LMFDB - Embedded newform 2738.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2738,2,Mod(1,2738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2738, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2738 = 2 \cdot 37^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2738.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:	$21.8630400734$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} -2.73205 q^{6} +4.00000 q^{7} +1.00000 q^{8} +4.46410 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} -2.73205 q^{6} +4.00000 q^{7} +1.00000 q^{8} +4.46410 q^{9} +1.73205 q^{10} -1.26795 q^{11} -2.73205 q^{12} -6.00000 q^{13} +4.00000 q^{14} -4.73205 q^{15} +1.00000 q^{16} -1.73205 q^{17} +4.46410 q^{18} -4.73205 q^{19} +1.73205 q^{20} -10.9282 q^{21} -1.26795 q^{22} -4.73205 q^{23} -2.73205 q^{24} -2.00000 q^{25} -6.00000 q^{26} -4.00000 q^{27} +4.00000 q^{28} -7.73205 q^{29} -4.73205 q^{30} -4.73205 q^{31} +1.00000 q^{32} +3.46410 q^{33} -1.73205 q^{34} +6.92820 q^{35} +4.46410 q^{36} -4.73205 q^{38} +16.3923 q^{39} +1.73205 q^{40} +6.46410 q^{41} -10.9282 q^{42} -2.53590 q^{43} -1.26795 q^{44} +7.73205 q^{45} -4.73205 q^{46} -5.66025 q^{47} -2.73205 q^{48} +9.00000 q^{49} -2.00000 q^{50} +4.73205 q^{51} -6.00000 q^{52} -9.46410 q^{53} -4.00000 q^{54} -2.19615 q^{55} +4.00000 q^{56} +12.9282 q^{57} -7.73205 q^{58} +9.46410 q^{59} -4.73205 q^{60} +2.66025 q^{61} -4.73205 q^{62} +17.8564 q^{63} +1.00000 q^{64} -10.3923 q^{65} +3.46410 q^{66} +4.19615 q^{67} -1.73205 q^{68} +12.9282 q^{69} +6.92820 q^{70} +9.46410 q^{71} +4.46410 q^{72} -8.39230 q^{73} +5.46410 q^{75} -4.73205 q^{76} -5.07180 q^{77} +16.3923 q^{78} +2.19615 q^{79} +1.73205 q^{80} -2.46410 q^{81} +6.46410 q^{82} -5.66025 q^{83} -10.9282 q^{84} -3.00000 q^{85} -2.53590 q^{86} +21.1244 q^{87} -1.26795 q^{88} -5.19615 q^{89} +7.73205 q^{90} -24.0000 q^{91} -4.73205 q^{92} +12.9282 q^{93} -5.66025 q^{94} -8.19615 q^{95} -2.73205 q^{96} +5.19615 q^{97} +9.00000 q^{98} -5.66025 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 8 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 8 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 8 q^{7} + 2 q^{8} + 2 q^{9} - 6 q^{11} - 2 q^{12} - 12 q^{13} + 8 q^{14} - 6 q^{15} + 2 q^{16} + 2 q^{18} - 6 q^{19} - 8 q^{21} - 6 q^{22} - 6 q^{23} - 2 q^{24} - 4 q^{25} - 12 q^{26} - 8 q^{27} + 8 q^{28} - 12 q^{29} - 6 q^{30} - 6 q^{31} + 2 q^{32} + 2 q^{36} - 6 q^{38} + 12 q^{39} + 6 q^{41} - 8 q^{42} - 12 q^{43} - 6 q^{44} + 12 q^{45} - 6 q^{46} + 6 q^{47} - 2 q^{48} + 18 q^{49} - 4 q^{50} + 6 q^{51} - 12 q^{52} - 12 q^{53} - 8 q^{54} + 6 q^{55} + 8 q^{56} + 12 q^{57} - 12 q^{58} + 12 q^{59} - 6 q^{60} - 12 q^{61} - 6 q^{62} + 8 q^{63} + 2 q^{64} - 2 q^{67} + 12 q^{69} + 12 q^{71} + 2 q^{72} + 4 q^{73} + 4 q^{75} - 6 q^{76} - 24 q^{77} + 12 q^{78} - 6 q^{79} + 2 q^{81} + 6 q^{82} + 6 q^{83} - 8 q^{84} - 6 q^{85} - 12 q^{86} + 18 q^{87} - 6 q^{88} + 12 q^{90} - 48 q^{91} - 6 q^{92} + 12 q^{93} + 6 q^{94} - 6 q^{95} - 2 q^{96} + 18 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 8 * q^7 + 2 * q^8 + 2 * q^9 - 6 * q^11 - 2 * q^12 - 12 * q^13 + 8 * q^14 - 6 * q^15 + 2 * q^16 + 2 * q^18 - 6 * q^19 - 8 * q^21 - 6 * q^22 - 6 * q^23 - 2 * q^24 - 4 * q^25 - 12 * q^26 - 8 * q^27 + 8 * q^28 - 12 * q^29 - 6 * q^30 - 6 * q^31 + 2 * q^32 + 2 * q^36 - 6 * q^38 + 12 * q^39 + 6 * q^41 - 8 * q^42 - 12 * q^43 - 6 * q^44 + 12 * q^45 - 6 * q^46 + 6 * q^47 - 2 * q^48 + 18 * q^49 - 4 * q^50 + 6 * q^51 - 12 * q^52 - 12 * q^53 - 8 * q^54 + 6 * q^55 + 8 * q^56 + 12 * q^57 - 12 * q^58 + 12 * q^59 - 6 * q^60 - 12 * q^61 - 6 * q^62 + 8 * q^63 + 2 * q^64 - 2 * q^67 + 12 * q^69 + 12 * q^71 + 2 * q^72 + 4 * q^73 + 4 * q^75 - 6 * q^76 - 24 * q^77 + 12 * q^78 - 6 * q^79 + 2 * q^81 + 6 * q^82 + 6 * q^83 - 8 * q^84 - 6 * q^85 - 12 * q^86 + 18 * q^87 - 6 * q^88 + 12 * q^90 - 48 * q^91 - 6 * q^92 + 12 * q^93 + 6 * q^94 - 6 * q^95 - 2 * q^96 + 18 * q^98 + 6 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.73205	−1.57735	−0.788675	−	0.614810i	$-0.789233\pi$
$3$	−2.73205	−1.57735	−0.788675	+	0.614810i	$0.789233\pi$
$4$	1.00000	0.500000
$5$	1.73205	0.774597	0.387298	−	0.921954i	$-0.373408\pi$
$5$	1.73205	0.774597	0.387298	+	0.921954i	$0.373408\pi$
$6$	−2.73205	−1.11536
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	1.00000	0.353553
$9$	4.46410	1.48803
$10$	1.73205	0.547723
$11$	−1.26795	−0.382301	−0.191151	−	0.981561i	$-0.561222\pi$
$11$	−1.26795	−0.382301	−0.191151	+	0.981561i	$0.561222\pi$
$12$	−2.73205	−0.788675
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	4.00000	1.06904
$15$	−4.73205	−1.22181
$16$	1.00000	0.250000
$17$	−1.73205	−0.420084	−0.210042	−	0.977692i	$-0.567360\pi$
$17$	−1.73205	−0.420084	−0.210042	+	0.977692i	$0.567360\pi$
$18$	4.46410	1.05220
$19$	−4.73205	−1.08561	−0.542803	−	0.839860i	$-0.682637\pi$
$19$	−4.73205	−1.08561	−0.542803	+	0.839860i	$0.682637\pi$
$20$	1.73205	0.387298
$21$	−10.9282	−2.38473
$22$	−1.26795	−0.270328
$23$	−4.73205	−0.986701	−0.493350	−	0.869831i	$-0.664228\pi$
$23$	−4.73205	−0.986701	−0.493350	+	0.869831i	$0.664228\pi$
$24$	−2.73205	−0.557678
$25$	−2.00000	−0.400000
$26$	−6.00000	−1.17670
$27$	−4.00000	−0.769800
$28$	4.00000	0.755929
$29$	−7.73205	−1.43581	−0.717903	−	0.696143i	$-0.754898\pi$
$29$	−7.73205	−1.43581	−0.717903	+	0.696143i	$0.754898\pi$
$30$	−4.73205	−0.863950
