14.6513	−0.903436	−0.451718	−	0.892161i	$-0.649189\pi$
$263$	−14.6513	−0.903436	−0.451718	+	0.892161i	$0.649189\pi$
$264$	−3.63743	−0.223868
$265$	−2.54336	−0.156237
$266$	18.6724	1.14488
$267$	−7.00043	−0.428419
$268$	0.599384	0.0366132
$269$	4.96083	0.302467	0.151234	−	0.988498i	$-0.451675\pi$
$269$	4.96083	0.302467	0.151234	+	0.988498i	$0.451675\pi$
$270$	−9.80769	−0.596877
$271$	12.7684	0.775626	0.387813	−	0.921738i	$-0.373231\pi$
$271$	12.7684	0.775626	0.387813	+	0.921738i	$0.373231\pi$
$272$	−27.0334	−1.63914
$273$	4.13849	0.250473
$274$	13.5190	0.816713
$275$	−4.73907	−0.285777
$276$	0.0757551	0.00455992
$277$	−19.1362	−1.14978	−0.574892	−	0.818229i	$-0.694956\pi$
$277$	−19.1362	−1.14978	−0.574892	+	0.818229i	$0.694956\pi$
$278$	−1.45467	−0.0872450
$279$	24.8268	1.48634
$280$	−25.8650	−1.54573
$281$	18.7341	1.11758	0.558790	−	0.829309i	$-0.311266\pi$
$281$	18.7341	1.11758	0.558790	+	0.829309i	$0.311266\pi$
$282$	−2.90281	−0.172860
$283$	−27.5753	−1.63918	−0.819590	−	0.572951i	$-0.805799\pi$
$283$	−27.5753	−1.63918	−0.819590	+	0.572951i	$0.805799\pi$
$284$	0.443095	0.0262928
$285$	4.06952	0.241057
$286$	10.6426	0.629309
$287$	2.14368	0.126538
$288$	−1.83287	−0.108003
$289$	24.0635	1.41550
$290$	3.74136	0.219700
$291$	3.53839	0.207424
$292$	−1.77661	−0.103968
$293$	−5.89088	−0.344149	−0.172074	−	0.985084i	$-0.555047\pi$
$293$	−5.89088	−0.344149	−0.172074	+	0.985084i	$0.555047\pi$
$294$	−4.25430	−0.248116
$295$	−17.2147	−1.00228
$296$	−7.49751	−0.435784
$297$	7.69211	0.446342
$298$	−9.77546	−0.566277
$299$	3.59817	0.208088
$300$	0.0847793	0.00489474
$301$	2.14198	0.123462
$302$	7.72297	0.444407
$303$	−1.06073	−0.0609372
$304$	14.7569	0.846365
$305$	−14.9394	−0.855428
$306$	26.0576	1.48962
$307$	−24.9475	−1.42383	−0.711913	−	0.702267i	$-0.752171\pi$
$307$	−24.9475	−1.42383	−0.711913	+	0.702267i	$0.752171\pi$
$308$	−1.24961	−0.0712029
$309$	0.800092	0.0455156
$310$	−33.2282	−1.88723
$311$	−16.7694	−0.950906	−0.475453	−	0.879741i	$-0.657716\pi$
$311$	−16.7694	−0.950906	−0.475453	+	0.879741i	$0.657716\pi$
$312$	3.09073	0.174978
$313$	25.9100	1.46452	0.732260	−	0.681026i	$-0.238466\pi$
$313$	25.9100	1.46452	0.732260	+	0.681026i	$0.238466\pi$
$314$	2.08411	0.117613
$315$	26.3830	1.48651
$316$	−0.424432	−0.0238762
$317$	−27.9231	−1.56832	−0.784158	−	0.620562i	$-0.786905\pi$
$317$	−27.9231	−1.56832	−0.784158	+	0.620562i	$0.786905\pi$
$318$	−0.650666	−0.0364875
$319$	−2.93433	−0.164291
$320$	−19.2473	−1.07596
$321$	−8.01871	−0.447561
$322$	−7.70341	−0.429294
$323$	−22.4156	−1.24724
$324$	0.835625	0.0464236
$325$	4.02680	0.223367
$326$	−1.10418	−0.0611548
$327$	−3.19447	−0.176654
$328$	1.60096	0.0883980
$329$	16.1888	0.892519
$330$	−4.96583	−0.273360
$331$	6.87398	0.377828	0.188914	−	0.981994i	$-0.439503\pi$
$331$	6.87398	0.377828	0.188914	+	0.981994i	$0.439503\pi$
$332$	1.33426	0.0732268
$333$	7.64766	0.419089
$334$	−26.8101	−1.46699
$335$	−13.2837	−0.725768
$336$	−7.00228	−0.382005
$337$	−3.13247	−0.170636	−0.0853182	−	0.996354i	$-0.527191\pi$
$337$	−3.13247	−0.170636	−0.0853182	+	0.996354i	$0.527191\pi$
$338$	9.86763	0.536729
$339$	4.69938	0.255235
$340$	−1.91270	−0.103731
$341$	26.0607	1.41126
$342$	−14.2243	−0.769159
$343$	−1.96090	−0.105878
$344$	1.59968	0.0862491
$345$	−1.67891	−0.0903893
$346$	0.429226	0.0230754
$347$	21.8717	1.17413	0.587067	−	0.809538i	$-0.300283\pi$
$347$	21.8717	1.17413	0.587067	+	0.809538i	$0.300283\pi$
$348$	0.0524935	0.00281394
$349$	28.1698	1.50789	0.753947	−	0.656935i	$-0.228147\pi$
$349$	28.1698	1.50789	0.753947	+	0.656935i	$0.228147\pi$
$350$	−8.62107	−0.460816
$351$	−6.53600	−0.348866
$352$	−1.92396	−0.102548
$353$	−21.3897	−1.13846	−0.569230	−	0.822178i	$-0.692759\pi$
$353$	−21.3897	−1.13846	−0.569230	+	0.822178i	$0.692759\pi$
$354$	−4.40403	−0.234072
$355$	−9.82000	−0.521191
$356$	−1.79607	−0.0951913
$357$	10.6364	0.562939
$358$	−15.9812	−0.844634
$359$	23.4995	1.24025	0.620127	−	0.784502i	$-0.287081\pi$
$359$	23.4995	1.24025	0.620127	+	0.784502i	$0.287081\pi$
$360$	19.7035	1.03846
$361$	−6.76384	−0.355992
$362$	38.3386	2.01503
$363$	−1.08094	−0.0567347
$364$	1.06179	0.0556531
$365$	39.3738	2.06092
