LMFDB - Embedded newform 4017.2.a.k.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.18767 q^{2} +1.00000 q^{3} -0.589432 q^{4} +3.30029 q^{5} +1.18767 q^{6} +1.53427 q^{7} -3.07540 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.18767 q^{2} +1.00000 q^{3} -0.589432 q^{4} +3.30029 q^{5} +1.18767 q^{6} +1.53427 q^{7} -3.07540 q^{8} +1.00000 q^{9} +3.91966 q^{10} +5.55819 q^{11} -0.589432 q^{12} +1.00000 q^{13} +1.82221 q^{14} +3.30029 q^{15} -2.47371 q^{16} -2.82703 q^{17} +1.18767 q^{18} +1.07094 q^{19} -1.94530 q^{20} +1.53427 q^{21} +6.60131 q^{22} -2.30711 q^{23} -3.07540 q^{24} +5.89190 q^{25} +1.18767 q^{26} +1.00000 q^{27} -0.904345 q^{28} -5.84262 q^{29} +3.91966 q^{30} +3.69248 q^{31} +3.21284 q^{32} +5.55819 q^{33} -3.35759 q^{34} +5.06352 q^{35} -0.589432 q^{36} +7.77972 q^{37} +1.27193 q^{38} +1.00000 q^{39} -10.1497 q^{40} -0.611788 q^{41} +1.82221 q^{42} +8.51311 q^{43} -3.27617 q^{44} +3.30029 q^{45} -2.74010 q^{46} +1.59873 q^{47} -2.47371 q^{48} -4.64603 q^{49} +6.99765 q^{50} -2.82703 q^{51} -0.589432 q^{52} +8.75545 q^{53} +1.18767 q^{54} +18.3436 q^{55} -4.71848 q^{56} +1.07094 q^{57} -6.93912 q^{58} -4.74342 q^{59} -1.94530 q^{60} -12.4363 q^{61} +4.38546 q^{62} +1.53427 q^{63} +8.76322 q^{64} +3.30029 q^{65} +6.60131 q^{66} -6.68080 q^{67} +1.66634 q^{68} -2.30711 q^{69} +6.01380 q^{70} -8.98566 q^{71} -3.07540 q^{72} +8.58241 q^{73} +9.23977 q^{74} +5.89190 q^{75} -0.631249 q^{76} +8.52773 q^{77} +1.18767 q^{78} -1.83010 q^{79} -8.16394 q^{80} +1.00000 q^{81} -0.726604 q^{82} -8.52138 q^{83} -0.904345 q^{84} -9.33001 q^{85} +10.1108 q^{86} -5.84262 q^{87} -17.0936 q^{88} +12.3784 q^{89} +3.91966 q^{90} +1.53427 q^{91} +1.35989 q^{92} +3.69248 q^{93} +1.89876 q^{94} +3.53443 q^{95} +3.21284 q^{96} -6.02554 q^{97} -5.51797 q^{98} +5.55819 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * 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 $

$2$	1.18767	0.839812	0.419906	−	0.907568i	$-0.362063\pi$
$2$	1.18767	0.839812	0.419906	+	0.907568i	$0.362063\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.589432	−0.294716
$5$	3.30029	1.47593	0.737967	−	0.674837i	$-0.235786\pi$
$5$	3.30029	1.47593	0.737967	+	0.674837i	$0.235786\pi$
$6$	1.18767	0.484866
$7$	1.53427	0.579898	0.289949	−	0.957042i	$-0.406362\pi$
$7$	1.53427	0.579898	0.289949	+	0.957042i	$0.406362\pi$
$8$	−3.07540	−1.08732
$9$	1.00000	0.333333
$10$	3.91966	1.23951
$11$	5.55819	1.67586	0.837928	−	0.545781i	$-0.183767\pi$
$11$	5.55819	1.67586	0.837928	+	0.545781i	$0.183767\pi$
$12$	−0.589432	−0.170154
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.82221	0.487005
$15$	3.30029	0.852131
$16$	−2.47371	−0.618426
$17$	−2.82703	−0.685656	−0.342828	−	0.939398i	$-0.611385\pi$
$17$	−2.82703	−0.685656	−0.342828	+	0.939398i	$0.611385\pi$
$18$	1.18767	0.279937
$19$	1.07094	0.245692	0.122846	−	0.992426i	$-0.460798\pi$
$19$	1.07094	0.245692	0.122846	+	0.992426i	$0.460798\pi$
$20$	−1.94530	−0.434981
$21$	1.53427	0.334804
$22$	6.60131	1.40740
$23$	−2.30711	−0.481066	−0.240533	−	0.970641i	$-0.577322\pi$
$23$	−2.30711	−0.481066	−0.240533	+	0.970641i	$0.577322\pi$
$24$	−3.07540	−0.627763
$25$	5.89190	1.17838
$26$	1.18767	0.232922
$27$	1.00000	0.192450
$28$	−0.904345	−0.170905
$29$	−5.84262	−1.08495	−0.542474	−	0.840073i	$-0.682512\pi$
$29$	−5.84262	−1.08495	−0.542474	+	0.840073i	$0.682512\pi$
$30$	3.91966	0.715629
$31$	3.69248	0.663189	0.331594	−	0.943422i	$-0.392413\pi$
$31$	3.69248	0.663189	0.331594	+	0.943422i	$0.392413\pi$
$32$	3.21284	0.567956
$33$	5.55819	0.967556
$34$	−3.35759	−0.575822
$35$	5.06352	0.855891
$36$	−0.589432	−0.0982387
$37$	7.77972	1.27898	0.639489	−	0.768800i	$-0.279146\pi$
$37$	7.77972	1.27898	0.639489	+	0.768800i	$0.279146\pi$
$38$	1.27193	0.206335
$39$	1.00000	0.160128
$40$	−10.1497	−1.60481
$41$	−0.611788	−0.0955452	−0.0477726	−	0.998858i	$-0.515212\pi$
$41$	−0.611788	−0.0955452	−0.0477726	+	0.998858i	$0.515212\pi$
$42$	1.82221	0.281172
$43$	8.51311	1.29824	0.649119	−	0.760687i	$-0.275138\pi$
$43$	8.51311	1.29824	0.649119	+	0.760687i	$0.275138\pi$
$44$	−3.27617	−0.493902
$45$	3.30029	0.491978
$46$	−2.74010	−0.404005
$47$	1.59873	0.233198	0.116599	−	0.993179i	$-0.462801\pi$
$47$	1.59873	0.233198	0.116599	+	0.993179i	$0.462801\pi$
$48$	−2.47371	−0.357049
$49$	−4.64603	−0.663719
$50$	6.99765	0.989617
$51$	−2.82703	−0.395863
$52$	−0.589432	−0.0817395
$53$	8.75545	1.20265	0.601327	−	0.799003i	$-0.294639\pi$
$53$	8.75545	1.20265	0.601327	+	0.799003i	$0.294639\pi$
$54$	1.18767	0.161622
$55$	18.3436	2.47345
$56$	−4.71848	−0.630533
$57$	1.07094	0.141850
$58$	−6.93912	−0.911152
$59$	−4.74342	−0.617540	−0.308770	−	0.951137i	$-0.599917\pi$
$59$	−4.74342	−0.617540	−0.308770	+	0.951137i	$0.599917\pi$
$60$	−1.94530	−0.251137
$61$	−12.4363	−1.59231	−0.796155	−	0.605093i	$-0.793136\pi$
$61$	−12.4363	−1.59231	−0.796155	+	0.605093i	$0.793136\pi$
$62$	4.38546	0.556954
$63$	1.53427	0.193299
$64$	8.76322	1.09540
$65$	3.30029	0.409350
$66$	6.60131	0.812565
$67$	−6.68080	−0.816190	−0.408095	−	0.912940i	$-0.633807\pi$
$67$	−6.68080	−0.816190	−0.408095	+	0.912940i	$0.633807\pi$
$68$	1.66634	0.202074
$69$	−2.30711	−0.277744
$70$	6.01380	0.718787
$71$	−8.98566	−1.06640	−0.533201	−	0.845989i	$-0.679011\pi$
$71$	−8.98566	−1.06640	−0.533201	+	0.845989i	$0.679011\pi$
$72$	−3.07540	−0.362439
$73$	8.58241	1.00450	0.502248	−	0.864724i	$-0.332507\pi$
$73$	8.58241	1.00450	0.502248	+	0.864724i	$0.332507\pi$
$74$	9.23977	1.07410
$75$	5.89190	0.680338
$76$	−0.631249	−0.0724093
