LMFDB - Embedded newform 6047.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6047,2,Mod(1,6047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6047, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6047 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6047.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:	$48.2855381023$
Analytic rank:	$0$
Dimension:	$287$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54598 q^{2} +0.470310 q^{3} +4.48203 q^{4} +0.162012 q^{5} -1.19740 q^{6} +3.47622 q^{7} -6.31920 q^{8} -2.77881 q^{9} +O(q^{10})$	\(q-2.54598 q^{2} +0.470310 q^{3} +4.48203 q^{4} +0.162012 q^{5} -1.19740 q^{6} +3.47622 q^{7} -6.31920 q^{8} -2.77881 q^{9} -0.412479 q^{10} -5.20975 q^{11} +2.10794 q^{12} -4.02752 q^{13} -8.85040 q^{14} +0.0761957 q^{15} +7.12452 q^{16} -2.07698 q^{17} +7.07480 q^{18} +7.45713 q^{19} +0.726140 q^{20} +1.63490 q^{21} +13.2639 q^{22} -6.17842 q^{23} -2.97199 q^{24} -4.97375 q^{25} +10.2540 q^{26} -2.71783 q^{27} +15.5805 q^{28} +0.133325 q^{29} -0.193993 q^{30} -0.744677 q^{31} -5.50050 q^{32} -2.45020 q^{33} +5.28794 q^{34} +0.563188 q^{35} -12.4547 q^{36} +3.93287 q^{37} -18.9857 q^{38} -1.89418 q^{39} -1.02378 q^{40} -6.76896 q^{41} -4.16243 q^{42} +9.71634 q^{43} -23.3502 q^{44} -0.450199 q^{45} +15.7302 q^{46} -0.360810 q^{47} +3.35074 q^{48} +5.08411 q^{49} +12.6631 q^{50} -0.976823 q^{51} -18.0514 q^{52} -4.30725 q^{53} +6.91956 q^{54} -0.844040 q^{55} -21.9669 q^{56} +3.50716 q^{57} -0.339443 q^{58} +1.61117 q^{59} +0.341511 q^{60} +6.78216 q^{61} +1.89594 q^{62} -9.65975 q^{63} -0.244856 q^{64} -0.652504 q^{65} +6.23817 q^{66} -0.362210 q^{67} -9.30906 q^{68} -2.90578 q^{69} -1.43387 q^{70} -7.62843 q^{71} +17.5598 q^{72} -10.7239 q^{73} -10.0130 q^{74} -2.33921 q^{75} +33.4230 q^{76} -18.1102 q^{77} +4.82256 q^{78} -12.1902 q^{79} +1.15425 q^{80} +7.05820 q^{81} +17.2336 q^{82} +8.02287 q^{83} +7.32768 q^{84} -0.336494 q^{85} -24.7376 q^{86} +0.0627042 q^{87} +32.9215 q^{88} +7.18236 q^{89} +1.14620 q^{90} -14.0005 q^{91} -27.6919 q^{92} -0.350229 q^{93} +0.918616 q^{94} +1.20814 q^{95} -2.58694 q^{96} +3.64943 q^{97} -12.9441 q^{98} +14.4769 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) $ 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * 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 $

$2$	−2.54598	−1.80028	−0.900141	−	0.435599i	$-0.856537\pi$
$2$	−2.54598	−1.80028	−0.900141	+	0.435599i	$0.856537\pi$
$3$	0.470310	0.271534	0.135767	−	0.990741i	$-0.456650\pi$
$3$	0.470310	0.271534	0.135767	+	0.990741i	$0.456650\pi$
$4$	4.48203	2.24101
$5$	0.162012	0.0724538	0.0362269	−	0.999344i	$-0.488466\pi$
$5$	0.162012	0.0724538	0.0362269	+	0.999344i	$0.488466\pi$
$6$	−1.19740	−0.488837
$7$	3.47622	1.31389	0.656944	−	0.753939i	$-0.271849\pi$
$7$	3.47622	1.31389	0.656944	+	0.753939i	$0.271849\pi$
$8$	−6.31920	−2.23417
$9$	−2.77881	−0.926269
$10$	−0.412479	−0.130437
$11$	−5.20975	−1.57080	−0.785400	−	0.618989i	$-0.787542\pi$
$11$	−5.20975	−1.57080	−0.785400	+	0.618989i	$0.787542\pi$
$12$	2.10794	0.608511
$13$	−4.02752	−1.11703	−0.558516	−	0.829494i	$-0.688629\pi$
$13$	−4.02752	−1.11703	−0.558516	+	0.829494i	$0.688629\pi$
$14$	−8.85040	−2.36537
$15$	0.0761957	0.0196737
$16$	7.12452	1.78113
$17$	−2.07698	−0.503740	−0.251870	−	0.967761i	$-0.581046\pi$
$17$	−2.07698	−0.503740	−0.251870	+	0.967761i	$0.581046\pi$
$18$	7.07480	1.66755
$19$	7.45713	1.71078	0.855391	−	0.517983i	$-0.173317\pi$
$19$	7.45713	1.71078	0.855391	+	0.517983i	$0.173317\pi$
$20$	0.726140	0.162370
$21$	1.63490	0.356765
$22$	13.2639	2.82788
$23$	−6.17842	−1.28829	−0.644145	−	0.764903i	$-0.722787\pi$
$23$	−6.17842	−1.28829	−0.644145	+	0.764903i	$0.722787\pi$
$24$	−2.97199	−0.606654
$25$	−4.97375	−0.994750
$26$	10.2540	2.01097
$27$	−2.71783	−0.523047
$28$	15.5805	2.94444
$29$	0.133325	0.0247578	0.0123789	−	0.999923i	$-0.496060\pi$
$29$	0.133325	0.0247578	0.0123789	+	0.999923i	$0.496060\pi$
$30$	−0.193993	−0.0354181
$31$	−0.744677	−0.133748	−0.0668740	−	0.997761i	$-0.521303\pi$
$31$	−0.744677	−0.133748	−0.0668740	+	0.997761i	$0.521303\pi$
$32$	−5.50050	−0.972360
$33$	−2.45020	−0.426525
$34$	5.28794	0.906875
$35$	0.563188	0.0951961
$36$	−12.4547	−2.07578
$37$	3.93287	0.646559	0.323280	−	0.946303i	$-0.395215\pi$
$37$	3.93287	0.646559	0.323280	+	0.946303i	$0.395215\pi$
$38$	−18.9857	−3.07989
$39$	−1.89418	−0.303312
$40$	−1.02378	−0.161874
$41$	−6.76896	−1.05713	−0.528567	−	0.848892i	$-0.677270\pi$
$41$	−6.76896	−1.05713	−0.528567	+	0.848892i	$0.677270\pi$
$42$	−4.16243	−0.642278
$43$	9.71634	1.48173	0.740864	−	0.671655i	$-0.234416\pi$
$43$	9.71634	1.48173	0.740864	+	0.671655i	$0.234416\pi$
$44$	−23.3502	−3.52018
$45$	−0.450199	−0.0671117
$46$	15.7302	2.31929
$47$	−0.360810	−0.0526296	−0.0263148	−	0.999654i	$-0.508377\pi$
$47$	−0.360810	−0.0526296	−0.0263148	+	0.999654i	$0.508377\pi$
$48$	3.35074	0.483637
$49$	5.08411	0.726302
$50$	12.6631	1.79083
$51$	−0.976823	−0.136783
$52$	−18.0514	−2.50329
$53$	−4.30725	−0.591647	−0.295823	−	0.955243i	$-0.595594\pi$
$53$	−4.30725	−0.591647	−0.295823	+	0.955243i	$0.595594\pi$
$54$	6.91956	0.941632
$55$	−0.844040	−0.113810
$56$	−21.9669	−2.93546
$57$	3.50716	0.464535
$58$	−0.339443	−0.0445711
$59$	1.61117	0.209757	0.104878	−	0.994485i	$-0.466555\pi$
$59$	1.61117	0.209757	0.104878	+	0.994485i	$0.466555\pi$
$60$	0.341511	0.0440889
$61$	6.78216	0.868366	0.434183	−	0.900825i	$-0.357037\pi$
$61$	6.78216	0.868366	0.434183	+	0.900825i	$0.357037\pi$
$62$	1.89594	0.240784
$63$	−9.65975	−1.21701
$64$	−0.244856	−0.0306071
$65$	−0.652504	−0.0809332
$66$	6.23817	0.767865