$31$	−4.73205	−0.849901	−0.424951	−	0.905216i	$-0.639709\pi$
$31$	−4.73205	−0.849901	−0.424951	+	0.905216i	$0.639709\pi$
$32$	1.00000	0.176777
$33$	3.46410	0.603023
$34$	−1.73205	−0.297044
$35$	6.92820	1.17108
$36$	4.46410	0.744017
$37$	0	0
$37$	0	0
$38$	−4.73205	−0.767640
$39$	16.3923	2.62487
$40$	1.73205	0.273861
$41$	6.46410	1.00952	0.504762	−	0.863259i	$-0.331580\pi$
$41$	6.46410	1.00952	0.504762	+	0.863259i	$0.331580\pi$
$42$	−10.9282	−1.68626
$43$	−2.53590	−0.386721	−0.193360	−	0.981128i	$-0.561939\pi$
$43$	−2.53590	−0.386721	−0.193360	+	0.981128i	$0.561939\pi$
$44$	−1.26795	−0.191151
$45$	7.73205	1.15263
$46$	−4.73205	−0.697703
$47$	−5.66025	−0.825633	−0.412816	−	0.910814i	$-0.635455\pi$
$47$	−5.66025	−0.825633	−0.412816	+	0.910814i	$0.635455\pi$
$48$	−2.73205	−0.394338
$49$	9.00000	1.28571
$50$	−2.00000	−0.282843
$51$	4.73205	0.662620
$52$	−6.00000	−0.832050
$53$	−9.46410	−1.29999	−0.649997	−	0.759937i	$-0.725230\pi$
$53$	−9.46410	−1.29999	−0.649997	+	0.759937i	$0.725230\pi$
$54$	−4.00000	−0.544331
$55$	−2.19615	−0.296129
$56$	4.00000	0.534522
$57$	12.9282	1.71238
$58$	−7.73205	−1.01527
$59$	9.46410	1.23212	0.616061	−	0.787699i	$-0.288728\pi$
$59$	9.46410	1.23212	0.616061	+	0.787699i	$0.288728\pi$
$60$	−4.73205	−0.610905
$61$	2.66025	0.340611	0.170305	−	0.985391i	$-0.445525\pi$
$61$	2.66025	0.340611	0.170305	+	0.985391i	$0.445525\pi$
$62$	−4.73205	−0.600971
$63$	17.8564	2.24970
$64$	1.00000	0.125000
$65$	−10.3923	−1.28901
$66$	3.46410	0.426401
$67$	4.19615	0.512642	0.256321	−	0.966592i	$-0.417490\pi$
$67$	4.19615	0.512642	0.256321	+	0.966592i	$0.417490\pi$
$68$	−1.73205	−0.210042
$69$	12.9282	1.55637
$70$	6.92820	0.828079
$71$	9.46410	1.12318	0.561591	−	0.827415i	$-0.310189\pi$
$71$	9.46410	1.12318	0.561591	+	0.827415i	$0.310189\pi$
$72$	4.46410	0.526099
$73$	−8.39230	−0.982245	−0.491122	−	0.871091i	$-0.663413\pi$
$73$	−8.39230	−0.982245	−0.491122	+	0.871091i	$0.663413\pi$
$74$	0	0
$75$	5.46410	0.630940
$76$	−4.73205	−0.542803
$77$	−5.07180	−0.577985
$78$	16.3923	1.85606
$79$	2.19615	0.247086	0.123543	−	0.992339i	$-0.460574\pi$
$79$	2.19615	0.247086	0.123543	+	0.992339i	$0.460574\pi$
$80$	1.73205	0.193649
$81$	−2.46410	−0.273789
$82$	6.46410	0.713841
$83$	−5.66025	−0.621294	−0.310647	−	0.950525i	$-0.600546\pi$
$83$	−5.66025	−0.621294	−0.310647	+	0.950525i	$0.600546\pi$
$84$	−10.9282	−1.19236
$85$	−3.00000	−0.325396
$86$	−2.53590	−0.273453
$87$	21.1244	2.26477
$88$	−1.26795	−0.135164
$89$	−5.19615	−0.550791	−0.275396	−	0.961331i	$-0.588809\pi$
$89$	−5.19615	−0.550791	−0.275396	+	0.961331i	$0.588809\pi$
$90$	7.73205	0.815030
$91$	−24.0000	−2.51588
$92$	−4.73205	−0.493350
$93$	12.9282	1.34059
$94$	−5.66025	−0.583811
$95$	−8.19615	−0.840907
$96$	−2.73205	−0.278839
$97$	5.19615	0.527589	0.263795	−	0.964579i	$-0.415026\pi$
$97$	5.19615	0.527589	0.263795	+	0.964579i	$0.415026\pi$
$98$	9.00000	0.909137
$99$	−5.66025	−0.568877
$100$	−2.00000	−0.200000
$101$	−6.46410	−0.643202	−0.321601	−	0.946875i	$-0.604221\pi$
$101$	−6.46410	−0.643202	−0.321601	+	0.946875i	$0.604221\pi$
$102$	4.73205	0.468543
$103$	−6.92820	−0.682656	−0.341328	−	0.939944i	$-0.610877\pi$
$103$	−6.92820	−0.682656	−0.341328	+	0.939944i	$0.610877\pi$
$104$	−6.00000	−0.588348
$105$	−18.9282	−1.84720
$106$	−9.46410	−0.919235
$107$	4.39230	0.424620	0.212310	−	0.977202i	$-0.431901\pi$
$107$	4.39230	0.424620	0.212310	+	0.977202i	$0.431901\pi$
$108$	−4.00000	−0.384900
$109$	4.26795	0.408795	0.204398	−	0.978888i	$-0.434476\pi$
$109$	4.26795	0.408795	0.204398	+	0.978888i	$0.434476\pi$
$110$	−2.19615	−0.209395
$111$	0	0
$112$	4.00000	0.377964
$113$	−7.85641	−0.739069	−0.369534	−	0.929217i	$-0.620483\pi$
$113$	−7.85641	−0.739069	−0.369534	+	0.929217i	$0.620483\pi$
$114$	12.9282	1.21084
$115$	−8.19615	−0.764295
$116$	−7.73205	−0.717903
$117$	−26.7846	−2.47624
$118$	9.46410	0.871241
$119$	−6.92820	−0.635107
$120$	−4.73205	−0.431975
$121$	−9.39230	−0.853846
$122$	2.66025	0.240848
$123$	−17.6603	−1.59237
$124$	−4.73205	−0.424951
$125$	−12.1244	−1.08444
$126$	17.8564	1.59078
$127$	20.5885	1.82693	0.913465	−	0.406917i	$-0.133396\pi$
$127$	20.5885	1.82693	0.913465	+	0.406917i	$0.133396\pi$
$128$	1.00000	0.0883883
$129$	6.92820	0.609994
$130$	−10.3923	−0.911465
$131$	2.19615	0.191879	0.0959394	−	0.995387i	$-0.469415\pi$
$131$	2.19615	0.191879	0.0959394	+	0.995387i	$0.469415\pi$
$132$	3.46410	0.301511
$133$	−18.9282	−1.64128
$134$	4.19615	0.362492
$135$	−6.92820	−0.596285
$136$	−1.73205	−0.148522
$137$	7.39230	0.631567	0.315784	−	0.948831i	$-0.397733\pi$
$137$	7.39230	0.631567	0.315784	+	0.948831i	$0.397733\pi$
$138$	12.9282	1.10052
$139$	−12.1962	−1.03446	−0.517232	−	0.855845i	$-0.673038\pi$
$139$	−12.1962	−1.03446	−0.517232	+	0.855845i	$0.673038\pi$
$140$	6.92820	0.585540
$141$	15.4641	1.30231
$142$	9.46410	0.794210
$143$	7.60770	0.636187
$144$	4.46410	0.372008
$145$	−13.3923	−1.11217
$146$	−8.39230	−0.694552
$147$	−24.5885	−2.02802
$148$	0	0
$149$	−9.92820	−0.813350	−0.406675	−	0.913573i	$-0.633312\pi$
$149$	−9.92820	−0.813350	−0.406675	+	0.913573i	$0.633312\pi$
$150$	5.46410	0.446142
$151$	12.1962	0.992509	0.496254	−	0.868177i	$-0.334708\pi$
$151$	12.1962	0.992509	0.496254	+	0.868177i	$0.334708\pi$
$152$	−4.73205	−0.383820
$153$	−7.73205	−0.625099
$154$	−5.07180	−0.408697
$155$	−8.19615	−0.658331
$156$	16.3923	1.31243
$157$	11.3923	0.909205	0.454602	−	0.890694i	$-0.349781\pi$
