LMFDB - Embedded newform 8049.2.a.c.1.17

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:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-2.22986 q^{2} -1.00000 q^{3} +2.97225 q^{4} +2.09159 q^{5} +2.22986 q^{6} +2.90452 q^{7} -2.16799 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.22986 q^{2} -1.00000 q^{3} +2.97225 q^{4} +2.09159 q^{5} +2.22986 q^{6} +2.90452 q^{7} -2.16799 q^{8} +1.00000 q^{9} -4.66395 q^{10} +3.89669 q^{11} -2.97225 q^{12} +3.55760 q^{13} -6.47666 q^{14} -2.09159 q^{15} -1.11021 q^{16} +2.94993 q^{17} -2.22986 q^{18} -0.689249 q^{19} +6.21675 q^{20} -2.90452 q^{21} -8.68906 q^{22} +5.42209 q^{23} +2.16799 q^{24} -0.625236 q^{25} -7.93293 q^{26} -1.00000 q^{27} +8.63298 q^{28} -6.18357 q^{29} +4.66395 q^{30} -3.10575 q^{31} +6.81159 q^{32} -3.89669 q^{33} -6.57792 q^{34} +6.07508 q^{35} +2.97225 q^{36} +4.93177 q^{37} +1.53692 q^{38} -3.55760 q^{39} -4.53455 q^{40} -6.23104 q^{41} +6.47666 q^{42} +10.0568 q^{43} +11.5820 q^{44} +2.09159 q^{45} -12.0905 q^{46} -11.4965 q^{47} +1.11021 q^{48} +1.43625 q^{49} +1.39419 q^{50} -2.94993 q^{51} +10.5741 q^{52} -2.13147 q^{53} +2.22986 q^{54} +8.15030 q^{55} -6.29696 q^{56} +0.689249 q^{57} +13.7885 q^{58} +3.78373 q^{59} -6.21675 q^{60} -0.267250 q^{61} +6.92537 q^{62} +2.90452 q^{63} -12.9684 q^{64} +7.44105 q^{65} +8.68906 q^{66} +0.427400 q^{67} +8.76794 q^{68} -5.42209 q^{69} -13.5465 q^{70} -10.6982 q^{71} -2.16799 q^{72} -1.25274 q^{73} -10.9971 q^{74} +0.625236 q^{75} -2.04862 q^{76} +11.3180 q^{77} +7.93293 q^{78} -11.4346 q^{79} -2.32212 q^{80} +1.00000 q^{81} +13.8943 q^{82} +17.8509 q^{83} -8.63298 q^{84} +6.17006 q^{85} -22.4252 q^{86} +6.18357 q^{87} -8.44797 q^{88} +8.46852 q^{89} -4.66395 q^{90} +10.3331 q^{91} +16.1158 q^{92} +3.10575 q^{93} +25.6356 q^{94} -1.44163 q^{95} -6.81159 q^{96} -0.117045 q^{97} -3.20262 q^{98} +3.89669 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) $ 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * 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 $

$2$	−2.22986	−1.57675	−0.788373	−	0.615198i	$-0.789076\pi$
$2$	−2.22986	−1.57675	−0.788373	+	0.615198i	$0.789076\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.97225	1.48613
$5$	2.09159	0.935389	0.467695	−	0.883890i	$-0.345085\pi$
$5$	2.09159	0.935389	0.467695	+	0.883890i	$0.345085\pi$
$6$	2.22986	0.910335
$7$	2.90452	1.09781	0.548903	−	0.835886i	$-0.315046\pi$
$7$	2.90452	1.09781	0.548903	+	0.835886i	$0.315046\pi$
$8$	−2.16799	−0.766499
$9$	1.00000	0.333333
$10$	−4.66395	−1.47487
$11$	3.89669	1.17490	0.587449	−	0.809262i	$-0.300132\pi$
$11$	3.89669	1.17490	0.587449	+	0.809262i	$0.300132\pi$
$12$	−2.97225	−0.858016
$13$	3.55760	0.986700	0.493350	−	0.869831i	$-0.335772\pi$
$13$	3.55760	0.986700	0.493350	+	0.869831i	$0.335772\pi$
$14$	−6.47666	−1.73096
$15$	−2.09159	−0.540047
$16$	−1.11021	−0.277553
$17$	2.94993	0.715463	0.357732	−	0.933824i	$-0.383550\pi$
$17$	2.94993	0.715463	0.357732	+	0.933824i	$0.383550\pi$
$18$	−2.22986	−0.525582
$19$	−0.689249	−0.158124	−0.0790622	−	0.996870i	$-0.525193\pi$
$19$	−0.689249	−0.158124	−0.0790622	+	0.996870i	$0.525193\pi$
$20$	6.21675	1.39011
$21$	−2.90452	−0.633819
$22$	−8.68906	−1.85251
$23$	5.42209	1.13058	0.565292	−	0.824891i	$-0.308764\pi$
$23$	5.42209	1.13058	0.565292	+	0.824891i	$0.308764\pi$
$24$	2.16799	0.442538
$25$	−0.625236	−0.125047
$26$	−7.93293	−1.55578
$27$	−1.00000	−0.192450
$28$	8.63298	1.63148
$29$	−6.18357	−1.14826	−0.574130	−	0.818764i	$-0.694659\pi$
$29$	−6.18357	−1.14826	−0.574130	+	0.818764i	$0.694659\pi$
$30$	4.66395	0.851517
$31$	−3.10575	−0.557809	−0.278904	−	0.960319i	$-0.589971\pi$
$31$	−3.10575	−0.557809	−0.278904	+	0.960319i	$0.589971\pi$
$32$	6.81159	1.20413
$33$	−3.89669	−0.678327
$34$	−6.57792	−1.12810
$35$	6.07508	1.02688
$36$	2.97225	0.495376
$37$	4.93177	0.810778	0.405389	−	0.914144i	$-0.367136\pi$
$37$	4.93177	0.810778	0.405389	+	0.914144i	$0.367136\pi$
$38$	1.53692	0.249322
$39$	−3.55760	−0.569672
$40$	−4.53455	−0.716975
$41$	−6.23104	−0.973125	−0.486562	−	0.873646i	$-0.661749\pi$
$41$	−6.23104	−0.973125	−0.486562	+	0.873646i	$0.661749\pi$
$42$	6.47666	0.999371
$43$	10.0568	1.53364	0.766822	−	0.641859i	$-0.221837\pi$
$43$	10.0568	1.53364	0.766822	+	0.641859i	$0.221837\pi$
$44$	11.5820	1.74605
$45$	2.09159	0.311796
$46$	−12.0905	−1.78264
$47$	−11.4965	−1.67694	−0.838469	−	0.544949i	$-0.816549\pi$
$47$	−11.4965	−1.67694	−0.838469	+	0.544949i	$0.816549\pi$
$48$	1.11021	0.160246
$49$	1.43625	0.205178
$50$	1.39419	0.197168
$51$	−2.94993	−0.413073
$52$	10.5741	1.46636
$53$	−2.13147	−0.292780	−0.146390	−	0.989227i	$-0.546765\pi$
$53$	−2.13147	−0.292780	−0.146390	+	0.989227i	$0.546765\pi$
$54$	2.22986	0.303445
$55$	8.15030	1.09899
$56$	−6.29696	−0.841467
$57$	0.689249	0.0912932
$58$	13.7885	1.81051
$59$	3.78373	0.492600	0.246300	−	0.969194i	$-0.420785\pi$
$59$	3.78373	0.492600	0.246300	+	0.969194i	$0.420785\pi$
$60$	−6.21675	−0.802579
$61$	−0.267250	−0.0342178	−0.0171089	−	0.999854i	$-0.505446\pi$
$61$	−0.267250	−0.0342178	−0.0171089	+	0.999854i	$0.505446\pi$
$62$	6.92537	0.879523
$63$	2.90452	0.365935
$64$	−12.9684	−1.62105
$65$	7.44105	0.922949
$66$	8.68906	1.06955
$67$	0.427400	0.0522153	0.0261076	−	0.999659i	$-0.491689\pi$
$67$	0.427400	0.0522153	0.0261076	+	0.999659i	$0.491689\pi$
$68$	8.76794	1.06327
$69$	−5.42209	−0.652743
$70$	−13.5465	−1.61912
$71$	−10.6982	−1.26964	−0.634820	−	0.772660i	$-0.718926\pi$
$71$	−10.6982	−1.26964	−0.634820	+	0.772660i	$0.718926\pi$
$72$	−2.16799	−0.255500
