LMFDB - Embedded newform 5077.2.a.b.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:	$1$
Dimension:	$205$
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)

$f(q)$	$=$	$q-2.72893 q^{2} +1.44573 q^{3} +5.44706 q^{4} +1.77131 q^{5} -3.94530 q^{6} -0.914980 q^{7} -9.40679 q^{8} -0.909861 q^{9} +O(q^{10})$	\(q-2.72893 q^{2} +1.44573 q^{3} +5.44706 q^{4} +1.77131 q^{5} -3.94530 q^{6} -0.914980 q^{7} -9.40679 q^{8} -0.909861 q^{9} -4.83377 q^{10} -0.878808 q^{11} +7.87499 q^{12} +3.26590 q^{13} +2.49692 q^{14} +2.56083 q^{15} +14.7764 q^{16} -2.98851 q^{17} +2.48295 q^{18} +7.16745 q^{19} +9.64841 q^{20} -1.32282 q^{21} +2.39821 q^{22} -5.30627 q^{23} -13.5997 q^{24} -1.86247 q^{25} -8.91240 q^{26} -5.65261 q^{27} -4.98395 q^{28} -2.17044 q^{29} -6.98833 q^{30} +7.58424 q^{31} -21.5101 q^{32} -1.27052 q^{33} +8.15545 q^{34} -1.62071 q^{35} -4.95607 q^{36} -2.65249 q^{37} -19.5595 q^{38} +4.72161 q^{39} -16.6623 q^{40} -6.41073 q^{41} +3.60987 q^{42} -4.93882 q^{43} -4.78692 q^{44} -1.61164 q^{45} +14.4804 q^{46} -1.36893 q^{47} +21.3626 q^{48} -6.16281 q^{49} +5.08256 q^{50} -4.32059 q^{51} +17.7895 q^{52} -10.3172 q^{53} +15.4256 q^{54} -1.55664 q^{55} +8.60703 q^{56} +10.3622 q^{57} +5.92298 q^{58} +2.47746 q^{59} +13.9490 q^{60} -10.3254 q^{61} -20.6969 q^{62} +0.832505 q^{63} +29.1468 q^{64} +5.78490 q^{65} +3.46716 q^{66} +3.90281 q^{67} -16.2786 q^{68} -7.67144 q^{69} +4.42281 q^{70} +5.02004 q^{71} +8.55887 q^{72} -8.16882 q^{73} +7.23845 q^{74} -2.69264 q^{75} +39.0415 q^{76} +0.804092 q^{77} -12.8849 q^{78} +14.9908 q^{79} +26.1735 q^{80} -5.44257 q^{81} +17.4944 q^{82} +5.38061 q^{83} -7.20546 q^{84} -5.29358 q^{85} +13.4777 q^{86} -3.13787 q^{87} +8.26677 q^{88} -2.20802 q^{89} +4.39806 q^{90} -2.98823 q^{91} -28.9036 q^{92} +10.9648 q^{93} +3.73570 q^{94} +12.6957 q^{95} -31.0978 q^{96} -1.13594 q^{97} +16.8179 q^{98} +0.799593 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) $ 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * 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 $

$2$	−2.72893	−1.92965	−0.964823	−	0.262902i	$-0.915321\pi$
$2$	−2.72893	−1.92965	−0.964823	+	0.262902i	$0.915321\pi$
$3$	1.44573	0.834693	0.417347	−	0.908747i	$-0.362960\pi$
$3$	1.44573	0.834693	0.417347	+	0.908747i	$0.362960\pi$
$4$	5.44706	2.72353
$5$	1.77131	0.792152	0.396076	−	0.918218i	$-0.370372\pi$
$5$	1.77131	0.792152	0.396076	+	0.918218i	$0.370372\pi$
$6$	−3.94530	−1.61066
$7$	−0.914980	−0.345830	−0.172915	−	0.984937i	$-0.555319\pi$
$7$	−0.914980	−0.345830	−0.172915	+	0.984937i	$0.555319\pi$
$8$	−9.40679	−3.32580
$9$	−0.909861	−0.303287
$10$	−4.83377	−1.52857
$11$	−0.878808	−0.264971	−0.132485	−	0.991185i	$-0.542296\pi$
$11$	−0.878808	−0.264971	−0.132485	+	0.991185i	$0.542296\pi$
$12$	7.87499	2.27331
$13$	3.26590	0.905797	0.452898	−	0.891562i	$-0.350390\pi$
$13$	3.26590	0.905797	0.452898	+	0.891562i	$0.350390\pi$
$14$	2.49692	0.667329
$15$	2.56083	0.661204
$16$	14.7764	3.69409
$17$	−2.98851	−0.724821	−0.362411	−	0.932019i	$-0.618046\pi$
$17$	−2.98851	−0.724821	−0.362411	+	0.932019i	$0.618046\pi$
$18$	2.48295	0.585236
$19$	7.16745	1.64433	0.822163	−	0.569252i	$-0.192767\pi$
$19$	7.16745	1.64433	0.822163	+	0.569252i	$0.192767\pi$
$20$	9.64841	2.15745
$21$	−1.32282	−0.288662
$22$	2.39821	0.511299
$23$	−5.30627	−1.10643	−0.553217	−	0.833037i	$-0.686600\pi$
$23$	−5.30627	−1.10643	−0.553217	+	0.833037i	$0.686600\pi$
$24$	−13.5997	−2.77603
$25$	−1.86247	−0.372495
$26$	−8.91240	−1.74787
$27$	−5.65261	−1.08785
$28$	−4.98395	−0.941879
$29$	−2.17044	−0.403040	−0.201520	−	0.979484i	$-0.564588\pi$
$29$	−2.17044	−0.403040	−0.201520	+	0.979484i	$0.564588\pi$
$30$	−6.98833	−1.27589
$31$	7.58424	1.36217	0.681085	−	0.732205i	$-0.261509\pi$
$31$	7.58424	1.36217	0.681085	+	0.732205i	$0.261509\pi$
$32$	−21.5101	−3.80248
$33$	−1.27052	−0.221169
$34$	8.15545	1.39865
$35$	−1.62071	−0.273950
$36$	−4.95607	−0.826012
$37$	−2.65249	−0.436066	−0.218033	−	0.975941i	$-0.569964\pi$
$37$	−2.65249	−0.436066	−0.218033	+	0.975941i	$0.569964\pi$
$38$	−19.5595	−3.17297
$39$	4.72161	0.756062
$40$	−16.6623	−2.63454
$41$	−6.41073	−1.00119	−0.500594	−	0.865682i	$-0.666885\pi$
$41$	−6.41073	−1.00119	−0.500594	+	0.865682i	$0.666885\pi$
$42$	3.60987	0.557015
$43$	−4.93882	−0.753163	−0.376582	−	0.926383i	$-0.622901\pi$
$43$	−4.93882	−0.753163	−0.376582	+	0.926383i	$0.622901\pi$
$44$	−4.78692	−0.721656
$45$	−1.61164	−0.240250
$46$	14.4804	2.13503
$47$	−1.36893	−0.199678	−0.0998392	−	0.995004i	$-0.531833\pi$
$47$	−1.36893	−0.199678	−0.0998392	+	0.995004i	$0.531833\pi$
$48$	21.3626	3.08343
$49$	−6.16281	−0.880402
$50$	5.08256	0.718783
$51$	−4.32059	−0.605004
$52$	17.7895	2.46697
$53$	−10.3172	−1.41718	−0.708591	−	0.705620i	$-0.750669\pi$
$53$	−10.3172	−1.41718	−0.708591	+	0.705620i	$0.750669\pi$
$54$	15.4256	2.09915
$55$	−1.55664	−0.209897
$56$	8.60703	1.15016
$57$	10.3622	1.37251
$58$	5.92298	0.777725
$59$	2.47746	0.322538	0.161269	−	0.986910i	$-0.448441\pi$
$59$	2.47746	0.322538	0.161269	+	0.986910i	$0.448441\pi$
$60$	13.9490	1.80081
$61$	−10.3254	−1.32203	−0.661013	−	0.750374i	$-0.729873\pi$
$61$	−10.3254	−1.32203	−0.661013	+	0.750374i	$0.729873\pi$
$62$	−20.6969	−2.62850
$63$	0.832505	0.104886
$64$	29.1468	3.64335
$65$	5.78490	0.717529
$66$	3.46716	0.426778
$67$	3.90281	0.476805	0.238402	−	0.971166i	$-0.423376\pi$
$67$	3.90281	0.476805	0.238402	+	0.971166i	$0.423376\pi$
$68$	−16.2786	−1.97407
$69$	−7.67144	−0.923533
$70$	4.42281	0.528626
$71$	5.02004	0.595769	0.297884	−	0.954602i	$-0.403719\pi$