$77$	8.52773	0.971825
$78$	1.18767	0.134478
$79$	−1.83010	−0.205902	−0.102951	−	0.994686i	$-0.532828\pi$
$79$	−1.83010	−0.205902	−0.102951	+	0.994686i	$0.532828\pi$
$80$	−8.16394	−0.912756
$81$	1.00000	0.111111
$82$	−0.726604	−0.0802400
$83$	−8.52138	−0.935343	−0.467671	−	0.883902i	$-0.654907\pi$
$83$	−8.52138	−0.935343	−0.467671	+	0.883902i	$0.654907\pi$
$84$	−0.904345	−0.0986721
$85$	−9.33001	−1.01198
$86$	10.1108	1.09028
$87$	−5.84262	−0.626395
$88$	−17.0936	−1.82219
$89$	12.3784	1.31211	0.656053	−	0.754715i	$-0.272225\pi$
$89$	12.3784	1.31211	0.656053	+	0.754715i	$0.272225\pi$
$90$	3.91966	0.413169
$91$	1.53427	0.160835
$92$	1.35989	0.141778
$93$	3.69248	0.382892
$94$	1.89876	0.195843
$95$	3.53443	0.362625
$96$	3.21284	0.327910
$97$	−6.02554	−0.611801	−0.305901	−	0.952063i	$-0.598958\pi$
$97$	−6.02554	−0.611801	−0.305901	+	0.952063i	$0.598958\pi$
$98$	−5.51797	−0.557399
$99$	5.55819	0.558619
$100$	−3.47287	−0.347287
$101$	−1.43580	−0.142867	−0.0714337	−	0.997445i	$-0.522757\pi$
$101$	−1.43580	−0.142867	−0.0714337	+	0.997445i	$0.522757\pi$
$102$	−3.35759	−0.332451
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−3.07540	−0.301568
$105$	5.06352	0.494149
$106$	10.3986	1.01000
$107$	−16.9235	−1.63605	−0.818026	−	0.575181i	$-0.804932\pi$
$107$	−16.9235	−1.63605	−0.818026	+	0.575181i	$0.804932\pi$
$108$	−0.589432	−0.0567181
$109$	−3.23938	−0.310276	−0.155138	−	0.987893i	$-0.549582\pi$
$109$	−3.23938	−0.310276	−0.155138	+	0.987893i	$0.549582\pi$
$110$	21.7862	2.07723
$111$	7.77972	0.738419
$112$	−3.79532	−0.358624
$113$	7.41466	0.697513	0.348757	−	0.937213i	$-0.386604\pi$
$113$	7.41466	0.697513	0.348757	+	0.937213i	$0.386604\pi$
$114$	1.27193	0.119127
$115$	−7.61414	−0.710022
$116$	3.44383	0.319751
$117$	1.00000	0.0924500
$118$	−5.63363	−0.518618
$119$	−4.33741	−0.397610
$120$	−10.1497	−0.926537
$121$	19.8934	1.80849
$122$	−14.7703	−1.33724
$123$	−0.611788	−0.0551630
$124$	−2.17647	−0.195452
$125$	2.94352	0.263277
$126$	1.82221	0.162335
$127$	−12.9543	−1.14951	−0.574756	−	0.818325i	$-0.694903\pi$
$127$	−12.9543	−1.14951	−0.574756	+	0.818325i	$0.694903\pi$
$128$	3.98216	0.351976
$129$	8.51311	0.749538
$130$	3.91966	0.343777
$131$	−3.15646	−0.275782	−0.137891	−	0.990447i	$-0.544032\pi$
$131$	−3.15646	−0.275782	−0.137891	+	0.990447i	$0.544032\pi$
$132$	−3.27617	−0.285154
$133$	1.64311	0.142476
$134$	−7.93461	−0.685446
$135$	3.30029	0.284044
$136$	8.69425	0.745526
$137$	7.31046	0.624575	0.312288	−	0.949988i	$-0.398905\pi$
$137$	7.31046	0.624575	0.312288	+	0.949988i	$0.398905\pi$
$138$	−2.74010	−0.233252
$139$	−3.82072	−0.324070	−0.162035	−	0.986785i	$-0.551806\pi$
$139$	−3.82072	−0.324070	−0.162035	+	0.986785i	$0.551806\pi$
$140$	−2.98460	−0.252245
$141$	1.59873	0.134637
$142$	−10.6720	−0.895576
$143$	5.55819	0.464799
$144$	−2.47371	−0.206142
$145$	−19.2823	−1.60131
$146$	10.1931	0.843587
$147$	−4.64603	−0.383198
$148$	−4.58562	−0.376935
$149$	20.6581	1.69238	0.846188	−	0.532884i	$-0.178892\pi$
$149$	20.6581	1.69238	0.846188	+	0.532884i	$0.178892\pi$
$150$	6.99765	0.571356
$151$	10.9011	0.887118	0.443559	−	0.896245i	$-0.353716\pi$
$151$	10.9011	0.887118	0.443559	+	0.896245i	$0.353716\pi$
$152$	−3.29358	−0.267145
$153$	−2.82703	−0.228552
$154$	10.1282	0.816150
$155$	12.1862	0.978823
$156$	−0.589432	−0.0471923
$157$	−19.8285	−1.58249	−0.791243	−	0.611501i	$-0.790566\pi$
$157$	−19.8285	−1.58249	−0.791243	+	0.611501i	$0.790566\pi$
$158$	−2.17356	−0.172919
$159$	8.75545	0.694353
$160$	10.6033	0.838265
$161$	−3.53972	−0.278969
$162$	1.18767	0.0933124
$163$	10.2500	0.802842	0.401421	−	0.915894i	$-0.368516\pi$
$163$	10.2500	0.802842	0.401421	+	0.915894i	$0.368516\pi$
$164$	0.360607	0.0281587
$165$	18.3436	1.42805
$166$	−10.1206	−0.785512
$167$	−18.6881	−1.44613	−0.723064	−	0.690781i	$-0.757267\pi$
$167$	−18.6881	−1.44613	−0.723064	+	0.690781i	$0.757267\pi$
$168$	−4.71848	−0.364039
$169$	1.00000	0.0769231
$170$	−11.0810	−0.849875
$171$	1.07094	0.0818972
$172$	−5.01790	−0.382611
$173$	20.5469	1.56215	0.781074	−	0.624438i	$-0.214672\pi$
$173$	20.5469	1.56215	0.781074	+	0.624438i	$0.214672\pi$
$174$	−6.93912	−0.526054
$175$	9.03974	0.683340
$176$	−13.7493	−1.03639
$177$	−4.74342	−0.356537
$178$	14.7015	1.10192
$179$	13.1031	0.979370	0.489685	−	0.871899i	$-0.337112\pi$
$179$	13.1031	0.979370	0.489685	+	0.871899i	$0.337112\pi$
$180$	−1.94530	−0.144994
$181$	15.5945	1.15913	0.579565	−	0.814926i	$-0.303223\pi$
$181$	15.5945	1.15913	0.579565	+	0.814926i	$0.303223\pi$
$182$	1.82221	0.135071
$183$	−12.4363	−0.919320
$184$	7.09529	0.523072
$185$	25.6753	1.88769
$186$	4.38546	0.321557
$187$	−15.7132	−1.14906
$188$	−0.942340	−0.0687272
$189$	1.53427	0.111601
$190$	4.19774	0.304536
$191$	25.4368	1.84054	0.920270	−	0.391284i	$-0.127969\pi$
$191$	25.4368	1.84054	0.920270	+	0.391284i	$0.127969\pi$
$192$	8.76322	0.632431
$193$	8.69011	0.625528	0.312764	−	0.949831i	$-0.398745\pi$
$193$	8.69011	0.625528	0.312764	+	0.949831i	$0.398745\pi$
$194$	−7.15638	−0.513798
$195$	3.30029	0.236339
$196$	2.73852	0.195608
$197$	−22.4608	−1.60027	−0.800135	−	0.599821i	$-0.795239\pi$
$197$	−22.4608	−1.60027	−0.800135	+	0.599821i	$0.795239\pi$
$198$	6.60131	0.469135
$199$	15.7871	1.11912	0.559558	−	0.828791i	$-0.310971\pi$
$199$	15.7871	1.11912	0.559558	+	0.828791i	$0.310971\pi$
$200$	−18.1199	−1.28127
$201$	−6.68080	−0.471227
$202$	−1.70526	−0.119982
$203$	−8.96413	−0.629159
$204$	1.66634	0.116667
$205$	−2.01908	−0.141018
$206$	1.18767	0.0827491
$207$	−2.30711	−0.160355
$208$	−2.47371	−0.171521
$209$	5.95251	0.411744
