LMFDB - Embedded newform 5077.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5077,2,Mod(1,5077)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5077, 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("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.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:	$40.5400491062$
Analytic rank:	$0$
Dimension:	$216$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	5077.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71273 q^{2} -1.56061 q^{3} +5.35892 q^{4} +1.41855 q^{5} +4.23352 q^{6} -1.24026 q^{7} -9.11187 q^{8} -0.564498 q^{9} +O(q^{10})$	\(q-2.71273 q^{2} -1.56061 q^{3} +5.35892 q^{4} +1.41855 q^{5} +4.23352 q^{6} -1.24026 q^{7} -9.11187 q^{8} -0.564498 q^{9} -3.84815 q^{10} -1.09049 q^{11} -8.36319 q^{12} -1.70420 q^{13} +3.36451 q^{14} -2.21381 q^{15} +14.0002 q^{16} +0.0690599 q^{17} +1.53133 q^{18} -5.12812 q^{19} +7.60191 q^{20} +1.93557 q^{21} +2.95821 q^{22} +5.50957 q^{23} +14.2201 q^{24} -2.98771 q^{25} +4.62305 q^{26} +5.56279 q^{27} -6.64649 q^{28} -3.90043 q^{29} +6.00546 q^{30} -1.98239 q^{31} -19.7551 q^{32} +1.70183 q^{33} -0.187341 q^{34} -1.75938 q^{35} -3.02510 q^{36} +10.5208 q^{37} +13.9112 q^{38} +2.65959 q^{39} -12.9257 q^{40} -2.16444 q^{41} -5.25068 q^{42} -7.04361 q^{43} -5.84386 q^{44} -0.800770 q^{45} -14.9460 q^{46} -6.34939 q^{47} -21.8489 q^{48} -5.46174 q^{49} +8.10486 q^{50} -0.107775 q^{51} -9.13269 q^{52} -9.99502 q^{53} -15.0904 q^{54} -1.54692 q^{55} +11.3011 q^{56} +8.00299 q^{57} +10.5808 q^{58} -7.58854 q^{59} -11.8636 q^{60} -7.37657 q^{61} +5.37770 q^{62} +0.700127 q^{63} +25.5900 q^{64} -2.41750 q^{65} -4.61661 q^{66} +7.07625 q^{67} +0.370087 q^{68} -8.59829 q^{69} +4.77273 q^{70} +5.26521 q^{71} +5.14363 q^{72} +8.99661 q^{73} -28.5400 q^{74} +4.66265 q^{75} -27.4812 q^{76} +1.35250 q^{77} -7.21477 q^{78} +4.05163 q^{79} +19.8600 q^{80} -6.98785 q^{81} +5.87156 q^{82} +1.64902 q^{83} +10.3726 q^{84} +0.0979650 q^{85} +19.1074 q^{86} +6.08706 q^{87} +9.93641 q^{88} +8.31856 q^{89} +2.17228 q^{90} +2.11366 q^{91} +29.5254 q^{92} +3.09374 q^{93} +17.2242 q^{94} -7.27450 q^{95} +30.8301 q^{96} -7.87488 q^{97} +14.8163 q^{98} +0.615580 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) $ 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * 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 $

$2$	−2.71273	−1.91819	−0.959096	−	0.283080i	$-0.908644\pi$
$2$	−2.71273	−1.91819	−0.959096	+	0.283080i	$0.908644\pi$
$3$	−1.56061	−0.901018	−0.450509	−	0.892772i	$-0.648758\pi$
$3$	−1.56061	−0.901018	−0.450509	+	0.892772i	$0.648758\pi$
$4$	5.35892	2.67946
$5$	1.41855	0.634396	0.317198	−	0.948359i	$-0.397258\pi$
$5$	1.41855	0.634396	0.317198	+	0.948359i	$0.397258\pi$
$6$	4.23352	1.72833
$7$	−1.24026	−0.468776	−0.234388	−	0.972143i	$-0.575309\pi$
$7$	−1.24026	−0.468776	−0.234388	+	0.972143i	$0.575309\pi$
$8$	−9.11187	−3.22153
$9$	−0.564498	−0.188166
$10$	−3.84815	−1.21689
$11$	−1.09049	−0.328795	−0.164398	−	0.986394i	$-0.552568\pi$
$11$	−1.09049	−0.328795	−0.164398	+	0.986394i	$0.552568\pi$
$12$	−8.36319	−2.41424
$13$	−1.70420	−0.472661	−0.236330	−	0.971673i	$-0.575945\pi$
$13$	−1.70420	−0.472661	−0.236330	+	0.971673i	$0.575945\pi$
$14$	3.36451	0.899203
$15$	−2.21381	−0.571602
$16$	14.0002	3.50006
$17$	0.0690599	0.0167495	0.00837474	−	0.999965i	$-0.497334\pi$
$17$	0.0690599	0.0167495	0.00837474	+	0.999965i	$0.497334\pi$
$18$	1.53133	0.360939
$19$	−5.12812	−1.17647	−0.588236	−	0.808690i	$-0.700177\pi$
$19$	−5.12812	−1.17647	−0.588236	+	0.808690i	$0.700177\pi$
$20$	7.60191	1.69984
$21$	1.93557	0.422376
$22$	2.95821	0.630693
$23$	5.50957	1.14882	0.574412	−	0.818566i	$-0.305231\pi$
$23$	5.50957	1.14882	0.574412	+	0.818566i	$0.305231\pi$
$24$	14.2201	2.90266
$25$	−2.98771	−0.597542
$26$	4.62305	0.906654
$27$	5.56279	1.07056
$28$	−6.64649	−1.25607
$29$	−3.90043	−0.724293	−0.362146	−	0.932121i	$-0.617956\pi$
$29$	−3.90043	−0.724293	−0.362146	+	0.932121i	$0.617956\pi$
$30$	6.00546	1.09644
$31$	−1.98239	−0.356048	−0.178024	−	0.984026i	$-0.556970\pi$
$31$	−1.98239	−0.356048	−0.178024	+	0.984026i	$0.556970\pi$
$32$	−19.7551	−3.49225
$33$	1.70183	0.296251
$34$	−0.187341	−0.0321287
$35$	−1.75938	−0.297389
$36$	−3.02510	−0.504184
$37$	10.5208	1.72960	0.864801	−	0.502115i	$-0.167445\pi$
$37$	10.5208	1.72960	0.864801	+	0.502115i	$0.167445\pi$
$38$	13.9112	2.25670
$39$	2.65959	0.425876
$40$	−12.9257	−2.04373
$41$	−2.16444	−0.338029	−0.169015	−	0.985614i	$-0.554059\pi$
$41$	−2.16444	−0.338029	−0.169015	+	0.985614i	$0.554059\pi$
$42$	−5.25068	−0.810198
$43$	−7.04361	−1.07414	−0.537070	−	0.843538i	$-0.680469\pi$
$43$	−7.04361	−1.07414	−0.537070	+	0.843538i	$0.680469\pi$
$44$	−5.84386	−0.880995
$45$	−0.800770	−0.119372
$46$	−14.9460	−2.20367
$47$	−6.34939	−0.926154	−0.463077	−	0.886318i	$-0.653255\pi$
$47$	−6.34939	−0.926154	−0.463077	+	0.886318i	$0.653255\pi$
$48$	−21.8489	−3.15361
$49$	−5.46174	−0.780249
$50$	8.10486	1.14620
$51$	−0.107775	−0.0150916
$52$	−9.13269	−1.26648
$53$	−9.99502	−1.37292	−0.686461	−	0.727167i	$-0.740837\pi$
$53$	−9.99502	−1.37292	−0.686461	+	0.727167i	$0.740837\pi$
$54$	−15.0904	−2.05354
$55$	−1.54692	−0.208586
$56$	11.3011	1.51018
$57$	8.00299	1.06002
$58$	10.5808	1.38933
$59$	−7.58854	−0.987943	−0.493972	−	0.869478i	$-0.664455\pi$
$59$	−7.58854	−0.987943	−0.493972	+	0.869478i	$0.664455\pi$
$60$	−11.8636	−1.53159
$61$	−7.37657	−0.944473	−0.472236	−	0.881472i	$-0.656553\pi$
$61$	−7.37657	−0.944473	−0.472236	+	0.881472i	$0.656553\pi$
$62$	5.37770	0.682969
$63$	0.700127	0.0882078
$64$	25.5900	3.19875