$73$	−1.25274	−0.146622	−0.0733108	−	0.997309i	$-0.523357\pi$
$73$	−1.25274	−0.146622	−0.0733108	+	0.997309i	$0.523357\pi$
$74$	−10.9971	−1.27839
$75$	0.625236	0.0721960
$76$	−2.04862	−0.234993
$77$	11.3180	1.28981
$78$	7.93293	0.898227
$79$	−11.4346	−1.28649	−0.643246	−	0.765659i	$-0.722413\pi$
$79$	−11.4346	−1.28649	−0.643246	+	0.765659i	$0.722413\pi$
$80$	−2.32212	−0.259620
$81$	1.00000	0.111111
$82$	13.8943	1.53437
$83$	17.8509	1.95939	0.979695	−	0.200495i	$-0.0642551\pi$
$83$	17.8509	1.95939	0.979695	+	0.200495i	$0.0642551\pi$
$84$	−8.63298	−0.941935
$85$	6.17006	0.669237
$86$	−22.4252	−2.41817
$87$	6.18357	0.662948
$88$	−8.44797	−0.900557
$89$	8.46852	0.897662	0.448831	−	0.893617i	$-0.351841\pi$
$89$	8.46852	0.897662	0.448831	+	0.893617i	$0.351841\pi$
$90$	−4.66395	−0.491624
$91$	10.3331	1.08321
$92$	16.1158	1.68019
$93$	3.10575	0.322051
$94$	25.6356	2.64411
$95$	−1.44163	−0.147908
$96$	−6.81159	−0.695205
$97$	−0.117045	−0.0118842	−0.00594208	−	0.999982i	$-0.501891\pi$
$97$	−0.117045	−0.0118842	−0.00594208	+	0.999982i	$0.501891\pi$
$98$	−3.20262	−0.323514
$99$	3.89669	0.391632
$100$	−1.85836	−0.185836
$101$	19.0827	1.89880	0.949402	−	0.314063i	$-0.101690\pi$
$101$	19.0827	1.89880	0.949402	+	0.314063i	$0.101690\pi$
$102$	6.57792	0.651311
$103$	−3.52058	−0.346893	−0.173446	−	0.984843i	$-0.555490\pi$
$103$	−3.52058	−0.346893	−0.173446	+	0.984843i	$0.555490\pi$
$104$	−7.71282	−0.756304
$105$	−6.07508	−0.592867
$106$	4.75287	0.461639
$107$	15.1126	1.46099	0.730497	−	0.682915i	$-0.239288\pi$
$107$	15.1126	1.46099	0.730497	+	0.682915i	$0.239288\pi$
$108$	−2.97225	−0.286005
$109$	14.5022	1.38906	0.694529	−	0.719465i	$-0.255613\pi$
$109$	14.5022	1.38906	0.694529	+	0.719465i	$0.255613\pi$
$110$	−18.1740	−1.73282
$111$	−4.93177	−0.468103
$112$	−3.22464	−0.304700
$113$	13.9480	1.31212	0.656058	−	0.754710i	$-0.272223\pi$
$113$	13.9480	1.31212	0.656058	+	0.754710i	$0.272223\pi$
$114$	−1.53692	−0.143946
$115$	11.3408	1.05754
$116$	−18.3791	−1.70646
$117$	3.55760	0.328900
$118$	−8.43717	−0.776704
$119$	8.56814	0.785440
$120$	4.53455	0.413945
$121$	4.18421	0.380383
$122$	0.595928	0.0539528
$123$	6.23104	0.561834
$124$	−9.23107	−0.828975
$125$	−11.7657	−1.05236
$126$	−6.47666	−0.576987
$127$	−16.3664	−1.45229	−0.726144	−	0.687543i	$-0.758689\pi$
$127$	−16.3664	−1.45229	−0.726144	+	0.687543i	$0.758689\pi$
$128$	15.2945	1.35186
$129$	−10.0568	−0.885450
$130$	−16.5925	−1.45526
$131$	−1.92244	−0.167964	−0.0839822	−	0.996467i	$-0.526764\pi$
$131$	−1.92244	−0.167964	−0.0839822	+	0.996467i	$0.526764\pi$
$132$	−11.5820	−1.00808
$133$	−2.00194	−0.173590
$134$	−0.953041	−0.0823302
$135$	−2.09159	−0.180016
$136$	−6.39541	−0.548402
$137$	−0.696073	−0.0594695	−0.0297348	−	0.999558i	$-0.509466\pi$
$137$	−0.696073	−0.0594695	−0.0297348	+	0.999558i	$0.509466\pi$
$138$	12.0905	1.02921
$139$	11.1349	0.944450	0.472225	−	0.881478i	$-0.343451\pi$
$139$	11.1349	0.944450	0.472225	+	0.881478i	$0.343451\pi$
$140$	18.0567	1.52607
$141$	11.4965	0.968181
$142$	23.8554	2.00190
$143$	13.8629	1.15927
$144$	−1.11021	−0.0925178
$145$	−12.9335	−1.07407
$146$	2.79342	0.231185
$147$	−1.43625	−0.118460
$148$	14.6585	1.20492
$149$	17.7637	1.45526	0.727630	−	0.685969i	$-0.240622\pi$
$149$	17.7637	1.45526	0.727630	+	0.685969i	$0.240622\pi$
$150$	−1.39419	−0.113835
$151$	−14.7830	−1.20302	−0.601511	−	0.798864i	$-0.705435\pi$
$151$	−14.7830	−1.20302	−0.601511	+	0.798864i	$0.705435\pi$
$152$	1.49428	0.121202
$153$	2.94993	0.238488
$154$	−25.2376	−2.03370
$155$	−6.49596	−0.521768
$156$	−10.5741	−0.846604
$157$	−17.6471	−1.40839	−0.704194	−	0.710007i	$-0.748692\pi$
$157$	−17.6471	−1.40839	−0.704194	+	0.710007i	$0.748692\pi$
$158$	25.4975	2.02847
$159$	2.13147	0.169037
$160$	14.2471	1.12633
$161$	15.7486	1.24116
$162$	−2.22986	−0.175194
$163$	−2.75577	−0.215848	−0.107924	−	0.994159i	$-0.534420\pi$
$163$	−2.75577	−0.215848	−0.107924	+	0.994159i	$0.534420\pi$
$164$	−18.5202	−1.44619
$165$	−8.15030	−0.634500
$166$	−39.8049	−3.08946
$167$	14.3382	1.10953	0.554763	−	0.832008i	$-0.312809\pi$
$167$	14.3382	1.10953	0.554763	+	0.832008i	$0.312809\pi$
$168$	6.29696	0.485821
$169$	−0.343496	−0.0264228
$170$	−13.7583	−1.05522
$171$	−0.689249	−0.0527082
$172$	29.8913	2.27919
$173$	22.6564	1.72254	0.861269	−	0.508150i	$-0.169670\pi$
$173$	22.6564	1.72254	0.861269	+	0.508150i	$0.169670\pi$
$174$	−13.7885	−1.04530
$175$	−1.81601	−0.137278
$176$	−4.32616	−0.326097
$177$	−3.78373	−0.284403
$178$	−18.8836	−1.41538
$179$	−4.28991	−0.320643	−0.160321	−	0.987065i	$-0.551253\pi$
$179$	−4.28991	−0.320643	−0.160321	+	0.987065i	$0.551253\pi$
$180$	6.21675	0.463369
$181$	0.163101	0.0121232	0.00606161	−	0.999982i	$-0.498071\pi$
$181$	0.163101	0.0121232	0.00606161	+	0.999982i	$0.498071\pi$
$182$	−23.0414	−1.70794
$183$	0.267250	0.0197557
$184$	−11.7550	−0.866591
$185$	10.3153	0.758393
$186$	−6.92537	−0.507793
$187$	11.4950	0.840596
$188$	−34.1706	−2.49214
$189$	−2.90452	−0.211273
$190$	3.21462	0.233213
$191$	6.14344	0.444523	0.222262	−	0.974987i	$-0.428656\pi$
$191$	6.14344	0.444523	0.222262	+	0.974987i	$0.428656\pi$
$192$	12.9684	0.935916
$193$	−1.09385	−0.0787369	−0.0393684	−	0.999225i	$-0.512535\pi$
$193$	−1.09385	−0.0787369	−0.0393684	+	0.999225i	$0.512535\pi$
$194$	0.260994	0.0187383
$195$	−7.44105	−0.532865
$196$	4.26889	0.304921
$197$	15.8973	1.13263	0.566317	−	0.824187i	$-0.308368\pi$
$197$	15.8973	1.13263	0.566317	+	0.824187i	$0.308368\pi$
$198$	−8.68906	−0.617505
$199$	16.8331	1.19327	0.596633	−	0.802514i	$-0.296505\pi$
$199$	16.8331	1.19327	0.596633	+	0.802514i	$0.296505\pi$
