LMFDB - Embedded newform 6047.2.a.a.1.10

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:	$1$
Dimension:	$217$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-2.62503 q^{2} +1.59617 q^{3} +4.89080 q^{4} +2.83370 q^{5} -4.19001 q^{6} -4.08027 q^{7} -7.58846 q^{8} -0.452230 q^{9} +O(q^{10})$	\(q-2.62503 q^{2} +1.59617 q^{3} +4.89080 q^{4} +2.83370 q^{5} -4.19001 q^{6} -4.08027 q^{7} -7.58846 q^{8} -0.452230 q^{9} -7.43856 q^{10} -4.35517 q^{11} +7.80657 q^{12} +1.46745 q^{13} +10.7108 q^{14} +4.52308 q^{15} +10.1384 q^{16} +0.159171 q^{17} +1.18712 q^{18} +6.75436 q^{19} +13.8591 q^{20} -6.51281 q^{21} +11.4325 q^{22} +2.68913 q^{23} -12.1125 q^{24} +3.02987 q^{25} -3.85211 q^{26} -5.51036 q^{27} -19.9558 q^{28} +4.32781 q^{29} -11.8732 q^{30} +3.01180 q^{31} -11.4366 q^{32} -6.95161 q^{33} -0.417829 q^{34} -11.5623 q^{35} -2.21177 q^{36} -6.79443 q^{37} -17.7304 q^{38} +2.34231 q^{39} -21.5034 q^{40} +10.9065 q^{41} +17.0964 q^{42} -5.59742 q^{43} -21.3003 q^{44} -1.28149 q^{45} -7.05905 q^{46} -3.88077 q^{47} +16.1826 q^{48} +9.64856 q^{49} -7.95350 q^{50} +0.254064 q^{51} +7.17702 q^{52} -10.8337 q^{53} +14.4649 q^{54} -12.3413 q^{55} +30.9629 q^{56} +10.7811 q^{57} -11.3606 q^{58} -2.01215 q^{59} +22.1215 q^{60} -11.7386 q^{61} -7.90607 q^{62} +1.84522 q^{63} +9.74479 q^{64} +4.15832 q^{65} +18.2482 q^{66} -9.50300 q^{67} +0.778473 q^{68} +4.29231 q^{69} +30.3513 q^{70} -2.45794 q^{71} +3.43173 q^{72} -5.70698 q^{73} +17.8356 q^{74} +4.83619 q^{75} +33.0342 q^{76} +17.7703 q^{77} -6.14864 q^{78} +11.2325 q^{79} +28.7291 q^{80} -7.43880 q^{81} -28.6301 q^{82} +11.6365 q^{83} -31.8529 q^{84} +0.451042 q^{85} +14.6934 q^{86} +6.90794 q^{87} +33.0491 q^{88} -4.27952 q^{89} +3.36394 q^{90} -5.98759 q^{91} +13.1520 q^{92} +4.80735 q^{93} +10.1871 q^{94} +19.1398 q^{95} -18.2548 q^{96} -3.38747 q^{97} -25.3278 q^{98} +1.96954 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) $ 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * 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 $

$2$	−2.62503	−1.85618	−0.928090	−	0.372357i	$-0.878550\pi$
$2$	−2.62503	−1.85618	−0.928090	+	0.372357i	$0.878550\pi$
$3$	1.59617	0.921551	0.460776	−	0.887517i	$-0.347571\pi$
$3$	1.59617	0.921551	0.460776	+	0.887517i	$0.347571\pi$
$4$	4.89080	2.44540
$5$	2.83370	1.26727	0.633635	−	0.773632i	$-0.281562\pi$
$5$	2.83370	1.26727	0.633635	+	0.773632i	$0.281562\pi$
$6$	−4.19001	−1.71056
$7$	−4.08027	−1.54220	−0.771098	−	0.636717i	$-0.780292\pi$
$7$	−4.08027	−1.54220	−0.771098	+	0.636717i	$0.780292\pi$
$8$	−7.58846	−2.68293
$9$	−0.452230	−0.150743
$10$	−7.43856	−2.35228
$11$	−4.35517	−1.31313	−0.656567	−	0.754268i	$-0.727992\pi$
$11$	−4.35517	−1.31313	−0.656567	+	0.754268i	$0.727992\pi$
$12$	7.80657	2.25356
$13$	1.46745	0.406998	0.203499	−	0.979075i	$-0.434769\pi$
$13$	1.46745	0.406998	0.203499	+	0.979075i	$0.434769\pi$
$14$	10.7108	2.86259
$15$	4.52308	1.16785
$16$	10.1384	2.53459
$17$	0.159171	0.0386046	0.0193023	−	0.999814i	$-0.493856\pi$
$17$	0.159171	0.0386046	0.0193023	+	0.999814i	$0.493856\pi$
$18$	1.18712	0.279807
$19$	6.75436	1.54956	0.774778	−	0.632233i	$-0.217862\pi$
$19$	6.75436	1.54956	0.774778	+	0.632233i	$0.217862\pi$
$20$	13.8591	3.09898
$21$	−6.51281	−1.42121
$22$	11.4325	2.43741
$23$	2.68913	0.560721	0.280361	−	0.959895i	$-0.409546\pi$
$23$	2.68913	0.560721	0.280361	+	0.959895i	$0.409546\pi$
$24$	−12.1125	−2.47245
$25$	3.02987	0.605973
$26$	−3.85211	−0.755461
$27$	−5.51036	−1.06047
$28$	−19.9558	−3.77129
$29$	4.32781	0.803654	0.401827	−	0.915716i	$-0.368375\pi$
$29$	4.32781	0.803654	0.401827	+	0.915716i	$0.368375\pi$
$30$	−11.8732	−2.16775
$31$	3.01180	0.540934	0.270467	−	0.962729i	$-0.412822\pi$
$31$	3.01180	0.540934	0.270467	+	0.962729i	$0.412822\pi$
$32$	−11.4366	−2.02173
$33$	−6.95161	−1.21012
$34$	−0.417829	−0.0716570
$35$	−11.5623	−1.95438
$36$	−2.21177	−0.368628
$37$	−6.79443	−1.11700	−0.558499	−	0.829505i	$-0.688622\pi$
$37$	−6.79443	−1.11700	−0.558499	+	0.829505i	$0.688622\pi$
$38$	−17.7304	−2.87625
$39$	2.34231	0.375069
$40$	−21.5034	−3.39999
$41$	10.9065	1.70332	0.851658	−	0.524098i	$-0.175597\pi$
$41$	10.9065	1.70332	0.851658	+	0.524098i	$0.175597\pi$
$42$	17.0964	2.63802
$43$	−5.59742	−0.853599	−0.426799	−	0.904346i	$-0.640359\pi$
$43$	−5.59742	−0.853599	−0.426799	+	0.904346i	$0.640359\pi$
$44$	−21.3003	−3.21114
$45$	−1.28149	−0.191033
$46$	−7.05905	−1.04080
$47$	−3.88077	−0.566068	−0.283034	−	0.959110i	$-0.591341\pi$
$47$	−3.88077	−0.566068	−0.283034	+	0.959110i	$0.591341\pi$
$48$	16.1826	2.33575
$49$	9.64856	1.37837
$50$	−7.95350	−1.12480
$51$	0.254064	0.0355761
$52$	7.17702	0.995273
$53$	−10.8337	−1.48812	−0.744061	−	0.668111i	$-0.767103\pi$
$53$	−10.8337	−1.48812	−0.744061	+	0.668111i	$0.767103\pi$
$54$	14.4649	1.96842
$55$	−12.3413	−1.66410
$56$	30.9629	4.13760
$57$	10.7811	1.42800
$58$	−11.3606	−1.49173
$59$	−2.01215	−0.261960	−0.130980	−	0.991385i	$-0.541812\pi$
$59$	−2.01215	−0.261960	−0.130980	+	0.991385i	$0.541812\pi$
$60$	22.1215	2.85587
$61$	−11.7386	−1.50298	−0.751489	−	0.659745i	$-0.770664\pi$
$61$	−11.7386	−1.50298	−0.751489	+	0.659745i	$0.770664\pi$
$62$	−7.90607	−1.00407
$63$	1.84522	0.232476
$64$	9.74479	1.21810
$65$	4.15832	0.515776
$66$	18.2482	2.24620
$67$	−9.50300	−1.16098	−0.580488	−	0.814269i	$-0.697138\pi$
$67$	−9.50300	−1.16098	−0.580488	+	0.814269i	$0.697138\pi$
$68$	0.778473	0.0944037
$69$	4.29231	0.516733
$70$	30.3513	3.62768
$71$	−2.45794	−0.291703	−0.145852	−	0.989306i	$-0.546592\pi$