$65$	−2.41750	−0.299854
$66$	−4.61661	−0.568266
$67$	7.07625	0.864501	0.432251	−	0.901753i	$-0.357720\pi$
$67$	7.07625	0.864501	0.432251	+	0.901753i	$0.357720\pi$
$68$	0.370087	0.0448796
$69$	−8.59829	−1.03511
$70$	4.77273	0.570450
$71$	5.26521	0.624865	0.312433	−	0.949940i	$-0.398856\pi$
$71$	5.26521	0.624865	0.312433	+	0.949940i	$0.398856\pi$
$72$	5.14363	0.606183
$73$	8.99661	1.05297	0.526487	−	0.850183i	$-0.323509\pi$
$73$	8.99661	1.05297	0.526487	+	0.850183i	$0.323509\pi$
$74$	−28.5400	−3.31771
$75$	4.66265	0.538396
$76$	−27.4812	−3.15231
$77$	1.35250	0.154131
$78$	−7.21477	−0.816912
$79$	4.05163	0.455844	0.227922	−	0.973679i	$-0.426807\pi$
$79$	4.05163	0.455844	0.227922	+	0.973679i	$0.426807\pi$
$80$	19.8600	2.22042
$81$	−6.98785	−0.776427
$82$	5.87156	0.648405
$83$	1.64902	0.181004	0.0905019	−	0.995896i	$-0.471153\pi$
$83$	1.64902	0.181004	0.0905019	+	0.995896i	$0.471153\pi$
$84$	10.3726	1.13174
$85$	0.0979650	0.0106258
$86$	19.1074	2.06041
$87$	6.08706	0.652601
$88$	9.93641	1.05922
$89$	8.31856	0.881765	0.440883	−	0.897565i	$-0.354666\pi$
$89$	8.31856	0.881765	0.440883	+	0.897565i	$0.354666\pi$
$90$	2.17228	0.228978
$91$	2.11366	0.221572
$92$	29.5254	3.07823
$93$	3.09374	0.320806
$94$	17.2242	1.77654
$95$	−7.27450	−0.746348
$96$	30.8301	3.14658
$97$	−7.87488	−0.799573	−0.399787	−	0.916608i	$-0.630916\pi$
$97$	−7.87488	−0.799573	−0.399787	+	0.916608i	$0.630916\pi$
$98$	14.8163	1.49667
$99$	0.615580	0.0618681
$100$	−16.0109	−1.60109
$101$	9.96459	0.991514	0.495757	−	0.868461i	$-0.334891\pi$
$101$	9.96459	0.991514	0.495757	+	0.868461i	$0.334891\pi$
$102$	0.292366	0.0289486
$103$	2.20029	0.216801	0.108401	−	0.994107i	$-0.465427\pi$
$103$	2.20029	0.216801	0.108401	+	0.994107i	$0.465427\pi$
$104$	15.5285	1.52269
$105$	2.74570	0.267953
$106$	27.1138	2.63353
$107$	8.25043	0.797599	0.398800	−	0.917038i	$-0.369427\pi$
$107$	8.25043	0.797599	0.398800	+	0.917038i	$0.369427\pi$
$108$	29.8106	2.86852
$109$	−15.6141	−1.49556	−0.747778	−	0.663949i	$-0.768879\pi$
$109$	−15.6141	−1.49556	−0.747778	+	0.663949i	$0.768879\pi$
$110$	4.19638	0.400109
$111$	−16.4188	−1.55840
$112$	−17.3640	−1.64074
$113$	−3.89674	−0.366574	−0.183287	−	0.983059i	$-0.558674\pi$
$113$	−3.89674	−0.366574	−0.183287	+	0.983059i	$0.558674\pi$
$114$	−21.7100	−2.03333
$115$	7.81561	0.728809
$116$	−20.9021	−1.94071
$117$	0.962020	0.0889387
$118$	20.5857	1.89507
$119$	−0.0856525	−0.00785175
$120$	20.1719	1.84143
$121$	−9.81083	−0.891894
$122$	20.0107	1.81168
$123$	3.37785	0.304571
$124$	−10.6235	−0.954017
$125$	−11.3310	−1.01347
$126$	−1.89926	−0.169199
$127$	−21.5257	−1.91010	−0.955051	−	0.296443i	$-0.904200\pi$
$127$	−21.5257	−1.91010	−0.955051	+	0.296443i	$0.904200\pi$
$128$	−29.9086	−2.64357
$129$	10.9923	0.967820
$130$	6.55803	0.575178
$131$	1.83015	0.159901	0.0799506	−	0.996799i	$-0.474524\pi$
$131$	1.83015	0.159901	0.0799506	+	0.996799i	$0.474524\pi$
$132$	9.11998	0.793792
$133$	6.36023	0.551502
$134$	−19.1960	−1.65828
$135$	7.89111	0.679158
$136$	−0.629264	−0.0539590
$137$	9.20913	0.786789	0.393394	−	0.919370i	$-0.371301\pi$
$137$	9.20913	0.786789	0.393394	+	0.919370i	$0.371301\pi$
$138$	23.3249	1.98554
$139$	−2.40481	−0.203973	−0.101987	−	0.994786i	$-0.532520\pi$
$139$	−2.40481	−0.203973	−0.101987	+	0.994786i	$0.532520\pi$
$140$	−9.42838	−0.796844
$141$	9.90892	0.834482
$142$	−14.2831	−1.19861
$143$	1.85842	0.155409
$144$	−7.90310	−0.658592
$145$	−5.53297	−0.459488
$146$	−24.4054	−2.01981
$147$	8.52365	0.703019
$148$	56.3799	4.63440
$149$	−2.10140	−0.172153	−0.0860767	−	0.996289i	$-0.527433\pi$
$149$	−2.10140	−0.172153	−0.0860767	+	0.996289i	$0.527433\pi$
$150$	−12.6485	−1.03275
$151$	1.80539	0.146921	0.0734604	−	0.997298i	$-0.476596\pi$
$151$	1.80539	0.146921	0.0734604	+	0.997298i	$0.476596\pi$
$152$	46.7268	3.79004
$153$	−0.0389842	−0.00315168
$154$	−3.66897	−0.295654
$155$	−2.81212	−0.225875
$156$	14.2526	1.14112
$157$	7.36639	0.587902	0.293951	−	0.955821i	$-0.405030\pi$
$157$	7.36639	0.587902	0.293951	+	0.955821i	$0.405030\pi$
$158$	−10.9910	−0.874396
$159$	15.5983	1.23703
$160$	−28.0237	−2.21547
$161$	−6.83332	−0.538541
$162$	18.9562	1.48934
$163$	16.9298	1.32605	0.663023	−	0.748599i	$-0.269273\pi$
$163$	16.9298	1.32605	0.663023	+	0.748599i	$0.269273\pi$
$164$	−11.5991	−0.905737
$165$	2.41413	0.187940
$166$	−4.47336	−0.347200
$167$	17.8943	1.38470	0.692350	−	0.721562i	$-0.256575\pi$
$167$	17.8943	1.38470	0.692350	+	0.721562i	$0.256575\pi$
$168$	−17.6366	−1.36070
$169$	−10.0957	−0.776592
$170$	−0.265753	−0.0203823
$171$	2.89481	0.221372
$172$	−37.7462	−2.87812
$173$	9.02172	0.685909	0.342954	−	0.939352i	$-0.388572\pi$
$173$	9.02172	0.685909	0.342954	+	0.939352i	$0.388572\pi$
$174$	−16.5126	−1.25181
$175$	3.70555	0.280113
$176$	−15.2671	−1.15080
$177$	11.8427	0.890155
$178$	−22.5660	−1.69140
$179$	20.7408	1.55024	0.775121	−	0.631813i	$-0.217689\pi$
$179$	20.7408	1.55024	0.775121	+	0.631813i	$0.217689\pi$
$180$	−4.29127	−0.319852
$181$	3.48264	0.258863	0.129431	−	0.991588i	$-0.458685\pi$
$181$	3.48264	0.258863	0.129431	+	0.991588i	$0.458685\pi$
$182$	−5.73380	−0.425018
$183$	11.5119	0.850987
$184$	−50.2025	−3.70098
$185$	14.9242	1.09725
$186$	−8.39249	−0.615367
$187$	−0.0753092	−0.00550715
$188$	−34.0259	−2.48159
$189$	−6.89933	−0.501853
$190$	19.7338	1.43164
$191$	−1.74317	−0.126131	−0.0630656	−	0.998009i	$-0.520088\pi$
$191$	−1.74317	−0.126131	−0.0630656	+	0.998009i	$0.520088\pi$
$192$	−39.9360	−2.88213
$193$	−7.67337	−0.552341	−0.276171	−	0.961109i	$-0.589065\pi$
$193$	−7.67337	−0.552341	−0.276171	+	0.961109i	$0.589065\pi$
$194$	21.3625	1.53374
