LMFDB - Embedded newform 5077.2.a.c.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.65348 q^{2} -0.258723 q^{3} +5.04097 q^{4} -1.45018 q^{5} +0.686516 q^{6} -0.380682 q^{7} -8.06916 q^{8} -2.93306 q^{9} +O(q^{10})$	\(q-2.65348 q^{2} -0.258723 q^{3} +5.04097 q^{4} -1.45018 q^{5} +0.686516 q^{6} -0.380682 q^{7} -8.06916 q^{8} -2.93306 q^{9} +3.84804 q^{10} +3.71187 q^{11} -1.30421 q^{12} -1.35004 q^{13} +1.01013 q^{14} +0.375196 q^{15} +11.3294 q^{16} +6.71319 q^{17} +7.78283 q^{18} +6.09366 q^{19} -7.31033 q^{20} +0.0984910 q^{21} -9.84939 q^{22} +7.60569 q^{23} +2.08768 q^{24} -2.89697 q^{25} +3.58231 q^{26} +1.53502 q^{27} -1.91900 q^{28} +2.33364 q^{29} -0.995575 q^{30} +10.0394 q^{31} -13.9242 q^{32} -0.960346 q^{33} -17.8133 q^{34} +0.552058 q^{35} -14.7855 q^{36} +9.80297 q^{37} -16.1694 q^{38} +0.349287 q^{39} +11.7018 q^{40} +4.45567 q^{41} -0.261344 q^{42} +1.19870 q^{43} +18.7114 q^{44} +4.25348 q^{45} -20.1816 q^{46} +3.67836 q^{47} -2.93118 q^{48} -6.85508 q^{49} +7.68705 q^{50} -1.73685 q^{51} -6.80552 q^{52} +7.76728 q^{53} -4.07314 q^{54} -5.38290 q^{55} +3.07178 q^{56} -1.57657 q^{57} -6.19229 q^{58} -9.70096 q^{59} +1.89135 q^{60} -5.93375 q^{61} -26.6394 q^{62} +1.11656 q^{63} +14.2886 q^{64} +1.95781 q^{65} +2.54826 q^{66} -6.73084 q^{67} +33.8410 q^{68} -1.96776 q^{69} -1.46488 q^{70} -12.6011 q^{71} +23.6674 q^{72} -11.2724 q^{73} -26.0120 q^{74} +0.749511 q^{75} +30.7180 q^{76} -1.41304 q^{77} -0.926826 q^{78} -13.4256 q^{79} -16.4298 q^{80} +8.40204 q^{81} -11.8230 q^{82} -4.18949 q^{83} +0.496490 q^{84} -9.73536 q^{85} -3.18072 q^{86} -0.603767 q^{87} -29.9517 q^{88} +1.66114 q^{89} -11.2865 q^{90} +0.513936 q^{91} +38.3401 q^{92} -2.59742 q^{93} -9.76047 q^{94} -8.83693 q^{95} +3.60249 q^{96} +8.53803 q^{97} +18.1898 q^{98} -10.8872 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65348	−1.87630	−0.938148	−	0.346235i	$-0.887460\pi$
$2$	−2.65348	−1.87630	−0.938148	+	0.346235i	$0.887460\pi$
$3$	−0.258723	−0.149374	−0.0746868	−	0.997207i	$-0.523796\pi$
$3$	−0.258723	−0.149374	−0.0746868	+	0.997207i	$0.523796\pi$
$4$	5.04097	2.52049
$5$	−1.45018	−0.648542	−0.324271	−	0.945964i	$-0.605119\pi$
$5$	−1.45018	−0.648542	−0.324271	+	0.945964i	$0.605119\pi$
$6$	0.686516	0.280269
$7$	−0.380682	−0.143884	−0.0719420	−	0.997409i	$-0.522920\pi$
$7$	−0.380682	−0.143884	−0.0719420	+	0.997409i	$0.522920\pi$
$8$	−8.06916	−2.85288
$9$	−2.93306	−0.977688
$10$	3.84804	1.21686
$11$	3.71187	1.11917	0.559586	−	0.828772i	$-0.310960\pi$
$11$	3.71187	1.11917	0.559586	+	0.828772i	$0.310960\pi$
$12$	−1.30421	−0.376494
$13$	−1.35004	−0.374434	−0.187217	−	0.982319i	$-0.559947\pi$
$13$	−1.35004	−0.374434	−0.187217	+	0.982319i	$0.559947\pi$
$14$	1.01013	0.269969
$15$	0.375196	0.0968751
$16$	11.3294	2.83236
$17$	6.71319	1.62819	0.814094	−	0.580733i	$-0.197234\pi$
$17$	6.71319	1.62819	0.814094	+	0.580733i	$0.197234\pi$
$18$	7.78283	1.83443
$19$	6.09366	1.39798	0.698991	−	0.715130i	$-0.253633\pi$
$19$	6.09366	1.39798	0.698991	+	0.715130i	$0.253633\pi$
$20$	−7.31033	−1.63464
$21$	0.0984910	0.0214925
$22$	−9.84939	−2.09990
$23$	7.60569	1.58590	0.792948	−	0.609289i	$-0.208545\pi$
$23$	7.60569	1.58590	0.792948	+	0.609289i	$0.208545\pi$
$24$	2.08768	0.426145
$25$	−2.89697	−0.579393
$26$	3.58231	0.702549
$27$	1.53502	0.295414
$28$	−1.91900	−0.362658
$29$	2.33364	0.433347	0.216673	−	0.976244i	$-0.430479\pi$
$29$	2.33364	0.433347	0.216673	+	0.976244i	$0.430479\pi$
$30$	−0.995575	−0.181766
$31$	10.0394	1.80313	0.901566	−	0.432642i	$-0.142419\pi$
$31$	10.0394	1.80313	0.901566	+	0.432642i	$0.142419\pi$
$32$	−13.9242	−2.46147
$33$	−0.960346	−0.167175
$34$	−17.8133	−3.05496
$35$	0.552058	0.0933149
$36$	−14.7855	−2.46425
$37$	9.80297	1.61160	0.805799	−	0.592189i	$-0.201736\pi$
$37$	9.80297	1.61160	0.805799	+	0.592189i	$0.201736\pi$
$38$	−16.1694	−2.62303
$39$	0.349287	0.0559306
$40$	11.7018	1.85021
$41$	4.45567	0.695859	0.347929	−	0.937521i	$-0.386885\pi$
$41$	4.45567	0.695859	0.347929	+	0.937521i	$0.386885\pi$
$42$	−0.261344	−0.0403263
$43$	1.19870	0.182800	0.0913998	−	0.995814i	$-0.470866\pi$
$43$	1.19870	0.182800	0.0913998	+	0.995814i	$0.470866\pi$
$44$	18.7114	2.82086
$45$	4.25348	0.634071
$46$	−20.1816	−2.97561
$47$	3.67836	0.536544	0.268272	−	0.963343i	$-0.413547\pi$
$47$	3.67836	0.536544	0.268272	+	0.963343i	$0.413547\pi$
$48$	−2.93118	−0.423080
$49$	−6.85508	−0.979297
$50$	7.68705	1.08711
$51$	−1.73685	−0.243208
$52$	−6.80552	−0.943756
$53$	7.76728	1.06692	0.533459	−	0.845826i	$-0.320892\pi$
$53$	7.76728	1.06692	0.533459	+	0.845826i	$0.320892\pi$
$54$	−4.07314	−0.554285
$55$	−5.38290	−0.725830
$56$	3.07178	0.410484
$57$	−1.57657	−0.208822
$58$	−6.19229	−0.813087
$59$	−9.70096	−1.26296	−0.631479	−	0.775393i	$-0.717552\pi$
$59$	−9.70096	−1.26296	−0.631479	+	0.775393i	$0.717552\pi$
$60$	1.89135	0.244172
$61$	−5.93375	−0.759739	−0.379870	−	0.925040i	$-0.624031\pi$
$61$	−5.93375	−0.759739	−0.379870	+	0.925040i	$0.624031\pi$
$62$	−26.6394	−3.38321
$63$	1.11656	0.140674
$64$	14.2886	1.78608
$65$	1.95781	0.242836
$66$	2.54826	0.313669
$67$	−6.73084	−0.822302	−0.411151	−	0.911567i	$-0.634873\pi$
$67$	−6.73084	−0.822302	−0.411151	+	0.911567i	$0.634873\pi$
$68$	33.8410	4.10382
$69$	−1.96776	−0.236891
$70$	−1.46488	−0.175086
$71$	−12.6011	−1.49547	−0.747735	−	0.663997i	$-0.768859\pi$
$71$	−12.6011	−1.49547	−0.747735	+	0.663997i	$0.768859\pi$
$72$	23.6674	2.78922
$73$	−11.2724	−1.31934	−0.659669	−	0.751556i	$-0.729304\pi$
$73$	−11.2724	−1.31934	−0.659669	+	0.751556i	$0.729304\pi$