$71$	−2.45794	−0.291703	−0.145852	+	0.989306i	$0.546592\pi$
$72$	3.43173	0.404433
$73$	−5.70698	−0.667952	−0.333976	−	0.942582i	$-0.608390\pi$
$73$	−5.70698	−0.667952	−0.333976	+	0.942582i	$0.608390\pi$
$74$	17.8356	2.07335
$75$	4.83619	0.558435
$76$	33.0342	3.78929
$77$	17.7703	2.02511
$78$	−6.14864	−0.696196
$79$	11.2325	1.26376	0.631879	−	0.775067i	$-0.282284\pi$
$79$	11.2325	1.26376	0.631879	+	0.775067i	$0.282284\pi$
$80$	28.7291	3.21201
$81$	−7.43880	−0.826533
$82$	−28.6301	−3.16166
$83$	11.6365	1.27727	0.638636	−	0.769509i	$-0.279499\pi$
$83$	11.6365	1.27727	0.638636	+	0.769509i	$0.279499\pi$
$84$	−31.8529	−3.47543
$85$	0.451042	0.0489224
$86$	14.6934	1.58443
$87$	6.90794	0.740608
$88$	33.0491	3.52304
$89$	−4.27952	−0.453629	−0.226814	−	0.973938i	$-0.572831\pi$
$89$	−4.27952	−0.453629	−0.226814	+	0.973938i	$0.572831\pi$
$90$	3.36394	0.354591
$91$	−5.98759	−0.627670
$92$	13.1520	1.37119
$93$	4.80735	0.498499
$94$	10.1871	1.05072
$95$	19.1398	1.96371
$96$	−18.2548	−1.86312
$97$	−3.38747	−0.343946	−0.171973	−	0.985102i	$-0.555014\pi$
$97$	−3.38747	−0.343946	−0.171973	+	0.985102i	$0.555014\pi$
$98$	−25.3278	−2.55850
$99$	1.96954	0.197946
$100$	14.8185	1.48185
$101$	−8.26141	−0.822041	−0.411020	−	0.911626i	$-0.634827\pi$
$101$	−8.26141	−0.822041	−0.411020	+	0.911626i	$0.634827\pi$
$102$	−0.666927	−0.0660356
$103$	8.96269	0.883120	0.441560	−	0.897232i	$-0.354425\pi$
$103$	8.96269	0.883120	0.441560	+	0.897232i	$0.354425\pi$
$104$	−11.1357	−1.09194
$105$	−18.4554	−1.80106
$106$	28.4388	2.76222
$107$	3.83017	0.370276	0.185138	−	0.982713i	$-0.440727\pi$
$107$	3.83017	0.370276	0.185138	+	0.982713i	$0.440727\pi$
$108$	−26.9501	−2.59327
$109$	6.24446	0.598111	0.299055	−	0.954236i	$-0.403328\pi$
$109$	6.24446	0.598111	0.299055	+	0.954236i	$0.403328\pi$
$110$	32.3962	3.08886
$111$	−10.8451	−1.02937
$112$	−41.3672	−3.90883
$113$	4.52680	0.425845	0.212923	−	0.977069i	$-0.431702\pi$
$113$	4.52680	0.425845	0.212923	+	0.977069i	$0.431702\pi$
$114$	−28.3008	−2.65062
$115$	7.62018	0.710585
$116$	21.1665	1.96526
$117$	−0.663626	−0.0613522
$118$	5.28196	0.486244
$119$	−0.649459	−0.0595358
$120$	−34.3232	−3.13327
$121$	7.96753	0.724321
$122$	30.8143	2.78980
$123$	17.4087	1.56969
$124$	14.7301	1.32280
$125$	−5.58277	−0.499338
$126$	−4.84376	−0.431517
$127$	5.55519	0.492943	0.246472	−	0.969150i	$-0.420729\pi$
$127$	5.55519	0.492943	0.246472	+	0.969150i	$0.420729\pi$
$128$	−2.70717	−0.239282
$129$	−8.93446	−0.786635
$130$	−10.9157	−0.957373
$131$	−13.5798	−1.18647	−0.593236	−	0.805029i	$-0.702150\pi$
$131$	−13.5798	−1.18647	−0.593236	+	0.805029i	$0.702150\pi$
$132$	−33.9990	−2.95923
$133$	−27.5596	−2.38972
$134$	24.9457	2.15498
$135$	−15.6147	−1.34390
$136$	−1.20786	−0.103573
$137$	−13.6882	−1.16946	−0.584731	−	0.811227i	$-0.698800\pi$
$137$	−13.6882	−1.16946	−0.584731	+	0.811227i	$0.698800\pi$
$138$	−11.2675	−0.959150
$139$	0.845489	0.0717134	0.0358567	−	0.999357i	$-0.488584\pi$
$139$	0.845489	0.0717134	0.0358567	+	0.999357i	$0.488584\pi$
$140$	−56.5487	−4.77924
$141$	−6.19438	−0.521661
$142$	6.45217	0.541454
$143$	−6.39101	−0.534443
$144$	−4.58487	−0.382073
$145$	12.2637	1.01845
$146$	14.9810	1.23984
$147$	15.4008	1.27024
$148$	−33.2302	−2.73151
$149$	−13.6187	−1.11569	−0.557845	−	0.829945i	$-0.688372\pi$
$149$	−13.6187	−1.11569	−0.557845	+	0.829945i	$0.688372\pi$
$150$	−12.6952	−1.03656
$151$	−3.32677	−0.270729	−0.135364	−	0.990796i	$-0.543221\pi$
$151$	−3.32677	−0.270729	−0.135364	+	0.990796i	$0.543221\pi$
$152$	−51.2552	−4.15734
$153$	−0.0719818	−0.00581938
$154$	−46.6475	−3.75897
$155$	8.53453	0.685510
$156$	11.4558	0.917195
$157$	−13.7185	−1.09486	−0.547429	−	0.836852i	$-0.684393\pi$
$157$	−13.7185	−1.09486	−0.547429	+	0.836852i	$0.684393\pi$
$158$	−29.4858	−2.34576
$159$	−17.2925	−1.37138
$160$	−32.4080	−2.56207
$161$	−10.9723	−0.864742
$162$	19.5271	1.53419
$163$	−12.9331	−1.01300	−0.506500	−	0.862240i	$-0.669061\pi$
$163$	−12.9331	−1.01300	−0.506500	+	0.862240i	$0.669061\pi$
$164$	53.3418	4.16529
$165$	−19.6988	−1.53355
$166$	−30.5462	−2.37085
$167$	20.5685	1.59164	0.795819	−	0.605535i	$-0.207041\pi$
$167$	20.5685	1.59164	0.795819	+	0.605535i	$0.207041\pi$
$168$	49.4222	3.81301
$169$	−10.8466	−0.834353
$170$	−1.18400	−0.0908088
$171$	−3.05452	−0.233585
$172$	−27.3759	−2.08739
$173$	−17.4901	−1.32975	−0.664875	−	0.746955i	$-0.731515\pi$
$173$	−17.4901	−1.32975	−0.664875	+	0.746955i	$0.731515\pi$
$174$	−18.1336	−1.37470
$175$	−12.3627	−0.934529
$176$	−44.1543	−3.32826
$177$	−3.21174	−0.241409
$178$	11.2339	0.842016
$179$	3.53375	0.264125	0.132062	−	0.991241i	$-0.457840\pi$
$179$	3.53375	0.264125	0.132062	+	0.991241i	$0.457840\pi$
$180$	−6.26749	−0.467151
$181$	16.8008	1.24879	0.624395	−	0.781109i	$-0.285345\pi$
$181$	16.8008	1.24879	0.624395	+	0.781109i	$0.285345\pi$
$182$	15.7176	1.16507
$183$	−18.7369	−1.38507
$184$	−20.4063	−1.50437
$185$	−19.2534	−1.41554
$186$	−12.6195	−0.925303
$187$	−0.693216	−0.0506930
$188$	−18.9801	−1.38426
$189$	22.4837	1.63545
$190$	−50.2427	−3.64499
$191$	16.7452	1.21164	0.605820	−	0.795602i	$-0.292845\pi$
$191$	16.7452	1.21164	0.605820	+	0.795602i	$0.292845\pi$
$192$	15.5544	1.12254
$193$	−14.4285	−1.03859	−0.519294	−	0.854596i	$-0.673805\pi$
$193$	−14.4285	−1.03859	−0.519294	+	0.854596i	$0.673805\pi$
$194$	8.89223	0.638425
$195$	6.63740	0.475314
$196$	47.1892	3.37066
$197$	12.4474	0.886842	0.443421	−	0.896313i	$-0.353765\pi$
$197$	12.4474	0.886842	0.443421	+	0.896313i	$0.353765\pi$
$198$	−5.17011	−0.367424
$199$	12.8130	0.908287	0.454144	−	0.890928i	$-0.349945\pi$