$210$	6.01380	0.414992
$211$	−13.6627	−0.940576	−0.470288	−	0.882513i	$-0.655850\pi$
$211$	−13.6627	−0.940576	−0.470288	+	0.882513i	$0.655850\pi$
$212$	−5.16075	−0.354441
$213$	−8.98566	−0.615687
$214$	−20.0995	−1.37398
$215$	28.0957	1.91611
$216$	−3.07540	−0.209254
$217$	5.66524	0.384582
$218$	−3.84733	−0.260574
$219$	8.58241	0.579946
$220$	−10.8123	−0.728966
$221$	−2.82703	−0.190167
$222$	9.23977	0.620133
$223$	1.28174	0.0858319	0.0429159	−	0.999079i	$-0.486335\pi$
$223$	1.28174	0.0858319	0.0429159	+	0.999079i	$0.486335\pi$
$224$	4.92936	0.329356
$225$	5.89190	0.392793
$226$	8.80620	0.585780
$227$	−25.2539	−1.67616	−0.838079	−	0.545548i	$-0.816321\pi$
$227$	−25.2539	−1.67616	−0.838079	+	0.545548i	$0.816321\pi$
$228$	−0.631249	−0.0418055
$229$	14.2735	0.943221	0.471610	−	0.881807i	$-0.343673\pi$
$229$	14.2735	0.943221	0.471610	+	0.881807i	$0.343673\pi$
$230$	−9.04311	−0.596285
$231$	8.52773	0.561084
$232$	17.9684	1.17968
$233$	14.8912	0.975554	0.487777	−	0.872968i	$-0.337808\pi$
$233$	14.8912	0.975554	0.487777	+	0.872968i	$0.337808\pi$
$234$	1.18767	0.0776406
$235$	5.27626	0.344185
$236$	2.79592	0.181999
$237$	−1.83010	−0.118877
$238$	−5.15143	−0.333918
$239$	1.40720	0.0910245	0.0455122	−	0.998964i	$-0.485508\pi$
$239$	1.40720	0.0910245	0.0455122	+	0.998964i	$0.485508\pi$
$240$	−8.16394	−0.526980
$241$	−28.3869	−1.82856	−0.914281	−	0.405080i	$-0.867244\pi$
$241$	−28.3869	−1.82856	−0.914281	+	0.405080i	$0.867244\pi$
$242$	23.6269	1.51879
$243$	1.00000	0.0641500
$244$	7.33037	0.469279
$245$	−15.3332	−0.979604
$246$	−0.726604	−0.0463266
$247$	1.07094	0.0681426
$248$	−11.3558	−0.721097
$249$	−8.52138	−0.540020
$250$	3.49594	0.221103
$251$	6.23115	0.393306	0.196653	−	0.980473i	$-0.436993\pi$
$251$	6.23115	0.393306	0.196653	+	0.980473i	$0.436993\pi$
$252$	−0.904345	−0.0569684
$253$	−12.8234	−0.806198
$254$	−15.3855	−0.965374
$255$	−9.33001	−0.584268
$256$	−12.7969	−0.799809
$257$	−4.90426	−0.305919	−0.152960	−	0.988232i	$-0.548880\pi$
$257$	−4.90426	−0.305919	−0.152960	+	0.988232i	$0.548880\pi$
$258$	10.1108	0.629471
$259$	11.9362	0.741677
$260$	−1.94530	−0.120642
$261$	−5.84262	−0.361649
$262$	−3.74885	−0.231605
$263$	6.34300	0.391126	0.195563	−	0.980691i	$-0.437347\pi$
$263$	6.34300	0.391126	0.195563	+	0.980691i	$0.437347\pi$
$264$	−17.0936	−1.05204
$265$	28.8955	1.77504
$266$	1.95148	0.119653
$267$	12.3784	0.757545
$268$	3.93788	0.240544
$269$	−21.5346	−1.31299	−0.656493	−	0.754332i	$-0.727961\pi$
$269$	−21.5346	−1.31299	−0.656493	+	0.754332i	$0.727961\pi$
$270$	3.91966	0.238543
$271$	−26.6778	−1.62056	−0.810280	−	0.586043i	$-0.800685\pi$
$271$	−26.6778	−1.62056	−0.810280	+	0.586043i	$0.800685\pi$
$272$	6.99324	0.424028
$273$	1.53427	0.0928580
$274$	8.68244	0.524526
$275$	32.7483	1.97479
$276$	1.35989	0.0818555
$277$	26.3853	1.58534	0.792669	−	0.609652i	$-0.208691\pi$
$277$	26.3853	1.58534	0.792669	+	0.609652i	$0.208691\pi$
$278$	−4.53777	−0.272157
$279$	3.69248	0.221063
$280$	−15.5723	−0.930625
$281$	−2.93062	−0.174826	−0.0874131	−	0.996172i	$-0.527860\pi$
$281$	−2.93062	−0.174826	−0.0874131	+	0.996172i	$0.527860\pi$
$282$	1.89876	0.113070
$283$	6.26012	0.372125	0.186063	−	0.982538i	$-0.440427\pi$
$283$	6.26012	0.372125	0.186063	+	0.982538i	$0.440427\pi$
$284$	5.29643	0.314285
$285$	3.53443	0.209361
$286$	6.60131	0.390344
$287$	−0.938645	−0.0554064
$288$	3.21284	0.189319
$289$	−9.00790	−0.529876
$290$	−22.9011	−1.34480
$291$	−6.02554	−0.353224
$292$	−5.05875	−0.296041
$293$	−16.3476	−0.955038	−0.477519	−	0.878621i	$-0.658464\pi$
$293$	−16.3476	−0.955038	−0.477519	+	0.878621i	$0.658464\pi$
$294$	−5.51797	−0.321814
$295$	−15.6546	−0.911449
$296$	−23.9258	−1.39066
$297$	5.55819	0.322519
$298$	24.5351	1.42128
$299$	−2.30711	−0.133424
$300$	−3.47287	−0.200506
$301$	13.0614	0.752845
$302$	12.9469	0.745012
$303$	−1.43580	−0.0824846
$304$	−2.64920	−0.151942
$305$	−41.0435	−2.35014
$306$	−3.35759	−0.191941
$307$	17.9320	1.02343	0.511715	−	0.859155i	$-0.329010\pi$
$307$	17.9320	1.02343	0.511715	+	0.859155i	$0.329010\pi$
$308$	−5.02652	−0.286412
$309$	1.00000	0.0568880
$310$	14.4733	0.822027
$311$	10.4442	0.592237	0.296118	−	0.955151i	$-0.404308\pi$
$311$	10.4442	0.592237	0.296118	+	0.955151i	$0.404308\pi$
$312$	−3.07540	−0.174110
$313$	−0.381373	−0.0215565	−0.0107782	−	0.999942i	$-0.503431\pi$
$313$	−0.381373	−0.0215565	−0.0107782	+	0.999942i	$0.503431\pi$
$314$	−23.5498	−1.32899
$315$	5.06352	0.285297
$316$	1.07872	0.0606826
$317$	−4.34032	−0.243777	−0.121888	−	0.992544i	$-0.538895\pi$
$317$	−4.34032	−0.243777	−0.121888	+	0.992544i	$0.538895\pi$
$318$	10.3986	0.583126
$319$	−32.4744	−1.81822
$320$	28.9212	1.61674
$321$	−16.9235	−0.944576
$322$	−4.20403	−0.234282
$323$	−3.02759	−0.168460
$324$	−0.589432	−0.0327462
$325$	5.89190	0.326824
$326$	12.1737	0.674236
$327$	−3.23938	−0.179138
$328$	1.88149	0.103888
$329$	2.45287	0.135231
$330$	21.7862	1.19929
$331$	13.8865	0.763269	0.381634	−	0.924313i	$-0.375361\pi$
$331$	13.8865	0.763269	0.381634	+	0.924313i	$0.375361\pi$
$332$	5.02277	0.275661
$333$	7.77972	0.426326
$334$	−22.1953	−1.21448
$335$	−22.0486	−1.20464
$336$	−3.79532	−0.207052
$337$	−24.2778	−1.32250	−0.661248	−	0.750168i	$-0.729973\pi$
$337$	−24.2778	−1.32250	−0.661248	+	0.750168i	$0.729973\pi$
$338$	1.18767	0.0646009
$339$	7.41466	0.402709
$340$	5.49941	0.298247
$341$	20.5235	1.11141
$342$	1.27193	0.0687782
$343$	−17.8681	−0.964787
$344$	−26.1812	−1.41160
$345$	−7.61414	−0.409931
$346$	24.4030	1.31191
$347$	−20.4830	−1.09958	−0.549791	−	0.835302i	$-0.685293\pi$
