LMFDB - Embedded newform 2011.2.a.a.1.44

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2011,2,Mod(1,2011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2011, 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("2011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2011.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:	$16.0579158465$
Analytic rank:	$1$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.44
Character	$\chi$	$=$	2011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.172850 q^{2} +0.746844 q^{3} -1.97012 q^{4} -0.0730882 q^{5} +0.129092 q^{6} +4.33353 q^{7} -0.686237 q^{8} -2.44222 q^{9} +O(q^{10})$	\(q+0.172850 q^{2} +0.746844 q^{3} -1.97012 q^{4} -0.0730882 q^{5} +0.129092 q^{6} +4.33353 q^{7} -0.686237 q^{8} -2.44222 q^{9} -0.0126333 q^{10} +1.52114 q^{11} -1.47137 q^{12} -3.62971 q^{13} +0.749052 q^{14} -0.0545854 q^{15} +3.82163 q^{16} -5.01752 q^{17} -0.422139 q^{18} -5.32846 q^{19} +0.143993 q^{20} +3.23647 q^{21} +0.262930 q^{22} +0.598843 q^{23} -0.512512 q^{24} -4.99466 q^{25} -0.627396 q^{26} -4.06449 q^{27} -8.53759 q^{28} -5.55980 q^{29} -0.00943511 q^{30} +4.77027 q^{31} +2.03304 q^{32} +1.13605 q^{33} -0.867281 q^{34} -0.316730 q^{35} +4.81148 q^{36} +1.49202 q^{37} -0.921025 q^{38} -2.71082 q^{39} +0.0501558 q^{40} +6.47585 q^{41} +0.559425 q^{42} -3.84696 q^{43} -2.99683 q^{44} +0.178498 q^{45} +0.103510 q^{46} +10.0632 q^{47} +2.85416 q^{48} +11.7795 q^{49} -0.863328 q^{50} -3.74731 q^{51} +7.15097 q^{52} -6.90594 q^{53} -0.702548 q^{54} -0.111177 q^{55} -2.97383 q^{56} -3.97952 q^{57} -0.961013 q^{58} -5.30466 q^{59} +0.107540 q^{60} -9.00096 q^{61} +0.824543 q^{62} -10.5835 q^{63} -7.29185 q^{64} +0.265289 q^{65} +0.196367 q^{66} -11.7886 q^{67} +9.88514 q^{68} +0.447242 q^{69} -0.0547468 q^{70} -10.0500 q^{71} +1.67594 q^{72} +13.9968 q^{73} +0.257896 q^{74} -3.73023 q^{75} +10.4977 q^{76} +6.59191 q^{77} -0.468567 q^{78} -10.2123 q^{79} -0.279316 q^{80} +4.29114 q^{81} +1.11935 q^{82} -17.1459 q^{83} -6.37624 q^{84} +0.366722 q^{85} -0.664948 q^{86} -4.15230 q^{87} -1.04386 q^{88} +6.52052 q^{89} +0.0308534 q^{90} -15.7294 q^{91} -1.17979 q^{92} +3.56265 q^{93} +1.73943 q^{94} +0.389447 q^{95} +1.51837 q^{96} +8.77225 q^{97} +2.03609 q^{98} -3.71497 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9}+O(q^{10}) $ 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9	\( 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9} - 21 q^{10} - 34 q^{11} - 36 q^{12} - 34 q^{13} - 49 q^{14} - 12 q^{15} + 47 q^{16} - 59 q^{17} - 24 q^{18} - 31 q^{19} - 82 q^{20} - 71 q^{21} - 3 q^{22} - 28 q^{23} - 50 q^{24} + 68 q^{25} - 54 q^{26} - 43 q^{27} - 2 q^{28} - 151 q^{29} + q^{30} - 37 q^{31} - 59 q^{32} - 35 q^{33} - q^{34} - 58 q^{35} + 19 q^{36} - 29 q^{37} - 22 q^{38} - 40 q^{39} - 41 q^{40} - 142 q^{41} + 16 q^{42} - 23 q^{43} - 89 q^{44} - 119 q^{45} - 6 q^{46} - 36 q^{47} - 46 q^{48} + 45 q^{49} - 29 q^{50} - 53 q^{51} - 11 q^{52} - 69 q^{53} - 50 q^{54} - 13 q^{55} - 122 q^{56} - 14 q^{57} + 31 q^{58} - 92 q^{59} + 20 q^{60} - 115 q^{61} - 66 q^{62} - 25 q^{63} + 37 q^{64} - 57 q^{65} - 17 q^{66} - 108 q^{68} - 160 q^{69} + 40 q^{70} - 67 q^{71} - 35 q^{72} - 36 q^{73} - 55 q^{74} - 51 q^{75} - 56 q^{76} - 116 q^{77} + 22 q^{78} - 42 q^{79} - 114 q^{80} + 37 q^{81} + 18 q^{82} - 42 q^{83} - 77 q^{84} - 18 q^{85} - 33 q^{86} - 7 q^{87} - 2 q^{88} - 93 q^{89} - 34 q^{90} - 37 q^{91} - 55 q^{92} - 8 q^{93} - 35 q^{94} - 64 q^{95} - 83 q^{96} - 16 q^{97} - 57 q^{98} - 65 q^{99}+O(q^{100}) \) 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9 - 21 * q^10 - 34 * q^11 - 36 * q^12 - 34 * q^13 - 49 * q^14 - 12 * q^15 + 47 * q^16 - 59 * q^17 - 24 * q^18 - 31 * q^19 - 82 * q^20 - 71 * q^21 - 3 * q^22 - 28 * q^23 - 50 * q^24 + 68 * q^25 - 54 * q^26 - 43 * q^27 - 2 * q^28 - 151 * q^29 + q^30 - 37 * q^31 - 59 * q^32 - 35 * q^33 - q^34 - 58 * q^35 + 19 * q^36 - 29 * q^37 - 22 * q^38 - 40 * q^39 - 41 * q^40 - 142 * q^41 + 16 * q^42 - 23 * q^43 - 89 * q^44 - 119 * q^45 - 6 * q^46 - 36 * q^47 - 46 * q^48 + 45 * q^49 - 29 * q^50 - 53 * q^51 - 11 * q^52 - 69 * q^53 - 50 * q^54 - 13 * q^55 - 122 * q^56 - 14 * q^57 + 31 * q^58 - 92 * q^59 + 20 * q^60 - 115 * q^61 - 66 * q^62 - 25 * q^63 + 37 * q^64 - 57 * q^65 - 17 * q^66 - 108 * q^68 - 160 * q^69 + 40 * q^70 - 67 * q^71 - 35 * q^72 - 36 * q^73 - 55 * q^74 - 51 * q^75 - 56 * q^76 - 116 * q^77 + 22 * q^78 - 42 * q^79 - 114 * q^80 + 37 * q^81 + 18 * q^82 - 42 * q^83 - 77 * q^84 - 18 * q^85 - 33 * q^86 - 7 * q^87 - 2 * q^88 - 93 * q^89 - 34 * q^90 - 37 * q^91 - 55 * q^92 - 8 * q^93 - 35 * q^94 - 64 * q^95 - 83 * q^96 - 16 * q^97 - 57 * q^98 - 65 * 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 $

$2$	0.172850	0.122224	0.0611118	−	0.998131i	$-0.480535\pi$
$2$	0.172850	0.122224	0.0611118	+	0.998131i	$0.480535\pi$
$3$	0.746844	0.431190	0.215595	−	0.976483i	$-0.430831\pi$
$3$	0.746844	0.431190	0.215595	+	0.976483i	$0.430831\pi$
$4$	−1.97012	−0.985061
$5$	−0.0730882	−0.0326860	−0.0163430	−	0.999866i	$-0.505202\pi$
$5$	−0.0730882	−0.0326860	−0.0163430	+	0.999866i	$0.505202\pi$
$6$	0.129092	0.0527016
$7$	4.33353	1.63792	0.818960	−	0.573850i	$-0.194551\pi$
$7$	4.33353	1.63792	0.818960	+	0.573850i	$0.194551\pi$
$8$	−0.686237	−0.242621
$9$	−2.44222	−0.814075
$10$	−0.0126333	−0.00399500
$11$	1.52114	0.458641	0.229321	−	0.973351i	$-0.426350\pi$
$11$	1.52114	0.458641	0.229321	+	0.973351i	$0.426350\pi$
$12$	−1.47137	−0.424749
$13$	−3.62971	−1.00670	−0.503350	−	0.864083i	$-0.667899\pi$
$13$	−3.62971	−1.00670	−0.503350	+	0.864083i	$0.667899\pi$
$14$	0.749052	0.200193
$15$	−0.0545854	−0.0140939
$16$	3.82163	0.955407
$17$	−5.01752	−1.21693	−0.608464	−	0.793581i	$-0.708214\pi$
$17$	−5.01752	−1.21693	−0.608464	+	0.793581i	$0.708214\pi$
$18$	−0.422139	−0.0994992
$19$	−5.32846	−1.22243	−0.611216	−	0.791464i	$-0.709319\pi$
$19$	−5.32846	−1.22243	−0.611216	+	0.791464i	$0.709319\pi$
$20$	0.143993	0.0321977
$21$	3.23647	0.706256
$22$	0.262930	0.0560568
$23$	0.598843	0.124867	0.0624337	−	0.998049i	$-0.480114\pi$
$23$	0.598843	0.124867	0.0624337	+	0.998049i	$0.480114\pi$
$24$	−0.512512	−0.104616
$25$	−4.99466	−0.998932
$26$	−0.627396	−0.123042
$27$	−4.06449	−0.782212
$28$	−8.53759	−1.61345
