LMFDB - Embedded newform 4031.2.a.d.1.19

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:	$0$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-1.93664 q^{2} +0.437969 q^{3} +1.75056 q^{4} +3.14696 q^{5} -0.848187 q^{6} +5.11562 q^{7} +0.483081 q^{8} -2.80818 q^{9} +O(q^{10})$	\(q-1.93664 q^{2} +0.437969 q^{3} +1.75056 q^{4} +3.14696 q^{5} -0.848187 q^{6} +5.11562 q^{7} +0.483081 q^{8} -2.80818 q^{9} -6.09452 q^{10} +3.65345 q^{11} +0.766690 q^{12} +0.354272 q^{13} -9.90708 q^{14} +1.37827 q^{15} -4.43666 q^{16} +2.81074 q^{17} +5.43843 q^{18} +3.46494 q^{19} +5.50894 q^{20} +2.24048 q^{21} -7.07539 q^{22} -6.34848 q^{23} +0.211575 q^{24} +4.90338 q^{25} -0.686096 q^{26} -2.54381 q^{27} +8.95517 q^{28} +1.00000 q^{29} -2.66921 q^{30} +3.54310 q^{31} +7.62604 q^{32} +1.60010 q^{33} -5.44337 q^{34} +16.0987 q^{35} -4.91588 q^{36} -6.77448 q^{37} -6.71032 q^{38} +0.155160 q^{39} +1.52024 q^{40} -11.0478 q^{41} -4.33900 q^{42} +2.18313 q^{43} +6.39556 q^{44} -8.83725 q^{45} +12.2947 q^{46} -1.16359 q^{47} -1.94312 q^{48} +19.1695 q^{49} -9.49606 q^{50} +1.23102 q^{51} +0.620173 q^{52} +7.73616 q^{53} +4.92643 q^{54} +11.4973 q^{55} +2.47126 q^{56} +1.51754 q^{57} -1.93664 q^{58} +5.89300 q^{59} +2.41275 q^{60} +1.44485 q^{61} -6.86169 q^{62} -14.3656 q^{63} -5.89553 q^{64} +1.11488 q^{65} -3.09881 q^{66} +5.71890 q^{67} +4.92035 q^{68} -2.78044 q^{69} -31.1772 q^{70} -2.85712 q^{71} -1.35658 q^{72} +4.02953 q^{73} +13.1197 q^{74} +2.14753 q^{75} +6.06557 q^{76} +18.6896 q^{77} -0.300489 q^{78} -3.64360 q^{79} -13.9620 q^{80} +7.31044 q^{81} +21.3957 q^{82} +15.4430 q^{83} +3.92209 q^{84} +8.84529 q^{85} -4.22793 q^{86} +0.437969 q^{87} +1.76491 q^{88} -1.38864 q^{89} +17.1145 q^{90} +1.81232 q^{91} -11.1134 q^{92} +1.55177 q^{93} +2.25345 q^{94} +10.9040 q^{95} +3.33997 q^{96} -6.62731 q^{97} -37.1244 q^{98} -10.2595 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) $ 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * 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 $

$2$	−1.93664	−1.36941	−0.684704	−	0.728821i	$-0.740069\pi$
$2$	−1.93664	−1.36941	−0.684704	+	0.728821i	$0.740069\pi$
$3$	0.437969	0.252862	0.126431	−	0.991975i	$-0.459648\pi$
$3$	0.437969	0.252862	0.126431	+	0.991975i	$0.459648\pi$
$4$	1.75056	0.875278
$5$	3.14696	1.40736	0.703682	−	0.710515i	$-0.251538\pi$
$5$	3.14696	1.40736	0.703682	+	0.710515i	$0.251538\pi$
$6$	−0.848187	−0.346271
$7$	5.11562	1.93352	0.966760	−	0.255684i	$-0.0823007\pi$
$7$	5.11562	1.93352	0.966760	+	0.255684i	$0.0823007\pi$
$8$	0.483081	0.170795
$9$	−2.80818	−0.936061
$10$	−6.09452	−1.92726
$11$	3.65345	1.10156	0.550778	−	0.834652i	$-0.314331\pi$
$11$	3.65345	1.10156	0.550778	+	0.834652i	$0.314331\pi$
$12$	0.766690	0.221324
$13$	0.354272	0.0982574	0.0491287	−	0.998792i	$-0.484356\pi$
$13$	0.354272	0.0982574	0.0491287	+	0.998792i	$0.484356\pi$
$14$	−9.90708	−2.64778
$15$	1.37827	0.355869
$16$	−4.43666	−1.10917
$17$	2.81074	0.681704	0.340852	−	0.940117i	$-0.389285\pi$
$17$	2.81074	0.681704	0.340852	+	0.940117i	$0.389285\pi$
$18$	5.43843	1.28185
$19$	3.46494	0.794911	0.397455	−	0.917622i	$-0.369893\pi$
$19$	3.46494	0.794911	0.397455	+	0.917622i	$0.369893\pi$
$20$	5.50894	1.23184
$21$	2.24048	0.488914
$22$	−7.07539	−1.50848
$23$	−6.34848	−1.32375	−0.661875	−	0.749614i	$-0.730239\pi$
$23$	−6.34848	−1.32375	−0.661875	+	0.749614i	$0.730239\pi$
$24$	0.211575	0.0431875
$25$	4.90338	0.980676
$26$	−0.686096	−0.134554
$27$	−2.54381	−0.489556
$28$	8.95517	1.69237
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−2.66921	−0.487330
$31$	3.54310	0.636360	0.318180	−	0.948030i	$-0.396928\pi$
$31$	3.54310	0.636360	0.318180	+	0.948030i	$0.396928\pi$
$32$	7.62604	1.34811
$33$	1.60010	0.278541
$34$	−5.44337	−0.933531
$35$	16.0987	2.72117
$36$	−4.91588	−0.819314
$37$	−6.77448	−1.11372	−0.556859	−	0.830607i	$-0.687993\pi$
$37$	−6.77448	−1.11372	−0.556859	+	0.830607i	$0.687993\pi$
$38$	−6.71032	−1.08856
$39$	0.155160	0.0248455
$40$	1.52024	0.240371
$41$	−11.0478	−1.72538	−0.862692	−	0.505730i	$-0.831223\pi$
$41$	−11.0478	−1.72538	−0.862692	+	0.505730i	$0.831223\pi$
$42$	−4.33900	−0.669522
$43$	2.18313	0.332924	0.166462	−	0.986048i	$-0.446766\pi$
$43$	2.18313	0.332924	0.166462	+	0.986048i	$0.446766\pi$
$44$	6.39556	0.964167
$45$	−8.83725	−1.31738
$46$	12.2947	1.81275
$47$	−1.16359	−0.169727	−0.0848634	−	0.996393i	$-0.527045\pi$
$47$	−1.16359	−0.169727	−0.0848634	+	0.996393i	$0.527045\pi$
$48$	−1.94312	−0.280466
$49$	19.1695	2.73850
$50$	−9.49606	−1.34295
$51$	1.23102	0.172377
$52$	0.620173	0.0860026
$53$	7.73616	1.06264	0.531322	−	0.847170i	$-0.321696\pi$
$53$	7.73616	1.06264	0.531322	+	0.847170i	$0.321696\pi$
$54$	4.92643	0.670402
$55$	11.4973	1.55029
$56$	2.47126	0.330236
$57$	1.51754	0.201003
$58$	−1.93664	−0.254293
$59$	5.89300	0.767204	0.383602	−	0.923499i	$-0.374684\pi$
$59$	5.89300	0.767204	0.383602	+	0.923499i	$0.374684\pi$
$60$	2.41275	0.311484
$61$	1.44485	0.184994	0.0924972	−	0.995713i	$-0.470515\pi$
$61$	1.44485	0.184994	0.0924972	+	0.995713i	$0.470515\pi$
$62$	−6.86169	−0.871436
$63$	−14.3656	−1.80989
$64$	−5.89553	−0.736941
$65$	1.11488	0.138284
$66$	−3.09881	−0.381437
$67$	5.71890	0.698675	0.349338	−	0.936997i	$-0.386407\pi$
$67$	5.71890	0.698675	0.349338	+	0.936997i	$0.386407\pi$
$68$	4.92035	0.596680
$69$	−2.78044	−0.334726
$70$	−31.1772	−3.72639
$71$	−2.85712	−0.339078	−0.169539	−	0.985524i	$-0.554228\pi$
$71$	−2.85712	−0.339078	−0.169539	+	0.985524i	$0.554228\pi$
$72$	−1.35658	−0.159874