$157$	11.3923	0.909205	0.454602	+	0.890694i	$0.349781\pi$
$158$	2.19615	0.174717
$159$	25.8564	2.05055
$160$	1.73205	0.136931
$161$	−18.9282	−1.49175
$162$	−2.46410	−0.193598
$163$	−9.46410	−0.741286	−0.370643	−	0.928775i	$-0.620863\pi$
$163$	−9.46410	−0.741286	−0.370643	+	0.928775i	$0.620863\pi$
$164$	6.46410	0.504762
$165$	6.00000	0.467099
$166$	−5.66025	−0.439321
$167$	6.92820	0.536120	0.268060	−	0.963402i	$-0.413617\pi$
$167$	6.92820	0.536120	0.268060	+	0.963402i	$0.413617\pi$
$168$	−10.9282	−0.843129
$169$	23.0000	1.76923
$170$	−3.00000	−0.230089
$171$	−21.1244	−1.61542
$172$	−2.53590	−0.193360
$173$	−3.92820	−0.298656	−0.149328	−	0.988788i	$-0.547711\pi$
$173$	−3.92820	−0.298656	−0.149328	+	0.988788i	$0.547711\pi$
$174$	21.1244	1.60143
$175$	−8.00000	−0.604743
$176$	−1.26795	−0.0955753
$177$	−25.8564	−1.94349
$178$	−5.19615	−0.389468
$179$	23.3205	1.74306	0.871528	−	0.490345i	$-0.163129\pi$
$179$	23.3205	1.74306	0.871528	+	0.490345i	$0.163129\pi$
$180$	7.73205	0.576313
$181$	5.39230	0.400807	0.200403	−	0.979713i	$-0.435775\pi$
$181$	5.39230	0.400807	0.200403	+	0.979713i	$0.435775\pi$
$182$	−24.0000	−1.77900
$183$	−7.26795	−0.537262
$184$	−4.73205	−0.348851
$185$	0	0
$186$	12.9282	0.947942
$187$	2.19615	0.160599
$188$	−5.66025	−0.412816
$189$	−16.0000	−1.16383
$190$	−8.19615	−0.594611
$191$	6.58846	0.476724	0.238362	−	0.971176i	$-0.423390\pi$
$191$	6.58846	0.476724	0.238362	+	0.971176i	$0.423390\pi$
$192$	−2.73205	−0.197169
$193$	−12.1244	−0.872730	−0.436365	−	0.899770i	$-0.643734\pi$
$193$	−12.1244	−0.872730	−0.436365	+	0.899770i	$0.643734\pi$
$194$	5.19615	0.373062
$195$	28.3923	2.03322
$196$	9.00000	0.642857
$197$	−8.32051	−0.592812	−0.296406	−	0.955062i	$-0.595788\pi$
$197$	−8.32051	−0.592812	−0.296406	+	0.955062i	$0.595788\pi$
$198$	−5.66025	−0.402257
$199$	−18.9282	−1.34178	−0.670892	−	0.741555i	$-0.734089\pi$
$199$	−18.9282	−1.34178	−0.670892	+	0.741555i	$0.734089\pi$
$200$	−2.00000	−0.141421
$201$	−11.4641	−0.808615
$202$	−6.46410	−0.454813
$203$	−30.9282	−2.17073
$204$	4.73205	0.331310
$205$	11.1962	0.781973
$206$	−6.92820	−0.482711
$207$	−21.1244	−1.46824
$208$	−6.00000	−0.416025
$209$	6.00000	0.415029
$210$	−18.9282	−1.30617
$211$	−8.39230	−0.577750	−0.288875	−	0.957367i	$-0.593281\pi$
$211$	−8.39230	−0.577750	−0.288875	+	0.957367i	$0.593281\pi$
$212$	−9.46410	−0.649997
$213$	−25.8564	−1.77165
$214$	4.39230	0.300252
$215$	−4.39230	−0.299553
$216$	−4.00000	−0.272166
$217$	−18.9282	−1.28493
$218$	4.26795	0.289062
$219$	22.9282	1.54934
$220$	−2.19615	−0.148065
$221$	10.3923	0.699062
$222$	0	0
$223$	8.58846	0.575126	0.287563	−	0.957762i	$-0.407155\pi$
$223$	8.58846	0.575126	0.287563	+	0.957762i	$0.407155\pi$
$224$	4.00000	0.267261
$225$	−8.92820	−0.595214
$226$	−7.85641	−0.522600
$227$	−4.73205	−0.314077	−0.157039	−	0.987592i	$-0.550195\pi$
$227$	−4.73205	−0.314077	−0.157039	+	0.987592i	$0.550195\pi$
$228$	12.9282	0.856191
$229$	−19.0000	−1.25556	−0.627778	−	0.778393i	$-0.716035\pi$
$229$	−19.0000	−1.25556	−0.627778	+	0.778393i	$0.716035\pi$
$230$	−8.19615	−0.540438
$231$	13.8564	0.911685
$232$	−7.73205	−0.507634
$233$	25.3923	1.66351	0.831753	−	0.555146i	$-0.187338\pi$
$233$	25.3923	1.66351	0.831753	+	0.555146i	$0.187338\pi$
$234$	−26.7846	−1.75096
$235$	−9.80385	−0.639532
$236$	9.46410	0.616061
$237$	−6.00000	−0.389742
$238$	−6.92820	−0.449089
$239$	18.9282	1.22436	0.612182	−	0.790717i	$-0.290292\pi$
$239$	18.9282	1.22436	0.612182	+	0.790717i	$0.290292\pi$
$240$	−4.73205	−0.305453
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	−9.39230	−0.603760
$243$	18.7321	1.20166
$244$	2.66025	0.170305
$245$	15.5885	0.995910
$246$	−17.6603	−1.12598
$247$	28.3923	1.80656
$248$	−4.73205	−0.300486
$249$	15.4641	0.979998
$250$	−12.1244	−0.766812
$251$	−18.9282	−1.19474	−0.597369	−	0.801967i	$-0.703787\pi$
$251$	−18.9282	−1.19474	−0.597369	+	0.801967i	$0.703787\pi$
$252$	17.8564	1.12485
$253$	6.00000	0.377217
$254$	20.5885	1.29183
$255$	8.19615	0.513263
$256$	1.00000	0.0625000
$257$	−0.803848	−0.0501426	−0.0250713	−	0.999686i	$-0.507981\pi$
$257$	−0.803848	−0.0501426	−0.0250713	+	0.999686i	$0.507981\pi$
$258$	6.92820	0.431331
$259$	0	0
$260$	−10.3923	−0.644503
$261$	−34.5167	−2.13653
$262$	2.19615	0.135679
$263$	11.3205	0.698052	0.349026	−	0.937113i	$-0.386512\pi$
$263$	11.3205	0.698052	0.349026	+	0.937113i	$0.386512\pi$
$264$	3.46410	0.213201
$265$	−16.3923	−1.00697
$266$	−18.9282	−1.16056
$267$	14.1962	0.868790
$268$	4.19615	0.256321
$269$	−28.3923	−1.73111	−0.865555	−	0.500814i	$-0.833034\pi$
$269$	−28.3923	−1.73111	−0.865555	+	0.500814i	$0.833034\pi$
$270$	−6.92820	−0.421637
$271$	16.5885	1.00768	0.503839	−	0.863798i	$-0.331921\pi$
$271$	16.5885	1.00768	0.503839	+	0.863798i	$0.331921\pi$
$272$	−1.73205	−0.105021
$273$	65.5692	3.96843
$274$	7.39230	0.446585
$275$	2.53590	0.152920
$276$	12.9282	0.778186
$277$	17.1962	1.03322	0.516608	−	0.856222i	$-0.327194\pi$
$277$	17.1962	1.03322	0.516608	+	0.856222i	$0.327194\pi$
$278$	−12.1962	−0.731477
$279$	−21.1244	−1.26468
$280$	6.92820	0.414039
$281$	0.803848	0.0479535	0.0239768	−	0.999713i	$-0.492367\pi$
$281$	0.803848	0.0479535	0.0239768	+	0.999713i	$0.492367\pi$
$282$	15.4641	0.920874
$283$	−9.46410	−0.562582	−0.281291	−	0.959622i	$-0.590763\pi$
$283$	−9.46410	−0.562582	−0.281291	+	0.959622i	$0.590763\pi$
$284$	9.46410	0.561591