$71$	5.02004	0.595769	0.297884	+	0.954602i	$0.403719\pi$
$72$	8.55887	1.00867
$73$	−8.16882	−0.956088	−0.478044	−	0.878336i	$-0.658654\pi$
$73$	−8.16882	−0.956088	−0.478044	+	0.878336i	$0.658654\pi$
$74$	7.23845	0.841453
$75$	−2.69264	−0.310919
$76$	39.0415	4.47837
$77$	0.804092	0.0916348
$78$	−12.8849	−1.45893
$79$	14.9908	1.68659	0.843296	−	0.537450i	$-0.180612\pi$
$79$	14.9908	1.68659	0.843296	+	0.537450i	$0.180612\pi$
$80$	26.1735	2.92628
$81$	−5.44257	−0.604730
$82$	17.4944	1.93194
$83$	5.38061	0.590599	0.295299	−	0.955405i	$-0.404581\pi$
$83$	5.38061	0.590599	0.295299	+	0.955405i	$0.404581\pi$
$84$	−7.20546	−0.786180
$85$	−5.29358	−0.574169
$86$	13.4777	1.45334
$87$	−3.13787	−0.336415
$88$	8.26677	0.881240
$89$	−2.20802	−0.234050	−0.117025	−	0.993129i	$-0.537336\pi$
$89$	−2.20802	−0.234050	−0.117025	+	0.993129i	$0.537336\pi$
$90$	4.39806	0.463596
$91$	−2.98823	−0.313252
$92$	−28.9036	−3.01341
$93$	10.9648	1.13699
$94$	3.73570	0.385308
$95$	12.6957	1.30256
$96$	−31.0978	−3.17390
$97$	−1.13594	−0.115337	−0.0576687	−	0.998336i	$-0.518367\pi$
$97$	−1.13594	−0.115337	−0.0576687	+	0.998336i	$0.518367\pi$
$98$	16.8179	1.69886
$99$	0.799593	0.0803622
$100$	−10.1450	−1.01450
$101$	0.359825	0.0358040	0.0179020	−	0.999840i	$-0.494301\pi$
$101$	0.359825	0.0358040	0.0179020	+	0.999840i	$0.494301\pi$
$102$	11.7906	1.16744
$103$	−11.0303	−1.08685	−0.543426	−	0.839457i	$-0.682873\pi$
$103$	−11.0303	−1.08685	−0.543426	+	0.839457i	$0.682873\pi$
$104$	−30.7216	−3.01250
$105$	−2.34311	−0.228664
$106$	28.1550	2.73466
$107$	5.95647	0.575834	0.287917	−	0.957655i	$-0.407037\pi$
$107$	5.95647	0.575834	0.287917	+	0.957655i	$0.407037\pi$
$108$	−30.7901	−2.96278
$109$	0.772680	0.0740093	0.0370046	−	0.999315i	$-0.488218\pi$
$109$	0.772680	0.0740093	0.0370046	+	0.999315i	$0.488218\pi$
$110$	4.24796	0.405027
$111$	−3.83478	−0.363981
$112$	−13.5201	−1.27753
$113$	4.44430	0.418084	0.209042	−	0.977907i	$-0.432965\pi$
$113$	4.44430	0.418084	0.209042	+	0.977907i	$0.432965\pi$
$114$	−28.2777	−2.64845
$115$	−9.39903	−0.876464
$116$	−11.8225	−1.09769
$117$	−2.97151	−0.274716
$118$	−6.76082	−0.622384
$119$	2.73443	0.250665
$120$	−24.0892	−2.19903
$121$	−10.2277	−0.929791
$122$	28.1772	2.55104
$123$	−9.26819	−0.835684
$124$	41.3118	3.70991
$125$	−12.1555	−1.08722
$126$	−2.27185	−0.202392
$127$	−8.32356	−0.738596	−0.369298	−	0.929311i	$-0.620402\pi$
$127$	−8.32356	−0.738596	−0.369298	+	0.929311i	$0.620402\pi$
$128$	−36.5194	−3.22789
$129$	−7.14021	−0.628660
$130$	−15.7866	−1.38458
$131$	3.90199	0.340918	0.170459	−	0.985365i	$-0.445475\pi$
$131$	3.90199	0.340918	0.170459	+	0.985365i	$0.445475\pi$
$132$	−6.92060	−0.602361
$133$	−6.55808	−0.568657
$134$	−10.6505	−0.920064
$135$	−10.0125	−0.861739
$136$	28.1123	2.41061
$137$	−15.8730	−1.35612	−0.678060	−	0.735007i	$-0.737179\pi$
$137$	−15.8730	−1.35612	−0.678060	+	0.735007i	$0.737179\pi$
$138$	20.9348	1.78209
$139$	3.14581	0.266824	0.133412	−	0.991061i	$-0.457407\pi$
$139$	3.14581	0.266824	0.133412	+	0.991061i	$0.457407\pi$
$140$	−8.82811	−0.746111
$141$	−1.97910	−0.166670
$142$	−13.6993	−1.14962
$143$	−2.87010	−0.240010
$144$	−13.4444	−1.12037
$145$	−3.84451	−0.319269
$146$	22.2921	1.84491
$147$	−8.90977	−0.734865
$148$	−14.4483	−1.18764
$149$	1.70290	0.139507	0.0697537	−	0.997564i	$-0.477779\pi$
$149$	1.70290	0.139507	0.0697537	+	0.997564i	$0.477779\pi$
$150$	7.34802	0.599963
$151$	−14.7531	−1.20059	−0.600296	−	0.799778i	$-0.704951\pi$
$151$	−14.7531	−1.20059	−0.600296	+	0.799778i	$0.704951\pi$
$152$	−67.4227	−5.46870
$153$	2.71913	0.219829
$154$	−2.19431	−0.176823
$155$	13.4340	1.07905
$156$	25.7189	2.05916
$157$	4.23880	0.338293	0.169147	−	0.985591i	$-0.445899\pi$
$157$	4.23880	0.338293	0.169147	+	0.985591i	$0.445899\pi$
$158$	−40.9087	−3.25452
$159$	−14.9159	−1.18291
$160$	−38.1009	−3.01214
$161$	4.85513	0.382638
$162$	14.8524	1.16691
$163$	0.141353	0.0110716	0.00553579	−	0.999985i	$-0.498238\pi$
$163$	0.141353	0.0110716	0.00553579	+	0.999985i	$0.498238\pi$
$164$	−34.9196	−2.72676
$165$	−2.25048	−0.175200
$166$	−14.6833	−1.13965
$167$	−6.20764	−0.480361	−0.240181	−	0.970728i	$-0.577207\pi$
$167$	−6.20764	−0.480361	−0.240181	+	0.970728i	$0.577207\pi$
$168$	12.4435	0.960033
$169$	−2.33392	−0.179532
$170$	14.4458	1.10794
$171$	−6.52139	−0.498703
$172$	−26.9021	−2.05126
$173$	0.864899	0.0657571	0.0328785	−	0.999459i	$-0.489533\pi$
$173$	0.864899	0.0657571	0.0328785	+	0.999459i	$0.489533\pi$
$174$	8.56303	0.649162
$175$	1.70413	0.128820
$176$	−12.9856	−0.978825
$177$	3.58174	0.269220
$178$	6.02553	0.451633
$179$	−17.3043	−1.29339	−0.646693	−	0.762750i	$-0.723848\pi$
$179$	−17.3043	−1.29339	−0.646693	+	0.762750i	$0.723848\pi$
$180$	−8.77872	−0.654327
$181$	4.86827	0.361856	0.180928	−	0.983496i	$-0.442090\pi$
$181$	4.86827	0.361856	0.180928	+	0.983496i	$0.442090\pi$
$182$	8.15468	0.604465
$183$	−14.9277	−1.10349
$184$	49.9150	3.67978
$185$	−4.69836	−0.345431
$186$	−29.9221	−2.19399
$187$	2.62633	0.192056
$188$	−7.45662	−0.543830
$189$	5.17203	0.376210
$190$	−34.6458	−2.51347
$191$	−13.8335	−1.00096	−0.500479	−	0.865749i	$-0.666843\pi$
$191$	−13.8335	−1.00096	−0.500479	+	0.865749i	$0.666843\pi$
$192$	42.1384	3.04108
$193$	8.87348	0.638727	0.319364	−	0.947632i	$-0.396531\pi$
$193$	8.87348	0.638727	0.319364	+	0.947632i	$0.396531\pi$
$194$	3.09991	0.222560
$195$	8.36341	0.598917
$196$	−33.5692	−2.39780
$197$	3.60883	0.257118	0.128559	−	0.991702i	$-0.458965\pi$
$197$	3.60883	0.257118	0.128559	+	0.991702i	$0.458965\pi$
$198$	−2.18204	−0.155070