$200$	1.35550	0.0958485
$201$	−0.427400	−0.0301465
$202$	−42.5518	−2.99393
$203$	−17.9603	−1.26057
$204$	−8.76794	−0.613879
$205$	−13.0328	−0.910250
$206$	7.85038	0.546962
$207$	5.42209	0.376861
$208$	−3.94969	−0.273862
$209$	−2.68579	−0.185780
$210$	13.5465	0.934801
$211$	6.70281	0.461441	0.230720	−	0.973020i	$-0.425892\pi$
$211$	6.70281	0.461441	0.230720	+	0.973020i	$0.425892\pi$
$212$	−6.33527	−0.435108
$213$	10.6982	0.733027
$214$	−33.6990	−2.30362
$215$	21.0347	1.43455
$216$	2.16799	0.147513
$217$	−9.02071	−0.612366
$218$	−32.3378	−2.19019
$219$	1.25274	0.0846520
$220$	24.2248	1.63323
$221$	10.4947	0.705948
$222$	10.9971	0.738079
$223$	−11.0905	−0.742677	−0.371339	−	0.928498i	$-0.621101\pi$
$223$	−11.0905	−0.742677	−0.371339	+	0.928498i	$0.621101\pi$
$224$	19.7844	1.32190
$225$	−0.625236	−0.0416824
$226$	−31.1020	−2.06887
$227$	5.41443	0.359369	0.179684	−	0.983724i	$-0.442492\pi$
$227$	5.41443	0.359369	0.179684	+	0.983724i	$0.442492\pi$
$228$	2.04862	0.135673
$229$	21.2234	1.40248	0.701242	−	0.712923i	$-0.252629\pi$
$229$	21.2234	1.40248	0.701242	+	0.712923i	$0.252629\pi$
$230$	−25.2884	−1.66746
$231$	−11.3180	−0.744672
$232$	13.4059	0.880139
$233$	−8.63043	−0.565398	−0.282699	−	0.959209i	$-0.591230\pi$
$233$	−8.63043	−0.565398	−0.282699	+	0.959209i	$0.591230\pi$
$234$	−7.93293	−0.518592
$235$	−24.0460	−1.56859
$236$	11.2462	0.732066
$237$	11.4346	0.742757
$238$	−19.1057	−1.23844
$239$	2.92054	0.188914	0.0944571	−	0.995529i	$-0.469888\pi$
$239$	2.92054	0.188914	0.0944571	+	0.995529i	$0.469888\pi$
$240$	2.32212	0.149892
$241$	22.6831	1.46115	0.730575	−	0.682833i	$-0.239252\pi$
$241$	22.6831	1.46115	0.730575	+	0.682833i	$0.239252\pi$
$242$	−9.33019	−0.599767
$243$	−1.00000	−0.0641500
$244$	−0.794334	−0.0508520
$245$	3.00405	0.191921
$246$	−13.8943	−0.885869
$247$	−2.45207	−0.156021
$248$	6.73322	0.427560
$249$	−17.8509	−1.13125
$250$	26.2358	1.65930
$251$	18.0486	1.13922	0.569610	−	0.821915i	$-0.307094\pi$
$251$	18.0486	1.13922	0.569610	+	0.821915i	$0.307094\pi$
$252$	8.63298	0.543826
$253$	21.1282	1.32832
$254$	36.4948	2.28989
$255$	−6.17006	−0.386384
$256$	−8.16775	−0.510484
$257$	−13.9843	−0.872316	−0.436158	−	0.899870i	$-0.643661\pi$
$257$	−13.9843	−0.872316	−0.436158	+	0.899870i	$0.643661\pi$
$258$	22.4252	1.39613
$259$	14.3244	0.890077
$260$	22.1167	1.37162
$261$	−6.18357	−0.382753
$262$	4.28676	0.264837
$263$	7.27211	0.448417	0.224209	−	0.974541i	$-0.428020\pi$
$263$	7.27211	0.448417	0.224209	+	0.974541i	$0.428020\pi$
$264$	8.44797	0.519937
$265$	−4.45817	−0.273863
$266$	4.46403	0.273707
$267$	−8.46852	−0.518265
$268$	1.27034	0.0775985
$269$	4.61072	0.281121	0.140560	−	0.990072i	$-0.455110\pi$
$269$	4.61072	0.281121	0.140560	+	0.990072i	$0.455110\pi$
$270$	4.66395	0.283839
$271$	8.34469	0.506904	0.253452	−	0.967348i	$-0.418434\pi$
$271$	8.34469	0.506904	0.253452	+	0.967348i	$0.418434\pi$
$272$	−3.27505	−0.198579
$273$	−10.3331	−0.625389
$274$	1.55214	0.0937683
$275$	−2.43635	−0.146918
$276$	−16.1158	−0.970059
$277$	−7.39540	−0.444346	−0.222173	−	0.975007i	$-0.571315\pi$
$277$	−7.39540	−0.444346	−0.222173	+	0.975007i	$0.571315\pi$
$278$	−24.8292	−1.48916
$279$	−3.10575	−0.185936
$280$	−13.1707	−0.787099
$281$	−32.8967	−1.96245	−0.981226	−	0.192864i	$-0.938222\pi$
$281$	−32.8967	−1.96245	−0.981226	+	0.192864i	$0.938222\pi$
$282$	−25.6356	−1.52658
$283$	−20.2100	−1.20136	−0.600680	−	0.799489i	$-0.705104\pi$
$283$	−20.2100	−1.20136	−0.600680	+	0.799489i	$0.705104\pi$
$284$	−31.7977	−1.88685
$285$	1.44163	0.0853947
$286$	−30.9122	−1.82788
$287$	−18.0982	−1.06830
$288$	6.81159	0.401377
$289$	−8.29791	−0.488112
$290$	28.8398	1.69353
$291$	0.117045	0.00686132
$292$	−3.72345	−0.217898
$293$	5.25182	0.306815	0.153407	−	0.988163i	$-0.450975\pi$
$293$	5.25182	0.306815	0.153407	+	0.988163i	$0.450975\pi$
$294$	3.20262	0.186781
$295$	7.91403	0.460772
$296$	−10.6920	−0.621460
$297$	−3.89669	−0.226109
$298$	−39.6105	−2.29458
$299$	19.2896	1.11555
$300$	1.85836	0.107292
$301$	29.2101	1.68364
$302$	32.9639	1.89686
$303$	−19.0827	−1.09628
$304$	0.765213	0.0438880
$305$	−0.558977	−0.0320070
$306$	−6.57792	−0.376035
$307$	−19.9287	−1.13739	−0.568697	−	0.822547i	$-0.692552\pi$
$307$	−19.9287	−1.13739	−0.568697	+	0.822547i	$0.692552\pi$
$308$	33.6401	1.91682
$309$	3.52058	0.200279
$310$	14.4851	0.822696
$311$	13.6547	0.774287	0.387143	−	0.922020i	$-0.373462\pi$
$311$	13.6547	0.774287	0.387143	+	0.922020i	$0.373462\pi$
$312$	7.71282	0.436653
$313$	−27.9120	−1.57768	−0.788839	−	0.614600i	$-0.789317\pi$
$313$	−27.9120	−1.57768	−0.788839	+	0.614600i	$0.789317\pi$
$314$	39.3504	2.22067
$315$	6.07508	0.342292
$316$	−33.9865	−1.91189
$317$	3.08740	0.173406	0.0867028	−	0.996234i	$-0.472367\pi$
$317$	3.08740	0.173406	0.0867028	+	0.996234i	$0.472367\pi$
$318$	−4.75287	−0.266528
$319$	−24.0955	−1.34909
$320$	−27.1247	−1.51632
$321$	−15.1126	−0.843506
$322$	−35.1170	−1.95700
$323$	−2.03324	−0.113132
$324$	2.97225	0.165125
$325$	−2.22434	−0.123384
$326$	6.14496	0.340338
$327$	−14.5022	−0.801973
$328$	13.5088	0.745899
$329$	−33.3919	−1.84095
$330$	18.1740	1.00044
$331$	−13.5617	−0.745420	−0.372710	−	0.927948i	$-0.621571\pi$
$331$	−13.5617	−0.745420	−0.372710	+	0.927948i	$0.621571\pi$
$332$	53.0574	2.91190
$333$	4.93177	0.270259
$334$	−31.9722	−1.74944
$335$	0.893948	0.0488416
$336$	3.22464	0.175919
$337$	−19.4030	−1.05695	−0.528476	−	0.848948i	$-0.677236\pi$
$337$	−19.4030	−1.05695	−0.528476	+	0.848948i	$0.677236\pi$
$338$	0.765947	0.0416620
$339$	−13.9480	−0.757551
$340$	18.3390	0.994571