$199$	12.8130	0.908287	0.454144	+	0.890928i	$0.349945\pi$
$200$	−22.9920	−1.62578
$201$	−15.1684	−1.06990
$202$	21.6865	1.52585
$203$	−17.6586	−1.23939
$204$	1.24258	0.0869979
$205$	30.9059	2.15856
$206$	−23.5274	−1.63923
$207$	−1.21610	−0.0845250
$208$	14.8775	1.03157
$209$	−29.4164	−2.03477
$210$	48.4460	3.34309
$211$	−1.14362	−0.0787300	−0.0393650	−	0.999225i	$-0.512534\pi$
$211$	−1.14362	−0.0787300	−0.0393650	+	0.999225i	$0.512534\pi$
$212$	−52.9855	−3.63906
$213$	−3.92329	−0.268820
$214$	−10.0543	−0.687299
$215$	−15.8614	−1.08174
$216$	41.8151	2.84516
$217$	−12.2889	−0.834226
$218$	−16.3919	−1.11020
$219$	−9.10933	−0.615552
$220$	−60.3587	−4.06938
$221$	0.233575	0.0157120
$222$	28.4687	1.91070
$223$	−28.6960	−1.92163	−0.960815	−	0.277192i	$-0.910596\pi$
$223$	−28.6960	−1.92163	−0.960815	+	0.277192i	$0.910596\pi$
$224$	46.6644	3.11790
$225$	−1.37020	−0.0913465
$226$	−11.8830	−0.790445
$227$	24.5098	1.62677	0.813386	−	0.581725i	$-0.197622\pi$
$227$	24.5098	1.62677	0.813386	+	0.581725i	$0.197622\pi$
$228$	52.7284	3.49202
$229$	−27.2245	−1.79904	−0.899522	−	0.436875i	$-0.856085\pi$
$229$	−27.2245	−1.79904	−0.899522	+	0.436875i	$0.856085\pi$
$230$	−20.0032	−1.31897
$231$	28.3644	1.86624
$232$	−32.8414	−2.15614
$233$	−18.4644	−1.20964	−0.604821	−	0.796362i	$-0.706755\pi$
$233$	−18.4644	−1.20964	−0.604821	+	0.796362i	$0.706755\pi$
$234$	1.74204	0.113881
$235$	−10.9969	−0.717361
$236$	−9.84103	−0.640597
$237$	17.9291	1.16462
$238$	1.70485	0.110509
$239$	−16.0912	−1.04085	−0.520427	−	0.853906i	$-0.674227\pi$
$239$	−16.0912	−1.04085	−0.520427	+	0.853906i	$0.674227\pi$
$240$	45.8566	2.96003
$241$	26.4312	1.70258	0.851290	−	0.524695i	$-0.175821\pi$
$241$	26.4312	1.70258	0.851290	+	0.524695i	$0.175821\pi$
$242$	−20.9150	−1.34447
$243$	4.65746	0.298776
$244$	−57.4114	−3.67539
$245$	27.3412	1.74676
$246$	−45.6985	−2.91363
$247$	9.91169	0.630666
$248$	−22.8549	−1.45129
$249$	18.5739	1.17707
$250$	14.6550	0.926861
$251$	−8.36179	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$251$	−8.36179	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$252$	9.02460	0.568497
$253$	−11.7116	−0.736302
$254$	−14.5826	−0.914991
$255$	0.719942	0.0450845
$256$	−12.3832	−0.773947
$257$	11.1136	0.693245	0.346622	−	0.938005i	$-0.387328\pi$
$257$	11.1136	0.693245	0.346622	+	0.938005i	$0.387328\pi$
$258$	23.4533	1.46014
$259$	27.7231	1.72263
$260$	20.3375	1.26128
$261$	−1.95717	−0.121146
$262$	35.6474	2.20230
$263$	12.8396	0.791722	0.395861	−	0.918310i	$-0.370446\pi$
$263$	12.8396	0.791722	0.395861	+	0.918310i	$0.370446\pi$
$264$	52.7520	3.24666
$265$	−30.6995	−1.88585
$266$	72.3448	4.43574
$267$	−6.83086	−0.418042
$268$	−46.4773	−2.83905
$269$	9.21004	0.561546	0.280773	−	0.959774i	$-0.409409\pi$
$269$	9.21004	0.561546	0.280773	+	0.959774i	$0.409409\pi$
$270$	40.9892	2.49452
$271$	2.06421	0.125392	0.0626959	−	0.998033i	$-0.480030\pi$
$271$	2.06421	0.125392	0.0626959	+	0.998033i	$0.480030\pi$
$272$	1.61373	0.0978467
$273$	−9.55723	−0.578430
$274$	35.9320	2.17073
$275$	−13.1956	−0.795724
$276$	20.9928	1.26362
$277$	−14.1120	−0.847910	−0.423955	−	0.905683i	$-0.639359\pi$
$277$	−14.1120	−0.847910	−0.423955	+	0.905683i	$0.639359\pi$
$278$	−2.21944	−0.133113
$279$	−1.36202	−0.0815423
$280$	87.7397	5.24345
$281$	−7.56810	−0.451475	−0.225737	−	0.974188i	$-0.572479\pi$
$281$	−7.56810	−0.451475	−0.225737	+	0.974188i	$0.572479\pi$
$282$	16.2605	0.968296
$283$	25.3302	1.50573	0.752863	−	0.658178i	$-0.228672\pi$
$283$	25.3302	1.50573	0.752863	+	0.658178i	$0.228672\pi$
$284$	−12.0213	−0.713332
$285$	30.5505	1.80966
$286$	16.7766	0.992022
$287$	−44.5016	−2.62685
$288$	5.17198	0.304762
$289$	−16.9747	−0.998510
$290$	−32.1927	−1.89042
$291$	−5.40699	−0.316963
$292$	−27.9117	−1.63341
$293$	−4.60976	−0.269305	−0.134653	−	0.990893i	$-0.542992\pi$
$293$	−4.60976	−0.269305	−0.134653	+	0.990893i	$0.542992\pi$
$294$	−40.4276	−2.35778
$295$	−5.70183	−0.331974
$296$	51.5593	2.99682
$297$	23.9986	1.39254
$298$	35.7496	2.07092
$299$	3.94616	0.228212
$300$	23.6529	1.36560
$301$	22.8390	1.31642
$302$	8.73289	0.502521
$303$	−13.1866	−0.757552
$304$	68.4781	3.92749
$305$	−33.2638	−1.90468
$306$	0.188955	0.0108018
$307$	4.39386	0.250771	0.125385	−	0.992108i	$-0.459983\pi$
$307$	4.39386	0.250771	0.125385	+	0.992108i	$0.459983\pi$
$308$	86.9109	4.95221
$309$	14.3060	0.813841
$310$	−22.4034	−1.27243
$311$	1.98084	0.112323	0.0561614	−	0.998422i	$-0.482114\pi$
$311$	1.98084	0.112323	0.0561614	+	0.998422i	$0.482114\pi$
$312$	−17.7745	−1.00628
$313$	−2.68152	−0.151569	−0.0757843	−	0.997124i	$-0.524146\pi$
$313$	−2.68152	−0.151569	−0.0757843	+	0.997124i	$0.524146\pi$
$314$	36.0116	2.03225
$315$	5.22880	0.294610
$316$	54.9361	3.09040
$317$	9.72262	0.546077	0.273038	−	0.962003i	$-0.411971\pi$
$317$	9.72262	0.546077	0.273038	+	0.962003i	$0.411971\pi$
$318$	45.3933	2.54553
$319$	−18.8484	−1.05531
$320$	27.6138	1.54366
$321$	6.11361	0.341229
$322$	28.8028	1.60512
$323$	1.07510	0.0598200
$324$	−36.3817	−2.02121
$325$	4.44618	0.246630
$326$	33.9499	1.88031
$327$	9.96724	0.551190
$328$	−82.7639	−4.56987
$329$	15.8346	0.872988
$330$	51.7100	2.84654
$331$	−13.1429	−0.722399	−0.361199	−	0.932489i	$-0.617633\pi$
$331$	−13.1429	−0.722399	−0.361199	+	0.932489i	$0.617633\pi$
$332$	56.9119	3.12344
$333$	3.07265	0.168380
$334$	−53.9930	−2.95436
$335$	−26.9287	−1.47127
$336$	−66.0292	−3.60219
$337$	−30.6858	−1.67156	−0.835781	−	0.549063i	$-0.814985\pi$
$337$	−30.6858	−1.67156	−0.835781	+	0.549063i	$0.814985\pi$