$195$	3.77277	0.270174
$196$	−29.2691	−2.09065
$197$	−1.20267	−0.0856864	−0.0428432	−	0.999082i	$-0.513642\pi$
$197$	−1.20267	−0.0856864	−0.0428432	+	0.999082i	$0.513642\pi$
$198$	−1.66991	−0.118675
$199$	−4.30631	−0.305266	−0.152633	−	0.988283i	$-0.548775\pi$
$199$	−4.30631	−0.305266	−0.152633	+	0.988283i	$0.548775\pi$
$200$	27.2236	1.92500
$201$	−11.0433	−0.778932
$202$	−27.0313	−1.90191
$203$	4.83757	0.339531
$204$	−0.577561	−0.0404373
$205$	−3.07038	−0.214444
$206$	−5.96881	−0.415867
$207$	−3.11014	−0.216170
$208$	−23.8592	−1.65434
$209$	5.59217	0.386818
$210$	−7.44837	−0.513986
$211$	−3.37008	−0.232006	−0.116003	−	0.993249i	$-0.537008\pi$
$211$	−3.37008	−0.232006	−0.116003	+	0.993249i	$0.537008\pi$
$212$	−53.5626	−3.67869
$213$	−8.21693	−0.563015
$214$	−22.3812	−1.52995
$215$	−9.99172	−0.681430
$216$	−50.6874	−3.44884
$217$	2.45869	0.166907
$218$	42.3568	2.86876
$219$	−14.0402	−0.948749
$220$	−8.28982	−0.558899
$221$	−0.117692	−0.00791682
$222$	44.5398	2.98932
$223$	−11.8886	−0.796122	−0.398061	−	0.917359i	$-0.630317\pi$
$223$	−11.8886	−0.796122	−0.398061	+	0.917359i	$0.630317\pi$
$224$	24.5016	1.63708
$225$	1.68656	0.112437
$226$	10.5708	0.703160
$227$	−7.46056	−0.495175	−0.247588	−	0.968866i	$-0.579638\pi$
$227$	−7.46056	−0.495175	−0.247588	+	0.968866i	$0.579638\pi$
$228$	42.8874	2.84029
$229$	−30.1797	−1.99433	−0.997166	−	0.0752269i	$-0.976032\pi$
$229$	−30.1797	−1.99433	−0.997166	+	0.0752269i	$0.976032\pi$
$230$	−21.2017	−1.39800
$231$	−2.11072	−0.138875
$232$	35.5403	2.33333
$233$	11.9243	0.781189	0.390594	−	0.920563i	$-0.372270\pi$
$233$	11.9243	0.781189	0.390594	+	0.920563i	$0.372270\pi$
$234$	−2.60970	−0.170602
$235$	−9.00694	−0.587548
$236$	−40.6664	−2.64716
$237$	−6.32301	−0.410724
$238$	0.232352	0.0150612
$239$	−13.9164	−0.900180	−0.450090	−	0.892983i	$-0.648608\pi$
$239$	−13.9164	−0.900180	−0.450090	+	0.892983i	$0.648608\pi$
$240$	−30.9938	−2.00064
$241$	−23.3562	−1.50451	−0.752253	−	0.658874i	$-0.771033\pi$
$241$	−23.3562	−1.50451	−0.752253	+	0.658874i	$0.771033\pi$
$242$	26.6142	1.71082
$243$	−5.78307	−0.370984
$244$	−39.5305	−2.53068
$245$	−7.74777	−0.494987
$246$	−9.16321	−0.584225
$247$	8.73936	0.556072
$248$	18.0633	1.14702
$249$	−2.57348	−0.163088
$250$	30.7379	1.94404
$251$	25.2226	1.59204	0.796019	−	0.605271i	$-0.206935\pi$
$251$	25.2226	1.59204	0.796019	+	0.605271i	$0.206935\pi$
$252$	3.75193	0.236349
$253$	−6.00814	−0.377728
$254$	58.3936	3.66394
$255$	−0.152885	−0.00957404
$256$	29.9540	1.87213
$257$	26.4096	1.64739	0.823694	−	0.567035i	$-0.191910\pi$
$257$	26.4096	1.64739	0.823694	+	0.567035i	$0.191910\pi$
$258$	−29.8192	−1.85646
$259$	−13.0485	−0.810796
$260$	−12.9552	−0.803447
$261$	2.20179	0.136287
$262$	−4.96472	−0.306721
$263$	6.08434	0.375176	0.187588	−	0.982248i	$-0.439933\pi$
$263$	6.08434	0.375176	0.187588	+	0.982248i	$0.439933\pi$
$264$	−15.5069	−0.954381
$265$	−14.1785	−0.870976
$266$	−17.2536	−1.05789
$267$	−12.9820	−0.794486
$268$	37.9211	2.31640
$269$	7.04730	0.429682	0.214841	−	0.976649i	$-0.431077\pi$
$269$	7.04730	0.429682	0.214841	+	0.976649i	$0.431077\pi$
$270$	−21.4065	−1.30276
$271$	−1.49702	−0.0909375	−0.0454688	−	0.998966i	$-0.514478\pi$
$271$	−1.49702	−0.0909375	−0.0454688	+	0.998966i	$0.514478\pi$
$272$	0.966854	0.0586241
$273$	−3.29860	−0.199640
$274$	−24.9819	−1.50921
$275$	3.25807	0.196469
$276$	−46.0776	−2.77354
$277$	9.25506	0.556083	0.278041	−	0.960569i	$-0.410315\pi$
$277$	9.25506	0.556083	0.278041	+	0.960569i	$0.410315\pi$
$278$	6.52361	0.391260
$279$	1.11906	0.0669962
$280$	16.0312	0.958050
$281$	3.53201	0.210702	0.105351	−	0.994435i	$-0.466403\pi$
$281$	3.53201	0.210702	0.105351	+	0.994435i	$0.466403\pi$
$282$	−26.8803	−1.60070
$283$	−8.81917	−0.524245	−0.262123	−	0.965035i	$-0.584422\pi$
$283$	−8.81917	−0.524245	−0.262123	+	0.965035i	$0.584422\pi$
$284$	28.2159	1.67430
$285$	11.3527	0.672473
$286$	−5.04139	−0.298104
$287$	2.68448	0.158460
$288$	11.1517	0.657123
$289$	−16.9952	−0.999719
$290$	15.0095	0.881387
$291$	12.2896	0.720430
$292$	48.2122	2.82140
$293$	−25.0376	−1.46271	−0.731357	−	0.681995i	$-0.761113\pi$
$293$	−25.0376	−1.46271	−0.731357	+	0.681995i	$0.761113\pi$
$294$	−23.1224	−1.34853
$295$	−10.7647	−0.626747
$296$	−95.8638	−5.57197
$297$	−6.06617	−0.351995
$298$	5.70054	0.330223
$299$	−9.38942	−0.543004
$300$	24.9868	1.44261
$301$	8.73594	0.503531
$302$	−4.89755	−0.281823
$303$	−15.5508	−0.893372
$304$	−71.7948	−4.11772
$305$	−10.4640	−0.599169
$306$	0.105754	0.00604554
$307$	−1.59450	−0.0910032	−0.0455016	−	0.998964i	$-0.514489\pi$
$307$	−1.59450	−0.0910032	−0.0455016	+	0.998964i	$0.514489\pi$
$308$	7.24793	0.412989
$309$	−3.43380	−0.195342
$310$	7.62855	0.433272
$311$	16.8063	0.952999	0.476499	−	0.879175i	$-0.341905\pi$
$311$	16.8063	0.952999	0.476499	+	0.879175i	$0.341905\pi$
$312$	−24.2339	−1.37197
$313$	−11.9435	−0.675085	−0.337543	−	0.941310i	$-0.609596\pi$
$313$	−11.9435	−0.675085	−0.337543	+	0.941310i	$0.609596\pi$
$314$	−19.9830	−1.12771
$315$	0.993167	0.0559586
$316$	21.7124	1.22142
$317$	−11.2285	−0.630654	−0.315327	−	0.948983i	$-0.602114\pi$
$317$	−11.2285	−0.630654	−0.315327	+	0.948983i	$0.602114\pi$
$318$	−42.3141	−2.37286
$319$	4.25339	0.238144
$320$	36.3008	2.02927
$321$	−12.8757	−0.718652
$322$	18.5370	1.03303
$323$	−0.354147	−0.0197053
$324$	−37.4473	−2.08041
$325$	5.09166	0.282435
$326$	−45.9261	−2.54361
$327$	24.3675	1.34752
$328$	19.7221	1.08897
$329$	7.87493	0.434159
$330$	−6.54890	−0.360505
$331$	4.88661	0.268592	0.134296	−	0.990941i	$-0.457123\pi$
$331$	4.88661	0.268592	0.134296	+	0.990941i	$0.457123\pi$
$332$	8.83699	0.484993