$347$	−20.4830	−1.09958	−0.549791	+	0.835302i	$0.685293\pi$
$348$	3.44383	0.184609
$349$	−23.5256	−1.25930	−0.629648	−	0.776880i	$-0.716801\pi$
$349$	−23.5256	−1.25930	−0.629648	+	0.776880i	$0.716801\pi$
$350$	10.7363	0.573877
$351$	1.00000	0.0533761
$352$	17.8576	0.951813
$353$	−28.2140	−1.50168	−0.750840	−	0.660484i	$-0.770351\pi$
$353$	−28.2140	−1.50168	−0.750840	+	0.660484i	$0.770351\pi$
$354$	−5.63363	−0.299424
$355$	−29.6552	−1.57394
$356$	−7.29622	−0.386699
$357$	−4.33741	−0.229560
$358$	15.5622	0.822487
$359$	−8.01675	−0.423108	−0.211554	−	0.977366i	$-0.567852\pi$
$359$	−8.01675	−0.423108	−0.211554	+	0.977366i	$0.567852\pi$
$360$	−10.1497	−0.534936
$361$	−17.8531	−0.939636
$362$	18.5212	0.973450
$363$	19.8934	1.04413
$364$	−0.904345	−0.0474006
$365$	28.3244	1.48257
$366$	−14.7703	−0.772056
$367$	−18.1642	−0.948164	−0.474082	−	0.880481i	$-0.657220\pi$
$367$	−18.1642	−0.948164	−0.474082	+	0.880481i	$0.657220\pi$
$368$	5.70712	0.297504
$369$	−0.611788	−0.0318484
$370$	30.4939	1.58530
$371$	13.4332	0.697416
$372$	−2.17647	−0.112844
$373$	12.9917	0.672687	0.336343	−	0.941739i	$-0.390810\pi$
$373$	12.9917	0.672687	0.336343	+	0.941739i	$0.390810\pi$
$374$	−18.6621	−0.964994
$375$	2.94352	0.152003
$376$	−4.91672	−0.253561
$377$	−5.84262	−0.300910
$378$	1.82221	0.0937242
$379$	−28.9476	−1.48694	−0.743469	−	0.668771i	$-0.766821\pi$
$379$	−28.9476	−1.48694	−0.743469	+	0.668771i	$0.766821\pi$
$380$	−2.08330	−0.106871
$381$	−12.9543	−0.663671
$382$	30.2106	1.54571
$383$	26.5943	1.35891	0.679453	−	0.733719i	$-0.262217\pi$
$383$	26.5943	1.35891	0.679453	+	0.733719i	$0.262217\pi$
$384$	3.98216	0.203214
$385$	28.1440	1.43435
$386$	10.3210	0.525326
$387$	8.51311	0.432746
$388$	3.55165	0.180308
$389$	−22.0269	−1.11681	−0.558403	−	0.829570i	$-0.688586\pi$
$389$	−22.0269	−1.11681	−0.558403	+	0.829570i	$0.688586\pi$
$390$	3.91966	0.198480
$391$	6.52228	0.329846
$392$	14.2884	0.721673
$393$	−3.15646	−0.159223
$394$	−26.6761	−1.34392
$395$	−6.03984	−0.303897
$396$	−3.27617	−0.164634
$397$	4.74844	0.238317	0.119159	−	0.992875i	$-0.461980\pi$
$397$	4.74844	0.238317	0.119159	+	0.992875i	$0.461980\pi$
$398$	18.7499	0.939846
$399$	1.64311	0.0822586
$400$	−14.5748	−0.728741
$401$	23.1731	1.15721	0.578604	−	0.815608i	$-0.303598\pi$
$401$	23.1731	1.15721	0.578604	+	0.815608i	$0.303598\pi$
$402$	−7.93461	−0.395742
$403$	3.69248	0.183935
$404$	0.846307	0.0421053
$405$	3.30029	0.163993
$406$	−10.6465	−0.528375
$407$	43.2411	2.14338
$408$	8.69425	0.430429
$409$	−2.23452	−0.110490	−0.0552449	−	0.998473i	$-0.517594\pi$
$409$	−2.23452	−0.110490	−0.0552449	+	0.998473i	$0.517594\pi$
$410$	−2.39800	−0.118429
$411$	7.31046	0.360599
$412$	−0.589432	−0.0290392
$413$	−7.27766	−0.358110
$414$	−2.74010	−0.134668
$415$	−28.1230	−1.38050
$416$	3.21284	0.157523
$417$	−3.82072	−0.187102
$418$	7.06964	0.345787
$419$	32.0181	1.56419	0.782093	−	0.623162i	$-0.214152\pi$
$419$	32.0181	1.56419	0.782093	+	0.623162i	$0.214152\pi$
$420$	−2.98460	−0.145634
$421$	5.48709	0.267424	0.133712	−	0.991020i	$-0.457310\pi$
$421$	5.48709	0.267424	0.133712	+	0.991020i	$0.457310\pi$
$422$	−16.2268	−0.789907
$423$	1.59873	0.0777327
$424$	−26.9265	−1.30767
$425$	−16.6566	−0.807963
$426$	−10.6720	−0.517061
$427$	−19.0806	−0.923377
$428$	9.97523	0.482171
$429$	5.55819	0.268352
$430$	33.3685	1.60917
$431$	−12.5537	−0.604691	−0.302345	−	0.953198i	$-0.597770\pi$
$431$	−12.5537	−0.604691	−0.302345	+	0.953198i	$0.597770\pi$
$432$	−2.47371	−0.119016
$433$	−29.1676	−1.40170	−0.700852	−	0.713307i	$-0.747197\pi$
$433$	−29.1676	−1.40170	−0.700852	+	0.713307i	$0.747197\pi$
$434$	6.72846	0.322976
$435$	−19.2823	−0.924517
$436$	1.90939	0.0914434
$437$	−2.47079	−0.118194
$438$	10.1931	0.487045
$439$	−6.73102	−0.321254	−0.160627	−	0.987015i	$-0.551352\pi$
$439$	−6.73102	−0.321254	−0.160627	+	0.987015i	$0.551352\pi$
$440$	−56.4139	−2.68943
$441$	−4.64603	−0.221240
$442$	−3.35759	−0.159704
$443$	−15.9531	−0.757952	−0.378976	−	0.925406i	$-0.623724\pi$
$443$	−15.9531	−0.757952	−0.378976	+	0.925406i	$0.623724\pi$
$444$	−4.58562	−0.217624
$445$	40.8522	1.93658
$446$	1.52229	0.0720826
$447$	20.6581	0.977094
$448$	13.4451	0.635222
$449$	−16.5299	−0.780095	−0.390048	−	0.920795i	$-0.627541\pi$
$449$	−16.5299	−0.780095	−0.390048	+	0.920795i	$0.627541\pi$
$450$	6.99765	0.329872
$451$	−3.40043	−0.160120
$452$	−4.37044	−0.205568
$453$	10.9011	0.512178
$454$	−29.9934	−1.40766
$455$	5.06352	0.237381
$456$	−3.29358	−0.154236
$457$	−18.3322	−0.857543	−0.428771	−	0.903413i	$-0.641053\pi$
$457$	−18.3322	−0.857543	−0.428771	+	0.903413i	$0.641053\pi$
$458$	16.9523	0.792128
$459$	−2.82703	−0.131954
$460$	4.48802	0.209255
$461$	−13.5625	−0.631666	−0.315833	−	0.948815i	$-0.602284\pi$
$461$	−13.5625	−0.631666	−0.315833	+	0.948815i	$0.602284\pi$
$462$	10.1282	0.471205
$463$	−10.2598	−0.476813	−0.238406	−	0.971166i	$-0.576625\pi$
$463$	−10.2598	−0.476813	−0.238406	+	0.971166i	$0.576625\pi$
$464$	14.4529	0.670960
$465$	12.1862	0.565124
$466$	17.6859	0.819282
$467$	−18.2245	−0.843328	−0.421664	−	0.906752i	$-0.638554\pi$
$467$	−18.2245	−0.843328	−0.421664	+	0.906752i	$0.638554\pi$
$468$	−0.589432	−0.0272465
$469$	−10.2501	−0.473307
$470$	6.26647	0.289051
$471$	−19.8285	−0.913649
$472$	14.5879	0.671463
$473$	47.3175	2.17566
$474$	−2.17356	−0.0998347
$475$	6.30990	0.289518
$476$	2.55661	0.117182
$477$	8.75545	0.400885
$478$	1.67130	0.0764434
$479$	17.4430	0.796990	0.398495	−	0.917171i	$-0.369533\pi$
$479$	17.4430	0.796990	0.398495	+	0.917171i	$0.369533\pi$