$199$	−2.84962	−0.202004	−0.101002	−	0.994886i	$-0.532205\pi$
$199$	−2.84962	−0.202004	−0.101002	+	0.994886i	$0.532205\pi$
$200$	17.5199	1.23884
$201$	5.64242	0.397986
$202$	−0.981939	−0.0690890
$203$	1.98591	0.139384
$204$	−23.5345	−1.64775
$205$	−11.3554	−0.793093
$206$	30.1010	2.09724
$207$	4.82797	0.335567
$208$	48.2581	3.34609
$209$	−6.29881	−0.435698
$210$	6.39419	0.441241
$211$	21.6053	1.48737	0.743684	−	0.668531i	$-0.233077\pi$
$211$	21.6053	1.48737	0.743684	+	0.668531i	$0.233077\pi$
$212$	−56.1986	−3.85974
$213$	7.25762	0.497284
$214$	−16.2548	−1.11116
$215$	−8.74817	−0.596620
$216$	53.1729	3.61796
$217$	−6.93943	−0.471079
$218$	−2.10859	−0.142812
$219$	−11.8099	−0.798040
$220$	−8.47910	−0.571661
$221$	−9.76018	−0.656541
$222$	10.4649	0.702355
$223$	6.58370	0.440877	0.220438	−	0.975401i	$-0.429251\pi$
$223$	6.58370	0.440877	0.220438	+	0.975401i	$0.429251\pi$
$224$	19.6813	1.31501
$225$	1.69459	0.112973
$226$	−12.1282	−0.806755
$227$	11.3505	0.753356	0.376678	−	0.926344i	$-0.377066\pi$
$227$	11.3505	0.753356	0.376678	+	0.926344i	$0.377066\pi$
$228$	56.4436	3.73807
$229$	−14.1612	−0.935796	−0.467898	−	0.883782i	$-0.654989\pi$
$229$	−14.1612	−0.935796	−0.467898	+	0.883782i	$0.654989\pi$
$230$	25.6493	1.69127
$231$	1.16250	0.0764870
$232$	20.4169	1.34043
$233$	5.36407	0.351412	0.175706	−	0.984443i	$-0.443779\pi$
$233$	5.36407	0.351412	0.175706	+	0.984443i	$0.443779\pi$
$234$	8.10905	0.530105
$235$	−2.42479	−0.158176
$236$	13.4949	0.878442
$237$	21.6726	1.40779
$238$	−7.46208	−0.483695
$239$	22.3626	1.44652	0.723259	−	0.690577i	$-0.242643\pi$
$239$	22.3626	1.44652	0.723259	+	0.690577i	$0.242643\pi$
$240$	37.8398	2.44255
$241$	20.6048	1.32727	0.663637	−	0.748055i	$-0.269012\pi$
$241$	20.6048	1.32727	0.663637	+	0.748055i	$0.269012\pi$
$242$	27.9107	1.79417
$243$	9.08933	0.583081
$244$	−56.2428	−3.60058
$245$	−10.9162	−0.697412
$246$	25.2922	1.61257
$247$	23.4081	1.48942
$248$	−71.3434	−4.53031
$249$	7.77892	0.492969
$250$	33.1716	2.09796
$251$	−3.43137	−0.216586	−0.108293	−	0.994119i	$-0.534539\pi$
$251$	−3.43137	−0.216586	−0.108293	+	0.994119i	$0.534539\pi$
$252$	4.53471	0.285660
$253$	4.66320	0.293173
$254$	22.7144	1.42523
$255$	−7.65309	−0.479255
$256$	41.3653	2.58533
$257$	16.0988	1.00421	0.502107	−	0.864806i	$-0.332558\pi$
$257$	16.0988	1.00421	0.502107	+	0.864806i	$0.332558\pi$
$258$	19.4851	1.21309
$259$	2.42697	0.150805
$260$	31.5107	1.95421
$261$	1.97480	0.122237
$262$	−10.6482	−0.657851
$263$	−15.9326	−0.982444	−0.491222	−	0.871034i	$-0.663450\pi$
$263$	−15.9326	−0.982444	−0.491222	+	0.871034i	$0.663450\pi$
$264$	11.9515	0.735565
$265$	−18.2750	−1.12262
$266$	17.8965	1.09731
$267$	−3.19220	−0.195360
$268$	21.2589	1.29859
$269$	11.3641	0.692880	0.346440	−	0.938072i	$-0.387390\pi$
$269$	11.3641	0.692880	0.346440	+	0.938072i	$0.387390\pi$
$270$	27.3234	1.66285
$271$	−22.5311	−1.36866	−0.684332	−	0.729171i	$-0.739906\pi$
$271$	−22.5311	−1.36866	−0.684332	+	0.729171i	$0.739906\pi$
$272$	−44.1594	−2.67755
$273$	−4.32018	−0.261469
$274$	43.3162	2.61683
$275$	1.63676	0.0987002
$276$	−41.7868	−2.51527
$277$	−6.73561	−0.404704	−0.202352	−	0.979313i	$-0.564858\pi$
$277$	−6.73561	−0.404704	−0.202352	+	0.979313i	$0.564858\pi$
$278$	−8.58470	−0.514876
$279$	−6.90061	−0.413128
$280$	15.2457	0.911104
$281$	5.56434	0.331941	0.165970	−	0.986131i	$-0.446924\pi$
$281$	5.56434	0.331941	0.165970	+	0.986131i	$0.446924\pi$
$282$	5.40082	0.321614
$283$	−16.9235	−1.00600	−0.502999	−	0.864287i	$-0.667770\pi$
$283$	−16.9235	−1.00600	−0.502999	+	0.864287i	$0.667770\pi$
$284$	27.3444	1.62259
$285$	18.3546	1.08724
$286$	7.83229	0.463133
$287$	5.86569	0.346241
$288$	19.5712	1.15324
$289$	−8.06878	−0.474634
$290$	10.4914	0.616077
$291$	−1.64227	−0.0962714
$292$	−44.4961	−2.60394
$293$	−30.0657	−1.75646	−0.878228	−	0.478241i	$-0.841274\pi$
$293$	−30.0657	−1.75646	−0.878228	+	0.478241i	$0.841274\pi$
$294$	24.3141	1.41803
$295$	4.38834	0.255499
$296$	24.9514	1.45027
$297$	4.96756	0.288247
$298$	−4.64711	−0.269200
$299$	−17.3297	−1.00220
$300$	−14.6670	−0.846797
$301$	4.51893	0.260467
$302$	40.2602	2.31672
$303$	0.520211	0.0298853
$304$	105.909	6.07429
$305$	−18.2894	−1.04725
$306$	−7.42033	−0.424192
$307$	−22.9963	−1.31247	−0.656233	−	0.754558i	$-0.727851\pi$
$307$	−22.9963	−1.31247	−0.656233	+	0.754558i	$0.727851\pi$
$308$	4.37994	0.249570
$309$	−15.9469	−0.907188
$310$	−36.6605	−2.08218
$311$	−0.871583	−0.0494229	−0.0247115	−	0.999695i	$-0.507867\pi$
$311$	−0.871583	−0.0494229	−0.0247115	+	0.999695i	$0.507867\pi$
$312$	−44.4152	−2.51451
$313$	−8.46160	−0.478278	−0.239139	−	0.970985i	$-0.576865\pi$
$313$	−8.46160	−0.478278	−0.239139	+	0.970985i	$0.576865\pi$
$314$	−11.5674	−0.652786
$315$	1.47462	0.0830855
$316$	81.6556	4.59348
$317$	16.3869	0.920378	0.460189	−	0.887821i	$-0.347782\pi$
$317$	16.3869	0.920378	0.460189	+	0.887821i	$0.347782\pi$
$318$	40.7046	2.28260
$319$	1.90740	0.106794
$320$	51.6278	2.88608
$321$	8.61146	0.480645
$322$	−13.2493	−0.738356
$323$	−21.4200	−1.19184
$324$	−29.6460	−1.64700
$325$	−6.08265	−0.337405
$326$	−0.385741	−0.0213642
$327$	1.11709	0.0617751
$328$	60.3044	3.32975
$329$	1.25254	0.0690548
$330$	6.14141	0.338073
$331$	−21.3620	−1.17416	−0.587081	−	0.809528i	$-0.699723\pi$
$331$	−21.3620	−1.17416	−0.587081	+	0.809528i	$0.699723\pi$
$332$	29.3085	1.60851
$333$	2.41339	0.132253
$334$	16.9402	0.926927
$335$	6.91308	0.377702
$336$	−19.5464	−1.06634
$337$	25.4229	1.38487	0.692436	−	0.721479i	$-0.256537\pi$
$337$	25.4229	1.38487	0.692436	+	0.721479i	$0.256537\pi$
$338$	6.36911	0.346434
