LMFDB - Embedded newform 8049.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34737 q^{2} -1.00000 q^{3} +3.51014 q^{4} -3.81233 q^{5} +2.34737 q^{6} -0.357303 q^{7} -3.54486 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.34737 q^{2} -1.00000 q^{3} +3.51014 q^{4} -3.81233 q^{5} +2.34737 q^{6} -0.357303 q^{7} -3.54486 q^{8} +1.00000 q^{9} +8.94895 q^{10} +0.955838 q^{11} -3.51014 q^{12} -1.52421 q^{13} +0.838722 q^{14} +3.81233 q^{15} +1.30081 q^{16} +4.18208 q^{17} -2.34737 q^{18} -7.16757 q^{19} -13.3818 q^{20} +0.357303 q^{21} -2.24370 q^{22} +5.85676 q^{23} +3.54486 q^{24} +9.53386 q^{25} +3.57789 q^{26} -1.00000 q^{27} -1.25418 q^{28} +2.91708 q^{29} -8.94895 q^{30} -4.19969 q^{31} +4.03624 q^{32} -0.955838 q^{33} -9.81689 q^{34} +1.36216 q^{35} +3.51014 q^{36} +6.30106 q^{37} +16.8249 q^{38} +1.52421 q^{39} +13.5142 q^{40} +8.33479 q^{41} -0.838722 q^{42} -0.324058 q^{43} +3.35513 q^{44} -3.81233 q^{45} -13.7480 q^{46} +0.363639 q^{47} -1.30081 q^{48} -6.87233 q^{49} -22.3795 q^{50} -4.18208 q^{51} -5.35020 q^{52} -7.17112 q^{53} +2.34737 q^{54} -3.64397 q^{55} +1.26659 q^{56} +7.16757 q^{57} -6.84747 q^{58} +1.05269 q^{59} +13.3818 q^{60} -4.48499 q^{61} +9.85823 q^{62} -0.357303 q^{63} -12.0762 q^{64} +5.81080 q^{65} +2.24370 q^{66} +7.33541 q^{67} +14.6797 q^{68} -5.85676 q^{69} -3.19749 q^{70} +10.5336 q^{71} -3.54486 q^{72} +2.74211 q^{73} -14.7909 q^{74} -9.53386 q^{75} -25.1592 q^{76} -0.341524 q^{77} -3.57789 q^{78} +6.56556 q^{79} -4.95912 q^{80} +1.00000 q^{81} -19.5648 q^{82} -5.73202 q^{83} +1.25418 q^{84} -15.9435 q^{85} +0.760685 q^{86} -2.91708 q^{87} -3.38831 q^{88} +1.44604 q^{89} +8.94895 q^{90} +0.544606 q^{91} +20.5580 q^{92} +4.19969 q^{93} -0.853596 q^{94} +27.3251 q^{95} -4.03624 q^{96} +0.567376 q^{97} +16.1319 q^{98} +0.955838 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) $ 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.34737	−1.65984	−0.829920	−	0.557882i	$-0.811614\pi$
$2$	−2.34737	−1.65984	−0.829920	+	0.557882i	$0.811614\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.51014	1.75507
$5$	−3.81233	−1.70493	−0.852463	−	0.522788i	$-0.824892\pi$
$5$	−3.81233	−1.70493	−0.852463	+	0.522788i	$0.824892\pi$
$6$	2.34737	0.958309
$7$	−0.357303	−0.135048	−0.0675240	−	0.997718i	$-0.521510\pi$
$7$	−0.357303	−0.135048	−0.0675240	+	0.997718i	$0.521510\pi$
$8$	−3.54486	−1.25330
$9$	1.00000	0.333333
$10$	8.94895	2.82991
$11$	0.955838	0.288196	0.144098	−	0.989563i	$-0.453972\pi$
$11$	0.955838	0.288196	0.144098	+	0.989563i	$0.453972\pi$
$12$	−3.51014	−1.01329
$13$	−1.52421	−0.422740	−0.211370	−	0.977406i	$-0.567793\pi$
$13$	−1.52421	−0.422740	−0.211370	+	0.977406i	$0.567793\pi$
$14$	0.838722	0.224158
$15$	3.81233	0.984339
$16$	1.30081	0.325203
$17$	4.18208	1.01430	0.507152	−	0.861857i	$-0.330698\pi$
$17$	4.18208	1.01430	0.507152	+	0.861857i	$0.330698\pi$
$18$	−2.34737	−0.553280
$19$	−7.16757	−1.64435	−0.822177	−	0.569232i	$-0.807240\pi$
$19$	−7.16757	−1.64435	−0.822177	+	0.569232i	$0.807240\pi$
$20$	−13.3818	−2.99227
$21$	0.357303	0.0779699
$22$	−2.24370	−0.478359
$23$	5.85676	1.22122	0.610609	−	0.791932i	$-0.290925\pi$
$23$	5.85676	1.22122	0.610609	+	0.791932i	$0.290925\pi$
$24$	3.54486	0.723591
$25$	9.53386	1.90677
$26$	3.57789	0.701682
$27$	−1.00000	−0.192450
$28$	−1.25418	−0.237019
$29$	2.91708	0.541688	0.270844	−	0.962623i	$-0.412697\pi$
$29$	2.91708	0.541688	0.270844	+	0.962623i	$0.412697\pi$
$30$	−8.94895	−1.63385
$31$	−4.19969	−0.754287	−0.377144	−	0.926155i	$-0.623094\pi$
$31$	−4.19969	−0.754287	−0.377144	+	0.926155i	$0.623094\pi$
$32$	4.03624	0.713513
$33$	−0.955838	−0.166390
$34$	−9.81689	−1.68358
$35$	1.36216	0.230247
$36$	3.51014	0.585024
$37$	6.30106	1.03589	0.517944	−	0.855414i	$-0.326697\pi$
$37$	6.30106	1.03589	0.517944	+	0.855414i	$0.326697\pi$
$38$	16.8249	2.72936
$39$	1.52421	0.244069
$40$	13.5142	2.13678
$41$	8.33479	1.30168	0.650838	−	0.759217i	$-0.274418\pi$
$41$	8.33479	1.30168	0.650838	+	0.759217i	$0.274418\pi$
$42$	−0.838722	−0.129418
$43$	−0.324058	−0.0494184	−0.0247092	−	0.999695i	$-0.507866\pi$
$43$	−0.324058	−0.0494184	−0.0247092	+	0.999695i	$0.507866\pi$
$44$	3.35513	0.505804
$45$	−3.81233	−0.568309
$46$	−13.7480	−2.02703
$47$	0.363639	0.0530423	0.0265211	−	0.999648i	$-0.491557\pi$
$47$	0.363639	0.0530423	0.0265211	+	0.999648i	$0.491557\pi$
$48$	−1.30081	−0.187756
$49$	−6.87233	−0.981762
$50$	−22.3795	−3.16494
$51$	−4.18208	−0.585609
$52$	−5.35020	−0.741939
$53$	−7.17112	−0.985030	−0.492515	−	0.870304i	$-0.663922\pi$
$53$	−7.17112	−0.985030	−0.492515	+	0.870304i	$0.663922\pi$
$54$	2.34737	0.319436
$55$	−3.64397	−0.491353
$56$	1.26659	0.169255
$57$	7.16757	0.949368
$58$	−6.84747	−0.899116
$59$	1.05269	0.137049	0.0685243	−	0.997649i	$-0.478171\pi$
$59$	1.05269	0.137049	0.0685243	+	0.997649i	$0.478171\pi$
$60$	13.3818	1.72759
$61$	−4.48499	−0.574244	−0.287122	−	0.957894i	$-0.592699\pi$
$61$	−4.48499	−0.574244	−0.287122	+	0.957894i	$0.592699\pi$
$62$	9.85823	1.25200
$63$	−0.357303	−0.0450160
$64$	−12.0762	−1.50952
$65$	5.81080	0.720741
$66$	2.24370	0.276181
$67$	7.33541	0.896164	0.448082	−	0.893993i	$-0.352107\pi$
$67$	7.33541	0.896164	0.448082	+	0.893993i	$0.352107\pi$
$68$	14.6797	1.78018
$69$	−5.85676	−0.705071
$70$	−3.19749	−0.382173
$71$	10.5336	1.25011	0.625053	−	0.780582i	$-0.285077\pi$
$71$	10.5336	1.25011	0.625053	+	0.780582i	$0.285077\pi$
$72$	−3.54486	−0.417766
$73$	2.74211	0.320940	0.160470	−	0.987041i	$-0.448699\pi$
$73$	2.74211	0.320940	0.160470	+	0.987041i	$0.448699\pi$