$341$	−12.1021	−0.655368
$342$	1.53692	0.0831074
$343$	−16.1600	−0.872560
$344$	−21.8030	−1.17554
$345$	−11.3408	−0.610569
$346$	−50.5206	−2.71600
$347$	11.6520	0.625514	0.312757	−	0.949833i	$-0.398747\pi$
$347$	11.6520	0.625514	0.312757	+	0.949833i	$0.398747\pi$
$348$	18.3791	0.985225
$349$	−0.00783174	−0.000419224 0	−0.000209612	−	1.00000i	$-0.500067\pi$
$349$	−0.00783174	−0.000419224 0	−0.000209612		1.00000i	$0.500067\pi$
$350$	4.04944	0.216452
$351$	−3.55760	−0.189891
$352$	26.5427	1.41473
$353$	8.59526	0.457480	0.228740	−	0.973488i	$-0.426540\pi$
$353$	8.59526	0.457480	0.228740	+	0.973488i	$0.426540\pi$
$354$	8.43717	0.448430
$355$	−22.3762	−1.18761
$356$	25.1706	1.33404
$357$	−8.56814	−0.453474
$358$	9.56588	0.505572
$359$	−1.15836	−0.0611360	−0.0305680	−	0.999533i	$-0.509732\pi$
$359$	−1.15836	−0.0611360	−0.0305680	+	0.999533i	$0.509732\pi$
$360$	−4.53455	−0.238992
$361$	−18.5249	−0.974997
$362$	−0.363692	−0.0191152
$363$	−4.18421	−0.219614
$364$	30.7127	1.60978
$365$	−2.62021	−0.137148
$366$	−0.595928	−0.0311496
$367$	−8.34367	−0.435536	−0.217768	−	0.976001i	$-0.569878\pi$
$367$	−8.34367	−0.435536	−0.217768	+	0.976001i	$0.569878\pi$
$368$	−6.01968	−0.313797
$369$	−6.23104	−0.324375
$370$	−23.0015	−1.19579
$371$	−6.19090	−0.321415
$372$	9.23107	0.478609
$373$	25.6216	1.32664	0.663318	−	0.748338i	$-0.269148\pi$
$373$	25.6216	1.32664	0.663318	+	0.748338i	$0.269148\pi$
$374$	−25.6321	−1.32541
$375$	11.7657	0.607579
$376$	24.9243	1.28537
$377$	−21.9986	−1.13299
$378$	6.47666	0.333124
$379$	33.8389	1.73819	0.869093	−	0.494648i	$-0.164703\pi$
$379$	33.8389	1.73819	0.869093	+	0.494648i	$0.164703\pi$
$380$	−4.28488	−0.219810
$381$	16.3664	0.838478
$382$	−13.6990	−0.700900
$383$	−27.3896	−1.39954	−0.699771	−	0.714368i	$-0.746714\pi$
$383$	−27.3896	−1.39954	−0.699771	+	0.714368i	$0.746714\pi$
$384$	−15.2945	−0.780496
$385$	23.6727	1.20647
$386$	2.43912	0.124148
$387$	10.0568	0.511215
$388$	−0.347889	−0.0176614
$389$	−16.0330	−0.812907	−0.406453	−	0.913671i	$-0.633235\pi$
$389$	−16.0330	−0.812907	−0.406453	+	0.913671i	$0.633235\pi$
$390$	16.5925	0.840192
$391$	15.9948	0.808891
$392$	−3.11376	−0.157269
$393$	1.92244	0.0969743
$394$	−35.4486	−1.78588
$395$	−23.9165	−1.20337
$396$	11.5820	0.582015
$397$	17.5268	0.879643	0.439822	−	0.898085i	$-0.355042\pi$
$397$	17.5268	0.879643	0.439822	+	0.898085i	$0.355042\pi$
$398$	−37.5354	−1.88148
$399$	2.00194	0.100222
$400$	0.694145	0.0347073
$401$	6.44681	0.321938	0.160969	−	0.986959i	$-0.448538\pi$
$401$	6.44681	0.321938	0.160969	+	0.986959i	$0.448538\pi$
$402$	0.953041	0.0475334
$403$	−11.0490	−0.550390
$404$	56.7188	2.82186
$405$	2.09159	0.103932
$406$	40.0489	1.98759
$407$	19.2176	0.952581
$408$	6.39541	0.316620
$409$	15.2352	0.753330	0.376665	−	0.926350i	$-0.377071\pi$
$409$	15.2352	0.753330	0.376665	+	0.926350i	$0.377071\pi$
$410$	29.0613	1.43523
$411$	0.696073	0.0343348
$412$	−10.4640	−0.515527
$413$	10.9899	0.540779
$414$	−12.0905	−0.594214
$415$	37.3368	1.83279
$416$	24.2329	1.18812
$417$	−11.1349	−0.545279
$418$	5.98892	0.292928
$419$	−1.07395	−0.0524657	−0.0262329	−	0.999656i	$-0.508351\pi$
$419$	−1.07395	−0.0524657	−0.0262329	+	0.999656i	$0.508351\pi$
$420$	−18.0567	−0.881076
$421$	−38.1037	−1.85706	−0.928531	−	0.371254i	$-0.878928\pi$
$421$	−38.1037	−1.85706	−0.928531	+	0.371254i	$0.878928\pi$
$422$	−14.9463	−0.727575
$423$	−11.4965	−0.558980
$424$	4.62100	0.224415
$425$	−1.84440	−0.0894667
$426$	−23.8554	−1.15580
$427$	−0.776232	−0.0375645
$428$	44.9186	2.17122
$429$	−13.8629	−0.669305
$430$	−46.9043	−2.26193
$431$	−3.99737	−0.192547	−0.0962734	−	0.995355i	$-0.530692\pi$
$431$	−3.99737	−0.192547	−0.0962734	+	0.995355i	$0.530692\pi$
$432$	1.11021	0.0534152
$433$	−4.46455	−0.214553	−0.107276	−	0.994229i	$-0.534213\pi$
$433$	−4.46455	−0.214553	−0.107276	+	0.994229i	$0.534213\pi$
$434$	20.1149	0.965545
$435$	12.9335	0.620114
$436$	43.1042	2.06432
$437$	−3.73717	−0.178773
$438$	−2.79342	−0.133475
$439$	32.5749	1.55471	0.777356	−	0.629060i	$-0.216560\pi$
$439$	32.5749	1.55471	0.777356	+	0.629060i	$0.216560\pi$
$440$	−17.6697	−0.842371
$441$	1.43625	0.0683927
$442$	−23.4016	−1.11310
$443$	4.68651	0.222663	0.111331	−	0.993783i	$-0.464489\pi$
$443$	4.68651	0.222663	0.111331	+	0.993783i	$0.464489\pi$
$444$	−14.6585	−0.695661
$445$	17.7127	0.839663
$446$	24.7303	1.17101
$447$	−17.7637	−0.840195
$448$	−37.6671	−1.77960
$449$	29.3205	1.38372	0.691861	−	0.722031i	$-0.256791\pi$
$449$	29.3205	1.38372	0.691861	+	0.722031i	$0.256791\pi$
$450$	1.39419	0.0657225
$451$	−24.2804	−1.14332
$452$	41.4570	1.94997
$453$	14.7830	0.694565
$454$	−12.0734	−0.566633
$455$	21.6127	1.01322
$456$	−1.49428	−0.0699761
$457$	−34.7450	−1.62530	−0.812651	−	0.582750i	$-0.801977\pi$
$457$	−34.7450	−1.62530	−0.812651	+	0.582750i	$0.801977\pi$
$458$	−47.3252	−2.21136
$459$	−2.94993	−0.137691
$460$	33.7078	1.57163
$461$	−18.4815	−0.860767	−0.430384	−	0.902646i	$-0.641622\pi$
$461$	−18.4815	−0.860767	−0.430384	+	0.902646i	$0.641622\pi$
$462$	25.2376	1.17416
$463$	6.05917	0.281594	0.140797	−	0.990039i	$-0.455034\pi$
$463$	6.05917	0.281594	0.140797	+	0.990039i	$0.455034\pi$
$464$	6.86508	0.318703
$465$	6.49596	0.301243
$466$	19.2446	0.891489
$467$	−17.1793	−0.794963	−0.397481	−	0.917610i	$-0.630116\pi$
$467$	−17.1793	−0.794963	−0.397481	+	0.917610i	$0.630116\pi$
$468$	10.5741	0.488787
$469$	1.24139	0.0573223
$470$	53.6192	2.47327
$471$	17.6471	0.813134
$472$	−8.20307	−0.377577
$473$	39.1882	1.80187
$474$	−25.4975	−1.17114
$475$	0.430943	0.0197730