$333$	−5.93895	−0.325452
$334$	−48.5424	−2.65612
$335$	10.0380	0.548436
$336$	27.0984	1.47834
$337$	26.2853	1.43185	0.715927	−	0.698175i	$-0.246004\pi$
$337$	26.2853	1.43185	0.715927	+	0.698175i	$0.246004\pi$
$338$	27.3869	1.48965
$339$	6.08129	0.330290
$340$	0.524987	0.0284714
$341$	2.16178	0.117067
$342$	−7.85286	−0.424634
$343$	15.4559	0.834538
$344$	64.1804	3.46038
$345$	−12.1971	−0.656671
$346$	−24.4735	−1.31570
$347$	−24.5843	−1.31976	−0.659878	−	0.751373i	$-0.729392\pi$
$347$	−24.5843	−1.31976	−0.659878	+	0.751373i	$0.729392\pi$
$348$	32.6201	1.74862
$349$	−6.61163	−0.353913	−0.176956	−	0.984219i	$-0.556625\pi$
$349$	−6.61163	−0.353913	−0.176956	+	0.984219i	$0.556625\pi$
$350$	−10.0522	−0.537311
$351$	−9.48012	−0.506011
$352$	21.5428	1.14824
$353$	−25.4699	−1.35563	−0.677814	−	0.735233i	$-0.737073\pi$
$353$	−25.4699	−1.35563	−0.677814	+	0.735233i	$0.737073\pi$
$354$	−32.1262	−1.70749
$355$	7.46897	0.396412
$356$	44.5785	2.36266
$357$	0.133670	0.00707457
$358$	−56.2643	−2.97366
$359$	17.3540	0.915907	0.457954	−	0.888976i	$-0.348583\pi$
$359$	17.3540	0.915907	0.457954	+	0.888976i	$0.348583\pi$
$360$	7.29651	0.384560
$361$	7.29761	0.384085
$362$	−9.44748	−0.496549
$363$	15.3109	0.803612
$364$	11.3270	0.593694
$365$	12.7622	0.668002
$366$	−31.2288	−1.63236
$367$	11.0514	0.576881	0.288440	−	0.957498i	$-0.406863\pi$
$367$	11.0514	0.576881	0.288440	+	0.957498i	$0.406863\pi$
$368$	77.1352	4.02095
$369$	1.22182	0.0636057
$370$	−40.4855	−2.10474
$371$	12.3965	0.643593
$372$	16.5791	0.859587
$373$	17.2130	0.891257	0.445628	−	0.895218i	$-0.352980\pi$
$373$	17.2130	0.891257	0.445628	+	0.895218i	$0.352980\pi$
$374$	0.204294	0.0105638
$375$	17.6832	0.913158
$376$	57.8548	2.98363
$377$	6.64713	0.342345
$378$	18.7161	0.962650
$379$	21.6062	1.10984	0.554919	−	0.831905i	$-0.312749\pi$
$379$	21.6062	1.10984	0.554919	+	0.831905i	$0.312749\pi$
$380$	−38.9835	−1.99981
$381$	33.5933	1.72104
$382$	4.72875	0.241944
$383$	16.9682	0.867037	0.433518	−	0.901145i	$-0.357272\pi$
$383$	16.9682	0.867037	0.433518	+	0.901145i	$0.357272\pi$
$384$	46.6756	2.38191
$385$	1.91859	0.0977803
$386$	20.8158	1.05950
$387$	3.97610	0.202117
$388$	−42.2009	−2.14243
$389$	3.91854	0.198678	0.0993388	−	0.995054i	$-0.468327\pi$
$389$	3.91854	0.198678	0.0993388	+	0.995054i	$0.468327\pi$
$390$	−10.2345	−0.518246
$391$	0.380490	0.0192422
$392$	49.7667	2.51360
$393$	−2.85615	−0.144074
$394$	3.26251	0.164363
$395$	5.74745	0.289185
$396$	3.29885	0.165773
$397$	28.6515	1.43798	0.718988	−	0.695023i	$-0.244606\pi$
$397$	28.6515	1.43798	0.718988	+	0.695023i	$0.244606\pi$
$398$	11.6819	0.585560
$399$	−9.92583	−0.496913
$400$	−41.8286	−2.09143
$401$	11.9504	0.596775	0.298388	−	0.954445i	$-0.403551\pi$
$401$	11.9504	0.596775	0.298388	+	0.954445i	$0.403551\pi$
$402$	29.9574	1.49414
$403$	3.37840	0.168290
$404$	53.3995	2.65672
$405$	−9.91262	−0.492562
$406$	−13.1230	−0.651286
$407$	−11.4728	−0.568685
$408$	0.982036	0.0486180
$409$	−22.8418	−1.12946	−0.564728	−	0.825277i	$-0.691019\pi$
$409$	−22.8418	−1.12946	−0.564728	+	0.825277i	$0.691019\pi$
$410$	8.32911	0.411346
$411$	−14.3719	−0.708911
$412$	11.7912	0.580911
$413$	9.41179	0.463124
$414$	8.43699	0.414655
$415$	2.33922	0.114828
$416$	33.6668	1.65065
$417$	3.75297	0.183784
$418$	−15.1701	−0.741992
$419$	6.95482	0.339765	0.169883	−	0.985464i	$-0.445661\pi$
$419$	6.95482	0.339765	0.169883	+	0.985464i	$0.445661\pi$
$420$	14.7140	0.717971
$421$	31.0666	1.51409	0.757046	−	0.653362i	$-0.226642\pi$
$421$	31.0666	1.51409	0.757046	+	0.653362i	$0.226642\pi$
$422$	9.14213	0.445032
$423$	3.58422	0.174271
$424$	91.0734	4.42291
$425$	−0.206331	−0.0100085
$426$	22.2904	1.07997
$427$	9.14890	0.442746
$428$	44.2134	2.13714
$429$	−2.90026	−0.140026
$430$	27.1049	1.30711
$431$	35.8846	1.72850	0.864249	−	0.503064i	$-0.167794\pi$
$431$	35.8846	1.72850	0.864249	+	0.503064i	$0.167794\pi$
$432$	77.8803	3.74702
$433$	35.6337	1.71244	0.856222	−	0.516608i	$-0.172805\pi$
$433$	35.6337	1.71244	0.856222	+	0.516608i	$0.172805\pi$
$434$	−6.66977	−0.320159
$435$	8.63480	0.414007
$436$	−83.6746	−4.00729
$437$	−28.2537	−1.35156
$438$	38.0873	1.81988
$439$	−32.3343	−1.54323	−0.771617	−	0.636088i	$-0.780552\pi$
$439$	−32.3343	−1.54323	−0.771617	+	0.636088i	$0.780552\pi$
$440$	14.0953	0.671968
$441$	3.08314	0.146816
$442$	0.319267	0.0151860
$443$	−20.8139	−0.988898	−0.494449	−	0.869207i	$-0.664630\pi$
$443$	−20.8139	−0.988898	−0.494449	+	0.869207i	$0.664630\pi$
$444$	−87.9871	−4.17568
$445$	11.8003	0.559388
$446$	32.2507	1.52711
$447$	3.27946	0.155113
$448$	−31.7384	−1.49950
$449$	−9.33986	−0.440775	−0.220388	−	0.975412i	$-0.570732\pi$
$449$	−9.33986	−0.440775	−0.220388	+	0.975412i	$0.570732\pi$
$450$	−4.57518	−0.215676
$451$	2.36031	0.111142
$452$	−20.8823	−0.982222
$453$	−2.81751	−0.132378
$454$	20.2385	0.949841
$455$	2.99834	0.140564
$456$	−72.9222	−3.41490
$457$	−21.9286	−1.02578	−0.512888	−	0.858456i	$-0.671424\pi$
$457$	−21.9286	−1.02578	−0.512888	+	0.858456i	$0.671424\pi$
$458$	81.8696	3.82551
$459$	0.384166	0.0179313
$460$	41.8833	1.95282
$461$	19.2143	0.894899	0.447449	−	0.894309i	$-0.352332\pi$
$461$	19.2143	0.894899	0.447449	+	0.894309i	$0.352332\pi$
$462$	5.72582	0.266389
$463$	−17.7095	−0.823030	−0.411515	−	0.911403i	$-0.635000\pi$
$463$	−17.7095	−0.823030	−0.411515	+	0.911403i	$0.635000\pi$
$464$	−54.6070	−2.53506
$465$	4.38863	0.203518
$466$	−32.3475	−1.49847
$467$	−22.8629	−1.05797	−0.528984	−	0.848632i	$-0.677427\pi$
$467$	−22.8629	−1.05797	−0.528984	+	0.848632i	$0.677427\pi$
$468$	5.15539	0.238308
$469$	−8.77642	−0.405258
