LMFDB - Embedded newform 503.2.a.f.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(1,503)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, 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("503.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.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:	$4.01647522167$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	503.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.43135 q^{2} +2.32813 q^{3} +0.0487521 q^{4} +1.62138 q^{5} -3.33236 q^{6} +3.43484 q^{7} +2.79291 q^{8} +2.42020 q^{9} +O(q^{10})$	\(q-1.43135 q^{2} +2.32813 q^{3} +0.0487521 q^{4} +1.62138 q^{5} -3.33236 q^{6} +3.43484 q^{7} +2.79291 q^{8} +2.42020 q^{9} -2.32076 q^{10} -0.695688 q^{11} +0.113501 q^{12} +2.78704 q^{13} -4.91645 q^{14} +3.77480 q^{15} -4.09513 q^{16} -6.87472 q^{17} -3.46414 q^{18} -1.23169 q^{19} +0.0790460 q^{20} +7.99676 q^{21} +0.995771 q^{22} +8.03473 q^{23} +6.50227 q^{24} -2.37111 q^{25} -3.98922 q^{26} -1.34986 q^{27} +0.167456 q^{28} -8.02844 q^{29} -5.40304 q^{30} +9.59158 q^{31} +0.275723 q^{32} -1.61965 q^{33} +9.84011 q^{34} +5.56920 q^{35} +0.117990 q^{36} -0.0454896 q^{37} +1.76297 q^{38} +6.48860 q^{39} +4.52838 q^{40} +10.0330 q^{41} -11.4461 q^{42} -10.6292 q^{43} -0.0339163 q^{44} +3.92407 q^{45} -11.5005 q^{46} +1.72424 q^{47} -9.53400 q^{48} +4.79813 q^{49} +3.39388 q^{50} -16.0053 q^{51} +0.135874 q^{52} -6.66671 q^{53} +1.93211 q^{54} -1.12798 q^{55} +9.59320 q^{56} -2.86753 q^{57} +11.4915 q^{58} -7.83234 q^{59} +0.184029 q^{60} +8.48076 q^{61} -13.7289 q^{62} +8.31299 q^{63} +7.79560 q^{64} +4.51887 q^{65} +2.31829 q^{66} +0.128627 q^{67} -0.335157 q^{68} +18.7059 q^{69} -7.97145 q^{70} +9.36773 q^{71} +6.75940 q^{72} +11.6801 q^{73} +0.0651114 q^{74} -5.52026 q^{75} -0.0600474 q^{76} -2.38958 q^{77} -9.28744 q^{78} +9.03774 q^{79} -6.63978 q^{80} -10.4032 q^{81} -14.3607 q^{82} -0.939830 q^{83} +0.389859 q^{84} -11.1466 q^{85} +15.2141 q^{86} -18.6913 q^{87} -1.94300 q^{88} -16.8653 q^{89} -5.61671 q^{90} +9.57305 q^{91} +0.391710 q^{92} +22.3305 q^{93} -2.46798 q^{94} -1.99704 q^{95} +0.641919 q^{96} +10.0789 q^{97} -6.86778 q^{98} -1.68370 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) $ 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9 + 4 * q^10 - 17 * q^11 + 19 * q^12 + 14 * q^13 + q^14 + 18 * q^15 + 48 * q^16 + 17 * q^17 - 10 * q^18 - 22 * q^19 - 19 * q^20 - 16 * q^21 + 38 * q^22 + 27 * q^23 - 9 * q^24 + 93 * q^25 + q^26 + 31 * q^27 - 9 * q^28 + 13 * q^29 - 28 * q^30 + 26 * q^31 + 5 * q^32 + 6 * q^33 - 32 * q^34 - 22 * q^35 + 52 * q^36 + 55 * q^37 - 24 * q^38 - 15 * q^39 - 7 * q^40 + 24 * q^41 - 50 * q^42 + 20 * q^43 - 27 * q^44 - 8 * q^45 + 6 * q^46 - 25 * q^47 + 29 * q^48 + 65 * q^49 - 16 * q^50 + 7 * q^51 + 32 * q^52 + 30 * q^53 - 82 * q^54 + 25 * q^55 + 3 * q^56 + 9 * q^57 + 58 * q^58 - 26 * q^59 - 68 * q^60 + 15 * q^61 - 12 * q^62 - 19 * q^63 + 44 * q^64 + 20 * q^65 - 55 * q^66 - 20 * q^67 - 4 * q^68 - 27 * q^69 + 2 * q^70 - 35 * q^71 - 26 * q^72 + 38 * q^73 - 59 * q^74 + 2 * q^75 - 42 * q^76 - 6 * q^77 - 47 * q^78 + 21 * q^79 - 100 * q^80 + 70 * q^81 - 59 * q^82 - 48 * q^83 - 116 * q^84 + 6 * q^85 - 7 * q^86 - 9 * q^87 + 106 * q^88 - 5 * q^89 - 118 * q^90 - 24 * q^91 + 26 * q^92 - 8 * q^93 - 22 * q^94 + 43 * q^95 - 100 * q^96 + 142 * q^97 - 38 * q^98 - 50 * 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 $

$2$	−1.43135	−1.01211	−0.506057	−	0.862500i	$-0.668898\pi$
$2$	−1.43135	−1.01211	−0.506057	+	0.862500i	$0.668898\pi$
$3$	2.32813	1.34415	0.672074	−	0.740484i	$-0.265404\pi$
$3$	2.32813	1.34415	0.672074	+	0.740484i	$0.265404\pi$
$4$	0.0487521	0.0243761
$5$	1.62138	0.725105	0.362553	−	0.931963i	$-0.381905\pi$
$5$	1.62138	0.725105	0.362553	+	0.931963i	$0.381905\pi$
$6$	−3.33236	−1.36043
$7$	3.43484	1.29825	0.649124	−	0.760683i	$-0.275136\pi$
$7$	3.43484	1.29825	0.649124	+	0.760683i	$0.275136\pi$
$8$	2.79291	0.987443
$9$	2.42020	0.806732
$10$	−2.32076	−0.733890
$11$	−0.695688	−0.209758	−0.104879	−	0.994485i	$-0.533446\pi$
$11$	−0.695688	−0.209758	−0.104879	+	0.994485i	$0.533446\pi$
$12$	0.113501	0.0327650
$13$	2.78704	0.772987	0.386493	−	0.922292i	$-0.373686\pi$
$13$	2.78704	0.772987	0.386493	+	0.922292i	$0.373686\pi$
$14$	−4.91645	−1.31398
$15$	3.77480	0.974649
$16$	−4.09513	−1.02378
$17$	−6.87472	−1.66736	−0.833682	−	0.552244i	$-0.813772\pi$
$17$	−6.87472	−1.66736	−0.833682	+	0.552244i	$0.813772\pi$
$18$	−3.46414	−0.816506
$19$	−1.23169	−0.282569	−0.141284	−	0.989969i	$-0.545123\pi$
$19$	−1.23169	−0.282569	−0.141284	+	0.989969i	$0.545123\pi$
$20$	0.0790460	0.0176752
$21$	7.99676	1.74504
$22$	0.995771	0.212299
$23$	8.03473	1.67536	0.837678	−	0.546164i	$-0.183913\pi$
$23$	8.03473	1.67536	0.837678	+	0.546164i	$0.183913\pi$
$24$	6.50227	1.32727
$25$	−2.37111	−0.474222
$26$	−3.98922	−0.782351
$27$	−1.34986	−0.259780
$28$	0.167456	0.0316462
$29$	−8.02844	−1.49084	−0.745422	−	0.666593i	$-0.767752\pi$
$29$	−8.02844	−1.49084	−0.745422	+	0.666593i	$0.767752\pi$
$30$	−5.40304	−0.986456
$31$	9.59158	1.72270	0.861349	−	0.508013i	$-0.169620\pi$
$31$	9.59158	1.72270	0.861349	+	0.508013i	$0.169620\pi$
$32$	0.275723	0.0487414
$33$	−1.61965	−0.281946
$34$	9.84011	1.68756
$35$	5.56920	0.941366
$36$	0.117990	0.0196650
$37$	−0.0454896	−0.00747845	−0.00373922	−	0.999993i	$-0.501190\pi$
$37$	−0.0454896	−0.00747845	−0.00373922	+	0.999993i	$0.501190\pi$
$38$	1.76297	0.285992
$39$	6.48860	1.03901
$40$	4.52838	0.716000
$41$	10.0330	1.56690	0.783448	−	0.621457i	$-0.213459\pi$
$41$	10.0330	1.56690	0.783448	+	0.621457i	$0.213459\pi$
$42$	−11.4461	−1.76618
$43$	−10.6292	−1.62094	−0.810468	−	0.585782i	$-0.800787\pi$
$43$	−10.6292	−1.62094	−0.810468	+	0.585782i	$0.800787\pi$
$44$	−0.0339163	−0.00511307
$45$	3.92407	0.584966
$46$	−11.5005	−1.69565
$47$	1.72424	0.251506	0.125753	−	0.992062i	$-0.459865\pi$
$47$	1.72424	0.251506	0.125753	+	0.992062i	$0.459865\pi$