$73$	4.02953	0.471621	0.235811	−	0.971799i	$-0.424226\pi$
$73$	4.02953	0.471621	0.235811	+	0.971799i	$0.424226\pi$
$74$	13.1197	1.52513
$75$	2.14753	0.247975
$76$	6.06557	0.695768
$77$	18.6896	2.12988
$78$	−0.300489	−0.0340237
$79$	−3.64360	−0.409937	−0.204969	−	0.978769i	$-0.565709\pi$
$79$	−3.64360	−0.409937	−0.204969	+	0.978769i	$0.565709\pi$
$80$	−13.9620	−1.56100
$81$	7.31044	0.812271
$82$	21.3957	2.36275
$83$	15.4430	1.69509	0.847544	−	0.530726i	$-0.178081\pi$
$83$	15.4430	1.69509	0.847544	+	0.530726i	$0.178081\pi$
$84$	3.92209	0.427935
$85$	8.84529	0.959406
$86$	−4.22793	−0.455909
$87$	0.437969	0.0469553
$88$	1.76491	0.188140
$89$	−1.38864	−0.147195	−0.0735975	−	0.997288i	$-0.523448\pi$
$89$	−1.38864	−0.147195	−0.0735975	+	0.997288i	$0.523448\pi$
$90$	17.1145	1.80403
$91$	1.81232	0.189983
$92$	−11.1134	−1.15865
$93$	1.55177	0.160911
$94$	2.25345	0.232425
$95$	10.9040	1.11873
$96$	3.33997	0.340885
$97$	−6.62731	−0.672901	−0.336451	−	0.941701i	$-0.609227\pi$
$97$	−6.62731	−0.672901	−0.336451	+	0.941701i	$0.609227\pi$
$98$	−37.1244	−3.75013
$99$	−10.2595	−1.03112
$100$	8.58364	0.858364
$101$	14.3653	1.42940	0.714699	−	0.699432i	$-0.246563\pi$
$101$	14.3653	1.42940	0.714699	+	0.699432i	$0.246563\pi$
$102$	−2.38403	−0.236054
$103$	10.2005	1.00508	0.502542	−	0.864553i	$-0.332398\pi$
$103$	10.2005	1.00508	0.502542	+	0.864553i	$0.332398\pi$
$104$	0.171142	0.0167819
$105$	7.05072	0.688080
$106$	−14.9821	−1.45519
$107$	0.386089	0.0373246	0.0186623	−	0.999826i	$-0.494059\pi$
$107$	0.386089	0.0373246	0.0186623	+	0.999826i	$0.494059\pi$
$108$	−4.45308	−0.428498
$109$	−15.0176	−1.43843	−0.719215	−	0.694788i	$-0.755498\pi$
$109$	−15.0176	−1.43843	−0.719215	+	0.694788i	$0.755498\pi$
$110$	−22.2660	−2.12298
$111$	−2.96701	−0.281617
$112$	−22.6963	−2.14460
$113$	−3.94623	−0.371230	−0.185615	−	0.982623i	$-0.559428\pi$
$113$	−3.94623	−0.371230	−0.185615	+	0.982623i	$0.559428\pi$
$114$	−2.93891	−0.275254
$115$	−19.9784	−1.86300
$116$	1.75056	0.162535
$117$	−0.994861	−0.0919749
$118$	−11.4126	−1.05061
$119$	14.3786	1.31809
$120$	0.665818	0.0607806
$121$	2.34766	0.213424
$122$	−2.79815	−0.253333
$123$	−4.83862	−0.436284
$124$	6.20240	0.556992
$125$	−0.304061	−0.0271960
$126$	27.8209	2.47848
$127$	0.0907041	0.00804869	0.00402434	−	0.999992i	$-0.498719\pi$
$127$	0.0907041	0.00804869	0.00402434	+	0.999992i	$0.498719\pi$
$128$	−3.83459	−0.338933
$129$	0.956145	0.0841838
$130$	−2.15912	−0.189367
$131$	9.42719	0.823658	0.411829	−	0.911261i	$-0.364890\pi$
$131$	9.42719	0.823658	0.411829	+	0.911261i	$0.364890\pi$
$132$	2.80106	0.243801
$133$	17.7253	1.53698
$134$	−11.0754	−0.956772
$135$	−8.00527	−0.688984
$136$	1.35781	0.116432
$137$	7.55554	0.645513	0.322757	−	0.946482i	$-0.395390\pi$
$137$	7.55554	0.645513	0.322757	+	0.946482i	$0.395390\pi$
$138$	5.38470	0.458376
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	28.1816	2.38178
$141$	−0.509616	−0.0429174
$142$	5.53320	0.464336
$143$	1.29431	0.108236
$144$	12.4590	1.03825
$145$	3.14696	0.261341
$146$	−7.80373	−0.645842
$147$	8.39566	0.692463
$148$	−11.8591	−0.974812
$149$	−23.4761	−1.92324	−0.961620	−	0.274385i	$-0.911526\pi$
$149$	−23.4761	−1.92324	−0.961620	+	0.274385i	$0.911526\pi$
$150$	−4.15898	−0.339580
$151$	−9.39526	−0.764575	−0.382288	−	0.924043i	$-0.624864\pi$
$151$	−9.39526	−0.764575	−0.382288	+	0.924043i	$0.624864\pi$
$152$	1.67384	0.135767
$153$	−7.89306	−0.638116
$154$	−36.1950	−2.91667
$155$	11.1500	0.895590
$156$	0.271617	0.0217468
$157$	2.42743	0.193730	0.0968648	−	0.995298i	$-0.469119\pi$
$157$	2.42743	0.193730	0.0968648	+	0.995298i	$0.469119\pi$
$158$	7.05633	0.561371
$159$	3.38820	0.268702
$160$	23.9989	1.89728
$161$	−32.4764	−2.55950
$162$	−14.1577	−1.11233
$163$	20.8813	1.63555	0.817774	−	0.575539i	$-0.195208\pi$
$163$	20.8813	1.63555	0.817774	+	0.575539i	$0.195208\pi$
$164$	−19.3399	−1.51019
$165$	5.03545	0.392009
$166$	−29.9074	−2.32127
$167$	−22.5621	−1.74591	−0.872955	−	0.487801i	$-0.837799\pi$
$167$	−22.5621	−1.74591	−0.872955	+	0.487801i	$0.837799\pi$
$168$	1.08233	0.0835039
$169$	−12.8745	−0.990345
$170$	−17.1301	−1.31382
$171$	−9.73017	−0.744085
$172$	3.82169	0.291401
$173$	−7.55058	−0.574060	−0.287030	−	0.957922i	$-0.592668\pi$
$173$	−7.55058	−0.574060	−0.287030	+	0.957922i	$0.592668\pi$
$174$	−0.848187	−0.0643009
$175$	25.0838	1.89616
$176$	−16.2091	−1.22181
$177$	2.58096	0.193996
$178$	2.68928	0.201570
$179$	16.8953	1.26281	0.631406	−	0.775452i	$-0.282478\pi$
$179$	16.8953	1.26281	0.631406	+	0.775452i	$0.282478\pi$
$180$	−15.4701	−1.15307
$181$	−13.2486	−0.984762	−0.492381	−	0.870380i	$-0.663873\pi$
$181$	−13.2486	−0.984762	−0.492381	+	0.870380i	$0.663873\pi$
$182$	−3.50980	−0.260164
$183$	0.632801	0.0467780
$184$	−3.06683	−0.226090
$185$	−21.3190	−1.56741
$186$	−3.00521	−0.220353
$187$	10.2689	0.750934
$188$	−2.03693	−0.148558
$189$	−13.0131	−0.946566
$190$	−21.1171	−1.53200
$191$	−11.1152	−0.804266	−0.402133	−	0.915581i	$-0.631731\pi$
$191$	−11.1152	−0.804266	−0.402133	+	0.915581i	$0.631731\pi$
$192$	−2.58206	−0.186344
$193$	−10.2254	−0.736040	−0.368020	−	0.929818i	$-0.619964\pi$
$193$	−10.2254	−0.736040	−0.368020	+	0.929818i	$0.619964\pi$
$194$	12.8347	0.921477
$195$	0.488284	0.0349667
$196$	33.5573	2.39695
$197$	−15.7375	−1.12125	−0.560626	−	0.828069i	$-0.689439\pi$
$197$	−15.7375	−1.12125	−0.560626	+	0.828069i	$0.689439\pi$
$198$	19.8690	1.41203
$199$	−7.37785	−0.523002	−0.261501	−	0.965203i	$-0.584217\pi$
$199$	−7.37785	−0.523002	−0.261501	+	0.965203i	$0.584217\pi$
$200$	2.36873	0.167494
$201$	2.50471	0.176668
$202$	−27.8203	−1.95743