$338$	28.4727	1.54871
$339$	7.22556	0.392438
$340$	2.20596	0.119635
$341$	−13.1169	−0.710319
$342$	8.01823	0.433576
$343$	−10.8068	−0.583515
$344$	42.4758	2.29014
$345$	12.1631	0.654841
$346$	45.9122	2.46825
$347$	−5.98399	−0.321237	−0.160619	−	0.987017i	$-0.551349\pi$
$347$	−5.98399	−0.321237	−0.160619	+	0.987017i	$0.551349\pi$
$348$	33.7854	1.81109
$349$	−22.2652	−1.19183	−0.595914	−	0.803048i	$-0.703210\pi$
$349$	−22.2652	−1.19183	−0.595914	+	0.803048i	$0.703210\pi$
$350$	32.4524	1.73465
$351$	−8.08618	−0.431609
$352$	49.8084	2.65480
$353$	1.40596	0.0748315	0.0374157	−	0.999300i	$-0.488087\pi$
$353$	1.40596	0.0748315	0.0374157	+	0.999300i	$0.488087\pi$
$354$	8.43093	0.448099
$355$	−6.96506	−0.369667
$356$	−20.9303	−1.10930
$357$	−1.03665	−0.0548653
$358$	−9.27621	−0.490263
$359$	−17.7435	−0.936464	−0.468232	−	0.883606i	$-0.655109\pi$
$359$	−17.7435	−0.936464	−0.468232	+	0.883606i	$0.655109\pi$
$360$	9.72450	0.512526
$361$	26.6213	1.40112
$362$	−44.1026	−2.31798
$363$	12.7176	0.667499
$364$	−29.2841	−1.53491
$365$	−16.1719	−0.846475
$366$	49.1850	2.57094
$367$	−12.9260	−0.674731	−0.337366	−	0.941374i	$-0.609536\pi$
$367$	−12.9260	−0.674731	−0.337366	+	0.941374i	$0.609536\pi$
$368$	27.2633	1.42120
$369$	−4.93227	−0.256764
$370$	50.5408	2.62749
$371$	44.2044	2.29498
$372$	23.5118	1.21903
$373$	−15.3574	−0.795177	−0.397588	−	0.917564i	$-0.630153\pi$
$373$	−15.3574	−0.795177	−0.397588	+	0.917564i	$0.630153\pi$
$374$	1.81972	0.0940953
$375$	−8.91107	−0.460166
$376$	29.4491	1.51872
$377$	6.35085	0.327086
$378$	−59.0205	−3.03569
$379$	−32.6068	−1.67490	−0.837449	−	0.546516i	$-0.815954\pi$
$379$	−32.6068	−1.67490	−0.837449	+	0.546516i	$0.815954\pi$
$380$	93.6092	4.80205
$381$	8.86705	0.454273
$382$	−43.9567	−2.24902
$383$	−20.0159	−1.02277	−0.511384	−	0.859353i	$-0.670867\pi$
$383$	−20.0159	−1.02277	−0.511384	+	0.859353i	$0.670867\pi$
$384$	−4.32112	−0.220511
$385$	50.3556	2.56636
$386$	37.8754	1.92781
$387$	2.53132	0.128674
$388$	−16.5675	−0.841085
$389$	27.0756	1.37279	0.686393	−	0.727230i	$-0.259193\pi$
$389$	27.0756	1.37279	0.686393	+	0.727230i	$0.259193\pi$
$390$	−17.4234	−0.882268
$391$	0.428030	0.0216464
$392$	−73.2177	−3.69805
$393$	−21.6757	−1.09339
$394$	−32.6749	−1.64614
$395$	31.8296	1.60152
$396$	9.63264	0.484058
$397$	17.6271	0.884679	0.442340	−	0.896848i	$-0.354149\pi$
$397$	17.6271	0.884679	0.442340	+	0.896848i	$0.354149\pi$
$398$	−33.6345	−1.68594
$399$	−43.9899	−2.20225
$400$	30.7179	1.53589
$401$	−34.3268	−1.71420	−0.857098	−	0.515153i	$-0.827735\pi$
$401$	−34.3268	−1.71420	−0.857098	+	0.515153i	$0.827735\pi$
$402$	39.8177	1.98592
$403$	4.41966	0.220159
$404$	−40.4049	−2.01022
$405$	−21.0793	−1.04744
$406$	46.3545	2.30053
$407$	29.5909	1.46677
$408$	−1.92796	−0.0954480
$409$	−31.5756	−1.56131	−0.780656	−	0.624961i	$-0.785115\pi$
$409$	−31.5756	−1.56131	−0.780656	+	0.624961i	$0.785115\pi$
$410$	−81.1290	−4.00668
$411$	−21.8487	−1.07772
$412$	43.8348	2.15958
$413$	8.21011	0.403993
$414$	3.19231	0.156894
$415$	32.9744	1.61865
$416$	−16.7827	−0.822838
$417$	1.34955	0.0660876
$418$	77.2190	3.77691
$419$	29.4354	1.43801	0.719006	−	0.695003i	$-0.244597\pi$
$419$	29.4354	1.43801	0.719006	+	0.695003i	$0.244597\pi$
$420$	−90.2616	−4.40431
$421$	−24.2341	−1.18110	−0.590549	−	0.807002i	$-0.701089\pi$
$421$	−24.2341	−1.18110	−0.590549	+	0.807002i	$0.701089\pi$
$422$	3.00204	0.146137
$423$	1.75500	0.0853310
$424$	82.2111	3.99252
$425$	0.482266	0.0233933
$426$	10.2988	0.498977
$427$	47.8968	2.31789
$428$	18.7326	0.905474
$429$	−10.2012	−0.492516
$430$	41.6368	2.00790
$431$	−17.2810	−0.832396	−0.416198	−	0.909274i	$-0.636638\pi$
$431$	−17.2810	−0.832396	−0.416198	+	0.909274i	$0.636638\pi$
$432$	−55.8660	−2.68785
$433$	−10.1189	−0.486281	−0.243140	−	0.969991i	$-0.578178\pi$
$433$	−10.1189	−0.486281	−0.243140	+	0.969991i	$0.578178\pi$
$434$	32.2588	1.54847
$435$	19.5750	0.938551
$436$	30.5404	1.46262
$437$	18.1633	0.868869
$438$	23.9123	1.14257
$439$	−31.6553	−1.51082	−0.755411	−	0.655251i	$-0.772563\pi$
$439$	−31.6553	−1.51082	−0.755411	+	0.655251i	$0.772563\pi$
$440$	93.6512	4.46464
$441$	−4.36337	−0.207780
$442$	−0.613143	−0.0291643
$443$	−30.0671	−1.42853	−0.714265	−	0.699876i	$-0.753239\pi$
$443$	−30.0671	−1.42853	−0.714265	+	0.699876i	$0.753239\pi$
$444$	−53.0412	−2.51722
$445$	−12.1269	−0.574870
$446$	75.3281	3.56689
$447$	−21.7379	−1.02817
$448$	−39.7613	−1.87855
$449$	4.89363	0.230945	0.115472	−	0.993311i	$-0.463162\pi$
$449$	4.89363	0.230945	0.115472	+	0.993311i	$0.463162\pi$
$450$	3.59681	0.169555
$451$	−47.4999	−2.23668
$452$	22.1397	1.04136
$453$	−5.31010	−0.249490
$454$	−64.3390	−3.01958
$455$	−16.9670	−0.795428
$456$	−81.8121	−3.83120
$457$	−34.7775	−1.62682	−0.813412	−	0.581688i	$-0.802393\pi$
$457$	−34.7775	−1.62682	−0.813412	+	0.581688i	$0.802393\pi$
$458$	71.4652	3.33935
$459$	−0.877088	−0.0409390
$460$	37.2688	1.73767
$461$	25.0822	1.16819	0.584097	−	0.811684i	$-0.301449\pi$
$461$	25.0822	1.16819	0.584097	+	0.811684i	$0.301449\pi$
$462$	−74.4576	−3.46408
$463$	−20.6225	−0.958407	−0.479203	−	0.877704i	$-0.659074\pi$
$463$	−20.6225	−0.958407	−0.479203	+	0.877704i	$0.659074\pi$
$464$	43.8769	2.03693
$465$	13.6226	0.631732
$466$	48.4696	2.24531
$467$	−7.12670	−0.329784	−0.164892	−	0.986312i	$-0.552728\pi$
$467$	−7.12670	−0.329784	−0.164892	+	0.986312i	$0.552728\pi$
$468$	−3.24566	−0.150031
$469$	38.7748	1.79045
$470$	28.8673	1.33155
$471$	−21.8971	−1.00897
$472$	15.2691	0.702818
$473$	24.3777	1.12089
$474$	−47.0644	−2.16174