$48$	−9.53400	−1.37611
$49$	4.79813	0.685447
$50$	3.39388	0.479967
$51$	−16.0053	−2.24118
$52$	0.135874	0.0188424
$53$	−6.66671	−0.915743	−0.457871	−	0.889018i	$-0.651388\pi$
$53$	−6.66671	−0.915743	−0.457871	+	0.889018i	$0.651388\pi$
$54$	1.93211	0.262927
$55$	−1.12798	−0.152097
$56$	9.59320	1.28195
$57$	−2.86753	−0.379814
$58$	11.4915	1.50891
$59$	−7.83234	−1.01968	−0.509842	−	0.860268i	$-0.670296\pi$
$59$	−7.83234	−1.01968	−0.509842	+	0.860268i	$0.670296\pi$
$60$	0.184029	0.0237581
$61$	8.48076	1.08585	0.542925	−	0.839781i	$-0.317317\pi$
$61$	8.48076	1.08585	0.542925	+	0.839781i	$0.317317\pi$
$62$	−13.7289	−1.74357
$63$	8.31299	1.04734
$64$	7.79560	0.974450
$65$	4.51887	0.560497
$66$	2.31829	0.285361
$67$	0.128627	0.0157143	0.00785715	−	0.999969i	$-0.497499\pi$
$67$	0.128627	0.0157143	0.00785715	+	0.999969i	$0.497499\pi$
$68$	−0.335157	−0.0406438
$69$	18.7059	2.25193
$70$	−7.97145	−0.952771
$71$	9.36773	1.11174	0.555872	−	0.831268i	$-0.312384\pi$
$71$	9.36773	1.11174	0.555872	+	0.831268i	$0.312384\pi$
$72$	6.75940	0.796603
$73$	11.6801	1.36705	0.683526	−	0.729926i	$-0.260446\pi$
$73$	11.6801	1.36705	0.683526	+	0.729926i	$0.260446\pi$
$74$	0.0651114	0.00756905
$75$	−5.52026	−0.637425
$76$	−0.0600474	−0.00688791
$77$	−2.38958	−0.272318
$78$	−9.28744	−1.05160
$79$	9.03774	1.01682	0.508412	−	0.861114i	$-0.330233\pi$
$79$	9.03774	1.01682	0.508412	+	0.861114i	$0.330233\pi$
$80$	−6.63978	−0.742350
$81$	−10.4032	−1.15592
$82$	−14.3607	−1.58588
$83$	−0.939830	−0.103160	−0.0515799	−	0.998669i	$-0.516426\pi$
$83$	−0.939830	−0.103160	−0.0515799	+	0.998669i	$0.516426\pi$
$84$	0.389859	0.0425371
$85$	−11.1466	−1.20902
$86$	15.2141	1.64057
$87$	−18.6913	−2.00391
$88$	−1.94300	−0.207124
$89$	−16.8653	−1.78772	−0.893861	−	0.448344i	$-0.852014\pi$
$89$	−16.8653	−1.78772	−0.893861	+	0.448344i	$0.852014\pi$
$90$	−5.61671	−0.592053
$91$	9.57305	1.00353
$92$	0.391710	0.0408386
$93$	22.3305	2.31556
$94$	−2.46798	−0.254553
$95$	−1.99704	−0.204892
$96$	0.641919	0.0655156
$97$	10.0789	1.02336	0.511678	−	0.859177i	$-0.329024\pi$
$97$	10.0789	1.02336	0.511678	+	0.859177i	$0.329024\pi$
$98$	−6.86778	−0.693751
$99$	−1.68370	−0.169219
$100$	−0.115597	−0.0115597
$101$	−16.9764	−1.68921	−0.844607	−	0.535386i	$-0.820166\pi$
$101$	−16.9764	−1.68921	−0.844607	+	0.535386i	$0.820166\pi$
$102$	22.9091	2.26834
$103$	−3.81703	−0.376103	−0.188052	−	0.982159i	$-0.560217\pi$
$103$	−3.81703	−0.376103	−0.188052	+	0.982159i	$0.560217\pi$
$104$	7.78396	0.763280
$105$	12.9658	1.26534
$106$	9.54237	0.926837
$107$	−12.3085	−1.18991	−0.594953	−	0.803761i	$-0.702829\pi$
$107$	−12.3085	−1.18991	−0.594953	+	0.803761i	$0.702829\pi$
$108$	−0.0658084	−0.00633242
$109$	0.884124	0.0846837	0.0423419	−	0.999103i	$-0.486518\pi$
$109$	0.884124	0.0846837	0.0423419	+	0.999103i	$0.486518\pi$
$110$	1.61453	0.153939
$111$	−0.105906	−0.0100521
$112$	−14.0661	−1.32912
$113$	−14.4313	−1.35758	−0.678789	−	0.734333i	$-0.737495\pi$
$113$	−14.4313	−1.35758	−0.678789	+	0.734333i	$0.737495\pi$
$114$	4.10443	0.384415
$115$	13.0274	1.21481
$116$	−0.391404	−0.0363409
$117$	6.74519	0.623593
$118$	11.2108	1.03204
$119$	−23.6136	−2.16465
$120$	10.5427	0.962410
$121$	−10.5160	−0.956002
$122$	−12.1389	−1.09900
$123$	23.3582	2.10614
$124$	0.467610	0.0419926
$125$	−11.9514	−1.06897
$126$	−11.8988	−1.06003
$127$	−12.0092	−1.06564	−0.532821	−	0.846228i	$-0.678868\pi$
$127$	−12.0092	−1.06564	−0.532821	+	0.846228i	$0.678868\pi$
$128$	−11.7096	−1.03500
$129$	−24.7462	−2.17878
$130$	−6.46807	−0.567287
$131$	8.12927	0.710258	0.355129	−	0.934817i	$-0.384437\pi$
$131$	8.12927	0.710258	0.355129	+	0.934817i	$0.384437\pi$
$132$	−0.0789616	−0.00687272
$133$	−4.23065	−0.366844
$134$	−0.184110	−0.0159047
$135$	−2.18864	−0.188368
$136$	−19.2005	−1.64643
$137$	−1.79780	−0.153596	−0.0767981	−	0.997047i	$-0.524470\pi$
$137$	−1.79780	−0.153596	−0.0767981	+	0.997047i	$0.524470\pi$
$138$	−26.7746	−2.27921
$139$	−2.97405	−0.252256	−0.126128	−	0.992014i	$-0.540255\pi$
$139$	−2.97405	−0.252256	−0.126128	+	0.992014i	$0.540255\pi$
$140$	0.271510	0.0229468
$141$	4.01425	0.338061
$142$	−13.4085	−1.12521
$143$	−1.93891	−0.162140
$144$	−9.91102	−0.825918
$145$	−13.0172	−1.08102
$146$	−16.7183	−1.38361
$147$	11.1707	0.921342
$148$	−0.00221772	−0.000182295 0
$149$	−0.000281231 0	−2.30393e−5 0	−1.15197e−5	−	1.00000i	$-0.500004\pi$
$149$	−0.000281231 0	−2.30393e−5 0	−1.15197e−5		1.00000i	$0.500004\pi$
$150$	7.90140	0.645147
$151$	5.88133	0.478615	0.239308	−	0.970944i	$-0.423080\pi$
$151$	5.88133	0.478615	0.239308	+	0.970944i	$0.423080\pi$
$152$	−3.44000	−0.279020
$153$	−16.6382	−1.34512
$154$	3.42031	0.275617
$155$	15.5516	1.24914
$156$	0.316333	0.0253269
$157$	9.54018	0.761390	0.380695	−	0.924701i	$-0.375685\pi$
$157$	9.54018	0.761390	0.380695	+	0.924701i	$0.375685\pi$
$158$	−12.9361	−1.02914
$159$	−15.5210	−1.23089
$160$	0.447053	0.0353426
$161$	27.5980	2.17503
$162$	14.8906	1.16992
$163$	−1.44103	−0.112870	−0.0564351	−	0.998406i	$-0.517973\pi$
$163$	−1.44103	−0.112870	−0.0564351	+	0.998406i	$0.517973\pi$
$164$	0.489132	0.0381948
$165$	−2.62608	−0.204440
$166$	1.34522	0.104410
$167$	−11.4521	−0.886186	−0.443093	−	0.896476i	$-0.646119\pi$
$167$	−11.4521	−0.886186	−0.443093	+	0.896476i	$0.646119\pi$
$168$	22.3342	1.72312
$169$	−5.23239	−0.402492
$170$	15.9546	1.22366
$171$	−2.98093	−0.227957
$172$	−0.518196	−0.0395121
$173$	−9.03758	−0.687114	−0.343557	−	0.939132i	$-0.611632\pi$
$173$	−9.03758	−0.687114	−0.343557	+	0.939132i	$0.611632\pi$
$174$	26.7537	2.02819
$175$	−8.14439	−0.615658
$176$	2.84893	0.214746
$177$	−18.2347	−1.37061
$178$	24.1401	1.80938
$179$	8.49163	0.634694	0.317347	−	0.948309i	$-0.397208\pi$
$179$	8.49163	0.634694	0.317347	+	0.948309i	$0.397208\pi$
$180$	0.191307	0.0142592
$181$	1.18999	0.0884509	0.0442255	−	0.999022i	$-0.485918\pi$
$181$	1.18999	0.0884509	0.0442255	+	0.999022i	$0.485918\pi$
$182$	−13.7023	−1.01569
$183$	19.7443	1.45954