$203$	5.11562	0.359046
$204$	2.15496	0.150878
$205$	−34.7672	−2.42824
$206$	−19.7546	−1.37637
$207$	17.8277	1.23911
$208$	−1.57179	−0.108984
$209$	12.6590	0.875638
$210$	−13.6547	−0.942262
$211$	23.0402	1.58615	0.793076	−	0.609123i	$-0.208478\pi$
$211$	23.0402	1.58615	0.793076	+	0.609123i	$0.208478\pi$
$212$	13.5426	0.930109
$213$	−1.25133	−0.0857398
$214$	−0.747713	−0.0511126
$215$	6.87023	0.468546
$216$	−1.22886	−0.0836136
$217$	18.1251	1.23041
$218$	29.0837	1.96980
$219$	1.76481	0.119255
$220$	20.1266	1.35694
$221$	0.995766	0.0669824
$222$	5.74602	0.385648
$223$	−0.803997	−0.0538396	−0.0269198	−	0.999638i	$-0.508570\pi$
$223$	−0.803997	−0.0538396	−0.0269198	+	0.999638i	$0.508570\pi$
$224$	39.0119	2.60659
$225$	−13.7696	−0.917972
$226$	7.64241	0.508366
$227$	−2.51750	−0.167092	−0.0835460	−	0.996504i	$-0.526625\pi$
$227$	−2.51750	−0.167092	−0.0835460	+	0.996504i	$0.526625\pi$
$228$	2.65653	0.175933
$229$	9.34180	0.617323	0.308662	−	0.951172i	$-0.400119\pi$
$229$	9.34180	0.617323	0.308662	+	0.951172i	$0.400119\pi$
$230$	38.6909	2.55121
$231$	8.18548	0.538565
$232$	0.483081	0.0317158
$233$	13.4790	0.883036	0.441518	−	0.897253i	$-0.354440\pi$
$233$	13.4790	0.883036	0.441518	+	0.897253i	$0.354440\pi$
$234$	1.92668	0.125951
$235$	−3.66177	−0.238868
$236$	10.3160	0.671517
$237$	−1.59579	−0.103657
$238$	−27.8462	−1.80500
$239$	−18.7273	−1.21137	−0.605683	−	0.795706i	$-0.707100\pi$
$239$	−18.7273	−1.21137	−0.605683	+	0.795706i	$0.707100\pi$
$240$	−6.11494	−0.394718
$241$	27.2045	1.75240	0.876198	−	0.481952i	$-0.160072\pi$
$241$	27.2045	1.75240	0.876198	+	0.481952i	$0.160072\pi$
$242$	−4.54657	−0.292264
$243$	10.8332	0.694948
$244$	2.52930	0.161922
$245$	60.3258	3.85407
$246$	9.37064	0.597450
$247$	1.22753	0.0781059
$248$	1.71160	0.108687
$249$	6.76355	0.428623
$250$	0.588855	0.0372424
$251$	1.76427	0.111360	0.0556800	−	0.998449i	$-0.482267\pi$
$251$	1.76427	0.111360	0.0556800	+	0.998449i	$0.482267\pi$
$252$	−25.1478	−1.58416
$253$	−23.1938	−1.45818
$254$	−0.175661	−0.0110219
$255$	3.87396	0.242597
$256$	19.2173	1.20108
$257$	−16.1512	−1.00748	−0.503741	−	0.863855i	$-0.668043\pi$
$257$	−16.1512	−1.00748	−0.503741	+	0.863855i	$0.668043\pi$
$258$	−1.85170	−0.115282
$259$	−34.6556	−2.15340
$260$	1.95166	0.121037
$261$	−2.80818	−0.173822
$262$	−18.2570	−1.12792
$263$	−2.50495	−0.154462	−0.0772310	−	0.997013i	$-0.524608\pi$
$263$	−2.50495	−0.154462	−0.0772310	+	0.997013i	$0.524608\pi$
$264$	0.772977	0.0475734
$265$	24.3454	1.49553
$266$	−34.3274	−2.10475
$267$	−0.608180	−0.0372200
$268$	10.0113	0.611535
$269$	−8.81031	−0.537174	−0.268587	−	0.963255i	$-0.586557\pi$
$269$	−8.81031	−0.537174	−0.268587	+	0.963255i	$0.586557\pi$
$270$	15.5033	0.943500
$271$	−12.4384	−0.755578	−0.377789	−	0.925892i	$-0.623316\pi$
$271$	−12.4384	−0.755578	−0.377789	+	0.925892i	$0.623316\pi$
$272$	−12.4703	−0.756123
$273$	0.793741	0.0480394
$274$	−14.6323	−0.883971
$275$	17.9142	1.08027
$276$	−4.86732	−0.292978
$277$	31.2023	1.87476	0.937382	−	0.348302i	$-0.113242\pi$
$277$	31.2023	1.87476	0.937382	+	0.348302i	$0.113242\pi$
$278$	1.93664	0.116152
$279$	−9.94967	−0.595671
$280$	7.77695	0.464762
$281$	−15.9215	−0.949794	−0.474897	−	0.880041i	$-0.657515\pi$
$281$	−15.9215	−0.949794	−0.474897	+	0.880041i	$0.657515\pi$
$282$	0.986941	0.0587715
$283$	−5.12502	−0.304651	−0.152325	−	0.988330i	$-0.548676\pi$
$283$	−5.12502	−0.304651	−0.152325	+	0.988330i	$0.548676\pi$
$284$	−5.00155	−0.296787
$285$	4.77563	0.282884
$286$	−2.50661	−0.148219
$287$	−56.5165	−3.33607
$288$	−21.4153	−1.26191
$289$	−9.09976	−0.535280
$290$	−6.09452	−0.357883
$291$	−2.90256	−0.170151
$292$	7.05392	0.412800
$293$	−15.2258	−0.889503	−0.444752	−	0.895654i	$-0.646708\pi$
$293$	−15.2258	−0.889503	−0.444752	+	0.895654i	$0.646708\pi$
$294$	−16.2593	−0.948264
$295$	18.5451	1.07974
$296$	−3.27262	−0.190217
$297$	−9.29366	−0.539273
$298$	45.4647	2.63370
$299$	−2.24909	−0.130068
$300$	3.75937	0.217048
$301$	11.1681	0.643716
$302$	18.1952	1.04702
$303$	6.29155	0.361440
$304$	−15.3728	−0.881688
$305$	4.54690	0.260355
$306$	15.2860	0.873841
$307$	29.0946	1.66052	0.830258	−	0.557379i	$-0.188193\pi$
$307$	29.0946	1.66052	0.830258	+	0.557379i	$0.188193\pi$
$308$	32.7172	1.86424
$309$	4.46750	0.254147
$310$	−21.5935	−1.22643
$311$	16.9724	0.962416	0.481208	−	0.876606i	$-0.340198\pi$
$311$	16.9724	0.962416	0.481208	+	0.876606i	$0.340198\pi$
$312$	0.0749550	0.00424349
$313$	13.4328	0.759264	0.379632	−	0.925138i	$-0.376051\pi$
$313$	13.4328	0.759264	0.379632	+	0.925138i	$0.376051\pi$
$314$	−4.70104	−0.265295
$315$	−45.2080	−2.54718
$316$	−6.37833	−0.358809
$317$	−2.84993	−0.160068	−0.0800341	−	0.996792i	$-0.525503\pi$
$317$	−2.84993	−0.160068	−0.0800341	+	0.996792i	$0.525503\pi$
$318$	−6.56171	−0.367963
$319$	3.65345	0.204554
$320$	−18.5530	−1.03715
$321$	0.169095	0.00943796
$322$	62.8949	3.50500
$323$	9.73902	0.541894
$324$	12.7973	0.710963
$325$	1.73713	0.0963587
$326$	−40.4394	−2.23973
$327$	−6.57727	−0.363724
$328$	−5.33700	−0.294687
$329$	−5.95247	−0.328170
$330$	−9.75183	−0.536820
$331$	20.4214	1.12246	0.561229	−	0.827660i	$-0.310329\pi$
$331$	20.4214	1.12246	0.561229	+	0.827660i	$0.310329\pi$
$332$	27.0338	1.48367
$333$	19.0240	1.04251
$334$	43.6946	2.39086
$335$	17.9972	0.983291
$336$	−9.94027	−0.542286
$337$	9.39521	0.511790	0.255895	−	0.966705i	$-0.417630\pi$
$337$	9.39521	0.511790	0.255895	+	0.966705i	$0.417630\pi$
$338$	24.9332	1.35619
$339$	−1.72833	−0.0938699
$340$	15.4842	0.839747
$341$	12.9445	0.700985
$342$	18.8438	1.01896