$74$	−26.0120	−3.02383
$75$	0.749511	0.0865461
$76$	30.7180	3.52359
$77$	−1.41304	−0.161031
$78$	−0.926826	−0.104942
$79$	−13.4256	−1.51049	−0.755247	−	0.655440i	$-0.772483\pi$
$79$	−13.4256	−1.51049	−0.755247	+	0.655440i	$0.772483\pi$
$80$	−16.4298	−1.83690
$81$	8.40204	0.933560
$82$	−11.8230	−1.30564
$83$	−4.18949	−0.459856	−0.229928	−	0.973208i	$-0.573849\pi$
$83$	−4.18949	−0.459856	−0.229928	+	0.973208i	$0.573849\pi$
$84$	0.496490	0.0541715
$85$	−9.73536	−1.05595
$86$	−3.18072	−0.342986
$87$	−0.603767	−0.0647306
$88$	−29.9517	−3.19286
$89$	1.66114	0.176080	0.0880400	−	0.996117i	$-0.471940\pi$
$89$	1.66114	0.176080	0.0880400	+	0.996117i	$0.471940\pi$
$90$	−11.2865	−1.18971
$91$	0.513936	0.0538751
$92$	38.3401	3.99723
$93$	−2.59742	−0.269340
$94$	−9.76047	−1.00672
$95$	−8.83693	−0.906650
$96$	3.60249	0.367678
$97$	8.53803	0.866906	0.433453	−	0.901176i	$-0.357295\pi$
$97$	8.53803	0.866906	0.433453	+	0.901176i	$0.357295\pi$
$98$	18.1898	1.83745
$99$	−10.8872	−1.09420
$100$	−14.6035	−1.46035
$101$	4.80589	0.478204	0.239102	−	0.970995i	$-0.423147\pi$
$101$	4.80589	0.478204	0.239102	+	0.970995i	$0.423147\pi$
$102$	4.60871	0.456331
$103$	−6.35864	−0.626536	−0.313268	−	0.949665i	$-0.601424\pi$
$103$	−6.35864	−0.626536	−0.313268	+	0.949665i	$0.601424\pi$
$104$	10.8937	1.06822
$105$	−0.142830	−0.0139388
$106$	−20.6103	−2.00185
$107$	16.5123	1.59630	0.798152	−	0.602456i	$-0.205811\pi$
$107$	16.5123	1.59630	0.798152	+	0.602456i	$0.205811\pi$
$108$	7.73798	0.744588
$109$	−16.4850	−1.57898	−0.789490	−	0.613763i	$-0.789655\pi$
$109$	−16.4850	−1.57898	−0.789490	+	0.613763i	$0.789655\pi$
$110$	14.2834	1.36187
$111$	−2.53625	−0.240730
$112$	−4.31291	−0.407532
$113$	12.2026	1.14793	0.573963	−	0.818881i	$-0.305405\pi$
$113$	12.2026	1.14793	0.573963	+	0.818881i	$0.305405\pi$
$114$	4.18340	0.391811
$115$	−11.0296	−1.02852
$116$	11.7638	1.09224
$117$	3.95976	0.366080
$118$	25.7413	2.36968
$119$	−2.55559	−0.234270
$120$	−3.02751	−0.276373
$121$	2.77801	0.252546
$122$	15.7451	1.42550
$123$	−1.15278	−0.103943
$124$	50.6084	4.54477
$125$	11.4521	1.02430
$126$	−2.96278	−0.263945
$127$	12.2875	1.09034	0.545171	−	0.838325i	$-0.316465\pi$
$127$	12.2875	1.09034	0.545171	+	0.838325i	$0.316465\pi$
$128$	−10.0663	−0.889742
$129$	−0.310130	−0.0273054
$130$	−5.19501	−0.455633
$131$	7.04932	0.615902	0.307951	−	0.951402i	$-0.400357\pi$
$131$	7.04932	0.615902	0.307951	+	0.951402i	$0.400357\pi$
$132$	−4.84108	−0.421362
$133$	−2.31974	−0.201147
$134$	17.8602	1.54288
$135$	−2.22606	−0.191589
$136$	−54.1698	−4.64502
$137$	5.32777	0.455182	0.227591	−	0.973757i	$-0.426915\pi$
$137$	5.32777	0.455182	0.227591	+	0.973757i	$0.426915\pi$
$138$	5.22143	0.444478
$139$	15.4878	1.31366	0.656830	−	0.754039i	$-0.271897\pi$
$139$	15.4878	1.31366	0.656830	+	0.754039i	$0.271897\pi$
$140$	2.78291	0.235199
$141$	−0.951675	−0.0801455
$142$	33.4367	2.80594
$143$	−5.01119	−0.419056
$144$	−33.2300	−2.76916
$145$	−3.38421	−0.281044
$146$	29.9112	2.47547
$147$	1.77357	0.146281
$148$	49.4165	4.06201
$149$	6.54508	0.536194	0.268097	−	0.963392i	$-0.413605\pi$
$149$	6.54508	0.536194	0.268097	+	0.963392i	$0.413605\pi$
$150$	−1.98882	−0.162386
$151$	5.76426	0.469089	0.234544	−	0.972105i	$-0.424640\pi$
$151$	5.76426	0.469089	0.234544	+	0.972105i	$0.424640\pi$
$152$	−49.1708	−3.98827
$153$	−19.6902	−1.59186
$154$	3.74948	0.302142
$155$	−14.5590	−1.16941
$156$	1.76074	0.140972
$157$	14.0415	1.12063	0.560315	−	0.828279i	$-0.310680\pi$
$157$	14.0415	1.12063	0.560315	+	0.828279i	$0.310680\pi$
$158$	35.6245	2.83413
$159$	−2.00957	−0.159369
$160$	20.1926	1.59636
$161$	−2.89535	−0.228185
$162$	−22.2947	−1.75164
$163$	−15.5752	−1.21994	−0.609971	−	0.792424i	$-0.708819\pi$
$163$	−15.5752	−1.21994	−0.609971	+	0.792424i	$0.708819\pi$
$164$	22.4609	1.75390
$165$	1.39268	0.108420
$166$	11.1167	0.862826
$167$	1.78644	0.138239	0.0691193	−	0.997608i	$-0.477981\pi$
$167$	1.78644	0.138239	0.0691193	+	0.997608i	$0.477981\pi$
$168$	−0.794740	−0.0613155
$169$	−11.1774	−0.859799
$170$	25.8326	1.98127
$171$	−17.8731	−1.36679
$172$	6.04260	0.460744
$173$	−17.4448	−1.32631	−0.663153	−	0.748484i	$-0.730782\pi$
$173$	−17.4448	−1.32631	−0.663153	+	0.748484i	$0.730782\pi$
$174$	1.60209	0.121454
$175$	1.10282	0.0833655
$176$	42.0535	3.16990
$177$	2.50986	0.188653
$178$	−4.40780	−0.330378
$179$	−12.9890	−0.970843	−0.485421	−	0.874280i	$-0.661334\pi$
$179$	−12.9890	−0.970843	−0.485421	+	0.874280i	$0.661334\pi$
$180$	21.4417	1.59817
$181$	−4.61727	−0.343199	−0.171600	−	0.985167i	$-0.554894\pi$
$181$	−4.61727	−0.343199	−0.171600	+	0.985167i	$0.554894\pi$
$182$	−1.36372	−0.101086
$183$	1.53520	0.113485
$184$	−61.3715	−4.52437
$185$	−14.2161	−1.04519
$186$	6.89222	0.505362
$187$	24.9185	1.82222
$188$	18.5425	1.35235
$189$	−0.584353	−0.0425054
$190$	23.4486	1.70114
$191$	0.0907224	0.00656444	0.00328222	−	0.999995i	$-0.498955\pi$
$191$	0.0907224	0.00656444	0.00328222	+	0.999995i	$0.498955\pi$
$192$	−3.69679	−0.266793
$193$	1.58024	0.113748	0.0568741	−	0.998381i	$-0.481887\pi$
$193$	1.58024	0.113748	0.0568741	+	0.998381i	$0.481887\pi$
$194$	−22.6555	−1.62657
$195$	−0.506530	−0.0362733
$196$	−34.5563	−2.46830
$197$	3.04036	0.216617	0.108308	−	0.994117i	$-0.465457\pi$
$197$	3.04036	0.216617	0.108308	+	0.994117i	$0.465457\pi$
$198$	28.8889	2.05304
$199$	−10.2417	−0.726012	−0.363006	−	0.931787i	$-0.618250\pi$
$199$	−10.2417	−0.726012	−0.363006	+	0.931787i	$0.618250\pi$
$200$	23.3761	1.65294
$201$	1.74142	0.122830
$202$	−12.7523	−0.897251