$476$	25.4667	1.16726
$477$	−2.13147	−0.0975933
$478$	−6.51239	−0.297870
$479$	−4.52027	−0.206536	−0.103268	−	0.994654i	$-0.532930\pi$
$479$	−4.52027	−0.206536	−0.103268	+	0.994654i	$0.532930\pi$
$480$	−14.2471	−0.650287
$481$	17.5453	0.799995
$482$	−50.5801	−2.30386
$483$	−15.7486	−0.716585
$484$	12.4365	0.565298
$485$	−0.244811	−0.0111163
$486$	2.22986	0.101148
$487$	42.8789	1.94303	0.971514	−	0.236983i	$-0.0761584\pi$
$487$	42.8789	1.94303	0.971514	+	0.236983i	$0.0761584\pi$
$488$	0.579393	0.0262279
$489$	2.75577	0.124620
$490$	−6.69859	−0.302611
$491$	−14.1951	−0.640618	−0.320309	−	0.947313i	$-0.603787\pi$
$491$	−14.1951	−0.640618	−0.320309	+	0.947313i	$0.603787\pi$
$492$	18.5202	0.834956
$493$	−18.2411	−0.821537
$494$	5.46776	0.246006
$495$	8.15030	0.366329
$496$	3.44804	0.154822
$497$	−31.0731	−1.39382
$498$	39.8049	1.78370
$499$	−36.3469	−1.62711	−0.813556	−	0.581486i	$-0.802471\pi$
$499$	−36.3469	−1.62711	−0.813556	+	0.581486i	$0.802471\pi$
$500$	−34.9707	−1.56394
$501$	−14.3382	−0.640585
$502$	−40.2458	−1.79626
$503$	−5.74187	−0.256017	−0.128009	−	0.991773i	$-0.540859\pi$
$503$	−5.74187	−0.256017	−0.128009	+	0.991773i	$0.540859\pi$
$504$	−6.29696	−0.280489
$505$	39.9133	1.77612
$506$	−47.1129	−2.09442
$507$	0.343496	0.0152552
$508$	−48.6452	−2.15828
$509$	−30.2193	−1.33945	−0.669723	−	0.742611i	$-0.733587\pi$
$509$	−30.2193	−1.33945	−0.669723	+	0.742611i	$0.733587\pi$
$510$	13.7583	0.609229
$511$	−3.63860	−0.160962
$512$	−12.3762	−0.546955
$513$	0.689249	0.0304311
$514$	31.1830	1.37542
$515$	−7.36362	−0.324480
$516$	−29.8913	−1.31589
$517$	−44.7984	−1.97023
$518$	−31.9414	−1.40343
$519$	−22.6564	−0.994507
$520$	−16.1321	−0.707439
$521$	28.3786	1.24329	0.621644	−	0.783300i	$-0.286465\pi$
$521$	28.3786	1.24329	0.621644	+	0.783300i	$0.286465\pi$
$522$	13.7885	0.603504
$523$	−14.6558	−0.640853	−0.320427	−	0.947273i	$-0.603826\pi$
$523$	−14.6558	−0.640853	−0.320427	+	0.947273i	$0.603826\pi$
$524$	−5.71398	−0.249616
$525$	1.81601	0.0792572
$526$	−16.2157	−0.707040
$527$	−9.16174	−0.399092
$528$	4.32616	0.188272
$529$	6.39905	0.278219
$530$	9.94107	0.431812
$531$	3.78373	0.164200
$532$	−5.95027	−0.257977
$533$	−22.1675	−0.960182
$534$	18.8836	0.817173
$535$	31.6095	1.36660
$536$	−0.926598	−0.0400229
$537$	4.28991	0.185123
$538$	−10.2812	−0.443256
$539$	5.59662	0.241063
$540$	−6.21675	−0.267526
$541$	18.8900	0.812147	0.406073	−	0.913841i	$-0.366898\pi$
$541$	18.8900	0.812147	0.406073	+	0.913841i	$0.366898\pi$
$542$	−18.6074	−0.799258
$543$	−0.163101	−0.00699935
$544$	20.0937	0.861511
$545$	30.3327	1.29931
$546$	23.0414	0.986079
$547$	39.4285	1.68584	0.842920	−	0.538038i	$-0.180834\pi$
$547$	39.4285	1.68584	0.842920	+	0.538038i	$0.180834\pi$
$548$	−2.06891	−0.0883793
$549$	−0.267250	−0.0114059
$550$	5.43271	0.231652
$551$	4.26201	0.181568
$552$	11.7550	0.500327
$553$	−33.2120	−1.41232
$554$	16.4907	0.700621
$555$	−10.3153	−0.437858
$556$	33.0958	1.40357
$557$	16.1359	0.683700	0.341850	−	0.939754i	$-0.388946\pi$
$557$	16.1359	0.683700	0.341850	+	0.939754i	$0.388946\pi$
$558$	6.92537	0.293174
$559$	35.7780	1.51325
$560$	−6.74464	−0.285013
$561$	−11.4950	−0.485318
$562$	73.3548	3.09429
$563$	−24.4477	−1.03035	−0.515175	−	0.857085i	$-0.672273\pi$
$563$	−24.4477	−1.03035	−0.515175	+	0.857085i	$0.672273\pi$
$564$	34.1706	1.43884
$565$	29.1735	1.22734
$566$	45.0654	1.89424
$567$	2.90452	0.121978
$568$	23.1935	0.973178
$569$	−24.4054	−1.02313	−0.511564	−	0.859245i	$-0.670934\pi$
$569$	−24.4054	−1.02313	−0.511564	+	0.859245i	$0.670934\pi$
$570$	−3.21462	−0.134646
$571$	42.2073	1.76632	0.883159	−	0.469073i	$-0.155412\pi$
$571$	42.2073	1.76632	0.883159	+	0.469073i	$0.155412\pi$
$572$	41.2040	1.72282
$573$	−6.14344	−0.256646
$574$	40.3563	1.68444
$575$	−3.39008	−0.141376
$576$	−12.9684	−0.540351
$577$	−8.22412	−0.342375	−0.171187	−	0.985238i	$-0.554760\pi$
$577$	−8.22412	−0.342375	−0.171187	+	0.985238i	$0.554760\pi$
$578$	18.5031	0.769629
$579$	1.09385	0.0454588
$580$	−38.4417	−1.59620
$581$	51.8483	2.15103
$582$	−0.260994	−0.0108186
$583$	−8.30568	−0.343986
$584$	2.71591	0.112385
$585$	7.44105	0.307650
$586$	−11.7108	−0.483769
$587$	14.9798	0.618283	0.309141	−	0.951016i	$-0.399958\pi$
$587$	14.9798	0.618283	0.309141	+	0.951016i	$0.399958\pi$
$588$	−4.26889	−0.176046
$589$	2.14063	0.0882032
$590$	−17.6471	−0.726521
$591$	−15.8973	−0.653927
$592$	−5.47532	−0.225034
$593$	0.157192	0.00645511	0.00322755	−	0.999995i	$-0.498973\pi$
$593$	0.157192	0.00645511	0.00322755	+	0.999995i	$0.498973\pi$
$594$	8.68906	0.356516
$595$	17.9211	0.734692
$596$	52.7983	2.16270
$597$	−16.8331	−0.688933
$598$	−43.0130	−1.75893
$599$	−14.2640	−0.582809	−0.291405	−	0.956600i	$-0.594123\pi$
$599$	−14.2640	−0.582809	−0.291405	+	0.956600i	$0.594123\pi$
$600$	−1.35550	−0.0553382
$601$	−32.4898	−1.32529	−0.662643	−	0.748935i	$-0.730565\pi$
$601$	−32.4898	−1.32529	−0.662643	+	0.748935i	$0.730565\pi$
$602$	−65.1344	−2.65468
$603$	0.427400	0.0174051
$604$	−43.9388	−1.78784
$605$	8.75168	0.355806
$606$	42.5518	1.72855
$607$	29.4341	1.19469	0.597347	−	0.801983i	$-0.296222\pi$
$607$	29.4341	1.19469	0.597347	+	0.801983i	$0.296222\pi$
$608$	−4.69488	−0.190402
$609$	17.9603	0.727788
$610$	1.24644	0.0504668
$611$	−40.9000	−1.65464
$612$	8.76794	0.354423
$613$	−22.6378	−0.914331	−0.457166	−	0.889382i	$-0.651135\pi$
$613$	−22.6378	−0.914331	−0.457166	+	0.889382i	$0.651135\pi$
$614$	44.4382	1.79338
$615$	13.0328	0.525533
$616$	−24.5373	−0.988637
$617$	24.2941	0.978042	0.489021	−	0.872272i	$-0.337354\pi$
$617$	24.2941	0.978042	0.489021	+	0.872272i	$0.337354\pi$