$343$	62.2546	3.36143
$344$	1.05463	0.0568618
$345$	−8.74994	−0.471081
$346$	14.6227	0.786122
$347$	−29.9157	−1.60596	−0.802979	−	0.596007i	$-0.796753\pi$
$347$	−29.9157	−1.60596	−0.802979	+	0.596007i	$0.796753\pi$
$348$	0.766690	0.0410989
$349$	−5.51561	−0.295244	−0.147622	−	0.989044i	$-0.547162\pi$
$349$	−5.51561	−0.295244	−0.147622	+	0.989044i	$0.547162\pi$
$350$	−48.5782	−2.59661
$351$	−0.901200	−0.0481025
$352$	27.8613	1.48501
$353$	11.8548	0.630965	0.315483	−	0.948931i	$-0.397834\pi$
$353$	11.8548	0.630965	0.315483	+	0.948931i	$0.397834\pi$
$354$	−4.99837	−0.265660
$355$	−8.99125	−0.477206
$356$	−2.43089	−0.128837
$357$	6.29741	0.333294
$358$	−32.7200	−1.72931
$359$	−7.76461	−0.409801	−0.204900	−	0.978783i	$-0.565687\pi$
$359$	−7.76461	−0.409801	−0.204900	+	0.978783i	$0.565687\pi$
$360$	−4.26911	−0.225002
$361$	−6.99422	−0.368117
$362$	25.6577	1.34854
$363$	1.02820	0.0539668
$364$	3.17257	0.166288
$365$	12.6808	0.663743
$366$	−1.22551	−0.0640582
$367$	−29.2094	−1.52472	−0.762359	−	0.647154i	$-0.775959\pi$
$367$	−29.2094	−1.52472	−0.762359	+	0.647154i	$0.775959\pi$
$368$	28.1661	1.46826
$369$	31.0244	1.61506
$370$	41.2872	2.14642
$371$	39.5752	2.05464
$372$	2.71646	0.140842
$373$	−14.6608	−0.759109	−0.379555	−	0.925169i	$-0.623923\pi$
$373$	−14.6608	−0.759109	−0.379555	+	0.925169i	$0.623923\pi$
$374$	−19.8871	−1.02834
$375$	−0.133169	−0.00687683
$376$	−0.562108	−0.0289885
$377$	0.354272	0.0182459
$378$	25.2017	1.29624
$379$	6.45712	0.331680	0.165840	−	0.986153i	$-0.446967\pi$
$379$	6.45712	0.331680	0.165840	+	0.986153i	$0.446967\pi$
$380$	19.0881	0.979200
$381$	0.0397256	0.00203521
$382$	21.5260	1.10137
$383$	−19.3798	−0.990262	−0.495131	−	0.868818i	$-0.664880\pi$
$383$	−19.3798	−0.990262	−0.495131	+	0.868818i	$0.664880\pi$
$384$	−1.67943	−0.0857032
$385$	58.8156	2.99752
$386$	19.8029	1.00794
$387$	−6.13063	−0.311637
$388$	−11.6015	−0.588976
$389$	−2.76006	−0.139941	−0.0699703	−	0.997549i	$-0.522290\pi$
$389$	−2.76006	−0.139941	−0.0699703	+	0.997549i	$0.522290\pi$
$390$	−0.945628	−0.0478837
$391$	−17.8439	−0.902405
$392$	9.26043	0.467722
$393$	4.12882	0.208272
$394$	30.4778	1.53545
$395$	−11.4663	−0.576931
$396$	−17.9599	−0.902519
$397$	25.2103	1.26527	0.632635	−	0.774450i	$-0.281973\pi$
$397$	25.2103	1.26527	0.632635	+	0.774450i	$0.281973\pi$
$398$	14.2882	0.716203
$399$	7.76313	0.388643
$400$	−21.7547	−1.08773
$401$	−22.0504	−1.10115	−0.550573	−	0.834787i	$-0.685591\pi$
$401$	−22.0504	−1.10115	−0.550573	+	0.834787i	$0.685591\pi$
$402$	−4.85070	−0.241931
$403$	1.25522	0.0625270
$404$	25.1472	1.25112
$405$	23.0057	1.14316
$406$	−9.90708	−0.491680
$407$	−24.7502	−1.22682
$408$	0.594681	0.0294411
$409$	28.9698	1.43246	0.716232	−	0.697862i	$-0.245865\pi$
$409$	28.9698	1.43246	0.716232	+	0.697862i	$0.245865\pi$
$410$	67.3313	3.32526
$411$	3.30910	0.163226
$412$	17.8565	0.879728
$413$	30.1463	1.48340
$414$	−34.5257	−1.69685
$415$	48.5985	2.38561
$416$	2.70169	0.132461
$417$	−0.437969	−0.0214475
$418$	−24.5158	−1.19911
$419$	−22.0303	−1.07625	−0.538126	−	0.842865i	$-0.680867\pi$
$419$	−22.0303	−1.07625	−0.538126	+	0.842865i	$0.680867\pi$
$420$	12.3427	0.602261
$421$	−32.6691	−1.59220	−0.796098	−	0.605168i	$-0.793106\pi$
$421$	−32.6691	−1.59220	−0.796098	+	0.605168i	$0.793106\pi$
$422$	−44.6204	−2.17209
$423$	3.26757	0.158875
$424$	3.73719	0.181494
$425$	13.7821	0.668530
$426$	2.42337	0.117413
$427$	7.39131	0.357691
$428$	0.675870	0.0326694
$429$	0.566870	0.0273687
$430$	−13.3051	−0.641631
$431$	−0.742080	−0.0357447	−0.0178724	−	0.999840i	$-0.505689\pi$
$431$	−0.742080	−0.0357447	−0.0178724	+	0.999840i	$0.505689\pi$
$432$	11.2860	0.542999
$433$	37.7250	1.81295	0.906474	−	0.422263i	$-0.138764\pi$
$433$	37.7250	1.81295	0.906474	+	0.422263i	$0.138764\pi$
$434$	−35.1018	−1.68494
$435$	1.37827	0.0660832
$436$	−26.2892	−1.25903
$437$	−21.9971	−1.05226
$438$	−3.41780	−0.163309
$439$	−9.29694	−0.443719	−0.221859	−	0.975079i	$-0.571213\pi$
$439$	−9.29694	−0.443719	−0.221859	+	0.975079i	$0.571213\pi$
$440$	5.55411	0.264782
$441$	−53.8315	−2.56341
$442$	−1.92843	−0.0917263
$443$	28.4071	1.34966	0.674832	−	0.737971i	$-0.264216\pi$
$443$	28.4071	1.34966	0.674832	+	0.737971i	$0.264216\pi$
$444$	−5.19393	−0.246493
$445$	−4.36999	−0.207157
$446$	1.55705	0.0737284
$447$	−10.2818	−0.486314
$448$	−30.1593	−1.42489
$449$	15.4532	0.729280	0.364640	−	0.931149i	$-0.381192\pi$
$449$	15.4532	0.729280	0.364640	+	0.931149i	$0.381192\pi$
$450$	26.6667	1.25708
$451$	−40.3627	−1.90061
$452$	−6.90810	−0.324930
$453$	−4.11484	−0.193332
$454$	4.87547	0.228817
$455$	5.70330	0.267375
$456$	0.733093	0.0343302
$457$	−15.1953	−0.710808	−0.355404	−	0.934713i	$-0.615657\pi$
$457$	−15.1953	−0.710808	−0.355404	+	0.934713i	$0.615657\pi$
$458$	−18.0917	−0.845367
$459$	−7.14997	−0.333732
$460$	−34.9734	−1.63064
$461$	−0.803694	−0.0374318	−0.0187159	−	0.999825i	$-0.505958\pi$
$461$	−0.803694	−0.0374318	−0.0187159	+	0.999825i	$0.505958\pi$
$462$	−15.8523	−0.737516
$463$	16.9397	0.787256	0.393628	−	0.919270i	$-0.371220\pi$
$463$	16.9397	0.787256	0.393628	+	0.919270i	$0.371220\pi$
$464$	−4.43666	−0.205967
$465$	4.88336	0.226460
$466$	−26.1038	−1.20924
$467$	15.2664	0.706445	0.353222	−	0.935539i	$-0.385086\pi$
$467$	15.2664	0.706445	0.353222	+	0.935539i	$0.385086\pi$
$468$	−1.74156	−0.0805036
$469$	29.2557	1.35090
$470$	7.09152	0.327107
$471$	1.06314	0.0489868
$472$	2.84680	0.131034
$473$	7.97595	0.366735
$474$	3.09046	0.141949
$475$	16.9899	0.779550
$476$	25.1706	1.15369
$477$	−21.7246	−0.994699
$478$	36.2679	1.65885