$366$	−3.82194	−0.199776
$367$	−28.3023	−1.47737	−0.738683	−	0.674053i	$-0.764552\pi$
$367$	−28.3023	−1.47737	−0.738683	+	0.674053i	$0.764552\pi$
$368$	−6.08805	−0.317362
$369$	−1.63302	−0.0850115
$370$	−10.2356	−0.532125
$371$	3.62873	0.188394
$372$	−0.466211	−0.0241719
$373$	−14.8632	−0.769587	−0.384793	−	0.923003i	$-0.625727\pi$
$373$	−14.8632	−0.769587	−0.384793	+	0.923003i	$0.625727\pi$
$374$	27.3527	1.41437
$375$	3.93798	0.203356
$376$	12.0902	0.623505
$377$	2.49330	0.128412
$378$	13.9931	0.719727
$379$	16.0781	0.825878	0.412939	−	0.910759i	$-0.364502\pi$
$379$	16.0781	0.825878	0.412939	+	0.910759i	$0.364502\pi$
$380$	1.04410	0.0535610
$381$	−1.70385	−0.0872910
$382$	33.5529	1.71672
$383$	−30.7612	−1.57182	−0.785912	−	0.618338i	$-0.787806\pi$
$383$	−30.7612	−1.57182	−0.785912	+	0.618338i	$0.787806\pi$
$384$	−5.51719	−0.281548
$385$	27.6942	1.41143
$386$	23.7637	1.20954
$387$	−1.63172	−0.0829450
$388$	0.907828	0.0460880
$389$	−27.2329	−1.38076	−0.690380	−	0.723447i	$-0.742557\pi$
$389$	−27.2329	−1.38076	−0.690380	+	0.723447i	$0.742557\pi$
$390$	4.21948	0.213661
$391$	9.24772	0.467677
$392$	17.7192	0.894953
$393$	1.18934	0.0599940
$394$	−28.7599	−1.44890
$395$	9.40640	0.473287
$396$	0.951927	0.0478361
$397$	9.91379	0.497559	0.248779	−	0.968560i	$-0.419971\pi$
$397$	9.91379	0.497559	0.248779	+	0.968560i	$0.419971\pi$
$398$	37.2032	1.86483
$399$	−5.80617	−0.290672
$400$	−6.81329	−0.340664
$401$	5.23191	0.261269	0.130635	−	0.991431i	$-0.458299\pi$
$401$	5.23191	0.261269	0.130635	+	0.991431i	$0.458299\pi$
$402$	−3.39837	−0.169495
$403$	−22.1438	−1.10306
$404$	−0.272146	−0.0135398
$405$	−18.5194	−0.920235
$406$	−5.33797	−0.264919
$407$	8.02774	0.397920
$408$	7.94354	0.393264
$409$	−7.64002	−0.377775	−0.188887	−	0.981999i	$-0.560488\pi$
$409$	−7.64002	−0.377775	−0.188887	+	0.981999i	$0.560488\pi$
$410$	2.18563	0.107941
$411$	−4.20374	−0.207355
$412$	0.205276	0.0101132
$413$	24.5610	1.20857
$414$	5.86832	0.288412
$415$	−29.5702	−1.45154
$416$	1.63479	0.0801524
$417$	0.452328	0.0221506
$418$	−14.9312	−0.730308
$419$	−8.72697	−0.426340	−0.213170	−	0.977015i	$-0.568379\pi$
$419$	−8.72697	−0.426340	−0.213170	+	0.977015i	$0.568379\pi$
$420$	−0.495433	−0.0241747
$421$	−13.5233	−0.659085	−0.329542	−	0.944141i	$-0.606894\pi$
$421$	−13.5233	−0.659085	−0.329542	+	0.944141i	$0.606894\pi$
$422$	−26.1585	−1.27338
$423$	−12.3323	−0.599619
$424$	2.71002	0.131610
$425$	10.3493	0.502017
$426$	−2.51225	−0.121719
$427$	21.3148	1.03149
$428$	−2.05732	−0.0994444
$429$	−3.30931	−0.159775
$430$	2.18389	0.105317
$431$	−6.78982	−0.327054	−0.163527	−	0.986539i	$-0.552287\pi$
$431$	−6.78982	−0.327054	−0.163527	+	0.986539i	$0.552287\pi$
$432$	11.0588	0.532068
$433$	−30.3466	−1.45836	−0.729182	−	0.684319i	$-0.760099\pi$
$433$	−30.3466	−1.45836	−0.729182	+	0.684319i	$0.760099\pi$
$434$	47.4082	2.27567
$435$	−1.16338	−0.0557796
$436$	−0.819588	−0.0392512
$437$	−5.04811	−0.241484
$438$	10.0730	0.481306
$439$	−8.50975	−0.406148	−0.203074	−	0.979163i	$-0.565093\pi$
$439$	−8.50975	−0.406148	−0.203074	+	0.979163i	$0.565093\pi$
$440$	20.6827	0.986009
$441$	−18.0740	−0.860668
$442$	−23.2416	−1.10549
$443$	−21.2132	−1.00787	−0.503936	−	0.863741i	$-0.668115\pi$
$443$	−21.2132	−1.00787	−0.503936	+	0.863741i	$0.668115\pi$
$444$	−0.143612	−0.00681552
$445$	39.8050	1.88694
$446$	26.7355	1.26596
$447$	3.03968	0.143772
$448$	27.4611	1.29741
$449$	−4.15245	−0.195966	−0.0979832	−	0.995188i	$-0.531239\pi$
$449$	−4.15245	−0.195966	−0.0979832	+	0.995188i	$0.531239\pi$
$450$	6.56737	0.309589
$451$	−1.71418	−0.0807174
$452$	1.20570	0.0567112
$453$	−2.40146	−0.112830
$454$	31.0251	1.45608
$455$	−23.5318	−1.10319
$456$	−4.33619	−0.203061
$457$	27.0383	1.26480	0.632400	−	0.774642i	$-0.282070\pi$
$457$	27.0383	1.26480	0.632400	+	0.774642i	$0.282070\pi$
$458$	−18.4729	−0.863180
$459$	−16.7983	−0.784078
$460$	−0.430749	−0.0200838
$461$	−16.1662	−0.752933	−0.376467	−	0.926430i	$-0.622861\pi$
$461$	−16.1662	−0.752933	−0.376467	+	0.926430i	$0.622861\pi$
$462$	7.08498	0.329623
$463$	−17.2547	−0.801894	−0.400947	−	0.916101i	$-0.631319\pi$
$463$	−17.2547	−0.801894	−0.400947	+	0.916101i	$0.631319\pi$