$339$	6.42526	0.348972
$340$	−28.8344	−1.56377
$341$	−6.66509	−0.360935
$342$	17.7964	0.962319
$343$	12.0437	0.650299
$344$	46.4585	2.50487
$345$	−13.5885	−0.731579
$346$	−2.36025	−0.126888
$347$	−7.61667	−0.408884	−0.204442	−	0.978879i	$-0.565538\pi$
$347$	−7.61667	−0.408884	−0.204442	+	0.978879i	$0.565538\pi$
$348$	−17.0922	−0.916237
$349$	22.5572	1.20746	0.603731	−	0.797188i	$-0.293680\pi$
$349$	22.5572	1.20746	0.603731	+	0.797188i	$0.293680\pi$
$350$	−4.65045	−0.248577
$351$	−18.4608	−0.985366
$352$	18.9032	1.00755
$353$	3.33730	0.177626	0.0888132	−	0.996048i	$-0.471693\pi$
$353$	3.33730	0.177626	0.0888132	+	0.996048i	$0.471693\pi$
$354$	−9.77432	−0.519499
$355$	8.89202	0.471939
$356$	−12.0272	−0.637441
$357$	3.95325	0.209228
$358$	47.2223	2.49578
$359$	22.4253	1.18356	0.591782	−	0.806098i	$-0.298425\pi$
$359$	22.4253	1.18356	0.591782	+	0.806098i	$0.298425\pi$
$360$	15.1604	0.799023
$361$	32.3723	1.70381
$362$	−13.2852	−0.698253
$363$	−14.7865	−0.776090
$364$	−16.2771	−0.853151
$365$	−14.4695	−0.757367
$366$	40.7366	2.12934
$367$	−4.83349	−0.252306	−0.126153	−	0.992011i	$-0.540263\pi$
$367$	−4.83349	−0.252306	−0.126153	+	0.992011i	$0.540263\pi$
$368$	−78.4074	−4.08727
$369$	5.83287	0.303647
$370$	12.8215	0.666559
$371$	9.44007	0.490104
$372$	59.7258	3.09664
$373$	−4.26413	−0.220788	−0.110394	−	0.993888i	$-0.535211\pi$
$373$	−4.26413	−0.220788	−0.110394	+	0.993888i	$0.535211\pi$
$374$	−7.16708	−0.370601
$375$	−17.5736	−0.907499
$376$	12.8772	0.664091
$377$	−7.08843	−0.365073
$378$	−14.1141	−0.725951
$379$	−37.1956	−1.91061	−0.955305	−	0.295621i	$-0.904474\pi$
$379$	−37.1956	−1.91061	−0.955305	+	0.295621i	$0.904474\pi$
$380$	69.1545	3.54755
$381$	−12.0336	−0.616501
$382$	37.7507	1.93149
$383$	−29.9410	−1.52991	−0.764957	−	0.644082i	$-0.777240\pi$
$383$	−29.9410	−1.52991	−0.764957	+	0.644082i	$0.777240\pi$
$384$	−52.7972	−2.69429
$385$	1.42429	0.0725887
$386$	−24.2151	−1.23252
$387$	4.49364	0.228425
$388$	−6.18755	−0.314125
$389$	25.0600	1.27059	0.635297	−	0.772268i	$-0.280878\pi$
$389$	25.0600	1.27059	0.635297	+	0.772268i	$0.280878\pi$
$390$	−22.8232	−1.15570
$391$	15.8579	0.801967
$392$	57.9723	2.92804
$393$	5.64122	0.284562
$394$	−9.84824	−0.496147
$395$	26.5532	1.33604
$396$	4.35543	0.218869
$397$	−38.7680	−1.94571	−0.972856	−	0.231411i	$-0.925666\pi$
$397$	−38.7680	−1.94571	−0.972856	+	0.231411i	$0.925666\pi$
$398$	7.77642	0.389797
$399$	−9.48122	−0.474654
$400$	−27.5206	−1.37603
$401$	−3.09887	−0.154750	−0.0773752	−	0.997002i	$-0.524654\pi$
$401$	−3.09887	−0.154750	−0.0773752	+	0.997002i	$0.524654\pi$
$402$	−15.3978	−0.767971
$403$	24.7693	1.23385
$404$	1.95999	0.0975132
$405$	−9.64046	−0.479038
$406$	−5.41941	−0.268961
$407$	2.33103	0.115545
$408$	40.6429	2.01212
$409$	−1.22989	−0.0608142	−0.0304071	−	0.999538i	$-0.509680\pi$
$409$	−1.22989	−0.0608142	−0.0304071	+	0.999538i	$0.509680\pi$
$410$	30.9880	1.53039
$411$	−22.9480	−1.13194
$412$	−60.0829	−2.96007
$413$	−2.26683	−0.111543
$414$	−13.1752	−0.647526
$415$	9.53071	0.467844
$416$	−70.2497	−3.44427
$417$	4.54800	0.222716
$418$	17.1890	0.840743
$419$	−25.7595	−1.25844	−0.629218	−	0.777229i	$-0.716625\pi$
$419$	−25.7595	−1.25844	−0.629218	+	0.777229i	$0.716625\pi$
$420$	−12.7631	−0.622774
$421$	20.0266	0.976036	0.488018	−	0.872834i	$-0.337720\pi$
$421$	20.0266	0.976036	0.488018	+	0.872834i	$0.337720\pi$
$422$	−58.9593	−2.87009
$423$	1.24553	0.0605599
$424$	97.0521	4.71327
$425$	5.56603	0.269992
$426$	−19.8055	−0.959582
$427$	9.44750	0.457196
$428$	32.4453	1.56830
$429$	−4.14939	−0.200334
$430$	23.8731	1.15127
$431$	−33.1688	−1.59769	−0.798843	−	0.601540i	$-0.794554\pi$
$431$	−33.1688	−1.59769	−0.798843	+	0.601540i	$0.794554\pi$
$432$	−83.5250	−4.01860
$433$	5.88668	0.282896	0.141448	−	0.989946i	$-0.454824\pi$
$433$	5.88668	0.282896	0.141448	+	0.989946i	$0.454824\pi$
$434$	18.9372	0.909016
$435$	−5.55813	−0.266492
$436$	4.20883	0.201567
$437$	−38.0324	−1.81934
$438$	32.2284	1.53993
$439$	11.5375	0.550656	0.275328	−	0.961350i	$-0.411214\pi$
$439$	11.5375	0.550656	0.275328	+	0.961350i	$0.411214\pi$
$440$	14.6430	0.698076
$441$	5.60730	0.267014
$442$	26.6349	1.26689
$443$	−16.5875	−0.788094	−0.394047	−	0.919090i	$-0.628925\pi$
$443$	−16.5875	−0.788094	−0.394047	+	0.919090i	$0.628925\pi$
$444$	−20.8883	−0.991314
$445$	−3.91108	−0.185403
$446$	−17.9664	−0.850736
$447$	2.46194	0.116446
$448$	−26.6687	−1.25998
$449$	−39.5544	−1.86669	−0.933343	−	0.358986i	$-0.883122\pi$
$449$	−39.5544	−1.86669	−0.933343	+	0.358986i	$0.883122\pi$
$450$	−4.62443	−0.217998
$451$	5.63380	0.265285
$452$	24.2084	1.13867
$453$	−21.3291	−1.00213
$454$	−30.9746	−1.45371
$455$	−5.29307	−0.248143
$456$	−97.4751	−4.56469
$457$	29.1760	1.36479	0.682397	−	0.730982i	$-0.260938\pi$
$457$	29.1760	1.36479	0.682397	+	0.730982i	$0.260938\pi$
$458$	38.6448	1.80575
$459$	16.8929	0.788493
$460$	−51.1971	−2.38708
$461$	−33.6454	−1.56702	−0.783511	−	0.621378i	$-0.786573\pi$
$461$	−33.6454	−1.56702	−0.783511	+	0.621378i	$0.786573\pi$
$462$	−3.17239	−0.147593
$463$	−19.4905	−0.905799	−0.452899	−	0.891562i	$-0.649610\pi$
$463$	−19.4905	−0.905799	−0.452899	+	0.891562i	$0.649610\pi$
$464$	−32.0712	−1.48887
$465$	19.4220	0.900672
$466$	−14.6382	−0.678100
$467$	−6.29045	−0.291087	−0.145544	−	0.989352i	$-0.546493\pi$
$467$	−6.29045	−0.291087	−0.145544	+	0.989352i	$0.546493\pi$
$468$	−16.1860	−0.748199
$469$	−3.57100	−0.164893
$470$	6.61707	0.305223
$471$	6.12817	0.282371
$472$	−23.3050	−1.07270
$473$	4.34028	0.199566
$474$	−59.1430	−2.71653
$475$	−13.3492	−0.612503