$184$	22.4403	1.65432
$185$	−0.0737562	−0.00542266
$186$	−31.9626	−2.34361
$187$	4.78266	0.349743
$188$	0.0840602	0.00613072
$189$	−4.63654	−0.337259
$190$	2.85846	0.207374
$191$	17.6433	1.27662	0.638311	−	0.769778i	$-0.279633\pi$
$191$	17.6433	1.27662	0.638311	+	0.769778i	$0.279633\pi$
$192$	18.1492	1.30980
$193$	17.2303	1.24026	0.620132	−	0.784497i	$-0.287079\pi$
$193$	17.2303	1.24026	0.620132	+	0.784497i	$0.287079\pi$
$194$	−14.4264	−1.03575
$195$	10.5205	0.753390
$196$	0.233919	0.0167085
$197$	−7.14985	−0.509406	−0.254703	−	0.967019i	$-0.581978\pi$
$197$	−7.14985	−0.509406	−0.254703	+	0.967019i	$0.581978\pi$
$198$	2.40996	0.171269
$199$	−7.14453	−0.506462	−0.253231	−	0.967406i	$-0.581493\pi$
$199$	−7.14453	−0.506462	−0.253231	+	0.967406i	$0.581493\pi$
$200$	−6.62230	−0.468268
$201$	0.299461	0.0211223
$202$	24.2991	1.70968
$203$	−27.5764	−1.93549
$204$	−0.780290	−0.0546313
$205$	16.2674	1.13616
$206$	5.46349	0.380659
$207$	19.4456	1.35156
$208$	−11.4133	−0.791370
$209$	0.856871	0.0592710
$210$	−18.5586	−1.28066
$211$	−28.6407	−1.97171	−0.985855	−	0.167602i	$-0.946398\pi$
$211$	−28.6407	−1.97171	−0.985855	+	0.167602i	$0.946398\pi$
$212$	−0.325016	−0.0223222
$213$	21.8093	1.49435
$214$	17.6177	1.20432
$215$	−17.2340	−1.17535
$216$	−3.77003	−0.256518
$217$	32.9455	2.23649
$218$	−1.26549	−0.0857096
$219$	27.1928	1.83752
$220$	−0.0549914	−0.00370752
$221$	−19.1601	−1.28885
$222$	0.151588	0.0101739
$223$	19.3571	1.29624	0.648122	−	0.761536i	$-0.275555\pi$
$223$	19.3571	1.29624	0.648122	+	0.761536i	$0.275555\pi$
$224$	0.947064	0.0632783
$225$	−5.73856	−0.382570
$226$	20.6561	1.37402
$227$	−7.85883	−0.521609	−0.260804	−	0.965392i	$-0.583988\pi$
$227$	−7.85883	−0.521609	−0.260804	+	0.965392i	$0.583988\pi$
$228$	−0.139798	−0.00925837
$229$	6.47613	0.427955	0.213977	−	0.976839i	$-0.431358\pi$
$229$	6.47613	0.427955	0.213977	+	0.976839i	$0.431358\pi$
$230$	−18.6467	−1.22953
$231$	−5.56325	−0.366035
$232$	−22.4227	−1.47212
$233$	27.3747	1.79337	0.896687	−	0.442664i	$-0.145967\pi$
$233$	27.3747	1.79337	0.896687	+	0.442664i	$0.145967\pi$
$234$	−9.65471	−0.631148
$235$	2.79565	0.182368
$236$	−0.381843	−0.0248559
$237$	21.0410	1.36676
$238$	33.7992	2.19088
$239$	5.27155	0.340988	0.170494	−	0.985359i	$-0.445464\pi$
$239$	5.27155	0.340988	0.170494	+	0.985359i	$0.445464\pi$
$240$	−15.4583	−0.997828
$241$	−1.48633	−0.0957427	−0.0478714	−	0.998854i	$-0.515244\pi$
$241$	−1.48633	−0.0957427	−0.0478714	+	0.998854i	$0.515244\pi$
$242$	15.0521	0.967583
$243$	−20.1705	−1.29394
$244$	0.413455	0.0264687
$245$	7.77961	0.497021
$246$	−33.4337	−2.13165
$247$	−3.43277	−0.218422
$248$	26.7884	1.70107
$249$	−2.18805	−0.138662
$250$	17.1066	1.08192
$251$	0.130529	0.00823890	0.00411945	−	0.999992i	$-0.498689\pi$
$251$	0.130529	0.00823890	0.00411945	+	0.999992i	$0.498689\pi$
$252$	0.405276	0.0255300
$253$	−5.58967	−0.351419
$254$	17.1893	1.07855
$255$	−25.9507	−1.62509
$256$	1.16936	0.0730851
$257$	16.6727	1.04001	0.520007	−	0.854162i	$-0.325929\pi$
$257$	16.6727	1.04001	0.520007	+	0.854162i	$0.325929\pi$
$258$	35.4203	2.20517
$259$	−0.156250	−0.00970888
$260$	0.220304	0.0136627
$261$	−19.4304	−1.20271
$262$	−11.6358	−0.718862
$263$	−25.3669	−1.56419	−0.782094	−	0.623160i	$-0.785849\pi$
$263$	−25.3669	−1.56419	−0.782094	+	0.623160i	$0.785849\pi$
$264$	−4.52355	−0.278405
$265$	−10.8093	−0.664010
$266$	6.05553	0.371288
$267$	−39.2647	−2.40296
$268$	0.00627085	0.000383053 0
$269$	27.5757	1.68132	0.840661	−	0.541561i	$-0.182167\pi$
$269$	27.5757	1.68132	0.840661	+	0.541561i	$0.182167\pi$
$270$	3.13270	0.190650
$271$	8.30935	0.504757	0.252379	−	0.967629i	$-0.418787\pi$
$271$	8.30935	0.504757	0.252379	+	0.967629i	$0.418787\pi$
$272$	28.1529	1.70702
$273$	22.2873	1.34889
$274$	2.57327	0.155457
$275$	1.64955	0.0994719
$276$	0.911953	0.0548931
$277$	−14.4793	−0.869974	−0.434987	−	0.900437i	$-0.643247\pi$
$277$	−14.4793	−0.869974	−0.434987	+	0.900437i	$0.643247\pi$
$278$	4.25690	0.255312
$279$	23.2135	1.38976
$280$	15.5543	0.929546
$281$	−25.7545	−1.53639	−0.768193	−	0.640219i	$-0.778844\pi$
$281$	−25.7545	−1.53639	−0.768193	+	0.640219i	$0.778844\pi$
$282$	−5.74578	−0.342156
$283$	−0.0245165	−0.00145735	−0.000728677	−	1.00000i	$-0.500232\pi$
$283$	−0.0245165	−0.00145735	−0.000728677		1.00000i	$0.500232\pi$
$284$	0.456697	0.0271000
$285$	−4.64937	−0.275405
$286$	2.77526	0.164104
$287$	34.4619	2.03422
$288$	0.667303	0.0393212
$289$	30.2618	1.78011
$290$	18.6321	1.09412
$291$	23.4650	1.37554
$292$	0.569430	0.0333233
$293$	2.58192	0.150837	0.0754186	−	0.997152i	$-0.475971\pi$
$293$	2.58192	0.150837	0.0754186	+	0.997152i	$0.475971\pi$
$294$	−15.9891	−0.932503
$295$	−12.6992	−0.739378
$296$	−0.127048	−0.00738454
$297$	0.939080	0.0544909
$298$	0.000402539 0	2.33185e−5 0
$299$	22.3931	1.29503
$300$	−0.269124	−0.0155379
$301$	−36.5096	−2.10438
$302$	−8.41821	−0.484414
$303$	−39.5233	−2.27055
$304$	5.04392	0.289289
$305$	13.7506	0.787355
$306$	23.8150	1.36141
$307$	−12.9548	−0.739367	−0.369683	−	0.929158i	$-0.620534\pi$
$307$	−12.9548	−0.739367	−0.369683	+	0.929158i	$0.620534\pi$
$308$	−0.116497	−0.00663804
$309$	−8.88655	−0.505538
$310$	−22.2598	−1.26427
$311$	−8.10729	−0.459722	−0.229861	−	0.973223i	$-0.573827\pi$
$311$	−8.10729	−0.459722	−0.229861	+	0.973223i	$0.573827\pi$
$312$	18.1221	1.02596
$313$	10.0345	0.567183	0.283592	−	0.958945i	$-0.408474\pi$
$313$	10.0345	0.567183	0.283592	+	0.958945i	$0.408474\pi$
$314$	−13.6553	−0.770614
$315$	13.4786	0.759431
$316$	0.440609	0.0247862
$317$	34.0789	1.91406	0.957030	−	0.289990i	$-0.0936518\pi$
$317$	34.0789	1.91406	0.957030	+	0.289990i	$0.0936518\pi$
$318$	22.2159	1.24580
$319$	5.58529	0.312716
$320$	12.6397	0.706579
$321$	−28.6557	−1.59941
$322$	−39.5023	−2.20138
$323$	8.46751	0.471145
$324$	−0.507180	−0.0281767
$325$	−6.60839	−0.366567
$326$	2.06261	0.114238
$327$	2.05836	0.113827
$328$	28.0214	1.54722
$329$	5.92248	0.326517
$330$	3.75883	0.206917