$203$	−0.888375	−0.0623517
$204$	−8.75543	−0.613003
$205$	−6.46154	−0.451293
$206$	16.8725	1.17557
$207$	−22.3080	−1.55051
$208$	−15.2952	−1.06053
$209$	22.6189	1.56458
$210$	0.378997	0.0261533
$211$	10.3043	0.709375	0.354687	−	0.934985i	$-0.384587\pi$
$211$	10.3043	0.709375	0.354687	+	0.934985i	$0.384587\pi$
$212$	39.1546	2.68915
$213$	3.26018	0.223384
$214$	−43.8151	−2.99514
$215$	−1.73833	−0.118553
$216$	−12.3863	−0.842782
$217$	−3.82182	−0.259442
$218$	43.7428	2.96263
$219$	2.91643	0.197074
$220$	−27.1350	−1.82944
$221$	−9.06309	−0.609649
$222$	6.72990	0.451681
$223$	14.0899	0.943529	0.471764	−	0.881725i	$-0.343617\pi$
$223$	14.0899	0.943529	0.471764	+	0.881725i	$0.343617\pi$
$224$	5.30067	0.354166
$225$	8.49699	0.566466
$226$	−32.3795	−2.15385
$227$	6.84089	0.454046	0.227023	−	0.973889i	$-0.427101\pi$
$227$	6.84089	0.454046	0.227023	+	0.973889i	$0.427101\pi$
$228$	−7.94744	−0.526332
$229$	18.4901	1.22186	0.610929	−	0.791686i	$-0.290796\pi$
$229$	18.4901	1.22186	0.610929	+	0.791686i	$0.290796\pi$
$230$	29.2670	1.92981
$231$	0.365586	0.0240538
$232$	−18.8306	−1.23629
$233$	7.78140	0.509777	0.254888	−	0.966970i	$-0.417961\pi$
$233$	7.78140	0.509777	0.254888	+	0.966970i	$0.417961\pi$
$234$	−10.5071	−0.686874
$235$	−5.33430	−0.347971
$236$	−48.9022	−3.18326
$237$	3.47350	0.225628
$238$	6.78121	0.439560
$239$	20.7955	1.34515	0.672576	−	0.740028i	$-0.265188\pi$
$239$	20.7955	1.34515	0.672576	+	0.740028i	$0.265188\pi$
$240$	4.25076	0.274385
$241$	21.8046	1.40455	0.702277	−	0.711904i	$-0.252167\pi$
$241$	21.8046	1.40455	0.702277	+	0.711904i	$0.252167\pi$
$242$	−7.37140	−0.473851
$243$	−6.77885	−0.434864
$244$	−29.9119	−1.91491
$245$	9.94113	0.635115
$246$	3.05889	0.195028
$247$	−8.22670	−0.523452
$248$	−81.0096	−5.14412
$249$	1.08392	0.0686904
$250$	−30.3878	−1.92189
$251$	−25.9723	−1.63935	−0.819677	−	0.572826i	$-0.805847\pi$
$251$	−25.9723	−1.63935	−0.819677	+	0.572826i	$0.805847\pi$
$252$	5.62856	0.354566
$253$	28.2314	1.77489
$254$	−32.6048	−2.04580
$255$	2.51876	0.157731
$256$	−1.86652	−0.116658
$257$	13.5900	0.847721	0.423861	−	0.905727i	$-0.360675\pi$
$257$	13.5900	0.847721	0.423861	+	0.905727i	$0.360675\pi$
$258$	0.822925	0.0512331
$259$	−3.73181	−0.231883
$260$	9.86926	0.612065
$261$	−6.84473	−0.423678
$262$	−18.7053	−1.15561
$263$	−1.90884	−0.117704	−0.0588519	−	0.998267i	$-0.518744\pi$
$263$	−1.90884	−0.117704	−0.0588519	+	0.998267i	$0.518744\pi$
$264$	7.74919	0.476930
$265$	−11.2640	−0.691941
$266$	6.15540	0.377412
$267$	−0.429774	−0.0263017
$268$	−33.9299	−2.07260
$269$	−5.37022	−0.327428	−0.163714	−	0.986508i	$-0.552347\pi$
$269$	−5.37022	−0.327428	−0.163714	+	0.986508i	$0.552347\pi$
$270$	5.90681	0.359477
$271$	−20.3577	−1.23664	−0.618321	−	0.785926i	$-0.712187\pi$
$271$	−20.3577	−1.23664	−0.618321	+	0.785926i	$0.712187\pi$
$272$	76.0567	4.61161
$273$	−0.132967	−0.00804753
$274$	−14.1371	−0.854056
$275$	−10.7532	−0.648441
$276$	−9.91944	−0.597080
$277$	24.5615	1.47576	0.737878	−	0.674934i	$-0.235828\pi$
$277$	24.5615	1.47576	0.737878	+	0.674934i	$0.235828\pi$
$278$	−41.0967	−2.46481
$279$	−29.4462	−1.76290
$280$	−4.45465	−0.266216
$281$	7.66906	0.457498	0.228749	−	0.973485i	$-0.426537\pi$
$281$	7.66906	0.457498	0.228749	+	0.973485i	$0.426537\pi$
$282$	2.52525	0.150377
$283$	−32.7910	−1.94922	−0.974612	−	0.223899i	$-0.928121\pi$
$283$	−32.7910	−1.94922	−0.974612	+	0.223899i	$0.928121\pi$
$284$	−63.5215	−3.76931
$285$	2.28632	0.135430
$286$	13.2971	0.786274
$287$	−1.69619	−0.100123
$288$	40.8404	2.40654
$289$	28.0669	1.65099
$290$	8.97995	0.527321
$291$	−2.20898	−0.129493
$292$	−56.8240	−3.32537
$293$	−3.74366	−0.218707	−0.109353	−	0.994003i	$-0.534878\pi$
$293$	−3.74366	−0.218707	−0.109353	+	0.994003i	$0.534878\pi$
$294$	−4.70613	−0.274467
$295$	14.0682	0.819081
$296$	−79.1017	−4.59769
$297$	5.69779	0.330620
$298$	−17.3673	−1.00606
$299$	−10.2680	−0.593814
$300$	3.77826	0.218138
$301$	−0.456322	−0.0263019
$302$	−15.2954	−0.880149
$303$	−1.24339	−0.0714310
$304$	69.0378	3.95959
$305$	8.60503	0.492723
$306$	52.2476	2.98680
$307$	−15.8895	−0.906859	−0.453430	−	0.891292i	$-0.649800\pi$
$307$	−15.8895	−0.906859	−0.453430	+	0.891292i	$0.649800\pi$
$308$	−7.12310	−0.405876
$309$	1.64513	0.0935879
$310$	38.6320	2.19415
$311$	3.58626	0.203358	0.101679	−	0.994817i	$-0.467579\pi$
$311$	3.58626	0.203358	0.101679	+	0.994817i	$0.467579\pi$
$312$	−2.81845	−0.159563
$313$	21.1462	1.19525	0.597626	−	0.801775i	$-0.296111\pi$
$313$	21.1462	1.19525	0.597626	+	0.801775i	$0.296111\pi$
$314$	−37.2588	−2.10263
$315$	−1.61922	−0.0912328
$316$	−67.6779	−3.80718
$317$	29.8655	1.67741	0.838707	−	0.544583i	$-0.183312\pi$
$317$	29.8655	1.67741	0.838707	+	0.544583i	$0.183312\pi$
$318$	5.33236	0.299024
$319$	8.66220	0.484990
$320$	−20.7211	−1.15835
$321$	−4.27211	−0.238446
$322$	7.68275	0.428143
$323$	40.9079	2.27618
$324$	42.3545	2.35303
$325$	3.91103	0.216945
$326$	41.3284	2.28897
$327$	4.26505	0.235858
$328$	−35.9535	−1.98520
$329$	−1.40028	−0.0772001
$330$	−3.69545	−0.203428
$331$	−15.4579	−0.849644	−0.424822	−	0.905277i	$-0.639663\pi$
$331$	−15.4579	−0.849644	−0.424822	+	0.905277i	$0.639663\pi$
$332$	−21.1191	−1.15906
$333$	−28.7527	−1.57564
$334$	−4.74028	−0.259377
$335$	9.76095	0.533298
$336$	1.11585	0.0608745
$337$	6.24131	0.339986	0.169993	−	0.985445i	$-0.445626\pi$
$337$	6.24131	0.339986	0.169993	+	0.985445i	$0.445626\pi$
$338$	29.6590	1.61324
$339$	−3.15710	−0.171470
$340$	−49.0757	−2.66150
$341$	37.2650	2.01801
$342$	47.4259	2.56450
$343$	5.27437	0.284789