$476$	14.8946	0.682694
$477$	9.38725	0.429813
$478$	−61.0260	−2.79127
$479$	−3.20551	−0.146464	−0.0732318	−	0.997315i	$-0.523331\pi$
$479$	−3.20551	−0.146464	−0.0732318	+	0.997315i	$0.523331\pi$
$480$	−55.0837	−2.51421
$481$	−8.66274	−0.394987
$482$	−56.2291	−2.56117
$483$	7.01922	0.319386
$484$	−55.7109	−2.53231
$485$	−2.01210	−0.0913648
$486$	−24.8042	−1.12514
$487$	40.1846	1.82094	0.910469	−	0.413577i	$-0.135721\pi$
$487$	40.1846	1.82094	0.910469	+	0.413577i	$0.135721\pi$
$488$	97.1284	4.39680
$489$	0.204358	0.00924138
$490$	29.7896	1.34576
$491$	1.55581	0.0702129	0.0351064	−	0.999384i	$-0.488823\pi$
$491$	1.55581	0.0702129	0.0351064	+	0.999384i	$0.488823\pi$
$492$	−50.4844	−2.27601
$493$	6.48639	0.292132
$494$	−63.8792	−2.87406
$495$	1.41632	0.0636591
$496$	112.067	5.03198
$497$	−4.59323	−0.206035
$498$	−21.2281	−0.951255
$499$	14.0664	0.629696	0.314848	−	0.949142i	$-0.398046\pi$
$499$	14.0664	0.629696	0.314848	+	0.949142i	$0.398046\pi$
$500$	−66.2120	−2.96109
$501$	−8.97457	−0.400954
$502$	9.36398	0.417935
$503$	9.12626	0.406920	0.203460	−	0.979083i	$-0.434781\pi$
$503$	9.12626	0.406920	0.203460	+	0.979083i	$0.434781\pi$
$504$	−7.83120	−0.348829
$505$	0.637361	0.0283622
$506$	−12.7255	−0.565719
$507$	−3.37422	−0.149854
$508$	−45.3389	−2.01159
$509$	−15.6068	−0.691760	−0.345880	−	0.938279i	$-0.612420\pi$
$509$	−15.6068	−0.691760	−0.345880	+	0.938279i	$0.612420\pi$
$510$	20.8847	0.924792
$511$	7.47431	0.330644
$512$	−39.8442	−1.76088
$513$	−40.5148	−1.78877
$514$	−43.9324	−1.93778
$515$	−19.5381	−0.860952
$516$	−38.8932	−1.71218
$517$	1.20302	0.0529089
$518$	−6.62304	−0.291000
$519$	1.25041	0.0548870
$520$	−54.4174	−2.38636
$521$	14.8327	0.649833	0.324916	−	0.945743i	$-0.394664\pi$
$521$	14.8327	0.649833	0.324916	+	0.945743i	$0.394664\pi$
$522$	−5.38909	−0.235874
$523$	5.93682	0.259599	0.129800	−	0.991540i	$-0.458567\pi$
$523$	5.93682	0.259599	0.129800	+	0.991540i	$0.458567\pi$
$524$	21.2544	0.928501
$525$	2.46371	0.107525
$526$	43.4789	1.89577
$527$	−22.6656	−0.987330
$528$	−18.7737	−0.817019
$529$	5.15652	0.224197
$530$	49.8712	2.16626
$531$	−2.25415	−0.0978216
$532$	−35.7222	−1.54876
$533$	−20.9368	−0.906872
$534$	8.71130	0.376975
$535$	10.5507	0.456148
$536$	−36.7130	−1.58576
$537$	−25.0174	−1.07958
$538$	−31.0118	−1.33701
$539$	5.41593	0.233281
$540$	−54.5387	−2.34697
$541$	2.61073	0.112244	0.0561220	−	0.998424i	$-0.482126\pi$
$541$	2.61073	0.112244	0.0561220	+	0.998424i	$0.482126\pi$
$542$	61.4857	2.64104
$543$	7.03821	0.302038
$544$	64.2832	2.75612
$545$	1.36865	0.0586266
$546$	11.7895	0.504543
$547$	27.0329	1.15584	0.577922	−	0.816092i	$-0.303864\pi$
$547$	27.0329	1.15584	0.577922	+	0.816092i	$0.303864\pi$
$548$	−86.4610	−3.69343
$549$	9.39464	0.400953
$550$	−4.46660	−0.190456
$551$	−15.5565	−0.662730
$552$	72.1637	3.07149
$553$	−13.7162	−0.583274
$554$	18.3810	0.780935
$555$	−6.79257	−0.288329
$556$	17.1354	0.726704
$557$	−7.65186	−0.324220	−0.162110	−	0.986773i	$-0.551830\pi$
$557$	−7.65186	−0.324220	−0.162110	+	0.986773i	$0.551830\pi$
$558$	18.8313	0.797191
$559$	−16.1297	−0.682213
$560$	−23.9482	−1.01200
$561$	3.79697	0.160308
$562$	−15.1847	−0.640528
$563$	21.5497	0.908210	0.454105	−	0.890948i	$-0.349959\pi$
$563$	21.5497	0.908210	0.454105	+	0.890948i	$0.349959\pi$
$564$	−10.7803	−0.453931
$565$	7.87221	0.331186
$566$	46.1830	1.94122
$567$	4.97984	0.209134
$568$	−47.2224	−1.98141
$569$	21.9864	0.921717	0.460859	−	0.887474i	$-0.347542\pi$
$569$	21.9864	0.921717	0.460859	+	0.887474i	$0.347542\pi$
$570$	−50.0885	−2.09798
$571$	1.49736	0.0626625	0.0313313	−	0.999509i	$-0.490025\pi$
$571$	1.49736	0.0626625	0.0313313	+	0.999509i	$0.490025\pi$
$572$	−15.6336	−0.653673
$573$	−19.9995	−0.835493
$574$	−16.0071	−0.668122
$575$	9.88280	0.412141
$576$	−26.5195	−1.10498
$577$	18.5406	0.771853	0.385927	−	0.922529i	$-0.373882\pi$
$577$	18.5406	0.771853	0.385927	+	0.922529i	$0.373882\pi$
$578$	22.0191	0.915875
$579$	12.8287	0.533141
$580$	−20.9413	−0.869540
$581$	−4.92315	−0.204247
$582$	4.48163	0.185770
$583$	9.06687	0.375511
$584$	76.8424	3.17976
$585$	−5.26346	−0.217617
$586$	82.0472	3.38934
$587$	−5.01452	−0.206971	−0.103486	−	0.994631i	$-0.533000\pi$
$587$	−5.01452	−0.206971	−0.103486	+	0.994631i	$0.533000\pi$
$588$	−48.5321	−2.00143
$589$	54.3597	2.23985
$590$	−11.9755	−0.493023
$591$	5.21740	0.214615
$592$	−39.1941	−1.61087
$593$	0.414590	0.0170252	0.00851258	−	0.999964i	$-0.497290\pi$
$593$	0.414590	0.0170252	0.00851258	+	0.999964i	$0.497290\pi$
$594$	−13.5561	−0.556214
$595$	4.84352	0.198565
$596$	9.27583	0.379953
$597$	−4.11979	−0.168612
$598$	47.2916	1.93390
$599$	−24.4575	−0.999306	−0.499653	−	0.866226i	$-0.666539\pi$
$599$	−24.4575	−0.999306	−0.499653	+	0.866226i	$0.666539\pi$
$600$	25.3291	1.03406
$601$	20.9499	0.854563	0.427282	−	0.904119i	$-0.359471\pi$
$601$	20.9499	0.854563	0.427282	+	0.904119i	$0.359471\pi$
$602$	−12.3318	−0.502608
$603$	−3.55102	−0.144609
$604$	−80.3612	−3.26985
$605$	−18.1164	−0.736536
$606$	−1.41962	−0.0576681
$607$	−22.6223	−0.918212	−0.459106	−	0.888382i	$-0.651830\pi$
$607$	−22.6223	−0.918212	−0.459106	+	0.888382i	$0.651830\pi$
$608$	−154.172	−6.25251
$609$	2.87109	0.116342
$610$	49.9104	2.02081
$611$	−4.47077	−0.180868
$612$	14.8113	0.598711
$613$	−30.2922	−1.22349	−0.611744	−	0.791055i	$-0.709532\pi$
$613$	−30.2922	−1.22349	−0.611744	+	0.791055i	$0.709532\pi$
$614$	62.7552	2.53259
$615$	−16.4168	−0.661989
$616$	−7.56393	−0.304759
$617$	0.546504	0.0220014	0.0110007	−	0.999939i	$-0.496498\pi$