$331$	8.68978	0.477634	0.238817	−	0.971065i	$-0.423240\pi$
$331$	8.68978	0.477634	0.238817	+	0.971065i	$0.423240\pi$
$332$	−0.0458187	−0.00251463
$333$	−0.110094	−0.00603311
$334$	16.3919	0.896922
$335$	0.208554	0.0113945
$336$	−32.7478	−1.78654
$337$	−24.8121	−1.35160	−0.675799	−	0.737086i	$-0.736201\pi$
$337$	−24.8121	−1.35160	−0.675799	+	0.737086i	$0.736201\pi$
$338$	7.48937	0.407368
$339$	−33.5979	−1.82479
$340$	−0.543419	−0.0294710
$341$	−6.67275	−0.361350
$342$	4.26674	0.230719
$343$	−7.56308	−0.408368
$344$	−29.6864	−1.60058
$345$	30.3295	1.63288
$346$	12.9359	0.695439
$347$	14.3599	0.770877	0.385439	−	0.922733i	$-0.374050\pi$
$347$	14.3599	0.770877	0.385439	+	0.922733i	$0.374050\pi$
$348$	−0.911239	−0.0488476
$349$	1.08809	0.0582443	0.0291222	−	0.999576i	$-0.490729\pi$
$349$	1.08809	0.0582443	0.0291222	+	0.999576i	$0.490729\pi$
$350$	11.6574	0.623116
$351$	−3.76211	−0.200807
$352$	−0.191817	−0.0102239
$353$	20.6043	1.09666	0.548329	−	0.836262i	$-0.315264\pi$
$353$	20.6043	1.09666	0.548329	+	0.836262i	$0.315264\pi$
$354$	26.1002	1.38721
$355$	15.1887	0.806132
$356$	−0.822221	−0.0435776
$357$	−54.9755	−2.90961
$358$	−12.1545	−0.642384
$359$	−20.5135	−1.08266	−0.541330	−	0.840810i	$-0.682079\pi$
$359$	−20.5135	−1.08266	−0.541330	+	0.840810i	$0.682079\pi$
$360$	10.9596	0.577621
$361$	−17.4829	−0.920155
$362$	−1.70328	−0.0895225
$363$	−24.4827	−1.28501
$364$	0.466706	0.0244621
$365$	18.9379	0.991257
$366$	−28.2610	−1.47722
$367$	25.5549	1.33395	0.666976	−	0.745079i	$-0.267588\pi$
$367$	25.5549	1.33395	0.666976	+	0.745079i	$0.267588\pi$
$368$	−32.9032	−1.71520
$369$	24.2819	1.26407
$370$	0.105571	0.00548836
$371$	−22.8991	−1.18886
$372$	1.08866	0.0564443
$373$	0.136423	0.00706371	0.00353186	−	0.999994i	$-0.498876\pi$
$373$	0.136423	0.00706371	0.00353186	+	0.999994i	$0.498876\pi$
$374$	−6.84565	−0.353980
$375$	−27.8245	−1.43685
$376$	4.81564	0.248348
$377$	−22.3756	−1.15240
$378$	6.63650	0.341345
$379$	4.01675	0.206327	0.103163	−	0.994664i	$-0.467104\pi$
$379$	4.01675	0.206327	0.103163	+	0.994664i	$0.467104\pi$
$380$	−0.0973600	−0.00499446
$381$	−27.9589	−1.43238
$382$	−25.2536	−1.29209
$383$	−21.1948	−1.08301	−0.541503	−	0.840699i	$-0.682144\pi$
$383$	−21.1948	−1.08301	−0.541503	+	0.840699i	$0.682144\pi$
$384$	−27.2616	−1.39119
$385$	−3.87443	−0.197459
$386$	−24.6625	−1.25529
$387$	−25.7247	−1.30766
$388$	0.491367	0.0249454
$389$	−11.4478	−0.580427	−0.290213	−	0.956962i	$-0.593726\pi$
$389$	−11.4478	−0.580427	−0.290213	+	0.956962i	$0.593726\pi$
$390$	−15.0585	−0.762517
$391$	−55.2365	−2.79343
$392$	13.4007	0.676840
$393$	18.9260	0.954691
$394$	10.2339	0.515577
$395$	14.6536	0.737305
$396$	−0.0820841	−0.00412488
$397$	35.4863	1.78101	0.890503	−	0.454977i	$-0.150352\pi$
$397$	35.4863	1.78101	0.890503	+	0.454977i	$0.150352\pi$
$398$	10.2263	0.512598
$399$	−9.84951	−0.493092
$400$	9.71000	0.485500
$401$	7.10338	0.354726	0.177363	−	0.984146i	$-0.443243\pi$
$401$	7.10338	0.354726	0.177363	+	0.984146i	$0.443243\pi$
$402$	−0.428632	−0.0213782
$403$	26.7321	1.33162
$404$	−0.827635	−0.0411764
$405$	−16.8677	−0.838160
$406$	39.4714	1.95893
$407$	0.0316466	0.00156866
$408$	−44.7013	−2.21304
$409$	16.6490	0.823241	0.411621	−	0.911355i	$-0.364963\pi$
$409$	16.6490	0.823241	0.411621	+	0.911355i	$0.364963\pi$
$410$	−23.2843	−1.14993
$411$	−4.18551	−0.206456
$412$	−0.186088	−0.00916791
$413$	−26.9028	−1.32380
$414$	−27.8334	−1.36794
$415$	−1.52383	−0.0748017
$416$	0.768451	0.0376764
$417$	−6.92398	−0.339069
$418$	−1.22648	−0.0599891
$419$	18.7726	0.917100	0.458550	−	0.888668i	$-0.348369\pi$
$419$	18.7726	0.917100	0.458550	+	0.888668i	$0.348369\pi$
$420$	0.632112	0.0308439
$421$	−2.14317	−0.104452	−0.0522259	−	0.998635i	$-0.516632\pi$
$421$	−2.14317	−0.104452	−0.0522259	+	0.998635i	$0.516632\pi$
$422$	40.9948	1.99560
$423$	4.17299	0.202898
$424$	−18.6195	−0.904244
$425$	16.3007	0.790701
$426$	−31.2167	−1.51245
$427$	29.1300	1.40970
$428$	−0.600064	−0.0290052
$429$	−4.51405	−0.217940
$430$	24.6678	1.18959
$431$	9.41826	0.453662	0.226831	−	0.973934i	$-0.427164\pi$
$431$	9.41826	0.453662	0.226831	+	0.973934i	$0.427164\pi$
$432$	5.52784	0.265958
$433$	−20.1683	−0.969228	−0.484614	−	0.874728i	$-0.661040\pi$
$433$	−20.1683	−0.969228	−0.484614	+	0.874728i	$0.661040\pi$
$434$	−47.1565	−2.26358
$435$	−30.3057	−1.45305
$436$	0.0431029	0.00206426
$437$	−9.89628	−0.473403
$438$	−38.9223	−1.85978
$439$	−16.7247	−0.798227	−0.399114	−	0.916901i	$-0.630682\pi$
$439$	−16.7247	−0.798227	−0.399114	+	0.916901i	$0.630682\pi$
$440$	−3.15034	−0.150187
$441$	11.6124	0.552972
$442$	27.4248	1.30446
$443$	−3.17947	−0.151061	−0.0755305	−	0.997143i	$-0.524065\pi$
$443$	−3.17947	−0.151061	−0.0755305	+	0.997143i	$0.524065\pi$
$444$	−0.00516314	−0.000245032 0
$445$	−27.3452	−1.29629
$446$	−27.7067	−1.31195
$447$	−0.000654743 0	−3.09683e−5 0
$448$	26.7766	1.26508
$449$	19.2597	0.908921	0.454460	−	0.890767i	$-0.349832\pi$
$449$	19.2597	0.908921	0.454460	+	0.890767i	$0.349832\pi$
$450$	8.21386	0.387205
$451$	−6.97986	−0.328669
$452$	−0.703554	−0.0330924
$453$	13.6925	0.643330
$454$	11.2487	0.527928
$455$	15.5216	0.727663
$456$	−8.00876	−0.375045
$457$	31.4676	1.47199	0.735997	−	0.676985i	$-0.236714\pi$
$457$	31.4676	1.47199	0.735997	+	0.676985i	$0.236714\pi$
$458$	−9.26959	−0.433139
$459$	9.27989	0.433148
$460$	0.635113	0.0296123
$461$	4.06341	0.189252	0.0946260	−	0.995513i	$-0.469834\pi$
$461$	4.06341	0.189252	0.0946260	+	0.995513i	$0.469834\pi$
$462$	7.96294	0.370470
$463$	13.6213	0.633035	0.316517	−	0.948587i	$-0.397486\pi$
$463$	13.6213	0.633035	0.316517	+	0.948587i	$0.397486\pi$
$464$	32.8775	1.52630
$465$	36.2063	1.67903
$466$	−39.1826	−1.81510
$467$	3.22261	0.149124	0.0745622	−	0.997216i	$-0.476244\pi$
$467$	3.22261	0.149124	0.0745622	+	0.997216i	$0.476244\pi$
$468$	0.328843	0.0152008
$469$	0.441814	0.0204011
$470$	−4.00155	−0.184578
$471$	22.2108	1.02342
$472$	−21.8750	−1.00688