$67$	−0.362210	−0.0442510	−0.0221255	−	0.999755i	$-0.507043\pi$
$67$	−0.362210	−0.0442510	−0.0221255	+	0.999755i	$0.507043\pi$
$68$	−9.30906	−1.12889
$69$	−2.90578	−0.349814
$70$	−1.43387	−0.171380
$71$	−7.62843	−0.905328	−0.452664	−	0.891681i	$-0.649526\pi$
$71$	−7.62843	−0.905328	−0.452664	+	0.891681i	$0.649526\pi$
$72$	17.5598	2.06945
$73$	−10.7239	−1.25514	−0.627568	−	0.778562i	$-0.715950\pi$
$73$	−10.7239	−1.25514	−0.627568	+	0.778562i	$0.715950\pi$
$74$	−10.0130	−1.16399
$75$	−2.33921	−0.270108
$76$	33.4230	3.83389
$77$	−18.1102	−2.06385
$78$	4.82256	0.546047
$79$	−12.1902	−1.37150	−0.685750	−	0.727837i	$-0.740526\pi$
$79$	−12.1902	−1.37150	−0.685750	+	0.727837i	$0.740526\pi$
$80$	1.15425	0.129050
$81$	7.05820	0.784244
$82$	17.2336	1.90314
$83$	8.02287	0.880624	0.440312	−	0.897845i	$-0.354868\pi$
$83$	8.02287	0.880624	0.440312	+	0.897845i	$0.354868\pi$
$84$	7.32768	0.799515
$85$	−0.336494	−0.0364979
$86$	−24.7376	−2.66753
$87$	0.0627042	0.00672259
$88$	32.9215	3.50944
$89$	7.18236	0.761329	0.380665	−	0.924713i	$-0.375695\pi$
$89$	7.18236	0.761329	0.380665	+	0.924713i	$0.375695\pi$
$90$	1.14620	0.120820
$91$	−14.0005	−1.46766
$92$	−27.6919	−2.88708
$93$	−0.350229	−0.0363171
$94$	0.918616	0.0947480
$95$	1.20814	0.123953
$96$	−2.58694	−0.264029
$97$	3.64943	0.370543	0.185272	−	0.982687i	$-0.440683\pi$
$97$	3.64943	0.370543	0.185272	+	0.982687i	$0.440683\pi$
$98$	−12.9441	−1.30755
$99$	14.4769	1.45498
$100$	−22.2925	−2.22925
$101$	1.05450	0.104927	0.0524636	−	0.998623i	$-0.483293\pi$
$101$	1.05450	0.104927	0.0524636	+	0.998623i	$0.483293\pi$
$102$	2.48697	0.246247
$103$	10.7234	1.05660	0.528302	−	0.849057i	$-0.322829\pi$
$103$	10.7234	1.05660	0.528302	+	0.849057i	$0.322829\pi$
$104$	25.4507	2.49565
$105$	0.264873	0.0258490
$106$	10.9662	1.06513
$107$	19.9183	1.92558	0.962788	−	0.270259i	$-0.0871092\pi$
$107$	19.9183	1.92558	0.962788	+	0.270259i	$0.0871092\pi$
$108$	−12.1814	−1.17216
$109$	−2.54013	−0.243301	−0.121650	−	0.992573i	$-0.538819\pi$
$109$	−2.54013	−0.243301	−0.121650	+	0.992573i	$0.538819\pi$
$110$	2.14891	0.204891
$111$	1.84967	0.175563
$112$	24.7664	2.34021
$113$	7.08201	0.666219	0.333110	−	0.942888i	$-0.391902\pi$
$113$	7.08201	0.666219	0.333110	+	0.942888i	$0.391902\pi$
$114$	−8.92918	−0.836294
$115$	−1.00098	−0.0933415
$116$	0.597567	0.0554827
$117$	11.1917	1.03467
$118$	−4.10202	−0.377621
$119$	−7.22002	−0.661859
$120$	−0.481496	−0.0439544
$121$	16.1415	1.46741
$122$	−17.2673	−1.56330
$123$	−3.18351	−0.287047
$124$	−3.33766	−0.299731
$125$	−1.61586	−0.144527
$126$	24.5936	2.19097
$127$	−7.20697	−0.639515	−0.319758	−	0.947499i	$-0.603602\pi$
$127$	−7.20697	−0.639515	−0.319758	+	0.947499i	$0.603602\pi$
$128$	11.6244	1.02746
$129$	4.56970	0.402339
$130$	1.66126	0.145703
$131$	21.3232	1.86301	0.931506	−	0.363726i	$-0.118495\pi$
$131$	21.3232	1.86301	0.931506	+	0.363726i	$0.118495\pi$
$132$	−10.9819	−0.955849
$133$	25.9226	2.24778
$134$	0.922181	0.0796643
$135$	−0.440320	−0.0378968
$136$	13.1248	1.12544
$137$	−8.39436	−0.717179	−0.358589	−	0.933495i	$-0.616742\pi$
$137$	−8.39436	−0.717179	−0.358589	+	0.933495i	$0.616742\pi$
$138$	7.39806	0.629765
$139$	17.5103	1.48520	0.742602	−	0.669733i	$-0.233591\pi$
$139$	17.5103	1.48520	0.742602	+	0.669733i	$0.233591\pi$
$140$	2.52422	0.213336
$141$	−0.169693	−0.0142907
$142$	19.4218	1.62984
$143$	20.9824	1.75463
$144$	−19.7977	−1.64981
$145$	0.0216002	0.00179380
$146$	27.3028	2.25960
$147$	2.39111	0.197215
$148$	17.6272	1.44895
$149$	9.35310	0.766236	0.383118	−	0.923699i	$-0.374850\pi$
$149$	9.35310	0.766236	0.383118	+	0.923699i	$0.374850\pi$
$150$	5.95558	0.486271
$151$	1.03140	0.0839342	0.0419671	−	0.999119i	$-0.486638\pi$
$151$	1.03140	0.0839342	0.0419671	+	0.999119i	$0.486638\pi$
$152$	−47.1231	−3.82219
$153$	5.77152	0.466599
$154$	46.1084	3.71552
$155$	−0.120646	−0.00969055
$156$	−8.48978	−0.679727
$157$	−11.2374	−0.896844	−0.448422	−	0.893822i	$-0.648014\pi$
$157$	−11.2374	−0.896844	−0.448422	+	0.893822i	$0.648014\pi$
$158$	31.0359	2.46909
$159$	−2.02575	−0.160652
$160$	−0.891145	−0.0704512
$161$	−21.4776	−1.69267
$162$	−17.9701	−1.41186
$163$	−7.00703	−0.548833	−0.274417	−	0.961611i	$-0.588485\pi$
$163$	−7.00703	−0.548833	−0.274417	+	0.961611i	$0.588485\pi$
$164$	−30.3387	−2.36905
$165$	−0.396961	−0.0309034
$166$	−20.4261	−1.58537
$167$	15.0547	1.16497	0.582484	−	0.812842i	$-0.302081\pi$
$167$	15.0547	1.16497	0.582484	+	0.812842i	$0.302081\pi$
$168$	−10.3313	−0.797075
$169$	3.22090	0.247761
$170$	0.856708	0.0657065
$171$	−20.7219	−1.58464
$172$	43.5489	3.32057
$173$	13.6026	1.03419	0.517094	−	0.855928i	$-0.327014\pi$
$173$	13.6026	1.03419	0.517094	+	0.855928i	$0.327014\pi$
$174$	−0.159644	−0.0121026
$175$	−17.2899	−1.30699
$176$	−37.1170	−2.79780
$177$	0.757751	0.0569561
$178$	−18.2862	−1.37061
$179$	7.81725	0.584289	0.292145	−	0.956374i	$-0.405631\pi$
$179$	7.81725	0.584289	0.292145	+	0.956374i	$0.405631\pi$
$180$	−2.01780	−0.150398
$181$	−7.26022	−0.539648	−0.269824	−	0.962910i	$-0.586965\pi$
$181$	−7.26022	−0.539648	−0.269824	+	0.962910i	$0.586965\pi$
$182$	35.6451	2.64219
$183$	3.18972	0.235791
$184$	39.0427	2.87827
$185$	0.637170	0.0468457
$186$	0.891678	0.0653810
$187$	10.8205	0.791275
$188$	−1.61716	−0.117944
$189$	−9.44779	−0.687226
$190$	−3.07590	−0.223150
$191$	13.9358	1.00836	0.504181	−	0.863598i	$-0.331794\pi$
$191$	13.9358	1.00836	0.504181	+	0.863598i	$0.331794\pi$
$192$	−0.115159	−0.00831085
$193$	20.5237	1.47733	0.738664	−	0.674074i	$-0.235457\pi$
$193$	20.5237	1.47733	0.738664	+	0.674074i	$0.235457\pi$
$194$	−9.29138	−0.667082
$195$	−0.306880	−0.0219761
$196$	22.7871	1.62765