$617$	0.546504	0.0220014	0.0110007	+	0.999939i	$0.496498\pi$
$618$	43.5180	1.75055
$619$	−19.6935	−0.791547	−0.395773	−	0.918348i	$-0.629523\pi$
$619$	−19.6935	−0.791547	−0.395773	+	0.918348i	$0.629523\pi$
$620$	73.1759	2.93881
$621$	29.9943	1.20363
$622$	2.37849	0.0953687
$623$	2.02029	0.0809414
$624$	69.7682	2.79296
$625$	−12.2188	−0.488753
$626$	23.0911	0.922907
$627$	−9.10639	−0.363674
$628$	23.0890	0.921352
$629$	7.92699	0.316070
$630$	−4.02414	−0.160326
$631$	−33.2319	−1.32294	−0.661471	−	0.749971i	$-0.730068\pi$
$631$	−33.2319	−1.32294	−0.661471	+	0.749971i	$0.730068\pi$
$632$	−141.015	−5.60927
$633$	31.2354	1.24150
$634$	−44.7186	−1.77600
$635$	−14.7436	−0.585081
$636$	−81.2481	−3.22170
$637$	−20.1271	−0.797465
$638$	−5.20516	−0.206074
$639$	−4.56754	−0.180689
$640$	−64.6870	−2.55698
$641$	26.6867	1.05406	0.527031	−	0.849846i	$-0.323305\pi$
$641$	26.6867	1.05406	0.527031	+	0.849846i	$0.323305\pi$
$642$	−23.5001	−0.927474
$643$	4.00325	0.157873	0.0789365	−	0.996880i	$-0.474848\pi$
$643$	4.00325	0.157873	0.0789365	+	0.996880i	$0.474848\pi$
$644$	26.4462	1.04213
$645$	−12.6475	−0.497995
$646$	58.4538	2.29983
$647$	14.5894	0.573569	0.286785	−	0.957995i	$-0.407414\pi$
$647$	14.5894	0.573569	0.286785	+	0.957995i	$0.407414\pi$
$648$	51.1971	2.01121
$649$	−2.17721	−0.0854631
$650$	16.5991	0.651071
$651$	−10.0326	−0.393207
$652$	0.769956	0.0301538
$653$	36.2984	1.42047	0.710233	−	0.703967i	$-0.248590\pi$
$653$	36.2984	1.42047	0.710233	+	0.703967i	$0.248590\pi$
$654$	−3.04845	−0.119204
$655$	6.91161	0.270059
$656$	−94.7272	−3.69848
$657$	7.43249	0.289969
$658$	−3.41810	−0.133251
$659$	11.2864	0.439657	0.219829	−	0.975539i	$-0.429450\pi$
$659$	11.2864	0.439657	0.219829	+	0.975539i	$0.429450\pi$
$660$	−12.2585	−0.477162
$661$	47.6352	1.85279	0.926397	−	0.376549i	$-0.122889\pi$
$661$	47.6352	1.85279	0.926397	+	0.376549i	$0.122889\pi$
$662$	58.2955	2.26572
$663$	−14.1106	−0.548010
$664$	−50.6143	−1.96421
$665$	−11.6164	−0.450463
$666$	−6.58599	−0.255202
$667$	11.5169	0.445938
$668$	−33.8134	−1.30828
$669$	9.51826	0.367997
$670$	−18.8653	−0.728831
$671$	9.07400	0.350298
$672$	28.4539	1.09763
$673$	−41.0234	−1.58134	−0.790668	−	0.612245i	$-0.790267\pi$
$673$	−41.0234	−1.58134	−0.790668	+	0.612245i	$0.790267\pi$
$674$	−69.3773	−2.67231
$675$	10.5278	0.405217
$676$	−12.7130	−0.488962
$677$	−19.3357	−0.743131	−0.371566	−	0.928407i	$-0.621179\pi$
$677$	−19.3357	−0.743131	−0.371566	+	0.928407i	$0.621179\pi$
$678$	−17.5341	−0.673393
$679$	1.03937	0.0398872
$680$	49.7956	1.90957
$681$	16.4097	0.628821
$682$	18.1886	0.696476
$683$	5.87603	0.224840	0.112420	−	0.993661i	$-0.464140\pi$
$683$	5.87603	0.224840	0.112420	+	0.993661i	$0.464140\pi$
$684$	−35.5224	−1.35823
$685$	−28.1159	−1.07425
$686$	−32.8665	−1.25485
$687$	−20.4732	−0.781103
$688$	−72.9778	−2.78225
$689$	−33.6950	−1.28368
$690$	37.0820	1.41169
$691$	−6.28295	−0.239015	−0.119507	−	0.992833i	$-0.538131\pi$
$691$	−6.28295	−0.239015	−0.119507	+	0.992833i	$0.538131\pi$
$692$	4.71116	0.179091
$693$	−0.731612	−0.0277917
$694$	20.7854	0.789002
$695$	5.57219	0.211365
$696$	29.5173	1.11885
$697$	19.1586	0.725682
$698$	−61.5572	−2.32997
$699$	7.75500	0.293321
$700$	9.28249	0.350845
$701$	−0.169319	−0.00639509	−0.00319754	−	0.999995i	$-0.501018\pi$
$701$	−0.169319	−0.00639509	−0.00319754	+	0.999995i	$0.501018\pi$
$702$	50.3783	1.90141
$703$	−19.0116	−0.717035
$704$	−25.6144	−0.965380
$705$	−3.50559	−0.132028
$706$	−9.10725	−0.342756
$707$	−0.329233	−0.0123821
$708$	19.5100	0.733229
$709$	27.9709	1.05047	0.525235	−	0.850957i	$-0.323978\pi$
$709$	27.9709	1.05047	0.525235	+	0.850957i	$0.323978\pi$
$710$	−24.2657	−0.910676
$711$	−13.6395	−0.511521
$712$	20.7704	0.778403
$713$	−40.2440	−1.50715
$714$	−10.7882	−0.403737
$715$	−5.08382	−0.190124
$716$	−94.2577	−3.52258
$717$	32.3303	1.20740
$718$	−61.1972	−2.28386
$719$	−25.9025	−0.966000	−0.483000	−	0.875620i	$-0.660453\pi$
$719$	−25.9025	−0.966000	−0.483000	+	0.875620i	$0.660453\pi$
$720$	−23.8142	−0.887503
$721$	10.0925	0.375866
$722$	−88.3419	−3.28774
$723$	29.7890	1.10787
$724$	26.5178	0.985525
$725$	4.04239	0.150131
$726$	40.3513	1.49758
$727$	−9.84170	−0.365008	−0.182504	−	0.983205i	$-0.558420\pi$
$727$	−9.84170	−0.365008	−0.182504	+	0.983205i	$0.558420\pi$
$728$	28.1097	1.04181
$729$	29.4684	1.09142
$730$	39.4862	1.46145
$731$	14.7597	0.545909
$732$	−81.3120	−3.00538
$733$	49.3817	1.82395	0.911977	−	0.410242i	$-0.134556\pi$
$733$	49.3817	1.82395	0.911977	+	0.410242i	$0.134556\pi$
$734$	13.1903	0.486861
$735$	−15.7819	−0.582125
$736$	114.138	4.20719
$737$	−3.42983	−0.126339
$738$	−15.9175	−0.585931
$739$	−18.4267	−0.677836	−0.338918	−	0.940816i	$-0.610061\pi$
$739$	−18.4267	−0.677836	−0.338918	+	0.940816i	$0.610061\pi$
$740$	−25.5923	−0.940791
$741$	33.8419	1.24321
$742$	−25.7613	−0.945727
$743$	24.7301	0.907258	0.453629	−	0.891191i	$-0.350129\pi$
$743$	24.7301	0.907258	0.453629	+	0.891191i	$0.350129\pi$
$744$	−103.143	−3.78142
$745$	3.01637	0.110511
$746$	11.6365	0.426043
$747$	−4.89561	−0.179121
$748$	14.3058	0.523071
$749$	−5.45006	−0.199141
$750$	47.9573	1.75115
$751$	−16.7389	−0.610810	−0.305405	−	0.952223i	$-0.598792\pi$
$751$	−16.7389	−0.610810	−0.305405	+	0.952223i	$0.598792\pi$
$752$	−20.2277	−0.737630
$753$	−4.96084	−0.180783
$754$	19.3438	0.704461
$755$	−26.1323	−0.951052
$756$	28.1723	1.02462
$757$	−45.2636	−1.64514	−0.822568	−	0.568667i	$-0.807459\pi$
$757$	−45.2636	−1.64514	−0.822568	+	0.568667i	$0.807459\pi$
$758$	101.504	3.68680
$759$	6.74173	0.244709
$760$	−119.426	−4.33205
