LMFDB - Embedded newform 8049.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22425 q^{2} -1.00000 q^{3} +2.94729 q^{4} -0.996267 q^{5} +2.22425 q^{6} -4.15468 q^{7} -2.10702 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.22425 q^{2} -1.00000 q^{3} +2.94729 q^{4} -0.996267 q^{5} +2.22425 q^{6} -4.15468 q^{7} -2.10702 q^{8} +1.00000 q^{9} +2.21595 q^{10} +1.86449 q^{11} -2.94729 q^{12} -6.28408 q^{13} +9.24105 q^{14} +0.996267 q^{15} -1.20805 q^{16} +6.62066 q^{17} -2.22425 q^{18} -6.39219 q^{19} -2.93629 q^{20} +4.15468 q^{21} -4.14710 q^{22} -3.81830 q^{23} +2.10702 q^{24} -4.00745 q^{25} +13.9774 q^{26} -1.00000 q^{27} -12.2451 q^{28} -5.26872 q^{29} -2.21595 q^{30} +5.17457 q^{31} +6.90104 q^{32} -1.86449 q^{33} -14.7260 q^{34} +4.13917 q^{35} +2.94729 q^{36} +11.2193 q^{37} +14.2178 q^{38} +6.28408 q^{39} +2.09915 q^{40} -0.264551 q^{41} -9.24105 q^{42} +6.16741 q^{43} +5.49520 q^{44} -0.996267 q^{45} +8.49285 q^{46} -6.52827 q^{47} +1.20805 q^{48} +10.2614 q^{49} +8.91358 q^{50} -6.62066 q^{51} -18.5210 q^{52} +10.5849 q^{53} +2.22425 q^{54} -1.85753 q^{55} +8.75398 q^{56} +6.39219 q^{57} +11.7189 q^{58} -14.5565 q^{59} +2.93629 q^{60} +11.6930 q^{61} -11.5095 q^{62} -4.15468 q^{63} -12.9335 q^{64} +6.26062 q^{65} +4.14710 q^{66} -12.1628 q^{67} +19.5130 q^{68} +3.81830 q^{69} -9.20656 q^{70} -0.778190 q^{71} -2.10702 q^{72} +4.84379 q^{73} -24.9545 q^{74} +4.00745 q^{75} -18.8396 q^{76} -7.74636 q^{77} -13.9774 q^{78} -9.49644 q^{79} +1.20354 q^{80} +1.00000 q^{81} +0.588427 q^{82} +14.6286 q^{83} +12.2451 q^{84} -6.59595 q^{85} -13.7179 q^{86} +5.26872 q^{87} -3.92852 q^{88} -0.0269374 q^{89} +2.21595 q^{90} +26.1083 q^{91} -11.2536 q^{92} -5.17457 q^{93} +14.5205 q^{94} +6.36833 q^{95} -6.90104 q^{96} +5.75300 q^{97} -22.8238 q^{98} +1.86449 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9}+O(q^{10}) $ 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9	\( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9} + 8 q^{10} - 52 q^{11} - 87 q^{12} + 35 q^{13} - 23 q^{14} + 15 q^{15} + 53 q^{16} - 19 q^{17} - 9 q^{18} - 22 q^{19} - 35 q^{20} + 10 q^{21} - q^{22} - 70 q^{23} + 27 q^{24} + 79 q^{25} - 39 q^{26} - 104 q^{27} - 9 q^{28} - 37 q^{29} - 8 q^{30} - 47 q^{31} - 53 q^{32} + 52 q^{33} - 17 q^{34} - 54 q^{35} + 87 q^{36} + 65 q^{37} - 33 q^{38} - 35 q^{39} + 14 q^{40} - 47 q^{41} + 23 q^{42} - 30 q^{43} - 122 q^{44} - 15 q^{45} - 6 q^{46} - 101 q^{47} - 53 q^{48} + 78 q^{49} - 64 q^{50} + 19 q^{51} + 41 q^{52} - 48 q^{53} + 9 q^{54} - 29 q^{55} - 71 q^{56} + 22 q^{57} - 2 q^{58} - 86 q^{59} + 35 q^{60} + 34 q^{61} - 36 q^{62} - 10 q^{63} - 15 q^{64} - 64 q^{65} + q^{66} - 38 q^{67} - 33 q^{68} + 70 q^{69} - 29 q^{70} - 176 q^{71} - 27 q^{72} + 69 q^{73} - 86 q^{74} - 79 q^{75} - 54 q^{76} - 45 q^{77} + 39 q^{78} - 101 q^{79} - 76 q^{80} + 104 q^{81} + 38 q^{82} - 67 q^{83} + 9 q^{84} + 3 q^{85} - 90 q^{86} + 37 q^{87} + 7 q^{88} - 91 q^{89} + 8 q^{90} - 47 q^{91} - 136 q^{92} + 47 q^{93} - 20 q^{94} - 130 q^{95} + 53 q^{96} + 86 q^{97} - 44 q^{98} - 52 q^{99}+O(q^{100}) \) 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9 + 8 * q^10 - 52 * q^11 - 87 * q^12 + 35 * q^13 - 23 * q^14 + 15 * q^15 + 53 * q^16 - 19 * q^17 - 9 * q^18 - 22 * q^19 - 35 * q^20 + 10 * q^21 - q^22 - 70 * q^23 + 27 * q^24 + 79 * q^25 - 39 * q^26 - 104 * q^27 - 9 * q^28 - 37 * q^29 - 8 * q^30 - 47 * q^31 - 53 * q^32 + 52 * q^33 - 17 * q^34 - 54 * q^35 + 87 * q^36 + 65 * q^37 - 33 * q^38 - 35 * q^39 + 14 * q^40 - 47 * q^41 + 23 * q^42 - 30 * q^43 - 122 * q^44 - 15 * q^45 - 6 * q^46 - 101 * q^47 - 53 * q^48 + 78 * q^49 - 64 * q^50 + 19 * q^51 + 41 * q^52 - 48 * q^53 + 9 * q^54 - 29 * q^55 - 71 * q^56 + 22 * q^57 - 2 * q^58 - 86 * q^59 + 35 * q^60 + 34 * q^61 - 36 * q^62 - 10 * q^63 - 15 * q^64 - 64 * q^65 + q^66 - 38 * q^67 - 33 * q^68 + 70 * q^69 - 29 * q^70 - 176 * q^71 - 27 * q^72 + 69 * q^73 - 86 * q^74 - 79 * q^75 - 54 * q^76 - 45 * q^77 + 39 * q^78 - 101 * q^79 - 76 * q^80 + 104 * q^81 + 38 * q^82 - 67 * q^83 + 9 * q^84 + 3 * q^85 - 90 * q^86 + 37 * q^87 + 7 * q^88 - 91 * q^89 + 8 * q^90 - 47 * q^91 - 136 * q^92 + 47 * q^93 - 20 * q^94 - 130 * q^95 + 53 * q^96 + 86 * q^97 - 44 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.22425	−1.57278	−0.786392	−	0.617728i	$-0.788053\pi$
$2$	−2.22425	−1.57278	−0.786392	+	0.617728i	$0.788053\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.94729	1.47365
$5$	−0.996267	−0.445544	−0.222772	−	0.974871i	$-0.571511\pi$
$5$	−0.996267	−0.445544	−0.222772	+	0.974871i	$0.571511\pi$
$6$	2.22425	0.908047
$7$	−4.15468	−1.57032	−0.785161	−	0.619292i	$-0.787420\pi$
$7$	−4.15468	−1.57032	−0.785161	+	0.619292i	$0.787420\pi$
$8$	−2.10702	−0.744943
$9$	1.00000	0.333333
$10$	2.21595	0.700744
$11$	1.86449	0.562165	0.281083	−	0.959684i	$-0.409306\pi$
$11$	1.86449	0.562165	0.281083	+	0.959684i	$0.409306\pi$
$12$	−2.94729	−0.850810
$13$	−6.28408	−1.74289	−0.871445	−	0.490494i	$-0.836816\pi$
$13$	−6.28408	−1.74289	−0.871445	+	0.490494i	$0.836816\pi$
$14$	9.24105	2.46977
$15$	0.996267	0.257235
$16$	−1.20805	−0.302013
$17$	6.62066	1.60575	0.802873	−	0.596150i	$-0.203304\pi$
$17$	6.62066	1.60575	0.802873	+	0.596150i	$0.203304\pi$
$18$	−2.22425	−0.524261
$19$	−6.39219	−1.46647	−0.733234	−	0.679976i	$-0.761990\pi$
$19$	−6.39219	−1.46647	−0.733234	+	0.679976i	$0.761990\pi$
$20$	−2.93629	−0.656575
$21$	4.15468	0.906625
$22$	−4.14710	−0.884164
$23$	−3.81830	−0.796170	−0.398085	−	0.917348i	$-0.630325\pi$
$23$	−3.81830	−0.796170	−0.398085	+	0.917348i	$0.630325\pi$
$24$	2.10702	0.430093
$25$	−4.00745	−0.801490
$26$	13.9774	2.74119
$27$	−1.00000	−0.192450
$28$	−12.2451	−2.31410
$29$	−5.26872	−0.978376	−0.489188	−	0.872178i	$-0.662707\pi$
$29$	−5.26872	−0.978376	−0.489188	+	0.872178i	$0.662707\pi$
$30$	−2.21595	−0.404575
$31$	5.17457	0.929379	0.464690	−	0.885474i	$-0.346166\pi$
$31$	5.17457	0.929379	0.464690	+	0.885474i	$0.346166\pi$
$32$	6.90104	1.21994
$33$	−1.86449	−0.324566
$34$	−14.7260	−2.52549
$35$	4.13917	0.699648
$36$	2.94729	0.491215
$37$	11.2193	1.84444	0.922221	−	0.386663i	$-0.126372\pi$