$285$	22.3923	1.32641
$286$	7.60770	0.449852
$287$	25.8564	1.52626
$288$	4.46410	0.263050
$289$	−14.0000	−0.823529
$290$	−13.3923	−0.786423
$291$	−14.1962	−0.832193
$292$	−8.39230	−0.491122
$293$	4.60770	0.269184	0.134592	−	0.990901i	$-0.457028\pi$
$293$	4.60770	0.269184	0.134592	+	0.990901i	$0.457028\pi$
$294$	−24.5885	−1.43403
$295$	16.3923	0.954397
$296$	0	0
$297$	5.07180	0.294295
$298$	−9.92820	−0.575125
$299$	28.3923	1.64197
$300$	5.46410	0.315470
$301$	−10.1436	−0.584667
$302$	12.1962	0.701810
$303$	17.6603	1.01456
$304$	−4.73205	−0.271402
$305$	4.60770	0.263836
$306$	−7.73205	−0.442012
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	−5.07180	−0.288992
$309$	18.9282	1.07679
$310$	−8.19615	−0.465510
$311$	−4.39230	−0.249065	−0.124532	−	0.992216i	$-0.539743\pi$
$311$	−4.39230	−0.249065	−0.124532	+	0.992216i	$0.539743\pi$
$312$	16.3923	0.928032
$313$	9.58846	0.541972	0.270986	−	0.962583i	$-0.412650\pi$
$313$	9.58846	0.541972	0.270986	+	0.962583i	$0.412650\pi$
$314$	11.3923	0.642905
$315$	30.9282	1.74261
$316$	2.19615	0.123543
$317$	−9.00000	−0.505490	−0.252745	−	0.967533i	$-0.581333\pi$
$317$	−9.00000	−0.505490	−0.252745	+	0.967533i	$0.581333\pi$
$318$	25.8564	1.44996
$319$	9.80385	0.548910
$320$	1.73205	0.0968246
$321$	−12.0000	−0.669775
$322$	−18.9282	−1.05483
$323$	8.19615	0.456046
$324$	−2.46410	−0.136895
$325$	12.0000	0.665640
$326$	−9.46410	−0.524168
$327$	−11.6603	−0.644814
$328$	6.46410	0.356920
$329$	−22.6410	−1.24824
$330$	6.00000	0.330289
$331$	17.0718	0.938351	0.469175	−	0.883105i	$-0.344551\pi$
$331$	17.0718	0.938351	0.469175	+	0.883105i	$0.344551\pi$
$332$	−5.66025	−0.310647
$333$	0	0
$334$	6.92820	0.379094
$335$	7.26795	0.397090
$336$	−10.9282	−0.596182
$337$	7.00000	0.381314	0.190657	−	0.981657i	$-0.438938\pi$
$337$	7.00000	0.381314	0.190657	+	0.981657i	$0.438938\pi$
$338$	23.0000	1.25104
$339$	21.4641	1.16577
$340$	−3.00000	−0.162698
$341$	6.00000	0.324918
$342$	−21.1244	−1.14227
$343$	8.00000	0.431959
$344$	−2.53590	−0.136726
$345$	22.3923	1.20556
$346$	−3.92820	−0.211182
$347$	−28.0526	−1.50594	−0.752970	−	0.658055i	$-0.771380\pi$
$347$	−28.0526	−1.50594	−0.752970	+	0.658055i	$0.771380\pi$
$348$	21.1244	1.13238
$349$	−27.3923	−1.46628	−0.733138	−	0.680080i	$-0.761945\pi$
$349$	−27.3923	−1.46628	−0.733138	+	0.680080i	$0.761945\pi$
$350$	−8.00000	−0.427618
$351$	24.0000	1.28103
$352$	−1.26795	−0.0675819
$353$	5.87564	0.312729	0.156364	−	0.987699i	$-0.450023\pi$
$353$	5.87564	0.312729	0.156364	+	0.987699i	$0.450023\pi$
$354$	−25.8564	−1.37425
$355$	16.3923	0.870013
$356$	−5.19615	−0.275396
$357$	18.9282	1.00179
$358$	23.3205	1.23253
$359$	26.5359	1.40051	0.700256	−	0.713892i	$-0.253069\pi$
$359$	26.5359	1.40051	0.700256	+	0.713892i	$0.253069\pi$
$360$	7.73205	0.407515
$361$	3.39230	0.178542
$362$	5.39230	0.283413
$363$	25.6603	1.34681
$364$	−24.0000	−1.25794
$365$	−14.5359	−0.760844
$366$	−7.26795	−0.379902
$367$	−20.3923	−1.06447	−0.532235	−	0.846597i	$-0.678648\pi$
$367$	−20.3923	−1.06447	−0.532235	+	0.846597i	$0.678648\pi$
$368$	−4.73205	−0.246675
$369$	28.8564	1.50220
$370$	0	0
$371$	−37.8564	−1.96541
$372$	12.9282	0.670296
$373$	−21.7846	−1.12796	−0.563982	−	0.825787i	$-0.690731\pi$
$373$	−21.7846	−1.12796	−0.563982	+	0.825787i	$0.690731\pi$
$374$	2.19615	0.113560
$375$	33.1244	1.71053
$376$	−5.66025	−0.291905
$377$	46.3923	2.38933
$378$	−16.0000	−0.822951
$379$	−16.7846	−0.862167	−0.431084	−	0.902312i	$-0.641869\pi$
$379$	−16.7846	−0.862167	−0.431084	+	0.902312i	$0.641869\pi$
$380$	−8.19615	−0.420454
$381$	−56.2487	−2.88171
$382$	6.58846	0.337095
$383$	−1.85641	−0.0948579	−0.0474290	−	0.998875i	$-0.515103\pi$
$383$	−1.85641	−0.0948579	−0.0474290	+	0.998875i	$0.515103\pi$
$384$	−2.73205	−0.139419
$385$	−8.78461	−0.447705
$386$	−12.1244	−0.617113
$387$	−11.3205	−0.575454
$388$	5.19615	0.263795
$389$	11.1962	0.567667	0.283834	−	0.958874i	$-0.408394\pi$
$389$	11.1962	0.567667	0.283834	+	0.958874i	$0.408394\pi$
$390$	28.3923	1.43770
$391$	8.19615	0.414497
$392$	9.00000	0.454569
$393$	−6.00000	−0.302660
$394$	−8.32051	−0.419181
$395$	3.80385	0.191392
$396$	−5.66025	−0.284438
$397$	5.00000	0.250943	0.125471	−	0.992097i	$-0.459956\pi$
$397$	5.00000	0.250943	0.125471	+	0.992097i	$0.459956\pi$
$398$	−18.9282	−0.948785
$399$	51.7128	2.58888
$400$	−2.00000	−0.100000
$401$	26.7846	1.33756	0.668780	−	0.743461i	$-0.266817\pi$
$401$	26.7846	1.33756	0.668780	+	0.743461i	$0.266817\pi$
$402$	−11.4641	−0.571777
$403$	28.3923	1.41432
$404$	−6.46410	−0.321601
$405$	−4.26795	−0.212076
$406$	−30.9282	−1.53494
$407$	0	0
$408$	4.73205	0.234271
$409$	−2.41154	−0.119243	−0.0596216	−	0.998221i	$-0.518989\pi$
$409$	−2.41154	−0.119243	−0.0596216	+	0.998221i	$0.518989\pi$
$410$	11.1962	0.552939
$411$	−20.1962	−0.996203
$412$	−6.92820	−0.341328
$413$	37.8564	1.86279
$414$	−21.1244	−1.03821
$415$	−9.80385	−0.481252
$416$	−6.00000	−0.294174
$417$	33.3205	1.63171
$418$	6.00000	0.293470
$419$	37.8564	1.84941	0.924703	−	0.380689i	$-0.124313\pi$
$419$	37.8564	1.84941	0.924703	+	0.380689i	$0.124313\pi$
$420$	−18.9282	−0.923602
$421$	20.6603	1.00692	0.503460	−	0.864019i	$-0.332060\pi$
$421$	20.6603	1.00692	0.503460	+	0.864019i	$0.332060\pi$
$422$	−8.39230	−0.408531
$423$	−25.2679	−1.22857
$424$	−9.46410	−0.459617
$425$	3.46410	0.168034
$426$	−25.8564	−1.25275
$427$	10.6410	0.514955
$428$	4.39230	0.212310