$761$	−11.3737	−0.412298	−0.206149	−	0.978521i	$-0.566093\pi$
$761$	−11.3737	−0.412298	−0.206149	+	0.978521i	$0.566093\pi$
$762$	32.8389	1.18963
$763$	−0.706987	−0.0255946
$764$	−75.3520	−2.72614
$765$	4.81642	0.174138
$766$	81.7069	2.95219
$767$	8.09113	0.292154
$768$	59.8031	2.15796
$769$	−23.8092	−0.858582	−0.429291	−	0.903166i	$-0.641237\pi$
$769$	−23.8092	−0.858582	−0.429291	+	0.903166i	$0.641237\pi$
$770$	−3.88680	−0.140070
$771$	23.2745	0.838211
$772$	48.3344	1.73959
$773$	−2.86185	−0.102934	−0.0514668	−	0.998675i	$-0.516390\pi$
$773$	−2.86185	−0.102934	−0.0514668	+	0.998675i	$0.516390\pi$
$774$	−12.2628	−0.440779
$775$	−14.1255	−0.507401
$776$	10.6856	0.383590
$777$	3.50875	0.125876
$778$	−68.3871	−2.45180
$779$	−45.9486	−1.64628
$780$	45.5560	1.63117
$781$	−4.41165	−0.157861
$782$	−43.2750	−1.54751
$783$	12.2686	0.438446
$784$	−91.0639	−3.25228
$785$	7.50822	0.267980
$786$	−15.3945	−0.549104
$787$	32.7640	1.16791	0.583956	−	0.811786i	$-0.301504\pi$
$787$	32.7640	1.16791	0.583956	+	0.811786i	$0.301504\pi$
$788$	19.6575	0.700270
$789$	−23.0342	−0.820039
$790$	−72.4619	−2.57808
$791$	−4.06645	−0.144586
$792$	−7.52161	−0.267269
$793$	−33.7215	−1.19749
$794$	105.795	3.75453
$795$	−26.4207	−0.937046
$796$	−15.5221	−0.550165
$797$	−24.6528	−0.873248	−0.436624	−	0.899644i	$-0.643826\pi$
$797$	−24.6528	−0.873248	−0.436624	+	0.899644i	$0.643826\pi$
$798$	25.8736	0.915915
$799$	4.09106	0.144731
$800$	40.0620	1.41640
$801$	2.00899	0.0709842
$802$	8.45661	0.298613
$803$	7.17883	0.253335
$804$	30.7346	1.08393
$805$	8.59993	0.303108
$806$	−67.5938	−2.38089
$807$	16.4294	0.578343
$808$	−3.38480	−0.119077
$809$	4.86859	0.171171	0.0855853	−	0.996331i	$-0.472724\pi$
$809$	4.86859	0.171171	0.0855853	+	0.996331i	$0.472724\pi$
$810$	26.3081	0.924374
$811$	−30.7719	−1.08055	−0.540273	−	0.841490i	$-0.681679\pi$
$811$	−30.7719	−1.08055	−0.540273	+	0.841490i	$0.681679\pi$
$812$	10.8174	0.379615
$813$	−32.5738	−1.14241
$814$	−6.36121	−0.222960
$815$	0.250379	0.00877038
$816$	−63.8426	−2.23494
$817$	−35.3988	−1.23845
$818$	3.35629	0.117350
$819$	2.71888	0.0950052
$820$	−61.8533	−2.16001
$821$	54.1219	1.88887	0.944434	−	0.328700i	$-0.106610\pi$
$821$	54.1219	1.88887	0.944434	+	0.328700i	$0.106610\pi$
$822$	62.6236	2.18425
$823$	−12.1724	−0.424304	−0.212152	−	0.977237i	$-0.568047\pi$
$823$	−12.1724	−0.424304	−0.212152	+	0.977237i	$0.568047\pi$
$824$	103.760	3.61465
$825$	2.36631	0.0823844
$826$	6.18601	0.215239
$827$	36.3084	1.26257	0.631284	−	0.775552i	$-0.282528\pi$
$827$	36.3084	1.26257	0.631284	+	0.775552i	$0.282528\pi$
$828$	26.2983	0.913928
$829$	41.1309	1.42854	0.714268	−	0.699872i	$-0.246760\pi$
$829$	41.1309	1.42854	0.714268	+	0.699872i	$0.246760\pi$
$830$	−26.0086	−0.902773
$831$	−9.73789	−0.337804
$832$	95.1903	3.30013
$833$	18.4177	0.638134
$834$	−12.4112	−0.429763
$835$	−10.9956	−0.380519
$836$	−34.3100	−1.18664
$837$	−42.8707	−1.48183
$838$	70.2960	2.42833
$839$	−21.1547	−0.730342	−0.365171	−	0.930941i	$-0.618989\pi$
$839$	−21.1547	−0.730342	−0.365171	+	0.930941i	$0.618989\pi$
$840$	22.0412	0.760492
$841$	−24.2892	−0.837558
$842$	−54.6511	−1.88340
$843$	8.04454	0.277069
$844$	117.685	4.05089
$845$	−4.13409	−0.142217
$846$	−3.39897	−0.116859
$847$	9.35814	0.321550
$848$	−152.451	−5.23519
$849$	−24.4668	−0.839699
$850$	−15.1893	−0.520989
$851$	14.0748	0.482478
$852$	39.5327	1.35437
$853$	48.6509	1.66578	0.832888	−	0.553442i	$-0.186686\pi$
$853$	48.6509	1.66578	0.832888	+	0.553442i	$0.186686\pi$
$854$	−25.7816	−0.882227
$855$	−11.5514	−0.395048
$856$	−56.0313	−1.91511
$857$	−21.9478	−0.749723	−0.374862	−	0.927081i	$-0.622310\pi$
$857$	−21.9478	−0.749723	−0.374862	+	0.927081i	$0.622310\pi$
$858$	11.3234	0.386574
$859$	−15.8928	−0.542257	−0.271128	−	0.962543i	$-0.587397\pi$
$859$	−15.8928	−0.542257	−0.271128	+	0.962543i	$0.587397\pi$
$860$	−47.6518	−1.62491
$861$	8.48021	0.289005
$862$	90.5154	3.08297
$863$	−25.0964	−0.854291	−0.427146	−	0.904183i	$-0.640481\pi$
$863$	−25.0964	−0.854291	−0.427146	+	0.904183i	$0.640481\pi$
$864$	121.588	4.13651
$865$	1.53200	0.0520896
$866$	−16.0643	−0.545888
$867$	−11.6653	−0.396174
$868$	−37.7995	−1.28300
$869$	−13.1740	−0.446897
$870$	15.1678	0.514235
$871$	12.7462	0.431888
$872$	−7.26844	−0.246140
$873$	1.03355	0.0349804
$874$	103.788	3.51068
$875$	11.1221	0.375995
$876$	−64.3294	−2.17349
$877$	−32.3817	−1.09345	−0.546726	−	0.837311i	$-0.684126\pi$
$877$	−32.3817	−1.09345	−0.546726	+	0.837311i	$0.684126\pi$
$878$	−31.4851	−1.06257
$879$	−43.4669	−1.46610
$880$	−23.0014	−0.775378
$881$	46.9662	1.58233	0.791165	−	0.611602i	$-0.209475\pi$
$881$	46.9662	1.58233	0.791165	+	0.611602i	$0.209475\pi$
$882$	−15.3019	−0.515243
$883$	58.5405	1.97005	0.985023	−	0.172426i	$-0.0551604\pi$
$883$	58.5405	1.97005	0.985023	+	0.172426i	$0.0551604\pi$
$884$	−53.1643	−1.78811
$885$	6.34436	0.213263
$886$	45.2660	1.52074
$887$	−22.1087	−0.742336	−0.371168	−	0.928566i	$-0.621043\pi$
$887$	−22.1087	−0.742336	−0.371168	+	0.928566i	$0.621043\pi$
$888$	36.0730	1.21053
$889$	7.61589	0.255429
$890$	10.6731	0.357762
$891$	4.78297	0.160236
$892$	35.8618	1.20074
$893$	−9.81171	−0.328336
$894$	−6.71847	−0.224699
$895$	−30.6513	−1.02456
$896$	33.4145	1.11630
$897$	−25.0541	−0.836533
$898$	107.941	3.60204
$899$	−16.4611	−0.549009
$900$	9.23055	0.307685
$901$	30.8332	1.02720
$902$	−15.3742	−0.511906
$903$	6.53315	0.217410
$904$	−41.8066	−1.39047
$905$	8.62319	0.286645
$906$	58.2055	1.93375
$907$	−2.79584	−0.0928344	−0.0464172	−	0.998922i	$-0.514780\pi$
$907$	−2.79584	−0.0928344	−0.0464172	+	0.998922i	$0.514780\pi$