$344$	−9.67248	−0.521505
$345$	2.85362	0.153634
$346$	46.2896	2.48854
$347$	−2.08629	−0.111998	−0.0559990	−	0.998431i	$-0.517834\pi$
$347$	−2.08629	−0.111998	−0.0559990	+	0.998431i	$0.517834\pi$
$348$	−3.04357	−0.163153
$349$	0.137009	0.00733393	0.00366697	−	0.999993i	$-0.498833\pi$
$349$	0.137009	0.00733393	0.00366697	+	0.999993i	$0.498833\pi$
$350$	−2.92632	−0.156418
$351$	−2.07234	−0.110613
$352$	−51.6847	−2.75480
$353$	−9.08273	−0.483425	−0.241713	−	0.970348i	$-0.577709\pi$
$353$	−9.08273	−0.483425	−0.241713	+	0.970348i	$0.577709\pi$
$354$	−6.65987	−0.353968
$355$	18.2738	0.969875
$356$	8.37374	0.443807
$357$	0.661188	0.0349938
$358$	34.4661	1.82159
$359$	−20.9067	−1.10341	−0.551707	−	0.834038i	$-0.686023\pi$
$359$	−20.9067	−1.10341	−0.551707	+	0.834038i	$0.686023\pi$
$360$	−34.3220	−1.80893
$361$	18.1327	0.954354
$362$	12.2519	0.643943
$363$	−0.718734	−0.0377237
$364$	2.59074	0.135791
$365$	16.3471	0.855646
$366$	−4.07362	−0.212931
$367$	4.30378	0.224656	0.112328	−	0.993671i	$-0.464169\pi$
$367$	4.30378	0.224656	0.112328	+	0.993671i	$0.464169\pi$
$368$	86.1682	4.49183
$369$	−13.0688	−0.680332
$370$	37.7222	1.96108
$371$	−2.95686	−0.153512
$372$	−13.0935	−0.678868
$373$	−28.8018	−1.49130	−0.745650	−	0.666338i	$-0.767861\pi$
$373$	−28.8018	−1.49130	−0.745650	+	0.666338i	$0.767861\pi$
$374$	−66.1208	−3.41903
$375$	−2.96291	−0.153004
$376$	−29.6813	−1.53070
$377$	−3.15052	−0.162260
$378$	1.55057	0.0797528
$379$	13.7141	0.704448	0.352224	−	0.935916i	$-0.385426\pi$
$379$	13.7141	0.704448	0.352224	+	0.935916i	$0.385426\pi$
$380$	−44.5467	−2.28520
$381$	−3.17906	−0.162868
$382$	−0.240730	−0.0123168
$383$	−4.61563	−0.235848	−0.117924	−	0.993023i	$-0.537624\pi$
$383$	−4.61563	−0.235848	−0.117924	+	0.993023i	$0.537624\pi$
$384$	2.60438	0.132904
$385$	2.04917	0.104435
$386$	−4.19314	−0.213425
$387$	−3.51585	−0.178721
$388$	43.0400	2.18502
$389$	−20.9676	−1.06310	−0.531550	−	0.847027i	$-0.678390\pi$
$389$	−20.9676	−1.06310	−0.531550	+	0.847027i	$0.678390\pi$
$390$	1.34407	0.0680595
$391$	51.0584	2.58214
$392$	55.3148	2.79382
$393$	−1.82382	−0.0919995
$394$	−8.06754	−0.406437
$395$	19.4695	0.979619
$396$	−54.8818	−2.75792
$397$	−27.7210	−1.39127	−0.695637	−	0.718393i	$-0.744878\pi$
$397$	−27.7210	−1.39127	−0.695637	+	0.718393i	$0.744878\pi$
$398$	27.1761	1.36221
$399$	0.600171	0.0300461
$400$	−32.8210	−1.64105
$401$	22.2959	1.11340	0.556701	−	0.830713i	$-0.312067\pi$
$401$	22.2959	1.11340	0.556701	+	0.830713i	$0.312067\pi$
$402$	−4.62083	−0.230466
$403$	−13.5536	−0.675154
$404$	24.2263	1.20531
$405$	−12.1845	−0.605453
$406$	2.35729	0.116990
$407$	36.3874	1.80366
$408$	14.0150	0.693844
$409$	−21.3442	−1.05540	−0.527701	−	0.849430i	$-0.676946\pi$
$409$	−21.3442	−1.05540	−0.527701	+	0.849430i	$0.676946\pi$
$410$	17.1456	0.846760
$411$	−1.37842	−0.0679922
$412$	−32.0537	−1.57917
$413$	3.69298	0.181719
$414$	59.1938	2.90922
$415$	6.07553	0.298236
$416$	18.7982	0.921657
$417$	−4.00705	−0.196226
$418$	−60.0189	−2.93562
$419$	36.4555	1.78097	0.890485	−	0.455013i	$-0.150365\pi$
$419$	36.4555	1.78097	0.890485	+	0.455013i	$0.150365\pi$
$420$	−0.720002	−0.0351325
$421$	−17.7023	−0.862755	−0.431378	−	0.902172i	$-0.641972\pi$
$421$	−17.7023	−0.862755	−0.431378	+	0.902172i	$0.641972\pi$
$422$	−27.3422	−1.33100
$423$	−10.7889	−0.524572
$424$	−62.6754	−3.04379
$425$	−19.4479	−0.943361
$426$	−8.65083	−0.419134
$427$	2.25887	0.109314
$428$	83.2380	4.02346
$429$	1.29651	0.0625960
$430$	4.61263	0.222441
$431$	−5.46445	−0.263213	−0.131607	−	0.991302i	$-0.542014\pi$
$431$	−5.46445	−0.263213	−0.131607	+	0.991302i	$0.542014\pi$
$432$	17.3909	0.836720
$433$	−33.2146	−1.59619	−0.798096	−	0.602531i	$-0.794159\pi$
$433$	−33.2146	−1.59619	−0.798096	+	0.602531i	$0.794159\pi$
$434$	10.1411	0.486790
$435$	0.875573	0.0419805
$436$	−83.1006	−3.97980
$437$	46.3465	2.21705
$438$	−7.73871	−0.369770
$439$	13.1244	0.626393	0.313197	−	0.949688i	$-0.398600\pi$
$439$	13.1244	0.626393	0.313197	+	0.949688i	$0.398600\pi$
$440$	43.4355	2.07071
$441$	20.1064	0.957447
$442$	24.0487	1.14388
$443$	30.5879	1.45327	0.726637	−	0.687021i	$-0.241082\pi$
$443$	30.5879	1.45327	0.726637	+	0.687021i	$0.241082\pi$
$444$	−12.7852	−0.606757
$445$	−2.40895	−0.114195
$446$	−37.3873	−1.77034
$447$	−1.69336	−0.0800933
$448$	−5.43941	−0.256988
$449$	12.8196	0.604997	0.302498	−	0.953150i	$-0.402179\pi$
$449$	12.8196	0.604997	0.302498	+	0.953150i	$0.402179\pi$
$450$	−22.5466	−1.06286
$451$	16.5389	0.778785
$452$	61.5131	2.89333
$453$	−1.49134	−0.0700695
$454$	−18.1522	−0.851924
$455$	−0.745302	−0.0349403
$456$	12.7216	0.595743
$457$	−22.0826	−1.03298	−0.516490	−	0.856293i	$-0.672762\pi$
$457$	−22.0826	−1.03298	−0.516490	+	0.856293i	$0.672762\pi$
$458$	−49.0630	−2.29257
$459$	10.3049	0.480990
$460$	−55.6001	−2.59237
$461$	23.8680	1.11165	0.555823	−	0.831301i	$-0.312403\pi$
$461$	23.8680	1.11165	0.555823	+	0.831301i	$0.312403\pi$
$462$	−0.970076	−0.0451320
$463$	7.84127	0.364415	0.182207	−	0.983260i	$-0.441676\pi$
$463$	7.84127	0.364415	0.182207	+	0.983260i	$0.441676\pi$
$464$	26.4389	1.22739
$465$	3.76674	0.174679
$466$	−20.6478	−0.956492
$467$	−3.93530	−0.182104	−0.0910519	−	0.995846i	$-0.529023\pi$
$467$	−3.93530	−0.182104	−0.0910519	+	0.995846i	$0.529023\pi$
$468$	19.9610	0.922699
$469$	2.56230	0.118316
$470$	14.1545	0.652897
$471$	−3.63284	−0.167393
$472$	78.2786	3.60306
$473$	4.44941	0.204584
$474$	−9.21687	−0.423345
$475$	−17.6531	−0.809982
$476$	−12.8826	−0.590475
$477$	−22.7819	−1.04311
$478$	−55.1806	−2.52390