$464$	−4.21864	−0.195845
$465$	10.3323	0.479149
$466$	19.1895	0.888937
$467$	−30.2582	−1.40018	−0.700092	−	0.714052i	$-0.746858\pi$
$467$	−30.2582	−1.40018	−0.700092	+	0.714052i	$0.746858\pi$
$468$	−0.808854	−0.0373893
$469$	18.9525	0.875147
$470$	16.5056	0.761347
$471$	−0.648055	−0.0298608
$472$	18.3428	0.844296
$473$	−1.71281	−0.0787553
$474$	2.40643	0.110531
$475$	−5.64946	−0.259215
$476$	2.72893	0.125080
$477$	−2.76430	−0.126569
$478$	10.3380	0.472848
$479$	6.81778	0.311512	0.155756	−	0.987796i	$-0.450219\pi$
$479$	6.81778	0.311512	0.155756	+	0.987796i	$0.450219\pi$
$480$	−0.762796	−0.0348167
$481$	−6.82119	−0.311019
$482$	19.4586	0.886314
$483$	2.39538	0.108993
$484$	−0.277332	−0.0126060
$485$	−20.1196	−0.913583
$486$	−16.1777	−0.733835
$487$	13.4922	0.611389	0.305694	−	0.952130i	$-0.401111\pi$
$487$	13.4922	0.611389	0.305694	+	0.952130i	$0.401111\pi$
$488$	15.9184	0.720592
$489$	0.343344	0.0155266
$490$	24.1903	1.09280
$491$	−13.9827	−0.631031	−0.315515	−	0.948920i	$-0.602177\pi$
$491$	−13.9827	−0.631031	−0.315515	+	0.948920i	$0.602177\pi$
$492$	0.0306657	0.00138251
$493$	6.40808	0.288606
$494$	12.6871	0.570817
$495$	−21.0969	−0.948235
$496$	37.4670	1.68232
$497$	14.0107	0.628464
$498$	−7.56493	−0.338993
$499$	−36.6499	−1.64068	−0.820338	−	0.571878i	$-0.806215\pi$
$499$	−36.6499	−1.64068	−0.820338	+	0.571878i	$0.806215\pi$
$500$	1.01035	0.0451841
$501$	8.33661	0.372452
$502$	1.37769	0.0614892
$503$	8.23735	0.367285	0.183643	−	0.982993i	$-0.441211\pi$
$503$	8.23735	0.367285	0.183643	+	0.982993i	$0.441211\pi$
$504$	−28.1118	−1.25220
$505$	6.03138	0.268393
$506$	6.15996	0.273844
$507$	−3.06834	−0.136270
$508$	−0.437149	−0.0193953
$509$	−4.35286	−0.192937	−0.0964686	−	0.995336i	$-0.530755\pi$
$509$	−4.35286	−0.192937	−0.0964686	+	0.995336i	$0.530755\pi$
$510$	10.8446	0.480205
$511$	−56.1765	−2.48510
$512$	20.3564	0.899635
$513$	9.16980	0.404856
$514$	6.04940	0.266827
$515$	−4.54938	−0.200470
$516$	0.0306413	0.00134891
$517$	−12.9452	−0.569331
$518$	14.6037	0.641648
$519$	−0.133468	−0.00585859
$520$	−17.5741	−0.770676
$521$	−14.7970	−0.648270	−0.324135	−	0.946011i	$-0.605073\pi$
$521$	−14.7970	−0.648270	−0.324135	+	0.946011i	$0.605073\pi$
$522$	4.06637	0.177980
$523$	30.3359	1.32650	0.663248	−	0.748400i	$-0.269178\pi$
$523$	30.3359	1.32650	0.663248	+	0.748400i	$0.269178\pi$
$524$	0.305142	0.0133302
$525$	2.68072	0.116996
$526$	21.3127	0.929278
$527$	−56.9122	−2.47913
$528$	5.59931	0.243679
$529$	−20.9174	−0.909451
$530$	3.69973	0.160706
$531$	−18.7102	−0.811951
$532$	−1.48966	−0.0645850
$533$	1.45654	0.0630897
$534$	10.1833	0.440674
$535$	45.5950	1.97124
$536$	14.1542	0.611370
$537$	4.96936	0.214444
$538$	−7.21635	−0.311119
$539$	−18.9723	−0.817194
$540$	0.782447	0.0336712
$541$	−24.6002	−1.05765	−0.528823	−	0.848732i	$-0.677366\pi$
$541$	−24.6002	−1.05765	−0.528823	+	0.848732i	$0.677366\pi$
$542$	−18.5738	−0.797812
$543$	−11.9214	−0.511596
$544$	4.20161	0.180143
$545$	18.1640	0.778059
$546$	−6.02012	−0.257638
$547$	8.49200	0.363092	0.181546	−	0.983382i	$-0.441890\pi$
$547$	8.49200	0.363092	0.181546	+	0.983382i	$0.441890\pi$
$548$	−1.07853	−0.0460726
$549$	−16.2372	−0.692987
$550$	6.89376	0.293951
$551$	−3.49802	−0.149021
$552$	1.78893	0.0761418
$553$	−13.4206	−0.570700
$554$	27.8368	1.18267
$555$	3.18277	0.135101
$556$	0.116052	0.00492169
$557$	11.7983	0.499910	0.249955	−	0.968258i	$-0.419584\pi$
$557$	11.7983	0.499910	0.249955	+	0.968258i	$0.419584\pi$
$558$	−36.1147	−1.52886
$559$	1.45538	0.0615561
$560$	39.8155	1.68251
$561$	−8.50532	−0.359095
$562$	−27.2518	−1.14955
$563$	34.0787	1.43625	0.718123	−	0.695916i	$-0.245002\pi$
$563$	34.0787	1.43625	0.718123	+	0.695916i	$0.245002\pi$
$564$	0.231583	0.00975141
$565$	−26.7210	−1.12416
$566$	40.1128	1.68607
$567$	26.4225	1.10964
$568$	10.4635	0.439039
$569$	1.18453	0.0496582	0.0248291	−	0.999692i	$-0.492096\pi$
$569$	1.18453	0.0496582	0.0248291	+	0.999692i	$0.492096\pi$
$570$	−5.91978	−0.247952
$571$	18.1572	0.759855	0.379928	−	0.925016i	$-0.375949\pi$
$571$	18.1572	0.759855	0.379928	+	0.925016i	$0.375949\pi$
$572$	−0.849053	−0.0355007
$573$	−10.4333	−0.435857
$574$	−3.11834	−0.130157