$475$	20.4648	0.938989
$476$	−3.17638	−0.145589
$477$	4.89932	0.224325
$478$	42.2400	1.93201
$479$	−6.29914	−0.287815	−0.143907	−	0.989591i	$-0.545967\pi$
$479$	−6.29914	−0.287815	−0.143907	+	0.989591i	$0.545967\pi$
$480$	−51.7287	−2.36108
$481$	−9.97050	−0.454616
$482$	−69.3827	−3.16029
$483$	−17.5138	−0.796904
$484$	38.9676	1.77126
$485$	−9.59908	−0.435872
$486$	−12.2260	−0.554583
$487$	−19.0471	−0.863108	−0.431554	−	0.902087i	$-0.642035\pi$
$487$	−19.0471	−0.863108	−0.431554	+	0.902087i	$0.642035\pi$
$488$	89.0782	4.03238
$489$	−20.6435	−0.933531
$490$	−71.7715	−3.24230
$491$	−32.8632	−1.48310	−0.741548	−	0.670900i	$-0.765908\pi$
$491$	−32.8632	−1.48310	−0.741548	+	0.670900i	$0.765908\pi$
$492$	85.1427	3.83853
$493$	0.688861	0.0310247
$494$	−26.0185	−1.17063
$495$	5.58109	0.250851
$496$	30.5347	1.37105
$497$	10.0290	0.449864
$498$	−48.7571	−2.18486
$499$	22.2917	0.997911	0.498956	−	0.866627i	$-0.333717\pi$
$499$	22.2917	0.997911	0.498956	+	0.866627i	$0.333717\pi$
$500$	−27.3042	−1.22108
$501$	32.8309	1.46678
$502$	21.9500	0.979675
$503$	20.1406	0.898024	0.449012	−	0.893526i	$-0.351776\pi$
$503$	20.1406	0.898024	0.449012	+	0.893526i	$0.351776\pi$
$504$	−14.0024	−0.623715
$505$	−23.4104	−1.04175
$506$	30.7434	1.36671
$507$	−17.3130	−0.768899
$508$	27.1693	1.20544
$509$	−38.4784	−1.70553	−0.852763	−	0.522298i	$-0.825075\pi$
$509$	−38.4784	−1.70553	−0.852763	+	0.522298i	$0.825075\pi$
$510$	−1.88987	−0.0836850
$511$	23.2860	1.03011
$512$	37.9206	1.67587
$513$	−37.2189	−1.64326
$514$	−29.1735	−1.28679
$515$	25.3976	1.11915
$516$	−43.6967	−1.92364
$517$	16.9014	0.743323
$518$	−72.7740	−3.19751
$519$	−27.9173	−1.22543
$520$	−31.5552	−1.38379
$521$	29.3759	1.28698	0.643491	−	0.765454i	$-0.277485\pi$
$521$	29.3759	1.28698	0.643491	+	0.765454i	$0.277485\pi$
$522$	5.13763	0.224868
$523$	−2.88943	−0.126346	−0.0631730	−	0.998003i	$-0.520122\pi$
$523$	−2.88943	−0.126346	−0.0631730	+	0.998003i	$0.520122\pi$
$524$	−66.4161	−2.90140
$525$	−19.7329	−0.861216
$526$	−33.7043	−1.46958
$527$	0.479390	0.0208825
$528$	−70.4779	−3.06716
$529$	−15.7686	−0.685592
$530$	80.5871	3.50048
$531$	0.909955	0.0394887
$532$	−134.788	−5.84382
$533$	16.0048	0.693246
$534$	17.9312	0.775961
$535$	10.8536	0.469240
$536$	72.1131	3.11481
$537$	5.64048	0.243405
$538$	−24.1767	−1.04233
$539$	−42.0212	−1.80998
$540$	−76.3685	−3.28638
$541$	6.22221	0.267514	0.133757	−	0.991014i	$-0.457296\pi$
$541$	6.22221	0.267514	0.133757	+	0.991014i	$0.457296\pi$
$542$	−5.41862	−0.232750
$543$	26.8169	1.15082
$544$	−1.82037	−0.0780479
$545$	17.6949	0.757968
$546$	25.0881	1.07367
$547$	35.3320	1.51069	0.755344	−	0.655329i	$-0.227470\pi$
$547$	35.3320	1.51069	0.755344	+	0.655329i	$0.227470\pi$
$548$	−66.9463	−2.85980
$549$	5.30857	0.226564
$550$	34.6389	1.47701
$551$	29.2316	1.24531
$552$	−32.5720	−1.38636
$553$	−45.8317	−1.94896
$554$	37.0446	1.57387
$555$	−30.7318	−1.30449
$556$	4.13512	0.175368
$557$	−45.8297	−1.94187	−0.970934	−	0.239346i	$-0.923067\pi$
$557$	−45.8297	−1.94187	−0.970934	+	0.239346i	$0.923067\pi$
$558$	3.57536	0.151357
$559$	−8.21395	−0.347413
$560$	−117.222	−4.95354
$561$	−1.10649	−0.0467162
$562$	19.8665	0.838018
$563$	−15.3774	−0.648079	−0.324039	−	0.946044i	$-0.605041\pi$
$563$	−15.3774	−0.648079	−0.324039	+	0.946044i	$0.605041\pi$
$564$	−30.2955	−1.27567
$565$	12.8276	0.539661
$566$	−66.4927	−2.79490
$567$	30.3523	1.27468
$568$	18.6519	0.782618
$569$	38.4097	1.61022	0.805110	−	0.593125i	$-0.202106\pi$
$569$	38.4097	1.61022	0.805110	+	0.593125i	$0.202106\pi$
$570$	−80.1961	−3.35905
$571$	−23.2921	−0.974743	−0.487371	−	0.873195i	$-0.662044\pi$
$571$	−23.2921	−0.974743	−0.487371	+	0.873195i	$0.662044\pi$
$572$	−31.2572	−1.30693
$573$	26.7283	1.11659
$574$	116.818	4.87590
$575$	8.14769	0.339782
$576$	−4.40689	−0.183620
$577$	−9.37557	−0.390310	−0.195155	−	0.980772i	$-0.562521\pi$
$577$	−9.37557	−0.390310	−0.195155	+	0.980772i	$0.562521\pi$
$578$	44.5591	1.85341
$579$	−23.0304	−0.957112
$580$	59.9795	2.49051
$581$	−47.4800	−1.96980
$582$	14.1935	0.588341
$583$	47.1826	1.95410
$584$	43.3072	1.79206
$585$	−1.88052	−0.0777498
$586$	12.1008	0.499879
$587$	27.9399	1.15320	0.576602	−	0.817025i	$-0.304378\pi$
$587$	27.9399	1.15320	0.576602	+	0.817025i	$0.304378\pi$
$588$	75.3222	3.10624
$589$	20.3427	0.838208
$590$	14.9675	0.616203
$591$	19.8683	0.817271
$592$	−68.8844	−2.83113
$593$	−5.27502	−0.216619	−0.108310	−	0.994117i	$-0.534544\pi$
$593$	−5.27502	−0.216619	−0.108310	+	0.994117i	$0.534544\pi$
$594$	−62.9970	−2.58480
$595$	−1.84037	−0.0754479
$596$	−66.6065	−2.72831
$597$	20.4517	0.837033
$598$	−10.3588	−0.423603
$599$	30.8260	1.25952	0.629759	−	0.776791i	$-0.283154\pi$
$599$	30.8260	1.25952	0.629759	+	0.776791i	$0.283154\pi$
$600$	−36.6993	−1.49824
$601$	4.66282	0.190200	0.0951001	−	0.995468i	$-0.469683\pi$
$601$	4.66282	0.190200	0.0951001	+	0.995468i	$0.469683\pi$
$602$	−59.9531	−2.44350
$603$	4.29754	0.175009
$604$	−16.2706	−0.662041
$605$	22.5776	0.917910
$606$	34.6154	1.40615
$607$	10.8487	0.440333	0.220167	−	0.975462i	$-0.429340\pi$
$607$	10.8487	0.440333	0.220167	+	0.975462i	$0.429340\pi$
$608$	−77.2470	−3.13278
$609$	−28.1862	−1.14216
$610$	87.3186	3.53543
$611$	−5.69484	−0.230389
$612$	−0.352049	−0.0142307
$613$	−29.7304	−1.20080	−0.600401	−	0.799699i	$-0.704992\pi$
$613$	−29.7304	−1.20080	−0.600401	+	0.799699i	$0.704992\pi$
$614$	−11.5340	−0.465475
$615$	49.3312	1.98922
$616$	−134.849	−5.43322
$617$	35.3186	1.42187	0.710937	−	0.703256i	$-0.248271\pi$
$617$	35.3186	1.42187	0.710937	+	0.703256i	$0.248271\pi$