$37$	11.2193	1.84444	0.922221	+	0.386663i	$0.126372\pi$
$38$	14.2178	2.30644
$39$	6.28408	1.00626
$40$	2.09915	0.331905
$41$	−0.264551	−0.0413159	−0.0206579	−	0.999787i	$-0.506576\pi$
$41$	−0.264551	−0.0413159	−0.0206579	+	0.999787i	$0.506576\pi$
$42$	−9.24105	−1.42592
$43$	6.16741	0.940521	0.470261	−	0.882528i	$-0.344160\pi$
$43$	6.16741	0.940521	0.470261	+	0.882528i	$0.344160\pi$
$44$	5.49520	0.828433
$45$	−0.996267	−0.148515
$46$	8.49285	1.25220
$47$	−6.52827	−0.952247	−0.476123	−	0.879379i	$-0.657958\pi$
$47$	−6.52827	−0.952247	−0.476123	+	0.879379i	$0.657958\pi$
$48$	1.20805	0.174367
$49$	10.2614	1.46591
$50$	8.91358	1.26057
$51$	−6.62066	−0.927078
$52$	−18.5210	−2.56840
$53$	10.5849	1.45394	0.726972	−	0.686667i	$-0.240927\pi$
$53$	10.5849	1.45394	0.726972	+	0.686667i	$0.240927\pi$
$54$	2.22425	0.302682
$55$	−1.85753	−0.250470
$56$	8.75398	1.16980
$57$	6.39219	0.846666
$58$	11.7189	1.53877
$59$	−14.5565	−1.89509	−0.947545	−	0.319623i	$-0.896444\pi$
$59$	−14.5565	−1.89509	−0.947545	+	0.319623i	$0.896444\pi$
$60$	2.93629	0.379074
$61$	11.6930	1.49714	0.748571	−	0.663055i	$-0.230740\pi$
$61$	11.6930	1.49714	0.748571	+	0.663055i	$0.230740\pi$
$62$	−11.5095	−1.46171
$63$	−4.15468	−0.523440
$64$	−12.9335	−1.61669
$65$	6.26062	0.776534
$66$	4.14710	0.510472
$67$	−12.1628	−1.48592	−0.742962	−	0.669334i	$-0.766580\pi$
$67$	−12.1628	−1.48592	−0.742962	+	0.669334i	$0.766580\pi$
$68$	19.5130	2.36630
$69$	3.81830	0.459669
$70$	−9.20656	−1.10039
$71$	−0.778190	−0.0923541	−0.0461771	−	0.998933i	$-0.514704\pi$
$71$	−0.778190	−0.0923541	−0.0461771	+	0.998933i	$0.514704\pi$
$72$	−2.10702	−0.248314
$73$	4.84379	0.566923	0.283461	−	0.958984i	$-0.408517\pi$
$73$	4.84379	0.566923	0.283461	+	0.958984i	$0.408517\pi$
$74$	−24.9545	−2.90091
$75$	4.00745	0.462741
$76$	−18.8396	−2.16106
$77$	−7.74636	−0.882780
$78$	−13.9774	−1.58263
$79$	−9.49644	−1.06843	−0.534216	−	0.845348i	$-0.679393\pi$
$79$	−9.49644	−1.06843	−0.534216	+	0.845348i	$0.679393\pi$
$80$	1.20354	0.134560
$81$	1.00000	0.111111
$82$	0.588427	0.0649809
$83$	14.6286	1.60570	0.802851	−	0.596179i	$-0.203315\pi$
$83$	14.6286	1.60570	0.802851	+	0.596179i	$0.203315\pi$
$84$	12.2451	1.33605
$85$	−6.59595	−0.715431
$86$	−13.7179	−1.47924
$87$	5.26872	0.564866
$88$	−3.92852	−0.418781
$89$	−0.0269374	−0.00285536	−0.00142768	−	0.999999i	$-0.500454\pi$
$89$	−0.0269374	−0.00285536	−0.00142768	+	0.999999i	$0.500454\pi$
$90$	2.21595	0.233581
$91$	26.1083	2.73690
$92$	−11.2536	−1.17327
$93$	−5.17457	−0.536577
$94$	14.5205	1.49768
$95$	6.36833	0.653377
$96$	−6.90104	−0.704335
$97$	5.75300	0.584129	0.292064	−	0.956399i	$-0.405658\pi$
$97$	5.75300	0.584129	0.292064	+	0.956399i	$0.405658\pi$
$98$	−22.8238	−2.30556
$99$	1.86449	0.187388
$100$	−11.8111	−1.18111
$101$	6.16911	0.613850	0.306925	−	0.951734i	$-0.400700\pi$
$101$	6.16911	0.613850	0.306925	+	0.951734i	$0.400700\pi$
$102$	14.7260	1.45809
$103$	−2.49917	−0.246251	−0.123125	−	0.992391i	$-0.539292\pi$
$103$	−2.49917	−0.246251	−0.123125	+	0.992391i	$0.539292\pi$
$104$	13.2407	1.29835
$105$	−4.13917	−0.403942
$106$	−23.5434	−2.28674
$107$	1.07670	0.104088	0.0520442	−	0.998645i	$-0.483426\pi$
$107$	1.07670	0.104088	0.0520442	+	0.998645i	$0.483426\pi$
$108$	−2.94729	−0.283603
$109$	−8.65970	−0.829448	−0.414724	−	0.909947i	$-0.636122\pi$
$109$	−8.65970	−0.829448	−0.414724	+	0.909947i	$0.636122\pi$
$110$	4.13162	0.393934
$111$	−11.2193	−1.06489
$112$	5.01906	0.474257
$113$	13.4838	1.26845	0.634225	−	0.773148i	$-0.281319\pi$
$113$	13.4838	1.26845	0.634225	+	0.773148i	$0.281319\pi$
$114$	−14.2178	−1.33162
$115$	3.80405	0.354729
$116$	−15.5285	−1.44178
$117$	−6.28408	−0.580963
$118$	32.3772	2.98057
$119$	−27.5067	−2.52154
$120$	−2.09915	−0.191626
$121$	−7.52367	−0.683970
$122$	−26.0083	−2.35468
$123$	0.264551	0.0238537
$124$	15.2510	1.36958
$125$	8.97383	0.802644
$126$	9.24105	0.823258
$127$	19.0453	1.69000	0.844999	−	0.534768i	$-0.179601\pi$
$127$	19.0453	1.69000	0.844999	+	0.534768i	$0.179601\pi$
$128$	14.9654	1.32276
$129$	−6.16741	−0.543010
$130$	−13.9252	−1.22132
$131$	4.30555	0.376177	0.188089	−	0.982152i	$-0.439771\pi$
$131$	4.30555	0.376177	0.188089	+	0.982152i	$0.439771\pi$
$132$	−5.49520	−0.478296
$133$	26.5575	2.30283
$134$	27.0531	2.33704
$135$	0.996267	0.0857450
$136$	−13.9498	−1.19619
$137$	−3.03826	−0.259576	−0.129788	−	0.991542i	$-0.541430\pi$
$137$	−3.03826	−0.259576	−0.129788	+	0.991542i	$0.541430\pi$
$138$	−8.49285	−0.722960
$139$	3.12191	0.264797	0.132398	−	0.991197i	$-0.457732\pi$
$139$	3.12191	0.264797	0.132398	+	0.991197i	$0.457732\pi$
$140$	12.1993	1.03103
$141$	6.52827	0.549780
$142$	1.73089	0.145253
$143$	−11.7166	−0.979792
$144$	−1.20805	−0.100671
$145$	5.24905	0.435910
$146$	−10.7738	−0.891647
$147$	−10.2614	−0.846343
$148$	33.0666	2.71806
$149$	−14.3298	−1.17394	−0.586971	−	0.809608i	$-0.699680\pi$
$149$	−14.3298	−1.17394	−0.586971	+	0.809608i	$0.699680\pi$
$150$	−8.91358	−0.727791
$151$	−18.8278	−1.53218	−0.766092	−	0.642731i	$-0.777801\pi$
$151$	−18.8278	−1.53218	−0.766092	+	0.642731i	$0.777801\pi$
$152$	13.4684	1.09244
$153$	6.62066	0.535249
$154$	17.2299	1.38842
$155$	−5.15525	−0.414080
$156$	18.5210	1.48287
$157$	14.5447	1.16079	0.580395	−	0.814335i	$-0.302898\pi$
$157$	14.5447	1.16079	0.580395	+	0.814335i	$0.302898\pi$
$158$	21.1225	1.68041
$159$	−10.5849	−0.839435
$160$	−6.87528	−0.543539
$161$	15.8638	1.25024
$162$	−2.22425	−0.174754
$163$	2.94089	0.230348	0.115174	−	0.993345i	$-0.463257\pi$
$163$	2.94089	0.230348	0.115174	+	0.993345i	$0.463257\pi$
$164$	−0.779708	−0.0608850
$165$	1.85753	0.144609
$166$	−32.5378	−2.52542
$167$	−4.04744	−0.313201	−0.156600	−	0.987662i	$-0.550053\pi$
$167$	−4.04744	−0.313201	−0.156600	+	0.987662i	$0.550053\pi$
$168$	−8.75398	−0.675384
$169$	26.4896	2.03766
$170$	14.6710	1.12522
$171$	−6.39219	−0.488823
$172$	18.1772	1.38600
$173$	18.7957	1.42901	0.714505	−	0.699630i	$-0.246652\pi$
$173$	18.7957	1.42901	0.714505	+	0.699630i	$0.246652\pi$
$174$	−11.7189	−0.888411
$175$	16.6497	1.25860
$176$	−2.25240	−0.169781
$177$	14.5565	1.09413
$178$	0.0599156	0.00449086
$179$	−18.4141	−1.37633	−0.688166	−	0.725553i	$-0.741584\pi$