$618$	−7.85038	−0.315788
$619$	48.3304	1.94256	0.971281	−	0.237936i	$-0.0764707\pi$
$619$	48.3304	1.94256	0.971281	+	0.237936i	$0.0764707\pi$
$620$	−19.3076	−0.775414
$621$	−5.42209	−0.217581
$622$	−30.4480	−1.22085
$623$	24.5970	0.985459
$624$	3.94969	0.158114
$625$	−21.4829	−0.859316
$626$	62.2396	2.48760
$627$	2.68579	0.107260
$628$	−52.4516	−2.09304
$629$	14.5484	0.580082
$630$	−13.5465	−0.539707
$631$	3.57339	0.142255	0.0711273	−	0.997467i	$-0.477340\pi$
$631$	3.57339	0.142255	0.0711273	+	0.997467i	$0.477340\pi$
$632$	24.7900	0.986095
$633$	−6.70281	−0.266413
$634$	−6.88445	−0.273416
$635$	−34.2320	−1.35845
$636$	6.33527	0.251210
$637$	5.10959	0.202449
$638$	53.7294	2.12717
$639$	−10.6982	−0.423213
$640$	31.9900	1.26451
$641$	−21.6114	−0.853597	−0.426799	−	0.904347i	$-0.640359\pi$
$641$	−21.6114	−0.853597	−0.426799	+	0.904347i	$0.640359\pi$
$642$	33.6990	1.32999
$643$	14.8946	0.587386	0.293693	−	0.955900i	$-0.405116\pi$
$643$	14.8946	0.587386	0.293693	+	0.955900i	$0.405116\pi$
$644$	46.8088	1.84452
$645$	−21.0347	−0.828241
$646$	4.53382	0.178381
$647$	−17.3031	−0.680256	−0.340128	−	0.940379i	$-0.610470\pi$
$647$	−17.3031	−0.680256	−0.340128	+	0.940379i	$0.610470\pi$
$648$	−2.16799	−0.0851665
$649$	14.7440	0.578754
$650$	4.95995	0.194545
$651$	9.02071	0.353550
$652$	−8.19084	−0.320778
$653$	12.9324	0.506083	0.253042	−	0.967455i	$-0.418569\pi$
$653$	12.9324	0.506083	0.253042	+	0.967455i	$0.418569\pi$
$654$	32.3378	1.26451
$655$	−4.02096	−0.157112
$656$	6.91778	0.270094
$657$	−1.25274	−0.0488739
$658$	74.4591	2.90272
$659$	7.96096	0.310115	0.155058	−	0.987905i	$-0.450444\pi$
$659$	7.96096	0.310115	0.155058	+	0.987905i	$0.450444\pi$
$660$	−24.2248	−0.942947
$661$	2.91796	0.113496	0.0567478	−	0.998389i	$-0.481927\pi$
$661$	2.91796	0.113496	0.0567478	+	0.998389i	$0.481927\pi$
$662$	30.2407	1.17534
$663$	−10.4947	−0.407579
$664$	−38.7005	−1.50187
$665$	−4.18724	−0.162374
$666$	−10.9971	−0.426130
$667$	−33.5278	−1.29820
$668$	42.6169	1.64890
$669$	11.0905	0.428785
$670$	−1.99337	−0.0770108
$671$	−1.04139	−0.0402024
$672$	−19.7844	−0.763200
$673$	−32.6592	−1.25892	−0.629460	−	0.777033i	$-0.716724\pi$
$673$	−32.6592	−1.25892	−0.629460	+	0.777033i	$0.716724\pi$
$674$	43.2660	1.66654
$675$	0.625236	0.0240653
$676$	−1.02096	−0.0392676
$677$	26.7618	1.02854	0.514270	−	0.857628i	$-0.328063\pi$
$677$	26.7618	1.02854	0.514270	+	0.857628i	$0.328063\pi$
$678$	31.1020	1.19447
$679$	−0.339961	−0.0130465
$680$	−13.3766	−0.512969
$681$	−5.41443	−0.207482
$682$	26.9860	1.03335
$683$	−32.2627	−1.23450	−0.617249	−	0.786767i	$-0.711753\pi$
$683$	−32.2627	−1.23450	−0.617249	+	0.786767i	$0.711753\pi$
$684$	−2.04862	−0.0783310
$685$	−1.45590	−0.0556272
$686$	36.0346	1.37581
$687$	−21.2234	−0.809725
$688$	−11.1652	−0.425668
$689$	−7.58291	−0.288886
$690$	25.2884	0.962711
$691$	−4.24703	−0.161565	−0.0807824	−	0.996732i	$-0.525742\pi$
$691$	−4.24703	−0.161565	−0.0807824	+	0.996732i	$0.525742\pi$
$692$	67.3407	2.55991
$693$	11.3180	0.429936
$694$	−25.9823	−0.986276
$695$	23.2897	0.883428
$696$	−13.4059	−0.508149
$697$	−18.3811	−0.696235
$698$	0.0174637	0.000661009 0
$699$	8.63043	0.326433
$700$	−5.39765	−0.204012
$701$	−6.49289	−0.245233	−0.122617	−	0.992454i	$-0.539129\pi$
$701$	−6.49289	−0.245233	−0.122617	+	0.992454i	$0.539129\pi$
$702$	7.93293	0.299409
$703$	−3.39922	−0.128204
$704$	−50.5340	−1.90457
$705$	24.0460	0.905626
$706$	−19.1662	−0.721329
$707$	55.4262	2.08452
$708$	−11.2462	−0.422658
$709$	−5.89677	−0.221458	−0.110729	−	0.993851i	$-0.535319\pi$
$709$	−5.89677	−0.221458	−0.110729	+	0.993851i	$0.535319\pi$
$710$	49.8958	1.87256
$711$	−11.4346	−0.428831
$712$	−18.3596	−0.688057
$713$	−16.8396	−0.630649
$714$	19.1057	0.715013
$715$	28.9955	1.08437
$716$	−12.7507	−0.476516
$717$	−2.92054	−0.109070
$718$	2.58298	0.0963960
$719$	31.0236	1.15699	0.578493	−	0.815688i	$-0.303641\pi$
$719$	31.0236	1.15699	0.578493	+	0.815688i	$0.303641\pi$
$720$	−2.32212	−0.0865401
$721$	−10.2256	−0.380821
$722$	41.3079	1.53732
$723$	−22.6831	−0.843595
$724$	0.484779	0.0180167
$725$	3.86619	0.143587
$726$	9.33019	0.346276
$727$	23.7574	0.881113	0.440556	−	0.897725i	$-0.354781\pi$
$727$	23.7574	0.881113	0.440556	+	0.897725i	$0.354781\pi$
$728$	−22.4021	−0.830276
$729$	1.00000	0.0370370
$730$	5.84270	0.216248
$731$	29.6668	1.09727
$732$	0.794334	0.0293594
$733$	−22.1131	−0.816765	−0.408383	−	0.912811i	$-0.633907\pi$
$733$	−22.1131	−0.816765	−0.408383	+	0.912811i	$0.633907\pi$
$734$	18.6052	0.686730
$735$	−3.00405	−0.110806
$736$	36.9330	1.36137
$737$	1.66545	0.0613476
$738$	13.8943	0.511457
$739$	4.74315	0.174480	0.0872398	−	0.996187i	$-0.472195\pi$
$739$	4.74315	0.174480	0.0872398	+	0.996187i	$0.472195\pi$
$740$	30.6596	1.12707
$741$	2.45207	0.0900790
$742$	13.8048	0.506790
$743$	37.1510	1.36294	0.681468	−	0.731848i	$-0.261342\pi$
$743$	37.1510	1.36294	0.681468	+	0.731848i	$0.261342\pi$
$744$	−6.73322	−0.246852
$745$	37.1545	1.36124
$746$	−57.1324	−2.09177
$747$	17.8509	0.653130
$748$	34.1660	1.24923
$749$	43.8950	1.60389
$750$	−26.2358	−0.957997
$751$	8.33373	0.304102	0.152051	−	0.988373i	$-0.451412\pi$
$751$	8.33373	0.304102	0.152051	+	0.988373i	$0.451412\pi$
$752$	12.7636	0.465440
$753$	−18.0486	−0.657729
$754$	49.0538	1.78643
$755$	−30.9200	−1.12529
$756$	−8.63298	−0.313978
$757$	20.6675	0.751172	0.375586	−	0.926788i	$-0.377441\pi$
$757$	20.6675	0.751172	0.375586	+	0.926788i	$0.377441\pi$
$758$	−75.4558	−2.74068
$759$	−21.1282	−0.766906
$760$	3.12543	0.113371