$473$	7.39461	0.340004
$474$	−30.1170	−1.38332
$475$	2.92047	0.134000
$476$	−1.15121	−0.0527657
$477$	−16.1347	−0.738759
$478$	−7.54541	−0.345119
$479$	−6.83879	−0.312472	−0.156236	−	0.987720i	$-0.549936\pi$
$479$	−6.83879	−0.312472	−0.156236	+	0.987720i	$0.549936\pi$
$480$	1.04080	0.0475057
$481$	−0.126782	−0.00578074
$482$	2.12745	0.0969026
$483$	64.2518	2.92356
$484$	−0.512678	−0.0233036
$485$	16.3418	0.742041
$486$	28.8710	1.30962
$487$	−22.5419	−1.02147	−0.510734	−	0.859739i	$-0.670626\pi$
$487$	−22.5419	−1.02147	−0.510734	+	0.859739i	$0.670626\pi$
$488$	23.6860	1.07221
$489$	−3.35491	−0.151714
$490$	−11.1353	−0.503042
$491$	−24.5019	−1.10575	−0.552877	−	0.833263i	$-0.686470\pi$
$491$	−24.5019	−1.10575	−0.552877	+	0.833263i	$0.686470\pi$
$492$	1.13876	0.0513394
$493$	55.1933	2.48578
$494$	4.91348	0.221068
$495$	−2.72993	−0.122701
$496$	−39.2787	−1.76367
$497$	32.1767	1.44332
$498$	3.13186	0.140342
$499$	−4.84063	−0.216697	−0.108348	−	0.994113i	$-0.534556\pi$
$499$	−4.84063	−0.216697	−0.108348	+	0.994113i	$0.534556\pi$
$500$	−0.582657	−0.0260572
$501$	−26.6619	−1.19117
$502$	−0.186832	−0.00833871
$503$	1.00000	0.0445878
$503$	1.00000	0.0445878
$504$	23.2174	1.03419
$505$	−27.5253	−1.22486
$506$	8.00075	0.355677
$507$	−12.1817	−0.541008
$508$	−0.585473	−0.0259762
$509$	2.61918	0.116093	0.0580467	−	0.998314i	$-0.481513\pi$
$509$	2.61918	0.116093	0.0580467	+	0.998314i	$0.481513\pi$
$510$	37.1444	1.64478
$511$	40.1193	1.77477
$512$	21.7455	0.961026
$513$	1.66260	0.0734057
$514$	−23.8644	−1.05261
$515$	−6.18887	−0.272714
$516$	−1.20643	−0.0531100
$517$	−1.19953	−0.0527553
$518$	0.223647	0.00982650
$519$	−21.0407	−0.923583
$520$	12.6208	0.553459
$521$	−27.8461	−1.21996	−0.609980	−	0.792417i	$-0.708823\pi$
$521$	−27.8461	−1.21996	−0.609980	+	0.792417i	$0.708823\pi$
$522$	27.8117	1.21728
$523$	−27.2966	−1.19360	−0.596800	−	0.802390i	$-0.703561\pi$
$523$	−27.2966	−1.19360	−0.596800	+	0.802390i	$0.703561\pi$
$524$	0.396319	0.0173133
$525$	−18.9612	−0.827535
$526$	36.3088	1.58314
$527$	−65.9394	−2.87237
$528$	6.63269	0.288651
$529$	41.5568	1.80682
$530$	15.4718	0.672054
$531$	−18.9558	−0.822612
$532$	−0.206253	−0.00894221
$533$	27.9625	1.21119
$534$	56.2014	2.43207
$535$	−19.9568	−0.862807
$536$	0.359244	0.0155170
$537$	19.7696	0.853123
$538$	−39.4704	−1.70169
$539$	−3.33800	−0.143778
$540$	−0.106701	−0.00459167
$541$	−30.1441	−1.29600	−0.647998	−	0.761642i	$-0.724393\pi$
$541$	−30.1441	−1.29600	−0.647998	+	0.761642i	$0.724393\pi$
$542$	−11.8936	−0.510872
$543$	2.77044	0.118891
$544$	−1.89552	−0.0812696
$545$	1.43351	0.0614046
$546$	−31.9009	−1.36523
$547$	−15.0768	−0.644636	−0.322318	−	0.946631i	$-0.604462\pi$
$547$	−15.0768	−0.644636	−0.322318	+	0.946631i	$0.604462\pi$
$548$	−0.0876465	−0.00374407
$549$	20.5251	0.875990
$550$	−2.36108	−0.100677
$551$	9.88854	0.421266
$552$	52.2439	2.22365
$553$	31.0432	1.32009
$554$	20.7248	0.880514
$555$	−0.171714	−0.00728886
$556$	−0.144991	−0.00614900
$557$	38.1097	1.61476	0.807380	−	0.590032i	$-0.200885\pi$
$557$	38.1097	1.61476	0.807380	+	0.590032i	$0.200885\pi$
$558$	−33.2266	−1.40659
$559$	−29.6240	−1.25296
$560$	−22.8066	−0.963754
$561$	11.1347	0.470106
$562$	36.8636	1.55500
$563$	44.0769	1.85762	0.928811	−	0.370554i	$-0.120832\pi$
$563$	44.0769	1.85762	0.928811	+	0.370554i	$0.120832\pi$
$564$	0.195703	0.00824059
$565$	−23.3986	−0.984387
$566$	0.0350916	0.00147501
$567$	−35.7335	−1.50066
$568$	26.1632	1.09779
$569$	23.1026	0.968511	0.484256	−	0.874927i	$-0.339090\pi$
$569$	23.1026	0.968511	0.484256	+	0.874927i	$0.339090\pi$
$570$	6.65486	0.278742
$571$	−22.2356	−0.930533	−0.465266	−	0.885171i	$-0.654041\pi$
$571$	−22.2356	−0.930533	−0.465266	+	0.885171i	$0.654041\pi$
$572$	−0.0945262	−0.00395234
$573$	41.0759	1.71597
$574$	−49.3268	−2.05886
$575$	−19.0512	−0.794491
$576$	18.8669	0.786120
$577$	11.9626	0.498010	0.249005	−	0.968502i	$-0.419896\pi$
$577$	11.9626	0.498010	0.249005	+	0.968502i	$0.419896\pi$
$578$	−43.3151	−1.80167
$579$	40.1144	1.66710
$580$	−0.634616	−0.0263510
$581$	−3.22817	−0.133927
$582$	−33.5865	−1.39221
$583$	4.63795	0.192084
$584$	32.6215	1.34989
$585$	10.9366	0.452171
$586$	−3.69562	−0.152665
$587$	1.64277	0.0678046	0.0339023	−	0.999425i	$-0.489207\pi$
$587$	1.64277	0.0678046	0.0339023	+	0.999425i	$0.489207\pi$
$588$	0.544594	0.0224587
$589$	−11.8138	−0.486780
$590$	18.1770	0.748336
$591$	−16.6458	−0.684717
$592$	0.186286	0.00765630
$593$	13.6181	0.559227	0.279614	−	0.960113i	$-0.409794\pi$
$593$	13.6181	0.559227	0.279614	+	0.960113i	$0.409794\pi$
$594$	−1.34415	−0.0551511
$595$	−38.2867	−1.56960
$596$	−1.37106e−5 0	−5.61609e−7 0
$597$	−16.6334	−0.680760
$598$	−32.0523	−1.31072
$599$	15.2924	0.624832	0.312416	−	0.949945i	$-0.398862\pi$
$599$	15.2924	0.624832	0.312416	+	0.949945i	$0.398862\pi$
$600$	−15.4176	−0.629421
$601$	19.4107	0.791779	0.395890	−	0.918298i	$-0.370436\pi$
$601$	19.4107	0.791779	0.395890	+	0.918298i	$0.370436\pi$
$602$	52.2579	2.12987
$603$	0.311303	0.0126772
$604$	0.286727	0.0116668
$605$	−17.0505	−0.693202
$606$	56.5715	2.29806
$607$	−0.827856	−0.0336016	−0.0168008	−	0.999859i	$-0.505348\pi$
$607$	−0.827856	−0.0336016	−0.0168008	+	0.999859i	$0.505348\pi$
$608$	−0.339604	−0.0137728
$609$	−64.2015	−2.60158
$610$	−19.6818	−0.796894
$611$	4.80552	0.194411
$612$	−0.811147	−0.0327887
$613$	−4.99298	−0.201665	−0.100832	−	0.994903i	$-0.532151\pi$
$613$	−4.99298	−0.201665	−0.100832	+	0.994903i	$0.532151\pi$
$614$	18.5427	0.748324
$615$	37.8727	1.52717
$616$	−6.67388	−0.268898
$617$	1.11916	0.0450557	0.0225279	−	0.999746i	$-0.492829\pi$
$617$	1.11916	0.0450557	0.0225279	+	0.999746i	$0.492829\pi$
$618$	12.7197	0.511662
$619$	−1.74728	−0.0702291	−0.0351146	−	0.999383i	$-0.511180\pi$
$619$	−1.74728	−0.0702291	−0.0351146	+	0.999383i	$0.511180\pi$
$620$	0.758176	0.0304491
$621$	−10.8457	−0.435224
$622$	11.6043	0.465292
$623$	−57.9298	−2.32091
$624$	−26.5717	−1.06372
$625$	−7.52228	−0.300891