$29$	−5.55980	−1.03243	−0.516215	−	0.856459i	$-0.672659\pi$
$29$	−5.55980	−1.03243	−0.516215	+	0.856459i	$0.672659\pi$
$30$	−0.00943511	−0.00172261
$31$	4.77027	0.856766	0.428383	−	0.903597i	$-0.359083\pi$
$31$	4.77027	0.856766	0.428383	+	0.903597i	$0.359083\pi$
$32$	2.03304	0.359395
$33$	1.13605	0.197762
$34$	−0.867281	−0.148737
$35$	−0.316730	−0.0535371
$36$	4.81148	0.801914
$37$	1.49202	0.245287	0.122643	−	0.992451i	$-0.460863\pi$
$37$	1.49202	0.245287	0.122643	+	0.992451i	$0.460863\pi$
$38$	−0.921025	−0.149410
$39$	−2.71082	−0.434079
$40$	0.0501558	0.00793033
$41$	6.47585	1.01136	0.505679	−	0.862722i	$-0.331242\pi$
$41$	6.47585	1.01136	0.505679	+	0.862722i	$0.331242\pi$
$42$	0.559425	0.0863211
$43$	−3.84696	−0.586656	−0.293328	−	0.956012i	$-0.594763\pi$
$43$	−3.84696	−0.586656	−0.293328	+	0.956012i	$0.594763\pi$
$44$	−2.99683	−0.451790
$45$	0.178498	0.0266089
$46$	0.103510	0.0152617
$47$	10.0632	1.46788	0.733938	−	0.679217i	$-0.237680\pi$
$47$	10.0632	1.46788	0.733938	+	0.679217i	$0.237680\pi$
$48$	2.85416	0.411962
$49$	11.7795	1.68278
$50$	−0.863328	−0.122093
$51$	−3.74731	−0.524728
$52$	7.15097	0.991661
$53$	−6.90594	−0.948603	−0.474302	−	0.880362i	$-0.657299\pi$
$53$	−6.90594	−0.948603	−0.474302	+	0.880362i	$0.657299\pi$
$54$	−0.702548	−0.0956047
$55$	−0.111177	−0.0149912
$56$	−2.97383	−0.397395
$57$	−3.97952	−0.527101
$58$	−0.961013	−0.126187
$59$	−5.30466	−0.690608	−0.345304	−	0.938491i	$-0.612224\pi$
$59$	−5.30466	−0.690608	−0.345304	+	0.938491i	$0.612224\pi$
$60$	0.107540	0.0138834
$61$	−9.00096	−1.15245	−0.576227	−	0.817290i	$-0.695476\pi$
$61$	−9.00096	−1.15245	−0.576227	+	0.817290i	$0.695476\pi$
$62$	0.824543	0.104717
$63$	−10.5835	−1.33339
$64$	−7.29185	−0.911481
$65$	0.265289	0.0329050
$66$	0.196367	0.0241711
$67$	−11.7886	−1.44021	−0.720105	−	0.693865i	$-0.755906\pi$
$67$	−11.7886	−1.44021	−0.720105	+	0.693865i	$0.755906\pi$
$68$	9.88514	1.19875
$69$	0.447242	0.0538416
$70$	−0.0547468	−0.00654350
$71$	−10.0500	−1.19272	−0.596359	−	0.802718i	$-0.703387\pi$
$71$	−10.0500	−1.19272	−0.596359	+	0.802718i	$0.703387\pi$
$72$	1.67594	0.197512
$73$	13.9968	1.63821	0.819103	−	0.573647i	$-0.194472\pi$
$73$	13.9968	1.63821	0.819103	+	0.573647i	$0.194472\pi$
$74$	0.257896	0.0299798
$75$	−3.73023	−0.430730
$76$	10.4977	1.20417
$77$	6.59191	0.751218
$78$	−0.468567	−0.0530547
$79$	−10.2123	−1.14897	−0.574486	−	0.818514i	$-0.694798\pi$
$79$	−10.2123	−1.14897	−0.574486	+	0.818514i	$0.694798\pi$
$80$	−0.279316	−0.0312285
$81$	4.29114	0.476793
$82$	1.11935	0.123612
$83$	−17.1459	−1.88201	−0.941003	−	0.338397i	$-0.890115\pi$
$83$	−17.1459	−1.88201	−0.941003	+	0.338397i	$0.890115\pi$
$84$	−6.37624	−0.695705
$85$	0.366722	0.0397765
$86$	−0.664948	−0.0717032
$87$	−4.15230	−0.445174
$88$	−1.04386	−0.111276
$89$	6.52052	0.691173	0.345587	−	0.938387i	$-0.387680\pi$
$89$	6.52052	0.691173	0.345587	+	0.938387i	$0.387680\pi$
$90$	0.0308534	0.00325223
$91$	−15.7294	−1.64889
$92$	−1.17979	−0.123002
$93$	3.56265	0.369429
$94$	1.73943	0.179409
$95$	0.389447	0.0399564
$96$	1.51837	0.154968
$97$	8.77225	0.890687	0.445343	−	0.895360i	$-0.353082\pi$
$97$	8.77225	0.890687	0.445343	+	0.895360i	$0.353082\pi$
$98$	2.03609	0.205676
$99$	−3.71497	−0.373368
$100$	9.84009	0.984009
$101$	−7.87193	−0.783286	−0.391643	−	0.920117i	$-0.628093\pi$
$101$	−7.87193	−0.783286	−0.391643	+	0.920117i	$0.628093\pi$
$102$	−0.647723	−0.0641341
$103$	−1.40339	−0.138280	−0.0691401	−	0.997607i	$-0.522026\pi$
$103$	−1.40339	−0.138280	−0.0691401	+	0.997607i	$0.522026\pi$
$104$	2.49084	0.244247
$105$	−0.236548	−0.0230847
$106$	−1.19369	−0.115942
$107$	4.62103	0.446732	0.223366	−	0.974735i	$-0.428295\pi$
$107$	4.62103	0.446732	0.223366	+	0.974735i	$0.428295\pi$
$108$	8.00755	0.770526
$109$	3.48471	0.333774	0.166887	−	0.985976i	$-0.446628\pi$
$109$	3.48471	0.333774	0.166887	+	0.985976i	$0.446628\pi$
$110$	−0.0192170	−0.00183227
$111$	1.11431	0.105765
$112$	16.5612	1.56488
$113$	−12.6111	−1.18635	−0.593175	−	0.805073i	$-0.702126\pi$
$113$	−12.6111	−1.18635	−0.593175	+	0.805073i	$0.702126\pi$
$114$	−0.687862	−0.0644242
$115$	−0.0437683	−0.00408142
$116$	10.9535	1.01701
$117$	8.86456	0.819529
$118$	−0.916912	−0.0844086
$119$	−21.7436	−1.99323
$120$	0.0374585	0.00341948
$121$	−8.68613	−0.789648
$122$	−1.55582	−0.140857
$123$	4.83644	0.436088
$124$	−9.39802	−0.843967
$125$	0.730491	0.0653371
$126$	−1.82935	−0.162972
$127$	0.505978	0.0448983	0.0224491	−	0.999748i	$-0.492854\pi$
$127$	0.505978	0.0448983	0.0224491	+	0.999748i	$0.492854\pi$
$128$	−5.32648	−0.470799
$129$	−2.87308	−0.252960
$130$	0.0458552	0.00402177
$131$	−17.2175	−1.50430	−0.752148	−	0.658994i	$-0.770982\pi$
$131$	−17.2175	−1.50430	−0.752148	+	0.658994i	$0.770982\pi$
$132$	−2.23817	−0.194807
$133$	−23.0910	−2.00225
$134$	−2.03767	−0.176028
$135$	0.297066	0.0255674
$136$	3.44321	0.295253
$137$	−1.79583	−0.153428	−0.0767140	−	0.997053i	$-0.524443\pi$
$137$	−1.79583	−0.153428	−0.0767140	+	0.997053i	$0.524443\pi$
$138$	0.0773059	0.00658072
$139$	−15.0967	−1.28048	−0.640241	−	0.768174i	$-0.721165\pi$
$139$	−15.0967	−1.28048	−0.640241	+	0.768174i	$0.721165\pi$
$140$	0.623997	0.0527373
$141$	7.51567	0.632934
$142$	−1.73715	−0.145778
$143$	−5.52129	−0.461714
$144$	−9.33328	−0.777773
$145$	0.406356	0.0337460
$146$	2.41936	0.200227
$147$	8.79744	0.725601
$148$	−2.93946	−0.241622
$149$	−14.4939	−1.18739	−0.593695	−	0.804690i	$-0.702332\pi$
$149$	−14.4939	−1.18739	−0.593695	+	0.804690i	$0.702332\pi$
$150$	−0.644771	−0.0526453
$151$	11.9393	0.971603	0.485802	−	0.874069i	$-0.338528\pi$
$151$	11.9393	0.971603	0.485802	+	0.874069i	$0.338528\pi$
$152$	3.65658	0.296588
$153$	12.2539	0.990671
$154$	1.13941	0.0918166
$155$	−0.348650	−0.0280043
$156$	5.34065	0.427595
$157$	3.98662	0.318167	0.159083	−	0.987265i	$-0.449146\pi$
$157$	3.98662	0.318167	0.159083	+	0.987265i	$0.449146\pi$
$158$	−1.76520	−0.140432
$159$	−5.15765	−0.409029
$160$	−0.148591	−0.0117472
$161$	2.59510	0.204523
$162$	0.741724	0.0582753
$163$	−9.04649	−0.708576	−0.354288	−	0.935136i	$-0.615277\pi$
$163$	−9.04649	−0.708576	−0.354288	+	0.935136i	$0.615277\pi$
$164$	−12.7582	−0.996249
$165$	−0.0830321	−0.00646404
$166$	−2.96367	−0.230026
$167$	16.5427	1.28011	0.640057	−	0.768328i	$-0.278911\pi$
$167$	16.5427	1.28011	0.640057	+	0.768328i	$0.278911\pi$