$179$	−18.4141	−1.37633	−0.688166	+	0.725553i	$0.741584\pi$
$180$	−2.93629	−0.218858
$181$	5.63489	0.418838	0.209419	−	0.977826i	$-0.432843\pi$
$181$	5.63489	0.418838	0.209419	+	0.977826i	$0.432843\pi$
$182$	−58.0715	−4.30454
$183$	−11.6930	−0.864375
$184$	8.04522	0.593102
$185$	−11.1774	−0.821780
$186$	11.5095	0.843920
$187$	12.3442	0.902695
$188$	−19.2407	−1.40327
$189$	4.15468	0.302208
$190$	−14.1648	−1.02762
$191$	21.4381	1.55121	0.775603	−	0.631221i	$-0.217446\pi$
$191$	21.4381	1.55121	0.775603	+	0.631221i	$0.217446\pi$
$192$	12.9335	0.933399
$193$	23.9055	1.72075	0.860376	−	0.509659i	$-0.170229\pi$
$193$	23.9055	1.72075	0.860376	+	0.509659i	$0.170229\pi$
$194$	−12.7961	−0.918708
$195$	−6.26062	−0.448332
$196$	30.2432	2.16023
$197$	−13.9866	−0.996501	−0.498250	−	0.867033i	$-0.666024\pi$
$197$	−13.9866	−0.996501	−0.498250	+	0.867033i	$0.666024\pi$
$198$	−4.14710	−0.294721
$199$	−2.76519	−0.196019	−0.0980096	−	0.995185i	$-0.531248\pi$
$199$	−2.76519	−0.196019	−0.0980096	+	0.995185i	$0.531248\pi$
$200$	8.44377	0.597065
$201$	12.1628	0.857898
$202$	−13.7217	−0.965453
$203$	21.8898	1.53636
$204$	−19.5130	−1.36619
$205$	0.263563	0.0184080
$206$	5.55879	0.387299
$207$	−3.81830	−0.265390
$208$	7.59148	0.526375
$209$	−11.9182	−0.824398
$210$	9.20656	0.635313
$211$	15.5487	1.07042	0.535210	−	0.844719i	$-0.320232\pi$
$211$	15.5487	1.07042	0.535210	+	0.844719i	$0.320232\pi$
$212$	31.1967	2.14260
$213$	0.778190	0.0533207
$214$	−2.39485	−0.163708
$215$	−6.14439	−0.419044
$216$	2.10702	0.143364
$217$	−21.4987	−1.45942
$218$	19.2613	1.30454
$219$	−4.84379	−0.327313
$220$	−5.47469	−0.369104
$221$	−41.6047	−2.79864
$222$	24.9545	1.67484
$223$	−2.08904	−0.139892	−0.0699462	−	0.997551i	$-0.522283\pi$
$223$	−2.08904	−0.139892	−0.0699462	+	0.997551i	$0.522283\pi$
$224$	−28.6716	−1.91570
$225$	−4.00745	−0.267163
$226$	−29.9914	−1.99500
$227$	1.51098	0.100287	0.0501435	−	0.998742i	$-0.484032\pi$
$227$	1.51098	0.100287	0.0501435	+	0.998742i	$0.484032\pi$
$228$	18.8396	1.24769
$229$	−9.35684	−0.618317	−0.309159	−	0.951010i	$-0.600047\pi$
$229$	−9.35684	−0.618317	−0.309159	+	0.951010i	$0.600047\pi$
$230$	−8.46115	−0.557912
$231$	7.74636	0.509673
$232$	11.1013	0.728835
$233$	−6.57651	−0.430842	−0.215421	−	0.976521i	$-0.569112\pi$
$233$	−6.57651	−0.430842	−0.215421	+	0.976521i	$0.569112\pi$
$234$	13.9774	0.913729
$235$	6.50390	0.424268
$236$	−42.9022	−2.79269
$237$	9.49644	0.616860
$238$	61.1819	3.96583
$239$	6.26391	0.405179	0.202589	−	0.979264i	$-0.435064\pi$
$239$	6.26391	0.405179	0.202589	+	0.979264i	$0.435064\pi$
$240$	−1.20354	−0.0776882
$241$	−10.8804	−0.700866	−0.350433	−	0.936588i	$-0.613966\pi$
$241$	−10.8804	−0.700866	−0.350433	+	0.936588i	$0.613966\pi$
$242$	16.7345	1.07574
$243$	−1.00000	−0.0641500
$244$	34.4628	2.20626
$245$	−10.2231	−0.653127
$246$	−0.588427	−0.0375167
$247$	40.1690	2.55589
$248$	−10.9029	−0.692335
$249$	−14.6286	−0.927053
$250$	−19.9600	−1.26238
$251$	7.02547	0.443444	0.221722	−	0.975110i	$-0.428832\pi$
$251$	7.02547	0.443444	0.221722	+	0.975110i	$0.428832\pi$
$252$	−12.2451	−0.771366
$253$	−7.11918	−0.447579
$254$	−42.3615	−2.65800
$255$	6.59595	0.413054
$256$	−7.41966	−0.463729
$257$	−22.3059	−1.39140	−0.695700	−	0.718332i	$-0.744906\pi$
$257$	−22.3059	−1.39140	−0.695700	+	0.718332i	$0.744906\pi$
$258$	13.7179	0.854037
$259$	−46.6126	−2.89637
$260$	18.4519	1.14434
$261$	−5.26872	−0.326125
$262$	−9.57662	−0.591645
$263$	−22.7861	−1.40505	−0.702526	−	0.711659i	$-0.747944\pi$
$263$	−22.7861	−1.40505	−0.702526	+	0.711659i	$0.747944\pi$
$264$	3.92852	0.241783
$265$	−10.5454	−0.647796
$266$	−59.0705	−3.62185
$267$	0.0269374	0.00164854
$268$	−35.8474	−2.18973
$269$	−0.896177	−0.0546409	−0.0273204	−	0.999627i	$-0.508697\pi$
$269$	−0.896177	−0.0546409	−0.0273204	+	0.999627i	$0.508697\pi$
$270$	−2.21595	−0.134858
$271$	20.6014	1.25145	0.625724	−	0.780044i	$-0.284804\pi$
$271$	20.6014	1.25145	0.625724	+	0.780044i	$0.284804\pi$
$272$	−7.99809	−0.484956
$273$	−26.1083	−1.58015
$274$	6.75785	0.408257
$275$	−7.47186	−0.450570
$276$	11.2536	0.677390
$277$	−26.9421	−1.61880	−0.809398	−	0.587261i	$-0.800206\pi$
$277$	−26.9421	−1.61880	−0.809398	+	0.587261i	$0.800206\pi$
$278$	−6.94391	−0.416468
$279$	5.17457	0.309793
$280$	−8.72130	−0.521198
$281$	23.4536	1.39913	0.699563	−	0.714571i	$-0.253378\pi$
$281$	23.4536	1.39913	0.699563	+	0.714571i	$0.253378\pi$
$282$	−14.5205	−0.864684
$283$	−4.00545	−0.238099	−0.119050	−	0.992888i	$-0.537985\pi$
$283$	−4.00545	−0.238099	−0.119050	+	0.992888i	$0.537985\pi$
$284$	−2.29355	−0.136097
$285$	−6.36833	−0.377227
$286$	26.0607	1.54100
$287$	1.09912	0.0648792
$288$	6.90104	0.406648
$289$	26.8332	1.57842
$290$	−11.6752	−0.685592
$291$	−5.75300	−0.337247
$292$	14.2761	0.835444
$293$	−4.67908	−0.273355	−0.136678	−	0.990616i	$-0.543642\pi$
$293$	−4.67908	−0.273355	−0.136678	+	0.990616i	$0.543642\pi$
$294$	22.8238	1.33111
$295$	14.5021	0.844346
$296$	−23.6393	−1.37400
$297$	−1.86449	−0.108189
$298$	31.8730	1.84635
$299$	23.9945	1.38764
$300$	11.8111	0.681916
$301$	−25.6236	−1.47692
$302$	41.8777	2.40979
$303$	−6.16911	−0.354406
$304$	7.72209	0.442892
$305$	−11.6494	−0.667043
$306$	−14.7260	−0.841830
$307$	26.7588	1.52721	0.763603	−	0.645686i	$-0.223428\pi$
$307$	26.7588	1.52721	0.763603	+	0.645686i	$0.223428\pi$
$308$	−22.8308	−1.30091
$309$	2.49917	0.142173
$310$	11.4666	0.651257
$311$	−15.4194	−0.874356	−0.437178	−	0.899375i	$-0.644022\pi$
$311$	−15.4194	−0.874356	−0.437178	+	0.899375i	$0.644022\pi$
$312$	−13.2407	−0.749605
$313$	7.61521	0.430437	0.215219	−	0.976566i	$-0.430954\pi$
$313$	7.61521	0.430437	0.215219	+	0.976566i	$0.430954\pi$
$314$	−32.3510	−1.82567
$315$	4.13917	0.233216
$316$	−27.9888	−1.57449
$317$	−6.86061	−0.385330	−0.192665	−	0.981265i	$-0.561713\pi$
$317$	−6.86061	−0.385330	−0.192665	+	0.981265i	$0.561713\pi$
$318$	23.5434	1.32025
$319$	−9.82348	−0.550009
$320$	12.8853	0.720309
$321$	−1.07670	−0.0600954
$322$	−35.2851	−1.96636
$323$	−42.3205	−2.35478
$324$	2.94729	0.163738
$325$	25.1831	1.39691
$326$	−6.54127	−0.362287
$327$	8.65970	0.478882