$575$	2.33073	0.0971980
$576$	−20.9193	−0.871639
$577$	29.9164	1.24544	0.622718	−	0.782446i	$-0.286028\pi$
$577$	29.9164	1.24544	0.622718	+	0.782446i	$0.286028\pi$
$578$	−35.0044	−1.45599
$579$	−7.38933	−0.307090
$580$	−0.298482	−0.0123938
$581$	42.1892	1.75030
$582$	−5.14718	−0.213357
$583$	−2.90168	−0.120175
$584$	−41.9540	−1.73607
$585$	17.9261	0.741152
$586$	8.56926	0.353993
$587$	20.2725	0.836736	0.418368	−	0.908278i	$-0.362602\pi$
$587$	20.2725	0.836736	0.418368	+	0.908278i	$0.362602\pi$
$588$	0.339403	0.0139968
$589$	31.0670	1.28009
$590$	25.0417	1.03095
$591$	8.94290	0.367862
$592$	11.5414	0.474347
$593$	14.9642	0.614506	0.307253	−	0.951628i	$-0.400590\pi$
$593$	14.9642	0.614506	0.307253	+	0.951628i	$0.400590\pi$
$594$	−11.1895	−0.459109
$595$	−60.4795	−2.47942
$596$	0.779876	0.0319450
$597$	−11.5683	−0.473461
$598$	−5.23413	−0.214040
$599$	−41.7091	−1.70419	−0.852095	−	0.523388i	$-0.824668\pi$
$599$	−41.7091	−1.70419	−0.852095	+	0.523388i	$0.824668\pi$
$600$	2.00203	0.0817326
$601$	−15.8339	−0.645877	−0.322939	−	0.946420i	$-0.604671\pi$
$601$	−15.8339	−0.645877	−0.322939	+	0.946420i	$0.604671\pi$
$602$	−3.11586	−0.126993
$603$	−14.4377	−0.587948
$604$	−0.616131	−0.0250700
$605$	6.14631	0.249883
$606$	1.54300	0.0626802
$607$	25.4985	1.03495	0.517476	−	0.855698i	$-0.326872\pi$
$607$	25.4985	1.03495	0.517476	+	0.855698i	$0.326872\pi$
$608$	−2.29356	−0.0930162
$609$	1.65984	0.0672603
$610$	21.7318	0.879897
$611$	10.9996	0.444996
$612$	−2.07885	−0.0840326
$613$	16.2613	0.656787	0.328393	−	0.944541i	$-0.393493\pi$
$613$	16.2613	0.656787	0.328393	+	0.944541i	$0.393493\pi$
$614$	36.2902	1.46455
$615$	−0.679622	−0.0274050
$616$	−29.5090	−1.18895
$617$	9.28613	0.373845	0.186923	−	0.982375i	$-0.440149\pi$
$617$	9.28613	0.373845	0.186923	+	0.982375i	$0.440149\pi$
$618$	−1.16387	−0.0468176
$619$	−2.38713	−0.0959467	−0.0479733	−	0.998849i	$-0.515276\pi$
$619$	−2.38713	−0.0959467	−0.0479733	+	0.998849i	$0.515276\pi$
$620$	2.65091	0.106463
$621$	−3.78306	−0.151809
$622$	24.3939	0.978106
$623$	−56.7916	−2.27531
$624$	−4.75774	−0.190462
$625$	−30.4669	−1.21867
$626$	−37.6904	−1.50641
$627$	4.64285	0.185418
$628$	−0.166268	−0.00663482
$629$	−17.5313	−0.699017
$630$	−38.3784	−1.52903
$631$	−45.3824	−1.80664	−0.903321	−	0.428964i	$-0.858879\pi$
$631$	−45.3824	−1.80664	−0.903321	+	0.428964i	$0.858879\pi$
$632$	−10.0228	−0.398686
$633$	8.13400	0.323298
$634$	40.6187	1.61318
$635$	9.68823	0.384466
$636$	0.0519094	0.00205834
$637$	16.1208	0.638729
$638$	4.26846	0.168990
$639$	−10.6731	−0.422220
$640$	31.3712	1.24005
$641$	12.4448	0.491541	0.245771	−	0.969328i	$-0.420959\pi$
$641$	12.4448	0.491541	0.245771	+	0.969328i	$0.420959\pi$
$642$	11.6645	0.460363
$643$	14.9156	0.588213	0.294106	−	0.955773i	$-0.404978\pi$
$643$	14.9156	0.588213	0.294106	+	0.955773i	$0.404978\pi$
$644$	0.614570	0.0242174
$645$	−0.679082	−0.0267388
$646$	32.6072	1.28291
$647$	−32.8140	−1.29005	−0.645025	−	0.764162i	$-0.723153\pi$
$647$	−32.8140	−1.29005	−0.645025	+	0.764162i	$0.723153\pi$
$648$	19.7329	0.775183
$649$	−19.6400	−0.770938
$650$	−5.85764	−0.229756
$651$	−14.7416	−0.577768
$652$	0.0880901	0.00344988
$653$	−20.9996	−0.821778	−0.410889	−	0.911685i	$-0.634782\pi$
$653$	−20.9996	−0.821778	−0.410889	+	0.911685i	$0.634782\pi$
$654$	4.64688	0.181707
$655$	−6.76265	−0.264239
$656$	−2.46444	−0.0962204
$657$	42.7942	1.66956
$658$	−23.5493	−0.918048
$659$	17.7959	0.693231	0.346616	−	0.938007i	$-0.387331\pi$
$659$	17.7959	0.693231	0.346616	+	0.938007i	$0.387331\pi$
$660$	0.396169	0.0154208
$661$	28.9288	1.12520	0.562600	−	0.826729i	$-0.309801\pi$
$661$	28.9288	1.12520	0.562600	+	0.826729i	$0.309801\pi$
$662$	−9.99934	−0.388635
$663$	7.22699	0.280673
$664$	31.5079	1.22275
$665$	33.0143	1.28024
$666$	−11.1248	−0.431077
$667$	1.44313	0.0558784
$668$	2.13888	0.0827559
$669$	−8.31342	−0.321415
$670$	19.3234	0.746528
$671$	−17.0442	−0.657983
$672$	1.08832	0.0419827
$673$	−27.1240	−1.04555	−0.522776	−	0.852470i	$-0.675104\pi$
$673$	−27.1240	−1.04555	−0.522776	+	0.852470i	$0.675104\pi$
$674$	4.55669	0.175517
$675$	−4.23372	−0.162956
$676$	−0.787229	−0.0302781