$479$	3.28094	0.149910	0.0749549	−	0.997187i	$-0.476119\pi$
$479$	3.28094	0.149910	0.0749549	+	0.997187i	$0.476119\pi$
$480$	10.5108	0.479749
$481$	−2.40001	−0.109431
$482$	−52.6852	−2.39974
$483$	−14.2237	−0.647199
$484$	4.10972	0.186805
$485$	−20.8559	−0.947018
$486$	−20.9799	−0.951667
$487$	17.4979	0.792905	0.396452	−	0.918055i	$-0.370241\pi$
$487$	17.4979	0.792905	0.396452	+	0.918055i	$0.370241\pi$
$488$	0.697981	0.0315961
$489$	9.14536	0.413568
$490$	−116.829	−5.27780
$491$	1.39417	0.0629181	0.0314591	−	0.999505i	$-0.489985\pi$
$491$	1.39417	0.0629181	0.0314591	+	0.999505i	$0.489985\pi$
$492$	−8.47028	−0.381870
$493$	2.81074	0.126589
$494$	−2.37728	−0.106959
$495$	−32.2864	−1.45117
$496$	−15.7195	−0.705828
$497$	−14.6159	−0.655614
$498$	−13.0985	−0.586959
$499$	25.9295	1.16076	0.580381	−	0.814345i	$-0.302904\pi$
$499$	25.9295	1.16076	0.580381	+	0.814345i	$0.302904\pi$
$500$	−0.532275	−0.0238041
$501$	−9.88152	−0.441474
$502$	−3.41675	−0.152497
$503$	−30.5122	−1.36047	−0.680237	−	0.732992i	$-0.738123\pi$
$503$	−30.5122	−1.36047	−0.680237	+	0.732992i	$0.738123\pi$
$504$	−6.93974	−0.309121
$505$	45.2070	2.01169
$506$	44.9180	1.99685
$507$	−5.63863	−0.250421
$508$	0.158783	0.00704484
$509$	−44.6002	−1.97687	−0.988435	−	0.151646i	$-0.951543\pi$
$509$	−44.6002	−1.97687	−0.988435	+	0.151646i	$0.951543\pi$
$510$	−7.50246	−0.332214
$511$	20.6135	0.911889
$512$	−29.5476	−1.30583
$513$	−8.81413	−0.389153
$514$	31.2789	1.37965
$515$	32.1006	1.41452
$516$	1.67379	0.0736843
$517$	−4.25111	−0.186963
$518$	67.1153	2.94888
$519$	−3.30692	−0.145158
$520$	0.538578	0.0236182
$521$	−3.13663	−0.137418	−0.0687091	−	0.997637i	$-0.521888\pi$
$521$	−3.13663	−0.137418	−0.0687091	+	0.997637i	$0.521888\pi$
$522$	5.43843	0.238033
$523$	14.1822	0.620145	0.310072	−	0.950713i	$-0.399647\pi$
$523$	14.1822	0.620145	0.310072	+	0.950713i	$0.399647\pi$
$524$	16.5028	0.720930
$525$	10.9859	0.479466
$526$	4.85118	0.211521
$527$	9.95872	0.433809
$528$	−7.09910	−0.308949
$529$	17.3032	0.752313
$530$	−47.1482	−2.04799
$531$	−16.5486	−0.718149
$532$	31.0291	1.34528
$533$	−3.91394	−0.169532
$534$	1.17782	0.0509694
$535$	1.21501	0.0525293
$536$	2.76269	0.119330
$537$	7.39962	0.319317
$538$	17.0624	0.735611
$539$	70.0348	3.01661
$540$	−14.0137	−0.603052
$541$	−21.0271	−0.904027	−0.452014	−	0.892011i	$-0.649294\pi$
$541$	−21.0271	−0.904027	−0.452014	+	0.892011i	$0.649294\pi$
$542$	24.0886	1.03470
$543$	−5.80249	−0.249009
$544$	21.4348	0.919009
$545$	−47.2600	−2.02440
$546$	−1.53719	−0.0657855
$547$	−13.6807	−0.584944	−0.292472	−	0.956274i	$-0.594478\pi$
$547$	−13.6807	−0.584944	−0.292472	+	0.956274i	$0.594478\pi$
$548$	13.2264	0.565004
$549$	−4.05741	−0.173166
$550$	−34.6933	−1.47933
$551$	3.46494	0.147611
$552$	−1.34318	−0.0571694
$553$	−18.6393	−0.792622
$554$	−60.4275	−2.56732
$555$	−9.33708	−0.396337
$556$	−1.75056	−0.0742401
$557$	−2.58587	−0.109567	−0.0547833	−	0.998498i	$-0.517447\pi$
$557$	−2.58587	−0.109567	−0.0547833	+	0.998498i	$0.517447\pi$
$558$	19.2689	0.815717
$559$	0.773422	0.0327123
$560$	−71.4243	−3.01823
$561$	4.49745	0.189883
$562$	30.8341	1.30066
$563$	15.0832	0.635680	0.317840	−	0.948144i	$-0.397042\pi$
$563$	15.0832	0.635680	0.317840	+	0.948144i	$0.397042\pi$
$564$	−0.892112	−0.0375647
$565$	−12.4186	−0.522456
$566$	9.92530	0.417191
$567$	37.3974	1.57054
$568$	−1.38022	−0.0579127
$569$	−18.8355	−0.789627	−0.394814	−	0.918761i	$-0.629191\pi$
$569$	−18.8355	−0.789627	−0.394814	+	0.918761i	$0.629191\pi$
$570$	−9.24865	−0.387384
$571$	−17.8052	−0.745124	−0.372562	−	0.928007i	$-0.621521\pi$
$571$	−17.8052	−0.745124	−0.372562	+	0.928007i	$0.621521\pi$
$572$	2.26577	0.0947366
$573$	−4.86811	−0.203368
$574$	109.452	4.56843
$575$	−31.1290	−1.29817
$576$	16.5557	0.689822
$577$	−31.7800	−1.32302	−0.661510	−	0.749937i	$-0.730084\pi$
$577$	−31.7800	−1.32302	−0.661510	+	0.749937i	$0.730084\pi$
$578$	17.6229	0.733017
$579$	−4.47841	−0.186116
$580$	5.50894	0.228746
$581$	79.0003	3.27749
$582$	5.62120	0.233006
$583$	28.2636	1.17056
$584$	1.94659	0.0805505
$585$	−3.13079	−0.129442
$586$	29.4869	1.21809
$587$	−4.55485	−0.187999	−0.0939994	−	0.995572i	$-0.529965\pi$
$587$	−4.55485	−0.187999	−0.0939994	+	0.995572i	$0.529965\pi$
$588$	14.6971	0.606098
$589$	12.2766	0.505849
$590$	−35.9150	−1.47860
$591$	−6.89255	−0.283522
$592$	30.0561	1.23530
$593$	−17.3778	−0.713619	−0.356810	−	0.934177i	$-0.616136\pi$
$593$	−17.3778	−0.713619	−0.356810	+	0.934177i	$0.616136\pi$
$594$	17.9984	0.738484
$595$	45.2491	1.85503
$596$	−41.0963	−1.68337
$597$	−3.23127	−0.132247
$598$	4.35567	0.178116
$599$	21.7886	0.890257	0.445128	−	0.895467i	$-0.353158\pi$
$599$	21.7886	0.890257	0.445128	+	0.895467i	$0.353158\pi$
$600$	1.03743	0.0423529
$601$	18.1609	0.740797	0.370399	−	0.928873i	$-0.379221\pi$
$601$	18.1609	0.740797	0.370399	+	0.928873i	$0.379221\pi$
$602$	−21.6285	−0.881510
$603$	−16.0597	−0.654003
$604$	−16.4469	−0.669216
$605$	7.38801	0.300365
$606$	−12.1844	−0.494959
$607$	−20.8792	−0.847459	−0.423730	−	0.905789i	$-0.639279\pi$
$607$	−20.8792	−0.847459	−0.423730	+	0.905789i	$0.639279\pi$
$608$	26.4237	1.07162
$609$	2.24048	0.0907890
$610$	−8.80568	−0.356532
$611$	−0.412227	−0.0166769
$612$	−13.8173	−0.558529
$613$	−41.0482	−1.65792	−0.828961	−	0.559306i	$-0.811068\pi$
$613$	−41.0482	−1.65792	−0.828961	+	0.559306i	$0.811068\pi$
$614$	−56.3456	−2.27393
$615$	−15.2270	−0.614010
$616$	9.02860	0.363773
$617$	−37.8197	−1.52256	−0.761281	−	0.648422i	$-0.775429\pi$
$617$	−37.8197	−1.52256	−0.761281	+	0.648422i	$0.775429\pi$
$618$	−8.65192	−0.348031