$618$	−37.5538	−1.51063
$619$	−40.6951	−1.63568	−0.817838	−	0.575449i	$-0.804827\pi$
$619$	−40.6951	−1.63568	−0.817838	+	0.575449i	$0.804827\pi$
$620$	41.7407	1.67635
$621$	−14.8180	−0.594628
$622$	−5.19976	−0.208491
$623$	17.4616	0.699584
$624$	23.7471	0.950647
$625$	−30.9692	−1.23877
$626$	7.03909	0.281339
$627$	−46.9537	−1.87515
$628$	−67.0946	−2.67737
$629$	−1.08147	−0.0431212
$630$	−13.7258	−0.546848
$631$	−11.9926	−0.477416	−0.238708	−	0.971091i	$-0.576724\pi$
$631$	−11.9926	−0.477416	−0.238708	+	0.971091i	$0.576724\pi$
$632$	−85.2376	−3.39057
$633$	−1.82541	−0.0725537
$634$	−25.5222	−1.01362
$635$	15.7418	0.624692
$636$	−84.5740	−3.35358
$637$	14.1588	0.560992
$638$	49.4776	1.95884
$639$	1.11155	0.0439724
$640$	−7.67132	−0.303235
$641$	−27.7186	−1.09482	−0.547410	−	0.836865i	$-0.684386\pi$
$641$	−27.7186	−1.09482	−0.547410	+	0.836865i	$0.684386\pi$
$642$	−16.0484	−0.633381
$643$	−31.8431	−1.25577	−0.627886	−	0.778306i	$-0.716079\pi$
$643$	−31.8431	−1.25577	−0.627886	+	0.778306i	$0.716079\pi$
$644$	−53.6636	−2.11464
$645$	−25.3176	−0.996879
$646$	−2.82216	−0.111037
$647$	18.3307	0.720655	0.360327	−	0.932826i	$-0.382665\pi$
$647$	18.3307	0.720655	0.360327	+	0.932826i	$0.382665\pi$
$648$	56.4490	2.21753
$649$	8.76326	0.343988
$650$	−11.6714	−0.457789
$651$	−19.6153	−0.768782
$652$	−63.2534	−2.47719
$653$	−8.48165	−0.331912	−0.165956	−	0.986133i	$-0.553071\pi$
$653$	−8.48165	−0.331912	−0.165956	+	0.986133i	$0.553071\pi$
$654$	−26.1643	−1.02311
$655$	−38.4811	−1.50358
$656$	110.574	4.31721
$657$	2.58087	0.100689
$658$	−41.5663	−1.62042
$659$	32.4044	1.26230	0.631149	−	0.775662i	$-0.282584\pi$
$659$	32.4044	1.26230	0.631149	+	0.775662i	$0.282584\pi$
$660$	−96.3429	−3.75014
$661$	29.9556	1.16514	0.582569	−	0.812781i	$-0.302048\pi$
$661$	29.9556	1.16514	0.582569	+	0.812781i	$0.302048\pi$
$662$	34.5005	1.34090
$663$	0.372827	0.0144794
$664$	−88.3031	−3.42683
$665$	−78.0956	−3.02842
$666$	−8.06580	−0.312544
$667$	11.6380	0.450626
$668$	100.596	3.89219
$669$	−45.8039	−1.77088
$670$	70.6887	2.73094
$671$	51.1238	1.97361
$672$	74.4845	2.87330
$673$	45.7702	1.76431	0.882155	−	0.470959i	$-0.156092\pi$
$673$	45.7702	1.76431	0.882155	+	0.470959i	$0.156092\pi$
$674$	80.5513	3.10272
$675$	−16.6956	−0.642616
$676$	−53.0485	−2.04033
$677$	16.0580	0.617158	0.308579	−	0.951199i	$-0.400147\pi$
$677$	16.0580	0.617158	0.308579	+	0.951199i	$0.400147\pi$
$678$	−18.9673	−0.728436
$679$	13.8218	0.530431
$680$	−3.42272	−0.131255
$681$	39.1219	1.49915
$682$	34.4323	1.31848
$683$	13.4133	0.513245	0.256623	−	0.966512i	$-0.417390\pi$
$683$	13.4133	0.513245	0.256623	+	0.966512i	$0.417390\pi$
$684$	−14.9391	−0.571210
$685$	−38.7883	−1.48202
$686$	28.3683	1.08311
$687$	−43.4550	−1.65791
$688$	−56.7487	−2.16352
$689$	−15.8979	−0.605663
$690$	−31.9286	−1.21550
$691$	13.1438	0.500015	0.250007	−	0.968244i	$-0.419567\pi$
$691$	13.1438	0.500015	0.250007	+	0.968244i	$0.419567\pi$
$692$	−85.5408	−3.25177
$693$	−8.03625	−0.305272
$694$	15.7082	0.596274
$695$	2.39586	0.0908803
$696$	−52.4206	−1.98700
$697$	1.73600	0.0657558
$698$	58.4469	2.21225
$699$	−29.4724	−1.11475
$700$	−60.4633	−2.28530
$701$	−11.3745	−0.429609	−0.214805	−	0.976657i	$-0.568911\pi$
$701$	−11.3745	−0.429609	−0.214805	+	0.976657i	$0.568911\pi$
$702$	21.2265	0.801143
$703$	−45.8920	−1.73085
$704$	−42.4402	−1.59953
$705$	−17.5530	−0.661085
$706$	−3.69068	−0.138901
$707$	33.7087	1.26775
$708$	−15.7080	−0.590343
$709$	19.3343	0.726116	0.363058	−	0.931767i	$-0.381733\pi$
$709$	19.3343	0.726116	0.363058	+	0.931767i	$0.381733\pi$
$710$	18.2835	0.686168
$711$	−5.07969	−0.190503
$712$	32.4750	1.21705
$713$	8.09909	0.303313
$714$	2.72124	0.101840
$715$	−18.1102	−0.677283
$716$	17.2829	0.645891
$717$	−25.6844	−0.959200
$718$	46.5772	1.73824
$719$	−9.36113	−0.349111	−0.174556	−	0.984647i	$-0.555849\pi$
$719$	−9.36113	−0.349111	−0.174556	+	0.984647i	$0.555849\pi$
$720$	−12.9922	−0.484189
$721$	−36.5702	−1.36194
$722$	−69.8819	−2.60074
$723$	42.1887	1.56901
$724$	82.1692	3.05380
$725$	13.1127	0.486993
$726$	−33.3840	−1.23900
$727$	−16.7137	−0.619876	−0.309938	−	0.950757i	$-0.600308\pi$
$727$	−16.7137	−0.619876	−0.309938	+	0.950757i	$0.600308\pi$
$728$	45.4366	1.68399
$729$	29.7505	1.10187
$730$	42.4518	1.57121
$731$	−0.890946	−0.0329528
$732$	−91.6385	−3.38706
$733$	−18.0210	−0.665621	−0.332810	−	0.942994i	$-0.607997\pi$
$733$	−18.0210	−0.665621	−0.332810	+	0.942994i	$0.607997\pi$
$734$	33.9312	1.25242
$735$	43.6412	1.60973
$736$	−30.7545	−1.13363
$737$	41.3872	1.52452
$738$	12.9474	0.476599
$739$	−22.0901	−0.812596	−0.406298	−	0.913741i	$-0.633181\pi$
$739$	−22.0901	−0.812596	−0.406298	+	0.913741i	$0.633181\pi$
$740$	−94.1646	−3.46156
$741$	15.8208	0.581191
$742$	−116.038	−4.25989
$743$	16.7001	0.612669	0.306334	−	0.951924i	$-0.400897\pi$
$743$	16.7001	0.612669	0.306334	+	0.951924i	$0.400897\pi$
$744$	−36.4804	−1.33744
$745$	−38.5914	−1.41388
$746$	40.3137	1.47599
$747$	−5.26238	−0.192540
$748$	−3.39038	−0.123965
$749$	−15.6281	−0.571038
$750$	23.3919	0.854150
$751$	35.9062	1.31024	0.655118	−	0.755526i	$-0.272619\pi$
$751$	35.9062	1.31024	0.655118	+	0.755526i	$0.272619\pi$
$752$	−39.3446	−1.43475
$753$	−13.3469	−0.486387
$754$	−16.6712	−0.607129
$755$	−9.42708	−0.343086
$756$	109.963	3.99933
$757$	0.282655	0.0102733	0.00513663	−	0.999987i	$-0.498365\pi$
$757$	0.282655	0.0102733	0.00513663	+	0.999987i	$0.498365\pi$
$758$	85.5939	3.10891
$759$	−18.6938	−0.678540
$760$	−145.242	−5.26848