$626$	−14.3628	−0.574055
$627$	1.99491	0.0796690
$628$	0.465104	0.0185597
$629$	0.312729	0.0124693
$630$	−19.2925	−0.768631
$631$	−25.1527	−1.00131	−0.500657	−	0.865646i	$-0.666908\pi$
$631$	−25.1527	−1.00131	−0.500657	+	0.865646i	$0.666908\pi$
$632$	25.2416	1.00406
$633$	−66.6794	−2.65027
$634$	−48.7787	−1.93725
$635$	−19.4715	−0.772703
$636$	−0.756680	−0.0300043
$637$	13.3726	0.529841
$638$	−7.99449	−0.316505
$639$	22.6718	0.896881
$640$	−18.9858	−0.750482
$641$	−33.9530	−1.34106	−0.670531	−	0.741881i	$-0.733934\pi$
$641$	−33.9530	−1.34106	−0.670531	+	0.741881i	$0.733934\pi$
$642$	41.0163	1.61878
$643$	−10.4416	−0.411778	−0.205889	−	0.978575i	$-0.566009\pi$
$643$	−10.4416	−0.411778	−0.205889	+	0.978575i	$0.566009\pi$
$644$	1.34546	0.0530186
$645$	−40.1231	−1.57984
$646$	−12.1199	−0.476853
$647$	1.28801	0.0506370	0.0253185	−	0.999679i	$-0.491940\pi$
$647$	1.28801	0.0506370	0.0253185	+	0.999679i	$0.491940\pi$
$648$	−29.0553	−1.14140
$649$	5.44887	0.213887
$650$	9.45889	0.371008
$651$	76.7016	3.00617
$652$	−0.0702533	−0.00275133
$653$	−9.35507	−0.366092	−0.183046	−	0.983104i	$-0.558596\pi$
$653$	−9.35507	−0.366092	−0.183046	+	0.983104i	$0.558596\pi$
$654$	−2.94622	−0.115206
$655$	13.1807	0.515012
$656$	−41.0865	−1.60416
$657$	28.2681	1.10284
$658$	−8.47712	−0.330472
$659$	3.13916	0.122284	0.0611422	−	0.998129i	$-0.480526\pi$
$659$	3.13916	0.122284	0.0611422	+	0.998129i	$0.480526\pi$
$660$	−0.128027	−0.00498345
$661$	25.5931	0.995454	0.497727	−	0.867334i	$-0.334168\pi$
$661$	25.5931	0.995454	0.497727	+	0.867334i	$0.334168\pi$
$662$	−12.4381	−0.483420
$663$	−44.6073	−1.73241
$664$	−2.62486	−0.101864
$665$	−6.85951	−0.266001
$666$	0.157582	0.00610620
$667$	−64.5063	−2.49770
$668$	−0.558312	−0.0216017
$669$	45.0658	1.74234
$670$	−0.298513	−0.0115326
$671$	−5.89996	−0.227766
$672$	2.20489	0.0850554
$673$	−13.4391	−0.518040	−0.259020	−	0.965872i	$-0.583400\pi$
$673$	−13.4391	−0.518040	−0.259020	+	0.965872i	$0.583400\pi$
$674$	35.5146	1.36797
$675$	3.20066	0.123193
$676$	−0.255090	−0.00981117
$677$	37.5397	1.44277	0.721383	−	0.692536i	$-0.243507\pi$
$677$	37.5397	1.44277	0.721383	+	0.692536i	$0.243507\pi$
$678$	48.0902	1.84689
$679$	34.6194	1.32857
$680$	−31.1314	−1.19383
$681$	−18.2964	−0.701119
$682$	9.55102	0.365727
$683$	−19.9976	−0.765188	−0.382594	−	0.923917i	$-0.624969\pi$
$683$	−19.9976	−0.765188	−0.382594	+	0.923917i	$0.624969\pi$
$684$	−0.145327	−0.00555670
$685$	−2.91492	−0.111373
$686$	10.8254	0.413315
$687$	15.0773	0.575234
$688$	43.5279	1.65949
$689$	−18.5804	−0.707857
$690$	−43.4120	−1.65267
$691$	37.6109	1.43078	0.715392	−	0.698723i	$-0.246248\pi$
$691$	37.6109	1.43078	0.715392	+	0.698723i	$0.246248\pi$
$692$	−0.440601	−0.0167491
$693$	−5.78325	−0.219688
$694$	−20.5539	−0.780216
$695$	−4.82208	−0.182912
$696$	−52.2031	−1.97875
$697$	−68.9743	−2.61259
$698$	−1.55744	−0.0589499
$699$	63.7319	2.41056
$700$	−0.397056	−0.0150073
$701$	36.2517	1.36921	0.684605	−	0.728914i	$-0.259975\pi$
$701$	36.2517	1.36921	0.684605	+	0.728914i	$0.259975\pi$
$702$	5.38488	0.203239
$703$	0.0560290	0.00211317
$704$	−5.42331	−0.204399
$705$	6.50864	0.245130
$706$	−29.4920	−1.10994
$707$	−58.3112	−2.19302
$708$	−0.888982	−0.0334100
$709$	7.64415	0.287082	0.143541	−	0.989644i	$-0.454151\pi$
$709$	7.64415	0.287082	0.143541	+	0.989644i	$0.454151\pi$
$710$	−21.7403	−0.815898
$711$	21.8731	0.820305
$712$	−47.1034	−1.76527
$713$	77.0657	2.88613
$714$	78.6890	2.94486
$715$	−3.14372	−0.117569
$716$	0.413985	0.0154714
$717$	12.2729	0.458338
$718$	29.3619	1.09578
$719$	−15.7591	−0.587716	−0.293858	−	0.955849i	$-0.594939\pi$
$719$	−15.7591	−0.587716	−0.293858	+	0.955849i	$0.594939\pi$
$720$	−16.0696	−0.598878
$721$	−13.1109	−0.488275
$722$	25.0241	0.931302
$723$	−3.46036	−0.128692
$724$	0.0580143	0.00215609
$725$	19.0363	0.706992
$726$	35.0432	1.30057
$727$	30.7425	1.14018	0.570088	−	0.821584i	$-0.306909\pi$
$727$	30.7425	1.14018	0.570088	+	0.821584i	$0.306909\pi$
$728$	26.7367	0.990927
$729$	−15.7500	−0.583332
$730$	−27.1067	−1.00327
$731$	73.0727	2.70269
$732$	0.962577	0.0355779
$733$	−31.7320	−1.17205	−0.586023	−	0.810294i	$-0.699307\pi$
$733$	−31.7320	−1.17205	−0.586023	+	0.810294i	$0.699307\pi$
$734$	−36.5778	−1.35011
$735$	18.1120	0.668070
$736$	2.21536	0.0816591
$737$	−0.0894844	−0.00329620
$738$	−34.7558	−1.27938
$739$	9.79630	0.360363	0.180181	−	0.983633i	$-0.442332\pi$
$739$	9.79630	0.360363	0.180181	+	0.983633i	$0.442332\pi$
$740$	−0.00359577	−0.000132183 0
$741$	−7.99193	−0.293591
$742$	32.7765	1.20326
$743$	49.5259	1.81693	0.908464	−	0.417963i	$-0.137256\pi$
$743$	49.5259	1.81693	0.908464	+	0.417963i	$0.137256\pi$
$744$	62.3670	2.28648
$745$	−0.000455984 0	−1.67060e−5 0
$746$	−0.195268	−0.00714929
$747$	−2.27458	−0.0832224
$748$	0.233165	0.00852536
$749$	−42.2776	−1.54479
$750$	39.8264	1.45426
$751$	23.7905	0.868128	0.434064	−	0.900882i	$-0.357079\pi$
$751$	23.7905	0.868128	0.434064	+	0.900882i	$0.357079\pi$
$752$	−7.06097	−0.257487
$753$	0.303888	0.0110743
$754$	32.0273	1.16636
$755$	9.53589	0.347047
$756$	−0.226041	−0.00822104
$757$	−3.18511	−0.115765	−0.0578824	−	0.998323i	$-0.518435\pi$
$757$	−3.18511	−0.115765	−0.0578824	+	0.998323i	$0.518435\pi$
$758$	−5.74936	−0.208826
$759$	−13.0135	−0.472359
$760$	−5.57756	−0.202319
$761$	12.5094	0.453465	0.226732	−	0.973957i	$-0.427196\pi$
$761$	12.5094	0.453465	0.226732	+	0.973957i	$0.427196\pi$
$762$	40.0189	1.44973
$763$	3.03682	0.109940
$764$	0.860148	0.0311190
$765$	−26.9769	−0.975352
$766$	30.3371	1.09613
$767$	−21.8291	−0.788202
$768$	2.72243	0.0982371
$769$	−43.5670	−1.57107	−0.785534	−	0.618819i	$-0.787612\pi$
$769$	−43.5670	−1.57107	−0.785534	+	0.618819i	$0.787612\pi$
$770$	5.54565	0.199851
$771$	38.8162	1.39793
$772$	0.840014	0.0302328
$773$	−12.4604	−0.448170	−0.224085	−	0.974570i	$-0.571939\pi$
$773$	−12.4604	−0.448170	−0.224085	+	0.974570i	$0.571939\pi$
$774$	36.8210	1.32350
$775$	−22.7427	−0.816942