$619$	29.2444	1.17543	0.587715	−	0.809068i	$-0.300027\pi$
$619$	29.2444	1.17543	0.587715	+	0.809068i	$0.300027\pi$
$620$	19.5187	0.783891
$621$	16.1493	0.648049
$622$	−32.8693	−1.31794
$623$	−7.10372	−0.284605
$624$	−0.688395	−0.0275578
$625$	−25.4738	−1.01895
$626$	−26.0143	−1.03974
$627$	5.54423	0.221415
$628$	4.24935	0.169567
$629$	−19.0413	−0.759225
$630$	87.5513	3.48813
$631$	−2.12484	−0.0845887	−0.0422944	−	0.999105i	$-0.513467\pi$
$631$	−2.12484	−0.0845887	−0.0422944	+	0.999105i	$0.513467\pi$
$632$	−1.76015	−0.0700152
$633$	10.0909	0.401077
$634$	5.51928	0.219199
$635$	0.285443	0.0113274
$636$	5.93124	0.235189
$637$	6.79123	0.269078
$638$	−7.07539	−0.280117
$639$	8.02331	0.317397
$640$	−12.0673	−0.477002
$641$	−15.9749	−0.630969	−0.315484	−	0.948931i	$-0.602167\pi$
$641$	−15.9749	−0.630969	−0.315484	+	0.948931i	$0.602167\pi$
$642$	−0.327475	−0.0129244
$643$	−8.12851	−0.320557	−0.160278	−	0.987072i	$-0.551239\pi$
$643$	−8.12851	−0.320557	−0.160278	+	0.987072i	$0.551239\pi$
$644$	−56.8517	−2.24027
$645$	3.00895	0.118477
$646$	−18.8609	−0.742073
$647$	−7.28364	−0.286349	−0.143175	−	0.989697i	$-0.545731\pi$
$647$	−7.28364	−0.286349	−0.143175	+	0.989697i	$0.545731\pi$
$648$	3.53153	0.138732
$649$	21.5298	0.845117
$650$	−3.36419	−0.131954
$651$	7.93826	0.311125
$652$	36.5539	1.43156
$653$	39.5428	1.54743	0.773714	−	0.633535i	$-0.218397\pi$
$653$	39.5428	1.54743	0.773714	+	0.633535i	$0.218397\pi$
$654$	12.7378	0.498086
$655$	29.6670	1.15919
$656$	49.0156	1.91374
$657$	−11.3157	−0.441466
$658$	11.5278	0.449399
$659$	44.5245	1.73443	0.867215	−	0.497935i	$-0.165908\pi$
$659$	44.5245	1.73443	0.867215	+	0.497935i	$0.165908\pi$
$660$	8.81484	0.343117
$661$	12.1857	0.473968	0.236984	−	0.971514i	$-0.423841\pi$
$661$	12.1857	0.473968	0.236984	+	0.971514i	$0.423841\pi$
$662$	−39.5487	−1.53710
$663$	0.436115	0.0169373
$664$	7.46021	0.289512
$665$	55.7808	2.16309
$666$	−36.8425	−1.42762
$667$	−6.34848	−0.245814
$668$	−39.4963	−1.52816
$669$	−0.352126	−0.0136140
$670$	−34.8540	−1.34653
$671$	5.27869	0.203782
$672$	17.0860	0.659107
$673$	4.63957	0.178842	0.0894212	−	0.995994i	$-0.471498\pi$
$673$	4.63957	0.178842	0.0894212	+	0.995994i	$0.471498\pi$
$674$	−18.1951	−0.700849
$675$	−12.4732	−0.480096
$676$	−22.5375	−0.866828
$677$	35.6684	1.37085	0.685424	−	0.728144i	$-0.259617\pi$
$677$	35.6684	1.37085	0.685424	+	0.728144i	$0.259617\pi$
$678$	3.34714	0.128546
$679$	−33.9028	−1.30107
$680$	4.27299	0.163862
$681$	−1.10259	−0.0422512
$682$	−25.0688	−0.959935
$683$	−42.8691	−1.64034	−0.820170	−	0.572120i	$-0.806121\pi$
$683$	−42.8691	−1.64034	−0.820170	+	0.572120i	$0.806121\pi$
$684$	−17.0332	−0.651281
$685$	23.7770	0.908473
$686$	−120.564	−4.60317
$687$	4.09142	0.156097
$688$	−9.68582	−0.369268
$689$	2.74071	0.104413
$690$	16.9454	0.645102
$691$	36.1758	1.37619	0.688097	−	0.725619i	$-0.258446\pi$
$691$	36.1758	1.37619	0.688097	+	0.725619i	$0.258446\pi$
$692$	−13.2177	−0.502462
$693$	−52.4839	−1.99370
$694$	57.9358	2.19921
$695$	−3.14696	−0.119371
$696$	0.211575	0.00801972
$697$	−31.0526	−1.17620
$698$	10.6817	0.404309
$699$	5.90337	0.223286
$700$	43.9106	1.65967
$701$	28.1243	1.06224	0.531120	−	0.847297i	$-0.321771\pi$
$701$	28.1243	1.06224	0.531120	+	0.847297i	$0.321771\pi$
$702$	1.74530	0.0658719
$703$	−23.4731	−0.885306
$704$	−21.5390	−0.811781
$705$	−1.60374	−0.0604005
$706$	−22.9583	−0.864049
$707$	73.4872	2.76377
$708$	4.51811	0.169801
$709$	18.4998	0.694774	0.347387	−	0.937722i	$-0.387069\pi$
$709$	18.4998	0.694774	0.347387	+	0.937722i	$0.387069\pi$
$710$	17.4128	0.653490
$711$	10.2319	0.383726
$712$	−0.670823	−0.0251402
$713$	−22.4933	−0.842381
$714$	−12.1958	−0.456416
$715$	4.07316	0.152327
$716$	29.5761	1.10531
$717$	−8.20197	−0.306308
$718$	15.0372	0.561184
$719$	33.5828	1.25243	0.626214	−	0.779651i	$-0.284604\pi$
$719$	33.5828	1.25243	0.626214	+	0.779651i	$0.284604\pi$
$720$	39.2079	1.46119
$721$	52.1818	1.94335
$722$	13.5453	0.504102
$723$	11.9147	0.443114
$724$	−23.1924	−0.861940
$725$	4.90338	0.182107
$726$	−1.99126	−0.0739025
$727$	16.5509	0.613839	0.306920	−	0.951735i	$-0.400702\pi$
$727$	16.5509	0.613839	0.306920	+	0.951735i	$0.400702\pi$
$728$	0.875497	0.0324481
$729$	−17.1867	−0.636545
$730$	−24.5581	−0.908935
$731$	6.13621	0.226956
$732$	1.10775	0.0409438
$733$	6.69353	0.247231	0.123615	−	0.992330i	$-0.460551\pi$
$733$	6.69353	0.247231	0.123615	+	0.992330i	$0.460551\pi$
$734$	56.5680	2.08796
$735$	26.4208	0.974548
$736$	−48.4138	−1.78455
$737$	20.8937	0.769630
$738$	−60.0829	−2.21168
$739$	−28.2035	−1.03748	−0.518741	−	0.854931i	$-0.673599\pi$
$739$	−28.2035	−1.03748	−0.518741	+	0.854931i	$0.673599\pi$
$740$	−37.3202	−1.37192
$741$	0.537621	0.0197500
$742$	−76.6428	−2.81365
$743$	−37.0395	−1.35885	−0.679425	−	0.733745i	$-0.737771\pi$
$743$	−37.0395	−1.35885	−0.679425	+	0.733745i	$0.737771\pi$
$744$	0.749630	0.0274828
$745$	−73.8785	−2.70670
$746$	28.3927	1.03953
$747$	−43.3667	−1.58670
$748$	17.9762	0.657277
$749$	1.97508	0.0721679
$750$	0.257900	0.00941719
$751$	−40.6728	−1.48417	−0.742087	−	0.670304i	$-0.766164\pi$
$751$	−40.6728	−1.48417	−0.742087	+	0.670304i	$0.766164\pi$
$752$	5.16245	0.188255
$753$	0.772698	0.0281587
$754$	−0.686096	−0.0249861
$755$	−29.5665	−1.07604
$756$	−22.7802	−0.828509
$757$	43.3677	1.57623	0.788113	−	0.615531i	$-0.211058\pi$
$757$	43.3677	1.57623	0.788113	+	0.615531i	$0.211058\pi$
$758$	−12.5051	−0.454205
$759$	−10.1582	−0.368719
$760$	5.26753	0.191073
$761$	25.8939	0.938653	0.469326	−	0.883025i	$-0.344497\pi$