$479$	−0.949575	−0.0433872	−0.0216936	−	0.999765i	$-0.506906\pi$
$479$	−0.949575	−0.0433872	−0.0216936	+	0.999765i	$0.506906\pi$
$480$	−5.22428	−0.238455
$481$	−13.2344	−0.603437
$482$	−57.8580	−2.63536
$483$	0.749092	0.0340849
$484$	14.0039	0.636539
$485$	−12.3817	−0.562225
$486$	17.9876	0.815933
$487$	−27.7112	−1.25571	−0.627857	−	0.778329i	$-0.716068\pi$
$487$	−27.7112	−1.25571	−0.627857	+	0.778329i	$0.716068\pi$
$488$	47.8804	2.16744
$489$	4.02965	0.182227
$490$	−26.3786	−1.19166
$491$	−26.6067	−1.20074	−0.600371	−	0.799722i	$-0.704980\pi$
$491$	−26.6067	−1.20074	−0.600371	+	0.799722i	$0.704980\pi$
$492$	−5.81114	−0.261987
$493$	15.6662	0.705570
$494$	21.8294	0.982152
$495$	15.7884	0.709635
$496$	113.741	5.10712
$497$	4.79699	0.215174
$498$	−2.87615	−0.128883
$499$	9.19984	0.411841	0.205921	−	0.978569i	$-0.433981\pi$
$499$	9.19984	0.411841	0.205921	+	0.978569i	$0.433981\pi$
$500$	57.7295	2.58174
$501$	−0.462192	−0.0206492
$502$	68.9169	3.07591
$503$	4.42759	0.197416	0.0987082	−	0.995116i	$-0.468529\pi$
$503$	4.42759	0.197416	0.0987082	+	0.995116i	$0.468529\pi$
$504$	−9.00973	−0.401325
$505$	−6.96942	−0.310135
$506$	−74.9114	−3.33022
$507$	2.89184	0.128431
$508$	61.9411	2.74819
$509$	16.3034	0.722634	0.361317	−	0.932443i	$-0.382327\pi$
$509$	16.3034	0.722634	0.361317	+	0.932443i	$0.382327\pi$
$510$	−6.68348	−0.295950
$511$	4.29121	0.189832
$512$	25.0853	1.10863
$513$	9.35388	0.412984
$514$	−36.0608	−1.59058
$515$	9.22120	0.406335
$516$	−1.56336	−0.0688230
$517$	13.6536	0.600485
$518$	9.90229	0.435082
$519$	4.51338	0.198115
$520$	−15.7979	−0.692783
$521$	−25.5523	−1.11947	−0.559734	−	0.828672i	$-0.689097\pi$
$521$	−25.5523	−1.11947	−0.559734	+	0.828672i	$0.689097\pi$
$522$	18.1624	0.794945
$523$	34.6595	1.51555	0.757777	−	0.652514i	$-0.226286\pi$
$523$	34.6595	1.51555	0.757777	+	0.652514i	$0.226286\pi$
$524$	35.5354	1.55237
$525$	−0.285325	−0.0124526
$526$	5.06506	0.220847
$527$	67.3965	2.93584
$528$	−10.8802	−0.473499
$529$	34.8465	1.51507
$530$	29.8888	1.29829
$531$	28.4535	1.23478
$532$	−11.6938	−0.506989
$533$	−6.01534	−0.260553
$534$	1.14040	0.0493498
$535$	−23.9459	−1.03527
$536$	54.3122	2.34593
$537$	3.36055	0.145018
$538$	14.2498	0.614352
$539$	−25.4452	−1.09600
$540$	−11.2215	−0.482896
$541$	−17.8441	−0.767179	−0.383589	−	0.923504i	$-0.625312\pi$
$541$	−17.8441	−0.767179	−0.383589	+	0.923504i	$0.625312\pi$
$542$	54.0188	2.32031
$543$	1.19459	0.0512649
$544$	−93.4755	−4.00773
$545$	23.9063	1.02403
$546$	0.352825	0.0150995
$547$	32.5133	1.39017	0.695084	−	0.718928i	$-0.255367\pi$
$547$	32.5133	1.39017	0.695084	+	0.718928i	$0.255367\pi$
$548$	26.8571	1.14728
$549$	17.4041	0.742787
$550$	28.5334	1.21667
$551$	14.2204	0.605811
$552$	15.8782	0.675822
$553$	5.11087	0.217336
$554$	−65.1734	−2.76895
$555$	3.67803	0.156124
$556$	78.0736	3.31106
$557$	23.3170	0.987971	0.493986	−	0.869470i	$-0.335540\pi$
$557$	23.3170	0.987971	0.493986	+	0.869470i	$0.335540\pi$
$558$	78.1350	3.30772
$559$	−1.61829	−0.0684464
$560$	6.25451	0.264301
$561$	−6.44699	−0.272192
$562$	−20.3497	−0.858401
$563$	−24.0641	−1.01418	−0.507091	−	0.861892i	$-0.669279\pi$
$563$	−24.0641	−1.01418	−0.507091	+	0.861892i	$0.669279\pi$
$564$	−4.79737	−0.202006
$565$	−17.6961	−0.744478
$566$	87.0104	3.65732
$567$	−3.19850	−0.134324
$568$	101.680	4.26640
$569$	−19.0905	−0.800314	−0.400157	−	0.916447i	$-0.631044\pi$
$569$	−19.0905	−0.800314	−0.400157	+	0.916447i	$0.631044\pi$
$570$	−6.06670	−0.254106
$571$	−10.1892	−0.426406	−0.213203	−	0.977008i	$-0.568390\pi$
$571$	−10.1892	−0.426406	−0.213203	+	0.977008i	$0.568390\pi$
$572$	−25.2612	−1.05623
$573$	−0.0234719	−0.000980554 0
$574$	4.50081	0.187860
$575$	−22.0334	−0.918858
$576$	−41.9094	−1.74622
$577$	−9.03063	−0.375950	−0.187975	−	0.982174i	$-0.560192\pi$
$577$	−9.03063	−0.375950	−0.187975	+	0.982174i	$0.560192\pi$
$578$	−74.4751	−3.09775
$579$	−0.408844	−0.0169910
$580$	−17.0597	−0.708366
$581$	1.59486	0.0661660
$582$	5.86150	0.242967
$583$	28.8311	1.19406
$584$	90.9591	3.76391
$585$	−5.74238	−0.237418
$586$	9.93374	0.410359
$587$	−20.2191	−0.834531	−0.417265	−	0.908785i	$-0.637011\pi$
$587$	−20.2191	−0.834531	−0.417265	+	0.908785i	$0.637011\pi$
$588$	8.94049	0.368700
$589$	61.1768	2.52075
$590$	−37.3297	−1.53684
$591$	−0.786610	−0.0323568
$592$	111.062	4.56463
$593$	31.0560	1.27532	0.637658	−	0.770319i	$-0.279903\pi$
$593$	31.0560	1.27532	0.637658	+	0.770319i	$0.279903\pi$
$594$	−15.1190	−0.620340
$595$	3.70607	0.151934
$596$	32.9936	1.35147
$597$	2.64975	0.108447
$598$	27.2460	1.11417
$599$	14.8953	0.608604	0.304302	−	0.952576i	$-0.401577\pi$
$599$	14.8953	0.608604	0.304302	+	0.952576i	$0.401577\pi$
$600$	−6.04793	−0.246906
$601$	−37.9245	−1.54697	−0.773487	−	0.633812i	$-0.781489\pi$
$601$	−37.9245	−1.54697	−0.773487	+	0.633812i	$0.781489\pi$
$602$	1.21084	0.0493502
$603$	19.7420	0.803955
$604$	29.0574	1.18233
$605$	−4.02862	−0.163787
$606$	3.29932	0.134026
$607$	8.03416	0.326097	0.163048	−	0.986618i	$-0.447867\pi$
$607$	8.03416	0.326097	0.163048	+	0.986618i	$0.447867\pi$
$608$	−84.8491	−3.44108
$609$	0.229843	0.00931371
$610$	−22.8333	−0.924493
$611$	−4.96594	−0.200900
$612$	−99.2577	−4.01226
$613$	36.3990	1.47014	0.735071	−	0.677990i	$-0.237149\pi$
$613$	36.3990	1.47014	0.735071	+	0.677990i	$0.237149\pi$
$614$	42.1624	1.70154
$615$	1.67175	0.0674113
$616$	11.4021	0.459402
$617$	−3.81701	−0.153667	−0.0768335	−	0.997044i	$-0.524481\pi$
$617$	−3.81701	−0.153667	−0.0768335	+	0.997044i	$0.524481\pi$
$618$	−4.36531	−0.175599
$619$	44.7561	1.79890	0.899449	−	0.437025i	$-0.143968\pi$