$429$	−20.7846	−1.00349
$430$	−4.39230	−0.211816
$431$	16.0526	0.773225	0.386612	−	0.922242i	$-0.373645\pi$
$431$	16.0526	0.773225	0.386612	+	0.922242i	$0.373645\pi$
$432$	−4.00000	−0.192450
$433$	−33.3923	−1.60473	−0.802366	−	0.596832i	$-0.796426\pi$
$433$	−33.3923	−1.60473	−0.802366	+	0.596832i	$0.796426\pi$
$434$	−18.9282	−0.908583
$435$	36.5885	1.75428
$436$	4.26795	0.204398
$437$	22.3923	1.07117
$438$	22.9282	1.09555
$439$	−9.46410	−0.451697	−0.225848	−	0.974162i	$-0.572515\pi$
$439$	−9.46410	−0.451697	−0.225848	+	0.974162i	$0.572515\pi$
$440$	−2.19615	−0.104697
$441$	40.1769	1.91319
$442$	10.3923	0.494312
$443$	2.53590	0.120484	0.0602421	−	0.998184i	$-0.480813\pi$
$443$	2.53590	0.120484	0.0602421	+	0.998184i	$0.480813\pi$
$444$	0	0
$445$	−9.00000	−0.426641
$446$	8.58846	0.406675
$447$	27.1244	1.28294
$448$	4.00000	0.188982
$449$	24.9282	1.17643	0.588217	−	0.808703i	$-0.299830\pi$
$449$	24.9282	1.17643	0.588217	+	0.808703i	$0.299830\pi$
$450$	−8.92820	−0.420880
$451$	−8.19615	−0.385942
$452$	−7.85641	−0.369534
$453$	−33.3205	−1.56553
$454$	−4.73205	−0.222086
$455$	−41.5692	−1.94880
$456$	12.9282	0.605419
$457$	−19.9808	−0.934661	−0.467330	−	0.884083i	$-0.654784\pi$
$457$	−19.9808	−0.934661	−0.467330	+	0.884083i	$0.654784\pi$
$458$	−19.0000	−0.887812
$459$	6.92820	0.323381
$460$	−8.19615	−0.382148
$461$	−33.7128	−1.57016	−0.785081	−	0.619393i	$-0.787379\pi$
$461$	−33.7128	−1.57016	−0.785081	+	0.619393i	$0.787379\pi$
$462$	13.8564	0.644658
$463$	14.5359	0.675540	0.337770	−	0.941229i	$-0.390327\pi$
$463$	14.5359	0.675540	0.337770	+	0.941229i	$0.390327\pi$
$464$	−7.73205	−0.358951
$465$	22.3923	1.03842
$466$	25.3923	1.17628
$467$	−30.2487	−1.39974	−0.699872	−	0.714269i	$-0.746760\pi$
$467$	−30.2487	−1.39974	−0.699872	+	0.714269i	$0.746760\pi$
$468$	−26.7846	−1.23812
$469$	16.7846	0.775041
$470$	−9.80385	−0.452218
$471$	−31.1244	−1.43413
$472$	9.46410	0.435621
$473$	3.21539	0.147844
$474$	−6.00000	−0.275589
$475$	9.46410	0.434243
$476$	−6.92820	−0.317554
$477$	−42.2487	−1.93444
$478$	18.9282	0.865756
$479$	−9.46410	−0.432426	−0.216213	−	0.976346i	$-0.569371\pi$
$479$	−9.46410	−0.432426	−0.216213	+	0.976346i	$0.569371\pi$
$480$	−4.73205	−0.215988
$481$	0	0
$482$	−18.0000	−0.819878
$483$	51.7128	2.35301
$484$	−9.39230	−0.426923
$485$	9.00000	0.408669
$486$	18.7321	0.849703
$487$	−28.0526	−1.27118	−0.635591	−	0.772026i	$-0.719244\pi$
$487$	−28.0526	−1.27118	−0.635591	+	0.772026i	$0.719244\pi$
$488$	2.66025	0.120424
$489$	25.8564	1.16927
$490$	15.5885	0.704215
$491$	28.9808	1.30788	0.653942	−	0.756545i	$-0.273114\pi$
$491$	28.9808	1.30788	0.653942	+	0.756545i	$0.273114\pi$
$492$	−17.6603	−0.796186
$493$	13.3923	0.603159
$494$	28.3923	1.27743
$495$	−9.80385	−0.440650
$496$	−4.73205	−0.212475
$497$	37.8564	1.69809
$498$	15.4641	0.692963
$499$	2.19615	0.0983133	0.0491566	−	0.998791i	$-0.484347\pi$
$499$	2.19615	0.0983133	0.0491566	+	0.998791i	$0.484347\pi$
$500$	−12.1244	−0.542218
$501$	−18.9282	−0.845650
$502$	−18.9282	−0.844807
$503$	18.5885	0.828818	0.414409	−	0.910091i	$-0.363988\pi$
$503$	18.5885	0.828818	0.414409	+	0.910091i	$0.363988\pi$
$504$	17.8564	0.795388
$505$	−11.1962	−0.498222
$506$	6.00000	0.266733
$507$	−62.8372	−2.79070
$508$	20.5885	0.913465
$509$	37.6410	1.66841	0.834204	−	0.551455i	$-0.185927\pi$
$509$	37.6410	1.66841	0.834204	+	0.551455i	$0.185927\pi$
$510$	8.19615	0.362932
$511$	−33.5692	−1.48501
$512$	1.00000	0.0441942
$513$	18.9282	0.835701
$514$	−0.803848	−0.0354562
$515$	−12.0000	−0.528783
$516$	6.92820	0.304997
$517$	7.17691	0.315640
$518$	0	0
$519$	10.7321	0.471085
$520$	−10.3923	−0.455733
$521$	−33.4641	−1.46609	−0.733044	−	0.680181i	$-0.761901\pi$
$521$	−33.4641	−1.46609	−0.733044	+	0.680181i	$0.761901\pi$
$522$	−34.5167	−1.51075
$523$	−18.5885	−0.812816	−0.406408	−	0.913692i	$-0.633219\pi$
$523$	−18.5885	−0.812816	−0.406408	+	0.913692i	$0.633219\pi$
$524$	2.19615	0.0959394
$525$	21.8564	0.953892
$526$	11.3205	0.493598
$527$	8.19615	0.357030
$528$	3.46410	0.150756
$529$	−0.607695	−0.0264215
$530$	−16.3923	−0.712036
$531$	42.2487	1.83344
$532$	−18.9282	−0.820642
$533$	−38.7846	−1.67995
$534$	14.1962	0.614328
$535$	7.60770	0.328909
$536$	4.19615	0.181246
$537$	−63.7128	−2.74941
$538$	−28.3923	−1.22408
$539$	−11.4115	−0.491530
$540$	−6.92820	−0.298142
$541$	27.5885	1.18612	0.593060	−	0.805158i	$-0.297920\pi$
$541$	27.5885	1.18612	0.593060	+	0.805158i	$0.297920\pi$
$542$	16.5885	0.712535
$543$	−14.7321	−0.632213
$544$	−1.73205	−0.0742611
$545$	7.39230	0.316652
$546$	65.5692	2.80610
$547$	18.5885	0.794785	0.397393	−	0.917649i	$-0.369915\pi$
$547$	18.5885	0.794785	0.397393	+	0.917649i	$0.369915\pi$
$548$	7.39230	0.315784
$549$	11.8756	0.506840
$550$	2.53590	0.108131
$551$	36.5885	1.55872
$552$	12.9282	0.550261
$553$	8.78461	0.373560
$554$	17.1962	0.730595
$555$	0	0
$556$	−12.1962	−0.517232
$557$	−34.5167	−1.46252	−0.731259	−	0.682100i	$-0.761067\pi$
$557$	−34.5167	−1.46252	−0.731259	+	0.682100i	$0.761067\pi$
$558$	−21.1244	−0.894265
$559$	15.2154	0.643542
$560$	6.92820	0.292770
$561$	−6.00000	−0.253320
$562$	0.803848	0.0339083
$563$	−42.5885	−1.79489	−0.897445	−	0.441127i	$-0.854579\pi$
$563$	−42.5885	−1.79489	−0.897445	+	0.441127i	$0.854579\pi$
$564$	15.4641	0.651156
$565$	−13.6077	−0.572480
$566$	−9.46410	−0.397806
$567$	−9.85641	−0.413930
$568$	9.46410	0.397105
$569$	16.5167	0.692414	0.346207	−	0.938158i	$-0.387469\pi$