$197$	−9.55324	−0.680640	−0.340320	−	0.940310i	$-0.610535\pi$
$197$	−9.55324	−0.680640	−0.340320	+	0.940310i	$0.610535\pi$
$198$	−36.8579	−2.61938
$199$	6.22717	0.441432	0.220716	−	0.975338i	$-0.429161\pi$
$199$	6.22717	0.441432	0.220716	+	0.975338i	$0.429161\pi$
$200$	31.4301	2.22245
$201$	−0.170351	−0.0120156
$202$	−2.68475	−0.188898
$203$	0.463467	0.0325290
$204$	−4.37815	−0.306532
$205$	−1.09665	−0.0765933
$206$	−27.3015	−1.90218
$207$	17.1687	1.19330
$208$	−28.6941	−1.98958
$209$	−38.8498	−2.68729
$210$	−0.674362	−0.0465354
$211$	−3.61899	−0.249142	−0.124571	−	0.992211i	$-0.539755\pi$
$211$	−3.61899	−0.249142	−0.124571	+	0.992211i	$0.539755\pi$
$212$	−19.3052	−1.32589
$213$	−3.58773	−0.245827
$214$	−50.7117	−3.46658
$215$	1.57416	0.107357
$216$	17.1745	1.16858
$217$	−2.58866	−0.175730
$218$	6.46714	0.438010
$219$	−5.04356	−0.340812
$220$	−3.78301	−0.255051
$221$	8.36505	0.562694
$222$	−4.70922	−0.316062
$223$	−1.92426	−0.128858	−0.0644290	−	0.997922i	$-0.520523\pi$
$223$	−1.92426	−0.128858	−0.0644290	+	0.997922i	$0.520523\pi$
$224$	−19.1210	−1.27757
$225$	13.8211	0.921407
$226$	−18.0307	−1.19938
$227$	−4.11964	−0.273430	−0.136715	−	0.990610i	$-0.543654\pi$
$227$	−4.11964	−0.273430	−0.136715	+	0.990610i	$0.543654\pi$
$228$	15.7192	1.04103
$229$	−22.9334	−1.51548	−0.757742	−	0.652555i	$-0.773697\pi$
$229$	−22.9334	−1.51548	−0.757742	+	0.652555i	$0.773697\pi$
$230$	2.54847	0.168041
$231$	−8.51744	−0.560406
$232$	−0.842508	−0.0553134
$233$	−10.6677	−0.698863	−0.349431	−	0.936962i	$-0.613625\pi$
$233$	−10.6677	−0.698863	−0.349431	+	0.936962i	$0.613625\pi$
$234$	−28.4939	−1.86270
$235$	−0.0584554	−0.00381321
$236$	7.22132	0.470068
$237$	−5.73316	−0.372409
$238$	18.3821	1.19153
$239$	7.03261	0.454902	0.227451	−	0.973790i	$-0.426961\pi$
$239$	7.03261	0.454902	0.227451	+	0.973790i	$0.426961\pi$
$240$	0.542858	0.0350413
$241$	16.4143	1.05734	0.528668	−	0.848829i	$-0.322692\pi$
$241$	16.4143	1.05734	0.528668	+	0.848829i	$0.322692\pi$
$242$	−41.0960	−2.64175
$243$	11.4730	0.735996
$244$	30.3978	1.94602
$245$	0.823685	0.0526233
$246$	8.10516	0.516766
$247$	−30.0337	−1.91100
$248$	4.70576	0.298816
$249$	3.77324	0.239119
$250$	4.11396	0.260190
$251$	30.2974	1.91236	0.956179	−	0.292784i	$-0.0945817\pi$
$251$	30.2974	1.91236	0.956179	+	0.292784i	$0.0945817\pi$
$252$	−43.2953	−2.72735
$253$	32.1881	2.02365
$254$	18.3488	1.15131
$255$	−0.158257	−0.00991041
$256$	−29.1058	−1.81911
$257$	−0.916468	−0.0571677	−0.0285839	−	0.999591i	$-0.509100\pi$
$257$	−0.916468	−0.0571677	−0.0285839	+	0.999591i	$0.509100\pi$
$258$	−11.6344	−0.724324
$259$	13.6715	0.849507
$260$	−2.92454	−0.181372
$261$	−0.370485	−0.0229324
$262$	−54.2884	−3.35395
$263$	1.07192	0.0660971	0.0330486	−	0.999454i	$-0.489478\pi$
$263$	1.07192	0.0660971	0.0330486	+	0.999454i	$0.489478\pi$
$264$	15.4833	0.952932
$265$	−0.697825	−0.0428671
$266$	−65.9985	−4.04663
$267$	3.37794	0.206727
$268$	−1.62344	−0.0991671
$269$	−23.8607	−1.45481	−0.727407	−	0.686206i	$-0.759275\pi$
$269$	−23.8607	−1.45481	−0.727407	+	0.686206i	$0.759275\pi$
$270$	1.12105	0.0682248
$271$	28.6900	1.74279	0.871397	−	0.490578i	$-0.163214\pi$
$271$	28.6900	1.74279	0.871397	+	0.490578i	$0.163214\pi$
$272$	−14.7974	−0.897227
$273$	−6.58460	−0.398518
$274$	21.3719	1.29112
$275$	25.9120	1.56255
$276$	−13.0238	−0.783939
$277$	−9.85561	−0.592166	−0.296083	−	0.955162i	$-0.595681\pi$
$277$	−9.85561	−0.592166	−0.296083	+	0.955162i	$0.595681\pi$
$278$	−44.5809	−2.67379
$279$	2.06932	0.123887
$280$	−3.55890	−0.212685
$281$	−24.4347	−1.45765	−0.728827	−	0.684698i	$-0.759934\pi$
$281$	−24.4347	−1.45765	−0.728827	+	0.684698i	$0.759934\pi$
$282$	0.432035	0.0257273
$283$	0.129400	0.00769206	0.00384603	−	0.999993i	$-0.498776\pi$
$283$	0.129400	0.00769206	0.00384603	+	0.999993i	$0.498776\pi$
$284$	−34.1908	−2.02885
$285$	0.568201	0.0336573
$286$	−53.4207	−3.15883
$287$	−23.5304	−1.38895
$288$	15.2848	0.900668
$289$	−12.6862	−0.746246
$290$	−0.0549938	−0.00322934
$291$	1.71636	0.100615
$292$	−48.0648	−2.81278
$293$	−2.91991	−0.170583	−0.0852913	−	0.996356i	$-0.527182\pi$
$293$	−2.91991	−0.170583	−0.0852913	+	0.996356i	$0.527182\pi$
$294$	−6.08773	−0.355043
$295$	0.261029	0.0151977
$296$	−24.8526	−1.44453
$297$	14.1592	0.821602
$298$	−23.8128	−1.37944
$299$	24.8837	1.43906
$300$	−10.4844	−0.605317
$301$	33.7762	1.94683
$302$	−2.62593	−0.151105
$303$	0.495945	0.0284913
$304$	53.1284	3.04712
$305$	1.09879	0.0629164
$306$	−14.6942	−0.840010
$307$	24.6029	1.40416	0.702080	−	0.712098i	$-0.252255\pi$
$307$	24.6029	1.40416	0.702080	+	0.712098i	$0.252255\pi$
$308$	−81.1706	−4.62513
$309$	5.04330	0.286904
$310$	0.307163	0.0174457
$311$	5.20166	0.294959	0.147479	−	0.989065i	$-0.452884\pi$
$311$	5.20166	0.294959	0.147479	+	0.989065i	$0.452884\pi$
$312$	11.9697	0.677652
$313$	−3.79648	−0.214590	−0.107295	−	0.994227i	$-0.534219\pi$
$313$	−3.79648	−0.214590	−0.107295	+	0.994227i	$0.534219\pi$
$314$	28.6103	1.61457
$315$	−1.56499	−0.0881773
$316$	−54.6366	−3.07355
$317$	−7.42967	−0.417292	−0.208646	−	0.977991i	$-0.566906\pi$
$317$	−7.42967	−0.417292	−0.208646	+	0.977991i	$0.566906\pi$
$318$	5.15752	0.289219
$319$	−0.694590	−0.0388896
$320$	−0.0396696	−0.00221760
$321$	9.36779	0.522859
$322$	54.6815	3.04728
$323$	−15.4883	−0.861790
$324$	31.6350	1.75750
$325$	20.0319	1.11117
$326$	17.8398	0.988054
$327$	−1.19465	−0.0660644
$328$	42.7744	2.36182
$329$	−1.25426	−0.0691493
$330$	1.01066	0.0556347
$331$	34.1995	1.87977	0.939886	−	0.341488i	$-0.110931\pi$
$331$	34.1995	1.87977	0.939886	+	0.341488i	$0.110931\pi$
$332$	35.9587	1.97349
$333$	−10.9287	−0.598888