$677$	0.243947	0.00937564	0.00468782	−	0.999989i	$-0.498508\pi$
$677$	0.243947	0.00937564	0.00468782	+	0.999989i	$0.498508\pi$
$678$	−6.83603	−0.262536
$679$	28.7055	1.10162
$680$	−45.1676	−1.73210
$681$	−9.64727	−0.369684
$682$	−37.9096	−1.45163
$683$	48.0076	1.83696	0.918479	−	0.395470i	$-0.129418\pi$
$683$	48.0076	1.83696	0.918479	+	0.395470i	$0.129418\pi$
$684$	1.13480	0.0433900
$685$	23.9028	0.913278
$686$	2.85245	0.108907
$687$	5.74414	0.219152
$688$	−2.46249	−0.0938814
$689$	2.46556	0.0939305
$690$	2.44225	0.0929748
$691$	−9.97504	−0.379468	−0.189734	−	0.981835i	$-0.560763\pi$
$691$	−9.97504	−0.379468	−0.189734	+	0.981835i	$0.560763\pi$
$692$	−0.0342432	−0.00130173
$693$	30.0999	1.14340
$694$	−31.8160	−1.20772
$695$	−2.57197	−0.0975605
$696$	1.23961	0.0469874
$697$	3.74348	0.141794
$698$	−40.9776	−1.55103
$699$	−5.96698	−0.225692
$700$	0.687780	0.0259956
$701$	5.36105	0.202484	0.101242	−	0.994862i	$-0.467718\pi$
$701$	5.36105	0.202484	0.101242	+	0.994862i	$0.467718\pi$
$702$	9.50770	0.358845
$703$	9.56990	0.360936
$704$	−21.9590	−0.827611
$705$	−5.13242	−0.193298
$706$	31.1149	1.17103
$707$	−8.60525	−0.323634
$708$	0.351349	0.0132045
$709$	−21.8751	−0.821536	−0.410768	−	0.911740i	$-0.634739\pi$
$709$	−21.8751	−0.821536	−0.410768	+	0.911740i	$0.634739\pi$
$710$	14.2848	0.536100
$711$	10.2235	0.383412
$712$	−42.4134	−1.58951
$713$	−12.8169	−0.479997
$714$	−15.4724	−0.579041
$715$	18.8170	0.703715
$716$	1.27497	0.0476477
$717$	−3.21459	−0.120051
$718$	−34.1838	−1.27573
$719$	8.20170	0.305872	0.152936	−	0.988236i	$-0.451127\pi$
$719$	8.20170	0.305872	0.152936	+	0.988236i	$0.451127\pi$
$720$	−30.3307	−1.13036
$721$	6.49082	0.241731
$722$	9.83913	0.366175
$723$	−6.05065	−0.225026
$724$	−3.05861	−0.113672
$725$	1.61505	0.0599813
$726$	1.57241	0.0583575
$727$	11.3264	0.420072	0.210036	−	0.977694i	$-0.432642\pi$
$727$	11.3264	0.420072	0.210036	+	0.977694i	$0.432642\pi$
$728$	25.0738	0.929298
$729$	−16.5709	−0.613737
$730$	−57.2758	−2.11987
$731$	3.74050	0.138347
$732$	0.304910	0.0112698
$733$	−10.6872	−0.394740	−0.197370	−	0.980329i	$-0.563240\pi$
$733$	−10.6872	−0.394740	−0.197370	+	0.980329i	$0.563240\pi$
$734$	41.1703	1.51962
$735$	−7.52196	−0.277452
$736$	0.946225	0.0348783
$737$	−15.1552	−0.558250
$738$	2.37549	0.0874432
$739$	29.0316	1.06795	0.533973	−	0.845502i	$-0.320698\pi$
$739$	29.0316	1.06795	0.533973	+	0.845502i	$0.320698\pi$
$740$	0.816588	0.0300184
$741$	−3.94504	−0.144925
$742$	−5.27858	−0.193783
$743$	10.5164	0.385810	0.192905	−	0.981217i	$-0.438209\pi$
$743$	10.5164	0.385810	0.192905	+	0.981217i	$0.438209\pi$
$744$	−11.0094	−0.403624
$745$	−17.2839	−0.633231
$746$	21.6210	0.791600
$747$	−32.1389	−1.17590
$748$	−2.18217	−0.0797879
$749$	−65.0525	−2.37697
$750$	−5.72844	−0.209173
$751$	23.5188	0.858212	0.429106	−	0.903254i	$-0.358829\pi$
$751$	23.5188	0.858212	0.429106	+	0.903254i	$0.358829\pi$
$752$	−18.6112	−0.678680
$753$	−0.428392	−0.0156115
$754$	−3.62692	−0.132085
$755$	13.6549	0.496952
$756$	−1.11635	−0.0406014
$757$	9.24881	0.336154	0.168077	−	0.985774i	$-0.446244\pi$
$757$	9.24881	0.336154	0.168077	+	0.985774i	$0.446244\pi$
$758$	−23.3883	−0.849501
$759$	−1.91544	−0.0695261
$760$	24.6559	0.894364
$761$	−21.0001	−0.761251	−0.380626	−	0.924729i	$-0.624291\pi$
$761$	−21.0001	−0.761251	−0.380626	+	0.924729i	$0.624291\pi$
$762$	2.47853	0.0897878
$763$	−25.9154	−0.938200
$764$	−2.67682	−0.0968438
$765$	46.0721	1.66574
$766$	44.7473	1.61678
$767$	16.6882	0.602575
$768$	1.25568	0.0453106
$769$	−15.8639	−0.572065	−0.286033	−	0.958220i	$-0.592337\pi$
$769$	−15.8639	−0.572065	−0.286033	+	0.958220i	$0.592337\pi$
$770$	−40.2857	−1.45180
$771$	−1.88106	−0.0677447
$772$	−1.89584	−0.0682329
$773$	21.7936	0.783861	0.391930	−	0.919995i	$-0.371807\pi$
$773$	21.7936	0.783861	0.391930	+	0.919995i	$0.371807\pi$
$774$	2.37361	0.0853175
$775$	−14.3437	−0.515242
$776$	21.4380	0.769580
$777$	−4.54101	−0.162908
$778$	39.6147	1.42026
$779$	−2.04348	−0.0732151
$780$	−0.336625	−0.0120531
$781$	−11.2035	−0.400893
$782$	−13.4523	−0.481055
$783$	−2.62142	−0.0936820
$784$	−27.2761	−0.974148
$785$	3.68489	0.131519
$786$	−1.73008	−0.0617101