$569$	16.5167	0.692414	0.346207	+	0.938158i	$0.387469\pi$
$570$	22.3923	0.937910
$571$	−36.9808	−1.54760	−0.773798	−	0.633432i	$-0.781646\pi$
$571$	−36.9808	−1.54760	−0.773798	+	0.633432i	$0.781646\pi$
$572$	7.60770	0.318094
$573$	−18.0000	−0.751961
$574$	25.8564	1.07923
$575$	9.46410	0.394680
$576$	4.46410	0.186004
$577$	−31.8564	−1.32620	−0.663100	−	0.748531i	$-0.730760\pi$
$577$	−31.8564	−1.32620	−0.663100	+	0.748531i	$0.730760\pi$
$578$	−14.0000	−0.582323
$579$	33.1244	1.37660
$580$	−13.3923	−0.556085
$581$	−22.6410	−0.939308
$582$	−14.1962	−0.588449
$583$	12.0000	0.496989
$584$	−8.39230	−0.347276
$585$	−46.3923	−1.91809
$586$	4.60770	0.190342
$587$	16.0526	0.662560	0.331280	−	0.943532i	$-0.392520\pi$
$587$	16.0526	0.662560	0.331280	+	0.943532i	$0.392520\pi$
$588$	−24.5885	−1.01401
$589$	22.3923	0.922659
$590$	16.3923	0.674861
$591$	22.7321	0.935072
$592$	0	0
$593$	30.4641	1.25101	0.625505	−	0.780220i	$-0.284893\pi$
$593$	30.4641	1.25101	0.625505	+	0.780220i	$0.284893\pi$
$594$	5.07180	0.208098
$595$	−12.0000	−0.491952
$596$	−9.92820	−0.406675
$597$	51.7128	2.11646
$598$	28.3923	1.16105
$599$	1.26795	0.0518070	0.0259035	−	0.999664i	$-0.491754\pi$
$599$	1.26795	0.0518070	0.0259035	+	0.999664i	$0.491754\pi$
$600$	5.46410	0.223071
$601$	15.7846	0.643868	0.321934	−	0.946762i	$-0.395667\pi$
$601$	15.7846	0.643868	0.321934	+	0.946762i	$0.395667\pi$
$602$	−10.1436	−0.413422
$603$	18.7321	0.762828
$604$	12.1962	0.496254
$605$	−16.2679	−0.661386
$606$	17.6603	0.717399
$607$	40.0526	1.62568	0.812842	−	0.582485i	$-0.197919\pi$
$607$	40.0526	1.62568	0.812842	+	0.582485i	$0.197919\pi$
$608$	−4.73205	−0.191910
$609$	84.4974	3.42401
$610$	4.60770	0.186560
$611$	33.9615	1.37394
$612$	−7.73205	−0.312550
$613$	−33.3923	−1.34870	−0.674351	−	0.738411i	$-0.735577\pi$
$613$	−33.3923	−1.34870	−0.674351	+	0.738411i	$0.735577\pi$
$614$	4.00000	0.161427
$615$	−30.5885	−1.23345
$616$	−5.07180	−0.204349
$617$	11.3205	0.455746	0.227873	−	0.973691i	$-0.426823\pi$
$617$	11.3205	0.455746	0.227873	+	0.973691i	$0.426823\pi$
$618$	18.9282	0.761404
$619$	41.1769	1.65504	0.827520	−	0.561436i	$-0.189751\pi$
$619$	41.1769	1.65504	0.827520	+	0.561436i	$0.189751\pi$
$620$	−8.19615	−0.329165
$621$	18.9282	0.759563
$622$	−4.39230	−0.176115
$623$	−20.7846	−0.832718
$624$	16.3923	0.656217
$625$	−11.0000	−0.440000
$626$	9.58846	0.383232
$627$	−16.3923	−0.654646
$628$	11.3923	0.454602
$629$	0	0
$630$	30.9282	1.23221
$631$	−12.3397	−0.491238	−0.245619	−	0.969367i	$-0.578991\pi$
$631$	−12.3397	−0.491238	−0.245619	+	0.969367i	$0.578991\pi$
$632$	2.19615	0.0873583
$633$	22.9282	0.911314
$634$	−9.00000	−0.357436
$635$	35.6603	1.41513
$636$	25.8564	1.02527
$637$	−54.0000	−2.13956
$638$	9.80385	0.388138
$639$	42.2487	1.67133
$640$	1.73205	0.0684653
$641$	−46.8564	−1.85072	−0.925358	−	0.379093i	$-0.876236\pi$
$641$	−46.8564	−1.85072	−0.925358	+	0.379093i	$0.876236\pi$
$642$	−12.0000	−0.473602
$643$	−9.12436	−0.359829	−0.179915	−	0.983682i	$-0.557582\pi$
$643$	−9.12436	−0.359829	−0.179915	+	0.983682i	$0.557582\pi$
$644$	−18.9282	−0.745876
$645$	12.0000	0.472500
$646$	8.19615	0.322473
$647$	−9.46410	−0.372072	−0.186036	−	0.982543i	$-0.559564\pi$
$647$	−9.46410	−0.372072	−0.186036	+	0.982543i	$0.559564\pi$
$648$	−2.46410	−0.0967991
$649$	−12.0000	−0.471041
$650$	12.0000	0.470679
$651$	51.7128	2.02678
$652$	−9.46410	−0.370643
$653$	6.80385	0.266255	0.133128	−	0.991099i	$-0.457498\pi$
$653$	6.80385	0.266255	0.133128	+	0.991099i	$0.457498\pi$
$654$	−11.6603	−0.455952
$655$	3.80385	0.148629
$656$	6.46410	0.252381
$657$	−37.4641	−1.46161
$658$	−22.6410	−0.882639
$659$	−14.5359	−0.566238	−0.283119	−	0.959085i	$-0.591369\pi$
$659$	−14.5359	−0.566238	−0.283119	+	0.959085i	$0.591369\pi$
$660$	6.00000	0.233550
$661$	29.1962	1.13560	0.567799	−	0.823167i	$-0.307795\pi$
$661$	29.1962	1.13560	0.567799	+	0.823167i	$0.307795\pi$
$662$	17.0718	0.663514
$663$	−28.3923	−1.10267
$664$	−5.66025	−0.219660
$665$	−32.7846	−1.27133
$666$	0	0
$667$	36.5885	1.41671
$668$	6.92820	0.268060
$669$	−23.4641	−0.907175
$670$	7.26795	0.280785
$671$	−3.37307	−0.130216
$672$	−10.9282	−0.421565
$673$	−12.3923	−0.477688	−0.238844	−	0.971058i	$-0.576768\pi$
$673$	−12.3923	−0.477688	−0.238844	+	0.971058i	$0.576768\pi$
$674$	7.00000	0.269630
$675$	8.00000	0.307920
$676$	23.0000	0.884615
$677$	−7.14359	−0.274551	−0.137275	−	0.990533i	$-0.543835\pi$
$677$	−7.14359	−0.274551	−0.137275	+	0.990533i	$0.543835\pi$
$678$	21.4641	0.824324
$679$	20.7846	0.797640
$680$	−3.00000	−0.115045
$681$	12.9282	0.495410
$682$	6.00000	0.229752
$683$	30.9282	1.18343	0.591717	−	0.806145i	$-0.298450\pi$
$683$	30.9282	1.18343	0.591717	+	0.806145i	$0.298450\pi$
$684$	−21.1244	−0.807710
$685$	12.8038	0.489210
$686$	8.00000	0.305441
$687$	51.9090	1.98045
$688$	−2.53590	−0.0966802
$689$	56.7846	2.16332
$690$	22.3923	0.852460
$691$	11.8038	0.449040	0.224520	−	0.974470i	$-0.427919\pi$
$691$	11.8038	0.449040	0.224520	+	0.974470i	$0.427919\pi$
$692$	−3.92820	−0.149328
$693$	−22.6410	−0.860061
$694$	−28.0526	−1.06486
$695$	−21.1244	−0.801292
$696$	21.1244	0.800717
$697$	−11.1962	−0.424085
$698$	−27.3923	−1.03681
$699$	−69.3731	−2.62393
$700$	−8.00000	−0.302372
$701$	25.8564	0.976583	0.488291	−	0.872681i	$-0.337620\pi$
$701$	25.8564	0.976583	0.488291	+	0.872681i	$0.337620\pi$
$702$	24.0000	0.905822
$703$	0	0