$334$	−38.3290	−2.09727
$335$	−0.0586822	−0.00320615
$336$	11.6479	0.635445
$337$	−18.6999	−1.01865	−0.509323	−	0.860575i	$-0.670104\pi$
$337$	−18.6999	−1.01865	−0.509323	+	0.860575i	$0.670104\pi$
$338$	−8.20035	−0.446040
$339$	3.33074	0.180901
$340$	−1.50818	−0.0817923
$341$	3.87958	0.210091
$342$	52.7577	2.85281
$343$	−6.66005	−0.359609
$344$	−61.3995	−3.31044
$345$	−0.470770	−0.0253454
$346$	−34.6321	−1.86183
$347$	4.57433	0.245563	0.122782	−	0.992434i	$-0.460819\pi$
$347$	4.57433	0.245563	0.122782	+	0.992434i	$0.460819\pi$
$348$	0.281042	0.0150654
$349$	6.57281	0.351835	0.175917	−	0.984405i	$-0.443711\pi$
$349$	6.57281	0.351835	0.175917	+	0.984405i	$0.443711\pi$
$350$	44.0197	2.35295
$351$	10.9461	0.584261
$352$	28.6562	1.52738
$353$	27.1059	1.44270	0.721352	−	0.692569i	$-0.243521\pi$
$353$	27.1059	1.44270	0.721352	+	0.692569i	$0.243521\pi$
$354$	−1.92922	−0.102537
$355$	−1.23589	−0.0655944
$356$	32.1916	1.70615
$357$	−3.39565	−0.179717
$358$	−19.9026	−1.05188
$359$	−14.9979	−0.791557	−0.395778	−	0.918346i	$-0.629525\pi$
$359$	−14.9979	−0.791557	−0.395778	+	0.918346i	$0.629525\pi$
$360$	2.84490	0.149939
$361$	36.6087	1.92677
$362$	18.4844	0.971518
$363$	7.59152	0.398451
$364$	−62.7508	−3.28904
$365$	−1.73739	−0.0909394
$366$	−8.12097	−0.424490
$367$	−17.5219	−0.914634	−0.457317	−	0.889304i	$-0.651190\pi$
$367$	−17.5219	−0.914634	−0.457317	+	0.889304i	$0.651190\pi$
$368$	−44.0183	−2.29461
$369$	18.8096	0.979190
$370$	−1.62222	−0.0843354
$371$	−14.9730	−0.777358
$372$	−1.56974	−0.0813871
$373$	−5.14064	−0.266172	−0.133086	−	0.991104i	$-0.542489\pi$
$373$	−5.14064	−0.266172	−0.133086	+	0.991104i	$0.542489\pi$
$374$	−27.5489	−1.42452
$375$	−0.759957	−0.0392440
$376$	2.28003	0.117584
$377$	−0.536969	−0.0276553
$378$	24.0539	1.23720
$379$	−32.5965	−1.67437	−0.837184	−	0.546921i	$-0.815800\pi$
$379$	−32.5965	−1.67437	−0.837184	+	0.546921i	$0.815800\pi$
$380$	5.41492	0.277780
$381$	−3.38951	−0.173650
$382$	−35.4804	−1.81534
$383$	22.5924	1.15442	0.577209	−	0.816596i	$-0.304142\pi$
$383$	22.5924	1.15442	0.577209	+	0.816596i	$0.304142\pi$
$384$	5.46708	0.278991
$385$	−2.93407	−0.149534
$386$	−52.2530	−2.65961
$387$	−26.9999	−1.37248
$388$	16.3568	0.830393
$389$	31.4433	1.59424	0.797119	−	0.603822i	$-0.206356\pi$
$389$	31.4433	1.59424	0.797119	+	0.603822i	$0.206356\pi$
$390$	0.781310	0.0395632
$391$	12.8324	0.648964
$392$	−32.1275	−1.62268
$393$	10.0285	0.505871
$394$	24.3224	1.22534
$395$	−1.97495	−0.0993703
$396$	64.8859	3.26064
$397$	6.01019	0.301643	0.150821	−	0.988561i	$-0.451808\pi$
$397$	6.01019	0.301643	0.150821	+	0.988561i	$0.451808\pi$
$398$	−15.8543	−0.794702
$399$	12.1917	0.610347
$400$	−35.4356	−1.77178
$401$	25.5124	1.27403	0.637014	−	0.770852i	$-0.280169\pi$
$401$	25.5124	1.27403	0.637014	+	0.770852i	$0.280169\pi$
$402$	0.433711	0.0216315
$403$	2.99920	0.149401
$404$	4.72632	0.235143
$405$	1.14351	0.0568215
$406$	−1.17998	−0.0585614
$407$	−20.4893	−1.01561
$408$	6.17274	0.305596
$409$	−29.2505	−1.44634	−0.723171	−	0.690669i	$-0.757316\pi$
$409$	−29.2505	−1.44634	−0.723171	+	0.690669i	$0.757316\pi$
$410$	2.79205	0.137890
$411$	−3.94796	−0.194738
$412$	48.0624	2.36786
$413$	5.60079	0.275597
$414$	−43.7111	−2.14828
$415$	1.29980	0.0638045
$416$	22.1534	1.08616
$417$	8.23528	0.403283
$418$	98.9108	4.83789
$419$	−14.6872	−0.717515	−0.358757	−	0.933431i	$-0.616799\pi$
$419$	−14.6872	−0.717515	−0.358757	+	0.933431i	$0.616799\pi$
$420$	1.18717	0.0579279
$421$	−11.3257	−0.551982	−0.275991	−	0.961160i	$-0.589006\pi$
$421$	−11.3257	−0.551982	−0.275991	+	0.961160i	$0.589006\pi$
$422$	9.21389	0.448525
$423$	1.00262	0.0487491
$424$	27.2184	1.32184
$425$	10.3304	0.501096
$426$	9.13429	0.442558
$427$	23.5763	1.14094
$428$	89.2744	4.31524
$429$	9.86822	0.476442
$430$	−4.00778	−0.193273
$431$	−23.1628	−1.11571	−0.557856	−	0.829938i	$-0.688376\pi$
$431$	−23.1628	−1.11571	−0.557856	+	0.829938i	$0.688376\pi$
$432$	−19.3633	−0.931615
$433$	−11.6382	−0.559297	−0.279648	−	0.960103i	$-0.590218\pi$
$433$	−11.6382	−0.559297	−0.279648	+	0.960103i	$0.590218\pi$
$434$	6.59069	0.316363
$435$	0.0101588	0.000487077 0
$436$	−11.3849	−0.545240
$437$	−46.0733	−2.20398
$438$	12.8408	0.613558
$439$	33.5399	1.60077	0.800387	−	0.599484i	$-0.204628\pi$
$439$	33.5399	1.60077	0.800387	+	0.599484i	$0.204628\pi$
$440$	5.33366	0.254272
$441$	−14.1278	−0.672751
$442$	−21.2973	−1.01301
$443$	−27.7662	−1.31921	−0.659605	−	0.751612i	$-0.729276\pi$
$443$	−27.7662	−1.31921	−0.659605	+	0.751612i	$0.729276\pi$
$444$	8.29026	0.393439
$445$	1.16363	0.0551612
$446$	4.89913	0.231981
$447$	4.39886	0.208059
$448$	−0.851175	−0.0402142
$449$	−34.8611	−1.64520	−0.822598	−	0.568623i	$-0.807476\pi$
$449$	−34.8611	−1.64520	−0.822598	+	0.568623i	$0.807476\pi$
$450$	−35.1883	−1.65879
$451$	35.2646	1.66054
$452$	31.7418	1.49301
$453$	0.485079	0.0227910
$454$	10.4885	0.492251
$455$	−2.26825	−0.106337
$456$	−22.1625	−1.03785
$457$	21.6162	1.01116	0.505581	−	0.862779i	$-0.331278\pi$
$457$	21.6162	1.01116	0.505581	+	0.862779i	$0.331278\pi$
$458$	58.3881	2.72830
$459$	5.64487	0.263480
$460$	−4.48640	−0.209180
$461$	21.2443	0.989446	0.494723	−	0.869051i	$-0.335269\pi$
$461$	21.2443	0.989446	0.494723	+	0.869051i	$0.335269\pi$
$462$	21.6852	1.00889
$463$	1.95084	0.0906634	0.0453317	−	0.998972i	$-0.485566\pi$
$463$	1.95084	0.0906634	0.0453317	+	0.998972i	$0.485566\pi$
$464$	0.949877	0.0440969
$465$	−0.0567412	−0.00263131
$466$	27.1597	1.25815
$467$	−26.6517	−1.23330	−0.616648	−	0.787239i	$-0.711510\pi$
$467$	−26.6517	−1.23330	−0.616648	+	0.787239i	$0.711510\pi$
$468$	50.1615	2.31872
$469$	−1.25912	−0.0581409