$761$	24.4477	0.886227	0.443113	−	0.896466i	$-0.353874\pi$
$761$	24.4477	0.886227	0.443113	+	0.896466i	$0.353874\pi$
$762$	−36.4948	−1.32207
$763$	42.1219	1.52492
$764$	18.2599	0.660618
$765$	6.17006	0.223079
$766$	61.0748	2.20672
$767$	13.4610	0.486048
$768$	8.16775	0.294728
$769$	11.4574	0.413165	0.206583	−	0.978429i	$-0.433766\pi$
$769$	11.4574	0.413165	0.206583	+	0.978429i	$0.433766\pi$
$770$	−52.7867	−1.90230
$771$	13.9843	0.503632
$772$	−3.25119	−0.117013
$773$	−48.7204	−1.75235	−0.876175	−	0.481993i	$-0.839913\pi$
$773$	−48.7204	−1.75235	−0.876175	+	0.481993i	$0.839913\pi$
$774$	−22.4252	−0.806056
$775$	1.94182	0.0697524
$776$	0.253753	0.00910919
$777$	−14.3244	−0.513886
$778$	35.7513	1.28175
$779$	4.29473	0.153875
$780$	−22.1167	−0.791905
$781$	−41.6875	−1.49170
$782$	−35.6661	−1.27542
$783$	6.18357	0.220983
$784$	−1.59454	−0.0569479
$785$	−36.9105	−1.31739
$786$	−4.28676	−0.152904
$787$	6.49099	0.231379	0.115689	−	0.993285i	$-0.463092\pi$
$787$	6.49099	0.231379	0.115689	+	0.993285i	$0.463092\pi$
$788$	47.2508	1.68324
$789$	−7.27211	−0.258894
$790$	53.3304	1.89741
$791$	40.5122	1.44045
$792$	−8.44797	−0.300186
$793$	−0.950766	−0.0337627
$794$	−39.0821	−1.38697
$795$	4.45817	0.158115
$796$	50.0322	1.77335
$797$	4.17397	0.147850	0.0739249	−	0.997264i	$-0.476447\pi$
$797$	4.17397	0.147850	0.0739249	+	0.997264i	$0.476447\pi$
$798$	−4.46403	−0.158025
$799$	−33.9139	−1.19979
$800$	−4.25885	−0.150573
$801$	8.46852	0.299221
$802$	−14.3754	−0.507615
$803$	−4.88152	−0.172265
$804$	−1.27034	−0.0448015
$805$	32.9396	1.16097
$806$	24.6377	0.867825
$807$	−4.61072	−0.162305
$808$	−41.3711	−1.45543
$809$	44.3278	1.55848	0.779242	−	0.626724i	$-0.215605\pi$
$809$	44.3278	1.55848	0.779242	+	0.626724i	$0.215605\pi$
$810$	−4.66395	−0.163875
$811$	−38.0807	−1.33719	−0.668597	−	0.743625i	$-0.733105\pi$
$811$	−38.0807	−1.33719	−0.668597	+	0.743625i	$0.733105\pi$
$812$	−53.3826	−1.87336
$813$	−8.34469	−0.292661
$814$	−42.8525	−1.50198
$815$	−5.76394	−0.201902
$816$	3.27505	0.114650
$817$	−6.93162	−0.242507
$818$	−33.9722	−1.18781
$819$	10.3331	0.361068
$820$	−38.7368	−1.35275
$821$	33.5641	1.17139	0.585697	−	0.810530i	$-0.300821\pi$
$821$	33.5641	1.17139	0.585697	+	0.810530i	$0.300821\pi$
$822$	−1.55214	−0.0541372
$823$	8.73259	0.304399	0.152199	−	0.988350i	$-0.451364\pi$
$823$	8.73259	0.304399	0.152199	+	0.988350i	$0.451364\pi$
$824$	7.63256	0.265893
$825$	2.43635	0.0848229
$826$	−24.5059	−0.852671
$827$	29.6919	1.03249	0.516245	−	0.856441i	$-0.327329\pi$
$827$	29.6919	1.03249	0.516245	+	0.856441i	$0.327329\pi$
$828$	16.1158	0.560064
$829$	−34.6231	−1.20251	−0.601255	−	0.799057i	$-0.705333\pi$
$829$	−34.6231	−1.20251	−0.601255	+	0.799057i	$0.705333\pi$
$830$	−83.2557	−2.88985
$831$	7.39540	0.256543
$832$	−46.1364	−1.59949
$833$	4.23683	0.146797
$834$	24.8292	0.859766
$835$	29.9898	1.03784
$836$	−7.98285	−0.276093
$837$	3.10575	0.107350
$838$	2.39475	0.0827251
$839$	−35.8036	−1.23608	−0.618040	−	0.786147i	$-0.712073\pi$
$839$	−35.8036	−1.23608	−0.618040	+	0.786147i	$0.712073\pi$
$840$	13.1707	0.454432
$841$	9.23648	0.318499
$842$	84.9658	2.92812
$843$	32.8967	1.13302
$844$	19.9225	0.685760
$845$	−0.718454	−0.0247156
$846$	25.6356	0.881369
$847$	12.1531	0.417587
$848$	2.36639	0.0812620
$849$	20.2100	0.693606
$850$	4.11275	0.141066
$851$	26.7405	0.916653
$852$	31.7977	1.08937
$853$	−23.8365	−0.816145	−0.408073	−	0.912949i	$-0.633799\pi$
$853$	−23.8365	−0.816145	−0.408073	+	0.912949i	$0.633799\pi$
$854$	1.73089	0.0592297
$855$	−1.44163	−0.0493026
$856$	−32.7640	−1.11985
$857$	46.7221	1.59600	0.797999	−	0.602659i	$-0.205892\pi$
$857$	46.7221	1.59600	0.797999	+	0.602659i	$0.205892\pi$
$858$	30.9122	1.05532
$859$	36.3763	1.24114	0.620571	−	0.784150i	$-0.286901\pi$
$859$	36.3763	1.24114	0.620571	+	0.784150i	$0.286901\pi$
$860$	62.5205	2.13193
$861$	18.0982	0.616785
$862$	8.91357	0.303597
$863$	51.1111	1.73984	0.869921	−	0.493192i	$-0.164170\pi$
$863$	51.1111	1.73984	0.869921	+	0.493192i	$0.164170\pi$
$864$	−6.81159	−0.231735
$865$	47.3881	1.61124
$866$	9.95531	0.338295
$867$	8.29791	0.281812
$868$	−26.8118	−0.910053
$869$	−44.5571	−1.51150
$870$	−28.8398	−0.977762
$871$	1.52052	0.0515208
$872$	−31.4405	−1.06471
$873$	−0.117045	−0.00396139
$874$	8.33334	0.281879
$875$	−34.1738	−1.15528
$876$	3.72345	0.125804
$877$	30.8851	1.04292	0.521458	−	0.853277i	$-0.325388\pi$
$877$	30.8851	1.04292	0.521458	+	0.853277i	$0.325388\pi$
$878$	−72.6372	−2.45139
$879$	−5.25182	−0.177140
$880$	−9.04857	−0.305027
$881$	−41.0388	−1.38263	−0.691317	−	0.722552i	$-0.742969\pi$
$881$	−41.0388	−1.38263	−0.691317	+	0.722552i	$0.742969\pi$
$882$	−3.20262	−0.107838
$883$	47.0021	1.58175	0.790874	−	0.611979i	$-0.209626\pi$
$883$	47.0021	1.58175	0.790874	+	0.611979i	$0.209626\pi$
$884$	31.1928	1.04913
$885$	−7.91403	−0.266027
$886$	−10.4502	−0.351083
$887$	−0.610338	−0.0204931	−0.0102466	−	0.999948i	$-0.503262\pi$
$887$	−0.610338	−0.0204931	−0.0102466	+	0.999948i	$0.503262\pi$
$888$	10.6920	0.358800
$889$	−47.5367	−1.59433
$890$	−39.4968	−1.32394
$891$	3.89669	0.130544
$892$	−32.9639	−1.10371
$893$	7.92396	0.265165
$894$	39.6105	1.32477
$895$	−8.97275	−0.299926
$896$	44.4233	1.48408
$897$	−19.2896	−0.644061
$898$	−65.3806	−2.18178
$899$	19.2046	0.640509
$900$	−1.85836	−0.0619453
$901$	−6.28769	−0.209473
$902$	54.1419	1.80273
$903$	−29.2101	−0.972053
$904$	−30.2390	−1.00574
$905$	0.341142	0.0113399
$906$	−32.9639	−1.09515
$907$	1.95914	0.0650522	0.0325261	−	0.999471i	$-0.489645\pi$
$907$	1.95914	0.0650522	0.0325261	+	0.999471i	$0.489645\pi$