$168$	−2.22099	−0.171353
$169$	0.174766	0.0134436
$170$	0.0633879	0.00486163
$171$	13.0133	0.995151
$172$	7.57898	0.577892
$173$	2.31862	0.176281	0.0881406	−	0.996108i	$-0.471908\pi$
$173$	2.31862	0.176281	0.0881406	+	0.996108i	$0.471908\pi$
$174$	−0.717727	−0.0544107
$175$	−21.6445	−1.63617
$176$	5.81324	0.438189
$177$	−3.96175	−0.297783
$178$	1.12707	0.0844777
$179$	11.6033	0.867269	0.433634	−	0.901089i	$-0.357231\pi$
$179$	11.6033	0.867269	0.433634	+	0.901089i	$0.357231\pi$
$180$	−0.351662	−0.0262114
$181$	22.6828	1.68600	0.842999	−	0.537916i	$-0.180788\pi$
$181$	22.6828	1.68600	0.842999	+	0.537916i	$0.180788\pi$
$182$	−2.71884	−0.201534
$183$	−6.72231	−0.496927
$184$	−0.410948	−0.0302955
$185$	−0.109049	−0.00801744
$186$	0.615804	0.0451530
$187$	−7.63236	−0.558134
$188$	−19.8258	−1.44595
$189$	−17.6136	−1.28120
$190$	0.0673160	0.00488362
$191$	18.5959	1.34555	0.672775	−	0.739847i	$-0.265102\pi$
$191$	18.5959	1.34555	0.672775	+	0.739847i	$0.265102\pi$
$192$	−5.44587	−0.393022
$193$	6.36295	0.458015	0.229008	−	0.973425i	$-0.426452\pi$
$193$	6.36295	0.458015	0.229008	+	0.973425i	$0.426452\pi$
$194$	1.51629	0.108863
$195$	0.198129	0.0141883
$196$	−23.2071	−1.65765
$197$	−2.02371	−0.144183	−0.0720917	−	0.997398i	$-0.522967\pi$
$197$	−2.02371	−0.144183	−0.0720917	+	0.997398i	$0.522967\pi$
$198$	−0.642133	−0.0456344
$199$	14.2645	1.01118	0.505592	−	0.862773i	$-0.331274\pi$
$199$	14.2645	1.01118	0.505592	+	0.862773i	$0.331274\pi$
$200$	3.42752	0.242362
$201$	−8.80426	−0.621005
$202$	−1.36067	−0.0957361
$203$	−24.0936	−1.69104
$204$	7.38265	0.516889
$205$	−0.473308	−0.0330572
$206$	−0.242577	−0.0169011
$207$	−1.46251	−0.101651
$208$	−13.8714	−0.961808
$209$	−8.10533	−0.560658
$210$	−0.0408873	−0.00282149
$211$	14.8342	1.02123	0.510615	−	0.859810i	$-0.329418\pi$
$211$	14.8342	1.02123	0.510615	+	0.859810i	$0.329418\pi$
$212$	13.6055	0.934432
$213$	−7.50580	−0.514289
$214$	0.798747	0.0546012
$215$	0.281167	0.0191754
$216$	2.78920	0.189781
$217$	20.6721	1.40331
$218$	0.602332	0.0407951
$219$	10.4534	0.706378
$220$	0.219033	0.0147672
$221$	18.2121	1.22508
$222$	0.192608	0.0129270
$223$	24.8569	1.66454	0.832270	−	0.554370i	$-0.187041\pi$
$223$	24.8569	1.66454	0.832270	+	0.554370i	$0.187041\pi$
$224$	8.81026	0.588660
$225$	12.1981	0.813205
$226$	−2.17983	−0.145000
$227$	−22.4377	−1.48924	−0.744622	−	0.667486i	$-0.767370\pi$
$227$	−22.4377	−1.48924	−0.744622	+	0.667486i	$0.767370\pi$
$228$	7.84015	0.519227
$229$	15.6362	1.03327	0.516635	−	0.856206i	$-0.327184\pi$
$229$	15.6362	1.03327	0.516635	+	0.856206i	$0.327184\pi$
$230$	−0.00756537	−0.000498846 0
$231$	4.92313	0.323918
$232$	3.81534	0.250489
$233$	−1.09032	−0.0714289	−0.0357145	−	0.999362i	$-0.511371\pi$
$233$	−1.09032	−0.0714289	−0.0357145	+	0.999362i	$0.511371\pi$
$234$	1.53224	0.100166
$235$	−0.735504	−0.0479790
$236$	10.4508	0.680291
$237$	−7.62698	−0.495426
$238$	−3.75839	−0.243620
$239$	14.1625	0.916097	0.458048	−	0.888927i	$-0.348549\pi$
$239$	14.1625	0.916097	0.458048	+	0.888927i	$0.348549\pi$
$240$	−0.208605	−0.0134654
$241$	−14.6769	−0.945421	−0.472711	−	0.881218i	$-0.656724\pi$
$241$	−14.6769	−0.945421	−0.472711	+	0.881218i	$0.656724\pi$
$242$	−1.50140	−0.0965137
$243$	15.3983	0.987800
$244$	17.7330	1.13524
$245$	−0.860942	−0.0550035
$246$	0.835981	0.0533002
$247$	19.3407	1.23062
$248$	−3.27354	−0.207870
$249$	−12.8053	−0.811503
$250$	0.126266	0.00798574
$251$	−13.8267	−0.872735	−0.436368	−	0.899768i	$-0.643735\pi$
$251$	−13.8267	−0.872735	−0.436368	+	0.899768i	$0.643735\pi$
$252$	20.8507	1.31347
$253$	0.910925	0.0572693
$254$	0.0874584	0.00548763
$255$	0.273884	0.0171513
$256$	13.6630	0.853938
$257$	−11.2838	−0.703867	−0.351934	−	0.936025i	$-0.614476\pi$
$257$	−11.2838	−0.703867	−0.351934	+	0.936025i	$0.614476\pi$
$258$	−0.496612	−0.0309177
$259$	6.46571	0.401760
$260$	−0.522651	−0.0324134
$261$	13.5783	0.840475
$262$	−2.97604	−0.183861
$263$	5.05124	0.311473	0.155736	−	0.987799i	$-0.450225\pi$
$263$	5.05124	0.311473	0.155736	+	0.987799i	$0.450225\pi$
$264$	−0.779602	−0.0479812
$265$	0.504742	0.0310061
$266$	−3.99129	−0.244722
$267$	4.86981	0.298027
$268$	23.2250	1.41870
$269$	15.7930	0.962916	0.481458	−	0.876469i	$-0.340107\pi$
$269$	15.7930	0.962916	0.481458	+	0.876469i	$0.340107\pi$
$270$	0.0513480	0.00312494
$271$	−4.66728	−0.283517	−0.141759	−	0.989901i	$-0.545276\pi$
$271$	−4.66728	−0.283517	−0.141759	+	0.989901i	$0.545276\pi$
$272$	−19.1751	−1.16266
$273$	−11.7474	−0.710987
$274$	−0.310410	−0.0187525
$275$	−7.59758	−0.458151
$276$	−0.881122	−0.0530373
$277$	−4.42653	−0.265964	−0.132982	−	0.991118i	$-0.542455\pi$
$277$	−4.42653	−0.265964	−0.132982	+	0.991118i	$0.542455\pi$
$278$	−2.60946	−0.156505
$279$	−11.6501	−0.697472
$280$	0.217352	0.0129892
$281$	−17.0003	−1.01415	−0.507077	−	0.861901i	$-0.669274\pi$
$281$	−17.0003	−1.01415	−0.507077	+	0.861901i	$0.669274\pi$
$282$	1.29909	0.0773594
$283$	−22.7646	−1.35322	−0.676608	−	0.736344i	$-0.736551\pi$
$283$	−22.7646	−1.35322	−0.676608	+	0.736344i	$0.736551\pi$
$284$	19.7998	1.17490
$285$	0.290856	0.0172288
$286$	−0.954357	−0.0564323
$287$	28.0633	1.65652
$288$	−4.96515	−0.292574
$289$	8.17555	0.480915
$290$	0.0702387	0.00412456
$291$	6.55150	0.384055
$292$	−27.5755	−1.61373
$293$	18.0358	1.05366	0.526831	−	0.849970i	$-0.323380\pi$
$293$	18.0358	1.05366	0.526831	+	0.849970i	$0.323380\pi$
$294$	1.52064	0.0886855
$295$	0.387708	0.0225732
$296$	−1.02388	−0.0595118
$297$	−6.18266	−0.358755
$298$	−2.50528	−0.145127
$299$	−2.17362	−0.125704
$300$	7.34901	0.424295
$301$	−16.6709	−0.960896
$302$	2.06370	0.118753
$303$	−5.87910	−0.337745
$304$	−20.3634	−1.16792
$305$	0.657863	0.0376691
$306$	2.11809	0.121083
$307$	−20.0950	−1.14688	−0.573440	−	0.819247i	$-0.694391\pi$
$307$	−20.0950	−1.14688	−0.573440	+	0.819247i	$0.694391\pi$
$308$	−12.9869	−0.739996
$309$	−1.04811	−0.0596251
$310$	−0.0602643	−0.00342278
$311$	21.4563	1.21668	0.608338	−	0.793678i	$-0.291836\pi$
$311$	21.4563	1.21668	0.608338	+	0.793678i	$0.291836\pi$
$312$	1.86027	0.105317
$313$	−4.56605	−0.258088	−0.129044	−	0.991639i	$-0.541191\pi$
$313$	−4.56605	−0.258088	−0.129044	+	0.991639i	$0.541191\pi$
$314$	0.689088	0.0388875
$315$	0.773525	0.0435832
$316$	20.1195	1.13181
$317$	−8.45942	−0.475129	−0.237564	−	0.971372i	$-0.576349\pi$