$470$	0.148826	0.00686485
$471$	−5.28508	−0.243523
$472$	−10.1813	−0.468633
$473$	−50.6197	−2.32750
$474$	14.5965	0.670440
$475$	−37.0899	−1.70180
$476$	−32.3604	−1.48323
$477$	11.9690	0.548024
$478$	−17.9049	−0.818951
$479$	3.65511	0.167006	0.0835032	−	0.996508i	$-0.473389\pi$
$479$	3.65511	0.167006	0.0835032	+	0.996508i	$0.473389\pi$
$480$	−0.419115	−0.0191299
$481$	−15.8397	−0.722228
$482$	−41.7904	−1.90350
$483$	−10.1011	−0.459617
$484$	72.3467	3.28849
$485$	0.591250	0.0268473
$486$	−29.2102	−1.32500
$487$	16.8405	0.763116	0.381558	−	0.924345i	$-0.375388\pi$
$487$	16.8405	0.763116	0.381558	+	0.924345i	$0.375388\pi$
$488$	−42.8578	−1.94008
$489$	−3.29548	−0.149027
$490$	−2.09709	−0.0947368
$491$	21.1388	0.953981	0.476990	−	0.878909i	$-0.341728\pi$
$491$	21.1388	0.953981	0.476990	+	0.878909i	$0.341728\pi$
$492$	−14.2686	−0.643277
$493$	−0.276913	−0.0124715
$494$	76.4653	3.44034
$495$	2.34542	0.105419
$496$	−5.30547	−0.238223
$497$	−26.5181	−1.18950
$498$	−9.60660	−0.430482
$499$	−8.36448	−0.374446	−0.187223	−	0.982317i	$-0.559949\pi$
$499$	−8.36448	−0.374446	−0.187223	+	0.982317i	$0.559949\pi$
$500$	−7.24234	−0.323887
$501$	7.08038	0.316328
$502$	−77.1367	−3.44278
$503$	7.30254	0.325604	0.162802	−	0.986659i	$-0.447947\pi$
$503$	7.30254	0.325604	0.162802	+	0.986659i	$0.447947\pi$
$504$	61.0419	2.71902
$505$	0.170842	0.00760237
$506$	−81.9502	−3.64313
$507$	1.51482	0.0672756
$508$	−32.3019	−1.43316
$509$	−40.0652	−1.77586	−0.887929	−	0.459981i	$-0.847856\pi$
$509$	−40.0652	−1.77586	−0.887929	+	0.459981i	$0.847856\pi$
$510$	0.402919	0.0178415
$511$	−37.2786	−1.64911
$512$	50.8541	2.24745
$513$	−20.2672	−0.894820
$514$	2.33331	0.102918
$515$	1.73731	0.0765549
$516$	20.4815	0.901648
$517$	1.87973	0.0826704
$518$	−34.8074	−1.52935
$519$	6.39746	0.280817
$520$	4.12331	0.180819
$521$	24.7499	1.08431	0.542157	−	0.840277i	$-0.317608\pi$
$521$	24.7499	1.08431	0.542157	+	0.840277i	$0.317608\pi$
$522$	0.943248	0.0412848
$523$	0.342623	0.0149819	0.00749093	−	0.999972i	$-0.497616\pi$
$523$	0.342623	0.0149819	0.00749093	+	0.999972i	$0.497616\pi$
$524$	95.5710	4.17504
$525$	−8.13160	−0.354892
$526$	−2.72908	−0.118993
$527$	1.54668	0.0673743
$528$	−17.4565	−0.759696
$529$	15.1729	0.659693
$530$	1.77665	0.0771728
$531$	−4.47714	−0.194291
$532$	116.186	5.03730
$533$	27.2621	1.18085
$534$	−8.60018	−0.372166
$535$	3.22700	0.139515
$536$	2.28888	0.0988645
$537$	3.67654	0.158654
$538$	60.7490	2.61907
$539$	−26.4870	−1.14087
$540$	−1.97353	−0.0849271
$541$	15.8273	0.680468	0.340234	−	0.940341i	$-0.389494\pi$
$541$	15.8273	0.680468	0.340234	+	0.940341i	$0.389494\pi$
$542$	−73.0443	−3.13752
$543$	−3.41455	−0.146533
$544$	11.4244	0.489817
$545$	−0.411531	−0.0176280
$546$	16.7643	0.717445
$547$	18.4173	0.787469	0.393734	−	0.919224i	$-0.371183\pi$
$547$	18.4173	0.787469	0.393734	+	0.919224i	$0.371183\pi$
$548$	−37.6238	−1.60721
$549$	−18.8463	−0.804341
$550$	−65.9715	−2.81304
$551$	0.994222	0.0423553
$552$	18.3622	0.781547
$553$	−42.3757	−1.80200
$554$	25.0922	1.06607
$555$	0.299668	0.0127202
$556$	78.4817	3.32836
$557$	−9.95978	−0.422010	−0.211005	−	0.977485i	$-0.567674\pi$
$557$	−9.95978	−0.422010	−0.211005	+	0.977485i	$0.567674\pi$
$558$	−5.26844	−0.223031
$559$	−39.1327	−1.65514
$560$	4.01244	0.169557
$561$	5.08900	0.214858
$562$	62.2104	2.62419
$563$	40.1943	1.69399	0.846995	−	0.531601i	$-0.178409\pi$
$563$	40.1943	1.69399	0.846995	+	0.531601i	$0.178409\pi$
$564$	−0.760567	−0.0320257
$565$	1.14737	0.0482701
$566$	−0.329451	−0.0138479
$567$	24.5359	1.03041
$568$	48.2056	2.02266
$569$	−18.0333	−0.755994	−0.377997	−	0.925807i	$-0.623387\pi$
$569$	−18.0333	−0.755994	−0.377997	+	0.925807i	$0.623387\pi$
$570$	−1.44663	−0.0605927
$571$	29.5891	1.23827	0.619133	−	0.785286i	$-0.287484\pi$
$571$	29.5891	1.23827	0.619133	+	0.785286i	$0.287484\pi$
$572$	94.0435	3.93216
$573$	6.55417	0.273804
$574$	59.9080	2.50051
$575$	30.7300	1.28153
$576$	0.680409	0.0283504
$577$	−0.179031	−0.00745315	−0.00372657	−	0.999993i	$-0.501186\pi$
$577$	−0.179031	−0.00745315	−0.00372657	+	0.999993i	$0.501186\pi$
$578$	32.2988	1.34345
$579$	9.65251	0.401144
$580$	0.0968127	0.00401993
$581$	27.8893	1.15704
$582$	−4.36983	−0.181135
$583$	22.4397	0.929358
$584$	67.7664	2.80419
$585$	1.81318	0.0749660
$586$	7.43403	0.307097
$587$	10.1437	0.418675	0.209338	−	0.977843i	$-0.432869\pi$
$587$	10.1437	0.418675	0.209338	+	0.977843i	$0.432869\pi$
$588$	10.7170	0.441963
$589$	−5.55315	−0.228814
$590$	−0.664574	−0.0273601
$591$	−4.49299	−0.184817
$592$	28.0198	1.15161
$593$	−30.8602	−1.26728	−0.633639	−	0.773629i	$-0.718440\pi$
$593$	−30.8602	−1.26728	−0.633639	+	0.773629i	$0.718440\pi$
$594$	−36.0492	−1.47912
$595$	−1.16973	−0.0479541
$596$	41.9209	1.71715
$597$	2.92870	0.119864
$598$	−63.3535	−2.59072
$599$	8.63123	0.352663	0.176331	−	0.984331i	$-0.443577\pi$
$599$	8.63123	0.352663	0.176331	+	0.984331i	$0.443577\pi$
$600$	14.7819	0.603469
$601$	2.83456	0.115624	0.0578121	−	0.998327i	$-0.481588\pi$
$601$	2.83456	0.115624	0.0578121	+	0.998327i	$0.481588\pi$
$602$	−85.9935	−3.50483
$603$	1.00651	0.0409884
$604$	4.62277	0.188098
$605$	2.61511	0.106319
$606$	−1.26267	−0.0512923
$607$	−5.65422	−0.229498	−0.114749	−	0.993395i	$-0.536606\pi$
$607$	−5.65422	−0.229498	−0.114749	+	0.993395i	$0.536606\pi$
$608$	−41.0179	−1.66350
$609$	0.217974	0.00883273
$610$	−2.79749	−0.113267
$611$	1.45317	0.0587889
$612$	25.8681	1.04566
$613$	28.0836	1.13429	0.567144	−	0.823619i	$-0.308048\pi$
$613$	28.0836	1.13429	0.567144	+	0.823619i	$0.308048\pi$
$614$	−62.6385	−2.52788
$615$	−0.515765	−0.0207977
$616$	114.442	4.61101