$328$	0.557413	0.0307780
$329$	27.1229	1.49533
$330$	−4.13162	−0.227438
$331$	32.4805	1.78529	0.892644	−	0.450763i	$-0.148848\pi$
$331$	32.4805	1.78529	0.892644	+	0.450763i	$0.148848\pi$
$332$	43.1149	2.36624
$333$	11.2193	0.614814
$334$	9.00253	0.492596
$335$	12.1174	0.662045
$336$	−5.01906	−0.273812
$337$	19.8066	1.07893	0.539467	−	0.842007i	$-0.318626\pi$
$337$	19.8066	1.07893	0.539467	+	0.842007i	$0.318626\pi$
$338$	−58.9196	−3.20480
$339$	−13.4838	−0.732340
$340$	−19.4402	−1.05429
$341$	9.64793	0.522465
$342$	14.2178	0.768812
$343$	−13.5499	−0.731626
$344$	−12.9948	−0.700635
$345$	−3.80405	−0.204803
$346$	−41.8064	−2.24752
$347$	24.7364	1.32792	0.663959	−	0.747769i	$-0.268875\pi$
$347$	24.7364	1.32792	0.663959	+	0.747769i	$0.268875\pi$
$348$	15.5285	0.832412
$349$	1.87856	0.100557	0.0502786	−	0.998735i	$-0.483989\pi$
$349$	1.87856	0.100557	0.0502786	+	0.998735i	$0.483989\pi$
$350$	−37.0331	−1.97950
$351$	6.28408	0.335419
$352$	12.8669	0.685810
$353$	−13.8675	−0.738092	−0.369046	−	0.929411i	$-0.620315\pi$
$353$	−13.8675	−0.738092	−0.369046	+	0.929411i	$0.620315\pi$
$354$	−32.3772	−1.72083
$355$	0.775285	0.0411479
$356$	−0.0793925	−0.00420779
$357$	27.5067	1.45581
$358$	40.9575	2.16467
$359$	0.534551	0.0282125	0.0141063	−	0.999901i	$-0.495510\pi$
$359$	0.534551	0.0282125	0.0141063	+	0.999901i	$0.495510\pi$
$360$	2.09915	0.110635
$361$	21.8601	1.15053
$362$	−12.5334	−0.658742
$363$	7.52367	0.394890
$364$	76.9489	4.03322
$365$	−4.82571	−0.252589
$366$	26.0083	1.35947
$367$	−5.83818	−0.304750	−0.152375	−	0.988323i	$-0.548692\pi$
$367$	−5.83818	−0.304750	−0.152375	+	0.988323i	$0.548692\pi$
$368$	4.61270	0.240453
$369$	−0.264551	−0.0137720
$370$	24.8614	1.29248
$371$	−43.9768	−2.28316
$372$	−15.2510	−0.790725
$373$	9.05207	0.468698	0.234349	−	0.972152i	$-0.424704\pi$
$373$	9.05207	0.468698	0.234349	+	0.972152i	$0.424704\pi$
$374$	−27.4565	−1.41974
$375$	−8.97383	−0.463407
$376$	13.7552	0.709369
$377$	33.1090	1.70520
$378$	−9.24105	−0.475308
$379$	29.6137	1.52115	0.760576	−	0.649249i	$-0.224917\pi$
$379$	29.6137	1.52115	0.760576	+	0.649249i	$0.224917\pi$
$380$	18.7693	0.962846
$381$	−19.0453	−0.975720
$382$	−47.6837	−2.43971
$383$	26.3832	1.34812	0.674058	−	0.738678i	$-0.264550\pi$
$383$	26.3832	1.34812	0.674058	+	0.738678i	$0.264550\pi$
$384$	−14.9654	−0.763699
$385$	7.71745	0.393318
$386$	−53.1717	−2.70637
$387$	6.16741	0.313507
$388$	16.9558	0.860800
$389$	−12.5764	−0.637650	−0.318825	−	0.947814i	$-0.603288\pi$
$389$	−12.5764	−0.637650	−0.318825	+	0.947814i	$0.603288\pi$
$390$	13.9252	0.705129
$391$	−25.2797	−1.27845
$392$	−21.6209	−1.09202
$393$	−4.30555	−0.217186
$394$	31.1096	1.56728
$395$	9.46099	0.476034
$396$	5.49520	0.276144
$397$	−16.4362	−0.824908	−0.412454	−	0.910979i	$-0.635328\pi$
$397$	−16.4362	−0.824908	−0.412454	+	0.910979i	$0.635328\pi$
$398$	6.15048	0.308296
$399$	−26.5575	−1.32954
$400$	4.84120	0.242060
$401$	−6.88986	−0.344063	−0.172032	−	0.985091i	$-0.555033\pi$
$401$	−6.88986	−0.344063	−0.172032	+	0.985091i	$0.555033\pi$
$402$	−27.0531	−1.34929
$403$	−32.5174	−1.61981
$404$	18.1822	0.904598
$405$	−0.996267	−0.0495049
$406$	−48.6885	−2.41637
$407$	20.9183	1.03688
$408$	13.9498	0.690620
$409$	−16.2426	−0.803144	−0.401572	−	0.915827i	$-0.631536\pi$
$409$	−16.2426	−0.803144	−0.401572	+	0.915827i	$0.631536\pi$
$410$	−0.586231	−0.0289519
$411$	3.03826	0.149866
$412$	−7.36580	−0.362887
$413$	60.4774	2.97590
$414$	8.49285	0.417401
$415$	−14.5740	−0.715412
$416$	−43.3667	−2.12623
$417$	−3.12191	−0.152881
$418$	26.5090	1.29660
$419$	4.81608	0.235281	0.117640	−	0.993056i	$-0.462467\pi$
$419$	4.81608	0.235281	0.117640	+	0.993056i	$0.462467\pi$
$420$	−12.1993	−0.595267
$421$	−16.7290	−0.815321	−0.407661	−	0.913133i	$-0.633655\pi$
$421$	−16.7290	−0.815321	−0.407661	+	0.913133i	$0.633655\pi$
$422$	−34.5843	−1.68354
$423$	−6.52827	−0.317416
$424$	−22.3025	−1.08311
$425$	−26.5320	−1.28699
$426$	−1.73089	−0.0838619
$427$	−48.5809	−2.35099
$428$	3.17334	0.153389
$429$	11.7166	0.565683
$430$	13.6667	0.659065
$431$	12.7643	0.614836	0.307418	−	0.951575i	$-0.400535\pi$
$431$	12.7643	0.614836	0.307418	+	0.951575i	$0.400535\pi$
$432$	1.20805	0.0581224
$433$	27.0497	1.29992	0.649962	−	0.759967i	$-0.274785\pi$
$433$	27.0497	1.29992	0.649962	+	0.759967i	$0.274785\pi$
$434$	47.8184	2.29536
$435$	−5.24905	−0.251673
$436$	−25.5227	−1.22231
$437$	24.4073	1.16756
$438$	10.7738	0.514792
$439$	−4.92893	−0.235245	−0.117623	−	0.993058i	$-0.537527\pi$
$439$	−4.92893	−0.235245	−0.117623	+	0.993058i	$0.537527\pi$
$440$	3.91385	0.186586
$441$	10.2614	0.488636
$442$	92.5394	4.40165
$443$	26.1587	1.24284	0.621418	−	0.783479i	$-0.286557\pi$
$443$	26.1587	1.24284	0.621418	+	0.783479i	$0.286557\pi$
$444$	−33.0666	−1.56927
$445$	0.0268369	0.00127219
$446$	4.64655	0.220020
$447$	14.3298	0.677775
$448$	53.7347	2.53873
$449$	20.6163	0.972944	0.486472	−	0.873696i	$-0.338284\pi$
$449$	20.6163	0.972944	0.486472	+	0.873696i	$0.338284\pi$
$450$	8.91358	0.420190
$451$	−0.493252	−0.0232263
$452$	39.7408	1.86925
$453$	18.8278	0.884607
$454$	−3.36079	−0.157730
$455$	−26.0109	−1.21941
$456$	−13.4684	−0.630718
$457$	7.13040	0.333546	0.166773	−	0.985995i	$-0.446665\pi$
$457$	7.13040	0.333546	0.166773	+	0.985995i	$0.446665\pi$
$458$	20.8120	0.972479
$459$	−6.62066	−0.309026
$460$	11.2116	0.522745
$461$	−36.9970	−1.72312	−0.861561	−	0.507654i	$-0.830513\pi$
$461$	−36.9970	−1.72312	−0.861561	+	0.507654i	$0.830513\pi$
$462$	−17.2299	−0.801606
$463$	−3.78265	−0.175794	−0.0878972	−	0.996130i	$-0.528015\pi$
$463$	−3.78265	−0.175794	−0.0878972	+	0.996130i	$0.528015\pi$
$464$	6.36488	0.295482
$465$	5.15525	0.239069
$466$	14.6278	0.677621
$467$	−7.67387	−0.355104	−0.177552	−	0.984111i	$-0.556818\pi$
$467$	−7.67387	−0.355104	−0.177552	+	0.984111i	$0.556818\pi$
$468$	−18.5210	−0.856134
$469$	50.5326	2.33338
$470$	−14.4663	−0.667281
$471$	−14.5447	−0.670182
$472$	30.6707	1.41173
$473$	11.4991	0.528728
$474$	−21.1225	−0.970187
$475$	25.6164	1.17536
$476$	−81.0704	−3.71585
$477$	10.5849	0.484648
$478$	−13.9325	−0.637258
$479$	−30.8309	−1.40870	−0.704350	−	0.709852i	$-0.748762\pi$