$74$	−14.7909	−1.71941
$75$	−9.53386	−1.10088
$76$	−25.1592	−2.88596
$77$	−0.341524	−0.0389203
$78$	−3.57789	−0.405116
$79$	6.56556	0.738683	0.369342	−	0.929294i	$-0.379583\pi$
$79$	6.56556	0.738683	0.369342	+	0.929294i	$0.379583\pi$
$80$	−4.95912	−0.554447
$81$	1.00000	0.111111
$82$	−19.5648	−2.16057
$83$	−5.73202	−0.629171	−0.314585	−	0.949229i	$-0.601865\pi$
$83$	−5.73202	−0.629171	−0.314585	+	0.949229i	$0.601865\pi$
$84$	1.25418	0.136843
$85$	−15.9435	−1.72931
$86$	0.760685	0.0820267
$87$	−2.91708	−0.312744
$88$	−3.38831	−0.361195
$89$	1.44604	0.153280	0.0766398	−	0.997059i	$-0.475581\pi$
$89$	1.44604	0.153280	0.0766398	+	0.997059i	$0.475581\pi$
$90$	8.94895	0.943302
$91$	0.544606	0.0570902
$92$	20.5580	2.14332
$93$	4.19969	0.435488
$94$	−0.853596	−0.0880417
$95$	27.3251	2.80350
$96$	−4.03624	−0.411947
$97$	0.567376	0.0576083	0.0288041	−	0.999585i	$-0.490830\pi$
$97$	0.567376	0.0576083	0.0288041	+	0.999585i	$0.490830\pi$
$98$	16.1319	1.62957
$99$	0.955838	0.0960653
$100$	33.4652	3.34652
$101$	11.0186	1.09640	0.548198	−	0.836349i	$-0.315314\pi$
$101$	11.0186	1.09640	0.548198	+	0.836349i	$0.315314\pi$
$102$	9.81689	0.972017
$103$	−6.67292	−0.657502	−0.328751	−	0.944417i	$-0.606628\pi$
$103$	−6.67292	−0.657502	−0.328751	+	0.944417i	$0.606628\pi$
$104$	5.40312	0.529819
$105$	−1.36216	−0.132933
$106$	16.8333	1.63499
$107$	−9.81781	−0.949124	−0.474562	−	0.880222i	$-0.657393\pi$
$107$	−9.81781	−0.949124	−0.474562	+	0.880222i	$0.657393\pi$
$108$	−3.51014	−0.337764
$109$	5.13528	0.491871	0.245935	−	0.969286i	$-0.420905\pi$
$109$	5.13528	0.491871	0.245935	+	0.969286i	$0.420905\pi$
$110$	8.55374	0.815567
$111$	−6.30106	−0.598070
$112$	−0.464784	−0.0439179
$113$	−16.5035	−1.55252	−0.776261	−	0.630411i	$-0.782886\pi$
$113$	−16.5035	−1.55252	−0.776261	+	0.630411i	$0.782886\pi$
$114$	−16.8249	−1.57580
$115$	−22.3279	−2.08209
$116$	10.2394	0.950701
$117$	−1.52421	−0.140913
$118$	−2.47105	−0.227479
$119$	−1.49427	−0.136980
$120$	−13.5142	−1.23367
$121$	−10.0864	−0.916943
$122$	10.5279	0.953154
$123$	−8.33479	−0.751523
$124$	−14.7415	−1.32383
$125$	−17.2846	−1.54598
$126$	0.838722	0.0747193
$127$	4.20701	0.373311	0.186656	−	0.982425i	$-0.440235\pi$
$127$	4.20701	0.373311	0.186656	+	0.982425i	$0.440235\pi$
$128$	20.2747	1.79205
$129$	0.324058	0.0285318
$130$	−13.6401	−1.19632
$131$	−0.854273	−0.0746382	−0.0373191	−	0.999303i	$-0.511882\pi$
$131$	−0.854273	−0.0746382	−0.0373191	+	0.999303i	$0.511882\pi$
$132$	−3.35513	−0.292026
$133$	2.56100	0.222066
$134$	−17.2189	−1.48749
$135$	3.81233	0.328113
$136$	−14.8249	−1.27122
$137$	15.7519	1.34577	0.672887	−	0.739745i	$-0.265054\pi$
$137$	15.7519	1.34577	0.672887	+	0.739745i	$0.265054\pi$
$138$	13.7480	1.17031
$139$	16.6920	1.41580	0.707898	−	0.706315i	$-0.249644\pi$
$139$	16.6920	1.41580	0.707898	+	0.706315i	$0.249644\pi$
$140$	4.78137	0.404099
$141$	−0.363639	−0.0306240
$142$	−24.7262	−2.07498
$143$	−1.45690	−0.121832
$144$	1.30081	0.108401
$145$	−11.1209	−0.923539
$146$	−6.43674	−0.532709
$147$	6.87233	0.566821
$148$	22.1176	1.81806
$149$	12.3755	1.01384	0.506918	−	0.861994i	$-0.330785\pi$
$149$	12.3755	1.01384	0.506918	+	0.861994i	$0.330785\pi$
$150$	22.3795	1.82728
$151$	4.66719	0.379811	0.189905	−	0.981802i	$-0.439182\pi$
$151$	4.66719	0.379811	0.189905	+	0.981802i	$0.439182\pi$
$152$	25.4080	2.06086
$153$	4.18208	0.338101
$154$	0.801682	0.0646014
$155$	16.0106	1.28600
$156$	5.35020	0.428359
$157$	−16.0936	−1.28441	−0.642206	−	0.766532i	$-0.721981\pi$
$157$	−16.0936	−1.28441	−0.642206	+	0.766532i	$0.721981\pi$
$158$	−15.4118	−1.22610
$159$	7.17112	0.568707
$160$	−15.3875	−1.21649
$161$	−2.09264	−0.164923
$162$	−2.34737	−0.184427
$163$	−5.82727	−0.456427	−0.228213	−	0.973611i	$-0.573288\pi$
$163$	−5.82727	−0.456427	−0.228213	+	0.973611i	$0.573288\pi$
$164$	29.2563	2.28453
$165$	3.64397	0.283683
$166$	13.4552	1.04432
$167$	5.52670	0.427669	0.213834	−	0.976870i	$-0.431405\pi$
$167$	5.52670	0.427669	0.213834	+	0.976870i	$0.431405\pi$
$168$	−1.26659	−0.0977195
$169$	−10.6768	−0.821291
$170$	37.4252	2.87038
$171$	−7.16757	−0.548118
$172$	−1.13749	−0.0867329
$173$	−21.0771	−1.60246	−0.801231	−	0.598355i	$-0.795821\pi$
$173$	−21.0771	−1.60246	−0.801231	+	0.598355i	$0.795821\pi$
$174$	6.84747	0.519105
$175$	−3.40648	−0.257506
$176$	1.24336	0.0937221
$177$	−1.05269	−0.0791250
$178$	−3.39438	−0.254420
$179$	−21.3159	−1.59323	−0.796613	−	0.604490i	$-0.793377\pi$
$179$	−21.3159	−1.59323	−0.796613	+	0.604490i	$0.793377\pi$
$180$	−13.3818	−0.997422
$181$	−24.1447	−1.79466	−0.897331	−	0.441358i	$-0.854497\pi$
$181$	−24.1447	−1.79466	−0.897331	+	0.441358i	$0.854497\pi$
$182$	−1.27839	−0.0947607
$183$	4.48499	0.331540
$184$	−20.7614	−1.53055
$185$	−24.0217	−1.76611
$186$	−9.85823	−0.722840
$187$	3.99739	0.292318
$188$	1.27643	0.0930929
$189$	0.357303	0.0259900
$190$	−64.1422	−4.65336
$191$	−8.79147	−0.636129	−0.318064	−	0.948069i	$-0.603033\pi$
$191$	−8.79147	−0.636129	−0.318064	+	0.948069i	$0.603033\pi$
$192$	12.0762	0.871522
$193$	3.71415	0.267350	0.133675	−	0.991025i	$-0.457322\pi$
$193$	3.71415	0.267350	0.133675	+	0.991025i	$0.457322\pi$
$194$	−1.33184	−0.0956205
$195$	−5.81080	−0.416120
$196$	−24.1229	−1.72306
$197$	2.84908	0.202989	0.101494	−	0.994836i	$-0.467638\pi$
$197$	2.84908	0.202989	0.101494	+	0.994836i	$0.467638\pi$
$198$	−2.24370	−0.159453
$199$	20.9673	1.48633	0.743165	−	0.669108i	$-0.233324\pi$
$199$	20.9673	1.48633	0.743165	+	0.669108i	$0.233324\pi$
$200$	−33.7962	−2.38975
$201$	−7.33541	−0.517400
$202$	−25.8648	−1.81984