$908$	61.8266	2.05179
$909$	−0.327391	−0.0108589
$910$	14.4444	0.478828
$911$	−22.5685	−0.747729	−0.373864	−	0.927483i	$-0.621967\pi$
$911$	−22.5685	−0.747729	−0.373864	+	0.927483i	$0.621967\pi$
$912$	153.116	5.07017
$913$	−4.72852	−0.156491
$914$	−79.6192	−2.63357
$915$	−26.4415	−0.874129
$916$	−77.1367	−2.54867
$917$	−3.57024	−0.117900
$918$	−46.0996	−1.52151
$919$	−44.5302	−1.46892	−0.734458	−	0.678654i	$-0.762564\pi$
$919$	−44.5302	−1.46892	−0.734458	+	0.678654i	$0.762564\pi$
$920$	88.4147	2.91495
$921$	−33.2464	−1.09551
$922$	91.8159	3.02380
$923$	16.3949	0.539645
$924$	6.33222	0.208315
$925$	4.94019	0.162432
$926$	53.1881	1.74787
$927$	10.0361	0.329628
$928$	46.6863	1.53255
$929$	3.11431	0.102177	0.0510886	−	0.998694i	$-0.483731\pi$
$929$	3.11431	0.102177	0.0510886	+	0.998694i	$0.483731\pi$
$930$	−53.0012	−1.73798
$931$	−44.1716	−1.44767
$932$	29.2184	0.957080
$933$	−1.26007	−0.0412530
$934$	17.1662	0.561695
$935$	4.65204	0.152138
$936$	27.9524	0.913653
$937$	−27.9585	−0.913363	−0.456682	−	0.889630i	$-0.650962\pi$
$937$	−27.9585	−0.913363	−0.456682	+	0.889630i	$0.650962\pi$
$938$	9.74501	0.318186
$939$	−12.2332	−0.399216
$940$	−13.2080	−0.430796
$941$	39.1771	1.27714	0.638568	−	0.769566i	$-0.279527\pi$
$941$	39.1771	1.27714	0.638568	+	0.769566i	$0.279527\pi$
$942$	−16.7233	−0.544876
$943$	34.0171	1.10775
$944$	36.6078	1.19148
$945$	9.16124	0.298015
$946$	−11.8443	−0.385092
$947$	−26.4597	−0.859826	−0.429913	−	0.902870i	$-0.641456\pi$
$947$	−26.4597	−0.859826	−0.429913	+	0.902870i	$0.641456\pi$
$948$	118.052	3.83415
$949$	−26.6785	−0.866022
$950$	36.4290	1.18191
$951$	23.6910	0.768233
$952$	−25.7222	−0.833663
$953$	−48.0162	−1.55540	−0.777699	−	0.628637i	$-0.783613\pi$
$953$	−48.0162	−1.55540	−0.777699	+	0.628637i	$0.783613\pi$
$954$	−25.6172	−0.829386
$955$	−24.5034	−0.792911
$956$	121.811	3.93963
$957$	2.75759	0.0891401
$958$	8.74762	0.282623
$959$	14.5235	0.468987
$960$	74.6400	2.40900
$961$	26.5207	0.855506
$962$	23.6400	0.762185
$963$	−5.41956	−0.174643
$964$	112.236	3.61487
$965$	15.7176	0.505969
$966$	−19.1550	−0.616301
$967$	−17.9829	−0.578290	−0.289145	−	0.957285i	$-0.593371\pi$
$967$	−17.9829	−0.578290	−0.289145	+	0.957285i	$0.593371\pi$
$968$	96.2098	3.09230
$969$	−30.9676	−0.994823
$970$	5.49089	0.176302
$971$	−10.2225	−0.328057	−0.164028	−	0.986456i	$-0.552449\pi$
$971$	−10.2225	−0.328057	−0.164028	+	0.986456i	$0.552449\pi$
$972$	49.5102	1.58804
$973$	−2.87835	−0.0922758
$974$	−109.661	−3.51376
$975$	−8.79388	−0.281629
$976$	−152.571	−4.88368
$977$	17.9027	0.572758	0.286379	−	0.958116i	$-0.407548\pi$
$977$	17.9027	0.572758	0.286379	+	0.958116i	$0.407548\pi$
$978$	−0.557678	−0.0178326
$979$	1.94043	0.0620163
$980$	−59.4613	−1.89942
$981$	−0.703031	−0.0224461
$982$	−4.24571	−0.135486
$983$	13.8815	0.442750	0.221375	−	0.975189i	$-0.428946\pi$
$983$	13.8815	0.442750	0.221375	+	0.975189i	$0.428946\pi$
$984$	87.1839	2.77932
$985$	6.39234	0.203677
$986$	−17.7009	−0.563712
$987$	1.81084	0.0576396
$988$	127.506	4.05649
$989$	26.2067	0.833326
$990$	−3.86505	−0.122839
$991$	56.1965	1.78514	0.892571	−	0.450907i	$-0.148899\pi$
$991$	56.1965	1.78514	0.892571	+	0.450907i	$0.148899\pi$
$992$	−163.137	−5.17962
$993$	−30.8837	−0.980066
$994$	12.5346	0.397574
$995$	−5.04755	−0.160018
$996$	42.3722	1.34262
$997$	50.0708	1.58576	0.792879	−	0.609379i	$-0.208581\pi$
$997$	50.0708	1.58576	0.792879	+	0.609379i	$0.208581\pi$
$998$	−38.3861	−1.21509
$999$	14.9935	0.474372

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.b.1.7	✓	205

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.b.1.7	✓	205	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)

\(f(q)\)	\(=\)	\(q-2.72893 q^{2} +1.44573 q^{3} +5.44706 q^{4} +1.77131 q^{5} -3.94530 q^{6} -0.914980 q^{7} -9.40679 q^{8} -0.909861 q^{9} +O(q^{10})\)	\(q-2.72893 q^{2} +1.44573 q^{3} +5.44706 q^{4} +1.77131 q^{5} -3.94530 q^{6} -0.914980 q^{7} -9.40679 q^{8} -0.909861 q^{9} -4.83377 q^{10} -0.878808 q^{11} +7.87499 q^{12} +3.26590 q^{13} +2.49692 q^{14} +2.56083 q^{15} +14.7764 q^{16} -2.98851 q^{17} +2.48295 q^{18} +7.16745 q^{19} +9.64841 q^{20} -1.32282 q^{21} +2.39821 q^{22} -5.30627 q^{23} -13.5997 q^{24} -1.86247 q^{25} -8.91240 q^{26} -5.65261 q^{27} -4.98395 q^{28} -2.17044 q^{29} -6.98833 q^{30} +7.58424 q^{31} -21.5101 q^{32} -1.27052 q^{33} +8.15545 q^{34} -1.62071 q^{35} -4.95607 q^{36} -2.65249 q^{37} -19.5595 q^{38} +4.72161 q^{39} -16.6623 q^{40} -6.41073 q^{41} +3.60987 q^{42} -4.93882 q^{43} -4.78692 q^{44} -1.61164 q^{45} +14.4804 q^{46} -1.36893 q^{47} +21.3626 q^{48} -6.16281 q^{49} +5.08256 q^{50} -4.32059 q^{51} +17.7895 q^{52} -10.3172 q^{53} +15.4256 q^{54} -1.55664 q^{55} +8.60703 q^{56} +10.3622 q^{57} +5.92298 q^{58} +2.47746 q^{59} +13.9490 q^{60} -10.3254 q^{61} -20.6969 q^{62} +0.832505 q^{63} +29.1468 q^{64} +5.78490 q^{65} +3.46716 q^{66} +3.90281 q^{67} -16.2786 q^{68} -7.67144 q^{69} +4.42281 q^{70} +5.02004 q^{71} +8.55887 q^{72} -8.16882 q^{73} +7.23845 q^{74} -2.69264 q^{75} +39.0415 q^{76} +0.804092 q^{77} -12.8849 q^{78} +14.9908 q^{79} +26.1735 q^{80} -5.44257 q^{81} +17.4944 q^{82} +5.38061 q^{83} -7.20546 q^{84} -5.29358 q^{85} +13.4777 q^{86} -3.13787 q^{87} +8.26677 q^{88} -2.20802 q^{89} +4.39806 q^{90} -2.98823 q^{91} -28.9036 q^{92} +10.9648 q^{93} +3.73570 q^{94} +12.6957 q^{95} -31.0978 q^{96} -1.13594 q^{97} +16.8179 q^{98} +0.799593 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * q^99

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