$317$	−8.45942	−0.475129	−0.237564	+	0.971372i	$0.576349\pi$
$318$	−0.891502	−0.0499929
$319$	−8.45724	−0.473515
$320$	0.532948	0.0297927
$321$	3.45119	0.192627
$322$	0.448565	0.0249975
$323$	26.7357	1.48761
$324$	−8.45406	−0.469670
$325$	18.1291	1.00562
$326$	−1.56369	−0.0866047
$327$	2.60253	0.143920
$328$	−4.44396	−0.245377
$329$	43.6094	2.40426
$330$	−0.0143521	−0.000790059 0
$331$	13.0092	0.715048	0.357524	−	0.933904i	$-0.383621\pi$
$331$	13.0092	0.715048	0.357524	+	0.933904i	$0.383621\pi$
$332$	33.7795	1.85389
$333$	−3.64385	−0.199682
$334$	2.85941	0.156460
$335$	0.861609	0.0470747
$336$	12.3686	0.674762
$337$	6.03048	0.328501	0.164250	−	0.986419i	$-0.447479\pi$
$337$	6.03048	0.328501	0.164250	+	0.986419i	$0.447479\pi$
$338$	0.0302084	0.00164312
$339$	−9.41850	−0.511543
$340$	−0.722487	−0.0391823
$341$	7.25625	0.392948
$342$	2.24935	0.121631
$343$	20.7121	1.11835
$344$	2.63993	0.142335
$345$	−0.0326881	−0.00175987
$346$	0.400774	0.0215457
$347$	−29.1723	−1.56605	−0.783026	−	0.621989i	$-0.786325\pi$
$347$	−29.1723	−1.56605	−0.783026	+	0.621989i	$0.786325\pi$
$348$	8.18055	0.438523
$349$	23.0241	1.23245	0.616226	−	0.787570i	$-0.288661\pi$
$349$	23.0241	1.23245	0.616226	+	0.787570i	$0.288661\pi$
$350$	−3.74126	−0.199979
$351$	14.7529	0.787452
$352$	3.09255	0.164833
$353$	17.9319	0.954421	0.477211	−	0.878789i	$-0.341648\pi$
$353$	17.9319	0.954421	0.477211	+	0.878789i	$0.341648\pi$
$354$	−0.684790	−0.0363962
$355$	0.734538	0.0389852
$356$	−12.8462	−0.680848
$357$	−16.2391	−0.859463
$358$	2.00563	0.106001
$359$	−22.2760	−1.17568	−0.587842	−	0.808976i	$-0.700022\pi$
$359$	−22.2760	−1.17568	−0.587842	+	0.808976i	$0.700022\pi$
$360$	−0.122492	−0.00645588
$361$	9.39245	0.494339
$362$	3.92072	0.206069
$363$	−6.48718	−0.340489
$364$	30.9889	1.62426
$365$	−1.02300	−0.0535464
$366$	−1.16195	−0.0607362
$367$	−30.5652	−1.59549	−0.797746	−	0.602994i	$-0.793974\pi$
$367$	−30.5652	−1.59549	−0.797746	+	0.602994i	$0.793974\pi$
$368$	2.28856	0.119299
$369$	−15.8155	−0.823321
$370$	−0.0188491	−0.000979920 0
$371$	−29.9271	−1.55374
$372$	−7.01885	−0.363910
$373$	36.0935	1.86885	0.934424	−	0.356161i	$-0.115915\pi$
$373$	36.0935	1.86885	0.934424	+	0.356161i	$0.115915\pi$
$374$	−1.31926	−0.0682171
$375$	0.545563	0.0281727
$376$	−6.90577	−0.356138
$377$	20.1804	1.03935
$378$	−3.04452	−0.156593
$379$	36.6269	1.88140	0.940699	−	0.339243i	$-0.110171\pi$
$379$	36.6269	1.88140	0.940699	+	0.339243i	$0.110171\pi$
$380$	−0.767259	−0.0393595
$381$	0.377886	0.0193597
$382$	3.21430	0.164458
$383$	5.55666	0.283932	0.141966	−	0.989872i	$-0.454658\pi$
$383$	5.55666	0.283932	0.141966	+	0.989872i	$0.454658\pi$
$384$	−3.97805	−0.203004
$385$	−0.481791	−0.0245543
$386$	1.09984	0.0559803
$387$	9.39514	0.477582
$388$	−17.2824	−0.877381
$389$	0.541877	0.0274743	0.0137371	−	0.999906i	$-0.495627\pi$
$389$	0.541877	0.0274743	0.0137371	+	0.999906i	$0.495627\pi$
$390$	0.0342467	0.00173415
$391$	−3.00471	−0.151955
$392$	−8.08352	−0.408280
$393$	−12.8587	−0.648638
$394$	−0.349799	−0.0176226
$395$	0.746397	0.0375553
$396$	7.31894	0.367791
$397$	21.2725	1.06763	0.533817	−	0.845600i	$-0.320757\pi$
$397$	21.2725	1.06763	0.533817	+	0.845600i	$0.320757\pi$
$398$	2.46563	0.123591
$399$	−17.2454	−0.863349
$400$	−19.0877	−0.954387
$401$	−28.0545	−1.40098	−0.700489	−	0.713664i	$-0.747035\pi$
$401$	−28.0545	−1.40098	−0.700489	+	0.713664i	$0.747035\pi$
$402$	−1.52182	−0.0759014
$403$	−17.3147	−0.862506
$404$	15.5087	0.771585
$405$	−0.313631	−0.0155845
$406$	−4.16458	−0.206685
$407$	2.26957	0.112499
$408$	2.57154	0.127310
$409$	−30.7425	−1.52012	−0.760059	−	0.649854i	$-0.774830\pi$
$409$	−30.7425	−1.52012	−0.760059	+	0.649854i	$0.774830\pi$
$410$	−0.0818114	−0.00404038
$411$	−1.34120	−0.0661567
$412$	2.76485	0.136214
$413$	−22.9879	−1.13116
$414$	−0.252795	−0.0124242
$415$	1.25316	0.0615153
$416$	−7.37935	−0.361802
$417$	−11.2748	−0.552131
$418$	−1.40101	−0.0685256
$419$	28.4351	1.38914	0.694572	−	0.719423i	$-0.255594\pi$
$419$	28.4351	1.38914	0.694572	+	0.719423i	$0.255594\pi$
$420$	0.466028	0.0227398
$421$	17.0114	0.829085	0.414543	−	0.910030i	$-0.363942\pi$
$421$	17.0114	0.829085	0.414543	+	0.910030i	$0.363942\pi$
$422$	2.56410	0.124818
$423$	−24.5767	−1.19496
$424$	4.73911	0.230151
$425$	25.0608	1.21563
$426$	−1.29738	−0.0628582
$427$	−39.0059	−1.88763
$428$	−9.10400	−0.440058
$429$	−4.12354	−0.199087
$430$	0.0485998	0.00234369
$431$	22.2579	1.07212	0.536062	−	0.844178i	$-0.319911\pi$
$431$	22.2579	1.07212	0.536062	+	0.844178i	$0.319911\pi$
$432$	−15.5330	−0.747331
$433$	0.0116545	0.000560078 0	0.000280039	−	1.00000i	$-0.499911\pi$
$433$	0.0116545	0.000560078 0	0.000280039		1.00000i	$0.499911\pi$
$434$	3.57318	0.171518
$435$	0.303484	0.0145509
$436$	−6.86530	−0.328788
$437$	−3.19091	−0.152642
$438$	1.80688	0.0863361
$439$	−12.6640	−0.604420	−0.302210	−	0.953241i	$-0.597724\pi$
$439$	−12.6640	−0.604420	−0.302210	+	0.953241i	$0.597724\pi$
$440$	0.0762940	0.00363717
$441$	−28.7682	−1.36991
$442$	3.14797	0.149734
$443$	28.2023	1.33993	0.669966	−	0.742392i	$-0.266309\pi$
$443$	28.2023	1.33993	0.669966	+	0.742392i	$0.266309\pi$
$444$	−2.19532	−0.104185
$445$	−0.476573	−0.0225917
$446$	4.29652	0.203446
$447$	−10.8247	−0.511991
$448$	−31.5994	−1.49293
$449$	−19.2060	−0.906386	−0.453193	−	0.891412i	$-0.649715\pi$
$449$	−19.2060	−0.906386	−0.453193	+	0.891412i	$0.649715\pi$
$450$	2.10844	0.0993929
$451$	9.85068	0.463850
$452$	24.8454	1.16863
$453$	8.91676	0.418946
$454$	−3.87837	−0.182021
$455$	1.14964	0.0538958
$456$	2.73090	0.127886
$457$	6.70408	0.313604	0.156802	−	0.987630i	$-0.449882\pi$
$457$	6.70408	0.313604	0.156802	+	0.987630i	$0.449882\pi$
$458$	2.70272	0.126290
$459$	20.3937	0.951896
$460$	0.0862290	0.00402045
$461$	−32.5194	−1.51458	−0.757290	−	0.653079i	$-0.773477\pi$
$461$	−32.5194	−1.51458	−0.757290	+	0.653079i	$0.773477\pi$
$462$	0.850964	0.0395904
$463$	−32.7335	−1.52125	−0.760627	−	0.649190i	$-0.775108\pi$
$463$	−32.7335	−1.52125	−0.760627	+	0.649190i	$0.775108\pi$
$464$	−21.2475	−0.986390
$465$	−0.260387	−0.0120752
$466$	−0.188461	−0.00873030
$467$	−11.7054	−0.541660	−0.270830	−	0.962627i	$-0.587298\pi$
$467$	−11.7054	−0.541660	−0.270830	+	0.962627i	$0.587298\pi$
$468$	−17.4643	−0.807286
$469$	−51.0864	−2.35895
$470$	−0.127132	−0.00586417