$203$	−1.04228	−0.0731539
$204$	−14.6797	−1.02778
$205$	−31.7750	−2.21926
$206$	15.6638	1.09135
$207$	5.85676	0.407073
$208$	−1.98271	−0.137476
$209$	−6.85103	−0.473896
$210$	3.19749	0.220648
$211$	19.0282	1.30996	0.654978	−	0.755648i	$-0.272678\pi$
$211$	19.0282	1.30996	0.654978	+	0.755648i	$0.272678\pi$
$212$	−25.1717	−1.72880
$213$	−10.5336	−0.721749
$214$	23.0460	1.57539
$215$	1.23542	0.0842548
$216$	3.54486	0.241197
$217$	1.50056	0.101865
$218$	−12.0544	−0.816427
$219$	−2.74211	−0.185295
$220$	−12.7908	−0.862359
$221$	−6.37438	−0.428787
$222$	14.7909	0.992702
$223$	−18.6133	−1.24644	−0.623219	−	0.782047i	$-0.714175\pi$
$223$	−18.6133	−1.24644	−0.623219	+	0.782047i	$0.714175\pi$
$224$	−1.44216	−0.0963584
$225$	9.53386	0.635591
$226$	38.7399	2.57694
$227$	−8.90781	−0.591232	−0.295616	−	0.955307i	$-0.595525\pi$
$227$	−8.90781	−0.591232	−0.295616	+	0.955307i	$0.595525\pi$
$228$	25.1592	1.66621
$229$	−25.3518	−1.67530	−0.837648	−	0.546211i	$-0.816070\pi$
$229$	−25.3518	−1.67530	−0.837648	+	0.546211i	$0.816070\pi$
$230$	52.4118	3.45593
$231$	0.341524	0.0224706
$232$	−10.3406	−0.678897
$233$	−20.9784	−1.37434	−0.687171	−	0.726495i	$-0.741148\pi$
$233$	−20.9784	−1.37434	−0.687171	+	0.726495i	$0.741148\pi$
$234$	3.57789	0.233894
$235$	−1.38631	−0.0904331
$236$	3.69509	0.240530
$237$	−6.56556	−0.426479
$238$	3.50761	0.227364
$239$	0.708666	0.0458398	0.0229199	−	0.999737i	$-0.492704\pi$
$239$	0.708666	0.0458398	0.0229199	+	0.999737i	$0.492704\pi$
$240$	4.95912	0.320110
$241$	−0.201124	−0.0129556	−0.00647778	−	0.999979i	$-0.502062\pi$
$241$	−0.201124	−0.0129556	−0.00647778	+	0.999979i	$0.502062\pi$
$242$	23.6764	1.52198
$243$	−1.00000	−0.0641500
$244$	−15.7430	−1.00784
$245$	26.1996	1.67383
$246$	19.5648	1.24741
$247$	10.9249	0.695135
$248$	14.8873	0.945346
$249$	5.73202	0.363252
$250$	40.5733	2.56608
$251$	16.0615	1.01379	0.506896	−	0.862007i	$-0.330793\pi$
$251$	16.0615	1.01379	0.506896	+	0.862007i	$0.330793\pi$
$252$	−1.25418	−0.0790062
$253$	5.59811	0.351950
$254$	−9.87539	−0.619637
$255$	15.9435	0.998419
$256$	−23.4400	−1.46500
$257$	−10.4350	−0.650917	−0.325458	−	0.945556i	$-0.605519\pi$
$257$	−10.4350	−0.650917	−0.325458	+	0.945556i	$0.605519\pi$
$258$	−0.760685	−0.0473582
$259$	−2.25139	−0.139895
$260$	20.3967	1.26495
$261$	2.91708	0.180563
$262$	2.00529	0.123888
$263$	2.43958	0.150431	0.0752154	−	0.997167i	$-0.476036\pi$
$263$	2.43958	0.150431	0.0752154	+	0.997167i	$0.476036\pi$
$264$	3.38831	0.208536
$265$	27.3387	1.67940
$266$	−6.01160	−0.368595
$267$	−1.44604	−0.0884961
$268$	25.7483	1.57283
$269$	28.6991	1.74982	0.874908	−	0.484290i	$-0.160922\pi$
$269$	28.6991	1.74982	0.874908	+	0.484290i	$0.160922\pi$
$270$	−8.94895	−0.544616
$271$	−25.2787	−1.53557	−0.767786	−	0.640707i	$-0.778641\pi$
$271$	−25.2787	−1.53557	−0.767786	+	0.640707i	$0.778641\pi$
$272$	5.44010	0.329854
$273$	−0.544606	−0.0329610
$274$	−36.9755	−2.23377
$275$	9.11282	0.549524
$276$	−20.5580	−1.23745
$277$	−13.9665	−0.839165	−0.419582	−	0.907717i	$-0.637823\pi$
$277$	−13.9665	−0.839165	−0.419582	+	0.907717i	$0.637823\pi$
$278$	−39.1823	−2.35000
$279$	−4.19969	−0.251429
$280$	−4.82866	−0.288567
$281$	1.37266	0.0818861	0.0409430	−	0.999161i	$-0.486964\pi$
$281$	1.37266	0.0818861	0.0409430	+	0.999161i	$0.486964\pi$
$282$	0.853596	0.0508309
$283$	0.844613	0.0502070	0.0251035	−	0.999685i	$-0.492008\pi$
$283$	0.844613	0.0502070	0.0251035	+	0.999685i	$0.492008\pi$
$284$	36.9744	2.19403
$285$	−27.3251	−1.61860
$286$	3.41988	0.202222
$287$	−2.97805	−0.175789
$288$	4.03624	0.237838
$289$	0.489814	0.0288126
$290$	26.1048	1.53293
$291$	−0.567376	−0.0332601
$292$	9.62519	0.563272
$293$	−7.85101	−0.458661	−0.229331	−	0.973349i	$-0.573654\pi$
$293$	−7.85101	−0.458661	−0.229331	+	0.973349i	$0.573654\pi$
$294$	−16.1319	−0.940832
$295$	−4.01320	−0.233658
$296$	−22.3364	−1.29828
$297$	−0.955838	−0.0554633
$298$	−29.0498	−1.68281
$299$	−8.92694	−0.516258
$300$	−33.4652	−1.93211
$301$	0.115787	0.00667386
$302$	−10.9556	−0.630426
$303$	−11.0186	−0.633004
$304$	−9.32365	−0.534748
$305$	17.0983	0.979044
$306$	−9.81689	−0.561194
$307$	−10.1872	−0.581414	−0.290707	−	0.956812i	$-0.593890\pi$
$307$	−10.1872	−0.581414	−0.290707	+	0.956812i	$0.593890\pi$
$308$	−1.19880	−0.0683078
$309$	6.67292	0.379609
$310$	−37.5828	−2.13456
$311$	0.601197	0.0340907	0.0170454	−	0.999855i	$-0.494574\pi$
$311$	0.601197	0.0340907	0.0170454	+	0.999855i	$0.494574\pi$
$312$	−5.40312	−0.305891
$313$	14.8096	0.837091	0.418545	−	0.908196i	$-0.362540\pi$
$313$	14.8096	0.837091	0.418545	+	0.908196i	$0.362540\pi$
$314$	37.7777	2.13192
$315$	1.36216	0.0767489
$316$	23.0460	1.29644
$317$	22.8369	1.28265	0.641325	−	0.767270i	$-0.278385\pi$
$317$	22.8369	1.28265	0.641325	+	0.767270i	$0.278385\pi$
$318$	−16.8333	−0.943963
$319$	2.78826	0.156112
$320$	46.0383	2.57362
$321$	9.81781	0.547977
$322$	4.91219	0.273746
$323$	−29.9754	−1.66787
$324$	3.51014	0.195008
$325$	−14.5316	−0.806070
$326$	13.6787	0.757595
$327$	−5.13528	−0.283982
$328$	−29.5457	−1.63139
$329$	−0.129930	−0.00716325
$330$	−8.55374	−0.470868
$331$	23.2797	1.27957	0.639783	−	0.768555i	$-0.279024\pi$
$331$	23.2797	1.27957	0.639783	+	0.768555i	$0.279024\pi$
$332$	−20.1202	−1.10424
$333$	6.30106	0.345296
$334$	−12.9732	−0.709862
$335$	−27.9650	−1.52789
$336$	0.464784	0.0253560
$337$	−3.28410	−0.178896	−0.0894482	−	0.995991i	$-0.528510\pi$
$337$	−3.28410	−0.178896	−0.0894482	+	0.995991i	$0.528510\pi$
$338$	25.0623	1.36321
$339$	16.5035	0.896350
$340$	−55.9639	−3.03507