$480$	10.6033	0.483973
$481$	7.77972	0.354725
$482$	−33.7144	−1.53565
$483$	−3.53972	−0.161063
$484$	−11.7258	−0.532992
$485$	−19.8860	−0.902978
$486$	1.18767	0.0538740
$487$	18.4886	0.837797	0.418899	−	0.908033i	$-0.362416\pi$
$487$	18.4886	0.837797	0.418899	+	0.908033i	$0.362416\pi$
$488$	38.2467	1.73135
$489$	10.2500	0.463521
$490$	−18.2109	−0.822683
$491$	4.30866	0.194447	0.0972236	−	0.995263i	$-0.469004\pi$
$491$	4.30866	0.194447	0.0972236	+	0.995263i	$0.469004\pi$
$492$	0.360607	0.0162574
$493$	16.5173	0.743900
$494$	1.27193	0.0572270
$495$	18.3436	0.824484
$496$	−9.13411	−0.410134
$497$	−13.7864	−0.618404
$498$	−10.1206	−0.453516
$499$	38.5604	1.72620	0.863100	−	0.505033i	$-0.168520\pi$
$499$	38.5604	1.72620	0.863100	+	0.505033i	$0.168520\pi$
$500$	−1.73501	−0.0775918
$501$	−18.6881	−0.834922
$502$	7.40057	0.330303
$503$	−29.7305	−1.32562	−0.662809	−	0.748789i	$-0.730636\pi$
$503$	−29.7305	−1.32562	−0.662809	+	0.748789i	$0.730636\pi$
$504$	−4.71848	−0.210178
$505$	−4.73855	−0.210863
$506$	−15.2300	−0.677055
$507$	1.00000	0.0444116
$508$	7.63570	0.338780
$509$	−28.7956	−1.27634	−0.638171	−	0.769895i	$-0.720309\pi$
$509$	−28.7956	−1.27634	−0.638171	+	0.769895i	$0.720309\pi$
$510$	−11.0810	−0.490675
$511$	13.1677	0.582505
$512$	−23.1629	−1.02367
$513$	1.07094	0.0472834
$514$	−5.82466	−0.256915
$515$	3.30029	0.145428
$516$	−5.01790	−0.220901
$517$	8.88602	0.390807
$518$	14.1763	0.622869
$519$	20.5469	0.901907
$520$	−10.1497	−0.445094
$521$	8.53883	0.374093	0.187046	−	0.982351i	$-0.440109\pi$
$521$	8.53883	0.374093	0.187046	+	0.982351i	$0.440109\pi$
$522$	−6.93912	−0.303717
$523$	−15.8578	−0.693414	−0.346707	−	0.937974i	$-0.612700\pi$
$523$	−15.8578	−0.693414	−0.346707	+	0.937974i	$0.612700\pi$
$524$	1.86052	0.0812773
$525$	9.03974	0.394526
$526$	7.53341	0.328472
$527$	−10.4388	−0.454719
$528$	−13.7493	−0.598362
$529$	−17.6772	−0.768575
$530$	34.3184	1.49070
$531$	−4.74342	−0.205847
$532$	−0.968504	−0.0419900
$533$	−0.611788	−0.0264995
$534$	14.7015	0.636195
$535$	−55.8523	−2.41471
$536$	20.5461	0.887458
$537$	13.1031	0.565440
$538$	−25.5760	−1.10266
$539$	−25.8235	−1.11230
$540$	−1.94530	−0.0837122
$541$	2.17390	0.0934632	0.0467316	−	0.998907i	$-0.485119\pi$
$541$	2.17390	0.0934632	0.0467316	+	0.998907i	$0.485119\pi$
$542$	−31.6845	−1.36097
$543$	15.5945	0.669224
$544$	−9.08281	−0.389422
$545$	−10.6909	−0.457947
$546$	1.82221	0.0779832
$547$	39.8929	1.70570	0.852848	−	0.522159i	$-0.174873\pi$
$547$	39.8929	1.70570	0.852848	+	0.522159i	$0.174873\pi$
$548$	−4.30902	−0.184072
$549$	−12.4363	−0.530770
$550$	38.8942	1.65846
$551$	−6.25713	−0.266562
$552$	7.09529	0.301996
$553$	−2.80785	−0.119402
$554$	31.3371	1.33139
$555$	25.6753	1.08986
$556$	2.25206	0.0955085
$557$	−2.48745	−0.105396	−0.0526982	−	0.998610i	$-0.516782\pi$
$557$	−2.48745	−0.105396	−0.0526982	+	0.998610i	$0.516782\pi$
$558$	4.38546	0.185651
$559$	8.51311	0.360066
$560$	−12.5257	−0.529305
$561$	−15.7132	−0.663410
$562$	−3.48062	−0.146821
$563$	33.2144	1.39982	0.699910	−	0.714231i	$-0.253224\pi$
$563$	33.2144	1.39982	0.699910	+	0.714231i	$0.253224\pi$
$564$	−0.942340	−0.0396797
$565$	24.4705	1.02948
$566$	7.43497	0.312515
$567$	1.53427	0.0644331
$568$	27.6345	1.15952
$569$	17.5819	0.737072	0.368536	−	0.929613i	$-0.379859\pi$
$569$	17.5819	0.737072	0.368536	+	0.929613i	$0.379859\pi$
$570$	4.19774	0.175824
$571$	24.3345	1.01837	0.509183	−	0.860658i	$-0.329948\pi$
$571$	24.3345	1.01837	0.509183	+	0.860658i	$0.329948\pi$
$572$	−3.27617	−0.136984
$573$	25.4368	1.06264
$574$	−1.11480	−0.0465310
$575$	−13.5933	−0.566879
$576$	8.76322	0.365134
$577$	44.3445	1.84609	0.923043	−	0.384696i	$-0.125694\pi$
$577$	44.3445	1.84609	0.923043	+	0.384696i	$0.125694\pi$
$578$	−10.6984	−0.444997
$579$	8.69011	0.361149
$580$	11.3656	0.471932
$581$	−13.0741	−0.542403
$582$	−7.15638	−0.296641
$583$	48.6644	2.01548
$584$	−26.3943	−1.09221
$585$	3.30029	0.136450
$586$	−19.4156	−0.802053
$587$	−21.4358	−0.884751	−0.442375	−	0.896830i	$-0.645864\pi$
$587$	−21.4358	−0.884751	−0.442375	+	0.896830i	$0.645864\pi$
$588$	2.73852	0.112935
$589$	3.95444	0.162940
$590$	−18.5926	−0.765445
$591$	−22.4608	−0.923916
$592$	−19.2447	−0.790954
$593$	−11.5486	−0.474243	−0.237122	−	0.971480i	$-0.576204\pi$
$593$	−11.5486	−0.474243	−0.237122	+	0.971480i	$0.576204\pi$
$594$	6.60131	0.270855
$595$	−14.3147	−0.586846
$596$	−12.1765	−0.498770
$597$	15.7871	0.646122
$598$	−2.74010	−0.112051
$599$	30.9689	1.26536	0.632678	−	0.774415i	$-0.281956\pi$
$599$	30.9689	1.26536	0.632678	+	0.774415i	$0.281956\pi$
$600$	−18.1199	−0.739743
$601$	−3.27928	−0.133765	−0.0668823	−	0.997761i	$-0.521305\pi$
$601$	−3.27928	−0.133765	−0.0668823	+	0.997761i	$0.521305\pi$
$602$	15.5126	0.632248
$603$	−6.68080	−0.272063
$604$	−6.42545	−0.261448
$605$	65.6541	2.66922
$606$	−1.70526	−0.0692715
$607$	11.8947	0.482793	0.241396	−	0.970427i	$-0.422395\pi$
$607$	11.8947	0.482793	0.241396	+	0.970427i	$0.422395\pi$
$608$	3.44078	0.139542
$609$	−8.96413	−0.363245
$610$	−48.7462	−1.97368
$611$	1.59873	0.0646775
$612$	1.66634	0.0673579
$613$	8.87989	0.358655	0.179328	−	0.983789i	$-0.442608\pi$
$613$	8.87989	0.358655	0.179328	+	0.983789i	$0.442608\pi$
$614$	21.2973	0.859489
$615$	−2.01908	−0.0814170
$616$	−26.2262	−1.05668
$617$	−35.1009	−1.41311	−0.706554	−	0.707659i	$-0.749751\pi$
$617$	−35.1009	−1.41311	−0.706554	+	0.707659i	$0.749751\pi$
$618$	1.18767	0.0477752
$619$	−7.18630	−0.288842	−0.144421	−	0.989516i	$-0.546132\pi$
$619$	−7.18630	−0.288842	−0.144421	+	0.989516i	$0.546132\pi$