$471$	2.97738	0.137190
$472$	3.64025	0.167556
$473$	−5.85177	−0.269065
$474$	−1.31833	−0.0605527
$475$	26.6138	1.22113
$476$	42.8376	1.96346
$477$	16.8658	0.772234
$478$	2.44799	0.111969
$479$	−33.2287	−1.51826	−0.759129	−	0.650940i	$-0.774375\pi$
$479$	−33.2287	−1.51826	−0.759129	+	0.650940i	$0.774375\pi$
$480$	−0.110975	−0.00506527
$481$	−5.41559	−0.246930
$482$	−2.53690	−0.115553
$483$	1.93814	0.0881883
$484$	17.1127	0.777852
$485$	−0.641147	−0.0291130
$486$	2.66160	0.120732
$487$	17.8088	0.806994	0.403497	−	0.914981i	$-0.367795\pi$
$487$	17.8088	0.806994	0.403497	+	0.914981i	$0.367795\pi$
$488$	6.17679	0.279610
$489$	−6.75631	−0.305531
$490$	−0.148814	−0.00672273
$491$	−3.78535	−0.170830	−0.0854152	−	0.996345i	$-0.527222\pi$
$491$	−3.78535	−0.170830	−0.0854152	+	0.996345i	$0.527222\pi$
$492$	−9.52839	−0.429573
$493$	27.8964	1.25639
$494$	3.34305	0.150411
$495$	0.271520	0.0122039
$496$	18.2302	0.818560
$497$	−43.5521	−1.95358
$498$	−2.21340	−0.0991848
$499$	12.4458	0.557151	0.278575	−	0.960414i	$-0.410138\pi$
$499$	12.4458	0.557151	0.278575	+	0.960414i	$0.410138\pi$
$500$	−1.43916	−0.0643611
$501$	12.3548	0.551972
$502$	−2.38995	−0.106669
$503$	−35.6224	−1.58833	−0.794163	−	0.607705i	$-0.792090\pi$
$503$	−35.6224	−1.58833	−0.794163	+	0.607705i	$0.792090\pi$
$504$	7.26276	0.323509
$505$	0.575345	0.0256025
$506$	0.157454	0.00699967
$507$	0.130523	0.00579674
$508$	−0.996838	−0.0442276
$509$	−9.20299	−0.407915	−0.203958	−	0.978980i	$-0.565381\pi$
$509$	−9.20299	−0.407915	−0.203958	+	0.978980i	$0.565381\pi$
$510$	0.0473409	0.00209629
$511$	60.6557	2.68325
$512$	13.0146	0.575171
$513$	21.6575	0.956200
$514$	−1.95042	−0.0860292
$515$	0.102571	0.00451983
$516$	5.66032	0.249181
$517$	15.3076	0.673228
$518$	1.11760	0.0491046
$519$	1.73164	0.0760108
$520$	−0.182051	−0.00798345
$521$	4.82281	0.211291	0.105646	−	0.994404i	$-0.466309\pi$
$521$	4.82281	0.211291	0.105646	+	0.994404i	$0.466309\pi$
$522$	2.34701	0.102726
$523$	−25.4269	−1.11184	−0.555920	−	0.831236i	$-0.687634\pi$
$523$	−25.4269	−1.11184	−0.555920	+	0.831236i	$0.687634\pi$
$524$	33.9205	1.48182
$525$	−16.1651	−0.705501
$526$	0.873109	0.0380694
$527$	−23.9349	−1.04262
$528$	4.34158	0.188943
$529$	−22.6414	−0.984408
$530$	0.0872448	0.00378967
$531$	12.9552	0.562206
$532$	45.4922	1.97234
$533$	−23.5054	−1.01813
$534$	0.841747	0.0364260
$535$	−0.337743	−0.0146019
$536$	8.08979	0.349426
$537$	8.66582	0.373958
$538$	2.72982	0.117691
$539$	17.9183	0.771795
$540$	−0.585257	−0.0251854
$541$	38.8465	1.67014	0.835070	−	0.550144i	$-0.185427\pi$
$541$	38.8465	1.67014	0.835070	+	0.550144i	$0.185427\pi$
$542$	−0.806741	−0.0346525
$543$	16.9405	0.726986
$544$	−10.2008	−0.437358
$545$	−0.254691	−0.0109098
$546$	−2.03055	−0.0868994
$547$	−4.80891	−0.205614	−0.102807	−	0.994701i	$-0.532782\pi$
$547$	−4.80891	−0.205614	−0.102807	+	0.994701i	$0.532782\pi$
$548$	3.53800	0.151136
$549$	21.9824	0.938184
$550$	−1.31324	−0.0559969
$551$	29.6252	1.26207
$552$	−0.306914	−0.0130631
$553$	−44.2553	−1.88193
$554$	−0.765126	−0.0325071
$555$	−0.0814425	−0.00345704
$556$	29.7423	1.26135
$557$	−9.04355	−0.383187	−0.191594	−	0.981474i	$-0.561366\pi$
$557$	−9.04355	−0.383187	−0.191594	+	0.981474i	$0.561366\pi$
$558$	−2.01372	−0.0852475
$559$	13.9633	0.590586
$560$	−1.21042	−0.0511497
$561$	−5.70018	−0.240662
$562$	−2.93851	−0.123954
$563$	23.8447	1.00494	0.502468	−	0.864596i	$-0.332425\pi$
$563$	23.8447	1.00494	0.502468	+	0.864596i	$0.332425\pi$
$564$	−14.8068	−0.623478
$565$	0.921720	0.0387771
$566$	−3.93487	−0.165395
$567$	18.5958	0.780949
$568$	6.89670	0.289379
$569$	34.6646	1.45321	0.726607	−	0.687053i	$-0.241096\pi$
$569$	34.6646	1.45321	0.726607	+	0.687053i	$0.241096\pi$
$570$	0.0502746	0.00210577
$571$	7.83681	0.327960	0.163980	−	0.986464i	$-0.447567\pi$
$571$	7.83681	0.327960	0.163980	+	0.986464i	$0.447567\pi$
$572$	10.8776	0.454816
$573$	13.8882	0.580188
$574$	4.85075	0.202466
$575$	−2.99102	−0.124734
$576$	17.8083	0.742014
$577$	−19.9798	−0.831768	−0.415884	−	0.909418i	$-0.636528\pi$
$577$	−19.9798	−0.831768	−0.415884	+	0.909418i	$0.636528\pi$
$578$	1.41315	0.0587791
$579$	4.75213	0.197492
$580$	−0.800570	−0.0332419
$581$	−74.3023	−3.08258
$582$	1.13243	0.0469406
$583$	−10.5049	−0.435069
$584$	−9.60514	−0.397464
$585$	−0.647894	−0.0267871
$586$	3.11749	0.128782
$587$	−21.9508	−0.906005	−0.453003	−	0.891509i	$-0.649647\pi$
$587$	−21.9508	−0.906005	−0.453003	+	0.891509i	$0.649647\pi$
$588$	−17.3320	−0.714761
$589$	−25.4182	−1.04734
$590$	0.0670154	0.00275898
$591$	−1.51140	−0.0621705
$592$	5.70195	0.234349
$593$	31.0606	1.27551	0.637753	−	0.770241i	$-0.279864\pi$
$593$	31.0606	1.27551	0.637753	+	0.770241i	$0.279864\pi$
$594$	−1.06868	−0.0438483
$595$	1.58920	0.0651508
$596$	28.5549	1.16965
$597$	10.6534	0.436013
$598$	−0.375712	−0.0153640
$599$	31.8036	1.29946	0.649729	−	0.760166i	$-0.274882\pi$
$599$	31.8036	1.29946	0.649729	+	0.760166i	$0.274882\pi$
$600$	2.55982	0.104504
$601$	−13.9429	−0.568744	−0.284372	−	0.958714i	$-0.591785\pi$
$601$	−13.9429	−0.568744	−0.284372	+	0.958714i	$0.591785\pi$
$602$	−2.88157	−0.117444
$603$	28.7905	1.17244
$604$	−23.5218	−0.957089
$605$	0.634853	0.0258105
$606$	−1.01620	−0.0412805
$607$	−35.5514	−1.44299	−0.721493	−	0.692421i	$-0.756544\pi$
$607$	−35.5514	−1.44299	−0.721493	+	0.692421i	$0.756544\pi$
$608$	−10.8330	−0.439336
$609$	−17.9941	−0.729159
$610$	0.113712	0.00460406
$611$	−36.5266	−1.47771
$612$	−24.1417	−0.975872
$613$	25.5695	1.03274	0.516370	−	0.856365i	$-0.327283\pi$
$613$	25.5695	1.03274	0.516370	+	0.856365i	$0.327283\pi$
$614$	−3.47342	−0.140176
$615$	−0.353487	−0.0142540
$616$	−4.52361	−0.182262
$617$	−11.4081	−0.459271	−0.229636	−	0.973277i	$-0.573753\pi$
$617$	−11.4081	−0.459271	−0.229636	+	0.973277i	$0.573753\pi$
$618$	−0.181167	−0.00728759
$619$	42.8742	1.72326	0.861631	−	0.507536i	$-0.169444\pi$
$619$	42.8742	1.72326	0.861631	+	0.507536i	$0.169444\pi$
$620$	0.686884	0.0275859
$621$	−2.43399	−0.0976727
$622$	3.70873	0.148707
$623$	28.2569	1.13209
$624$	−10.3598	−0.414722
$625$	24.9199	0.996796
$626$	−0.789243	−0.0315445
$627$	−6.05342	−0.241750
$628$	−7.85413	−0.313414
$629$	−7.48625	−0.298496
$630$	0.133704	0.00532690
$631$	18.4844	0.735854	0.367927	−	0.929855i	$-0.380068\pi$
$631$	18.4844	0.735854	0.367927	+	0.929855i	$0.380068\pi$