$341$	−4.01422	−0.217382
$342$	16.8249	0.909788
$343$	4.95663	0.267633
$344$	1.14874	0.0619360
$345$	22.3279	1.20209
$346$	49.4757	2.65983
$347$	−6.66172	−0.357620	−0.178810	−	0.983884i	$-0.557225\pi$
$347$	−6.66172	−0.357620	−0.178810	+	0.983884i	$0.557225\pi$
$348$	−10.2394	−0.548888
$349$	−22.2678	−1.19197	−0.595985	−	0.802995i	$-0.703238\pi$
$349$	−22.2678	−1.19197	−0.595985	+	0.802995i	$0.703238\pi$
$350$	7.99626	0.427418
$351$	1.52421	0.0813564
$352$	3.85799	0.205631
$353$	9.78082	0.520580	0.260290	−	0.965530i	$-0.416182\pi$
$353$	9.78082	0.520580	0.260290	+	0.965530i	$0.416182\pi$
$354$	2.47105	0.131335
$355$	−40.1575	−2.13134
$356$	5.07580	0.269017
$357$	1.49427	0.0790852
$358$	50.0363	2.64450
$359$	11.7232	0.618727	0.309363	−	0.950944i	$-0.399884\pi$
$359$	11.7232	0.618727	0.309363	+	0.950944i	$0.399884\pi$
$360$	13.5142	0.712260
$361$	32.3741	1.70390
$362$	56.6766	2.97885
$363$	10.0864	0.529397
$364$	1.91164	0.100197
$365$	−10.4538	−0.547178
$366$	−10.5279	−0.550304
$367$	1.15878	0.0604877	0.0302439	−	0.999543i	$-0.490372\pi$
$367$	1.15878	0.0604877	0.0302439	+	0.999543i	$0.490372\pi$
$368$	7.61853	0.397144
$369$	8.33479	0.433892
$370$	56.3879	2.93147
$371$	2.56227	0.133026
$372$	14.7415	0.764312
$373$	2.40940	0.124754	0.0623770	−	0.998053i	$-0.480132\pi$
$373$	2.40940	0.124754	0.0623770	+	0.998053i	$0.480132\pi$
$374$	−9.38335	−0.485202
$375$	17.2846	0.892572
$376$	−1.28905	−0.0664777
$377$	−4.44625	−0.228994
$378$	−0.838722	−0.0431392
$379$	36.0914	1.85389	0.926944	−	0.375199i	$-0.122426\pi$
$379$	36.0914	1.85389	0.926944	+	0.375199i	$0.122426\pi$
$380$	95.9151	4.92034
$381$	−4.20701	−0.215531
$382$	20.6368	1.05587
$383$	−6.69329	−0.342011	−0.171006	−	0.985270i	$-0.554702\pi$
$383$	−6.69329	−0.342011	−0.171006	+	0.985270i	$0.554702\pi$
$384$	−20.2747	−1.03464
$385$	1.30200	0.0663561
$386$	−8.71848	−0.443759
$387$	−0.324058	−0.0164728
$388$	1.99157	0.101107
$389$	34.3589	1.74206	0.871032	−	0.491226i	$-0.163451\pi$
$389$	34.3589	1.74206	0.871032	+	0.491226i	$0.163451\pi$
$390$	13.6401	0.690693
$391$	24.4934	1.23869
$392$	24.3615	1.23044
$393$	0.854273	0.0430924
$394$	−6.68785	−0.336929
$395$	−25.0301	−1.25940
$396$	3.35513	0.168601
$397$	−11.4887	−0.576599	−0.288300	−	0.957540i	$-0.593090\pi$
$397$	−11.4887	−0.576599	−0.288300	+	0.957540i	$0.593090\pi$
$398$	−49.2179	−2.46707
$399$	−2.56100	−0.128210
$400$	12.4018	0.620088
$401$	9.66150	0.482472	0.241236	−	0.970466i	$-0.422447\pi$
$401$	9.66150	0.482472	0.241236	+	0.970466i	$0.422447\pi$
$402$	17.2189	0.858802
$403$	6.40122	0.318868
$404$	38.6770	1.92425
$405$	−3.81233	−0.189436
$406$	2.44662	0.121424
$407$	6.02279	0.298539
$408$	14.8249	0.733942
$409$	25.3072	1.25136	0.625680	−	0.780080i	$-0.284822\pi$
$409$	25.3072	1.25136	0.625680	+	0.780080i	$0.284822\pi$
$410$	74.5876	3.68362
$411$	−15.7519	−0.776983
$412$	−23.4229	−1.15396
$413$	−0.376129	−0.0185081
$414$	−13.7480	−0.675676
$415$	21.8524	1.07269
$416$	−6.15208	−0.301631
$417$	−16.6920	−0.817410
$418$	16.0819	0.786592
$419$	−33.0785	−1.61599	−0.807996	−	0.589188i	$-0.799448\pi$
$419$	−33.0785	−1.61599	−0.807996	+	0.589188i	$0.799448\pi$
$420$	−4.78137	−0.233307
$421$	−22.7721	−1.10984	−0.554922	−	0.831903i	$-0.687252\pi$
$421$	−22.7721	−1.10984	−0.554922	+	0.831903i	$0.687252\pi$
$422$	−44.6662	−2.17432
$423$	0.363639	0.0176808
$424$	25.4206	1.23453
$425$	39.8714	1.93405
$426$	24.7262	1.19799
$427$	1.60250	0.0775505
$428$	−34.4619	−1.66578
$429$	1.45690	0.0703398
$430$	−2.89998	−0.139850
$431$	−31.1889	−1.50232	−0.751158	−	0.660123i	$-0.770504\pi$
$431$	−31.1889	−1.50232	−0.751158	+	0.660123i	$0.770504\pi$
$432$	−1.30081	−0.0625853
$433$	−30.1999	−1.45132	−0.725658	−	0.688056i	$-0.758464\pi$
$433$	−30.1999	−1.45132	−0.725658	+	0.688056i	$0.758464\pi$
$434$	−3.52238	−0.169079
$435$	11.1209	0.533205
$436$	18.0256	0.863268
$437$	−41.9787	−2.00811
$438$	6.43674	0.307560
$439$	5.89318	0.281266	0.140633	−	0.990062i	$-0.455086\pi$
$439$	5.89318	0.281266	0.140633	+	0.990062i	$0.455086\pi$
$440$	12.9174	0.615811
$441$	−6.87233	−0.327254
$442$	14.9630	0.711719
$443$	−22.5286	−1.07037	−0.535183	−	0.844736i	$-0.679757\pi$
$443$	−22.5286	−1.07037	−0.535183	+	0.844736i	$0.679757\pi$
$444$	−22.1176	−1.04966
$445$	−5.51277	−0.261330
$446$	43.6923	2.06889
$447$	−12.3755	−0.585339
$448$	4.31485	0.203857
$449$	−28.6393	−1.35157	−0.675787	−	0.737097i	$-0.736196\pi$
$449$	−28.6393	−1.35157	−0.675787	+	0.737097i	$0.736196\pi$
$450$	−22.3795	−1.05498
$451$	7.96671	0.375138
$452$	−57.9298	−2.72479
$453$	−4.66719	−0.219284
$454$	20.9099	0.981351
$455$	−2.07622	−0.0973346
$456$	−25.4080	−1.18984
$457$	27.3040	1.27723	0.638613	−	0.769528i	$-0.279509\pi$
$457$	27.3040	1.27723	0.638613	+	0.769528i	$0.279509\pi$
$458$	59.5101	2.78072
$459$	−4.18208	−0.195203
$460$	−78.3741	−3.65421
$461$	32.1919	1.49932	0.749662	−	0.661821i	$-0.230216\pi$
$461$	32.1919	1.49932	0.749662	+	0.661821i	$0.230216\pi$
$462$	−0.801682	−0.0372976
$463$	−32.9772	−1.53258	−0.766290	−	0.642494i	$-0.777900\pi$
$463$	−32.9772	−1.53258	−0.766290	+	0.642494i	$0.777900\pi$
$464$	3.79457	0.176159
$465$	−16.0106	−0.742475
$466$	49.2441	2.28119
$467$	−14.5361	−0.672649	−0.336324	−	0.941746i	$-0.609184\pi$
$467$	−14.5361	−0.672649	−0.336324	+	0.941746i	$0.609184\pi$
$468$	−5.35020	−0.247313
$469$	−2.62097	−0.121025
$470$	3.25419	0.150105
$471$	16.0936	0.741556
$472$	−3.73164	−0.171763
$473$	−0.309747	−0.0142422
$474$	15.4118	0.707887
$475$	−68.3346	−3.13541
$476$	−5.24510	−0.240409
$477$	−7.17112	−0.328343