$620$	−7.18296	−0.288475
$621$	−2.30711	−0.0925812
$622$	12.4043	0.497368
$623$	18.9917	0.760888
$624$	−2.47371	−0.0990275
$625$	−19.7450	−0.789801
$626$	−0.452946	−0.0181034
$627$	5.95251	0.237720
$628$	11.6876	0.466384
$629$	−21.9935	−0.876939
$630$	6.01380	0.239596
$631$	−33.9405	−1.35115	−0.675576	−	0.737291i	$-0.736105\pi$
$631$	−33.9405	−1.35115	−0.675576	+	0.737291i	$0.736105\pi$
$632$	5.62827	0.223881
$633$	−13.6627	−0.543042
$634$	−5.15489	−0.204727
$635$	−42.7531	−1.69660
$636$	−5.16075	−0.204637
$637$	−4.64603	−0.184082
$638$	−38.5689	−1.52696
$639$	−8.98566	−0.355467
$640$	13.1423	0.519493
$641$	−27.8309	−1.09925	−0.549627	−	0.835410i	$-0.685230\pi$
$641$	−27.8309	−1.09925	−0.549627	+	0.835410i	$0.685230\pi$
$642$	−20.0995	−0.793266
$643$	0.668554	0.0263652	0.0131826	−	0.999913i	$-0.495804\pi$
$643$	0.668554	0.0263652	0.0131826	+	0.999913i	$0.495804\pi$
$644$	2.08643	0.0822167
$645$	28.0957	1.10627
$646$	−3.59579	−0.141475
$647$	−5.75210	−0.226139	−0.113069	−	0.993587i	$-0.536068\pi$
$647$	−5.75210	−0.226139	−0.113069	+	0.993587i	$0.536068\pi$
$648$	−3.07540	−0.120813
$649$	−26.3648	−1.03491
$650$	6.99765	0.274470
$651$	5.66524	0.222038
$652$	−6.04168	−0.236610
$653$	0.0880097	0.00344409	0.00172204	−	0.999999i	$-0.499452\pi$
$653$	0.0880097	0.00344409	0.00172204	+	0.999999i	$0.499452\pi$
$654$	−3.84733	−0.150442
$655$	−10.4172	−0.407035
$656$	1.51338	0.0590877
$657$	8.58241	0.334832
$658$	2.91321	0.113569
$659$	0.812060	0.0316334	0.0158167	−	0.999875i	$-0.494965\pi$
$659$	0.812060	0.0316334	0.0158167	+	0.999875i	$0.494965\pi$
$660$	−10.8123	−0.420869
$661$	−9.66941	−0.376097	−0.188048	−	0.982160i	$-0.560216\pi$
$661$	−9.66941	−0.376097	−0.188048	+	0.982160i	$0.560216\pi$
$662$	16.4926	0.641002
$663$	−2.82703	−0.109793
$664$	26.2066	1.01701
$665$	5.42275	0.210285
$666$	9.23977	0.358034
$667$	13.4796	0.521932
$668$	11.0154	0.426197
$669$	1.28174	0.0495551
$670$	−26.1865	−1.01167
$671$	−69.1235	−2.66848
$672$	4.92936	0.190154
$673$	12.2480	0.472125	0.236062	−	0.971738i	$-0.424143\pi$
$673$	12.2480	0.472125	0.236062	+	0.971738i	$0.424143\pi$
$674$	−28.8341	−1.11065
$675$	5.89190	0.226779
$676$	−0.589432	−0.0226705
$677$	−44.4408	−1.70800	−0.853999	−	0.520275i	$-0.825829\pi$
$677$	−44.4408	−1.70800	−0.853999	+	0.520275i	$0.825829\pi$
$678$	8.80620	0.338200
$679$	−9.24478	−0.354782
$680$	28.6935	1.10035
$681$	−25.2539	−0.967731
$682$	24.3752	0.933375
$683$	−36.7845	−1.40752	−0.703759	−	0.710438i	$-0.748497\pi$
$683$	−36.7845	−1.40752	−0.703759	+	0.710438i	$0.748497\pi$
$684$	−0.631249	−0.0241364
$685$	24.1266	0.921831
$686$	−21.2215	−0.810239
$687$	14.2735	0.544569
$688$	−21.0589	−0.802864
$689$	8.75545	0.333556
$690$	−9.04311	−0.344265
$691$	−4.38805	−0.166929	−0.0834646	−	0.996511i	$-0.526599\pi$
$691$	−4.38805	−0.166929	−0.0834646	+	0.996511i	$0.526599\pi$
$692$	−12.1110	−0.460390
$693$	8.52773	0.323942
$694$	−24.3271	−0.923442
$695$	−12.6095	−0.478305
$696$	17.9684	0.681090
$697$	1.72954	0.0655111
$698$	−27.9407	−1.05757
$699$	14.8912	0.563237
$700$	−5.32831	−0.201391
$701$	−33.2055	−1.25415	−0.627077	−	0.778958i	$-0.715749\pi$
$701$	−33.2055	−1.25415	−0.627077	+	0.778958i	$0.715749\pi$
$702$	1.18767	0.0448258
$703$	8.33165	0.314234
$704$	48.7076	1.83574
$705$	5.27626	0.198715
$706$	−33.5090	−1.26113
$707$	−2.20290	−0.0828485
$708$	2.79592	0.105077
$709$	−3.16842	−0.118992	−0.0594962	−	0.998229i	$-0.518949\pi$
$709$	−3.16842	−0.118992	−0.0594962	+	0.998229i	$0.518949\pi$
$710$	−35.2207	−1.32181
$711$	−1.83010	−0.0686339
$712$	−38.0685	−1.42668
$713$	−8.51897	−0.319038
$714$	−5.15143	−0.192787
$715$	18.3436	0.686012
$716$	−7.72337	−0.288636
$717$	1.40720	0.0525530
$718$	−9.52128	−0.355331
$719$	23.7163	0.884470	0.442235	−	0.896899i	$-0.354186\pi$
$719$	23.7163	0.884470	0.442235	+	0.896899i	$0.354186\pi$
$720$	−8.16394	−0.304252
$721$	1.53427	0.0571390
$722$	−21.2036	−0.789117
$723$	−28.3869	−1.05572
$724$	−9.19189	−0.341614
$725$	−34.4241	−1.27848
$726$	23.6269	0.876877
$727$	−21.2613	−0.788539	−0.394269	−	0.918995i	$-0.629002\pi$
$727$	−21.2613	−0.788539	−0.394269	+	0.918995i	$0.629002\pi$
$728$	−4.71848	−0.174878
$729$	1.00000	0.0370370
$730$	33.6402	1.24508
$731$	−24.0668	−0.890144
$732$	7.33037	0.270938
$733$	23.0286	0.850580	0.425290	−	0.905057i	$-0.360172\pi$
$733$	23.0286	0.850580	0.425290	+	0.905057i	$0.360172\pi$
$734$	−21.5731	−0.796279
$735$	−15.3332	−0.565575
$736$	−7.41239	−0.273224
$737$	−37.1331	−1.36782
$738$	−0.726604	−0.0267467
$739$	43.7930	1.61095	0.805475	−	0.592630i	$-0.201910\pi$
$739$	43.7930	1.61095	0.805475	+	0.592630i	$0.201910\pi$
$740$	−15.1339	−0.556332
$741$	1.07094	0.0393421
$742$	15.9542	0.585699
$743$	−24.8865	−0.912997	−0.456498	−	0.889724i	$-0.650897\pi$
$743$	−24.8865	−0.912997	−0.456498	+	0.889724i	$0.650897\pi$
$744$	−11.3558	−0.416326
$745$	68.1776	2.49784
$746$	15.4299	0.564930
$747$	−8.52138	−0.311781
$748$	9.26184	0.338646
$749$	−25.9651	−0.948743
$750$	3.49594	0.127654
$751$	2.76177	0.100778	0.0503892	−	0.998730i	$-0.483954\pi$
$751$	2.76177	0.100778	0.0503892	+	0.998730i	$0.483954\pi$
$752$	−3.95478	−0.144216
$753$	6.23115	0.227076
$754$	−6.93912	−0.252708
$755$	35.9767	1.30933
$756$	−0.904345	−0.0328907
$757$	16.8676	0.613065	0.306532	−	0.951860i	$-0.400831\pi$
$757$	16.8676	0.613065	0.306532	+	0.951860i	$0.400831\pi$
$758$	−34.3803	−1.24875
$759$	−12.8234	−0.465459
$760$	−10.8698	−0.394288
$761$	16.4639	0.596815	0.298408	−	0.954439i	$-0.403545\pi$
$761$	16.4639	0.596815	0.298408	+	0.954439i	$0.403545\pi$