$479$	−30.8309	−1.40870	−0.704350	+	0.709852i	$0.748762\pi$
$480$	6.87528	0.313812
$481$	−70.5030	−3.21466
$482$	24.2007	1.10231
$483$	−15.8638	−0.721828
$484$	−22.1745	−1.00793
$485$	−5.73153	−0.260255
$486$	2.22425	0.100894
$487$	−27.0923	−1.22767	−0.613834	−	0.789435i	$-0.710374\pi$
$487$	−27.0923	−1.22767	−0.613834	+	0.789435i	$0.710374\pi$
$488$	−24.6375	−1.11529
$489$	−2.94089	−0.132991
$490$	22.7386	1.02723
$491$	9.64508	0.435277	0.217638	−	0.976030i	$-0.430165\pi$
$491$	9.64508	0.435277	0.217638	+	0.976030i	$0.430165\pi$
$492$	0.779708	0.0351520
$493$	−34.8824	−1.57102
$494$	−89.3459	−4.01986
$495$	−1.85753	−0.0834898
$496$	−6.25114	−0.280684
$497$	3.23313	0.145026
$498$	32.5378	1.45805
$499$	−35.6525	−1.59603	−0.798013	−	0.602640i	$-0.794116\pi$
$499$	−35.6525	−1.59603	−0.798013	+	0.602640i	$0.794116\pi$
$500$	26.4485	1.18281
$501$	4.04744	0.180826
$502$	−15.6264	−0.697441
$503$	−3.38282	−0.150833	−0.0754163	−	0.997152i	$-0.524029\pi$
$503$	−3.38282	−0.150833	−0.0754163	+	0.997152i	$0.524029\pi$
$504$	8.75398	0.389933
$505$	−6.14609	−0.273497
$506$	15.8349	0.703945
$507$	−26.4896	−1.17645
$508$	56.1321	2.49046
$509$	22.7566	1.00867	0.504335	−	0.863508i	$-0.331738\pi$
$509$	22.7566	1.00867	0.504335	+	0.863508i	$0.331738\pi$
$510$	−14.6710	−0.649645
$511$	−20.1244	−0.890251
$512$	−13.4276	−0.593420
$513$	6.39219	0.282222
$514$	49.6138	2.18837
$515$	2.48984	0.109716
$516$	−18.1772	−0.800205
$517$	−12.1719	−0.535320
$518$	103.678	4.55536
$519$	−18.7957	−0.825040
$520$	−13.1912	−0.578474
$521$	−6.57014	−0.287843	−0.143922	−	0.989589i	$-0.545971\pi$
$521$	−6.57014	−0.287843	−0.143922	+	0.989589i	$0.545971\pi$
$522$	11.7189	0.512924
$523$	38.2568	1.67285	0.836426	−	0.548080i	$-0.184641\pi$
$523$	38.2568	1.67285	0.836426	+	0.548080i	$0.184641\pi$
$524$	12.6897	0.554352
$525$	−16.6497	−0.726651
$526$	50.6820	2.20984
$527$	34.2590	1.49235
$528$	2.25240	0.0980231
$529$	−8.42060	−0.366113
$530$	23.4555	1.01884
$531$	−14.5565	−0.631697
$532$	78.2727	3.39355
$533$	1.66246	0.0720090
$534$	−0.0599156	−0.00259280
$535$	−1.07268	−0.0463760
$536$	25.6272	1.10693
$537$	18.4141	0.794625
$538$	1.99332	0.0859382
$539$	19.1322	0.824083
$540$	2.93629	0.126358
$541$	−40.1453	−1.72598	−0.862990	−	0.505221i	$-0.831411\pi$
$541$	−40.1453	−1.72598	−0.862990	+	0.505221i	$0.831411\pi$
$542$	−45.8228	−1.96826
$543$	−5.63489	−0.241816
$544$	45.6895	1.95892
$545$	8.62737	0.369556
$546$	58.0715	2.48523
$547$	11.0287	0.471554	0.235777	−	0.971807i	$-0.424236\pi$
$547$	11.0287	0.471554	0.235777	+	0.971807i	$0.424236\pi$
$548$	−8.95464	−0.382523
$549$	11.6930	0.499047
$550$	16.6193	0.708649
$551$	33.6786	1.43476
$552$	−8.04522	−0.342427
$553$	39.4547	1.67778
$554$	59.9261	2.54601
$555$	11.1774	0.474455
$556$	9.20118	0.390217
$557$	27.3140	1.15733	0.578666	−	0.815564i	$-0.303573\pi$
$557$	27.3140	1.15733	0.578666	+	0.815564i	$0.303573\pi$
$558$	−11.5095	−0.487237
$559$	−38.7565	−1.63922
$560$	−5.00033	−0.211302
$561$	−12.3442	−0.521171
$562$	−52.1667	−2.20052
$563$	−32.0133	−1.34920	−0.674600	−	0.738183i	$-0.735684\pi$
$563$	−32.0133	−1.34920	−0.674600	+	0.738183i	$0.735684\pi$
$564$	19.2407	0.810181
$565$	−13.4335	−0.565151
$566$	8.90912	0.374478
$567$	−4.15468	−0.174480
$568$	1.63966	0.0687986
$569$	9.93811	0.416627	0.208314	−	0.978062i	$-0.433203\pi$
$569$	9.93811	0.416627	0.208314	+	0.978062i	$0.433203\pi$
$570$	14.1648	0.593296
$571$	−46.7342	−1.95577	−0.977884	−	0.209150i	$-0.932930\pi$
$571$	−46.7342	−1.95577	−0.977884	+	0.209150i	$0.932930\pi$
$572$	−34.5323	−1.44387
$573$	−21.4381	−0.895589
$574$	−2.44473	−0.102041
$575$	15.3016	0.638123
$576$	−12.9335	−0.538898
$577$	1.79021	0.0745275	0.0372638	−	0.999305i	$-0.488136\pi$
$577$	1.79021	0.0745275	0.0372638	+	0.999305i	$0.488136\pi$
$578$	−59.6837	−2.48251
$579$	−23.9055	−0.993477
$580$	15.4705	0.642377
$581$	−60.7773	−2.52147
$582$	12.7961	0.530416
$583$	19.7354	0.817357
$584$	−10.2060	−0.422325
$585$	6.26062	0.258845
$586$	10.4075	0.429928
$587$	−37.9167	−1.56499	−0.782494	−	0.622658i	$-0.786053\pi$
$587$	−37.9167	−1.56499	−0.782494	+	0.622658i	$0.786053\pi$
$588$	−30.2432	−1.24721
$589$	−33.0768	−1.36291
$590$	−32.2564	−1.32797
$591$	13.9866	0.575330
$592$	−13.5535	−0.557045
$593$	10.5556	0.433468	0.216734	−	0.976231i	$-0.430460\pi$
$593$	10.5556	0.433468	0.216734	+	0.976231i	$0.430460\pi$
$594$	4.14710	0.170157
$595$	27.4040	1.12346
$596$	−42.2341	−1.72997
$597$	2.76519	0.113172
$598$	−53.3698	−2.18245
$599$	−4.52874	−0.185039	−0.0925196	−	0.995711i	$-0.529492\pi$
$599$	−4.52874	−0.185039	−0.0925196	+	0.995711i	$0.529492\pi$
$600$	−8.44377	−0.344715
$601$	−21.5067	−0.877276	−0.438638	−	0.898664i	$-0.644539\pi$
$601$	−21.5067	−0.877276	−0.438638	+	0.898664i	$0.644539\pi$
$602$	56.9933	2.32288
$603$	−12.1628	−0.495308
$604$	−55.4910	−2.25790
$605$	7.49559	0.304739
$606$	13.7217	0.557404
$607$	−18.8079	−0.763388	−0.381694	−	0.924289i	$-0.624659\pi$
$607$	−18.8079	−0.763388	−0.381694	+	0.924289i	$0.624659\pi$
$608$	−44.1128	−1.78901
$609$	−21.8898	−0.887021
$610$	25.9112	1.04911
$611$	41.0242	1.65966
$612$	19.5130	0.788767
$613$	−36.3251	−1.46716	−0.733578	−	0.679606i	$-0.762151\pi$
$613$	−36.3251	−1.46716	−0.733578	+	0.679606i	$0.762151\pi$
$614$	−59.5183	−2.40196
$615$	−0.263563	−0.0106279
$616$	16.3217	0.657621
$617$	−32.8581	−1.32282	−0.661408	−	0.750026i	$-0.730041\pi$
$617$	−32.8581	−1.32282	−0.661408	+	0.750026i	$0.730041\pi$
$618$	−5.55879	−0.223607
$619$	33.8810	1.36179	0.680896	−	0.732380i	$-0.261591\pi$
$619$	33.8810	1.36179	0.680896	+	0.732380i	$0.261591\pi$
$620$	−15.1940	−0.610207
$621$	3.81830	0.153223
$622$	34.2967	1.37517
$623$	0.111916	0.00448383
$624$	−7.59148	−0.303903
$625$	11.0969	0.443877
$626$	−16.9381	−0.676984
$627$	11.9182	0.475966
$628$	42.8673	1.71059
$629$	74.2792	2.96171
$630$	−9.20656	−0.366798
$631$	−28.4640	−1.13314	−0.566568	−	0.824015i	$-0.691729\pi$
$631$	−28.4640	−1.13314	−0.566568	+	0.824015i	$0.691729\pi$
$632$	20.0092	0.795922
$633$	−15.5487	−0.618007
$634$	15.2597	0.606041
$635$	−18.9742	−0.752969
$636$	−31.1967	−1.23703
$637$	−64.4832	−2.55492
$638$	21.8499	0.865045