$478$	−1.66350	−0.0760868
$479$	6.14393	0.280723	0.140362	−	0.990100i	$-0.455174\pi$
$479$	6.14393	0.280723	0.140362	+	0.990100i	$0.455174\pi$
$480$	15.3875	0.702338
$481$	−9.60416	−0.437912
$482$	0.472113	0.0215042
$483$	2.09264	0.0952183
$484$	−35.4046	−1.60930
$485$	−2.16302	−0.0982178
$486$	2.34737	0.106479
$487$	20.6873	0.937432	0.468716	−	0.883349i	$-0.344717\pi$
$487$	20.6873	0.937432	0.468716	+	0.883349i	$0.344717\pi$
$488$	15.8987	0.719699
$489$	5.82727	0.263518
$490$	−61.5002	−2.77829
$491$	−26.2364	−1.18403	−0.592016	−	0.805926i	$-0.701668\pi$
$491$	−26.2364	−1.18403	−0.592016	+	0.805926i	$0.701668\pi$
$492$	−29.2563	−1.31898
$493$	12.1995	0.549437
$494$	−25.6448	−1.15381
$495$	−3.64397	−0.163784
$496$	−5.46301	−0.245296
$497$	−3.76368	−0.168824
$498$	−13.4552	−0.602940
$499$	28.5664	1.27881	0.639405	−	0.768870i	$-0.279181\pi$
$499$	28.5664	1.27881	0.639405	+	0.768870i	$0.279181\pi$
$500$	−60.6713	−2.71330
$501$	−5.52670	−0.246915
$502$	−37.7022	−1.68273
$503$	16.9590	0.756166	0.378083	−	0.925772i	$-0.376583\pi$
$503$	16.9590	0.756166	0.378083	+	0.925772i	$0.376583\pi$
$504$	1.26659	0.0564184
$505$	−42.0067	−1.86927
$506$	−13.1408	−0.584181
$507$	10.6768	0.474172
$508$	14.7672	0.655188
$509$	−33.6542	−1.49170	−0.745848	−	0.666116i	$-0.767955\pi$
$509$	−33.6542	−1.49170	−0.745848	+	0.666116i	$0.767955\pi$
$510$	−37.4252	−1.65722
$511$	−0.979764	−0.0433422
$512$	14.4728	0.639612
$513$	7.16757	0.316456
$514$	24.4948	1.08042
$515$	25.4394	1.12099
$516$	1.13749	0.0500752
$517$	0.347580	0.0152866
$518$	5.28484	0.232203
$519$	21.0771	0.925182
$520$	−20.5985	−0.903303
$521$	−0.827756	−0.0362647	−0.0181323	−	0.999836i	$-0.505772\pi$
$521$	−0.827756	−0.0362647	−0.0181323	+	0.999836i	$0.505772\pi$
$522$	−6.84747	−0.299705
$523$	−12.3297	−0.539140	−0.269570	−	0.962981i	$-0.586882\pi$
$523$	−12.3297	−0.539140	−0.269570	+	0.962981i	$0.586882\pi$
$524$	−2.99862	−0.130995
$525$	3.40648	0.148671
$526$	−5.72659	−0.249691
$527$	−17.5635	−0.765076
$528$	−1.24336	−0.0541105
$529$	11.3016	0.491374
$530$	−64.1740	−2.78754
$531$	1.05269	0.0456828
$532$	8.98946	0.389742
$533$	−12.7040	−0.550271
$534$	3.39438	0.146889
$535$	37.4287	1.61819
$536$	−26.0030	−1.12316
$537$	21.3159	0.919849
$538$	−67.3674	−2.90441
$539$	−6.56884	−0.282940
$540$	13.3818	0.575862
$541$	9.55322	0.410725	0.205363	−	0.978686i	$-0.434163\pi$
$541$	9.55322	0.410725	0.205363	+	0.978686i	$0.434163\pi$
$542$	59.3384	2.54880
$543$	24.1447	1.03615
$544$	16.8799	0.723719
$545$	−19.5774	−0.838603
$546$	1.27839	0.0547101
$547$	29.6933	1.26960	0.634798	−	0.772678i	$-0.281083\pi$
$547$	29.6933	1.26960	0.634798	+	0.772678i	$0.281083\pi$
$548$	55.2914	2.36193
$549$	−4.48499	−0.191415
$550$	−21.3912	−0.912122
$551$	−20.9084	−0.890727
$552$	20.7614	0.883663
$553$	−2.34590	−0.0997576
$554$	32.7845	1.39288
$555$	24.0217	1.01967
$556$	58.5912	2.48482
$557$	−40.1653	−1.70186	−0.850930	−	0.525280i	$-0.823961\pi$
$557$	−40.1653	−1.70186	−0.850930	+	0.525280i	$0.823961\pi$
$558$	9.85823	0.417332
$559$	0.493934	0.0208912
$560$	1.77191	0.0748768
$561$	−3.99739	−0.168770
$562$	−3.22214	−0.135918
$563$	11.7477	0.495107	0.247554	−	0.968874i	$-0.420373\pi$
$563$	11.7477	0.495107	0.247554	+	0.968874i	$0.420373\pi$
$564$	−1.27643	−0.0537472
$565$	62.9170	2.64694
$566$	−1.98262	−0.0833357
$567$	−0.357303	−0.0150053
$568$	−37.3401	−1.56676
$569$	23.4722	0.984007	0.492003	−	0.870593i	$-0.336265\pi$
$569$	23.4722	0.984007	0.492003	+	0.870593i	$0.336265\pi$
$570$	64.1422	2.68662
$571$	−26.2245	−1.09746	−0.548731	−	0.835999i	$-0.684889\pi$
$571$	−26.2245	−1.09746	−0.548731	+	0.835999i	$0.684889\pi$
$572$	−5.11392	−0.213824
$573$	8.79147	0.367269
$574$	6.99058	0.291781
$575$	55.8375	2.32859
$576$	−12.0762	−0.503173
$577$	−11.0433	−0.459737	−0.229869	−	0.973222i	$-0.573830\pi$
$577$	−11.0433	−0.459737	−0.229869	+	0.973222i	$0.573830\pi$
$578$	−1.14978	−0.0478243
$579$	−3.71415	−0.154355
$580$	−39.0359	−1.62088
$581$	2.04807	0.0849682
$582$	1.33184	0.0552065
$583$	−6.85443	−0.283882
$584$	−9.72039	−0.402233
$585$	5.81080	0.240247
$586$	18.4292	0.761304
$587$	6.73670	0.278053	0.139027	−	0.990289i	$-0.455603\pi$
$587$	6.73670	0.278053	0.139027	+	0.990289i	$0.455603\pi$
$588$	24.1229	0.994810
$589$	30.1016	1.24031
$590$	9.42046	0.387834
$591$	−2.84908	−0.117196
$592$	8.19649	0.336874
$593$	19.2818	0.791807	0.395904	−	0.918292i	$-0.370431\pi$
$593$	19.2818	0.791807	0.395904	+	0.918292i	$0.370431\pi$
$594$	2.24370	0.0920603
$595$	5.69666	0.233540
$596$	43.4396	1.77936
$597$	−20.9673	−0.858133
$598$	20.9548	0.856907
$599$	47.8115	1.95352	0.976762	−	0.214328i	$-0.0687562\pi$
$599$	47.8115	1.95352	0.976762	+	0.214328i	$0.0687562\pi$
$600$	33.7962	1.37972
$601$	−12.2350	−0.499075	−0.249537	−	0.968365i	$-0.580279\pi$
$601$	−12.2350	−0.499075	−0.249537	+	0.968365i	$0.580279\pi$
$602$	−0.271795	−0.0110775
$603$	7.33541	0.298721
$604$	16.3825	0.666595
$605$	38.4526	1.56332
$606$	25.8648	1.05069
$607$	21.3221	0.865439	0.432720	−	0.901529i	$-0.357554\pi$
$607$	21.3221	0.865439	0.432720	+	0.901529i	$0.357554\pi$
$608$	−28.9300	−1.17327
$609$	1.04228	0.0422354
$610$	−40.1360	−1.62506
$611$	−0.554264	−0.0224231
$612$	14.6797	0.593392
$613$	32.5151	1.31327	0.656637	−	0.754207i	$-0.271978\pi$
$613$	32.5151	1.31327	0.656637	+	0.754207i	$0.271978\pi$
$614$	23.9131	0.965054
$615$	31.7750	1.28129
$616$	1.21065	0.0487786
$617$	24.8508	1.00046	0.500228	−	0.865894i	$-0.333249\pi$
$617$	24.8508	1.00046	0.500228	+	0.865894i	$0.333249\pi$
$618$	−15.6638	−0.630091