$617$	44.3895	1.78705	0.893526	−	0.449011i	$-0.148223\pi$
$617$	44.3895	1.78705	0.893526	+	0.449011i	$0.148223\pi$
$618$	−12.8402	−0.516507
$619$	27.5634	1.10787	0.553933	−	0.832561i	$-0.313126\pi$
$619$	27.5634	1.10787	0.553933	+	0.832561i	$0.313126\pi$
$620$	−0.540740	−0.0217167
$621$	16.7919	0.673837
$622$	−13.2433	−0.531009
$623$	24.9675	1.00030
$624$	−13.4951	−0.540238
$625$	24.6070	0.984279
$626$	9.66578	0.386322
$627$	−18.2714	−0.729691
$628$	−50.3664	−2.00984
$629$	−8.16847	−0.325698
$630$	3.98444	0.158744
$631$	−37.6130	−1.49735	−0.748675	−	0.662937i	$-0.769310\pi$
$631$	−37.6130	−1.49735	−0.748675	+	0.662937i	$0.769310\pi$
$632$	77.0320	3.06417
$633$	−1.70205	−0.0676504
$634$	18.9158	0.751243
$635$	−1.16761	−0.0463353
$636$	−9.07945	−0.360024
$637$	−20.4764	−0.811303
$638$	1.76842	0.0700122
$639$	21.1979	0.838577
$640$	1.88329	0.0744435
$641$	11.9702	0.472794	0.236397	−	0.971657i	$-0.424033\pi$
$641$	11.9702	0.472794	0.236397	+	0.971657i	$0.424033\pi$
$642$	−23.8502	−0.941293
$643$	48.0010	1.89297	0.946486	−	0.322744i	$-0.104605\pi$
$643$	48.0010	1.89297	0.946486	+	0.322744i	$0.104605\pi$
$644$	−96.2631	−3.79330
$645$	0.740344	0.0291510
$646$	39.4329	1.55146
$647$	22.7918	0.896039	0.448020	−	0.894024i	$-0.352129\pi$
$647$	22.7918	0.896039	0.448020	+	0.894024i	$0.352129\pi$
$648$	−44.6022	−1.75214
$649$	−8.39381	−0.329486
$650$	−51.0008	−2.00042
$651$	−1.21747	−0.0477166
$652$	−31.4057	−1.22994
$653$	6.59674	0.258150	0.129075	−	0.991635i	$-0.458799\pi$
$653$	6.59674	0.258150	0.129075	+	0.991635i	$0.458799\pi$
$654$	3.04156	0.118934
$655$	3.45460	0.134982
$656$	−48.2256	−1.88289
$657$	29.7996	1.16259
$658$	3.19331	0.124488
$659$	1.49350	0.0581784	0.0290892	−	0.999577i	$-0.490739\pi$
$659$	1.49350	0.0581784	0.0290892	+	0.999577i	$0.490739\pi$
$660$	−1.77919	−0.0692548
$661$	−36.4529	−1.41785	−0.708927	−	0.705282i	$-0.750820\pi$
$661$	−36.4529	−1.41785	−0.708927	+	0.705282i	$0.750820\pi$
$662$	−87.0712	−3.38412
$663$	3.93417	0.152791
$664$	−50.6981	−1.96747
$665$	4.19976	0.162860
$666$	27.8242	1.07817
$667$	−0.823739	−0.0318953
$668$	67.4756	2.61071
$669$	−0.905000	−0.0349893
$670$	0.149404	0.00577198
$671$	−35.3333	−1.36403
$672$	−8.99279	−0.346904
$673$	46.4374	1.79003	0.895016	−	0.446034i	$-0.147164\pi$
$673$	46.4374	1.79003	0.895016	+	0.446034i	$0.147164\pi$
$674$	47.6095	1.83385
$675$	13.5178	0.520302
$676$	14.4362	0.555237
$677$	27.8553	1.07057	0.535284	−	0.844672i	$-0.320205\pi$
$677$	27.8553	1.07057	0.535284	+	0.844672i	$0.320205\pi$
$678$	−8.48001	−0.325673
$679$	12.6862	0.486852
$680$	2.12637	0.0815427
$681$	−1.93751	−0.0742454
$682$	−9.87735	−0.378223
$683$	−6.76661	−0.258917	−0.129459	−	0.991585i	$-0.541324\pi$
$683$	−6.76661	−0.258917	−0.129459	+	0.991585i	$0.541324\pi$
$684$	−92.8762	−3.55121
$685$	−1.35998	−0.0519623
$686$	16.9564	0.647397
$687$	−10.7858	−0.411505
$688$	69.2243	2.63915
$689$	17.3475	0.660889
$690$	1.19857	0.0456288
$691$	3.25880	0.123970	0.0619852	−	0.998077i	$-0.480257\pi$
$691$	3.25880	0.123970	0.0619852	+	0.998077i	$0.480257\pi$
$692$	60.9673	2.31763
$693$	50.3249	1.91168
$694$	−11.6462	−0.442083
$695$	2.83687	0.107609
$696$	−0.396240	−0.0150194
$697$	14.0590	0.532521
$698$	−16.7343	−0.633401
$699$	−5.01712	−0.189765
$700$	−77.4936	−2.92898
$701$	−4.62359	−0.174631	−0.0873153	−	0.996181i	$-0.527829\pi$
$701$	−4.62359	−0.174631	−0.0873153	+	0.996181i	$0.527829\pi$
$702$	−27.8686	−1.05183
$703$	29.3279	1.10612
$704$	1.27564	0.0480775
$705$	−0.0274922	−0.00103542
$706$	−69.0112	−2.59727
$707$	3.66569	0.137863
$708$	3.39626	0.127639
$709$	−10.5865	−0.397583	−0.198792	−	0.980042i	$-0.563702\pi$
$709$	−10.5865	−0.397583	−0.198792	+	0.980042i	$0.563702\pi$
$710$	3.14656	0.118088
$711$	33.8741	1.27038
$712$	−45.3868	−1.70094
$713$	4.60093	0.172306
$714$	8.64527	0.323541
$715$	3.39939	0.127130
$716$	35.0372	1.30940
$717$	3.30751	0.123521
$718$	38.1843	1.42502
$719$	−32.6589	−1.21797	−0.608987	−	0.793180i	$-0.708424\pi$
$719$	−32.6589	−1.21797	−0.608987	+	0.793180i	$0.708424\pi$
$720$	−3.20745	−0.119535
$721$	37.2767	1.38826
$722$	−93.2052	−3.46874
$723$	7.71980	0.287102
$724$	−32.5405	−1.20936
$725$	−0.663126	−0.0246279
$726$	−19.3279	−0.717325
$727$	−19.9804	−0.741031	−0.370515	−	0.928826i	$-0.620819\pi$
$727$	−19.9804	−0.741031	−0.370515	+	0.928826i	$0.620819\pi$
$728$	88.4722	3.27900
$729$	−15.7787	−0.584396
$730$	4.42338	0.163716
$731$	−20.1806	−0.746407
$732$	14.2964	0.528410
$733$	−15.2126	−0.561889	−0.280944	−	0.959724i	$-0.590648\pi$
$733$	−15.2126	−0.561889	−0.280944	+	0.959724i	$0.590648\pi$
$734$	44.6104	1.64660
$735$	0.387388	0.0142890
$736$	33.9844	1.25268
$737$	1.88702	0.0695094
$738$	−47.8890	−1.76282
$739$	19.5551	0.719347	0.359673	−	0.933078i	$-0.382888\pi$
$739$	19.5551	0.719347	0.359673	+	0.933078i	$0.382888\pi$
$740$	2.85581	0.104982
$741$	−14.1252	−0.518901
$742$	38.1209	1.39946
$743$	−48.1506	−1.76647	−0.883236	−	0.468928i	$-0.844640\pi$
$743$	−48.1506	−1.76647	−0.883236	+	0.468928i	$0.844640\pi$
$744$	2.21317	0.0811388
$745$	1.51531	0.0555167
$746$	13.0880	0.479185
$747$	−22.2940	−0.815695
$748$	48.4979	1.77326
$749$	69.2404	2.52999
$750$	1.93484	0.0706503
$751$	−31.1075	−1.13513	−0.567564	−	0.823329i	$-0.692114\pi$
$751$	−31.1075	−1.13513	−0.567564	+	0.823329i	$0.692114\pi$
$752$	−2.57060	−0.0937401
$753$	14.2492	0.519270
$754$	1.36711	0.0497874
$755$	0.167099	0.00608135
$756$	−42.3453	−1.54008
$757$	−33.6336	−1.22243	−0.611217	−	0.791463i	$-0.709320\pi$
$757$	−33.6336	−1.22243	−0.611217	+	0.791463i	$0.709320\pi$
$758$	82.9901	3.01434
$759$	15.1384	0.549488
$760$	−7.63448	−0.276932