$787$	−31.4728	−1.12188	−0.560942	−	0.827855i	$-0.689561\pi$
$787$	−31.4728	−1.12188	−0.560942	+	0.827855i	$0.689561\pi$
$788$	2.29444	0.0817359
$789$	−6.62719	−0.235934
$790$	−13.6832	−0.486825
$791$	38.1242	1.35554
$792$	22.4794	0.798770
$793$	14.4825	0.514287
$794$	−14.4213	−0.511791
$795$	−1.15043	−0.0408016
$796$	−2.96803	−0.105199
$797$	−7.66543	−0.271523	−0.135762	−	0.990742i	$-0.543348\pi$
$797$	−7.66543	−0.271523	−0.135762	+	0.990742i	$0.543348\pi$
$798$	8.44603	0.298986
$799$	28.2703	1.00013
$800$	1.05894	0.0374393
$801$	43.2628	1.52862
$802$	−7.61068	−0.268743
$803$	44.9211	1.58523
$804$	0.271119	0.00956162
$805$	−13.6203	−0.480052
$806$	32.2118	1.13461
$807$	2.24393	0.0789899
$808$	−6.42661	−0.226087
$809$	25.1641	0.884724	0.442362	−	0.896837i	$-0.354141\pi$
$809$	25.1641	0.884724	0.442362	+	0.896837i	$0.354141\pi$
$810$	26.9395	0.946557
$811$	12.5757	0.441593	0.220797	−	0.975320i	$-0.429134\pi$
$811$	12.5757	0.441593	0.220797	+	0.975320i	$0.429134\pi$
$812$	0.425858	0.0149447
$813$	5.77552	0.202556
$814$	−11.6777	−0.409303
$815$	−1.95228	−0.0683854
$816$	−12.2280	−0.428064
$817$	−2.04185	−0.0714353
$818$	11.1137	0.388581
$819$	−25.5760	−0.893697
$820$	−0.174367	−0.00608917
$821$	5.56714	0.194295	0.0971473	−	0.995270i	$-0.469028\pi$
$821$	5.56714	0.194295	0.0971473	+	0.995270i	$0.469028\pi$
$822$	6.11503	0.213286
$823$	39.5808	1.37970	0.689849	−	0.723953i	$-0.257677\pi$
$823$	39.5808	1.37970	0.689849	+	0.723953i	$0.257677\pi$
$824$	4.84750	0.168871
$825$	−2.14362	−0.0746311
$826$	−35.7281	−1.24314
$827$	40.0374	1.39224	0.696118	−	0.717927i	$-0.254909\pi$
$827$	40.0374	1.39224	0.696118	+	0.717927i	$0.254909\pi$
$828$	−0.468168	−0.0162700
$829$	42.4014	1.47266	0.736331	−	0.676622i	$-0.236557\pi$
$829$	42.4014	1.47266	0.736331	+	0.676622i	$0.236557\pi$
$830$	43.0147	1.49306
$831$	−8.65585	−0.300268
$832$	18.6586	0.646870
$833$	41.4323	1.43554
$834$	−0.657986	−0.0227842
$835$	−47.4026	−1.64043
$836$	1.19119	0.0411983
$837$	23.2817	0.804733
$838$	12.6948	0.438535
$839$	5.58659	0.192871	0.0964353	−	0.995339i	$-0.469256\pi$
$839$	5.58659	0.192871	0.0964353	+	0.995339i	$0.469256\pi$
$840$	−11.6995	−0.403670
$841$	1.00000	0.0344828
$842$	19.6719	0.677937
$843$	8.47395	0.291858
$844$	2.08690	0.0718341
$845$	17.4468	0.600189
$846$	17.9394	0.616771
$847$	−8.76923	−0.301314
$848$	−4.17170	−0.143257
$849$	−12.4731	−0.428075
$850$	−15.0548	−0.516377
$851$	−3.94813	−0.135340
$852$	0.200424	0.00686642
$853$	−53.3606	−1.82703	−0.913515	−	0.406804i	$-0.866643\pi$
$853$	−53.3606	−1.82703	−0.913515	+	0.406804i	$0.866643\pi$
$854$	−31.0058	−1.06100
$855$	−25.1497	−0.860101
$856$	−48.5828	−1.66053
$857$	−27.2601	−0.931186	−0.465593	−	0.884999i	$-0.654159\pi$
$857$	−27.2601	−0.931186	−0.465593	+	0.884999i	$0.654159\pi$
$858$	4.81394	0.164345
$859$	57.3332	1.95618	0.978091	−	0.208177i	$-0.0667531\pi$
$859$	57.3332	1.95618	0.978091	+	0.208177i	$0.0667531\pi$
$860$	−0.174229	−0.00594115
$861$	0.969648	0.0330455
$862$	9.87692	0.336409
$863$	−18.3434	−0.624417	−0.312209	−	0.950014i	$-0.601069\pi$
$863$	−18.3434	−0.624417	−0.312209	+	0.950014i	$0.601069\pi$
$864$	−1.71880	−0.0584747
$865$	0.758909	0.0258037
$866$	44.1442	1.50008
$867$	10.8846	0.369661
$868$	−3.78218	−0.128375
$869$	10.7316	0.364045
$870$	1.69232	0.0573751
$871$	12.8774	0.436335
$872$	−19.3543	−0.655418
$873$	−21.8673	−0.740098
$874$	7.34331	0.248391
$875$	31.9472	1.08001
$876$	−0.803612	−0.0271515
$877$	40.9857	1.38399	0.691995	−	0.721902i	$-0.256732\pi$
$877$	40.9857	1.38399	0.691995	+	0.721902i	$0.256732\pi$
$878$	12.3788	0.417766
$879$	−2.66461	−0.0898751
$880$	−31.8381	−1.07326
$881$	−41.2195	−1.38872	−0.694361	−	0.719627i	$-0.744313\pi$
$881$	−41.2195	−1.38872	−0.694361	+	0.719627i	$0.744313\pi$
$882$	26.2917	0.885286
$883$	−15.6951	−0.528182	−0.264091	−	0.964498i	$-0.585072\pi$
$883$	−15.6951	−0.528182	−0.264091	+	0.964498i	$0.585072\pi$
$884$	1.85419	0.0623632
$885$	−7.78671	−0.261747
$886$	30.8582	1.03670
$887$	−21.2244	−0.712645	−0.356323	−	0.934363i	$-0.615970\pi$
$887$	−21.2244	−0.712645	−0.356323	+	0.934363i	$0.615970\pi$
$888$	−3.39134	−0.113806
$889$	−13.8227	−0.463597
$890$	−57.9029	−1.94091