$639$	−0.778190	−0.0307847
$640$	−14.9095	−0.589350
$641$	35.1354	1.38777	0.693883	−	0.720088i	$-0.255898\pi$
$641$	35.1354	1.38777	0.693883	+	0.720088i	$0.255898\pi$
$642$	2.39485	0.0945171
$643$	−18.7780	−0.740533	−0.370267	−	0.928925i	$-0.620734\pi$
$643$	−18.7780	−0.740533	−0.370267	+	0.928925i	$0.620734\pi$
$644$	46.7553	1.84242
$645$	6.14439	0.241935
$646$	94.1314	3.70355
$647$	−2.30288	−0.0905356	−0.0452678	−	0.998975i	$-0.514414\pi$
$647$	−2.30288	−0.0905356	−0.0452678	+	0.998975i	$0.514414\pi$
$648$	−2.10702	−0.0827715
$649$	−27.1404	−1.06535
$650$	−56.0136	−2.19703
$651$	21.4987	0.842599
$652$	8.66765	0.339452
$653$	−39.2176	−1.53470	−0.767351	−	0.641228i	$-0.778425\pi$
$653$	−39.2176	−1.53470	−0.767351	+	0.641228i	$0.778425\pi$
$654$	−19.2613	−0.753178
$655$	−4.28948	−0.167604
$656$	0.319591	0.0124779
$657$	4.84379	0.188974
$658$	−60.3281	−2.35183
$659$	46.5405	1.81296	0.906481	−	0.422246i	$-0.138758\pi$
$659$	46.5405	1.81296	0.906481	+	0.422246i	$0.138758\pi$
$660$	5.47469	0.213102
$661$	−11.9399	−0.464408	−0.232204	−	0.972667i	$-0.574594\pi$
$661$	−11.9399	−0.464408	−0.232204	+	0.972667i	$0.574594\pi$
$662$	−72.2447	−2.80787
$663$	41.6047	1.61579
$664$	−30.8228	−1.19616
$665$	−26.4584	−1.02601
$666$	−24.9545	−0.966969
$667$	20.1175	0.778954
$668$	−11.9290	−0.461547
$669$	2.08904	0.0807669
$670$	−26.9522	−1.04125
$671$	21.8016	0.841641
$672$	28.6716	1.10603
$673$	−7.27576	−0.280460	−0.140230	−	0.990119i	$-0.544784\pi$
$673$	−7.27576	−0.280460	−0.140230	+	0.990119i	$0.544784\pi$
$674$	−44.0548	−1.69693
$675$	4.00745	0.154247
$676$	78.0727	3.00280
$677$	−34.3865	−1.32158	−0.660790	−	0.750571i	$-0.729779\pi$
$677$	−34.3865	−1.32158	−0.660790	+	0.750571i	$0.729779\pi$
$678$	29.9914	1.15181
$679$	−23.9019	−0.917270
$680$	13.8978	0.532955
$681$	−1.51098	−0.0579007
$682$	−21.4594	−0.821724
$683$	−20.2709	−0.775643	−0.387821	−	0.921735i	$-0.626772\pi$
$683$	−20.2709	−0.775643	−0.387821	+	0.921735i	$0.626772\pi$
$684$	−18.8396	−0.720352
$685$	3.02692	0.115653
$686$	30.1384	1.15069
$687$	9.35684	0.356986
$688$	−7.45054	−0.284049
$689$	−66.5162	−2.53406
$690$	8.46115	0.322111
$691$	16.3843	0.623287	0.311643	−	0.950199i	$-0.399121\pi$
$691$	16.3843	0.623287	0.311643	+	0.950199i	$0.399121\pi$
$692$	55.3964	2.10586
$693$	−7.74636	−0.294260
$694$	−55.0199	−2.08853
$695$	−3.11026	−0.117979
$696$	−11.1013	−0.420793
$697$	−1.75150	−0.0663428
$698$	−4.17840	−0.158155
$699$	6.57651	0.248747
$700$	49.0715	1.85473
$701$	23.9477	0.904493	0.452247	−	0.891893i	$-0.350623\pi$
$701$	23.9477	0.904493	0.452247	+	0.891893i	$0.350623\pi$
$702$	−13.9774	−0.527542
$703$	−71.7159	−2.70482
$704$	−24.1145	−0.908849
$705$	−6.50390	−0.244951
$706$	30.8448	1.16086
$707$	−25.6307	−0.963941
$708$	42.9022	1.61236
$709$	24.4957	0.919955	0.459978	−	0.887931i	$-0.347857\pi$
$709$	24.4957	0.919955	0.459978	+	0.887931i	$0.347857\pi$
$710$	−1.72443	−0.0647166
$711$	−9.49644	−0.356144
$712$	0.0567576	0.00212708
$713$	−19.7580	−0.739944
$714$	−61.1819	−2.28967
$715$	11.6729	0.436541
$716$	−54.2716	−2.02823
$717$	−6.26391	−0.233930
$718$	−1.18898	−0.0443722
$719$	−18.7839	−0.700522	−0.350261	−	0.936652i	$-0.613907\pi$
$719$	−18.7839	−0.700522	−0.350261	+	0.936652i	$0.613907\pi$
$720$	1.20354	0.0448533
$721$	10.3833	0.386693
$722$	−48.6223	−1.80953
$723$	10.8804	0.404645
$724$	16.6077	0.617219
$725$	21.1141	0.784159
$726$	−16.7345	−0.621077
$727$	17.5712	0.651678	0.325839	−	0.945425i	$-0.394353\pi$
$727$	17.5712	0.651678	0.325839	+	0.945425i	$0.394353\pi$
$728$	−55.0107	−2.03883
$729$	1.00000	0.0370370
$730$	10.7336	0.397268
$731$	40.8323	1.51024
$732$	−34.4628	−1.27378
$733$	31.7052	1.17106	0.585530	−	0.810651i	$-0.300886\pi$
$733$	31.7052	1.17106	0.585530	+	0.810651i	$0.300886\pi$
$734$	12.9856	0.479306
$735$	10.2231	0.377083
$736$	−26.3502	−0.971283
$737$	−22.6775	−0.835335
$738$	0.588427	0.0216603
$739$	−1.75491	−0.0645553	−0.0322777	−	0.999479i	$-0.510276\pi$
$739$	−1.75491	−0.0645553	−0.0322777	+	0.999479i	$0.510276\pi$
$740$	−32.9431	−1.21101
$741$	−40.1690	−1.47565
$742$	97.8153	3.59091
$743$	3.34345	0.122659	0.0613296	−	0.998118i	$-0.480466\pi$
$743$	3.34345	0.122659	0.0613296	+	0.998118i	$0.480466\pi$
$744$	10.9029	0.399720
$745$	14.2763	0.523043
$746$	−20.1341	−0.737161
$747$	14.6286	0.535234
$748$	36.3819	1.33025
$749$	−4.47333	−0.163452
$750$	19.9600	0.728838
$751$	−23.2654	−0.848966	−0.424483	−	0.905436i	$-0.639544\pi$
$751$	−23.2654	−0.848966	−0.424483	+	0.905436i	$0.639544\pi$
$752$	7.88648	0.287590
$753$	−7.02547	−0.256023
$754$	−73.6428	−2.68191
$755$	18.7575	0.682656
$756$	12.2451	0.445348
$757$	22.9418	0.833834	0.416917	−	0.908944i	$-0.363111\pi$
$757$	22.9418	0.833834	0.416917	+	0.908944i	$0.363111\pi$
$758$	−65.8682	−2.39244
$759$	7.11918	0.258410
$760$	−13.4182	−0.486728
$761$	3.65256	0.132405	0.0662026	−	0.997806i	$-0.478912\pi$
$761$	3.65256	0.132405	0.0662026	+	0.997806i	$0.478912\pi$
$762$	42.3615	1.53460
$763$	35.9783	1.30250
$764$	63.1844	2.28593
$765$	−6.59595	−0.238477
$766$	−58.6828	−2.12029
$767$	91.4739	3.30293
$768$	7.41966	0.267734
$769$	2.44672	0.0882309	0.0441155	−	0.999026i	$-0.485953\pi$
$769$	2.44672	0.0882309	0.0441155	+	0.999026i	$0.485953\pi$
$770$	−17.1655	−0.618603
$771$	22.3059	0.803326
$772$	70.4564	2.53578
$773$	0.953638	0.0343000	0.0171500	−	0.999853i	$-0.494541\pi$
$773$	0.953638	0.0343000	0.0171500	+	0.999853i	$0.494541\pi$
$774$	−13.7179	−0.493079
$775$	−20.7368	−0.744889
$776$	−12.1217	−0.435143
$777$	46.6126	1.67222
$778$	27.9731	1.00289
$779$	1.69106	0.0605884
$780$	−18.4519	−0.660683
$781$	−1.45093	−0.0519183
$782$	56.2283	2.01072
$783$	5.26872	0.188289
$784$	−12.3962	−0.442723
$785$	−14.4904	−0.517183
$786$	9.57662	0.341587
$787$	−37.4003	−1.33318	−0.666589	−	0.745425i	$-0.732246\pi$
$787$	−37.4003	−1.33318	−0.666589	+	0.745425i	$0.732246\pi$
$788$	−41.2225	−1.46849
$789$	22.7861	0.811207
$790$	−21.0436	−0.748698
$791$	−56.0209	−1.99187
$792$	−3.92852	−0.139594
$793$	−73.4800	−2.60935
$794$	36.5582	1.29740
$795$	10.5454	0.374005
$796$	−8.14983	−0.288863
$797$	0.998644	0.0353738	0.0176869	−	0.999844i	$-0.494370\pi$