$704$	−1.26795	−0.0477876
$705$	26.7846	1.00877
$706$	5.87564	0.221133
$707$	−25.8564	−0.972430
$708$	−25.8564	−0.971743
$709$	30.0000	1.12667	0.563337	−	0.826227i	$-0.309517\pi$
$709$	30.0000	1.12667	0.563337	+	0.826227i	$0.309517\pi$
$710$	16.3923	0.615192
$711$	9.80385	0.367673
$712$	−5.19615	−0.194734
$713$	22.3923	0.838598
$714$	18.9282	0.708370
$715$	13.1769	0.492789
$716$	23.3205	0.871528
$717$	−51.7128	−1.93125
$718$	26.5359	0.990311
$719$	26.4449	0.986227	0.493114	−	0.869965i	$-0.335859\pi$
$719$	26.4449	0.986227	0.493114	+	0.869965i	$0.335859\pi$
$720$	7.73205	0.288157
$721$	−27.7128	−1.03208
$722$	3.39230	0.126249
$723$	49.1769	1.82891
$724$	5.39230	0.200403
$725$	15.4641	0.574322
$726$	25.6603	0.952341
$727$	−25.8564	−0.958961	−0.479481	−	0.877553i	$-0.659175\pi$
$727$	−25.8564	−0.958961	−0.479481	+	0.877553i	$0.659175\pi$
$728$	−24.0000	−0.889499
$729$	−43.7846	−1.62165
$730$	−14.5359	−0.537998
$731$	4.39230	0.162455
$732$	−7.26795	−0.268631
$733$	−36.3923	−1.34418	−0.672090	−	0.740469i	$-0.734603\pi$
$733$	−36.3923	−1.34418	−0.672090	+	0.740469i	$0.734603\pi$
$734$	−20.3923	−0.752694
$735$	−42.5885	−1.57090
$736$	−4.73205	−0.174426
$737$	−5.32051	−0.195983
$738$	28.8564	1.06222
$739$	44.9808	1.65464	0.827322	−	0.561728i	$-0.189863\pi$
$739$	44.9808	1.65464	0.827322	+	0.561728i	$0.189863\pi$
$740$	0	0
$741$	−77.5692	−2.84958
$742$	−37.8564	−1.38975
$743$	−23.9090	−0.877135	−0.438567	−	0.898698i	$-0.644514\pi$
$743$	−23.9090	−0.877135	−0.438567	+	0.898698i	$0.644514\pi$
$744$	12.9282	0.473971
$745$	−17.1962	−0.630018
$746$	−21.7846	−0.797591
$747$	−25.2679	−0.924506
$748$	2.19615	0.0802993
$749$	17.5692	0.641965
$750$	33.1244	1.20953
$751$	15.6077	0.569533	0.284766	−	0.958597i	$-0.408084\pi$
$751$	15.6077	0.569533	0.284766	+	0.958597i	$0.408084\pi$
$752$	−5.66025	−0.206408
$753$	51.7128	1.88452
$754$	46.3923	1.68951
$755$	21.1244	0.768794
$756$	−16.0000	−0.581914
$757$	−7.73205	−0.281026	−0.140513	−	0.990079i	$-0.544875\pi$
$757$	−7.73205	−0.281026	−0.140513	+	0.990079i	$0.544875\pi$
$758$	−16.7846	−0.609644
$759$	−16.3923	−0.595003
$760$	−8.19615	−0.297306
$761$	2.32051	0.0841184	0.0420592	−	0.999115i	$-0.486608\pi$
$761$	2.32051	0.0841184	0.0420592	+	0.999115i	$0.486608\pi$
$762$	−56.2487	−2.03768
$763$	17.0718	0.618041
$764$	6.58846	0.238362
$765$	−13.3923	−0.484200
$766$	−1.85641	−0.0670747
$767$	−56.7846	−2.05037
$768$	−2.73205	−0.0985844
$769$	−33.7128	−1.21572	−0.607858	−	0.794046i	$-0.707971\pi$
$769$	−33.7128	−1.21572	−0.607858	+	0.794046i	$0.707971\pi$
$770$	−8.78461	−0.316575
$771$	2.19615	0.0790925
$772$	−12.1244	−0.436365
$773$	−8.07180	−0.290322	−0.145161	−	0.989408i	$-0.546370\pi$
$773$	−8.07180	−0.290322	−0.145161	+	0.989408i	$0.546370\pi$
$774$	−11.3205	−0.406907
$775$	9.46410	0.339961
$776$	5.19615	0.186531
$777$	0	0
$778$	11.1962	0.401402
$779$	−30.5885	−1.09595
$780$	28.3923	1.01661
$781$	−12.0000	−0.429394
$782$	8.19615	0.293094
$783$	30.9282	1.10528
$784$	9.00000	0.321429
$785$	19.7321	0.704267
$786$	−6.00000	−0.214013
$787$	−29.1769	−1.04004	−0.520022	−	0.854153i	$-0.674076\pi$
$787$	−29.1769	−1.04004	−0.520022	+	0.854153i	$0.674076\pi$
$788$	−8.32051	−0.296406
$789$	−30.9282	−1.10107
$790$	3.80385	0.135335
$791$	−31.4256	−1.11737
$792$	−5.66025	−0.201128
$793$	−15.9615	−0.566810
$794$	5.00000	0.177443
$795$	44.7846	1.58835
$796$	−18.9282	−0.670892
$797$	−20.7846	−0.736229	−0.368114	−	0.929781i	$-0.619996\pi$
$797$	−20.7846	−0.736229	−0.368114	+	0.929781i	$0.619996\pi$
$798$	51.7128	1.83061
$799$	9.80385	0.346835
$800$	−2.00000	−0.0707107
$801$	−23.1962	−0.819596
$802$	26.7846	0.945797
$803$	10.6410	0.375513
$804$	−11.4641	−0.404308
$805$	−32.7846	−1.15551
$806$	28.3923	1.00008
$807$	77.5692	2.73057
$808$	−6.46410	−0.227406
$809$	−42.9282	−1.50928	−0.754638	−	0.656142i	$-0.772187\pi$
$809$	−42.9282	−1.50928	−0.754638	+	0.656142i	$0.772187\pi$
$810$	−4.26795	−0.149960
$811$	−15.6077	−0.548060	−0.274030	−	0.961721i	$-0.588357\pi$
$811$	−15.6077	−0.548060	−0.274030	+	0.961721i	$0.588357\pi$
$812$	−30.9282	−1.08537
$813$	−45.3205	−1.58946
$814$	0	0
$815$	−16.3923	−0.574197
$816$	4.73205	0.165655
$817$	12.0000	0.419827
$818$	−2.41154	−0.0843176
$819$	−107.138	−3.74372
$820$	11.1962	0.390987
$821$	−45.4641	−1.58671	−0.793354	−	0.608761i	$-0.791667\pi$
$821$	−45.4641	−1.58671	−0.793354	+	0.608761i	$0.791667\pi$
$822$	−20.1962	−0.704422
$823$	7.41154	0.258350	0.129175	−	0.991622i	$-0.458767\pi$
$823$	7.41154	0.258350	0.129175	+	0.991622i	$0.458767\pi$
$824$	−6.92820	−0.241355
$825$	−6.92820	−0.241209
$826$	37.8564	1.31719
$827$	−22.6410	−0.787305	−0.393653	−	0.919259i	$-0.628789\pi$
$827$	−22.6410	−0.787305	−0.393653	+	0.919259i	$0.628789\pi$
$828$	−21.1244	−0.734122
$829$	36.9282	1.28257	0.641285	−	0.767303i	$-0.278402\pi$
$829$	36.9282	1.28257	0.641285	+	0.767303i	$0.278402\pi$
$830$	−9.80385	−0.340297
$831$	−46.9808	−1.62974
$832$	−6.00000	−0.208013
$833$	−15.5885	−0.540108
$834$	33.3205	1.15379
$835$	12.0000	0.415277
$836$	6.00000	0.207514
$837$	18.9282	0.654254
$838$	37.8564	1.30773
$839$	−20.1962	−0.697249	−0.348624	−	0.937263i	$-0.613351\pi$
$839$	−20.1962	−0.697249	−0.348624	+	0.937263i	$0.613351\pi$
$840$	−18.9282	−0.653085
$841$	30.7846	1.06154
$842$	20.6603	0.711999
$843$	−2.19615	−0.0756395
$844$	−8.39230	−0.288875
$845$	39.8372	1.37044
$846$	−25.2679	−0.868730