$761$	−14.7292	−0.533932	−0.266966	−	0.963706i	$-0.586021\pi$
$761$	−14.7292	−0.533932	−0.266966	+	0.963706i	$0.586021\pi$
$762$	8.62964	0.312619
$763$	−8.83006	−0.319670
$764$	62.4608	2.25975
$765$	0.935052	0.0338069
$766$	−57.5199	−2.07828
$767$	−6.48903	−0.234305
$768$	−13.6888	−0.493951
$769$	−45.1525	−1.62824	−0.814120	−	0.580696i	$-0.802780\pi$
$769$	−45.1525	−1.62824	−0.814120	+	0.580696i	$0.802780\pi$
$770$	7.47009	0.269203
$771$	−0.431024	−0.0155230
$772$	91.9878	3.31071
$773$	44.8162	1.61193	0.805964	−	0.591965i	$-0.201648\pi$
$773$	44.8162	1.61193	0.805964	+	0.591965i	$0.201648\pi$
$774$	68.7412	2.47085
$775$	3.70384	0.133046
$776$	−23.0615	−0.827859
$777$	6.42986	0.230670
$778$	−80.0541	−2.87008
$779$	−50.4770	−1.80852
$780$	−1.37544	−0.0492488
$781$	39.7422	1.42209
$782$	−32.6712	−1.16832
$783$	−0.362355	−0.0129495
$784$	36.2219	1.29364
$785$	−1.82059	−0.0649797
$786$	−25.5324	−0.910710
$787$	34.2777	1.22187	0.610933	−	0.791682i	$-0.290794\pi$
$787$	34.2777	1.22187	0.610933	+	0.791682i	$0.290794\pi$
$788$	−42.8179	−1.52532
$789$	0.504133	0.0179476
$790$	5.02818	0.178895
$791$	24.6186	0.875337
$792$	−91.4824	−3.25069
$793$	−27.3152	−0.969993
$794$	−15.3018	−0.543042
$795$	−0.328194	−0.0116399
$796$	27.9103	0.989256
$797$	8.03224	0.284516	0.142258	−	0.989830i	$-0.454564\pi$
$797$	8.03224	0.284516	0.142258	+	0.989830i	$0.454564\pi$
$798$	−31.0398	−1.09880
$799$	0.749393	0.0265116
$800$	27.3581	0.967256
$801$	−19.9584	−0.705196
$802$	−64.9541	−2.29361
$803$	55.8688	1.97157
$804$	−0.763519	−0.0269272
$805$	−3.47961	−0.122640
$806$	−7.63591	−0.268964
$807$	−11.2219	−0.395031
$808$	−6.66363	−0.234426
$809$	−27.4349	−0.964558	−0.482279	−	0.876018i	$-0.660191\pi$
$809$	−27.4349	−0.964558	−0.482279	+	0.876018i	$0.660191\pi$
$810$	−2.91136	−0.102295
$811$	−37.7642	−1.32608	−0.663040	−	0.748584i	$-0.730734\pi$
$811$	−37.7642	−1.32608	−0.663040	+	0.748584i	$0.730734\pi$
$812$	2.07727	0.0728980
$813$	13.4932	0.473228
$814$	52.1653	1.82839
$815$	−1.13522	−0.0397650
$816$	−6.95939	−0.243627
$817$	72.4560	2.53491
$818$	74.4711	2.60382
$819$	38.9048	1.35944
$820$	−4.91521	−0.171647
$821$	−17.8087	−0.621527	−0.310763	−	0.950487i	$-0.600585\pi$
$821$	−17.8087	−0.621527	−0.310763	+	0.950487i	$0.600585\pi$
$822$	10.0514	0.350584
$823$	0.260435	0.00907821	0.00453910	−	0.999990i	$-0.498555\pi$
$823$	0.260435	0.00907821	0.00453910	+	0.999990i	$0.498555\pi$
$824$	−67.7630	−2.36064
$825$	12.1867	0.424286
$826$	−14.2595	−0.496152
$827$	1.84810	0.0642647	0.0321323	−	0.999484i	$-0.489770\pi$
$827$	1.84810	0.0642647	0.0321323	+	0.999484i	$0.489770\pi$
$828$	76.9504	2.67421
$829$	−37.2934	−1.29525	−0.647627	−	0.761957i	$-0.724239\pi$
$829$	−37.2934	−1.29525	−0.647627	+	0.761957i	$0.724239\pi$
$830$	−3.30926	−0.114866
$831$	−4.63520	−0.160793
$832$	0.986164	0.0341891
$833$	−10.5596	−0.365868
$834$	−20.9669	−0.726024
$835$	2.43904	0.0844063
$836$	−174.126	−6.02226
$837$	2.02391	0.0699565
$838$	37.3933	1.29173
$839$	−3.93990	−0.136021	−0.0680103	−	0.997685i	$-0.521665\pi$
$839$	−3.93990	−0.136021	−0.0680103	+	0.997685i	$0.521665\pi$
$840$	−1.67379	−0.0577511
$841$	−28.9822	−0.999387
$842$	28.8351	0.993722
$843$	−11.4919	−0.395802
$844$	−16.2204	−0.558330
$845$	0.521823	0.0179512
$846$	−2.55266	−0.0877622
$847$	56.1114	1.92801
$848$	−30.6871	−1.05380
$849$	0.0608584	0.00208865
$850$	−26.3009	−0.902114
$851$	−24.2989	−0.832956
$852$	−16.0803	−0.550902
$853$	6.62301	0.226768	0.113384	−	0.993551i	$-0.463831\pi$
$853$	6.62301	0.226768	0.113384	+	0.993551i	$0.463831\pi$
$854$	−60.0248	−2.05401
$855$	−3.35719	−0.114814
$856$	−125.868	−4.30207
$857$	21.5377	0.735715	0.367857	−	0.929882i	$-0.380091\pi$
$857$	21.5377	0.735715	0.367857	+	0.929882i	$0.380091\pi$
$858$	−25.1243	−0.857730
$859$	30.5130	1.04109	0.520544	−	0.853835i	$-0.325729\pi$
$859$	30.5130	1.04109	0.520544	+	0.853835i	$0.325729\pi$
$860$	7.05543	0.240588
$861$	−11.0666	−0.377148
$862$	58.9720	2.00860
$863$	21.9668	0.747760	0.373880	−	0.927477i	$-0.378027\pi$
$863$	21.9668	0.747760	0.373880	+	0.927477i	$0.378027\pi$
$864$	14.9494	0.508591
$865$	2.20378	0.0749309
$866$	29.6307	1.00689
$867$	−5.96644	−0.202631
$868$	−11.6025	−0.393813
$869$	63.5077	2.15435
$870$	−0.0258641	−0.000876876 0
$871$	1.45881	0.0494298
$872$	16.0516	0.543576
$873$	−10.1411	−0.343223
$874$	117.302	3.96779
$875$	−5.61710	−0.189893
$876$	−22.6054	−0.763765
$877$	40.7976	1.37764	0.688818	−	0.724935i	$-0.258130\pi$
$877$	40.7976	1.37764	0.688818	+	0.724935i	$0.258130\pi$
$878$	−85.3921	−2.88184
$879$	−1.37326	−0.0463190
$880$	−6.01338	−0.202711
$881$	0.920622	0.0310165	0.0155083	−	0.999880i	$-0.495063\pi$
$881$	0.920622	0.0310165	0.0155083	+	0.999880i	$0.495063\pi$
$882$	35.9691	1.21114
$883$	56.6951	1.90794	0.953971	−	0.299898i	$-0.0969526\pi$
$883$	56.6951	1.90794	0.953971	+	0.299898i	$0.0969526\pi$
$884$	37.4924	1.26101
$885$	0.122764	0.00412668
$886$	70.6922	2.37495
$887$	23.8816	0.801866	0.400933	−	0.916107i	$-0.368686\pi$
$887$	23.8816	0.801866	0.400933	+	0.916107i	$0.368686\pi$
$888$	−11.6884	−0.392238
$889$	−25.0530	−0.840252
$890$	−2.96257	−0.0993056
$891$	−36.7715	−1.23189
$892$	−8.62459	−0.288773
$893$	−2.69061	−0.0900377
$894$	−11.1994	−0.374565
$895$	1.26649	0.0423339
$896$	40.4090	1.34997
$897$	11.7031	0.390754
$898$	88.7557	2.96182
$899$	−0.0992842	−0.00331131
$900$	61.9466	2.06489
$901$	8.94606	0.298036
$902$	−89.7830	−2.98945
$903$	15.8853	0.528629
$904$	−44.7526	−1.48845
$905$	−1.17624	−0.0390995
$906$	−1.23500	−0.0410302
$907$	−24.7480	−0.821744	−0.410872	−	0.911693i	$-0.634776\pi$
$907$	−24.7480	−0.821744	−0.410872	+	0.911693i	$0.634776\pi$