$797$	0.998644	0.0353738	0.0176869	+	0.999844i	$0.494370\pi$
$798$	59.0705	2.09107
$799$	−43.2215	−1.52907
$800$	−27.6556	−0.977773
$801$	−0.0269374	−0.000951787 0
$802$	15.3248	0.541137
$803$	9.03121	0.318704
$804$	35.8474	1.26424
$805$	−15.8046	−0.557039
$806$	72.3268	2.54760
$807$	0.896177	0.0315469
$808$	−12.9984	−0.457283
$809$	−54.6200	−1.92034	−0.960169	−	0.279420i	$-0.909858\pi$
$809$	−54.6200	−1.92034	−0.960169	+	0.279420i	$0.909858\pi$
$810$	2.21595	0.0778605
$811$	−27.2524	−0.956962	−0.478481	−	0.878098i	$-0.658812\pi$
$811$	−27.2524	−0.956962	−0.478481	+	0.878098i	$0.658812\pi$
$812$	64.5157	2.26406
$813$	−20.6014	−0.722524
$814$	−46.5275	−1.63079
$815$	−2.92991	−0.102630
$816$	7.99809	0.279989
$817$	−39.4232	−1.37924
$818$	36.1276	1.26317
$819$	26.1083	0.912299
$820$	0.776798	0.0271270
$821$	9.11464	0.318103	0.159052	−	0.987270i	$-0.449156\pi$
$821$	9.11464	0.318103	0.159052	+	0.987270i	$0.449156\pi$
$822$	−6.75785	−0.235707
$823$	−0.668887	−0.0233159	−0.0116580	−	0.999932i	$-0.503711\pi$
$823$	−0.668887	−0.0233159	−0.0116580	+	0.999932i	$0.503711\pi$
$824$	5.26580	0.183443
$825$	7.47186	0.260137
$826$	−134.517	−4.68044
$827$	−47.7286	−1.65969	−0.829843	−	0.557997i	$-0.811570\pi$
$827$	−47.7286	−1.65969	−0.829843	+	0.557997i	$0.811570\pi$
$828$	−11.2536	−0.391091
$829$	34.9976	1.21552	0.607759	−	0.794121i	$-0.292069\pi$
$829$	34.9976	1.21552	0.607759	+	0.794121i	$0.292069\pi$
$830$	32.4163	1.12519
$831$	26.9421	0.934612
$832$	81.2754	2.81772
$833$	67.9370	2.35388
$834$	6.94391	0.240448
$835$	4.03233	0.139545
$836$	−35.1264	−1.21487
$837$	−5.17457	−0.178859
$838$	−10.7122	−0.370046
$839$	51.9876	1.79481	0.897405	−	0.441207i	$-0.145450\pi$
$839$	51.9876	1.79481	0.897405	+	0.441207i	$0.145450\pi$
$840$	8.72130	0.300914
$841$	−1.24063	−0.0427802
$842$	37.2095	1.28232
$843$	−23.4536	−0.807785
$844$	45.8267	1.57742
$845$	−26.3907	−0.907869
$846$	14.5205	0.499226
$847$	31.2584	1.07405
$848$	−12.7871	−0.439110
$849$	4.00545	0.137467
$850$	59.0138	2.02416
$851$	−42.8386	−1.46849
$852$	2.29355	0.0785758
$853$	13.5453	0.463781	0.231891	−	0.972742i	$-0.425509\pi$
$853$	13.5453	0.463781	0.231891	+	0.972742i	$0.425509\pi$
$854$	108.056	3.69760
$855$	6.36833	0.217792
$856$	−2.26862	−0.0775399
$857$	−32.4610	−1.10885	−0.554423	−	0.832235i	$-0.687061\pi$
$857$	−32.4610	−1.10885	−0.554423	+	0.832235i	$0.687061\pi$
$858$	−26.0607	−0.889697
$859$	2.31434	0.0789643	0.0394822	−	0.999220i	$-0.487429\pi$
$859$	2.31434	0.0789643	0.0394822	+	0.999220i	$0.487429\pi$
$860$	−18.1093	−0.617522
$861$	−1.09912	−0.0374580
$862$	−28.3911	−0.967004
$863$	−55.2088	−1.87933	−0.939665	−	0.342096i	$-0.888863\pi$
$863$	−55.2088	−1.87933	−0.939665	+	0.342096i	$0.888863\pi$
$864$	−6.90104	−0.234778
$865$	−18.7255	−0.636688
$866$	−60.1653	−2.04450
$867$	−26.8332	−0.911302
$868$	−63.3628	−2.15068
$869$	−17.7060	−0.600636
$870$	11.6752	0.395827
$871$	76.4320	2.58980
$872$	18.2461	0.617892
$873$	5.75300	0.194710
$874$	−54.2879	−1.83632
$875$	−37.2834	−1.26041
$876$	−14.2761	−0.482344
$877$	41.4434	1.39945	0.699723	−	0.714415i	$-0.253307\pi$
$877$	41.4434	1.39945	0.699723	+	0.714415i	$0.253307\pi$
$878$	10.9632	0.369989
$879$	4.67908	0.157822
$880$	2.24399	0.0756450
$881$	−11.6107	−0.391175	−0.195587	−	0.980686i	$-0.562661\pi$
$881$	−11.6107	−0.391175	−0.195587	+	0.980686i	$0.562661\pi$
$882$	−22.8238	−0.768519
$883$	0.879992	0.0296141	0.0148070	−	0.999890i	$-0.495287\pi$
$883$	0.879992	0.0296141	0.0148070	+	0.999890i	$0.495287\pi$
$884$	−122.621	−4.12420
$885$	−14.5021	−0.487484
$886$	−58.1834	−1.95471
$887$	−32.7008	−1.09799	−0.548993	−	0.835827i	$-0.684989\pi$
$887$	−32.7008	−1.09799	−0.548993	+	0.835827i	$0.684989\pi$
$888$	23.6393	0.793282
$889$	−79.1271	−2.65384
$890$	−0.0596919	−0.00200088
$891$	1.86449	0.0624628
$892$	−6.15701	−0.206152
$893$	41.7299	1.39644
$894$	−31.8730	−1.06599
$895$	18.3453	0.613217
$896$	−62.1763	−2.07717
$897$	−23.9945	−0.801152
$898$	−45.8559	−1.53023
$899$	−27.2633	−0.909283
$900$	−11.8111	−0.393704
$901$	70.0789	2.33467
$902$	1.09712	0.0365300
$903$	25.6236	0.852700
$904$	−28.4106	−0.944923
$905$	−5.61386	−0.186611
$906$	−41.8777	−1.39129
$907$	−55.3519	−1.83793	−0.918965	−	0.394340i	$-0.870973\pi$
$907$	−55.3519	−1.83793	−0.918965	+	0.394340i	$0.870973\pi$
$908$	4.45329	0.147788
$909$	6.16911	0.204617
$910$	57.8547	1.91786
$911$	−38.0632	−1.26109	−0.630545	−	0.776153i	$-0.717168\pi$
$911$	−38.0632	−1.26109	−0.630545	+	0.776153i	$0.717168\pi$
$912$	−7.72209	−0.255704
$913$	27.2750	0.902670
$914$	−15.8598	−0.524596
$915$	11.6494	0.385117
$916$	−27.5773	−0.911181
$917$	−17.8882	−0.590719
$918$	14.7260	0.486031
$919$	−5.20411	−0.171668	−0.0858339	−	0.996309i	$-0.527355\pi$
$919$	−5.20411	−0.171668	−0.0858339	+	0.996309i	$0.527355\pi$
$920$	−8.01519	−0.264253
$921$	−26.7588	−0.881733
$922$	82.2906	2.71010
$923$	4.89020	0.160963
$924$	22.8308	0.751078
$925$	−44.9608	−1.47830
$926$	8.41355	0.276487
$927$	−2.49917	−0.0820836
$928$	−36.3596	−1.19356
$929$	−27.1927	−0.892164	−0.446082	−	0.894992i	$-0.647181\pi$
$929$	−27.1927	−0.892164	−0.446082	+	0.894992i	$0.647181\pi$
$930$	−11.4666	−0.376004
$931$	−65.5925	−2.14971
$932$	−19.3829	−0.634908
$933$	15.4194	0.504810
$934$	17.0686	0.558502
$935$	−12.2981	−0.402190
$936$	13.2407	0.432784
$937$	−3.14429	−0.102719	−0.0513597	−	0.998680i	$-0.516356\pi$
$937$	−3.14429	−0.102719	−0.0513597	+	0.998680i	$0.516356\pi$
$938$	−112.397	−3.66990
$939$	−7.61521	−0.248513
$940$	19.1689	0.625221
$941$	−11.9563	−0.389763	−0.194881	−	0.980827i	$-0.562432\pi$
$941$	−11.9563	−0.389763	−0.194881	+	0.980827i	$0.562432\pi$
$942$	32.3510	1.05405
$943$	1.01013	0.0328945
$944$	17.5849	0.572341
$945$	−4.13917	−0.134647
$946$	−25.5768	−0.831575
$947$	−3.88146	−0.126131	−0.0630653	−	0.998009i	$-0.520088\pi$
$947$	−3.88146	−0.126131	−0.0630653	+	0.998009i	$0.520088\pi$
$948$	27.9888	0.909033
$949$	−30.4388	−0.988084
$950$	−56.9773	−1.84859
$951$	6.86061	0.222471
$952$	57.9571	1.87840
$953$	−41.9178	−1.35785	−0.678926	−	0.734207i	$-0.737554\pi$
$953$	−41.9178	−1.35785	−0.678926	+	0.734207i	$0.737554\pi$