$632$	7.00805	0.278765
$633$	11.0788	0.440344
$634$	−1.46221	−0.0580719
$635$	−0.0369810	−0.00146755
$636$	10.1612	0.402918
$637$	−42.7561	−1.69406
$638$	−1.46184	−0.0578747
$639$	24.5444	0.970962
$640$	0.389303	0.0153886
$641$	6.88762	0.272045	0.136022	−	0.990706i	$-0.456568\pi$
$641$	6.88762	0.272045	0.136022	+	0.990706i	$0.456568\pi$
$642$	0.596539	0.0235435
$643$	17.5701	0.692896	0.346448	−	0.938069i	$-0.387388\pi$
$643$	17.5701	0.692896	0.346448	+	0.938069i	$0.387388\pi$
$644$	−5.11268	−0.201468
$645$	0.209988	0.00826827
$646$	4.62127	0.181821
$647$	11.8480	0.465794	0.232897	−	0.972501i	$-0.425179\pi$
$647$	11.8480	0.465794	0.232897	+	0.972501i	$0.425179\pi$
$648$	−2.94474	−0.115680
$649$	−8.06913	−0.316741
$650$	3.13363	0.122911
$651$	15.4388	0.605096
$652$	17.8227	0.697991
$653$	−6.66144	−0.260682	−0.130341	−	0.991469i	$-0.541607\pi$
$653$	−6.66144	−0.260682	−0.130341	+	0.991469i	$0.541607\pi$
$654$	0.449848	0.0175905
$655$	1.25839	0.0491695
$656$	24.7483	0.966258
$657$	−34.1834	−1.33362
$658$	7.53790	0.293858
$659$	−16.3964	−0.638714	−0.319357	−	0.947634i	$-0.603467\pi$
$659$	−16.3964	−0.638714	−0.319357	+	0.947634i	$0.603467\pi$
$660$	0.163583	0.00636748
$661$	−12.0630	−0.469196	−0.234598	−	0.972092i	$-0.575377\pi$
$661$	−12.0630	−0.469196	−0.234598	+	0.972092i	$0.575377\pi$
$662$	2.24864	0.0873957
$663$	13.6016	0.528243
$664$	11.7661	0.456615
$665$	1.68768	0.0654455
$666$	−0.629840	−0.0244058
$667$	−3.32945	−0.128917
$668$	−32.5912	−1.26099
$669$	18.5642	0.717734
$670$	0.148929	0.00575364
$671$	−13.6917	−0.528563
$672$	6.57988	0.253825
$673$	−6.59565	−0.254244	−0.127122	−	0.991887i	$-0.540574\pi$
$673$	−6.59565	−0.254244	−0.127122	+	0.991887i	$0.540574\pi$
$674$	1.04237	0.0401506
$675$	20.3007	0.781376
$676$	−0.344311	−0.0132427
$677$	11.1957	0.430284	0.215142	−	0.976583i	$-0.430978\pi$
$677$	11.1957	0.430284	0.215142	+	0.976583i	$0.430978\pi$
$678$	−1.62799	−0.0625226
$679$	38.0148	1.45887
$680$	−0.251658	−0.00965064
$681$	−16.7575	−0.642148
$682$	1.25425	0.0480275
$683$	−31.1565	−1.19217	−0.596085	−	0.802922i	$-0.703278\pi$
$683$	−31.1565	−1.19217	−0.596085	+	0.802922i	$0.703278\pi$
$684$	−25.6378	−0.980285
$685$	0.131254	0.00501495
$686$	3.58009	0.136689
$687$	11.6778	0.445536
$688$	−14.7017	−0.560495
$689$	25.0665	0.954958
$690$	−0.00565015	−0.000215097 0
$691$	33.0382	1.25683	0.628417	−	0.777877i	$-0.283703\pi$
$691$	33.0382	1.25683	0.628417	+	0.777877i	$0.283703\pi$
$692$	−4.56796	−0.173648
$693$	−16.0989	−0.611548
$694$	−5.04244	−0.191408
$695$	1.10339	0.0418538
$696$	2.84946	0.108009
$697$	−32.4927	−1.23075
$698$	3.97972	0.150635
$699$	−0.814295	−0.0307995
$700$	42.6423	1.61173
$701$	17.3384	0.654862	0.327431	−	0.944875i	$-0.393817\pi$
$701$	17.3384	0.654862	0.327431	+	0.944875i	$0.393817\pi$
$702$	2.55004	0.0962452
$703$	−7.95016	−0.299846
$704$	−11.0919	−0.418043
$705$	−0.549306	−0.0206881
$706$	3.09954	0.116653
$707$	−34.1133	−1.28296
$708$	7.80513	0.293335
$709$	−9.58301	−0.359897	−0.179949	−	0.983676i	$-0.557593\pi$
$709$	−9.58301	−0.359897	−0.179949	+	0.983676i	$0.557593\pi$
$710$	0.126965	0.00476492
$711$	24.9407	0.935349
$712$	−4.47462	−0.167693
$713$	2.85664	0.106982
$714$	−2.80693	−0.105047
$715$	0.403541	0.0150916
$716$	−22.8599	−0.854313
$717$	10.5772	0.395012
$718$	−3.85042	−0.143696
$719$	−38.6714	−1.44220	−0.721100	−	0.692831i	$-0.756363\pi$
$719$	−38.6714	−1.44220	−0.721100	+	0.692831i	$0.756363\pi$
$720$	0.682152	0.0254223
$721$	−6.08164	−0.226492
$722$	1.62349	0.0604200
$723$	−10.9613	−0.407656
$724$	−44.6879	−1.66081
$725$	27.7693	1.03133
$726$	−1.12131	−0.0416158
$727$	39.2921	1.45726	0.728631	−	0.684906i	$-0.240157\pi$
$727$	39.2921	1.45726	0.728631	+	0.684906i	$0.240157\pi$
$728$	10.7941	0.400057
$729$	−1.37330	−0.0508630
$730$	−0.176826	−0.00654464
$731$	19.3022	0.713918
$732$	13.2438	0.489504
$733$	−12.2072	−0.450885	−0.225442	−	0.974257i	$-0.572383\pi$
$733$	−12.2072	−0.450885	−0.225442	+	0.974257i	$0.572383\pi$
$734$	−5.28321	−0.195007
$735$	−0.642989	−0.0237170
$736$	1.21747	0.0448767
$737$	−17.9322	−0.660540
$738$	−2.73371	−0.100629
$739$	−12.4961	−0.459675	−0.229838	−	0.973229i	$-0.573820\pi$
$739$	−12.4961	−0.459675	−0.229838	+	0.973229i	$0.573820\pi$
$740$	0.214840	0.00789767
$741$	14.4445	0.530632
$742$	−5.17291	−0.189903
$743$	32.9825	1.21001	0.605005	−	0.796221i	$-0.293171\pi$
$743$	32.9825	1.21001	0.605005	+	0.796221i	$0.293171\pi$
$744$	−2.44482	−0.0896314
$745$	1.05934	0.0388111
$746$	6.23877	0.228417
$747$	41.8741	1.53209
$748$	15.0367	0.549796
$749$	20.0254	0.731712
$750$	0.0943007	0.00344337
$751$	−20.1024	−0.733546	−0.366773	−	0.930310i	$-0.619537\pi$
$751$	−20.1024	−0.733546	−0.366773	+	0.930310i	$0.619537\pi$
$752$	38.4580	1.40242
$753$	−10.3264	−0.376315
$754$	3.48820	0.127033
$755$	−0.872618	−0.0317578
$756$	34.7010	1.26206
$757$	14.6002	0.530655	0.265327	−	0.964158i	$-0.414520\pi$
$757$	14.6002	0.530655	0.265327	+	0.964158i	$0.414520\pi$
$758$	6.33097	0.229951
$759$	0.680318	0.0246940
$760$	−0.267253	−0.00969428
$761$	8.89786	0.322547	0.161274	−	0.986910i	$-0.448440\pi$
$761$	8.89786	0.322547	0.161274	+	0.986910i	$0.448440\pi$
$762$	0.0653178	0.00236621
$763$	15.1011	0.546696
$764$	−36.6362	−1.32545
$765$	−0.895617	−0.0323811
$766$	0.960470	0.0347032
$767$	19.2544	0.695234
$768$	10.2041	0.368210
$769$	7.45526	0.268844	0.134422	−	0.990924i	$-0.457082\pi$
$769$	7.45526	0.268844	0.134422	+	0.990924i	$0.457082\pi$
$770$	−0.0832777	−0.00300112
$771$	−8.42727	−0.303501
$772$	−12.5358	−0.451173
$773$	−43.8278	−1.57638	−0.788189	−	0.615434i	$-0.788981\pi$
$773$	−43.8278	−1.57638	−0.788189	+	0.615434i	$0.788981\pi$
$774$	1.62395	0.0583718
$775$	−23.8259	−0.855850
$776$	−6.01984	−0.216100
$777$	4.82888	0.173235
$778$	0.0936636	0.00335800
$779$	−34.5063	−1.23632
$780$	−0.390339	−0.0139764
$781$	−15.2875	−0.547030
$782$	−0.519365	−0.0185725
$783$	22.5978	0.807578
$784$	45.0169	1.60775
$785$	−0.291375	−0.0103996
$786$	−2.22264	−0.0792789
$787$	15.2433	0.543363	0.271682	−	0.962387i	$-0.412420\pi$
$787$	15.2433	0.543363	0.271682	+	0.962387i	$0.412420\pi$
$788$	3.98696	0.142029
$789$	3.77249	0.134304
$790$	0.129015	0.00459015
$791$	−54.6505	−1.94315
$792$	2.54935	0.0905871
$793$	32.6708	1.16017
$794$	3.67695	0.130490