$619$	44.7561	1.79890	0.899449	+	0.437025i	$0.143968\pi$
$620$	−73.3914	−2.94747
$621$	11.6749	0.468496
$622$	−9.51607	−0.381560
$623$	−0.632364	−0.0253351
$624$	3.95722	0.158416
$625$	−2.12275	−0.0849099
$626$	−56.1110	−2.24265
$627$	−5.85203	−0.233707
$628$	70.7826	2.82453
$629$	65.8092	2.62398
$630$	4.29658	0.171180
$631$	−43.1509	−1.71781	−0.858905	−	0.512136i	$-0.828855\pi$
$631$	−43.1509	−1.71781	−0.858905	+	0.512136i	$0.828855\pi$
$632$	108.333	4.30926
$633$	−2.66595	−0.105962
$634$	−79.2476	−3.14732
$635$	−17.8192	−0.707133
$636$	−10.1302	−0.401688
$637$	9.25465	0.366683
$638$	−22.9850	−0.909984
$639$	36.9597	1.46210
$640$	14.5980	0.577035
$641$	16.3213	0.644652	0.322326	−	0.946629i	$-0.395535\pi$
$641$	16.3213	0.644652	0.322326	+	0.946629i	$0.395535\pi$
$642$	11.3360	0.447395
$643$	48.4018	1.90878	0.954390	−	0.298562i	$-0.0965071\pi$
$643$	48.4018	1.90878	0.954390	+	0.298562i	$0.0965071\pi$
$644$	−14.5953	−0.575137
$645$	0.449746	0.0177087
$646$	−108.548	−4.27078
$647$	−34.3404	−1.35006	−0.675030	−	0.737790i	$-0.735869\pi$
$647$	−34.3404	−1.35006	−0.675030	+	0.737790i	$0.735869\pi$
$648$	−67.7974	−2.66334
$649$	−36.0087	−1.41347
$650$	−10.3778	−0.407053
$651$	0.988791	0.0387538
$652$	−78.5140	−3.07484
$653$	−24.1910	−0.946665	−0.473333	−	0.880884i	$-0.656949\pi$
$653$	−24.1910	−0.946665	−0.473333	+	0.880884i	$0.656949\pi$
$654$	−11.3172	−0.442539
$655$	−10.2228	−0.399438
$656$	50.4802	1.97092
$657$	33.0627	1.28990
$658$	3.71563	0.144850
$659$	−20.5280	−0.799659	−0.399829	−	0.916590i	$-0.630931\pi$
$659$	−20.5280	−0.799659	−0.399829	+	0.916590i	$0.630931\pi$
$660$	7.02045	0.273271
$661$	3.60535	0.140232	0.0701160	−	0.997539i	$-0.477663\pi$
$661$	3.60535	0.140232	0.0701160	+	0.997539i	$0.477663\pi$
$662$	41.0173	1.59418
$663$	2.34483	0.0910655
$664$	33.8057	1.31191
$665$	3.36406	0.130453
$666$	76.2948	2.95636
$667$	17.7490	0.687243
$668$	9.00537	0.348428
$669$	−3.64537	−0.140938
$670$	−25.9005	−1.00062
$671$	−22.0253	−0.850279
$672$	−1.37140	−0.0529030
$673$	−23.6906	−0.913204	−0.456602	−	0.889671i	$-0.650934\pi$
$673$	−23.6906	−0.913204	−0.456602	+	0.889671i	$0.650934\pi$
$674$	−16.5612	−0.637913
$675$	−4.44690	−0.171161
$676$	−56.3449	−2.16711
$677$	−44.9389	−1.72714	−0.863571	−	0.504228i	$-0.831777\pi$
$677$	−44.9389	−1.72714	−0.863571	+	0.504228i	$0.831777\pi$
$678$	8.37730	0.321728
$679$	−3.25027	−0.124734
$680$	78.5562	3.01249
$681$	−1.76989	−0.0678225
$682$	−98.8821	−3.78639
$683$	3.17352	0.121432	0.0607158	−	0.998155i	$-0.480662\pi$
$683$	3.17352	0.121432	0.0607158	+	0.998155i	$0.480662\pi$
$684$	−90.0977	−3.44497
$685$	−7.72625	−0.295205
$686$	−13.9955	−0.534349
$687$	−4.78380	−0.182513
$688$	13.5806	0.517754
$689$	−10.4861	−0.399490
$690$	−7.57203	−0.288262
$691$	−24.8283	−0.944512	−0.472256	−	0.881461i	$-0.656560\pi$
$691$	−24.8283	−0.944512	−0.472256	+	0.881461i	$0.656560\pi$
$692$	−87.9389	−3.34294
$693$	4.14454	0.157438
$694$	5.53594	0.210141
$695$	−22.4602	−0.851963
$696$	4.87189	0.184669
$697$	29.9117	1.13299
$698$	−0.363551	−0.0137606
$699$	−2.01323	−0.0761472
$700$	5.55929	0.210121
$701$	8.20127	0.309758	0.154879	−	0.987933i	$-0.450501\pi$
$701$	8.20127	0.309758	0.154879	+	0.987933i	$0.450501\pi$
$702$	5.49892	0.207543
$703$	59.7360	2.25298
$704$	53.0375	1.99893
$705$	1.38010	0.0519777
$706$	24.1009	0.907048
$707$	−1.82951	−0.0688059
$708$	12.6521	0.475496
$709$	0.670226	0.0251709	0.0125854	−	0.999921i	$-0.495994\pi$
$709$	0.670226	0.0251709	0.0125854	+	0.999921i	$0.495994\pi$
$710$	−48.4893	−1.81977
$711$	39.3780	1.47679
$712$	−13.4040	−0.502335
$713$	76.3566	2.85958
$714$	−1.75445	−0.0656587
$715$	7.26714	0.271776
$716$	−65.4771	−2.44699
$717$	−5.38028	−0.200930
$718$	55.4756	2.07033
$719$	−19.3352	−0.721082	−0.360541	−	0.932743i	$-0.617408\pi$
$719$	−19.3352	−0.721082	−0.360541	+	0.932743i	$0.617408\pi$
$720$	48.1895	1.79592
$721$	2.42062	0.0901485
$722$	−48.1149	−1.79065
$723$	−5.64133	−0.209803
$724$	−23.2755	−0.865028
$725$	−6.76049	−0.251078
$726$	1.90715	0.0707809
$727$	17.4601	0.647560	0.323780	−	0.946132i	$-0.395046\pi$
$727$	17.4601	0.647560	0.323780	+	0.946132i	$0.395046\pi$
$728$	−4.14703	−0.153699
$729$	−23.4523	−0.868603
$730$	−43.3767	−1.60544
$731$	8.04708	0.297632
$732$	7.73888	0.286037
$733$	7.29128	0.269309	0.134655	−	0.990893i	$-0.457007\pi$
$733$	7.29128	0.269309	0.134655	+	0.990893i	$0.457007\pi$
$734$	−11.4200	−0.421520
$735$	−2.57200	−0.0948695
$736$	−105.903	−3.90363
$737$	−24.9840	−0.920298
$738$	34.6777	1.27650
$739$	43.5724	1.60284	0.801419	−	0.598103i	$-0.204079\pi$
$739$	43.5724	1.60284	0.801419	+	0.598103i	$0.204079\pi$
$740$	−71.6630	−2.63438
$741$	2.12843	0.0781900
$742$	7.84597	0.288035
$743$	1.38325	0.0507465	0.0253732	−	0.999678i	$-0.491923\pi$
$743$	1.38325	0.0507465	0.0253732	+	0.999678i	$0.491923\pi$
$744$	20.9590	0.768396
$745$	−9.49158	−0.347744
$746$	76.4250	2.79812
$747$	12.2880	0.449596
$748$	125.613	4.59288
$749$	−6.28593	−0.229683
$750$	7.86202	0.287080
$751$	45.9369	1.67626	0.838132	−	0.545468i	$-0.183648\pi$
$751$	45.9369	1.67626	0.838132	+	0.545468i	$0.183648\pi$
$752$	41.6738	1.51969
$753$	6.71961	0.244876
$754$	8.35985	0.304448
$755$	−8.35923	−0.304224
$756$	−2.94571	−0.107134
$757$	−14.9228	−0.542379	−0.271189	−	0.962526i	$-0.587417\pi$
$757$	−14.9228	−0.542379	−0.271189	+	0.962526i	$0.587417\pi$
$758$	−36.3902	−1.32175
$759$	−7.30409	−0.265122
$760$	71.3066	2.58656
$761$	26.8310	0.972623	0.486312	−	0.873785i	$-0.338342\pi$