$619$	13.1404	0.528158	0.264079	−	0.964501i	$-0.414932\pi$
$619$	13.1404	0.528158	0.264079	+	0.964501i	$0.414932\pi$
$620$	56.1995	2.25703
$621$	−5.85676	−0.235024
$622$	−1.41123	−0.0565852
$623$	−0.516674	−0.0207001
$624$	1.98271	0.0793720
$625$	18.2252	0.729008
$626$	−34.7637	−1.38944
$627$	6.85103	0.273604
$628$	−56.4909	−2.25423
$629$	26.3516	1.05071
$630$	−3.19749	−0.127391
$631$	−0.963843	−0.0383700	−0.0191850	−	0.999816i	$-0.506107\pi$
$631$	−0.963843	−0.0383700	−0.0191850	+	0.999816i	$0.506107\pi$
$632$	−23.2740	−0.925789
$633$	−19.0282	−0.756303
$634$	−53.6067	−2.12899
$635$	−16.0385	−0.636468
$636$	25.1717	0.998121
$637$	10.4749	0.415031
$638$	−6.54507	−0.259122
$639$	10.5336	0.416702
$640$	−77.2940	−3.05531
$641$	28.6621	1.13208	0.566042	−	0.824376i	$-0.308474\pi$
$641$	28.6621	1.13208	0.566042	+	0.824376i	$0.308474\pi$
$642$	−23.0460	−0.909554
$643$	15.4927	0.610974	0.305487	−	0.952196i	$-0.401181\pi$
$643$	15.4927	0.610974	0.305487	+	0.952196i	$0.401181\pi$
$644$	−7.34546	−0.289452
$645$	−1.23542	−0.0486445
$646$	70.3633	2.76841
$647$	6.00932	0.236251	0.118125	−	0.992999i	$-0.462312\pi$
$647$	6.00932	0.236251	0.118125	+	0.992999i	$0.462312\pi$
$648$	−3.54486	−0.139255
$649$	1.00620	0.0394968
$650$	34.1111	1.33795
$651$	−1.50056	−0.0588117
$652$	−20.4545	−0.801061
$653$	−23.5063	−0.919872	−0.459936	−	0.887952i	$-0.652128\pi$
$653$	−23.5063	−0.919872	−0.459936	+	0.887952i	$0.652128\pi$
$654$	12.0544	0.471364
$655$	3.25677	0.127253
$656$	10.8420	0.423309
$657$	2.74211	0.106980
$658$	0.304992	0.0118898
$659$	35.2202	1.37198	0.685992	−	0.727609i	$-0.259368\pi$
$659$	35.2202	1.37198	0.685992	+	0.727609i	$0.259368\pi$
$660$	12.7908	0.497883
$661$	7.93392	0.308594	0.154297	−	0.988025i	$-0.450689\pi$
$661$	7.93392	0.308594	0.154297	+	0.988025i	$0.450689\pi$
$662$	−54.6460	−2.12388
$663$	6.37438	0.247560
$664$	20.3192	0.788538
$665$	−9.76336	−0.378607
$666$	−14.7909	−0.573136
$667$	17.0846	0.661520
$668$	19.3995	0.750589
$669$	18.6133	0.719631
$670$	65.6442	2.53606
$671$	−4.28693	−0.165495
$672$	1.44216	0.0556325
$673$	32.0032	1.23363	0.616817	−	0.787107i	$-0.288422\pi$
$673$	32.0032	1.23363	0.616817	+	0.787107i	$0.288422\pi$
$674$	7.70900	0.296940
$675$	−9.53386	−0.366959
$676$	−37.4770	−1.44142
$677$	0.461911	0.0177527	0.00887635	−	0.999961i	$-0.497175\pi$
$677$	0.461911	0.0177527	0.00887635	+	0.999961i	$0.497175\pi$
$678$	−38.7399	−1.48780
$679$	−0.202725	−0.00777988
$680$	56.5174	2.16734
$681$	8.90781	0.341348
$682$	9.42287	0.360820
$683$	−23.0954	−0.883722	−0.441861	−	0.897084i	$-0.645682\pi$
$683$	−23.0954	−0.883722	−0.441861	+	0.897084i	$0.645682\pi$
$684$	−25.1592	−0.961985
$685$	−60.0514	−2.29445
$686$	−11.6350	−0.444228
$687$	25.3518	0.967232
$688$	−0.421539	−0.0160710
$689$	10.9303	0.416412
$690$	−52.4118	−1.99528
$691$	12.1585	0.462532	0.231266	−	0.972891i	$-0.425713\pi$
$691$	12.1585	0.462532	0.231266	+	0.972891i	$0.425713\pi$
$692$	−73.9836	−2.81244
$693$	−0.341524	−0.0129734
$694$	15.6375	0.593592
$695$	−63.6354	−2.41383
$696$	10.3406	0.391961
$697$	34.8568	1.32030
$698$	52.2709	1.97848
$699$	20.9784	0.793477
$700$	−11.9572	−0.451941
$701$	−34.3494	−1.29736	−0.648680	−	0.761061i	$-0.724679\pi$
$701$	−34.3494	−1.29736	−0.648680	+	0.761061i	$0.724679\pi$
$702$	−3.57789	−0.135039
$703$	−45.1633	−1.70337
$704$	−11.5428	−0.435037
$705$	1.38631	0.0522116
$706$	−22.9592	−0.864080
$707$	−3.93699	−0.148066
$708$	−3.69509	−0.138870
$709$	32.5852	1.22376	0.611882	−	0.790949i	$-0.290413\pi$
$709$	32.5852	1.22376	0.611882	+	0.790949i	$0.290413\pi$
$710$	94.2645	3.53768
$711$	6.56556	0.246228
$712$	−5.12600	−0.192105
$713$	−24.5966	−0.921149
$714$	−3.50761	−0.131269
$715$	5.55418	0.207715
$716$	−74.8218	−2.79622
$717$	−0.708666	−0.0264656
$718$	−27.5187	−1.02699
$719$	40.4887	1.50997	0.754986	−	0.655740i	$-0.227643\pi$
$719$	40.4887	1.50997	0.754986	+	0.655740i	$0.227643\pi$
$720$	−4.95912	−0.184816
$721$	2.38426	0.0887943
$722$	−75.9939	−2.82820
$723$	0.201124	0.00747990
$724$	−84.7514	−3.14976
$725$	27.8110	1.03288
$726$	−23.6764	−0.878715
$727$	35.5340	1.31788	0.658942	−	0.752194i	$-0.271004\pi$
$727$	35.5340	1.31788	0.658942	+	0.752194i	$0.271004\pi$
$728$	−1.93055	−0.0715510
$729$	1.00000	0.0370370
$730$	24.5390	0.908229
$731$	−1.35524	−0.0501253
$732$	15.7430	0.581877
$733$	−25.6400	−0.947033	−0.473517	−	0.880785i	$-0.657016\pi$
$733$	−25.6400	−0.947033	−0.473517	+	0.880785i	$0.657016\pi$
$734$	−2.72008	−0.100400
$735$	−26.1996	−0.966387
$736$	23.6393	0.871355
$737$	7.01147	0.258271
$738$	−19.5648	−0.720192
$739$	−51.5183	−1.89513	−0.947566	−	0.319560i	$-0.896465\pi$
$739$	−51.5183	−1.89513	−0.947566	+	0.319560i	$0.896465\pi$
$740$	−84.3197	−3.09965
$741$	−10.9249	−0.401336
$742$	−6.01458	−0.220802
$743$	27.3960	1.00506	0.502530	−	0.864560i	$-0.332403\pi$
$743$	27.3960	1.00506	0.502530	+	0.864560i	$0.332403\pi$
$744$	−14.8873	−0.545796
$745$	−47.1793	−1.72852
$746$	−5.65575	−0.207072
$747$	−5.73202	−0.209724
$748$	14.0314	0.513039
$749$	3.50793	0.128177
$750$	−40.5733	−1.48153
$751$	28.2769	1.03184	0.515919	−	0.856637i	$-0.327450\pi$
$751$	28.2769	1.03184	0.515919	+	0.856637i	$0.327450\pi$
$752$	0.473026	0.0172495
$753$	−16.0615	−0.585313
$754$	10.4370	0.380093
$755$	−17.7929	−0.647549
$756$	1.25418	0.0456143
$757$	−48.0219	−1.74539	−0.872693	−	0.488270i	$-0.837628\pi$
$757$	−48.0219	−1.74539	−0.872693	+	0.488270i	$0.837628\pi$
$758$	−84.7197	−3.07716
$759$	−5.59811	−0.203199
$760$	−96.8638	−3.51362
$761$	43.1110	1.56277	0.781387	−	0.624047i	$-0.214513\pi$