$795$	0.376963	0.0133695
$796$	−28.1028	−0.996079
$797$	12.0904	0.428263	0.214132	−	0.976805i	$-0.431308\pi$
$797$	12.0904	0.428263	0.214132	+	0.976805i	$0.431308\pi$
$798$	−2.98087	−0.105522
$799$	−50.4926	−1.78630
$800$	−10.1544	−0.359011
$801$	−15.9246	−0.562667
$802$	−4.84924	−0.171232
$803$	21.2912	0.751349
$804$	17.3455	0.611728
$805$	−0.189671	−0.00668504
$806$	−2.99285	−0.105419
$807$	11.7949	0.415200
$808$	5.40201	0.190042
$809$	28.8695	1.01500	0.507499	−	0.861652i	$-0.330570\pi$
$809$	28.8695	1.01500	0.507499	+	0.861652i	$0.330570\pi$
$810$	−0.0542112	−0.00190479
$811$	17.7602	0.623643	0.311822	−	0.950141i	$-0.399061\pi$
$811$	17.7602	0.623643	0.311822	+	0.950141i	$0.399061\pi$
$812$	47.4673	1.66578
$813$	−3.48573	−0.122250
$814$	0.392296	0.0137500
$815$	0.661191	0.0231605
$816$	−14.3208	−0.501329
$817$	20.4984	0.717147
$818$	−5.31385	−0.185794
$819$	38.4148	1.34232
$820$	0.932474	0.0325634
$821$	9.51664	0.332133	0.166067	−	0.986115i	$-0.446893\pi$
$821$	9.51664	0.332133	0.166067	+	0.986115i	$0.446893\pi$
$822$	−0.231827	−0.00808591
$823$	−19.0278	−0.663267	−0.331634	−	0.943408i	$-0.607600\pi$
$823$	−19.0278	−0.663267	−0.331634	+	0.943408i	$0.607600\pi$
$824$	0.963059	0.0335497
$825$	−5.67420	−0.197550
$826$	−3.97347	−0.138255
$827$	17.4952	0.608368	0.304184	−	0.952613i	$-0.401616\pi$
$827$	17.4952	0.608368	0.304184	+	0.952613i	$0.401616\pi$
$828$	2.88132	0.100133
$829$	13.8423	0.480764	0.240382	−	0.970678i	$-0.422727\pi$
$829$	13.8423	0.480764	0.240382	+	0.970678i	$0.422727\pi$
$830$	0.216609	0.00751862
$831$	−3.30592	−0.114681
$832$	26.4673	0.917587
$833$	−59.1039	−2.04783
$834$	−1.94886	−0.0674835
$835$	−1.20908	−0.0418418
$836$	15.9685	0.552282
$837$	−19.3887	−0.670172
$838$	4.91501	0.169786
$839$	14.0101	0.483683	0.241841	−	0.970316i	$-0.422249\pi$
$839$	14.0101	0.483683	0.241841	+	0.970316i	$0.422249\pi$
$840$	0.162328	0.00560084
$841$	1.91139	0.0659101
$842$	2.94043	0.101334
$843$	−12.6966	−0.437294
$844$	−29.2252	−1.00597
$845$	−0.0127734	−0.000439417 0
$846$	−4.24809	−0.146052
$847$	−37.6416	−1.29338
$848$	−26.3919	−0.906302
$849$	−17.0016	−0.583493
$850$	4.33177	0.148578
$851$	0.893486	0.0306283
$852$	14.7873	0.506606
$853$	28.4232	0.973191	0.486596	−	0.873627i	$-0.338239\pi$
$853$	28.4232	0.973191	0.486596	+	0.873627i	$0.338239\pi$
$854$	−6.74219	−0.230713
$855$	−0.951117	−0.0325275
$856$	−3.17112	−0.108387
$857$	−33.6147	−1.14826	−0.574128	−	0.818765i	$-0.694659\pi$
$857$	−33.6147	−1.14826	−0.574128	+	0.818765i	$0.694659\pi$
$858$	−0.712756	−0.0243331
$859$	−33.4001	−1.13960	−0.569798	−	0.821785i	$-0.692979\pi$
$859$	−33.4001	−1.13960	−0.569798	+	0.821785i	$0.692979\pi$
$860$	−0.553934	−0.0188890
$861$	20.9589	0.714277
$862$	3.84728	0.131039
$863$	−43.8625	−1.49310	−0.746549	−	0.665330i	$-0.768291\pi$
$863$	−43.8625	−1.49310	−0.746549	+	0.665330i	$0.768291\pi$
$864$	−8.26329	−0.281123
$865$	−0.169463	−0.00576193
$866$	0.00201448	6.84548e−5 0
$867$	6.10586	0.207366
$868$	−40.7266	−1.38235
$869$	−15.5343	−0.526966
$870$	0.0524573	0.00177847
$871$	42.7892	1.44986
$872$	−2.39133	−0.0809808
$873$	−21.4238	−0.725086
$874$	−0.551550	−0.0186564
$875$	3.16561	0.107017
$876$	−20.5946	−0.695826
$877$	−24.4763	−0.826507	−0.413253	−	0.910616i	$-0.635608\pi$
$877$	−24.4763	−0.826507	−0.413253	+	0.910616i	$0.635608\pi$
$878$	−2.18898	−0.0738744
$879$	13.4699	0.454329
$880$	−0.424879	−0.0143227
$881$	17.0963	0.575990	0.287995	−	0.957632i	$-0.407011\pi$
$881$	17.0963	0.575990	0.287995	+	0.957632i	$0.407011\pi$
$882$	−4.97259	−0.167436
$883$	−22.9820	−0.773406	−0.386703	−	0.922204i	$-0.626386\pi$
$883$	−22.9820	−0.773406	−0.386703	+	0.922204i	$0.626386\pi$
$884$	−35.8802	−1.20678
$885$	0.289557	0.00973335
$886$	4.87478	0.163771
$887$	16.6811	0.560098	0.280049	−	0.959986i	$-0.409649\pi$
$887$	16.6811	0.560098	0.280049	+	0.959986i	$0.409649\pi$
$888$	−0.764677	−0.0256609
$889$	2.19267	0.0735398
$890$	−0.0823757	−0.00276124
$891$	6.52742	0.218677
$892$	−48.9711	−1.63968
$893$	−53.6216	−1.79438
$894$	−1.87105	−0.0625774
$895$	−0.848061	−0.0283476
$896$	−23.0825	−0.771132
$897$	−1.62336	−0.0542023
$898$	−3.31976	−0.110782
$899$	−26.5218	−0.884550
$900$	−24.0317	−0.801057
$901$	34.6507	1.15438
$902$	1.70269	0.0566934
$903$	−12.4506	−0.414329
$904$	8.65419	0.287834
$905$	−1.65784	−0.0551085
$906$	1.54126	0.0512051
$907$	13.5053	0.448437	0.224219	−	0.974539i	$-0.428017\pi$
$907$	13.5053	0.448437	0.224219	+	0.974539i	$0.428017\pi$
$908$	44.2051	1.46700
$909$	19.2250	0.637654
$910$	0.198715	0.00658734
$911$	−20.9896	−0.695418	−0.347709	−	0.937603i	$-0.613040\pi$
$911$	−20.9896	−0.695418	−0.347709	+	0.937603i	$0.613040\pi$
$912$	−15.2083	−0.503596
$913$	−26.0813	−0.863166
$914$	1.15880	0.0383298
$915$	0.491321	0.0162426
$916$	−30.8053	−1.01783
$917$	−74.6124	−2.46392
$918$	3.52505	0.116344
$919$	12.9693	0.427818	0.213909	−	0.976854i	$-0.431380\pi$
$919$	12.9693	0.427818	0.213909	+	0.976854i	$0.431380\pi$
$920$	0.0300354	0.000990239 0
$921$	−15.0078	−0.494524
$922$	−5.62099	−0.185117
$923$	36.4786	1.20071
$924$	−9.69917	−0.319079
$925$	−7.45213	−0.245024
$926$	−5.65799	−0.185933
$927$	3.42740	0.112570
$928$	−11.3033	−0.371050
$929$	15.9150	0.522153	0.261077	−	0.965318i	$-0.415922\pi$
$929$	15.9150	0.522153	0.261077	+	0.965318i	$0.415922\pi$
$930$	−0.0450080	−0.00147587
$931$	−62.7665	−2.05709
$932$	2.14806	0.0703619
$933$	16.0245	0.524619
$934$	−2.02328	−0.0662037
$935$	0.557835	0.0182432
$936$	−6.08319	−0.198835
$937$	59.9795	1.95945	0.979723	−	0.200358i	$-0.0642105\pi$
$937$	59.9795	1.95945	0.979723	+	0.200358i	$0.0642105\pi$
$938$	−8.83030	−0.288319
$939$	−3.41012	−0.111285
$940$	1.44903	0.0472623
$941$	−54.1731	−1.76599	−0.882996	−	0.469380i	$-0.844478\pi$
$941$	−54.1731	−1.76599	−0.882996	+	0.469380i	$0.844478\pi$
$942$	0.514641	0.0167679
$943$	3.87802	0.126286
$944$	−20.2724	−0.659812
$945$	1.28735	0.0418773
$946$	−1.01148	−0.0328860
$947$	−60.8064	−1.97594	−0.987971	−	0.154640i	$-0.950578\pi$
$947$	−60.8064	−1.97594	−0.987971	+	0.154640i	$0.950578\pi$
$948$	15.0261	0.488025
$949$	−50.8044	−1.64918
$950$	4.60021	0.149250
$951$	−6.31787	−0.204871
$952$	14.9213	0.483601
$953$	−46.7601	−1.51471	−0.757354	−	0.653004i	$-0.773508\pi$
$953$	−46.7601	−1.51471	−0.757354	+	0.653004i	$0.773508\pi$