$762$	−15.3855	−0.557359
$763$	−4.97007	−0.179929
$764$	−14.9932	−0.542437
$765$	−9.33001	−0.337327
$766$	31.5854	1.14123
$767$	−4.74342	−0.171275
$768$	−12.7969	−0.461770
$769$	−18.8295	−0.679007	−0.339504	−	0.940605i	$-0.610259\pi$
$769$	−18.8295	−0.679007	−0.339504	+	0.940605i	$0.610259\pi$
$770$	33.4258	1.20458
$771$	−4.90426	−0.176622
$772$	−5.12223	−0.184353
$773$	−52.6223	−1.89269	−0.946346	−	0.323155i	$-0.895257\pi$
$773$	−52.6223	−1.89269	−0.946346	+	0.323155i	$0.895257\pi$
$774$	10.1108	0.363425
$775$	21.7557	0.781488
$776$	18.5310	0.665223
$777$	11.9362	0.428207
$778$	−26.1607	−0.937907
$779$	−0.655191	−0.0234747
$780$	−1.94530	−0.0696527
$781$	−49.9439	−1.78713
$782$	7.74634	0.277008
$783$	−5.84262	−0.208798
$784$	11.4929	0.410461
$785$	−65.4398	−2.33565
$786$	−3.74885	−0.133717
$787$	23.6312	0.842360	0.421180	−	0.906977i	$-0.361616\pi$
$787$	23.6312	0.842360	0.421180	+	0.906977i	$0.361616\pi$
$788$	13.2391	0.471625
$789$	6.34300	0.225817
$790$	−7.17336	−0.255217
$791$	11.3761	0.404486
$792$	−17.0936	−0.607396
$793$	−12.4363	−0.441627
$794$	5.63959	0.200142
$795$	28.8955	1.02482
$796$	−9.30540	−0.329821
$797$	−16.5601	−0.586590	−0.293295	−	0.956022i	$-0.594752\pi$
$797$	−16.5601	−0.586590	−0.293295	+	0.956022i	$0.594752\pi$
$798$	1.95148	0.0690817
$799$	−4.51965	−0.159894
$800$	18.9298	0.669268
$801$	12.3784	0.437369
$802$	27.5221	0.971838
$803$	47.7027	1.68339
$804$	3.93788	0.138878
$805$	−11.6821	−0.411740
$806$	4.38546	0.154471
$807$	−21.5346	−0.758053
$808$	4.41566	0.155342
$809$	−22.2177	−0.781132	−0.390566	−	0.920575i	$-0.627721\pi$
$809$	−22.2177	−0.781132	−0.390566	+	0.920575i	$0.627721\pi$
$810$	3.91966	0.137723
$811$	−13.5113	−0.474444	−0.237222	−	0.971455i	$-0.576237\pi$
$811$	−13.5113	−0.474444	−0.237222	+	0.971455i	$0.576237\pi$
$812$	5.28375	0.185423
$813$	−26.6778	−0.935631
$814$	51.3564	1.80004
$815$	33.8280	1.18494
$816$	6.99324	0.244812
$817$	9.11708	0.318966
$818$	−2.65388	−0.0927906
$819$	1.53427	0.0536116
$820$	1.19011	0.0415604
$821$	−1.47303	−0.0514090	−0.0257045	−	0.999670i	$-0.508183\pi$
$821$	−1.47303	−0.0514090	−0.0257045	+	0.999670i	$0.508183\pi$
$822$	8.68244	0.302835
$823$	−17.5378	−0.611331	−0.305665	−	0.952139i	$-0.598879\pi$
$823$	−17.5378	−0.611331	−0.305665	+	0.952139i	$0.598879\pi$
$824$	−3.07540	−0.107137
$825$	32.7483	1.14015
$826$	−8.64349	−0.300745
$827$	−31.2109	−1.08531	−0.542654	−	0.839956i	$-0.682581\pi$
$827$	−31.2109	−1.08531	−0.542654	+	0.839956i	$0.682581\pi$
$828$	1.35989	0.0472593
$829$	−0.888192	−0.0308482	−0.0154241	−	0.999881i	$-0.504910\pi$
$829$	−0.888192	−0.0308482	−0.0154241	+	0.999881i	$0.504910\pi$
$830$	−33.4009	−1.15936
$831$	26.3853	0.915295
$832$	8.76322	0.303810
$833$	13.1345	0.455082
$834$	−4.53777	−0.157130
$835$	−61.6761	−2.13439
$836$	−3.50860	−0.121348
$837$	3.69248	0.127631
$838$	38.0270	1.31362
$839$	−7.74904	−0.267526	−0.133763	−	0.991013i	$-0.542706\pi$
$839$	−7.74904	−0.267526	−0.133763	+	0.991013i	$0.542706\pi$
$840$	−15.5723	−0.537297
$841$	5.13622	0.177111
$842$	6.51687	0.224586
$843$	−2.93062	−0.100936
$844$	8.05320	0.277203
$845$	3.30029	0.113533
$846$	1.89876	0.0652809
$847$	30.5218	1.04874
$848$	−21.6584	−0.743753
$849$	6.26012	0.214847
$850$	−19.7826	−0.678537
$851$	−17.9487	−0.615273
$852$	5.29643	0.181453
$853$	34.4272	1.17876	0.589382	−	0.807854i	$-0.299371\pi$
$853$	34.4272	1.17876	0.589382	+	0.807854i	$0.299371\pi$
$854$	−22.6616	−0.775463
$855$	3.53443	0.120875
$856$	52.0464	1.77891
$857$	−21.9470	−0.749695	−0.374847	−	0.927087i	$-0.622305\pi$
$857$	−21.9470	−0.749695	−0.374847	+	0.927087i	$0.622305\pi$
$858$	6.60131	0.225365
$859$	6.23197	0.212632	0.106316	−	0.994332i	$-0.466094\pi$
$859$	6.23197	0.212632	0.106316	+	0.994332i	$0.466094\pi$
$860$	−16.5605	−0.564709
$861$	−0.938645	−0.0319889
$862$	−14.9097	−0.507826
$863$	−12.3836	−0.421543	−0.210772	−	0.977535i	$-0.567598\pi$
$863$	−12.3836	−0.421543	−0.210772	+	0.977535i	$0.567598\pi$
$864$	3.21284	0.109303
$865$	67.8106	2.30563
$866$	−34.6415	−1.17717
$867$	−9.00790	−0.305924
$868$	−3.33928	−0.113342
$869$	−10.1720	−0.345062
$870$	−22.9011	−0.776420
$871$	−6.68080	−0.226370
$872$	9.96239	0.337369
$873$	−6.02554	−0.203934
$874$	−2.93449	−0.0992607
$875$	4.51614	0.152673
$876$	−5.05875	−0.170919
$877$	−2.30449	−0.0778172	−0.0389086	−	0.999243i	$-0.512388\pi$
$877$	−2.30449	−0.0778172	−0.0389086	+	0.999243i	$0.512388\pi$
$878$	−7.99426	−0.269793
$879$	−16.3476	−0.551392
$880$	−45.3767	−1.52965
$881$	10.4703	0.352754	0.176377	−	0.984323i	$-0.443562\pi$
$881$	10.4703	0.352754	0.176377	+	0.984323i	$0.443562\pi$
$882$	−5.51797	−0.185800
$883$	29.1932	0.982429	0.491215	−	0.871039i	$-0.336553\pi$
$883$	29.1932	0.982429	0.491215	+	0.871039i	$0.336553\pi$
$884$	1.66634	0.0560452
$885$	−15.6546	−0.526225
$886$	−18.9470	−0.636537
$887$	−3.28175	−0.110190	−0.0550952	−	0.998481i	$-0.517546\pi$
$887$	−3.28175	−0.110190	−0.0550952	+	0.998481i	$0.517546\pi$
$888$	−23.9258	−0.802896
$889$	−19.8754	−0.666599
$890$	48.5191	1.62636
$891$	5.55819	0.186206
$892$	−0.755501	−0.0252960
$893$	1.71215	0.0572948
$894$	24.5351	0.820575
$895$	43.2439	1.44549
$896$	6.10968	0.204110
$897$	−2.30711	−0.0770323
$898$	−19.6321	−0.655133
$899$	−21.5738	−0.719525
$900$	−3.47287	−0.115762
$901$	−24.7519	−0.824606
$902$	−4.03860	−0.134471
$903$	13.0614	0.434655
$904$	−22.8031	−0.758418
$905$	51.4663	1.71080
$906$	12.9469	0.430133
$907$	16.1615	0.536634	0.268317	−	0.963331i	$-0.413533\pi$
$907$	16.1615	0.536634	0.268317	+	0.963331i	$0.413533\pi$