$761$	−25.6854	−0.931096	−0.465548	−	0.885023i	$-0.654143\pi$
$761$	−25.6854	−0.931096	−0.465548	+	0.885023i	$0.654143\pi$
$762$	−23.2763	−0.843211
$763$	−25.4791	−0.922404
$764$	81.8975	2.96295
$765$	−0.203975	−0.00737473
$766$	52.5425	1.89844
$767$	−2.95273	−0.106617
$768$	−19.7657	−0.713232
$769$	3.89942	0.140617	0.0703083	−	0.997525i	$-0.477602\pi$
$769$	3.89942	0.140617	0.0703083	+	0.997525i	$0.477602\pi$
$770$	−132.185	−4.76362
$771$	17.7392	0.638861
$772$	−70.5671	−2.53977
$773$	−22.5597	−0.811416	−0.405708	−	0.914003i	$-0.632975\pi$
$773$	−22.5597	−0.811416	−0.405708	+	0.914003i	$0.632975\pi$
$774$	−6.64481	−0.238843
$775$	9.12534	0.327792
$776$	25.7057	0.922780
$777$	44.2509	1.58749
$778$	−71.0743	−2.54814
$779$	73.6667	2.63938
$780$	32.4622	1.16233
$781$	10.7047	0.383046
$782$	−1.12359	−0.0401796
$783$	−23.8478	−0.852250
$784$	97.8206	3.49359
$785$	−38.8742	−1.38748
$786$	56.8995	2.02954
$787$	6.16961	0.219923	0.109961	−	0.993936i	$-0.464927\pi$
$787$	6.16961	0.219923	0.109961	+	0.993936i	$0.464927\pi$
$788$	60.8779	2.16869
$789$	20.4942	0.729613
$790$	−83.5539	−2.97271
$791$	−18.4705	−0.656737
$792$	−14.9458	−0.531075
$793$	−17.2259	−0.611709
$794$	−46.2718	−1.64212
$795$	−49.0017	−1.73791
$796$	62.6657	2.22113
$797$	−48.1768	−1.70651	−0.853254	−	0.521495i	$-0.825375\pi$
$797$	−48.1768	−1.70651	−0.853254	+	0.521495i	$0.825375\pi$
$798$	115.475	4.08777
$799$	−0.617705	−0.0218528
$800$	−34.6514	−1.22511
$801$	1.93533	0.0683815
$802$	90.1089	3.18186
$803$	24.8549	0.877110
$804$	−74.1858	−2.61633
$805$	−31.0924	−1.09586
$806$	−11.6018	−0.408655
$807$	14.7008	0.517494
$808$	62.6913	2.20547
$809$	−13.9473	−0.490360	−0.245180	−	0.969478i	$-0.578847\pi$
$809$	−13.9473	−0.490360	−0.245180	+	0.969478i	$0.578847\pi$
$810$	55.3340	1.94424
$811$	8.73705	0.306799	0.153400	−	0.988164i	$-0.450978\pi$
$811$	8.73705	0.306799	0.153400	+	0.988164i	$0.450978\pi$
$812$	−86.3648	−3.03081
$813$	3.29484	0.115555
$814$	−77.6772	−2.72258
$815$	−36.6486	−1.28374
$816$	2.57579	0.0901708
$817$	−37.8070	−1.32270
$818$	82.8870	2.89807
$819$	2.70777	0.0946171
$820$	151.155	5.27855
$821$	49.0432	1.71162	0.855810	−	0.517291i	$-0.173059\pi$
$821$	49.0432	1.71162	0.855810	+	0.517291i	$0.173059\pi$
$822$	57.3537	2.00044
$823$	−34.1875	−1.19170	−0.595851	−	0.803095i	$-0.703185\pi$
$823$	−34.1875	−1.19170	−0.595851	+	0.803095i	$0.703185\pi$
$824$	−68.0130	−2.36935
$825$	−21.0625	−0.733301
$826$	−21.5518	−0.749884
$827$	23.7110	0.824512	0.412256	−	0.911068i	$-0.364741\pi$
$827$	23.7110	0.824512	0.412256	+	0.911068i	$0.364741\pi$
$828$	−5.94772	−0.206698
$829$	18.4764	0.641711	0.320856	−	0.947128i	$-0.396030\pi$
$829$	18.4764	0.641711	0.320856	+	0.947128i	$0.396030\pi$
$830$	−86.5589	−3.00450
$831$	−22.5253	−0.781393
$832$	14.3000	0.495763
$833$	1.53577	0.0532113
$834$	−3.54261	−0.122670
$835$	58.2850	2.01703
$836$	−143.870	−4.97584
$837$	−16.5961	−0.573644
$838$	−77.2689	−2.66921
$839$	16.9350	0.584662	0.292331	−	0.956317i	$-0.405569\pi$
$839$	16.9350	0.584662	0.292331	+	0.956317i	$0.405569\pi$
$840$	140.048	4.83211
$841$	−10.2701	−0.354140
$842$	63.6153	2.19233
$843$	−12.0800	−0.416057
$844$	−5.59322	−0.192526
$845$	−30.7360	−1.05735
$846$	−4.60694	−0.158390
$847$	−32.5096	−1.11704
$848$	−109.836	−3.77178
$849$	40.4314	1.38760
$850$	−1.26597	−0.0434222
$851$	−18.2711	−0.626324
$852$	−19.1881	−0.657372
$853$	−28.5643	−0.978022	−0.489011	−	0.872278i	$-0.662642\pi$
$853$	−28.5643	−0.978022	−0.489011	+	0.872278i	$0.662642\pi$
$854$	−125.731	−4.30241
$855$	−8.65561	−0.296016
$856$	−29.0651	−0.993424
$857$	−5.17766	−0.176865	−0.0884327	−	0.996082i	$-0.528186\pi$
$857$	−5.17766	−0.176865	−0.0884327	+	0.996082i	$0.528186\pi$
$858$	26.7784	0.914199
$859$	35.1695	1.19997	0.599984	−	0.800012i	$-0.295174\pi$
$859$	35.1695	1.19997	0.599984	+	0.800012i	$0.295174\pi$
$860$	−77.5751	−2.64529
$861$	−71.0323	−2.42077
$862$	45.3632	1.54508
$863$	−40.5264	−1.37953	−0.689767	−	0.724031i	$-0.742287\pi$
$863$	−40.5264	−1.37953	−0.689767	+	0.724031i	$0.742287\pi$
$864$	63.0198	2.14398
$865$	−49.5618	−1.68515
$866$	26.5623	0.902625
$867$	−27.0945	−0.920178
$868$	−60.1027	−2.04002
$869$	−48.9196	−1.65948
$870$	−51.3851	−1.74212
$871$	−13.9452	−0.472515
$872$	−47.3858	−1.60469
$873$	1.53192	0.0518475
$874$	−47.6793	−1.61278
$875$	22.7792	0.770077
$876$	−44.5520	−1.50527
$877$	−4.37086	−0.147594	−0.0737968	−	0.997273i	$-0.523512\pi$
$877$	−4.37086	−0.147594	−0.0737968	+	0.997273i	$0.523512\pi$
$878$	83.0961	2.80436
$879$	−7.35798	−0.248179
$880$	−125.120	−4.21780
$881$	45.5309	1.53398	0.766988	−	0.641662i	$-0.221755\pi$
$881$	45.5309	1.53398	0.766988	+	0.641662i	$0.221755\pi$
$882$	11.4540	0.385676
$883$	2.53469	0.0852991	0.0426496	−	0.999090i	$-0.486420\pi$
$883$	2.53469	0.0852991	0.0426496	+	0.999090i	$0.486420\pi$
$884$	1.14237	0.0384221
$885$	−9.10112	−0.305931
$886$	78.9271	2.65161
$887$	−10.7805	−0.361972	−0.180986	−	0.983486i	$-0.557929\pi$
$887$	−10.7805	−0.361972	−0.180986	+	0.983486i	$0.557929\pi$
$888$	82.2975	2.76172
$889$	−22.6666	−0.760215
$890$	31.8335	1.06706
$891$	32.3972	1.08535
$892$	−140.347	−4.69916
$893$	−26.2121	−0.877154
$894$	57.0626	1.90846
$895$	10.0136	0.334717
$896$	11.0460	0.369020
$897$	6.29876	0.210309
$898$	−12.8459	−0.428675
$899$	13.0345	0.434724
$900$	−6.70136	−0.223379
$901$	−1.72441	−0.0574483
$902$	124.689	4.15168
$903$	36.4550	1.21314
$904$	−34.3514	−1.14251
$905$	47.6083	1.58255
$906$	13.9392	0.463099
$907$	16.1217	0.535312	0.267656	−	0.963515i	$-0.413751\pi$