$761$	43.1110	1.56277	0.781387	+	0.624047i	$0.214513\pi$
$762$	9.87539	0.357748
$763$	−1.83485	−0.0664261
$764$	−30.8593	−1.11645
$765$	−15.9435	−0.576438
$766$	15.7116	0.567684
$767$	−1.60452	−0.0579360
$768$	23.4400	0.845816
$769$	12.9011	0.465225	0.232612	−	0.972570i	$-0.425273\pi$
$769$	12.9011	0.465225	0.232612	+	0.972570i	$0.425273\pi$
$770$	−3.05628	−0.110141
$771$	10.4350	0.375807
$772$	13.0372	0.469219
$773$	16.4881	0.593036	0.296518	−	0.955027i	$-0.404175\pi$
$773$	16.4881	0.593036	0.296518	+	0.955027i	$0.404175\pi$
$774$	0.760685	0.0273422
$775$	−40.0393	−1.43825
$776$	−2.01127	−0.0722003
$777$	2.25139	0.0807682
$778$	−80.6530	−2.89155
$779$	−59.7402	−2.14042
$780$	−20.3967	−0.730320
$781$	10.0684	0.360276
$782$	−57.4952	−2.05602
$783$	−2.91708	−0.104248
$784$	−8.93961	−0.319272
$785$	61.3542	2.18983
$786$	−2.00529	−0.0715265
$787$	21.8195	0.777780	0.388890	−	0.921284i	$-0.372859\pi$
$787$	21.8195	0.777780	0.388890	+	0.921284i	$0.372859\pi$
$788$	10.0007	0.356260
$789$	−2.43958	−0.0868513
$790$	58.7548	2.09040
$791$	5.89677	0.209665
$792$	−3.38831	−0.120398
$793$	6.83608	0.242756
$794$	26.9681	0.957063
$795$	−27.3387	−0.969604
$796$	73.5981	2.60861
$797$	16.7029	0.591646	0.295823	−	0.955243i	$-0.404406\pi$
$797$	16.7029	0.591646	0.295823	+	0.955243i	$0.404406\pi$
$798$	6.01160	0.212808
$799$	1.52077	0.0538010
$800$	38.4809	1.36051
$801$	1.44604	0.0510932
$802$	−22.6791	−0.800827
$803$	2.62101	0.0924935
$804$	−25.7483	−0.908074
$805$	7.97783	0.281181
$806$	−15.0260	−0.529270
$807$	−28.6991	−1.01026
$808$	−39.0595	−1.37411
$809$	11.3112	0.397679	0.198840	−	0.980032i	$-0.436283\pi$
$809$	11.3112	0.397679	0.198840	+	0.980032i	$0.436283\pi$
$810$	8.94895	0.314434
$811$	33.6181	1.18049	0.590246	−	0.807224i	$-0.299031\pi$
$811$	33.6181	1.18049	0.590246	+	0.807224i	$0.299031\pi$
$812$	−3.65856	−0.128390
$813$	25.2787	0.886562
$814$	−14.1377	−0.495527
$815$	22.2155	0.778174
$816$	−5.44010	−0.190442
$817$	2.32271	0.0812614
$818$	−59.4053	−2.07706
$819$	0.544606	0.0190301
$820$	−111.535	−3.89496
$821$	46.0957	1.60875	0.804375	−	0.594121i	$-0.202500\pi$
$821$	46.0957	1.60875	0.804375	+	0.594121i	$0.202500\pi$
$822$	36.9755	1.28967
$823$	0.618695	0.0215664	0.0107832	−	0.999942i	$-0.496568\pi$
$823$	0.618695	0.0215664	0.0107832	+	0.999942i	$0.496568\pi$
$824$	23.6546	0.824046
$825$	−9.11282	−0.317268
$826$	0.882914	0.0307205
$827$	−28.8681	−1.00384	−0.501920	−	0.864914i	$-0.667373\pi$
$827$	−28.8681	−1.00384	−0.501920	+	0.864914i	$0.667373\pi$
$828$	20.5580	0.714442
$829$	7.53419	0.261673	0.130837	−	0.991404i	$-0.458234\pi$
$829$	7.53419	0.261673	0.130837	+	0.991404i	$0.458234\pi$
$830$	−51.2955	−1.78049
$831$	13.9665	0.484492
$832$	18.4066	0.638135
$833$	−28.7407	−0.995805
$834$	39.1823	1.35677
$835$	−21.0696	−0.729143
$836$	−24.0481	−0.831721
$837$	4.19969	0.145163
$838$	77.6475	2.68229
$839$	38.1569	1.31732	0.658661	−	0.752439i	$-0.271123\pi$
$839$	38.1569	1.31732	0.658661	+	0.752439i	$0.271123\pi$
$840$	4.82866	0.166605
$841$	−20.4906	−0.706574
$842$	53.4545	1.84216
$843$	−1.37266	−0.0472769
$844$	66.7917	2.29906
$845$	40.7034	1.40024
$846$	−0.853596	−0.0293472
$847$	3.60389	0.123831
$848$	−9.32828	−0.320334
$849$	−0.844613	−0.0289871
$850$	−93.5929	−3.21021
$851$	36.9038	1.26505
$852$	−36.9744	−1.26672
$853$	13.2072	0.452205	0.226103	−	0.974103i	$-0.427402\pi$
$853$	13.2072	0.452205	0.226103	+	0.974103i	$0.427402\pi$
$854$	−3.76166	−0.128721
$855$	27.3251	0.934500
$856$	34.8028	1.18953
$857$	4.61137	0.157521	0.0787606	−	0.996894i	$-0.474904\pi$
$857$	4.61137	0.157521	0.0787606	+	0.996894i	$0.474904\pi$
$858$	−3.41988	−0.116753
$859$	−25.7290	−0.877862	−0.438931	−	0.898521i	$-0.644643\pi$
$859$	−25.7290	−0.877862	−0.438931	+	0.898521i	$0.644643\pi$
$860$	4.33649	0.147873
$861$	2.97805	0.101492
$862$	73.2118	2.49360
$863$	26.2976	0.895179	0.447590	−	0.894239i	$-0.352283\pi$
$863$	26.2976	0.895179	0.447590	+	0.894239i	$0.352283\pi$
$864$	−4.03624	−0.137316
$865$	80.3529	2.73208
$866$	70.8904	2.40895
$867$	−0.489814	−0.0166350
$868$	5.26719	0.178780
$869$	6.27561	0.212885
$870$	−26.1048	−0.885036
$871$	−11.1807	−0.378845
$872$	−18.2039	−0.616460
$873$	0.567376	0.0192028
$874$	98.5395	3.33315
$875$	6.17583	0.208781
$876$	−9.62519	−0.325205
$877$	11.4348	0.386125	0.193063	−	0.981186i	$-0.438158\pi$
$877$	11.4348	0.386125	0.193063	+	0.981186i	$0.438158\pi$
$878$	−13.8335	−0.466857
$879$	7.85101	0.264808
$880$	−4.74011	−0.159789
$881$	15.2416	0.513502	0.256751	−	0.966478i	$-0.417348\pi$
$881$	15.2416	0.513502	0.256751	+	0.966478i	$0.417348\pi$
$882$	16.1319	0.543190
$883$	19.5016	0.656282	0.328141	−	0.944629i	$-0.393578\pi$
$883$	19.5016	0.656282	0.328141	+	0.944629i	$0.393578\pi$
$884$	−22.3750	−0.752552
$885$	4.01320	0.134902
$886$	52.8829	1.77664
$887$	−11.8951	−0.399399	−0.199699	−	0.979857i	$-0.563997\pi$
$887$	−11.8951	−0.399399	−0.199699	+	0.979857i	$0.563997\pi$
$888$	22.3364	0.749560
$889$	−1.50318	−0.0504149
$890$	12.9405	0.433767
$891$	0.955838	0.0320218
$892$	−65.3353	−2.18759
$893$	−2.60641	−0.0872202
$894$	29.0498	0.971569
$895$	81.2633	2.71633
$896$	−7.24422	−0.242013
$897$	8.92694	0.298062
$898$	67.2271	2.24340
$899$	−12.2508	−0.408589
$900$	33.4652	1.11551
$901$	−29.9902	−0.999120
$902$	−18.7008	−0.622669
$903$	−0.115787	−0.00385315
$904$	58.5028	1.94577
$905$	92.0476	3.05977
$906$	10.9556	0.363976
$907$	−56.1926	−1.86585	−0.932923	−	0.360077i	$-0.882750\pi$
$907$	−56.1926	−1.86585	−0.932923	+	0.360077i	$0.882750\pi$