$761$	25.8939	0.938653	0.469326	+	0.883025i	$0.344497\pi$
$762$	−0.0769341	−0.00278703
$763$	−76.8245	−2.78123
$764$	−19.4577	−0.703956
$765$	−24.8392	−0.898062
$766$	37.5316	1.35607
$767$	2.08773	0.0753834
$768$	8.41657	0.303707
$769$	32.1050	1.15773	0.578867	−	0.815422i	$-0.303495\pi$
$769$	32.1050	1.15773	0.578867	+	0.815422i	$0.303495\pi$
$770$	−113.904	−4.10483
$771$	−7.07371	−0.254754
$772$	−17.9001	−0.644240
$773$	27.4531	0.987420	0.493710	−	0.869627i	$-0.335641\pi$
$773$	27.4531	0.987420	0.493710	+	0.869627i	$0.335641\pi$
$774$	11.8728	0.426759
$775$	17.3732	0.624062
$776$	−3.20153	−0.114928
$777$	−15.1781	−0.544511
$778$	5.34523	0.191636
$779$	−38.2801	−1.37153
$780$	0.854769	0.0306056
$781$	−10.4383	−0.373513
$782$	34.5571	1.23576
$783$	−2.54381	−0.0909082
$784$	−85.0487	−3.03745
$785$	7.63902	0.272648
$786$	−7.99602	−0.285209
$787$	−11.1393	−0.397074	−0.198537	−	0.980093i	$-0.563619\pi$
$787$	−11.1393	−0.397074	−0.198537	+	0.980093i	$0.563619\pi$
$788$	−27.5494	−0.981407
$789$	−1.09709	−0.0390575
$790$	22.2060	0.790054
$791$	−20.1874	−0.717781
$792$	−4.95619	−0.176111
$793$	0.511871	0.0181771
$794$	−48.8232	−1.73267
$795$	10.6626	0.378162
$796$	−12.9153	−0.457772
$797$	34.6635	1.22785	0.613923	−	0.789366i	$-0.289591\pi$
$797$	34.6635	1.22785	0.613923	+	0.789366i	$0.289591\pi$
$798$	−15.0344	−0.532210
$799$	−3.27054	−0.115703
$800$	37.3934	1.32206
$801$	3.89954	0.137784
$802$	42.7036	1.50792
$803$	14.7217	0.519517
$804$	4.38463	0.154634
$805$	−102.202	−3.60215
$806$	−2.43091	−0.0856250
$807$	−3.85865	−0.135831
$808$	6.93959	0.244134
$809$	22.1675	0.779368	0.389684	−	0.920949i	$-0.372584\pi$
$809$	22.1675	0.779368	0.389684	+	0.920949i	$0.372584\pi$
$810$	−44.5536	−1.56545
$811$	51.5218	1.80918	0.904588	−	0.426287i	$-0.140178\pi$
$811$	51.5218	1.80918	0.904588	+	0.426287i	$0.140178\pi$
$812$	8.95517	0.314265
$813$	−5.44763	−0.191057
$814$	47.9321	1.68002
$815$	65.7126	2.30181
$816$	−5.46161	−0.191195
$817$	7.56441	0.264645
$818$	−56.1039	−1.96163
$819$	−5.08933	−0.177835
$820$	−60.8619	−2.12539
$821$	−13.5714	−0.473643	−0.236822	−	0.971553i	$-0.576106\pi$
$821$	−13.5714	−0.473643	−0.236822	+	0.971553i	$0.576106\pi$
$822$	−6.40851	−0.223523
$823$	−46.2379	−1.61175	−0.805875	−	0.592085i	$-0.798305\pi$
$823$	−46.2379	−1.61175	−0.805875	+	0.592085i	$0.798305\pi$
$824$	4.92766	0.171663
$825$	7.84589	0.273159
$826$	−58.3825	−2.03139
$827$	−28.6248	−0.995380	−0.497690	−	0.867355i	$-0.665818\pi$
$827$	−28.6248	−0.995380	−0.497690	+	0.867355i	$0.665818\pi$
$828$	31.2084	1.08457
$829$	−24.4069	−0.847687	−0.423843	−	0.905736i	$-0.639319\pi$
$829$	−24.4069	−0.847687	−0.423843	+	0.905736i	$0.639319\pi$
$830$	−94.1176	−3.26687
$831$	13.6657	0.474056
$832$	−2.08862	−0.0724099
$833$	53.8805	1.86685
$834$	0.848187	0.0293703
$835$	−71.0022	−2.45713
$836$	22.1602	0.766427
$837$	−9.01296	−0.311533
$838$	42.6647	1.47383
$839$	−55.1800	−1.90503	−0.952513	−	0.304499i	$-0.901511\pi$
$839$	−55.1800	−1.90503	−0.952513	+	0.304499i	$0.901511\pi$
$840$	3.40607	0.117521
$841$	1.00000	0.0344828
$842$	63.2682	2.18037
$843$	−6.97311	−0.240167
$844$	40.3331	1.38832
$845$	−40.5156	−1.39378
$846$	−6.32809	−0.217564
$847$	12.0097	0.412660
$848$	−34.3228	−1.17865
$849$	−2.24460	−0.0770346
$850$	−26.6909	−0.915491
$851$	43.0076	1.47428
$852$	−2.19053	−0.0750462
$853$	31.0248	1.06227	0.531134	−	0.847288i	$-0.321766\pi$
$853$	31.0248	1.06227	0.531134	+	0.847288i	$0.321766\pi$
$854$	−14.3143	−0.489824
$855$	−30.6205	−1.04720
$856$	0.186512	0.00637485
$857$	3.40672	0.116371	0.0581856	−	0.998306i	$-0.481468\pi$
$857$	3.40672	0.116371	0.0581856	+	0.998306i	$0.481468\pi$
$858$	−1.09782	−0.0374790
$859$	−36.0944	−1.23152	−0.615762	−	0.787932i	$-0.711152\pi$
$859$	−36.0944	−1.23152	−0.615762	+	0.787932i	$0.711152\pi$
$860$	12.0267	0.410108
$861$	−24.7525	−0.843563
$862$	1.43714	0.0489491
$863$	−19.4735	−0.662886	−0.331443	−	0.943475i	$-0.607535\pi$
$863$	−19.4735	−0.662886	−0.331443	+	0.943475i	$0.607535\pi$
$864$	−19.3992	−0.659973
$865$	−23.7614	−0.807912
$866$	−73.0595	−2.48266
$867$	−3.98542	−0.135352
$868$	31.7291	1.07695
$869$	−13.3117	−0.451568
$870$	−2.66921	−0.0904948
$871$	2.02605	0.0686500
$872$	−7.25474	−0.245677
$873$	18.6107	0.629877
$874$	42.6003	1.44098
$875$	−1.55546	−0.0525841
$876$	3.08940	0.104381
$877$	−21.4357	−0.723831	−0.361915	−	0.932211i	$-0.617877\pi$
$877$	−21.4357	−0.723831	−0.361915	+	0.932211i	$0.617877\pi$
$878$	18.0048	0.607632
$879$	−6.66846	−0.224921
$880$	−51.0095	−1.71953
$881$	27.1785	0.915666	0.457833	−	0.889038i	$-0.348626\pi$
$881$	27.1785	0.915666	0.457833	+	0.889038i	$0.348626\pi$
$882$	104.252	3.51035
$883$	22.4596	0.755824	0.377912	−	0.925841i	$-0.376642\pi$
$883$	22.4596	0.755824	0.377912	+	0.925841i	$0.376642\pi$
$884$	1.74314	0.0586283
$885$	8.12217	0.273024
$886$	−55.0143	−1.84824
$887$	−50.3585	−1.69087	−0.845436	−	0.534077i	$-0.820659\pi$
$887$	−50.3585	−1.69087	−0.845436	+	0.534077i	$0.820659\pi$
$888$	−1.43331	−0.0480987
$889$	0.464007	0.0155623
$890$	8.46307	0.283683
$891$	26.7083	0.894761
$892$	−1.40744	−0.0471247
$893$	−4.03176	−0.134918
$894$	19.9122	0.665962
$895$	53.1688	1.77724
$896$	−19.6163	−0.655334
$897$	−0.985032	−0.0328893
$898$	−29.9271	−0.998682
$899$	3.54310	0.118169
$900$	−24.1044	−0.803481
$901$	21.7443	0.724408
$902$	78.1678	2.60270
$903$	4.89127	0.162771
$904$	−1.90635	−0.0634042
$905$	−41.6929	−1.38592
$906$	7.96894	0.264750
$907$	39.5878	1.31449	0.657245	−	0.753677i	$-0.271722\pi$
$907$	39.5878	1.31449	0.657245	+	0.753677i	$0.271722\pi$
$908$	−4.40702	−0.146252