$954$	−23.5434	−0.762246
$955$	−21.3581	−0.691131
$956$	18.4616	0.597090
$957$	9.82348	0.317548
$958$	68.5757	2.21558
$959$	12.6230	0.407618
$960$	−12.8853	−0.415870
$961$	−4.22387	−0.136254
$962$	156.816	5.05596
$963$	1.07670	0.0346961
$964$	−32.0676	−1.03283
$965$	−23.8162	−0.766671
$966$	35.2851	1.13528
$967$	−1.35854	−0.0436877	−0.0218439	−	0.999761i	$-0.506954\pi$
$967$	−1.35854	−0.0436877	−0.0218439	+	0.999761i	$0.506954\pi$
$968$	15.8525	0.509519
$969$	42.3205	1.35953
$970$	12.7484	0.409325
$971$	−18.4934	−0.593480	−0.296740	−	0.954958i	$-0.595900\pi$
$971$	−18.4934	−0.593480	−0.296740	+	0.954958i	$0.595900\pi$
$972$	−2.94729	−0.0945345
$973$	−12.9705	−0.415816
$974$	60.2600	1.93086
$975$	−25.1831	−0.806506
$976$	−14.1258	−0.452156
$977$	−58.3491	−1.86675	−0.933377	−	0.358897i	$-0.883153\pi$
$977$	−58.3491	−1.86675	−0.933377	+	0.358897i	$0.883153\pi$
$978$	6.54127	0.209167
$979$	−0.0502246	−0.00160518
$980$	−30.1303	−0.962478
$981$	−8.65970	−0.276483
$982$	−21.4531	−0.684596
$983$	−1.69682	−0.0541203	−0.0270601	−	0.999634i	$-0.508615\pi$
$983$	−1.69682	−0.0541203	−0.0270601	+	0.999634i	$0.508615\pi$
$984$	−0.557413	−0.0177697
$985$	13.9343	0.443985
$986$	77.5872	2.47088
$987$	−27.1229	−0.863331
$988$	118.390	3.76648
$989$	−23.5490	−0.748815
$990$	4.13162	0.131311
$991$	−26.8836	−0.853986	−0.426993	−	0.904255i	$-0.640427\pi$
$991$	−26.8836	−0.853986	−0.426993	+	0.904255i	$0.640427\pi$
$992$	35.7099	1.13379
$993$	−32.4805	−1.03074
$994$	−7.19129	−0.228094
$995$	2.75487	0.0873352
$996$	−43.1149	−1.36615
$997$	36.8611	1.16740	0.583701	−	0.811969i	$-0.301604\pi$
$997$	36.8611	1.16740	0.583701	+	0.811969i	$0.301604\pi$
$998$	79.3002	2.51020
$999$	−11.2193	−0.354963

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.b.1.14	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.b.1.14	✓	104	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22425 q^{2} -1.00000 q^{3} +2.94729 q^{4} -0.996267 q^{5} +2.22425 q^{6} -4.15468 q^{7} -2.10702 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.22425 q^{2} -1.00000 q^{3} +2.94729 q^{4} -0.996267 q^{5} +2.22425 q^{6} -4.15468 q^{7} -2.10702 q^{8} +1.00000 q^{9} +2.21595 q^{10} +1.86449 q^{11} -2.94729 q^{12} -6.28408 q^{13} +9.24105 q^{14} +0.996267 q^{15} -1.20805 q^{16} +6.62066 q^{17} -2.22425 q^{18} -6.39219 q^{19} -2.93629 q^{20} +4.15468 q^{21} -4.14710 q^{22} -3.81830 q^{23} +2.10702 q^{24} -4.00745 q^{25} +13.9774 q^{26} -1.00000 q^{27} -12.2451 q^{28} -5.26872 q^{29} -2.21595 q^{30} +5.17457 q^{31} +6.90104 q^{32} -1.86449 q^{33} -14.7260 q^{34} +4.13917 q^{35} +2.94729 q^{36} +11.2193 q^{37} +14.2178 q^{38} +6.28408 q^{39} +2.09915 q^{40} -0.264551 q^{41} -9.24105 q^{42} +6.16741 q^{43} +5.49520 q^{44} -0.996267 q^{45} +8.49285 q^{46} -6.52827 q^{47} +1.20805 q^{48} +10.2614 q^{49} +8.91358 q^{50} -6.62066 q^{51} -18.5210 q^{52} +10.5849 q^{53} +2.22425 q^{54} -1.85753 q^{55} +8.75398 q^{56} +6.39219 q^{57} +11.7189 q^{58} -14.5565 q^{59} +2.93629 q^{60} +11.6930 q^{61} -11.5095 q^{62} -4.15468 q^{63} -12.9335 q^{64} +6.26062 q^{65} +4.14710 q^{66} -12.1628 q^{67} +19.5130 q^{68} +3.81830 q^{69} -9.20656 q^{70} -0.778190 q^{71} -2.10702 q^{72} +4.84379 q^{73} -24.9545 q^{74} +4.00745 q^{75} -18.8396 q^{76} -7.74636 q^{77} -13.9774 q^{78} -9.49644 q^{79} +1.20354 q^{80} +1.00000 q^{81} +0.588427 q^{82} +14.6286 q^{83} +12.2451 q^{84} -6.59595 q^{85} -13.7179 q^{86} +5.26872 q^{87} -3.92852 q^{88} -0.0269374 q^{89} +2.21595 q^{90} +26.1083 q^{91} -11.2536 q^{92} -5.17457 q^{93} +14.5205 q^{94} +6.36833 q^{95} -6.90104 q^{96} +5.75300 q^{97} -22.8238 q^{98} +1.86449 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9}+O(q^{10}) \) 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9	\( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9} + 8 q^{10} - 52 q^{11} - 87 q^{12} + 35 q^{13} - 23 q^{14} + 15 q^{15} + 53 q^{16} - 19 q^{17} - 9 q^{18} - 22 q^{19} - 35 q^{20} + 10 q^{21} - q^{22} - 70 q^{23} + 27 q^{24} + 79 q^{25} - 39 q^{26} - 104 q^{27} - 9 q^{28} - 37 q^{29} - 8 q^{30} - 47 q^{31} - 53 q^{32} + 52 q^{33} - 17 q^{34} - 54 q^{35} + 87 q^{36} + 65 q^{37} - 33 q^{38} - 35 q^{39} + 14 q^{40} - 47 q^{41} + 23 q^{42} - 30 q^{43} - 122 q^{44} - 15 q^{45} - 6 q^{46} - 101 q^{47} - 53 q^{48} + 78 q^{49} - 64 q^{50} + 19 q^{51} + 41 q^{52} - 48 q^{53} + 9 q^{54} - 29 q^{55} - 71 q^{56} + 22 q^{57} - 2 q^{58} - 86 q^{59} + 35 q^{60} + 34 q^{61} - 36 q^{62} - 10 q^{63} - 15 q^{64} - 64 q^{65} + q^{66} - 38 q^{67} - 33 q^{68} + 70 q^{69} - 29 q^{70} - 176 q^{71} - 27 q^{72} + 69 q^{73} - 86 q^{74} - 79 q^{75} - 54 q^{76} - 45 q^{77} + 39 q^{78} - 101 q^{79} - 76 q^{80} + 104 q^{81} + 38 q^{82} - 67 q^{83} + 9 q^{84} + 3 q^{85} - 90 q^{86} + 37 q^{87} + 7 q^{88} - 91 q^{89} + 8 q^{90} - 47 q^{91} - 136 q^{92} + 47 q^{93} - 20 q^{94} - 130 q^{95} + 53 q^{96} + 86 q^{97} - 44 q^{98} - 52 q^{99}+O(q^{100}) \) 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9 + 8 * q^10 - 52 * q^11 - 87 * q^12 + 35 * q^13 - 23 * q^14 + 15 * q^15 + 53 * q^16 - 19 * q^17 - 9 * q^18 - 22 * q^19 - 35 * q^20 + 10 * q^21 - q^22 - 70 * q^23 + 27 * q^24 + 79 * q^25 - 39 * q^26 - 104 * q^27 - 9 * q^28 - 37 * q^29 - 8 * q^30 - 47 * q^31 - 53 * q^32 + 52 * q^33 - 17 * q^34 - 54 * q^35 + 87 * q^36 + 65 * q^37 - 33 * q^38 - 35 * q^39 + 14 * q^40 - 47 * q^41 + 23 * q^42 - 30 * q^43 - 122 * q^44 - 15 * q^45 - 6 * q^46 - 101 * q^47 - 53 * q^48 + 78 * q^49 - 64 * q^50 + 19 * q^51 + 41 * q^52 - 48 * q^53 + 9 * q^54 - 29 * q^55 - 71 * q^56 + 22 * q^57 - 2 * q^58 - 86 * q^59 + 35 * q^60 + 34 * q^61 - 36 * q^62 - 10 * q^63 - 15 * q^64 - 64 * q^65 + q^66 - 38 * q^67 - 33 * q^68 + 70 * q^69 - 29 * q^70 - 176 * q^71 - 27 * q^72 + 69 * q^73 - 86 * q^74 - 79 * q^75 - 54 * q^76 - 45 * q^77 + 39 * q^78 - 101 * q^79 - 76 * q^80 + 104 * q^81 + 38 * q^82 - 67 * q^83 + 9 * q^84 + 3 * q^85 - 90 * q^86 + 37 * q^87 + 7 * q^88 - 91 * q^89 + 8 * q^90 - 47 * q^91 - 136 * q^92 + 47 * q^93 - 20 * q^94 - 130 * q^95 + 53 * q^96 + 86 * q^97 - 44 * q^98 - 52 * q^99

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