$908$	−31.2677	−1.03765
$909$	11.0186	0.365465
$910$	4.87365	0.161560
$911$	−27.4790	−0.910419	−0.455209	−	0.890384i	$-0.650436\pi$
$911$	−27.4790	−0.910419	−0.455209	+	0.890384i	$0.650436\pi$
$912$	9.32365	0.308737
$913$	−5.47888	−0.181324
$914$	−64.0925	−2.11999
$915$	−17.0983	−0.565251
$916$	−88.9885	−2.94026
$917$	0.305235	0.0100797
$918$	9.81689	0.324006
$919$	33.3953	1.10161	0.550805	−	0.834634i	$-0.314321\pi$
$919$	33.3953	1.10161	0.550805	+	0.834634i	$0.314321\pi$
$920$	79.1493	2.60947
$921$	10.1872	0.335679
$922$	−75.5662	−2.48864
$923$	−16.0554	−0.528471
$924$	1.19880	0.0394375
$925$	60.0735	1.97520
$926$	77.4097	2.54384
$927$	−6.67292	−0.219167
$928$	11.7740	0.386501
$929$	−7.28767	−0.239101	−0.119550	−	0.992828i	$-0.538145\pi$
$929$	−7.28767	−0.239101	−0.119550	+	0.992828i	$0.538145\pi$
$930$	37.5828	1.23239
$931$	49.2579	1.61436
$932$	−73.6373	−2.41207
$933$	−0.601197	−0.0196823
$934$	34.1215	1.11649
$935$	−15.2394	−0.498381
$936$	5.40312	0.176606
$937$	3.25902	0.106468	0.0532338	−	0.998582i	$-0.483047\pi$
$937$	3.25902	0.106468	0.0532338	+	0.998582i	$0.483047\pi$
$938$	6.15238	0.200882
$939$	−14.8096	−0.483295
$940$	−4.86616	−0.158717
$941$	49.6252	1.61774	0.808868	−	0.587991i	$-0.200081\pi$
$941$	49.6252	1.61774	0.808868	+	0.587991i	$0.200081\pi$
$942$	−37.7777	−1.23086
$943$	48.8149	1.58963
$944$	1.36935	0.0445685
$945$	−1.36216	−0.0443110
$946$	0.727091	0.0236398
$947$	20.7570	0.674512	0.337256	−	0.941413i	$-0.390501\pi$
$947$	20.7570	0.674512	0.337256	+	0.941413i	$0.390501\pi$
$948$	−23.0460	−0.748501
$949$	−4.17956	−0.135674
$950$	160.407	5.20428
$951$	−22.8369	−0.740538
$952$	5.29698	0.171676
$953$	−58.3855	−1.89129	−0.945646	−	0.325199i	$-0.894569\pi$
$953$	−58.3855	−1.89129	−0.945646	+	0.325199i	$0.894569\pi$
$954$	16.8333	0.544997
$955$	33.5160	1.08455
$956$	2.48752	0.0804521
$957$	−2.78826	−0.0901315
$958$	−14.4221	−0.465956
$959$	−5.62820	−0.181744
$960$	−46.0383	−1.48588
$961$	−13.3626	−0.431051
$962$	22.5445	0.726864
$963$	−9.81781	−0.316375
$964$	−0.705975	−0.0227379
$965$	−14.1596	−0.455813
$966$	−4.91219	−0.158047
$967$	3.43044	0.110315	0.0551577	−	0.998478i	$-0.482434\pi$
$967$	3.43044	0.110315	0.0551577	+	0.998478i	$0.482434\pi$
$968$	35.7548	1.14920
$969$	29.9754	0.962948
$970$	5.07741	0.163026
$971$	−9.27478	−0.297642	−0.148821	−	0.988864i	$-0.547548\pi$
$971$	−9.27478	−0.297642	−0.148821	+	0.988864i	$0.547548\pi$
$972$	−3.51014	−0.112588
$973$	−5.96410	−0.191200
$974$	−48.5608	−1.55599
$975$	14.5316	0.465385
$976$	−5.83413	−0.186746
$977$	−3.56185	−0.113954	−0.0569768	−	0.998376i	$-0.518146\pi$
$977$	−3.56185	−0.113954	−0.0569768	+	0.998376i	$0.518146\pi$
$978$	−13.6787	−0.437398
$979$	1.38218	0.0441746
$980$	91.9643	2.93769
$981$	5.13528	0.163957
$982$	61.5865	1.96530
$983$	9.50623	0.303202	0.151601	−	0.988442i	$-0.451557\pi$
$983$	9.50623	0.303202	0.151601	+	0.988442i	$0.451557\pi$
$984$	29.5457	0.941882
$985$	−10.8616	−0.346081
$986$	−28.6367	−0.911977
$987$	0.129930	0.00413570
$988$	38.3479	1.22001
$989$	−1.89793	−0.0603507
$990$	8.55374	0.271856
$991$	−5.12534	−0.162812	−0.0814060	−	0.996681i	$-0.525941\pi$
$991$	−5.12534	−0.162812	−0.0814060	+	0.996681i	$0.525941\pi$
$992$	−16.9510	−0.538193
$993$	−23.2797	−0.738758
$994$	8.83476	0.280221
$995$	−79.9341	−2.53408
$996$	20.1202	0.637533
$997$	42.0120	1.33053	0.665266	−	0.746606i	$-0.268318\pi$
$997$	42.0120	1.33053	0.665266	+	0.746606i	$0.268318\pi$
$998$	−67.0560	−2.12262
$999$	−6.30106	−0.199357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.c.1.11	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.c.1.11	✓	119	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34737 q^{2} -1.00000 q^{3} +3.51014 q^{4} -3.81233 q^{5} +2.34737 q^{6} -0.357303 q^{7} -3.54486 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.34737 q^{2} -1.00000 q^{3} +3.51014 q^{4} -3.81233 q^{5} +2.34737 q^{6} -0.357303 q^{7} -3.54486 q^{8} +1.00000 q^{9} +8.94895 q^{10} +0.955838 q^{11} -3.51014 q^{12} -1.52421 q^{13} +0.838722 q^{14} +3.81233 q^{15} +1.30081 q^{16} +4.18208 q^{17} -2.34737 q^{18} -7.16757 q^{19} -13.3818 q^{20} +0.357303 q^{21} -2.24370 q^{22} +5.85676 q^{23} +3.54486 q^{24} +9.53386 q^{25} +3.57789 q^{26} -1.00000 q^{27} -1.25418 q^{28} +2.91708 q^{29} -8.94895 q^{30} -4.19969 q^{31} +4.03624 q^{32} -0.955838 q^{33} -9.81689 q^{34} +1.36216 q^{35} +3.51014 q^{36} +6.30106 q^{37} +16.8249 q^{38} +1.52421 q^{39} +13.5142 q^{40} +8.33479 q^{41} -0.838722 q^{42} -0.324058 q^{43} +3.35513 q^{44} -3.81233 q^{45} -13.7480 q^{46} +0.363639 q^{47} -1.30081 q^{48} -6.87233 q^{49} -22.3795 q^{50} -4.18208 q^{51} -5.35020 q^{52} -7.17112 q^{53} +2.34737 q^{54} -3.64397 q^{55} +1.26659 q^{56} +7.16757 q^{57} -6.84747 q^{58} +1.05269 q^{59} +13.3818 q^{60} -4.48499 q^{61} +9.85823 q^{62} -0.357303 q^{63} -12.0762 q^{64} +5.81080 q^{65} +2.24370 q^{66} +7.33541 q^{67} +14.6797 q^{68} -5.85676 q^{69} -3.19749 q^{70} +10.5336 q^{71} -3.54486 q^{72} +2.74211 q^{73} -14.7909 q^{74} -9.53386 q^{75} -25.1592 q^{76} -0.341524 q^{77} -3.57789 q^{78} +6.56556 q^{79} -4.95912 q^{80} +1.00000 q^{81} -19.5648 q^{82} -5.73202 q^{83} +1.25418 q^{84} -15.9435 q^{85} +0.760685 q^{86} -2.91708 q^{87} -3.38831 q^{88} +1.44604 q^{89} +8.94895 q^{90} +0.544606 q^{91} +20.5580 q^{92} +4.19969 q^{93} -0.853596 q^{94} +27.3251 q^{95} -4.03624 q^{96} +0.567376 q^{97} +16.1319 q^{98} +0.955838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * q^99

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