$908$	−18.4643	−0.612760
$909$	−2.93027	−0.0971908
$910$	5.77492	0.191437
$911$	11.8801	0.393605	0.196802	−	0.980443i	$-0.436944\pi$
$911$	11.8801	0.393605	0.196802	+	0.980443i	$0.436944\pi$
$912$	24.9869	0.827397
$913$	−41.7971	−1.38328
$914$	−55.0344	−1.82038
$915$	0.516771	0.0170839
$916$	−102.788	−3.39622
$917$	74.1240	2.44779
$918$	−14.3717	−0.474338
$919$	37.5879	1.23991	0.619955	−	0.784637i	$-0.287151\pi$
$919$	37.5879	1.23991	0.619955	+	0.784637i	$0.287151\pi$
$920$	6.32537	0.208541
$921$	11.5710	0.381277
$922$	−54.0877	−1.78128
$923$	30.7236	1.01128
$924$	−38.1754	−1.25588
$925$	−19.5611	−0.643165
$926$	−4.96682	−0.163220
$927$	−29.7981	−0.978699
$928$	−0.733355	−0.0240736
$929$	14.1453	0.464093	0.232047	−	0.972705i	$-0.425458\pi$
$929$	14.1453	0.464093	0.232047	+	0.972705i	$0.425458\pi$
$930$	0.144462	0.00473710
$931$	37.9129	1.24254
$932$	−47.8128	−1.56616
$933$	2.44639	0.0800913
$934$	67.8548	2.22028
$935$	1.75305	0.0573309
$936$	−70.7226	−2.31164
$937$	50.7416	1.65766	0.828829	−	0.559503i	$-0.189008\pi$
$937$	50.7416	1.65766	0.828829	+	0.559503i	$0.189008\pi$
$938$	3.20570	0.104670
$939$	−1.78553	−0.0582684
$940$	−0.261999	−0.00854546
$941$	−53.3542	−1.73930	−0.869649	−	0.493671i	$-0.835655\pi$
$941$	−53.3542	−1.73930	−0.869649	+	0.493671i	$0.835655\pi$
$942$	13.4557	0.438411
$943$	41.8215	1.36189
$944$	11.4788	0.373604
$945$	−1.53065	−0.0497921
$946$	128.877	4.19015
$947$	−8.53493	−0.277348	−0.138674	−	0.990338i	$-0.544284\pi$
$947$	−8.53493	−0.277348	−0.138674	+	0.990338i	$0.544284\pi$
$948$	−25.6962	−0.834573
$949$	43.1907	1.40203
$950$	94.4302	3.06372
$951$	−3.49425	−0.113309
$952$	45.6248	1.47871
$953$	−36.6982	−1.18877	−0.594386	−	0.804180i	$-0.702605\pi$
$953$	−36.6982	−1.18877	−0.594386	+	0.804180i	$0.702605\pi$
$954$	−30.4730	−0.986598
$955$	2.25777	0.0730596
$956$	31.5204	1.01944
$957$	−0.326673	−0.0105598
$958$	−9.30586	−0.300659
$959$	−29.1807	−0.942293
$960$	−0.0186570	−0.000602152 0
$961$	−30.4455	−0.982111
$962$	40.3276	1.30021
$963$	−55.3492	−1.78360
$964$	73.5692	2.36950
$965$	3.32508	0.107038
$966$	25.7173	0.827440
$967$	34.7468	1.11738	0.558691	−	0.829376i	$-0.311304\pi$
$967$	34.7468	1.11738	0.558691	+	0.829376i	$0.311304\pi$
$968$	−102.001	−3.27845
$969$	−7.28429	−0.234005
$970$	−1.50531	−0.0483326
$971$	−11.7339	−0.376559	−0.188280	−	0.982115i	$-0.560291\pi$
$971$	−11.7339	−0.376559	−0.188280	+	0.982115i	$0.560291\pi$
$972$	51.4225	1.64938
$973$	60.8697	1.95139
$974$	−42.8756	−1.37382
$975$	9.42120	0.301720
$976$	48.3196	1.54667
$977$	29.1560	0.932782	0.466391	−	0.884579i	$-0.345554\pi$
$977$	29.1560	0.932782	0.466391	+	0.884579i	$0.345554\pi$
$978$	8.39024	0.268290
$979$	−37.4183	−1.19589
$980$	3.69178	0.117930
$981$	7.05854	0.225362
$982$	−53.8190	−1.71743
$983$	12.6169	0.402417	0.201209	−	0.979548i	$-0.435513\pi$
$983$	12.6169	0.402417	0.201209	+	0.979548i	$0.435513\pi$
$984$	20.1172	0.641314
$985$	−1.54774	−0.0493150
$986$	0.705015	0.0224523
$987$	−0.589889	−0.0187764
$988$	−134.612	−4.28258
$989$	−60.0317	−1.90890
$990$	−5.97141	−0.189784
$991$	41.9226	1.33171	0.665857	−	0.746080i	$-0.268066\pi$
$991$	41.9226	1.33171	0.665857	+	0.746080i	$0.268066\pi$
$992$	4.09610	0.130051
$993$	16.0844	0.510422
$994$	67.5146	2.14143
$995$	1.00887	0.0319834
$996$	16.9118	0.535870
$997$	13.7017	0.433938	0.216969	−	0.976179i	$-0.430383\pi$
$997$	13.7017	0.433938	0.216969	+	0.976179i	$0.430383\pi$
$998$	21.2958	0.674108
$999$	−10.6889	−0.338181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.b.1.20	✓	287

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.b.1.20	✓	287	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:	\( N \)	\(=\)	\( 6047 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54598 q^{2} +0.470310 q^{3} +4.48203 q^{4} +0.162012 q^{5} -1.19740 q^{6} +3.47622 q^{7} -6.31920 q^{8} -2.77881 q^{9} +O(q^{10})\)	\(q-2.54598 q^{2} +0.470310 q^{3} +4.48203 q^{4} +0.162012 q^{5} -1.19740 q^{6} +3.47622 q^{7} -6.31920 q^{8} -2.77881 q^{9} -0.412479 q^{10} -5.20975 q^{11} +2.10794 q^{12} -4.02752 q^{13} -8.85040 q^{14} +0.0761957 q^{15} +7.12452 q^{16} -2.07698 q^{17} +7.07480 q^{18} +7.45713 q^{19} +0.726140 q^{20} +1.63490 q^{21} +13.2639 q^{22} -6.17842 q^{23} -2.97199 q^{24} -4.97375 q^{25} +10.2540 q^{26} -2.71783 q^{27} +15.5805 q^{28} +0.133325 q^{29} -0.193993 q^{30} -0.744677 q^{31} -5.50050 q^{32} -2.45020 q^{33} +5.28794 q^{34} +0.563188 q^{35} -12.4547 q^{36} +3.93287 q^{37} -18.9857 q^{38} -1.89418 q^{39} -1.02378 q^{40} -6.76896 q^{41} -4.16243 q^{42} +9.71634 q^{43} -23.3502 q^{44} -0.450199 q^{45} +15.7302 q^{46} -0.360810 q^{47} +3.35074 q^{48} +5.08411 q^{49} +12.6631 q^{50} -0.976823 q^{51} -18.0514 q^{52} -4.30725 q^{53} +6.91956 q^{54} -0.844040 q^{55} -21.9669 q^{56} +3.50716 q^{57} -0.339443 q^{58} +1.61117 q^{59} +0.341511 q^{60} +6.78216 q^{61} +1.89594 q^{62} -9.65975 q^{63} -0.244856 q^{64} -0.652504 q^{65} +6.23817 q^{66} -0.362210 q^{67} -9.30906 q^{68} -2.90578 q^{69} -1.43387 q^{70} -7.62843 q^{71} +17.5598 q^{72} -10.7239 q^{73} -10.0130 q^{74} -2.33921 q^{75} +33.4230 q^{76} -18.1102 q^{77} +4.82256 q^{78} -12.1902 q^{79} +1.15425 q^{80} +7.05820 q^{81} +17.2336 q^{82} +8.02287 q^{83} +7.32768 q^{84} -0.336494 q^{85} -24.7376 q^{86} +0.0627042 q^{87} +32.9215 q^{88} +7.18236 q^{89} +1.14620 q^{90} -14.0005 q^{91} -27.6919 q^{92} -0.350229 q^{93} +0.918616 q^{94} +1.20814 q^{95} -2.58694 q^{96} +3.64943 q^{97} -12.9441 q^{98} +14.4769 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * q^99

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