$891$	−21.1285	−0.707831
$892$	−2.13293	−0.0714159
$893$	−15.4321	−0.516415
$894$	−4.42172	−0.147884
$895$	−28.2562	−0.944500
$896$	−44.7587	−1.49528
$897$	1.62755	0.0543425
$898$	6.04043	0.201572
$899$	−8.88131	−0.296208
$900$	−0.523938	−0.0174646
$901$	6.33679	0.211109
$902$	2.49355	0.0830263
$903$	0.968878	0.0322422
$904$	28.4721	0.946967
$905$	67.7859	2.25328
$906$	3.49332	0.116058
$907$	−26.0532	−0.865081	−0.432541	−	0.901614i	$-0.642383\pi$
$907$	−26.0532	−0.865081	−0.432541	+	0.901614i	$0.642383\pi$
$908$	−2.47515	−0.0821408
$909$	6.55532	0.217426
$910$	34.2309	1.13474
$911$	13.3378	0.441900	0.220950	−	0.975285i	$-0.429084\pi$
$911$	13.3378	0.441900	0.220950	+	0.975285i	$0.429084\pi$
$912$	6.67495	0.221030
$913$	−33.7362	−1.11651
$914$	−39.3317	−1.30098
$915$	−6.75752	−0.223397
$916$	1.47374	0.0486939
$917$	9.64859	0.318624
$918$	24.4359	0.806505
$919$	−0.475423	−0.0156828	−0.00784138	−	0.999969i	$-0.502496\pi$
$919$	−0.475423	−0.0156828	−0.00784138	+	0.999969i	$0.502496\pi$
$920$	−10.1720	−0.335360
$921$	−11.2844	−0.371835
$922$	23.5164	0.774470
$923$	9.51963	0.313343
$924$	−0.565232	−0.0185948
$925$	−4.41845	−0.145278
$926$	25.0998	0.824831
$927$	−4.94458	−0.162401
$928$	0.655674	0.0215236
$929$	30.3197	0.994758	0.497379	−	0.867533i	$-0.334296\pi$
$929$	30.3197	0.994758	0.497379	+	0.867533i	$0.334296\pi$
$930$	−15.0301	−0.492855
$931$	−22.6169	−0.741240
$932$	−1.53092	−0.0501469
$933$	−7.58528	−0.248331
$934$	44.0156	1.44024
$935$	48.3619	1.58160
$936$	−19.1008	−0.624328
$937$	0.0853592	0.00278856	0.00139428	−	0.999999i	$-0.499556\pi$
$937$	0.0853592	0.00278856	0.00139428	+	0.999999i	$0.499556\pi$
$938$	−27.5696	−0.900180
$939$	11.7198	0.382462
$940$	−1.31680	−0.0429493
$941$	−27.7946	−0.906079	−0.453039	−	0.891491i	$-0.649660\pi$
$941$	−27.7946	−0.906079	−0.453039	+	0.891491i	$0.649660\pi$
$942$	0.942703	0.0307149
$943$	0.843051	0.0274535
$944$	−28.2362	−0.919008
$945$	24.7410	0.804824
$946$	2.49157	0.0810080
$947$	31.4047	1.02052	0.510258	−	0.860021i	$-0.329550\pi$
$947$	31.4047	1.02052	0.510258	+	0.860021i	$0.329550\pi$
$948$	−0.191983	−0.00623531
$949$	−38.1695	−1.23903
$950$	8.21808	0.266630
$951$	−12.6304	−0.409569
$952$	64.4427	2.08860
$953$	−5.72063	−0.185309	−0.0926546	−	0.995698i	$-0.529535\pi$
$953$	−5.72063	−0.185309	−0.0926546	+	0.995698i	$0.529535\pi$
$954$	4.02113	0.130189
$955$	59.3244	1.91969
$956$	−0.824752	−0.0266744
$957$	−1.32728	−0.0429048
$958$	−9.91758	−0.320423
$959$	−34.1032	−1.10125
$960$	−8.70611	−0.280988
$961$	47.8777	1.54444
$962$	9.92255	0.319916
$963$	49.5558	1.59691
$964$	−1.55239	−0.0499990
$965$	42.0163	1.35255
$966$	−3.48447	−0.112111
$967$	−29.7803	−0.957671	−0.478835	−	0.877905i	$-0.658941\pi$
$967$	−29.7803	−0.957671	−0.478835	+	0.877905i	$0.658941\pi$
$968$	−6.54908	−0.210495
$969$	−10.1392	−0.325719
$970$	29.2672	0.939715
$971$	−5.97181	−0.191645	−0.0958223	−	0.995398i	$-0.530548\pi$
$971$	−5.97181	−0.191645	−0.0958223	+	0.995398i	$0.530548\pi$
$972$	1.29064	0.0413972
$973$	3.66955	0.117641
$974$	−19.6266	−0.628877
$975$	1.82144	0.0583326
$976$	−24.5041	−0.784358
$977$	51.5863	1.65039	0.825196	−	0.564846i	$-0.191065\pi$
$977$	51.5863	1.65039	0.825196	+	0.564846i	$0.191065\pi$
$978$	−0.499451	−0.0159707
$979$	45.4129	1.45140
$980$	−1.92987	−0.0616475
$981$	19.7419	0.630309
$982$	20.3402	0.649080
$983$	−20.9291	−0.667535	−0.333768	−	0.942655i	$-0.608320\pi$
$983$	−20.9291	−0.667535	−0.333768	+	0.942655i	$0.608320\pi$
$984$	0.724158	0.0230853
$985$	−50.8500	−1.62022
$986$	−9.32162	−0.296861
$987$	7.32266	0.233083
$988$	−1.01216	−0.0322011
$989$	0.842380	0.0267861
$990$	30.6889	0.975358
$991$	−5.93374	−0.188491	−0.0942457	−	0.995549i	$-0.530044\pi$
$991$	−5.93374	−0.188491	−0.0942457	+	0.995549i	$0.530044\pi$
$992$	−5.82325	−0.184888
$993$	3.10929	0.0986705
$994$	−20.3808	−0.646440
$995$	65.7785	2.08532
$996$	0.603522	0.0191233
$997$	−10.2541	−0.324752	−0.162376	−	0.986729i	$-0.551916\pi$
$997$	−10.2541	−0.324752	−0.162376	+	0.986729i	$0.551916\pi$
$998$	53.3134	1.68761
$999$	7.17170	0.226903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.b.1.16	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.b.1.16	✓	59	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)