$470$	24.4334	1.12703
$471$	−11.4961	−0.529710
$472$	69.1458	3.18269
$473$	7.68099	0.353172
$474$	17.1526	0.787847
$475$	15.3213	0.702991
$476$	−0.459005	−0.0210385
$477$	5.64217	0.258337
$478$	37.7516	1.72672
$479$	17.7932	0.812993	0.406496	−	0.913652i	$-0.366750\pi$
$479$	17.7932	0.812993	0.406496	+	0.913652i	$0.366750\pi$
$480$	43.7341	1.99618
$481$	−17.9295	−0.817515
$482$	63.3592	2.88593
$483$	10.6642	0.485236
$484$	−52.5755	−2.38980
$485$	−11.1709	−0.507246
$486$	15.6879	0.711619
$487$	14.0626	0.637237	0.318618	−	0.947883i	$-0.396781\pi$
$487$	14.0626	0.637237	0.318618	+	0.947883i	$0.396781\pi$
$488$	67.2143	3.04265
$489$	−26.4208	−1.19479
$490$	21.0176	0.949480
$491$	−9.39146	−0.423831	−0.211915	−	0.977288i	$-0.567970\pi$
$491$	−9.39146	−0.423831	−0.211915	+	0.977288i	$0.567970\pi$
$492$	18.1017	0.816086
$493$	−0.269364	−0.0121315
$494$	−23.7075	−1.06665
$495$	0.873233	0.0392489
$496$	−27.7539	−1.24619
$497$	−6.53025	−0.292922
$498$	6.98117	0.312834
$499$	−26.6825	−1.19447	−0.597237	−	0.802065i	$-0.703735\pi$
$499$	−26.6825	−1.19447	−0.597237	+	0.802065i	$0.703735\pi$
$500$	−60.7219	−2.71557
$501$	−27.9260	−1.24764
$502$	−68.4223	−3.05384
$503$	35.4839	1.58215	0.791075	−	0.611720i	$-0.209522\pi$
$503$	35.4839	1.58215	0.791075	+	0.611720i	$0.209522\pi$
$504$	−6.37947	−0.284164
$505$	14.1353	0.629012
$506$	16.2985	0.724555
$507$	15.7554	0.699723
$508$	−115.355	−5.11804
$509$	26.8679	1.19090	0.595449	−	0.803393i	$-0.296974\pi$
$509$	26.8679	1.19090	0.595449	+	0.803393i	$0.296974\pi$
$510$	0.414737	0.0183648
$511$	−11.1582	−0.493609
$512$	−21.4401	−0.947527
$513$	−28.5267	−1.25948
$514$	−71.6423	−3.16001
$515$	3.12123	0.137538
$516$	58.9070	2.59324
$517$	6.92395	0.304515
$518$	35.3972	1.55526
$519$	−14.0794	−0.618016
$520$	22.0279	0.965989
$521$	14.7647	0.646852	0.323426	−	0.946254i	$-0.395165\pi$
$521$	14.7647	0.646852	0.323426	+	0.946254i	$0.395165\pi$
$522$	−5.97287	−0.261425
$523$	31.8730	1.39371	0.696855	−	0.717212i	$-0.254582\pi$
$523$	31.8730	1.39371	0.696855	+	0.717212i	$0.254582\pi$
$524$	9.80765	0.428449
$525$	−5.78292	−0.252387
$526$	−16.5052	−0.719661
$527$	−0.136904	−0.00596362
$528$	23.8260	1.03689
$529$	7.35536	0.319798
$530$	38.4624	1.67070
$531$	4.28372	0.185897
$532$	34.0840	1.47773
$533$	3.68865	0.159773
$534$	35.2168	1.52398
$535$	11.7037	0.505994
$536$	−64.4779	−2.78502
$537$	−32.3683	−1.39680
$538$	−19.1175	−0.824212
$539$	5.95598	0.256542
$540$	42.2878	1.81978
$541$	−18.3107	−0.787237	−0.393618	−	0.919274i	$-0.628777\pi$
$541$	−18.3107	−0.787237	−0.393618	+	0.919274i	$0.628777\pi$
$542$	4.06102	0.174436
$543$	−5.43505	−0.233240
$544$	−1.36429	−0.0584934
$545$	−22.1494	−0.948774
$546$	8.94823	0.382949
$547$	14.0980	0.602789	0.301394	−	0.953500i	$-0.402548\pi$
$547$	14.0980	0.602789	0.301394	+	0.953500i	$0.402548\pi$
$548$	49.3510	2.10817
$549$	4.16406	0.177718
$550$	−8.83828	−0.376866
$551$	20.0019	0.852109
$552$	78.3465	3.33465
$553$	−5.02509	−0.213689
$554$	−25.1065	−1.06667
$555$	−23.2909	−0.988644
$556$	−12.8872	−0.546539
$557$	41.3339	1.75137	0.875687	−	0.482879i	$-0.160409\pi$
$557$	41.3339	1.75137	0.875687	+	0.482879i	$0.160409\pi$
$558$	−3.03570	−0.128512
$559$	12.0037	0.507704
$560$	−24.6317	−1.04088
$561$	0.117528	0.00496204
$562$	−9.58140	−0.404167
$563$	36.3540	1.53214	0.766069	−	0.642758i	$-0.222210\pi$
$563$	36.3540	1.53214	0.766069	+	0.642758i	$0.222210\pi$
$564$	53.1012	2.23596
$565$	−5.52773	−0.232553
$566$	23.9241	1.00560
$567$	8.66678	0.363971
$568$	−47.9759	−2.01302
$569$	6.66130	0.279256	0.139628	−	0.990204i	$-0.455409\pi$
$569$	6.66130	0.279256	0.139628	+	0.990204i	$0.455409\pi$
$570$	−30.7967	−1.28993
$571$	21.1023	0.883104	0.441552	−	0.897236i	$-0.354428\pi$
$571$	21.1023	0.883104	0.441552	+	0.897236i	$0.354428\pi$
$572$	9.95912	0.416412
$573$	2.72040	0.113646
$574$	−7.28229	−0.303957
$575$	−16.4610	−0.686471
$576$	−14.4455	−0.601897
$577$	20.5777	0.856661	0.428331	−	0.903622i	$-0.359102\pi$
$577$	20.5777	0.856661	0.428331	+	0.903622i	$0.359102\pi$
$578$	46.1035	1.91765
$579$	11.9751	0.497670
$580$	−29.6508	−1.23118
$581$	−2.04523	−0.0848502
$582$	−33.3385	−1.38192
$583$	10.8995	0.451410
$584$	−81.9760	−3.39219
$585$	1.36467	0.0564224
$586$	67.9204	2.80577
$587$	11.6165	0.479464	0.239732	−	0.970839i	$-0.422940\pi$
$587$	11.6165	0.479464	0.239732	+	0.970839i	$0.422940\pi$
$588$	45.6776	1.88371
$589$	10.1659	0.418880
$590$	29.2019	1.20222
$591$	1.87689	0.0772050
$592$	147.293	6.05370
$593$	−6.59952	−0.271010	−0.135505	−	0.990777i	$-0.543266\pi$
$593$	−6.59952	−0.271010	−0.135505	+	0.990777i	$0.543266\pi$
$594$	16.4559	0.675194
$595$	−0.121503	−0.00498112
$596$	−11.2612	−0.461278
$597$	6.72047	0.275051
$598$	25.4710	1.04159
$599$	24.9869	1.02094	0.510469	−	0.859896i	$-0.329472\pi$
$599$	24.9869	1.02094	0.510469	+	0.859896i	$0.329472\pi$
$600$	−42.4855	−1.73446
$601$	−14.4301	−0.588615	−0.294308	−	0.955711i	$-0.595089\pi$
$601$	−14.4301	−0.588615	−0.294308	+	0.955711i	$0.595089\pi$
$602$	−23.6983	−0.965870
$603$	−3.99453	−0.162670
$604$	9.67497	0.393669
$605$	−13.9172	−0.565813
$606$	42.1853	1.71366
$607$	−5.56243	−0.225772	−0.112886	−	0.993608i	$-0.536009\pi$
$607$	−5.56243	−0.225772	−0.112886	+	0.993608i	$0.536009\pi$
$608$	101.307	4.10853
$609$	−7.54956	−0.305924
$610$	28.3862	1.14932
$611$	10.8206	0.437757
$612$	−0.208913	−0.00844482
$613$	−6.45541	−0.260731	−0.130366	−	0.991466i	$-0.541615\pi$
$613$	−6.45541	−0.260731	−0.130366	+	0.991466i	$0.541615\pi$
$614$	4.32547	0.174562
$615$	4.79166	0.193218
$616$	−12.3238	−0.496539
$617$	−4.53749	−0.182673	−0.0913363	−	0.995820i	$-0.529114\pi$