$776$	28.1494	1.01051
$777$	−0.363770	−0.0130502
$778$	16.3858	0.587458
$779$	−12.3576	−0.442756
$780$	0.512898	0.0183647
$781$	−6.51702	−0.233197
$782$	79.0626	2.82727
$783$	10.8372	0.387292
$784$	−19.6489	−0.701748
$785$	15.4683	0.552088
$786$	−27.0897	−0.966257
$787$	4.52401	0.161264	0.0806318	−	0.996744i	$-0.474306\pi$
$787$	4.52401	0.161264	0.0806318	+	0.996744i	$0.474306\pi$
$788$	−0.348570	−0.0124173
$789$	−59.0574	−2.10250
$790$	−20.9744	−0.746237
$791$	−49.5690	−1.76247
$792$	−4.70243	−0.167094
$793$	23.6362	0.839347
$794$	−50.7932	−1.80258
$795$	−25.1655	−0.892527
$796$	−0.348311	−0.0123456
$797$	5.17026	0.183140	0.0915700	−	0.995799i	$-0.470811\pi$
$797$	5.17026	0.183140	0.0915700	+	0.995799i	$0.470811\pi$
$798$	14.0981	0.499066
$799$	−11.8536	−0.419352
$800$	−0.653769	−0.0231142
$801$	−40.8175	−1.44221
$802$	−10.1674	−0.359023
$803$	−8.12571	−0.286750
$804$	0.0145994	0.000514880 0
$805$	44.7470	1.57712
$806$	−38.2629	−1.34775
$807$	64.2000	2.25995
$808$	−47.4136	−1.66800
$809$	−32.0872	−1.12813	−0.564063	−	0.825732i	$-0.690762\pi$
$809$	−32.0872	−1.12813	−0.564063	+	0.825732i	$0.690762\pi$
$810$	24.1434	0.848314
$811$	−0.161609	−0.00567486	−0.00283743	−	0.999996i	$-0.500903\pi$
$811$	−0.161609	−0.00567486	−0.00283743	+	0.999996i	$0.500903\pi$
$812$	−1.34441	−0.0471795
$813$	19.3453	0.678468
$814$	−0.0452972	−0.00158767
$815$	−2.33647	−0.0818428
$816$	65.5436	2.29448
$817$	13.0918	0.458026
$818$	−23.8305	−0.833215
$819$	23.1687	0.809579
$820$	0.793071	0.0276952
$821$	28.5388	0.996009	0.498005	−	0.867174i	$-0.334066\pi$
$821$	28.5388	0.996009	0.498005	+	0.867174i	$0.334066\pi$
$822$	5.99092	0.208957
$823$	25.6473	0.894010	0.447005	−	0.894531i	$-0.352491\pi$
$823$	25.6473	0.894010	0.447005	+	0.894531i	$0.352491\pi$
$824$	−10.6606	−0.371380
$825$	3.84038	0.133705
$826$	38.5073	1.33984
$827$	−5.41254	−0.188212	−0.0941062	−	0.995562i	$-0.529999\pi$
$827$	−5.41254	−0.188212	−0.0941062	+	0.995562i	$0.529999\pi$
$828$	0.948016	0.0329458
$829$	42.5786	1.47882	0.739408	−	0.673258i	$-0.235106\pi$
$829$	42.5786	1.47882	0.739408	+	0.673258i	$0.235106\pi$
$830$	2.18112	0.0757079
$831$	−33.7096	−1.16937
$832$	21.7267	0.753237
$833$	−32.9858	−1.14289
$834$	9.91062	0.343177
$835$	−18.5682	−0.642578
$836$	0.0417743	0.00144479
$837$	−12.9473	−0.447523
$838$	−26.8701	−0.928211
$839$	−39.9785	−1.38021	−0.690106	−	0.723708i	$-0.742436\pi$
$839$	−39.9785	−1.38021	−0.690106	+	0.723708i	$0.742436\pi$
$840$	36.2124	1.24945
$841$	35.4559	1.22262
$842$	3.06762	0.105717
$843$	−59.9599	−2.06513
$844$	−1.39630	−0.0480625
$845$	−8.48372	−0.291849
$846$	−5.97300	−0.205356
$847$	−36.1208	−1.24113
$848$	27.3010	0.937521
$849$	−0.0570776	−0.00195890
$850$	−23.3320	−0.800281
$851$	−0.365497	−0.0125291
$852$	1.06325	0.0364264
$853$	−13.3730	−0.457884	−0.228942	−	0.973440i	$-0.573527\pi$
$853$	−13.3730	−0.457884	−0.228942	+	0.973440i	$0.573527\pi$
$854$	−41.6952	−1.42678
$855$	−4.83323	−0.165293
$856$	−34.3765	−1.17496
$857$	34.8819	1.19154	0.595772	−	0.803154i	$-0.296846\pi$
$857$	34.8819	1.19154	0.595772	+	0.803154i	$0.296846\pi$
$858$	6.46116	0.220580
$859$	6.79181	0.231733	0.115867	−	0.993265i	$-0.463035\pi$
$859$	6.79181	0.231733	0.115867	+	0.993265i	$0.463035\pi$
$860$	−0.840195	−0.0286504
$861$	80.2317	2.73429
$862$	−13.4808	−0.459157
$863$	13.5354	0.460749	0.230375	−	0.973102i	$-0.426005\pi$
$863$	13.5354	0.460749	0.230375	+	0.973102i	$0.426005\pi$
$864$	−0.372186	−0.0126620
$865$	−14.6534	−0.498230
$866$	28.8679	0.980970
$867$	70.4535	2.39273
$868$	1.60617	0.0545168
$869$	−6.28745	−0.213287
$870$	43.3780	1.47065
$871$	0.358489	0.0121469
$872$	2.46928	0.0836204
$873$	24.3929	0.825575
$874$	14.1650	0.479138
$875$	−41.0512	−1.38778
$876$	1.32571	0.0447915
$877$	−34.3058	−1.15842	−0.579212	−	0.815177i	$-0.696640\pi$
$877$	−34.3058	−1.15842	−0.579212	+	0.815177i	$0.696640\pi$
$878$	23.9389	0.807898
$879$	6.01105	0.202748
$880$	4.61922	0.155714
$881$	−5.40002	−0.181931	−0.0909657	−	0.995854i	$-0.528995\pi$
$881$	−5.40002	−0.181931	−0.0909657	+	0.995854i	$0.528995\pi$
$882$	−16.6214	−0.559671
$883$	−30.0119	−1.00998	−0.504990	−	0.863125i	$-0.668504\pi$
$883$	−30.0119	−1.00998	−0.504990	+	0.863125i	$0.668504\pi$
$884$	−0.934098	−0.0314171
$885$	−29.5655	−0.993834
$886$	4.55092	0.152891
$887$	15.3759	0.516272	0.258136	−	0.966109i	$-0.416892\pi$
$887$	15.3759	0.516272	0.258136	+	0.966109i	$0.416892\pi$
$888$	−0.295786	−0.00992592
$889$	−41.2496	−1.38347
$890$	39.1405	1.31199
$891$	7.23741	0.242462
$892$	0.943698	0.0315973
$893$	−2.12372	−0.0710676
$894$	0.000937164 0	3.13435e−5 0
$895$	13.7682	0.460220
$896$	−40.2208	−1.34368
$897$	52.1341	1.74071
$898$	−27.5673	−0.919932
$899$	−77.0054	−2.56828
$900$	−0.279767	−0.00932556
$901$	45.8318	1.52688
$902$	9.99060	0.332651
$903$	−84.9991	−2.82859
$904$	−40.3052	−1.34053
$905$	1.92942	0.0641362
$906$	−19.5987	−0.651123
$907$	1.35116	0.0448646	0.0224323	−	0.999748i	$-0.492859\pi$
$907$	1.35116	0.0448646	0.0224323	+	0.999748i	$0.492859\pi$
$908$	−0.383135	−0.0127148
$909$	−41.0862	−1.36274
$910$	−22.2168	−0.736479
$911$	12.2879	0.407116	0.203558	−	0.979063i	$-0.434749\pi$
$911$	12.2879	0.407116	0.203558	+	0.979063i	$0.434749\pi$
$912$	11.7429	0.388847
$913$	0.653829	0.0216386
$914$	−45.0411	−1.48983
$915$	32.0131	1.05832
$916$	0.315725	0.0104319
$917$	27.9227	0.922090
$918$	−13.2827	−0.438396
$919$	−26.0910	−0.860664	−0.430332	−	0.902671i	$-0.641604\pi$
$919$	−26.0910	−0.860664	−0.430332	+	0.902671i	$0.641604\pi$
$920$	36.3843	1.19956
$921$	−30.1604	−0.993818
$922$	−5.81615	−0.191545
$923$	26.1083	0.859364
$924$	−0.271220	−0.00892250
$925$	0.107861	0.00354645
$926$	−19.4968	−0.640704
$927$	−9.23796	−0.303415
$928$	−2.21362	−0.0726658
$929$	32.0841	1.05264	0.526322	−	0.850285i	$-0.323571\pi$
$929$	32.0841	1.05264	0.526322	+	0.850285i	$0.323571\pi$
$930$	−51.8237	−1.69937
$931$	−5.90980	−0.193686
$932$	1.33457	0.0437154