$761$	26.8310	0.972623	0.486312	+	0.873785i	$0.338342\pi$
$762$	8.43559	0.305589
$763$	6.27555	0.227190
$764$	0.457329	0.0165456
$765$	28.5544	1.03239
$766$	12.2475	0.442520
$767$	13.0967	0.472894
$768$	0.482912	0.0174256
$769$	29.6147	1.06793	0.533966	−	0.845506i	$-0.320701\pi$
$769$	29.6147	1.06793	0.533966	+	0.845506i	$0.320701\pi$
$770$	−5.43744	−0.195952
$771$	−3.51604	−0.126627
$772$	7.96595	0.286701
$773$	3.36259	0.120944	0.0604720	−	0.998170i	$-0.480739\pi$
$773$	3.36259	0.120944	0.0604720	+	0.998170i	$0.480739\pi$
$774$	9.32926	0.335333
$775$	−29.0838	−1.04472
$776$	−68.8948	−2.47318
$777$	0.965504	0.0346372
$778$	55.6372	1.99469
$779$	27.1513	0.972798
$780$	−2.55340	−0.0914264
$781$	−46.7735	−1.67369
$782$	−135.483	−4.84485
$783$	3.58219	0.128017
$784$	−77.6642	−2.77372
$785$	−20.3627	−0.726776
$786$	4.83947	0.172618
$787$	−14.6321	−0.521578	−0.260789	−	0.965396i	$-0.583983\pi$
$787$	−14.6321	−0.521578	−0.260789	+	0.965396i	$0.583983\pi$
$788$	15.3264	0.545979
$789$	0.493859	0.0175819
$790$	−51.6621	−1.83805
$791$	−4.64531	−0.165168
$792$	87.8502	3.12162
$793$	8.01082	0.284472
$794$	73.5571	2.61044
$795$	2.91425	0.103358
$796$	−51.6279	−1.82990
$797$	−11.4026	−0.403899	−0.201950	−	0.979396i	$-0.564728\pi$
$797$	−11.4026	−0.403899	−0.201950	+	0.979396i	$0.564728\pi$
$798$	−1.59254	−0.0563754
$799$	24.6935	0.873594
$800$	40.3378	1.42616
$801$	−4.87222	−0.172151
$802$	−59.1617	−2.08907
$803$	−41.8418	−1.47657
$804$	8.77845	0.309592
$805$	4.19878	0.147988
$806$	35.9643	1.26679
$807$	1.38940	0.0489091
$808$	−38.7795	−1.36426
$809$	11.1093	0.390581	0.195291	−	0.980745i	$-0.437435\pi$
$809$	11.1093	0.390581	0.195291	+	0.980745i	$0.437435\pi$
$810$	32.3314	1.13601
$811$	32.0357	1.12492	0.562462	−	0.826823i	$-0.309854\pi$
$811$	32.0357	1.12492	0.562462	+	0.826823i	$0.309854\pi$
$812$	−4.47827	−0.157157
$813$	5.26700	0.184722
$814$	−96.5533	−3.38419
$815$	22.5869	0.791183
$816$	−19.6776	−0.688854
$817$	7.30446	0.255551
$818$	56.6365	1.98025
$819$	−1.50741	−0.0526731
$820$	−32.5724	−1.13748
$821$	−33.9899	−1.18625	−0.593127	−	0.805109i	$-0.702107\pi$
$821$	−33.9899	−1.18625	−0.593127	+	0.805109i	$0.702107\pi$
$822$	3.65760	0.127573
$823$	−25.2151	−0.878942	−0.439471	−	0.898257i	$-0.644834\pi$
$823$	−25.2151	−0.878942	−0.439471	+	0.898257i	$0.644834\pi$
$824$	51.3089	1.78743
$825$	2.78209	0.0968600
$826$	−9.79925	−0.340959
$827$	−43.9644	−1.52879	−0.764397	−	0.644746i	$-0.776963\pi$
$827$	−43.9644	−1.52879	−0.764397	+	0.644746i	$0.776963\pi$
$828$	−112.454	−3.90804
$829$	−9.72078	−0.337617	−0.168808	−	0.985649i	$-0.553992\pi$
$829$	−9.72078	−0.337617	−0.168808	+	0.985649i	$0.553992\pi$
$830$	−16.1213	−0.559579
$831$	−6.35461	−0.220439
$832$	−19.2902	−0.668768
$833$	−46.0195	−1.59448
$834$	10.6326	0.368178
$835$	−2.59066	−0.0896535
$836$	114.021	3.94351
$837$	15.4107	0.532671
$838$	−96.7342	−3.34163
$839$	27.1608	0.937695	0.468847	−	0.883279i	$-0.344669\pi$
$839$	27.1608	0.937695	0.468847	+	0.883279i	$0.344669\pi$
$840$	1.15252	0.0397657
$841$	−23.5541	−0.812210
$842$	46.9726	1.61878
$843$	−1.98416	−0.0683381
$844$	51.9435	1.78797
$845$	16.2093	0.557616
$846$	28.6281	0.984253
$847$	−1.05754	−0.0363374
$848$	87.9989	3.02189
$849$	8.48379	0.291163
$850$	51.6046	1.77002
$851$	74.5583	2.55583
$852$	16.4345	0.563036
$853$	−6.90287	−0.236350	−0.118175	−	0.992993i	$-0.537704\pi$
$853$	−6.90287	−0.236350	−0.118175	+	0.992993i	$0.537704\pi$
$854$	−5.99387	−0.205106
$855$	25.9193	0.886420
$856$	−133.240	−4.55406
$857$	1.18637	0.0405257	0.0202629	−	0.999795i	$-0.493550\pi$
$857$	1.18637	0.0405257	0.0202629	+	0.999795i	$0.493550\pi$
$858$	−3.44026	−0.117449
$859$	−1.34963	−0.0460486	−0.0230243	−	0.999735i	$-0.507330\pi$
$859$	−1.34963	−0.0460486	−0.0230243	+	0.999735i	$0.507330\pi$
$860$	−8.76287	−0.298812
$861$	0.438843	0.0149557
$862$	14.4998	0.493866
$863$	13.3655	0.454969	0.227484	−	0.973782i	$-0.426950\pi$
$863$	13.3655	0.454969	0.227484	+	0.973782i	$0.426950\pi$
$864$	−21.3738	−0.727152
$865$	25.2982	0.860165
$866$	88.1344	2.99493
$867$	−7.26155	−0.246615
$868$	−19.2657	−0.653920
$869$	−49.8340	−1.69050
$870$	−2.32332	−0.0787679
$871$	9.08691	0.307898
$872$	133.020	4.50464
$873$	−25.0426	−0.847563
$874$	−122.980	−4.15985
$875$	−4.35959	−0.147381
$876$	14.7017	0.496723
$877$	21.6659	0.731605	0.365802	−	0.930693i	$-0.380795\pi$
$877$	21.6659	0.731605	0.365802	+	0.930693i	$0.380795\pi$
$878$	−34.8254	−1.17530
$879$	0.968570	0.0326691
$880$	−60.9852	−2.05581
$881$	−17.1146	−0.576607	−0.288304	−	0.957539i	$-0.593091\pi$
$881$	−17.1146	−0.576607	−0.288304	+	0.957539i	$0.593091\pi$
$882$	−53.3519	−1.79645
$883$	47.3580	1.59372	0.796861	−	0.604163i	$-0.206492\pi$
$883$	47.3580	1.59372	0.796861	+	0.604163i	$0.206492\pi$
$884$	−45.6868	−1.53661
$885$	−3.63976	−0.122349
$886$	−81.1644	−2.72677
$887$	25.0244	0.840236	0.420118	−	0.907469i	$-0.361989\pi$
$887$	25.0244	0.840236	0.420118	+	0.907469i	$0.361989\pi$
$888$	20.4654	0.686774
$889$	−4.67764	−0.156883
$890$	6.39211	0.214264
$891$	31.1873	1.04481
$892$	71.0267	2.37815
$893$	22.4147	0.750079
$894$	4.49331	0.150279
$895$	18.8364	0.629632
$896$	3.83205	0.128020
$897$	2.65657	0.0887001
$898$	−34.0167	−1.13515
$899$	23.4284	0.781382
$900$	42.8330	1.42777
$901$	52.1432	1.73714
$902$	−43.8856	−1.46123
$903$	0.118061	0.00392882
$904$	−98.4650	−3.27490
$905$	6.69589	0.222579
$906$	3.95726	0.131471
$907$	−25.3179	−0.840667	−0.420334	−	0.907370i	$-0.638087\pi$
$907$	−25.3179	−0.840667	−0.420334	+	0.907370i	$0.638087\pi$
$908$	34.4847	1.14442