$617$	−4.53749	−0.182673	−0.0913363	+	0.995820i	$0.529114\pi$
$618$	9.31499	0.374704
$619$	18.6434	0.749341	0.374671	−	0.927158i	$-0.377756\pi$
$619$	18.6434	0.749341	0.374671	+	0.927158i	$0.377756\pi$
$620$	−15.0700	−0.605224
$621$	30.6486	1.22988
$622$	−45.5911	−1.82804
$623$	−10.3172	−0.413350
$624$	37.2349	1.49059
$625$	−1.13503	−0.0454013
$626$	32.3995	1.29494
$627$	−8.72719	−0.348530
$628$	39.4759	1.57526
$629$	0.726562	0.0289699
$630$	−2.69420	−0.107339
$631$	5.88623	0.234327	0.117163	−	0.993113i	$-0.462620\pi$
$631$	5.88623	0.234327	0.117163	+	0.993113i	$0.462620\pi$
$632$	−36.9179	−1.46852
$633$	5.25938	0.209041
$634$	30.4598	1.20972
$635$	−30.5354	−1.21176
$636$	83.5903	3.31457
$637$	9.30792	0.368793
$638$	−11.5383	−0.456806
$639$	−2.97220	−0.117578
$640$	−42.4269	−1.67707
$641$	4.53080	0.178956	0.0894780	−	0.995989i	$-0.471480\pi$
$641$	4.53080	0.178956	0.0894780	+	0.995989i	$0.471480\pi$
$642$	34.9284	1.37851
$643$	42.2298	1.66538	0.832690	−	0.553740i	$-0.186800\pi$
$643$	42.2298	1.66538	0.832690	+	0.553740i	$0.186800\pi$
$644$	−36.6193	−1.44300
$645$	15.5932	0.613981
$646$	0.960707	0.0377985
$647$	−10.9571	−0.430768	−0.215384	−	0.976529i	$-0.569100\pi$
$647$	−10.9571	−0.430768	−0.215384	+	0.976529i	$0.569100\pi$
$648$	63.6723	2.50129
$649$	8.27523	0.324831
$650$	−13.8123	−0.541764
$651$	−3.83705	−0.150386
$652$	90.7256	3.55309
$653$	−17.4560	−0.683104	−0.341552	−	0.939863i	$-0.610953\pi$
$653$	−17.4560	−0.683104	−0.341552	+	0.939863i	$0.610953\pi$
$654$	−66.1024	−2.58481
$655$	2.59617	0.101441
$656$	−30.3027	−1.18312
$657$	−5.07857	−0.198134
$658$	−21.3626	−0.832800
$659$	−30.8964	−1.20355	−0.601776	−	0.798665i	$-0.705540\pi$
$659$	−30.8964	−1.20355	−0.601776	+	0.798665i	$0.705540\pi$
$660$	12.9372	0.503578
$661$	−14.8210	−0.576472	−0.288236	−	0.957559i	$-0.593069\pi$
$661$	−14.8210	−0.576472	−0.288236	+	0.957559i	$0.593069\pi$
$662$	−13.2561	−0.515212
$663$	0.183671	0.00713320
$664$	−15.0257	−0.583110
$665$	9.02231	0.349870
$666$	16.1108	0.624280
$667$	−21.4897	−0.832085
$668$	95.8940	3.71025
$669$	18.5535	0.717320
$670$	−27.2305	−1.05201
$671$	8.04408	0.310538
$672$	−38.2375	−1.47504
$673$	−10.5034	−0.404876	−0.202438	−	0.979295i	$-0.564886\pi$
$673$	−10.5034	−0.404876	−0.202438	+	0.979295i	$0.564886\pi$
$674$	−71.3051	−2.74657
$675$	−16.6200	−0.639704
$676$	−54.1021	−2.08085
$677$	−16.3383	−0.627931	−0.313965	−	0.949434i	$-0.601658\pi$
$677$	−16.3383	−0.627931	−0.313965	+	0.949434i	$0.601658\pi$
$678$	−16.4969	−0.633560
$679$	9.76694	0.374821
$680$	−0.892644	−0.0342313
$681$	11.6430	0.446162
$682$	−5.86433	−0.224557
$683$	−46.8851	−1.79401	−0.897004	−	0.442023i	$-0.854261\pi$
$683$	−46.8851	−1.79401	−0.897004	+	0.442023i	$0.854261\pi$
$684$	15.5131	0.593158
$685$	13.0636	0.499135
$686$	−41.9276	−1.60080
$687$	47.0988	1.79693
$688$	−98.6121	−3.75955
$689$	17.0335	0.648926
$690$	33.0875	1.25962
$691$	36.4325	1.38596	0.692978	−	0.720959i	$-0.256298\pi$
$691$	36.4325	1.38596	0.692978	+	0.720959i	$0.256298\pi$
$692$	48.3467	1.83787
$693$	−0.763482	−0.0290023
$694$	66.6907	2.53154
$695$	−3.41135	−0.129400
$696$	−55.4645	−2.10237
$697$	−0.149476	−0.00566182
$698$	17.9356	0.678873
$699$	−18.6092	−0.703865
$700$	19.8578	0.750553
$701$	−34.2157	−1.29231	−0.646155	−	0.763206i	$-0.723624\pi$
$701$	−34.2157	−1.29231	−0.646155	+	0.763206i	$0.723624\pi$
$702$	25.7170	0.970627
$703$	−53.9517	−2.03483
$704$	−27.9057	−1.05173
$705$	14.0563	0.529391
$706$	69.0932	2.60036
$707$	−12.3587	−0.464798
$708$	63.4644	2.38514
$709$	12.2729	0.460917	0.230459	−	0.973082i	$-0.425977\pi$
$709$	12.2729	0.460917	0.230459	+	0.973082i	$0.425977\pi$
$710$	−20.2613	−0.760394
$711$	−2.28714	−0.0857744
$712$	−75.7976	−2.84063
$713$	−10.9221	−0.409037
$714$	−0.362611	−0.0135704
$715$	2.63626	0.0985906
$716$	111.149	4.15382
$717$	21.7181	0.811079
$718$	−47.0767	−1.75689
$719$	24.9681	0.931152	0.465576	−	0.885008i	$-0.345847\pi$
$719$	24.9681	0.931152	0.465576	+	0.885008i	$0.345847\pi$
$720$	−11.2110	−0.417808
$721$	−2.72895	−0.101631
$722$	−19.7965	−0.736749
$723$	36.4499	1.35559
$724$	18.6632	0.693613
$725$	11.6534	0.432795
$726$	−41.5343	−1.54148
$727$	−5.82767	−0.216136	−0.108068	−	0.994143i	$-0.534466\pi$
$727$	−5.82767	−0.216136	−0.108068	+	0.994143i	$0.534466\pi$
$728$	−19.2594	−0.713801
$729$	29.9887	1.11069
$730$	−34.6203	−1.28136
$731$	−0.486431	−0.0179913
$732$	61.6916	2.28019
$733$	24.5041	0.905078	0.452539	−	0.891745i	$-0.350518\pi$
$733$	24.5041	0.905078	0.452539	+	0.891745i	$0.350518\pi$
$734$	−29.9796	−1.10657
$735$	12.0912	0.445992
$736$	−108.842	−4.01198
$737$	−7.71659	−0.284244
$738$	−3.31449	−0.122008
$739$	37.4422	1.37733	0.688666	−	0.725078i	$-0.258196\pi$
$739$	37.4422	1.37733	0.688666	+	0.725078i	$0.258196\pi$
$740$	79.9779	2.94004
$741$	−13.6387	−0.501031
$742$	−33.6283	−1.23454
$743$	20.1042	0.737551	0.368776	−	0.929518i	$-0.379777\pi$
$743$	20.1042	0.737551	0.368776	+	0.929518i	$0.379777\pi$
$744$	−28.1897	−1.03349
$745$	−2.98094	−0.109213
$746$	−46.6944	−1.70960
$747$	−0.930871	−0.0340588
$748$	−0.403576	−0.0147562
$749$	−10.2327	−0.373895
$750$	−47.9699	−1.75161
$751$	−38.3104	−1.39796	−0.698982	−	0.715139i	$-0.746363\pi$
$751$	−38.3104	−1.39796	−0.698982	+	0.715139i	$0.746363\pi$
$752$	−88.8929	−3.24159
$753$	−39.3627	−1.43446
$754$	−18.0319	−0.656683
$755$	2.56105	0.0932060
$756$	−36.9730	−1.34470
$757$	45.2296	1.64390	0.821949	−	0.569561i	$-0.192887\pi$
$757$	45.2296	1.64390	0.821949	+	0.569561i	$0.192887\pi$
$758$	−58.6120	−2.12888
$759$	9.37635	0.340340
$760$	66.2843	2.40439