$908$	14.8854	0.493991
$909$	−1.43580	−0.0476225
$910$	6.01380	0.199356
$911$	35.3041	1.16968	0.584838	−	0.811150i	$-0.301158\pi$
$911$	35.3041	1.16968	0.584838	+	0.811150i	$0.301158\pi$
$912$	−2.64920	−0.0877239
$913$	−47.3634	−1.56750
$914$	−21.7726	−0.720175
$915$	−41.0435	−1.35686
$916$	−8.41327	−0.277982
$917$	−4.84285	−0.159925
$918$	−3.35759	−0.110817
$919$	20.8616	0.688161	0.344080	−	0.938940i	$-0.388191\pi$
$919$	20.8616	0.688161	0.344080	+	0.938940i	$0.388191\pi$
$920$	23.4165	0.772019
$921$	17.9320	0.590878
$922$	−16.1078	−0.530481
$923$	−8.98566	−0.295766
$924$	−5.02652	−0.165360
$925$	45.8373	1.50712
$926$	−12.1853	−0.400433
$927$	1.00000	0.0328443
$928$	−18.7714	−0.616202
$929$	−37.3804	−1.22641	−0.613206	−	0.789923i	$-0.710120\pi$
$929$	−37.3804	−1.22641	−0.613206	+	0.789923i	$0.710120\pi$
$930$	14.4733	0.474597
$931$	−4.97564	−0.163070
$932$	−8.77734	−0.287511
$933$	10.4442	0.341928
$934$	−21.6447	−0.708237
$935$	−51.8580	−1.69594
$936$	−3.07540	−0.100523
$937$	47.5178	1.55234	0.776170	−	0.630524i	$-0.217160\pi$
$937$	47.5178	1.55234	0.776170	+	0.630524i	$0.217160\pi$
$938$	−12.1738	−0.397489
$939$	−0.381373	−0.0124456
$940$	−3.10999	−0.101437
$941$	6.73118	0.219430	0.109715	−	0.993963i	$-0.465006\pi$
$941$	6.73118	0.219430	0.109715	+	0.993963i	$0.465006\pi$
$942$	−23.5498	−0.767293
$943$	1.41146	0.0459636
$944$	11.7338	0.381903
$945$	5.06352	0.164716
$946$	56.1977	1.82714
$947$	0.893962	0.0290499	0.0145249	−	0.999895i	$-0.495376\pi$
$947$	0.893962	0.0290499	0.0145249	+	0.999895i	$0.495376\pi$
$948$	1.07872	0.0350351
$949$	8.58241	0.278597
$950$	7.49410	0.243141
$951$	−4.34032	−0.140745
$952$	13.3393	0.432329
$953$	−57.1992	−1.85286	−0.926431	−	0.376464i	$-0.877140\pi$
$953$	−57.1992	−1.85286	−0.926431	+	0.376464i	$0.877140\pi$
$954$	10.3986	0.336668
$955$	83.9486	2.71651
$956$	−0.829451	−0.0268264
$957$	−32.4744	−1.04975
$958$	20.7166	0.669321
$959$	11.2162	0.362190
$960$	28.9212	0.933426
$961$	−17.3656	−0.560181
$962$	9.23977	0.297902
$963$	−16.9235	−0.545351
$964$	16.7322	0.538907
$965$	28.6799	0.923238
$966$	−4.20403	−0.135263
$967$	−3.61546	−0.116265	−0.0581327	−	0.998309i	$-0.518515\pi$
$967$	−3.61546	−0.116265	−0.0581327	+	0.998309i	$0.518515\pi$
$968$	−61.1803	−1.96641
$969$	−3.02759	−0.0972603
$970$	−23.6181	−0.758332
$971$	−12.5822	−0.403780	−0.201890	−	0.979408i	$-0.564708\pi$
$971$	−12.5822	−0.403780	−0.201890	+	0.979408i	$0.564708\pi$
$972$	−0.589432	−0.0189060
$973$	−5.86200	−0.187927
$974$	21.9584	0.703592
$975$	5.89190	0.188692
$976$	30.7638	0.984726
$977$	35.7586	1.14402	0.572009	−	0.820247i	$-0.306164\pi$
$977$	35.7586	1.14402	0.572009	+	0.820247i	$0.306164\pi$
$978$	12.1737	0.389271
$979$	68.8014	2.19890
$980$	9.03790	0.288705
$981$	−3.23938	−0.103425
$982$	5.11728	0.163299
$983$	45.2002	1.44166	0.720832	−	0.693110i	$-0.243760\pi$
$983$	45.2002	1.44166	0.720832	+	0.693110i	$0.243760\pi$
$984$	1.88149	0.0599798
$985$	−74.1273	−2.36189
$986$	19.6171	0.624736
$987$	2.45287	0.0780757
$988$	−0.631249	−0.0200827
$989$	−19.6407	−0.624538
$990$	21.7862	0.692412
$991$	37.9728	1.20625	0.603123	−	0.797648i	$-0.293923\pi$
$991$	37.9728	1.20625	0.603123	+	0.797648i	$0.293923\pi$
$992$	11.8634	0.376662
$993$	13.8865	0.440674
$994$	−16.3737	−0.519343
$995$	52.1019	1.65174
$996$	5.02277	0.159153
$997$	−20.4961	−0.649117	−0.324558	−	0.945866i	$-0.605216\pi$
$997$	−20.4961	−0.649117	−0.324558	+	0.945866i	$0.605216\pi$
$998$	45.7972	1.44968
$999$	7.77972	0.246140

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.21	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.21	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+1.18767 q^{2} +1.00000 q^{3} -0.589432 q^{4} +3.30029 q^{5} +1.18767 q^{6} +1.53427 q^{7} -3.07540 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.18767 q^{2} +1.00000 q^{3} -0.589432 q^{4} +3.30029 q^{5} +1.18767 q^{6} +1.53427 q^{7} -3.07540 q^{8} +1.00000 q^{9} +3.91966 q^{10} +5.55819 q^{11} -0.589432 q^{12} +1.00000 q^{13} +1.82221 q^{14} +3.30029 q^{15} -2.47371 q^{16} -2.82703 q^{17} +1.18767 q^{18} +1.07094 q^{19} -1.94530 q^{20} +1.53427 q^{21} +6.60131 q^{22} -2.30711 q^{23} -3.07540 q^{24} +5.89190 q^{25} +1.18767 q^{26} +1.00000 q^{27} -0.904345 q^{28} -5.84262 q^{29} +3.91966 q^{30} +3.69248 q^{31} +3.21284 q^{32} +5.55819 q^{33} -3.35759 q^{34} +5.06352 q^{35} -0.589432 q^{36} +7.77972 q^{37} +1.27193 q^{38} +1.00000 q^{39} -10.1497 q^{40} -0.611788 q^{41} +1.82221 q^{42} +8.51311 q^{43} -3.27617 q^{44} +3.30029 q^{45} -2.74010 q^{46} +1.59873 q^{47} -2.47371 q^{48} -4.64603 q^{49} +6.99765 q^{50} -2.82703 q^{51} -0.589432 q^{52} +8.75545 q^{53} +1.18767 q^{54} +18.3436 q^{55} -4.71848 q^{56} +1.07094 q^{57} -6.93912 q^{58} -4.74342 q^{59} -1.94530 q^{60} -12.4363 q^{61} +4.38546 q^{62} +1.53427 q^{63} +8.76322 q^{64} +3.30029 q^{65} +6.60131 q^{66} -6.68080 q^{67} +1.66634 q^{68} -2.30711 q^{69} +6.01380 q^{70} -8.98566 q^{71} -3.07540 q^{72} +8.58241 q^{73} +9.23977 q^{74} +5.89190 q^{75} -0.631249 q^{76} +8.52773 q^{77} +1.18767 q^{78} -1.83010 q^{79} -8.16394 q^{80} +1.00000 q^{81} -0.726604 q^{82} -8.52138 q^{83} -0.904345 q^{84} -9.33001 q^{85} +10.1108 q^{86} -5.84262 q^{87} -17.0936 q^{88} +12.3784 q^{89} +3.91966 q^{90} +1.53427 q^{91} +1.35989 q^{92} +3.69248 q^{93} +1.89876 q^{94} +3.53443 q^{95} +3.21284 q^{96} -6.02554 q^{97} -5.51797 q^{98} +5.55819 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

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