$909$	−14.0960	−0.467534
$910$	1.97765	0.0655583
$911$	3.81822	0.126503	0.0632517	−	0.997998i	$-0.479853\pi$
$911$	3.81822	0.126503	0.0632517	+	0.997998i	$0.479853\pi$
$912$	−17.8616	−0.591458
$913$	−15.5509	−0.514658
$914$	58.5958	1.93818
$915$	−2.22632	−0.0735998
$916$	93.2078	3.07967
$917$	−2.68355	−0.0886185
$918$	−27.3438	−0.902479
$919$	27.3638	0.902649	0.451324	−	0.892360i	$-0.350952\pi$
$919$	27.3638	0.902649	0.451324	+	0.892360i	$0.350952\pi$
$920$	89.0000	2.93424
$921$	4.11096	0.135461
$922$	−63.3335	−2.08578
$923$	17.0120	0.559955
$924$	1.84291	0.0606272
$925$	−28.3989	−0.933749
$926$	−20.8067	−0.683750
$927$	18.6503	0.612556
$928$	−32.4940	−1.06667
$929$	−56.4287	−1.85137	−0.925683	−	0.378299i	$-0.876509\pi$
$929$	−56.4287	−1.85137	−0.925683	+	0.378299i	$0.876509\pi$
$930$	−9.99499	−0.327749
$931$	−41.7726	−1.36904
$932$	39.2258	1.28488
$933$	−0.927846	−0.0303763
$934$	10.4422	0.341681
$935$	−36.1364	−1.18179
$936$	−31.9519	−1.04438
$937$	6.00281	0.196103	0.0980517	−	0.995181i	$-0.468739\pi$
$937$	6.00281	0.196103	0.0980517	+	0.995181i	$0.468739\pi$
$938$	−6.79903	−0.221996
$939$	−5.47100	−0.178539
$940$	−26.8900	−0.877056
$941$	−32.8721	−1.07160	−0.535801	−	0.844344i	$-0.679990\pi$
$941$	−32.8721	−1.07160	−0.535801	+	0.844344i	$0.679990\pi$
$942$	9.63969	0.314078
$943$	33.8884	1.10356
$944$	−109.906	−3.57715
$945$	0.847419	0.0275666
$946$	−11.8064	−0.383860
$947$	−39.6640	−1.28891	−0.644453	−	0.764644i	$-0.722915\pi$
$947$	−39.6640	−1.28891	−0.644453	+	0.764644i	$0.722915\pi$
$948$	17.5098	0.568692
$949$	15.2183	0.494005
$950$	46.8423	1.51976
$951$	−7.72689	−0.250561
$952$	20.6214	0.668345
$953$	10.9335	0.354170	0.177085	−	0.984196i	$-0.443333\pi$
$953$	10.9335	0.354170	0.177085	+	0.984196i	$0.443333\pi$
$954$	60.4514	1.95719
$955$	−0.131564	−0.00425731
$956$	104.830	3.39044
$957$	−2.24111	−0.0724447
$958$	2.51968	0.0814072
$959$	−2.02818	−0.0654935
$960$	5.36102	0.173026
$961$	69.7898	2.25128
$962$	35.1173	1.13223
$963$	−48.4316	−1.56069
$964$	109.916	3.54016
$965$	−2.29164	−0.0737705
$966$	−1.98770	−0.0639533
$967$	−26.5962	−0.855276	−0.427638	−	0.903950i	$-0.640654\pi$
$967$	−26.5962	−0.855276	−0.427638	+	0.903950i	$0.640654\pi$
$968$	−22.4162	−0.720484
$969$	−10.5838	−0.340001
$970$	32.8547	1.05490
$971$	17.8997	0.574427	0.287214	−	0.957867i	$-0.407271\pi$
$971$	17.8997	0.574427	0.287214	+	0.957867i	$0.407271\pi$
$972$	−34.1720	−1.09607
$973$	−5.89593	−0.189015
$974$	73.5312	2.35609
$975$	−1.01187	−0.0324058
$976$	−67.2261	−2.15185
$977$	51.7978	1.65716	0.828579	−	0.559872i	$-0.189150\pi$
$977$	51.7978	1.65716	0.828579	+	0.559872i	$0.189150\pi$
$978$	−10.6926	−0.341912
$979$	6.16593	0.197064
$980$	50.1129	1.60080
$981$	48.3517	1.54375
$982$	70.6003	2.25295
$983$	21.5592	0.687631	0.343816	−	0.939037i	$-0.388280\pi$
$983$	21.5592	0.687631	0.343816	+	0.939037i	$0.388280\pi$
$984$	9.30199	0.296537
$985$	−4.40908	−0.140485
$986$	−41.5700	−1.32386
$987$	0.362285	0.0115317
$988$	−41.4706	−1.31935
$989$	9.11692	0.289901
$990$	−41.8942	−1.33148
$991$	17.3628	0.551547	0.275773	−	0.961223i	$-0.411066\pi$
$991$	17.3628	0.551547	0.275773	+	0.961223i	$0.411066\pi$
$992$	−139.790	−4.43835
$993$	3.99932	0.126914
$994$	−12.7287	−0.403731
$995$	14.8523	0.470849
$996$	5.46399	0.173133
$997$	−48.6764	−1.54160	−0.770798	−	0.637080i	$-0.780142\pi$
$997$	−48.6764	−1.54160	−0.770798	+	0.637080i	$0.780142\pi$
$998$	−24.4116	−0.772736
$999$	15.0477	0.476089

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.c.1.7	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.c.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.65348 q^{2} -0.258723 q^{3} +5.04097 q^{4} -1.45018 q^{5} +0.686516 q^{6} -0.380682 q^{7} -8.06916 q^{8} -2.93306 q^{9} +O(q^{10})\)	\(q-2.65348 q^{2} -0.258723 q^{3} +5.04097 q^{4} -1.45018 q^{5} +0.686516 q^{6} -0.380682 q^{7} -8.06916 q^{8} -2.93306 q^{9} +3.84804 q^{10} +3.71187 q^{11} -1.30421 q^{12} -1.35004 q^{13} +1.01013 q^{14} +0.375196 q^{15} +11.3294 q^{16} +6.71319 q^{17} +7.78283 q^{18} +6.09366 q^{19} -7.31033 q^{20} +0.0984910 q^{21} -9.84939 q^{22} +7.60569 q^{23} +2.08768 q^{24} -2.89697 q^{25} +3.58231 q^{26} +1.53502 q^{27} -1.91900 q^{28} +2.33364 q^{29} -0.995575 q^{30} +10.0394 q^{31} -13.9242 q^{32} -0.960346 q^{33} -17.8133 q^{34} +0.552058 q^{35} -14.7855 q^{36} +9.80297 q^{37} -16.1694 q^{38} +0.349287 q^{39} +11.7018 q^{40} +4.45567 q^{41} -0.261344 q^{42} +1.19870 q^{43} +18.7114 q^{44} +4.25348 q^{45} -20.1816 q^{46} +3.67836 q^{47} -2.93118 q^{48} -6.85508 q^{49} +7.68705 q^{50} -1.73685 q^{51} -6.80552 q^{52} +7.76728 q^{53} -4.07314 q^{54} -5.38290 q^{55} +3.07178 q^{56} -1.57657 q^{57} -6.19229 q^{58} -9.70096 q^{59} +1.89135 q^{60} -5.93375 q^{61} -26.6394 q^{62} +1.11656 q^{63} +14.2886 q^{64} +1.95781 q^{65} +2.54826 q^{66} -6.73084 q^{67} +33.8410 q^{68} -1.96776 q^{69} -1.46488 q^{70} -12.6011 q^{71} +23.6674 q^{72} -11.2724 q^{73} -26.0120 q^{74} +0.749511 q^{75} +30.7180 q^{76} -1.41304 q^{77} -0.926826 q^{78} -13.4256 q^{79} -16.4298 q^{80} +8.40204 q^{81} -11.8230 q^{82} -4.18949 q^{83} +0.496490 q^{84} -9.73536 q^{85} -3.18072 q^{86} -0.603767 q^{87} -29.9517 q^{88} +1.66114 q^{89} -11.2865 q^{90} +0.513936 q^{91} +38.3401 q^{92} -2.59742 q^{93} -9.76047 q^{94} -8.83693 q^{95} +3.60249 q^{96} +8.53803 q^{97} +18.1898 q^{98} -10.8872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) \) 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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