$761$	−24.9525	−0.904527	−0.452264	−	0.891884i	$-0.649383\pi$
$761$	−24.9525	−0.904527	−0.452264	+	0.891884i	$0.649383\pi$
$762$	−91.1296	−3.30128
$763$	19.3656	0.701081
$764$	−9.34150	−0.337964
$765$	−0.0553011	−0.00199941
$766$	−46.0303	−1.66314
$767$	12.9324	0.466962
$768$	−46.7465	−1.68682
$769$	34.7943	1.25471	0.627356	−	0.778732i	$-0.284137\pi$
$769$	34.7943	1.25471	0.627356	+	0.778732i	$0.284137\pi$
$770$	−5.20462	−0.187561
$771$	−41.2151	−1.48433
$772$	−41.1210	−1.47998
$773$	46.3049	1.66547	0.832737	−	0.553669i	$-0.186773\pi$
$773$	46.3049	1.66547	0.832737	+	0.553669i	$0.186773\pi$
$774$	−10.7861	−0.387699
$775$	5.92281	0.212754
$776$	71.7549	2.57585
$777$	20.3636	0.730542
$778$	−10.6299	−0.381102
$779$	11.0995	0.397682
$780$	20.2180	0.723921
$781$	−5.74166	−0.205453
$782$	−1.03217	−0.0369103
$783$	−21.6973	−0.775398
$784$	−76.4656	−2.73092
$785$	10.4496	0.372962
$786$	7.74798	0.276361
$787$	32.5825	1.16144	0.580720	−	0.814103i	$-0.302771\pi$
$787$	32.5825	1.16144	0.580720	+	0.814103i	$0.302771\pi$
$788$	−6.44500	−0.229594
$789$	−9.49528	−0.338041
$790$	−15.5913	−0.554713
$791$	4.83299	0.171841
$792$	−5.60909	−0.199310
$793$	12.5712	0.446415
$794$	−77.7238	−2.75831
$795$	22.1270	0.784765
$796$	−23.0772	−0.817950
$797$	26.2477	0.929742	0.464871	−	0.885378i	$-0.346101\pi$
$797$	26.2477	0.929742	0.464871	+	0.885378i	$0.346101\pi$
$798$	26.9261	0.953175
$799$	−0.438488	−0.0155126
$800$	59.0227	2.08677
$801$	−4.69581	−0.165918
$802$	−32.4183	−1.14473
$803$	−9.81072	−0.346213
$804$	−59.1800	−2.08712
$805$	−9.69343	−0.341648
$806$	−9.16469	−0.322812
$807$	−10.9981	−0.387151
$808$	−90.7960	−3.19419
$809$	−44.4026	−1.56111	−0.780555	−	0.625087i	$-0.785064\pi$
$809$	−44.4026	−1.56111	−0.780555	+	0.625087i	$0.785064\pi$
$810$	26.8903	0.944829
$811$	−9.46145	−0.332236	−0.166118	−	0.986106i	$-0.553123\pi$
$811$	−9.46145	−0.332236	−0.166118	+	0.986106i	$0.553123\pi$
$812$	25.9242	0.909760
$813$	2.33626	0.0819364
$814$	31.1226	1.09085
$815$	24.0158	0.841238
$816$	−1.50888	−0.0528214
$817$	36.1205	1.26370
$818$	61.9638	2.16651
$819$	−1.19316	−0.0416923
$820$	−16.4539	−0.574596
$821$	−36.4488	−1.27207	−0.636036	−	0.771659i	$-0.719427\pi$
$821$	−36.4488	−1.27207	−0.636036	+	0.771659i	$0.719427\pi$
$822$	38.9870	1.35983
$823$	42.2388	1.47235	0.736176	−	0.676790i	$-0.236630\pi$
$823$	42.2388	1.47235	0.736176	+	0.676790i	$0.236630\pi$
$824$	−20.0488	−0.698433
$825$	−5.08458	−0.177022
$826$	−25.5317	−0.888361
$827$	23.5979	0.820579	0.410289	−	0.911955i	$-0.365428\pi$
$827$	23.5979	0.820579	0.410289	+	0.911955i	$0.365428\pi$
$828$	−16.6670	−0.579219
$829$	−4.28163	−0.148707	−0.0743537	−	0.997232i	$-0.523689\pi$
$829$	−4.28163	−0.148707	−0.0743537	+	0.997232i	$0.523689\pi$
$830$	−6.34569	−0.220262
$831$	−14.4435	−0.501041
$832$	−43.6106	−1.51192
$833$	−0.377187	−0.0130688
$834$	−10.1808	−0.352532
$835$	25.3839	0.878448
$836$	29.9680	1.03647
$837$	−11.0276	−0.381170
$838$	−18.8666	−0.651735
$839$	7.84687	0.270904	0.135452	−	0.990784i	$-0.456751\pi$
$839$	7.84687	0.270904	0.135452	+	0.990784i	$0.456751\pi$
$840$	−25.0185	−0.863220
$841$	−13.7866	−0.475400
$842$	−84.2753	−2.90432
$843$	−5.51209	−0.189846
$844$	−18.0600	−0.621651
$845$	−14.3213	−0.492666
$846$	−9.72304	−0.334285
$847$	12.1680	0.418098
$848$	−139.933	−4.80531
$849$	13.7633	0.472354
$850$	0.559721	0.0191983
$851$	57.9648	1.98701
$852$	−44.0339	−1.50858
$853$	−32.1285	−1.10006	−0.550029	−	0.835146i	$-0.685383\pi$
$853$	−32.1285	−1.10006	−0.550029	+	0.835146i	$0.685383\pi$
$854$	−24.8185	−0.849272
$855$	4.10645	0.140437
$856$	−75.1769	−2.56949
$857$	−34.6350	−1.18311	−0.591554	−	0.806265i	$-0.701485\pi$
$857$	−34.6350	−1.18311	−0.591554	+	0.806265i	$0.701485\pi$
$858$	7.86764	0.268597
$859$	−0.335482	−0.0114465	−0.00572324	−	0.999984i	$-0.501822\pi$
$859$	−0.335482	−0.0114465	−0.00572324	+	0.999984i	$0.501822\pi$
$860$	−53.5449	−1.82587
$861$	−4.18943	−0.142775
$862$	−97.3453	−3.31559
$863$	−22.5853	−0.768812	−0.384406	−	0.923164i	$-0.625594\pi$
$863$	−22.5853	−0.768812	−0.384406	+	0.923164i	$0.625594\pi$
$864$	−109.894	−3.73866
$865$	12.7978	0.435137
$866$	−96.6646	−3.28480
$867$	26.5229	0.900765
$868$	13.1759	0.447220
$869$	−4.41826	−0.149879
$870$	−23.4239	−0.794145
$871$	−12.0594	−0.408616
$872$	142.273	4.81798
$873$	4.44536	0.150453
$874$	76.6449	2.59255
$875$	14.0534	0.475092
$876$	−75.2404	−2.54214
$877$	43.6009	1.47230	0.736148	−	0.676820i	$-0.236643\pi$
$877$	43.6009	1.47230	0.736148	+	0.676820i	$0.236643\pi$
$878$	87.7145	2.96022
$879$	39.0740	1.31793
$880$	−21.6572	−0.730064
$881$	−28.0497	−0.945020	−0.472510	−	0.881325i	$-0.656652\pi$
$881$	−28.0497	−0.945020	−0.472510	+	0.881325i	$0.656652\pi$
$882$	−8.36375	−0.281622
$883$	−43.6356	−1.46845	−0.734227	−	0.678904i	$-0.762455\pi$
$883$	−43.6356	−1.46845	−0.734227	+	0.678904i	$0.762455\pi$
$884$	−0.630703	−0.0212128
$885$	16.7995	0.564710
$886$	56.4625	1.89690
$887$	−17.8638	−0.599808	−0.299904	−	0.953969i	$-0.596955\pi$
$887$	−17.8638	−0.599808	−0.299904	+	0.953969i	$0.596955\pi$
$888$	149.606	5.02044
$889$	26.6976	0.895410
$890$	−32.0111	−1.07301
$891$	7.62018	0.255286
$892$	−63.7103	−2.13318
$893$	32.5604	1.08959
$894$	−8.89631	−0.297537
$895$	29.4219	0.983467
$896$	37.0946	1.23924
$897$	14.6532	0.489257
$898$	25.3366	0.845492
$899$	7.73219	0.257883
$900$	9.03814	0.301271
$901$	−0.690255	−0.0229957
$902$	−6.40288	−0.213193
$903$	−13.6334	−0.453691
$904$	35.5066	1.18093
$905$	4.94031	0.164221
$906$	7.64317	0.253927
$907$	−33.0466	−1.09729	−0.548647	−	0.836054i	$-0.684857\pi$
$907$	−33.0466	−1.09729	−0.548647	+	0.836054i	$0.684857\pi$