$909$	−40.3403	−1.33800
$910$	−11.0452	−0.366146
$911$	14.4387	0.478377	0.239189	−	0.970973i	$-0.423119\pi$
$911$	14.4387	0.478377	0.239189	+	0.970973i	$0.423119\pi$
$912$	−6.73280	−0.222945
$913$	56.4201	1.86723
$914$	29.4278	0.973386
$915$	1.99140	0.0658337
$916$	16.3533	0.540330
$917$	48.2259	1.59256
$918$	13.8469	0.457015
$919$	−12.5357	−0.413516	−0.206758	−	0.978392i	$-0.566291\pi$
$919$	−12.5357	−0.413516	−0.206758	+	0.978392i	$0.566291\pi$
$920$	−9.65120	−0.318191
$921$	12.7425	0.419881
$922$	1.55646	0.0512594
$923$	−1.01220	−0.0333169
$924$	14.3292	0.471394
$925$	−33.2178	−1.09220
$926$	−32.8061	−1.07807
$927$	−28.6448	−0.940820
$928$	7.62604	0.250337
$929$	−49.0000	−1.60764	−0.803819	−	0.594874i	$-0.797202\pi$
$929$	−49.0000	−1.60764	−0.803819	+	0.594874i	$0.797202\pi$
$930$	−9.45729	−0.310117
$931$	66.4211	2.17687
$932$	23.5957	0.772902
$933$	7.43339	0.243358
$934$	−29.5654	−0.967411
$935$	32.3158	1.05684
$936$	−0.480598	−0.0157088
$937$	−47.3583	−1.54713	−0.773564	−	0.633718i	$-0.781528\pi$
$937$	−47.3583	−1.54713	−0.773564	+	0.633718i	$0.781528\pi$
$938$	−56.6576	−1.84994
$939$	5.88314	0.191989
$940$	−6.41014	−0.209076
$941$	−33.2959	−1.08541	−0.542707	−	0.839922i	$-0.682601\pi$
$941$	−33.2959	−1.08541	−0.542707	+	0.839922i	$0.682601\pi$
$942$	−2.05891	−0.0670829
$943$	70.1370	2.28398
$944$	−26.1453	−0.850956
$945$	−40.9519	−1.33216
$946$	−15.4465	−0.502209
$947$	−53.8591	−1.75019	−0.875093	−	0.483956i	$-0.839200\pi$
$947$	−53.8591	−1.75019	−0.875093	+	0.483956i	$0.839200\pi$
$948$	−2.79351	−0.0907291
$949$	1.42755	0.0463403
$950$	−32.9032	−1.06752
$951$	−1.24818	−0.0404751
$952$	6.94605	0.225123
$953$	−8.07359	−0.261529	−0.130765	−	0.991413i	$-0.541743\pi$
$953$	−8.07359	−0.261529	−0.130765	+	0.991413i	$0.541743\pi$
$954$	42.0725	1.36215
$955$	−34.9790	−1.13190
$956$	−32.7831	−1.06028
$957$	1.60010	0.0517238
$958$	−6.35398	−0.205288
$959$	38.6512	1.24811
$960$	−8.12565	−0.262254
$961$	−18.4464	−0.595047
$962$	4.64794	0.149856
$963$	−1.08421	−0.0349381
$964$	47.6230	1.53383
$965$	−32.1789	−1.03588
$966$	27.5460	0.886279
$967$	6.75785	0.217318	0.108659	−	0.994079i	$-0.465344\pi$
$967$	6.75785	0.217318	0.108659	+	0.994079i	$0.465344\pi$
$968$	1.13411	0.0364517
$969$	4.26539	0.137024
$970$	40.3903	1.29685
$971$	4.97222	0.159566	0.0797830	−	0.996812i	$-0.474577\pi$
$971$	4.97222	0.159566	0.0797830	+	0.996812i	$0.474577\pi$
$972$	18.9641	0.608273
$973$	−5.11562	−0.163999
$974$	−33.8870	−1.08581
$975$	0.760810	0.0243654
$976$	−6.41033	−0.205190
$977$	−23.7129	−0.758644	−0.379322	−	0.925265i	$-0.623843\pi$
$977$	−23.7129	−0.758644	−0.379322	+	0.925265i	$0.623843\pi$
$978$	−17.7112	−0.566343
$979$	−5.07330	−0.162144
$980$	105.604	3.37339
$981$	42.1723	1.34646
$982$	−2.70000	−0.0861606
$983$	−38.0596	−1.21391	−0.606956	−	0.794735i	$-0.707610\pi$
$983$	−38.0596	−1.21391	−0.606956	+	0.794735i	$0.707610\pi$
$984$	−2.33744	−0.0745150
$985$	−49.5254	−1.57801
$986$	−5.44337	−0.173352
$987$	−2.60700	−0.0829817
$988$	2.14886	0.0683644
$989$	−13.8596	−0.440708
$990$	62.5270	1.98724
$991$	−48.3796	−1.53683	−0.768414	−	0.639953i	$-0.778954\pi$
$991$	−48.3796	−1.53683	−0.768414	+	0.639953i	$0.778954\pi$
$992$	27.0198	0.857880
$993$	8.94393	0.283827
$994$	28.3057	0.897803
$995$	−23.2178	−0.736054
$996$	11.8400	0.375164
$997$	−14.7231	−0.466286	−0.233143	−	0.972442i	$-0.574901\pi$
$997$	−14.7231	−0.466286	−0.233143	+	0.972442i	$0.574901\pi$
$998$	−50.2159	−1.58956
$999$	17.2330	0.545227

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.d.1.19	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.d.1.19	✓	98	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)

\(f(q)\)	\(=\)	\(q-1.93664 q^{2} +0.437969 q^{3} +1.75056 q^{4} +3.14696 q^{5} -0.848187 q^{6} +5.11562 q^{7} +0.483081 q^{8} -2.80818 q^{9} +O(q^{10})\)	\(q-1.93664 q^{2} +0.437969 q^{3} +1.75056 q^{4} +3.14696 q^{5} -0.848187 q^{6} +5.11562 q^{7} +0.483081 q^{8} -2.80818 q^{9} -6.09452 q^{10} +3.65345 q^{11} +0.766690 q^{12} +0.354272 q^{13} -9.90708 q^{14} +1.37827 q^{15} -4.43666 q^{16} +2.81074 q^{17} +5.43843 q^{18} +3.46494 q^{19} +5.50894 q^{20} +2.24048 q^{21} -7.07539 q^{22} -6.34848 q^{23} +0.211575 q^{24} +4.90338 q^{25} -0.686096 q^{26} -2.54381 q^{27} +8.95517 q^{28} +1.00000 q^{29} -2.66921 q^{30} +3.54310 q^{31} +7.62604 q^{32} +1.60010 q^{33} -5.44337 q^{34} +16.0987 q^{35} -4.91588 q^{36} -6.77448 q^{37} -6.71032 q^{38} +0.155160 q^{39} +1.52024 q^{40} -11.0478 q^{41} -4.33900 q^{42} +2.18313 q^{43} +6.39556 q^{44} -8.83725 q^{45} +12.2947 q^{46} -1.16359 q^{47} -1.94312 q^{48} +19.1695 q^{49} -9.49606 q^{50} +1.23102 q^{51} +0.620173 q^{52} +7.73616 q^{53} +4.92643 q^{54} +11.4973 q^{55} +2.47126 q^{56} +1.51754 q^{57} -1.93664 q^{58} +5.89300 q^{59} +2.41275 q^{60} +1.44485 q^{61} -6.86169 q^{62} -14.3656 q^{63} -5.89553 q^{64} +1.11488 q^{65} -3.09881 q^{66} +5.71890 q^{67} +4.92035 q^{68} -2.78044 q^{69} -31.1772 q^{70} -2.85712 q^{71} -1.35658 q^{72} +4.02953 q^{73} +13.1197 q^{74} +2.14753 q^{75} +6.06557 q^{76} +18.6896 q^{77} -0.300489 q^{78} -3.64360 q^{79} -13.9620 q^{80} +7.31044 q^{81} +21.3957 q^{82} +15.4430 q^{83} +3.92209 q^{84} +8.84529 q^{85} -4.22793 q^{86} +0.437969 q^{87} +1.76491 q^{88} -1.38864 q^{89} +17.1145 q^{90} +1.81232 q^{91} -11.1134 q^{92} +1.55177 q^{93} +2.25345 q^{94} +10.9040 q^{95} +3.33997 q^{96} -6.62731 q^{97} -37.1244 q^{98} -10.2595 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * q^99

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