$954$	2.91527	0.0943852
$955$	−1.35914	−0.0439807
$956$	−27.9019	−0.902411
$957$	−6.31624	−0.204175
$958$	−5.74359	−0.185567
$959$	−7.78228	−0.251303
$960$	0.398028	0.0128463
$961$	−8.24452	−0.265952
$962$	−0.936087	−0.0301807
$963$	−11.2856	−0.363673
$964$	28.9153	0.931298
$965$	−0.465056	−0.0149707
$966$	0.335008	0.0107787
$967$	2.74948	0.0884174	0.0442087	−	0.999022i	$-0.485923\pi$
$967$	2.74948	0.0884174	0.0442087	+	0.999022i	$0.485923\pi$
$968$	5.96074	0.191586
$969$	19.9674	0.641444
$970$	−0.110822	−0.00355830
$971$	−2.57850	−0.0827479	−0.0413739	−	0.999144i	$-0.513173\pi$
$971$	−2.57850	−0.0827479	−0.0413739	+	0.999144i	$0.513173\pi$
$972$	−30.3365	−0.973044
$973$	−65.4218	−2.09733
$974$	3.07826	0.0986337
$975$	13.5396	0.433615
$976$	−34.3983	−1.10106
$977$	9.86320	0.315552	0.157776	−	0.987475i	$-0.449568\pi$
$977$	9.86320	0.315552	0.157776	+	0.987475i	$0.449568\pi$
$978$	−1.16783	−0.0373431
$979$	9.91863	0.317001
$980$	1.69616	0.0541819
$981$	−8.51043	−0.271717
$982$	−0.654299	−0.0208795
$983$	−3.30936	−0.105552	−0.0527761	−	0.998606i	$-0.516807\pi$
$983$	−3.30936	−0.105552	−0.0527761	+	0.998606i	$0.516807\pi$
$984$	−3.31895	−0.105804
$985$	0.147909	0.00471278
$986$	4.82191	0.153561
$987$	32.5694	1.03670
$988$	−38.1036	−1.21224
$989$	−2.30372	−0.0732542
$990$	0.0469323	0.00149161
$991$	2.10401	0.0668360	0.0334180	−	0.999441i	$-0.489361\pi$
$991$	2.10401	0.0668360	0.0334180	+	0.999441i	$0.489361\pi$
$992$	9.69817	0.307917
$993$	9.71581	0.308322
$994$	−7.52799	−0.238773
$995$	−1.04257	−0.0330516
$996$	25.2280	0.799380
$997$	21.6667	0.686190	0.343095	−	0.939301i	$-0.388525\pi$
$997$	21.6667	0.686190	0.343095	+	0.939301i	$0.388525\pi$
$998$	2.15126	0.0680970
$999$	−6.06430	−0.191866

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2011.2.a.a.1.44	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2011.2.a.a.1.44	✓	77	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:	\( N \)	\(=\)	\( 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2011.a (trivial)

\(f(q)\)	\(=\)	\(q+0.172850 q^{2} +0.746844 q^{3} -1.97012 q^{4} -0.0730882 q^{5} +0.129092 q^{6} +4.33353 q^{7} -0.686237 q^{8} -2.44222 q^{9} +O(q^{10})\)	\(q+0.172850 q^{2} +0.746844 q^{3} -1.97012 q^{4} -0.0730882 q^{5} +0.129092 q^{6} +4.33353 q^{7} -0.686237 q^{8} -2.44222 q^{9} -0.0126333 q^{10} +1.52114 q^{11} -1.47137 q^{12} -3.62971 q^{13} +0.749052 q^{14} -0.0545854 q^{15} +3.82163 q^{16} -5.01752 q^{17} -0.422139 q^{18} -5.32846 q^{19} +0.143993 q^{20} +3.23647 q^{21} +0.262930 q^{22} +0.598843 q^{23} -0.512512 q^{24} -4.99466 q^{25} -0.627396 q^{26} -4.06449 q^{27} -8.53759 q^{28} -5.55980 q^{29} -0.00943511 q^{30} +4.77027 q^{31} +2.03304 q^{32} +1.13605 q^{33} -0.867281 q^{34} -0.316730 q^{35} +4.81148 q^{36} +1.49202 q^{37} -0.921025 q^{38} -2.71082 q^{39} +0.0501558 q^{40} +6.47585 q^{41} +0.559425 q^{42} -3.84696 q^{43} -2.99683 q^{44} +0.178498 q^{45} +0.103510 q^{46} +10.0632 q^{47} +2.85416 q^{48} +11.7795 q^{49} -0.863328 q^{50} -3.74731 q^{51} +7.15097 q^{52} -6.90594 q^{53} -0.702548 q^{54} -0.111177 q^{55} -2.97383 q^{56} -3.97952 q^{57} -0.961013 q^{58} -5.30466 q^{59} +0.107540 q^{60} -9.00096 q^{61} +0.824543 q^{62} -10.5835 q^{63} -7.29185 q^{64} +0.265289 q^{65} +0.196367 q^{66} -11.7886 q^{67} +9.88514 q^{68} +0.447242 q^{69} -0.0547468 q^{70} -10.0500 q^{71} +1.67594 q^{72} +13.9968 q^{73} +0.257896 q^{74} -3.73023 q^{75} +10.4977 q^{76} +6.59191 q^{77} -0.468567 q^{78} -10.2123 q^{79} -0.279316 q^{80} +4.29114 q^{81} +1.11935 q^{82} -17.1459 q^{83} -6.37624 q^{84} +0.366722 q^{85} -0.664948 q^{86} -4.15230 q^{87} -1.04386 q^{88} +6.52052 q^{89} +0.0308534 q^{90} -15.7294 q^{91} -1.17979 q^{92} +3.56265 q^{93} +1.73943 q^{94} +0.389447 q^{95} +1.51837 q^{96} +8.77225 q^{97} +2.03609 q^{98} -3.71497 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9}+O(q^{10}) \) 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9	\( 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9} - 21 q^{10} - 34 q^{11} - 36 q^{12} - 34 q^{13} - 49 q^{14} - 12 q^{15} + 47 q^{16} - 59 q^{17} - 24 q^{18} - 31 q^{19} - 82 q^{20} - 71 q^{21} - 3 q^{22} - 28 q^{23} - 50 q^{24} + 68 q^{25} - 54 q^{26} - 43 q^{27} - 2 q^{28} - 151 q^{29} + q^{30} - 37 q^{31} - 59 q^{32} - 35 q^{33} - q^{34} - 58 q^{35} + 19 q^{36} - 29 q^{37} - 22 q^{38} - 40 q^{39} - 41 q^{40} - 142 q^{41} + 16 q^{42} - 23 q^{43} - 89 q^{44} - 119 q^{45} - 6 q^{46} - 36 q^{47} - 46 q^{48} + 45 q^{49} - 29 q^{50} - 53 q^{51} - 11 q^{52} - 69 q^{53} - 50 q^{54} - 13 q^{55} - 122 q^{56} - 14 q^{57} + 31 q^{58} - 92 q^{59} + 20 q^{60} - 115 q^{61} - 66 q^{62} - 25 q^{63} + 37 q^{64} - 57 q^{65} - 17 q^{66} - 108 q^{68} - 160 q^{69} + 40 q^{70} - 67 q^{71} - 35 q^{72} - 36 q^{73} - 55 q^{74} - 51 q^{75} - 56 q^{76} - 116 q^{77} + 22 q^{78} - 42 q^{79} - 114 q^{80} + 37 q^{81} + 18 q^{82} - 42 q^{83} - 77 q^{84} - 18 q^{85} - 33 q^{86} - 7 q^{87} - 2 q^{88} - 93 q^{89} - 34 q^{90} - 37 q^{91} - 55 q^{92} - 8 q^{93} - 35 q^{94} - 64 q^{95} - 83 q^{96} - 16 q^{97} - 57 q^{98} - 65 q^{99}+O(q^{100}) \) 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9 - 21 * q^10 - 34 * q^11 - 36 * q^12 - 34 * q^13 - 49 * q^14 - 12 * q^15 + 47 * q^16 - 59 * q^17 - 24 * q^18 - 31 * q^19 - 82 * q^20 - 71 * q^21 - 3 * q^22 - 28 * q^23 - 50 * q^24 + 68 * q^25 - 54 * q^26 - 43 * q^27 - 2 * q^28 - 151 * q^29 + q^30 - 37 * q^31 - 59 * q^32 - 35 * q^33 - q^34 - 58 * q^35 + 19 * q^36 - 29 * q^37 - 22 * q^38 - 40 * q^39 - 41 * q^40 - 142 * q^41 + 16 * q^42 - 23 * q^43 - 89 * q^44 - 119 * q^45 - 6 * q^46 - 36 * q^47 - 46 * q^48 + 45 * q^49 - 29 * q^50 - 53 * q^51 - 11 * q^52 - 69 * q^53 - 50 * q^54 - 13 * q^55 - 122 * q^56 - 14 * q^57 + 31 * q^58 - 92 * q^59 + 20 * q^60 - 115 * q^61 - 66 * q^62 - 25 * q^63 + 37 * q^64 - 57 * q^65 - 17 * q^66 - 108 * q^68 - 160 * q^69 + 40 * q^70 - 67 * q^71 - 35 * q^72 - 36 * q^73 - 55 * q^74 - 51 * q^75 - 56 * q^76 - 116 * q^77 + 22 * q^78 - 42 * q^79 - 114 * q^80 + 37 * q^81 + 18 * q^82 - 42 * q^83 - 77 * q^84 - 18 * q^85 - 33 * q^86 - 7 * q^87 - 2 * q^88 - 93 * q^89 - 34 * q^90 - 37 * q^91 - 55 * q^92 - 8 * q^93 - 35 * q^94 - 64 * q^95 - 83 * q^96 - 16 * q^97 - 57 * q^98 - 65 * q^99

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