$908$	16.0931	0.534067
$909$	19.0827	0.632935
$910$	−48.1932	−1.59759
$911$	−27.6421	−0.915825	−0.457913	−	0.888997i	$-0.651403\pi$
$911$	−27.6421	−0.915825	−0.457913	+	0.888997i	$0.651403\pi$
$912$	−0.765213	−0.0253387
$913$	69.5594	2.30208
$914$	77.4763	2.56269
$915$	0.558977	0.0184792
$916$	63.0815	2.08427
$917$	−5.58377	−0.184392
$918$	6.57792	0.217104
$919$	25.2693	0.833558	0.416779	−	0.909008i	$-0.363159\pi$
$919$	25.2693	0.833558	0.416779	+	0.909008i	$0.363159\pi$
$920$	−24.5867	−0.810600
$921$	19.9287	0.656675
$922$	41.2110	1.35721
$923$	−38.0598	−1.25275
$924$	−33.6401	−1.10668
$925$	−3.08352	−0.101386
$926$	−13.5111	−0.444002
$927$	−3.52058	−0.115631
$928$	−42.1199	−1.38265
$929$	20.0317	0.657217	0.328609	−	0.944466i	$-0.393420\pi$
$929$	20.0317	0.657217	0.328609	+	0.944466i	$0.393420\pi$
$930$	−14.4851	−0.474984
$931$	−0.989931	−0.0324437
$932$	−25.6518	−0.840253
$933$	−13.6547	−0.447035
$934$	38.3073	1.25345
$935$	24.0428	0.786284
$936$	−7.71282	−0.252101
$937$	−57.0962	−1.86525	−0.932625	−	0.360846i	$-0.882488\pi$
$937$	−57.0962	−1.86525	−0.932625	+	0.360846i	$0.882488\pi$
$938$	−2.76813	−0.0903826
$939$	27.9120	0.910873
$940$	−71.4709	−2.33112
$941$	−40.1687	−1.30946	−0.654731	−	0.755862i	$-0.727218\pi$
$941$	−40.1687	−1.30946	−0.654731	+	0.755862i	$0.727218\pi$
$942$	−39.3504	−1.28211
$943$	−33.7852	−1.10020
$944$	−4.20075	−0.136723
$945$	−6.07508	−0.197622
$946$	−87.3840	−2.84110
$947$	15.2756	0.496389	0.248194	−	0.968710i	$-0.420163\pi$
$947$	15.2756	0.496389	0.248194	+	0.968710i	$0.420163\pi$
$948$	33.9865	1.10383
$949$	−4.45673	−0.144672
$950$	−0.960940	−0.0311770
$951$	−3.08740	−0.100116
$952$	−18.5756	−0.602039
$953$	−14.7577	−0.478048	−0.239024	−	0.971014i	$-0.576827\pi$
$953$	−14.7577	−0.478048	−0.239024	+	0.971014i	$0.576827\pi$
$954$	4.75287	0.153880
$955$	12.8496	0.415802
$956$	8.68060	0.280751
$957$	24.0955	0.778895
$958$	10.0795	0.325655
$959$	−2.02176	−0.0652860
$960$	27.1247	0.875445
$961$	−21.3543	−0.688849
$962$	−39.1234	−1.26139
$963$	15.1126	0.486998
$964$	67.4201	2.17145
$965$	−2.28788	−0.0736496
$966$	35.1170	1.12987
$967$	14.6376	0.470713	0.235356	−	0.971909i	$-0.424374\pi$
$967$	14.6376	0.470713	0.235356	+	0.971909i	$0.424374\pi$
$968$	−9.07132	−0.291563
$969$	2.03324	0.0653169
$970$	0.545894	0.0175276
$971$	36.7533	1.17947	0.589735	−	0.807596i	$-0.299232\pi$
$971$	36.7533	1.17947	0.589735	+	0.807596i	$0.299232\pi$
$972$	−2.97225	−0.0953351
$973$	32.3416	1.03682
$974$	−95.6137	−3.06366
$975$	2.22434	0.0712358
$976$	0.296704	0.00949727
$977$	−2.68474	−0.0858925	−0.0429463	−	0.999077i	$-0.513674\pi$
$977$	−2.68474	−0.0858925	−0.0429463	+	0.999077i	$0.513674\pi$
$978$	−6.14496	−0.196494
$979$	32.9992	1.05466
$980$	8.92879	0.285220
$981$	14.5022	0.463019
$982$	31.6531	1.01009
$983$	−13.5066	−0.430795	−0.215397	−	0.976526i	$-0.569105\pi$
$983$	−13.5066	−0.430795	−0.215397	+	0.976526i	$0.569105\pi$
$984$	−13.5088	−0.430645
$985$	33.2507	1.05945
$986$	40.6750	1.29536
$987$	33.3919	1.06288
$988$	−7.28817	−0.231868
$989$	54.5288	1.73391
$990$	−18.1740	−0.577607
$991$	28.8603	0.916779	0.458389	−	0.888751i	$-0.348426\pi$
$991$	28.8603	0.916779	0.458389	+	0.888751i	$0.348426\pi$
$992$	−21.1551	−0.671674
$993$	13.5617	0.430368
$994$	69.2885	2.19770
$995$	35.2080	1.11617
$996$	−53.0574	−1.68119
$997$	−28.6980	−0.908875	−0.454438	−	0.890779i	$-0.650160\pi$
$997$	−28.6980	−0.908875	−0.454438	+	0.890779i	$0.650160\pi$
$998$	81.0484	2.56554
$999$	−4.93177	−0.156034

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.c.1.17	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.c.1.17	✓	119	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)

\(f(q)\)	\(=\)	\(q-2.22986 q^{2} -1.00000 q^{3} +2.97225 q^{4} +2.09159 q^{5} +2.22986 q^{6} +2.90452 q^{7} -2.16799 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.22986 q^{2} -1.00000 q^{3} +2.97225 q^{4} +2.09159 q^{5} +2.22986 q^{6} +2.90452 q^{7} -2.16799 q^{8} +1.00000 q^{9} -4.66395 q^{10} +3.89669 q^{11} -2.97225 q^{12} +3.55760 q^{13} -6.47666 q^{14} -2.09159 q^{15} -1.11021 q^{16} +2.94993 q^{17} -2.22986 q^{18} -0.689249 q^{19} +6.21675 q^{20} -2.90452 q^{21} -8.68906 q^{22} +5.42209 q^{23} +2.16799 q^{24} -0.625236 q^{25} -7.93293 q^{26} -1.00000 q^{27} +8.63298 q^{28} -6.18357 q^{29} +4.66395 q^{30} -3.10575 q^{31} +6.81159 q^{32} -3.89669 q^{33} -6.57792 q^{34} +6.07508 q^{35} +2.97225 q^{36} +4.93177 q^{37} +1.53692 q^{38} -3.55760 q^{39} -4.53455 q^{40} -6.23104 q^{41} +6.47666 q^{42} +10.0568 q^{43} +11.5820 q^{44} +2.09159 q^{45} -12.0905 q^{46} -11.4965 q^{47} +1.11021 q^{48} +1.43625 q^{49} +1.39419 q^{50} -2.94993 q^{51} +10.5741 q^{52} -2.13147 q^{53} +2.22986 q^{54} +8.15030 q^{55} -6.29696 q^{56} +0.689249 q^{57} +13.7885 q^{58} +3.78373 q^{59} -6.21675 q^{60} -0.267250 q^{61} +6.92537 q^{62} +2.90452 q^{63} -12.9684 q^{64} +7.44105 q^{65} +8.68906 q^{66} +0.427400 q^{67} +8.76794 q^{68} -5.42209 q^{69} -13.5465 q^{70} -10.6982 q^{71} -2.16799 q^{72} -1.25274 q^{73} -10.9971 q^{74} +0.625236 q^{75} -2.04862 q^{76} +11.3180 q^{77} +7.93293 q^{78} -11.4346 q^{79} -2.32212 q^{80} +1.00000 q^{81} +13.8943 q^{82} +17.8509 q^{83} -8.63298 q^{84} +6.17006 q^{85} -22.4252 q^{86} +6.18357 q^{87} -8.44797 q^{88} +8.46852 q^{89} -4.66395 q^{90} +10.3331 q^{91} +16.1158 q^{92} +3.10575 q^{93} +25.6356 q^{94} -1.44163 q^{95} -6.81159 q^{96} -0.117045 q^{97} -3.20262 q^{98} +3.89669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * q^99

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