$907$	16.1217	0.535312	0.267656	+	0.963515i	$0.413751\pi$
$908$	119.873	3.97811
$909$	3.73606	0.123917
$910$	44.5391	1.47646
$911$	25.7819	0.854192	0.427096	−	0.904206i	$-0.359537\pi$
$911$	25.7819	0.854192	0.427096	+	0.904206i	$0.359537\pi$
$912$	109.303	3.61938
$913$	−50.6790	−1.67723
$914$	91.2922	3.01968
$915$	−53.0948	−1.75526
$916$	−133.150	−4.39939
$917$	55.4092	1.82977
$918$	2.30239	0.0759901
$919$	−13.8780	−0.457793	−0.228897	−	0.973451i	$-0.573512\pi$
$919$	−13.8780	−0.457793	−0.228897	+	0.973451i	$0.573512\pi$
$920$	−57.8254	−1.90645
$921$	7.01336	0.231098
$922$	−65.8416	−2.16838
$923$	−3.60690	−0.118723
$924$	138.725	4.56371
$925$	−20.5862	−0.676871
$926$	54.1347	1.77898
$927$	−4.05320	−0.133125
$928$	−49.4955	−1.62477
$929$	−52.9687	−1.73785	−0.868923	−	0.494947i	$-0.835187\pi$
$929$	−52.9687	−1.73785	−0.868923	+	0.494947i	$0.835187\pi$
$930$	−35.7598	−1.17261
$931$	65.1699	2.13586
$932$	−90.3057	−2.95806
$933$	3.16176	0.103511
$934$	18.7078	0.612139
$935$	−1.96437	−0.0642417
$936$	5.03590	0.164603
$937$	−26.2562	−0.857753	−0.428877	−	0.903363i	$-0.641090\pi$
$937$	−26.2562	−0.857753	−0.428877	+	0.903363i	$0.641090\pi$
$938$	−101.785	−3.32340
$939$	−4.28018	−0.139678
$940$	−53.7839	−1.75424
$941$	49.8404	1.62475	0.812375	−	0.583136i	$-0.198174\pi$
$941$	49.8404	1.62475	0.812375	+	0.583136i	$0.198174\pi$
$942$	57.4807	1.87282
$943$	29.3291	0.955086
$944$	−20.3999	−0.663960
$945$	63.7122	2.07256
$946$	−63.9924	−2.08057
$947$	52.4900	1.70570	0.852849	−	0.522158i	$-0.174873\pi$
$947$	52.4900	1.70570	0.852849	+	0.522158i	$0.174873\pi$
$948$	87.6875	2.84796
$949$	−8.37472	−0.271855
$950$	−53.7208	−1.74293
$951$	15.5190	0.503238
$952$	4.92839	0.159730
$953$	4.48607	0.145318	0.0726591	−	0.997357i	$-0.476852\pi$
$953$	4.48607	0.145318	0.0726591	+	0.997357i	$0.476852\pi$
$954$	−12.8609	−0.416387
$955$	47.4509	1.53548
$956$	−78.6990	−2.54531
$957$	−30.0853	−0.972518
$958$	16.5354	0.534236
$959$	55.8515	1.80354
$960$	44.0765	1.42256
$961$	−21.9291	−0.707390
$962$	26.1729	0.843848
$963$	−1.73212	−0.0558167
$964$	129.270	4.16349
$965$	−40.8861	−1.31617
$966$	45.9742	1.47920
$967$	−46.6336	−1.49964	−0.749818	−	0.661644i	$-0.769859\pi$
$967$	−46.6336	−1.49964	−0.749818	+	0.661644i	$0.769859\pi$
$968$	−60.4613	−1.94330
$969$	1.71604	0.0551271
$970$	25.1979	0.809057
$971$	55.6584	1.78616	0.893082	−	0.449894i	$-0.148538\pi$
$971$	55.6584	1.78616	0.893082	+	0.449894i	$0.148538\pi$
$972$	22.7787	0.730629
$973$	−3.44982	−0.110596
$974$	49.9994	1.60208
$975$	7.09688	0.227282
$976$	−119.011	−3.80943
$977$	1.60392	0.0513139	0.0256569	−	0.999671i	$-0.491832\pi$
$977$	1.60392	0.0513139	0.0256569	+	0.999671i	$0.491832\pi$
$978$	54.1899	1.73280
$979$	18.6381	0.595675
$980$	133.720	4.27154
$981$	−2.82393	−0.0901612
$982$	86.2670	2.75289
$983$	10.6627	0.340087	0.170044	−	0.985437i	$-0.445609\pi$
$983$	10.6627	0.340087	0.170044	+	0.985437i	$0.445609\pi$
$984$	−132.106	−4.21137
$985$	35.2723	1.12387
$986$	−1.80828	−0.0575875
$987$	25.2747	0.804503
$988$	48.4761	1.54223
$989$	−15.0522	−0.478631
$990$	−14.6506	−0.465625
$991$	12.4872	0.396669	0.198335	−	0.980134i	$-0.436447\pi$
$991$	12.4872	0.396669	0.198335	+	0.980134i	$0.436447\pi$
$992$	−34.4447	−1.09362
$993$	−20.9783	−0.665728
$994$	−26.3266	−0.835027
$995$	36.3081	1.15105
$996$	90.8412	2.87841
$997$	35.5503	1.12589	0.562945	−	0.826494i	$-0.309668\pi$
$997$	35.5503	1.12589	0.562945	+	0.826494i	$0.309668\pi$
$998$	−58.5163	−1.85230
$999$	37.4398	1.18454

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.a.1.10	✓	217

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.a.1.10	✓	217	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)

\(f(q)\)	\(=\)	\(q-2.62503 q^{2} +1.59617 q^{3} +4.89080 q^{4} +2.83370 q^{5} -4.19001 q^{6} -4.08027 q^{7} -7.58846 q^{8} -0.452230 q^{9} +O(q^{10})\)	\(q-2.62503 q^{2} +1.59617 q^{3} +4.89080 q^{4} +2.83370 q^{5} -4.19001 q^{6} -4.08027 q^{7} -7.58846 q^{8} -0.452230 q^{9} -7.43856 q^{10} -4.35517 q^{11} +7.80657 q^{12} +1.46745 q^{13} +10.7108 q^{14} +4.52308 q^{15} +10.1384 q^{16} +0.159171 q^{17} +1.18712 q^{18} +6.75436 q^{19} +13.8591 q^{20} -6.51281 q^{21} +11.4325 q^{22} +2.68913 q^{23} -12.1125 q^{24} +3.02987 q^{25} -3.85211 q^{26} -5.51036 q^{27} -19.9558 q^{28} +4.32781 q^{29} -11.8732 q^{30} +3.01180 q^{31} -11.4366 q^{32} -6.95161 q^{33} -0.417829 q^{34} -11.5623 q^{35} -2.21177 q^{36} -6.79443 q^{37} -17.7304 q^{38} +2.34231 q^{39} -21.5034 q^{40} +10.9065 q^{41} +17.0964 q^{42} -5.59742 q^{43} -21.3003 q^{44} -1.28149 q^{45} -7.05905 q^{46} -3.88077 q^{47} +16.1826 q^{48} +9.64856 q^{49} -7.95350 q^{50} +0.254064 q^{51} +7.17702 q^{52} -10.8337 q^{53} +14.4649 q^{54} -12.3413 q^{55} +30.9629 q^{56} +10.7811 q^{57} -11.3606 q^{58} -2.01215 q^{59} +22.1215 q^{60} -11.7386 q^{61} -7.90607 q^{62} +1.84522 q^{63} +9.74479 q^{64} +4.15832 q^{65} +18.2482 q^{66} -9.50300 q^{67} +0.778473 q^{68} +4.29231 q^{69} +30.3513 q^{70} -2.45794 q^{71} +3.43173 q^{72} -5.70698 q^{73} +17.8356 q^{74} +4.83619 q^{75} +33.0342 q^{76} +17.7703 q^{77} -6.14864 q^{78} +11.2325 q^{79} +28.7291 q^{80} -7.43880 q^{81} -28.6301 q^{82} +11.6365 q^{83} -31.8529 q^{84} +0.451042 q^{85} +14.6934 q^{86} +6.90794 q^{87} +33.0491 q^{88} -4.27952 q^{89} +3.36394 q^{90} -5.98759 q^{91} +13.1520 q^{92} +4.80735 q^{93} +10.1871 q^{94} +19.1398 q^{95} -18.2548 q^{96} -3.38747 q^{97} -25.3278 q^{98} +1.96954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * q^99

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