\(f(q)\)	\(=\)	\(q-1.45467 q^{2} +0.452328 q^{3} +0.116052 q^{4} -2.57197 q^{5} -0.657986 q^{6} +3.66955 q^{7} +2.74051 q^{8} -2.79540 q^{9} +O(q^{10})\)	\(q-1.45467 q^{2} +0.452328 q^{3} +0.116052 q^{4} -2.57197 q^{5} -0.657986 q^{6} +3.66955 q^{7} +2.74051 q^{8} -2.79540 q^{9} +3.74136 q^{10} -2.93433 q^{11} +0.0524935 q^{12} +2.49330 q^{13} -5.33797 q^{14} -1.16338 q^{15} -4.21864 q^{16} +6.40808 q^{17} +4.06637 q^{18} -3.49802 q^{19} -0.298482 q^{20} +1.65984 q^{21} +4.26846 q^{22} +1.44313 q^{23} +1.23961 q^{24} +1.61505 q^{25} -3.62692 q^{26} -2.62142 q^{27} +0.425858 q^{28} +1.00000 q^{29} +1.69232 q^{30} -8.88131 q^{31} +0.655674 q^{32} -1.32728 q^{33} -9.32162 q^{34} -9.43800 q^{35} -0.324411 q^{36} -2.73580 q^{37} +5.08845 q^{38} +1.12779 q^{39} -7.04853 q^{40} +0.584181 q^{41} -2.41452 q^{42} +0.583716 q^{43} -0.340534 q^{44} +7.18969 q^{45} -2.09928 q^{46} +4.41166 q^{47} -1.90821 q^{48} +6.46563 q^{49} -2.34935 q^{50} +2.89856 q^{51} +0.289352 q^{52} +0.988874 q^{53} +3.81329 q^{54} +7.54701 q^{55} +10.0565 q^{56} -1.58225 q^{57} -1.45467 q^{58} +6.69320 q^{59} -0.135012 q^{60} +5.80854 q^{61} +12.9193 q^{62} -10.2579 q^{63} +7.48348 q^{64} -6.41271 q^{65} +1.93075 q^{66} +5.16481 q^{67} +0.743669 q^{68} +0.652770 q^{69} +13.7291 q^{70} +3.81808 q^{71} -7.66083 q^{72} -15.3088 q^{73} +3.97968 q^{74} +0.730531 q^{75} -0.405951 q^{76} -10.7677 q^{77} -1.64056 q^{78} -3.65727 q^{79} +10.8502 q^{80} +7.20045 q^{81} -0.849787 q^{82} +11.4971 q^{83} +0.192628 q^{84} -16.4814 q^{85} -0.849112 q^{86} +0.452328 q^{87} -8.04157 q^{88} -15.4764 q^{89} -10.4586 q^{90} +9.14931 q^{91} +0.167478 q^{92} -4.01727 q^{93} -6.41749 q^{94} +8.99682 q^{95} +0.296580 q^{96} +7.82262 q^{97} -9.40533 q^{98} +8.20261 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9} - 18 q^{10} - 27 q^{11} - 8 q^{12} - 22 q^{13} - 24 q^{14} - 18 q^{15} + 5 q^{16} - 23 q^{17} + q^{18} - 32 q^{19} - 14 q^{20} - 36 q^{21} - 6 q^{22} - 3 q^{23} - 18 q^{24} - 8 q^{25} - q^{26} - 12 q^{27} - 9 q^{28} + 59 q^{29} - 18 q^{30} - 32 q^{31} - 39 q^{32} - 12 q^{33} - 18 q^{34} - 9 q^{35} + 10 q^{36} - 44 q^{37} + 5 q^{38} - 27 q^{39} - 68 q^{40} - 44 q^{41} - 25 q^{42} - 40 q^{43} - 56 q^{44} - 39 q^{45} - 40 q^{46} - 20 q^{47} - 9 q^{48} - 39 q^{49} - 21 q^{50} - 28 q^{51} - 49 q^{52} - 31 q^{53} - 32 q^{54} - 32 q^{55} - 48 q^{56} - 58 q^{57} - 5 q^{58} + 6 q^{59} - 44 q^{60} - 88 q^{61} + 35 q^{62} - 22 q^{63} - 10 q^{64} - 43 q^{65} - 31 q^{66} - 45 q^{67} - 29 q^{68} - 60 q^{69} - 14 q^{70} - 20 q^{71} - 4 q^{72} - 90 q^{73} - 25 q^{74} + 15 q^{75} - 64 q^{76} - 39 q^{77} - 28 q^{78} - 120 q^{79} + 24 q^{80} - 77 q^{81} - 71 q^{82} - 33 q^{83} - 14 q^{84} - 71 q^{85} - 61 q^{86} - 6 q^{87} - 34 q^{88} - 78 q^{89} - 88 q^{90} - 28 q^{91} - 31 q^{92} - 36 q^{93} - 4 q^{94} - 12 q^{95} - 29 q^{96} - 48 q^{97} - 4 q^{98} - 43 q^{99}+O(q^{100}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9 - 18 * q^10 - 27 * q^11 - 8 * q^12 - 22 * q^13 - 24 * q^14 - 18 * q^15 + 5 * q^16 - 23 * q^17 + q^18 - 32 * q^19 - 14 * q^20 - 36 * q^21 - 6 * q^22 - 3 * q^23 - 18 * q^24 - 8 * q^25 - q^26 - 12 * q^27 - 9 * q^28 + 59 * q^29 - 18 * q^30 - 32 * q^31 - 39 * q^32 - 12 * q^33 - 18 * q^34 - 9 * q^35 + 10 * q^36 - 44 * q^37 + 5 * q^38 - 27 * q^39 - 68 * q^40 - 44 * q^41 - 25 * q^42 - 40 * q^43 - 56 * q^44 - 39 * q^45 - 40 * q^46 - 20 * q^47 - 9 * q^48 - 39 * q^49 - 21 * q^50 - 28 * q^51 - 49 * q^52 - 31 * q^53 - 32 * q^54 - 32 * q^55 - 48 * q^56 - 58 * q^57 - 5 * q^58 + 6 * q^59 - 44 * q^60 - 88 * q^61 + 35 * q^62 - 22 * q^63 - 10 * q^64 - 43 * q^65 - 31 * q^66 - 45 * q^67 - 29 * q^68 - 60 * q^69 - 14 * q^70 - 20 * q^71 - 4 * q^72 - 90 * q^73 - 25 * q^74 + 15 * q^75 - 64 * q^76 - 39 * q^77 - 28 * q^78 - 120 * q^79 + 24 * q^80 - 77 * q^81 - 71 * q^82 - 33 * q^83 - 14 * q^84 - 71 * q^85 - 61 * q^86 - 6 * q^87 - 34 * q^88 - 78 * q^89 - 88 * q^90 - 28 * q^91 - 31 * q^92 - 36 * q^93 - 4 * q^94 - 12 * q^95 - 29 * q^96 - 48 * q^97 - 4 * q^98 - 43 * q^99

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