$933$	−18.8748	−0.617935
$934$	−4.61267	−0.150931
$935$	7.75454	0.253601
$936$	18.8387	0.615763
$937$	23.3834	0.763903	0.381952	−	0.924182i	$-0.375252\pi$
$937$	23.3834	0.763903	0.381952	+	0.924182i	$0.375252\pi$
$938$	−0.632388	−0.0206482
$939$	23.3616	0.762378
$940$	0.136294	0.00444542
$941$	12.8727	0.419639	0.209820	−	0.977740i	$-0.432712\pi$
$941$	12.8727	0.419639	0.209820	+	0.977740i	$0.432712\pi$
$942$	−31.7914	−1.03582
$943$	80.6126	2.62511
$944$	32.0744	1.04393
$945$	−7.51762	−0.244548
$946$	−10.5842	−0.344123
$947$	22.3917	0.727634	0.363817	−	0.931470i	$-0.381473\pi$
$947$	22.3917	0.727634	0.363817	+	0.931470i	$0.381473\pi$
$948$	1.02580	0.0333163
$949$	32.5529	1.05671
$950$	−4.18020	−0.135624
$951$	79.3401	2.57278
$952$	−65.9506	−2.13747
$953$	28.6568	0.928285	0.464143	−	0.885760i	$-0.346362\pi$
$953$	28.6568	0.928285	0.464143	+	0.885760i	$0.346362\pi$
$954$	23.0944	0.747709
$955$	28.6065	0.925686
$956$	0.256999	0.00831195
$957$	13.0033	0.420337
$958$	9.78868	0.316258
$959$	−6.17515	−0.199406
$960$	29.4268	0.949746
$961$	60.9984	1.96769
$962$	0.181468	0.00585077
$963$	−29.7889	−0.959935
$964$	−0.0724616	−0.00233383
$965$	27.9370	0.899322
$966$	−91.9665	−2.95898
$967$	35.0100	1.12585	0.562924	−	0.826509i	$-0.309677\pi$
$967$	35.0100	1.12585	0.562924	+	0.826509i	$0.309677\pi$
$968$	−29.3703	−0.943997
$969$	19.7135	0.633288
$970$	−23.3907	−0.751031
$971$	29.8123	0.956724	0.478362	−	0.878163i	$-0.341231\pi$
$971$	29.8123	0.956724	0.478362	+	0.878163i	$0.341231\pi$
$972$	−0.983357	−0.0315412
$973$	−10.2154	−0.327490
$974$	32.2652	1.03384
$975$	−15.3852	−0.492721
$976$	−34.7298	−1.11167
$977$	−39.4944	−1.26354	−0.631769	−	0.775157i	$-0.717671\pi$
$977$	−39.4944	−1.26354	−0.631769	+	0.775157i	$0.717671\pi$
$978$	4.80204	0.153552
$979$	11.7330	0.374989
$980$	0.379273	0.0121154
$981$	2.13975	0.0683171
$982$	35.0706	1.11915
$983$	10.7749	0.343667	0.171834	−	0.985126i	$-0.445031\pi$
$983$	10.7749	0.343667	0.171834	+	0.985126i	$0.445031\pi$
$984$	65.2374	2.07969
$985$	−11.5927	−0.369373
$986$	−79.0007	−2.51590
$987$	13.7883	0.438887
$988$	−0.167355	−0.00532426
$989$	−85.4027	−2.71565
$990$	3.90748	0.124188
$991$	−25.6135	−0.813640	−0.406820	−	0.913508i	$-0.633362\pi$
$991$	−25.6135	−0.813640	−0.406820	+	0.913508i	$0.633362\pi$
$992$	2.64462	0.0839666
$993$	20.2310	0.642010
$994$	−46.0559	−1.46081
$995$	−11.5840	−0.367239
$996$	−0.106672	−0.00338003
$997$	−8.06918	−0.255553	−0.127777	−	0.991803i	$-0.540784\pi$
$997$	−8.06918	−0.255553	−0.127777	+	0.991803i	$0.540784\pi$
$998$	6.92862	0.219322
$999$	0.0614045	0.00194275

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.f.1.8	✓	26
3.2	odd	2		4527.2.a.o.1.19		26
4.3	odd	2		8048.2.a.u.1.6		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.f.1.8	✓	26	1.1	even	1	trivial
4527.2.a.o.1.19		26	3.2	odd	2
8048.2.a.u.1.6		26	4.3	odd	2

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:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.a (trivial)

\(f(q)\)	\(=\)	\(q-1.43135 q^{2} +2.32813 q^{3} +0.0487521 q^{4} +1.62138 q^{5} -3.33236 q^{6} +3.43484 q^{7} +2.79291 q^{8} +2.42020 q^{9} +O(q^{10})\)	\(q-1.43135 q^{2} +2.32813 q^{3} +0.0487521 q^{4} +1.62138 q^{5} -3.33236 q^{6} +3.43484 q^{7} +2.79291 q^{8} +2.42020 q^{9} -2.32076 q^{10} -0.695688 q^{11} +0.113501 q^{12} +2.78704 q^{13} -4.91645 q^{14} +3.77480 q^{15} -4.09513 q^{16} -6.87472 q^{17} -3.46414 q^{18} -1.23169 q^{19} +0.0790460 q^{20} +7.99676 q^{21} +0.995771 q^{22} +8.03473 q^{23} +6.50227 q^{24} -2.37111 q^{25} -3.98922 q^{26} -1.34986 q^{27} +0.167456 q^{28} -8.02844 q^{29} -5.40304 q^{30} +9.59158 q^{31} +0.275723 q^{32} -1.61965 q^{33} +9.84011 q^{34} +5.56920 q^{35} +0.117990 q^{36} -0.0454896 q^{37} +1.76297 q^{38} +6.48860 q^{39} +4.52838 q^{40} +10.0330 q^{41} -11.4461 q^{42} -10.6292 q^{43} -0.0339163 q^{44} +3.92407 q^{45} -11.5005 q^{46} +1.72424 q^{47} -9.53400 q^{48} +4.79813 q^{49} +3.39388 q^{50} -16.0053 q^{51} +0.135874 q^{52} -6.66671 q^{53} +1.93211 q^{54} -1.12798 q^{55} +9.59320 q^{56} -2.86753 q^{57} +11.4915 q^{58} -7.83234 q^{59} +0.184029 q^{60} +8.48076 q^{61} -13.7289 q^{62} +8.31299 q^{63} +7.79560 q^{64} +4.51887 q^{65} +2.31829 q^{66} +0.128627 q^{67} -0.335157 q^{68} +18.7059 q^{69} -7.97145 q^{70} +9.36773 q^{71} +6.75940 q^{72} +11.6801 q^{73} +0.0651114 q^{74} -5.52026 q^{75} -0.0600474 q^{76} -2.38958 q^{77} -9.28744 q^{78} +9.03774 q^{79} -6.63978 q^{80} -10.4032 q^{81} -14.3607 q^{82} -0.939830 q^{83} +0.389859 q^{84} -11.1466 q^{85} +15.2141 q^{86} -18.6913 q^{87} -1.94300 q^{88} -16.8653 q^{89} -5.61671 q^{90} +9.57305 q^{91} +0.391710 q^{92} +22.3305 q^{93} -2.46798 q^{94} -1.99704 q^{95} +0.641919 q^{96} +10.0789 q^{97} -6.86778 q^{98} -1.68370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9 + 4 * q^10 - 17 * q^11 + 19 * q^12 + 14 * q^13 + q^14 + 18 * q^15 + 48 * q^16 + 17 * q^17 - 10 * q^18 - 22 * q^19 - 19 * q^20 - 16 * q^21 + 38 * q^22 + 27 * q^23 - 9 * q^24 + 93 * q^25 + q^26 + 31 * q^27 - 9 * q^28 + 13 * q^29 - 28 * q^30 + 26 * q^31 + 5 * q^32 + 6 * q^33 - 32 * q^34 - 22 * q^35 + 52 * q^36 + 55 * q^37 - 24 * q^38 - 15 * q^39 - 7 * q^40 + 24 * q^41 - 50 * q^42 + 20 * q^43 - 27 * q^44 - 8 * q^45 + 6 * q^46 - 25 * q^47 + 29 * q^48 + 65 * q^49 - 16 * q^50 + 7 * q^51 + 32 * q^52 + 30 * q^53 - 82 * q^54 + 25 * q^55 + 3 * q^56 + 9 * q^57 + 58 * q^58 - 26 * q^59 - 68 * q^60 + 15 * q^61 - 12 * q^62 - 19 * q^63 + 44 * q^64 + 20 * q^65 - 55 * q^66 - 20 * q^67 - 4 * q^68 - 27 * q^69 + 2 * q^70 - 35 * q^71 - 26 * q^72 + 38 * q^73 - 59 * q^74 + 2 * q^75 - 42 * q^76 - 6 * q^77 - 47 * q^78 + 21 * q^79 - 100 * q^80 + 70 * q^81 - 59 * q^82 - 48 * q^83 - 116 * q^84 + 6 * q^85 - 7 * q^86 - 9 * q^87 + 106 * q^88 - 5 * q^89 - 118 * q^90 - 24 * q^91 + 26 * q^92 - 8 * q^93 - 22 * q^94 + 43 * q^95 - 100 * q^96 + 142 * q^97 - 38 * q^98 - 50 * q^99

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