$908$	−39.9806	−1.32680
$909$	−5.62499	−0.186569
$910$	−8.13370	−0.269629
$911$	29.3063	0.970961	0.485480	−	0.874248i	$-0.338645\pi$
$911$	29.3063	0.970961	0.485480	+	0.874248i	$0.338645\pi$
$912$	112.044	3.71014
$913$	−1.79824	−0.0595132
$914$	59.4864	1.96764
$915$	16.3303	0.539863
$916$	−161.731	−5.34374
$917$	−2.26987	−0.0749578
$918$	−1.04214	−0.0343957
$919$	9.46268	0.312145	0.156072	−	0.987746i	$-0.450117\pi$
$919$	9.46268	0.312145	0.156072	+	0.987746i	$0.450117\pi$
$920$	−71.2148	−2.34788
$921$	2.48840	0.0819955
$922$	−52.1233	−1.71659
$923$	−8.97298	−0.295349
$924$	−11.3112	−0.372111
$925$	−31.4330	−1.03351
$926$	48.0412	1.57873
$927$	−1.24206	−0.0407947
$928$	77.0537	2.52941
$929$	−46.5486	−1.52721	−0.763605	−	0.645684i	$-0.776572\pi$
$929$	−46.5486	−1.52721	−0.763605	+	0.645684i	$0.776572\pi$
$930$	−11.9052	−0.390386
$931$	28.0085	0.917941
$932$	63.9016	2.09317
$933$	−26.2281	−0.858669
$934$	62.0209	2.02939
$935$	−0.106830	−0.00349371
$936$	−8.76580	−0.286519
$937$	−25.3352	−0.827665	−0.413833	−	0.910353i	$-0.635810\pi$
$937$	−25.3352	−0.827665	−0.413833	+	0.910353i	$0.635810\pi$
$938$	23.8081	0.777362
$939$	18.6391	0.608264
$940$	−48.2675	−1.57431
$941$	−8.99616	−0.293266	−0.146633	−	0.989191i	$-0.546844\pi$
$941$	−8.99616	−0.293266	−0.146633	+	0.989191i	$0.546844\pi$
$942$	31.1857	1.01609
$943$	−11.9252	−0.388336
$944$	−106.241	−3.45786
$945$	−9.78706	−0.318373
$946$	−20.8365	−0.677453
$947$	−3.44570	−0.111970	−0.0559852	−	0.998432i	$-0.517830\pi$
$947$	−3.44570	−0.111970	−0.0559852	+	0.998432i	$0.517830\pi$
$948$	−33.8845	−1.10052
$949$	−15.3321	−0.497699
$950$	−41.5627	−1.34847
$951$	17.5233	0.568230
$952$	0.780455	0.0252947
$953$	−24.5706	−0.795921	−0.397960	−	0.917403i	$-0.630282\pi$
$953$	−24.5706	−0.795921	−0.397960	+	0.917403i	$0.630282\pi$
$954$	−15.3057	−0.495541
$955$	−2.47277	−0.0800170
$956$	−74.5772	−2.41200
$957$	−6.63788	−0.214572
$958$	−48.2683	−1.55948
$959$	−11.4218	−0.368828
$960$	−56.6513	−1.82841
$961$	−27.0701	−0.873230
$962$	48.6380	1.56815
$963$	−4.65735	−0.150081
$964$	−125.164	−4.03127
$965$	−10.8851	−0.350403
$966$	−28.9290	−0.930775
$967$	46.0793	1.48181	0.740906	−	0.671609i	$-0.234396\pi$
$967$	46.0793	1.48181	0.740906	+	0.671609i	$0.234396\pi$
$968$	89.3950	2.87326
$969$	0.552686	0.0177548
$970$	30.3038	0.972995
$971$	16.7213	0.536612	0.268306	−	0.963334i	$-0.413536\pi$
$971$	16.7213	0.536612	0.268306	+	0.963334i	$0.413536\pi$
$972$	−30.9910	−0.994038
$973$	2.98260	0.0956178
$974$	−38.1481	−1.22234
$975$	−7.94610	−0.254479
$976$	−103.274	−3.30571
$977$	−13.3636	−0.427538	−0.213769	−	0.976884i	$-0.568574\pi$
$977$	−13.3636	−0.427538	−0.213769	+	0.976884i	$0.568574\pi$
$978$	71.6727	2.29184
$979$	−9.07131	−0.289920
$980$	−41.5197	−1.32630
$981$	8.81411	0.281413
$982$	25.4765	0.812989
$983$	34.0887	1.08726	0.543631	−	0.839325i	$-0.317049\pi$
$983$	34.0887	1.08726	0.543631	+	0.839325i	$0.317049\pi$
$984$	−30.7785	−0.981184
$985$	−1.70604	−0.0543591
$986$	0.730712	0.0232706
$987$	−12.2897	−0.391185
$988$	46.8336	1.48997
$989$	−38.8072	−1.23400
$990$	−2.36885	−0.0752869
$991$	26.0445	0.827332	0.413666	−	0.910429i	$-0.364248\pi$
$991$	26.0445	0.827332	0.413666	+	0.910429i	$0.364248\pi$
$992$	39.1624	1.24341
$993$	−7.62609	−0.242007
$994$	17.7148	0.561880
$995$	−6.10873	−0.193660
$996$	−13.7911	−0.436987
$997$	−42.0386	−1.33138	−0.665688	−	0.746230i	$-0.731862\pi$
$997$	−42.0386	−1.33138	−0.665688	+	0.746230i	$0.731862\pi$
$998$	72.3826	2.29123
$999$	58.5248	1.85164

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.c.1.3	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.c.1.3	✓	216	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:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71273 q^{2} -1.56061 q^{3} +5.35892 q^{4} +1.41855 q^{5} +4.23352 q^{6} -1.24026 q^{7} -9.11187 q^{8} -0.564498 q^{9} +O(q^{10})\)	\(q-2.71273 q^{2} -1.56061 q^{3} +5.35892 q^{4} +1.41855 q^{5} +4.23352 q^{6} -1.24026 q^{7} -9.11187 q^{8} -0.564498 q^{9} -3.84815 q^{10} -1.09049 q^{11} -8.36319 q^{12} -1.70420 q^{13} +3.36451 q^{14} -2.21381 q^{15} +14.0002 q^{16} +0.0690599 q^{17} +1.53133 q^{18} -5.12812 q^{19} +7.60191 q^{20} +1.93557 q^{21} +2.95821 q^{22} +5.50957 q^{23} +14.2201 q^{24} -2.98771 q^{25} +4.62305 q^{26} +5.56279 q^{27} -6.64649 q^{28} -3.90043 q^{29} +6.00546 q^{30} -1.98239 q^{31} -19.7551 q^{32} +1.70183 q^{33} -0.187341 q^{34} -1.75938 q^{35} -3.02510 q^{36} +10.5208 q^{37} +13.9112 q^{38} +2.65959 q^{39} -12.9257 q^{40} -2.16444 q^{41} -5.25068 q^{42} -7.04361 q^{43} -5.84386 q^{44} -0.800770 q^{45} -14.9460 q^{46} -6.34939 q^{47} -21.8489 q^{48} -5.46174 q^{49} +8.10486 q^{50} -0.107775 q^{51} -9.13269 q^{52} -9.99502 q^{53} -15.0904 q^{54} -1.54692 q^{55} +11.3011 q^{56} +8.00299 q^{57} +10.5808 q^{58} -7.58854 q^{59} -11.8636 q^{60} -7.37657 q^{61} +5.37770 q^{62} +0.700127 q^{63} +25.5900 q^{64} -2.41750 q^{65} -4.61661 q^{66} +7.07625 q^{67} +0.370087 q^{68} -8.59829 q^{69} +4.77273 q^{70} +5.26521 q^{71} +5.14363 q^{72} +8.99661 q^{73} -28.5400 q^{74} +4.66265 q^{75} -27.4812 q^{76} +1.35250 q^{77} -7.21477 q^{78} +4.05163 q^{79} +19.8600 q^{80} -6.98785 q^{81} +5.87156 q^{82} +1.64902 q^{83} +10.3726 q^{84} +0.0979650 q^{85} +19.1074 q^{86} +6.08706 q^{87} +9.93641 q^{88} +8.31856 q^{89} +2.17228 q^{90} +2.11366 q^{91} +29.5254 q^{92} +3.09374 q^{93} +17.2242 q^{94} -7.27450 q^{95} +30.8301 q^{96} -7.87488 q^{97} +14.8163 q^{98} +0.615580 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * q^99

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