$847$	−37.5692	−1.29089
$848$	−9.46410	−0.324999
$849$	25.8564	0.887390
$850$	3.46410	0.118818
$851$	0	0
$852$	−25.8564	−0.885826
$853$	−22.2679	−0.762440	−0.381220	−	0.924484i	$-0.624496\pi$
$853$	−22.2679	−0.762440	−0.381220	+	0.924484i	$0.624496\pi$
$854$	10.6410	0.364128
$855$	−36.5885	−1.25130
$856$	4.39230	0.150126
$857$	−37.0526	−1.26569	−0.632846	−	0.774278i	$-0.718113\pi$
$857$	−37.0526	−1.26569	−0.632846	+	0.774278i	$0.718113\pi$
$858$	−20.7846	−0.709575
$859$	−21.4641	−0.732346	−0.366173	−	0.930547i	$-0.619332\pi$
$859$	−21.4641	−0.732346	−0.366173	+	0.930547i	$0.619332\pi$
$860$	−4.39230	−0.149776
$861$	−70.6410	−2.40744
$862$	16.0526	0.546752
$863$	−16.3923	−0.558001	−0.279000	−	0.960291i	$-0.590003\pi$
$863$	−16.3923	−0.558001	−0.279000	+	0.960291i	$0.590003\pi$
$864$	−4.00000	−0.136083
$865$	−6.80385	−0.231338
$866$	−33.3923	−1.13472
$867$	38.2487	1.29899
$868$	−18.9282	−0.642465
$869$	−2.78461	−0.0944614
$870$	36.5885	1.24046
$871$	−25.1769	−0.853087
$872$	4.26795	0.144531
$873$	23.1962	0.785071
$874$	22.3923	0.757431
$875$	−48.4974	−1.63951
$876$	22.9282	0.774672
$877$	44.1769	1.49175	0.745874	−	0.666087i	$-0.232032\pi$
$877$	44.1769	1.49175	0.745874	+	0.666087i	$0.232032\pi$
$878$	−9.46410	−0.319398
$879$	−12.5885	−0.424598
$880$	−2.19615	−0.0740323
$881$	48.9615	1.64956	0.824778	−	0.565457i	$-0.191300\pi$
$881$	48.9615	1.64956	0.824778	+	0.565457i	$0.191300\pi$
$882$	40.1769	1.35283
$883$	35.6603	1.20006	0.600032	−	0.799976i	$-0.295155\pi$
$883$	35.6603	1.20006	0.600032	+	0.799976i	$0.295155\pi$
$884$	10.3923	0.349531
$885$	−44.7846	−1.50542
$886$	2.53590	0.0851952
$887$	−27.1244	−0.910747	−0.455373	−	0.890301i	$-0.650494\pi$
$887$	−27.1244	−0.910747	−0.455373	+	0.890301i	$0.650494\pi$
$888$	0	0
$889$	82.3538	2.76206
$890$	−9.00000	−0.301681
$891$	3.12436	0.104670
$892$	8.58846	0.287563
$893$	26.7846	0.896313
$894$	27.1244	0.907174
$895$	40.3923	1.35017
$896$	4.00000	0.133631
$897$	−77.5692	−2.58996
$898$	24.9282	0.831865
$899$	36.5885	1.22029
$900$	−8.92820	−0.297607
$901$	16.3923	0.546107
$902$	−8.19615	−0.272902
$903$	27.7128	0.922225
$904$	−7.85641	−0.261300
$905$	9.33975	0.310464
$906$	−33.3205	−1.10700
$907$	−46.3013	−1.53741	−0.768704	−	0.639604i	$-0.779098\pi$
$907$	−46.3013	−1.53741	−0.768704	+	0.639604i	$0.779098\pi$
$908$	−4.73205	−0.157039
$909$	−28.8564	−0.957107
$910$	−41.5692	−1.37801
$911$	−2.87564	−0.0952743	−0.0476372	−	0.998865i	$-0.515169\pi$
$911$	−2.87564	−0.0952743	−0.0476372	+	0.998865i	$0.515169\pi$
$912$	12.9282	0.428096
$913$	7.17691	0.237521
$914$	−19.9808	−0.660905
$915$	−12.5885	−0.416162
$916$	−19.0000	−0.627778
$917$	8.78461	0.290093
$918$	6.92820	0.228665
$919$	−28.0526	−0.925369	−0.462684	−	0.886523i	$-0.653114\pi$
$919$	−28.0526	−0.925369	−0.462684	+	0.886523i	$0.653114\pi$
$920$	−8.19615	−0.270219
$921$	−10.9282	−0.360097
$922$	−33.7128	−1.11027
$923$	−56.7846	−1.86909
$924$	13.8564	0.455842
$925$	0	0
$926$	14.5359	0.477679
$927$	−30.9282	−1.01582
$928$	−7.73205	−0.253817
$929$	37.3923	1.22680	0.613401	−	0.789772i	$-0.289801\pi$
$929$	37.3923	1.22680	0.613401	+	0.789772i	$0.289801\pi$
$930$	22.3923	0.734273
$931$	−42.5885	−1.39578
$932$	25.3923	0.831753
$933$	12.0000	0.392862
$934$	−30.2487	−0.989768
$935$	3.80385	0.124399
$936$	−26.7846	−0.875482
$937$	36.1769	1.18185	0.590924	−	0.806727i	$-0.298763\pi$
$937$	36.1769	1.18185	0.590924	+	0.806727i	$0.298763\pi$
$938$	16.7846	0.548037
$939$	−26.1962	−0.854879
$940$	−9.80385	−0.319766
$941$	59.7846	1.94892	0.974461	−	0.224556i	$-0.0720930\pi$
$941$	59.7846	1.94892	0.974461	+	0.224556i	$0.0720930\pi$
$942$	−31.1244	−1.01409
$943$	−30.5885	−0.996097
$944$	9.46410	0.308030
$945$	−27.7128	−0.901498
$946$	3.21539	0.104541
$947$	−52.3923	−1.70252	−0.851261	−	0.524743i	$-0.824161\pi$
$947$	−52.3923	−1.70252	−0.851261	+	0.524743i	$0.824161\pi$
$948$	−6.00000	−0.194871
$949$	50.3538	1.63455
$950$	9.46410	0.307056
$951$	24.5885	0.797335
$952$	−6.92820	−0.224544
$953$	−7.85641	−0.254494	−0.127247	−	0.991871i	$-0.540614\pi$
$953$	−7.85641	−0.254494	−0.127247	+	0.991871i	$0.540614\pi$
$954$	−42.2487	−1.36785
$955$	11.4115	0.369269
$956$	18.9282	0.612182
$957$	−26.7846	−0.865823
$958$	−9.46410	−0.305771
$959$	29.5692	0.954840
$960$	−4.73205	−0.152726
$961$	−8.60770	−0.277668
$962$	0	0
$963$	19.6077	0.631849
$964$	−18.0000	−0.579741
$965$	−21.0000	−0.676014
$966$	51.7128	1.66383
$967$	10.6410	0.342192	0.171096	−	0.985254i	$-0.445269\pi$
$967$	10.6410	0.342192	0.171096	+	0.985254i	$0.445269\pi$
$968$	−9.39230	−0.301880
$969$	−22.3923	−0.719344
$970$	9.00000	0.288973
$971$	−12.5885	−0.403983	−0.201991	−	0.979387i	$-0.564741\pi$
$971$	−12.5885	−0.403983	−0.201991	+	0.979387i	$0.564741\pi$
$972$	18.7321	0.600831
$973$	−48.7846	−1.56396
$974$	−28.0526	−0.898862
$975$	−32.7846	−1.04995
$976$	2.66025	0.0851527
$977$	57.7128	1.84640	0.923198	−	0.384324i	$-0.125565\pi$
$977$	57.7128	1.84640	0.923198	+	0.384324i	$0.125565\pi$
$978$	25.8564	0.826797
$979$	6.58846	0.210568
$980$	15.5885	0.497955
$981$	19.0526	0.608301
$982$	28.9808	0.924813
$983$	−19.5167	−0.622485	−0.311242	−	0.950331i	$-0.600745\pi$
$983$	−19.5167	−0.622485	−0.311242	+	0.950331i	$0.600745\pi$
$984$	−17.6603	−0.562988
$985$	−14.4115	−0.459190
$986$	13.3923	0.426498
$987$	61.8564	1.96891
$988$	28.3923	0.903280
$989$	12.0000	0.381578
$990$	−9.80385	−0.311587
$991$	44.1051	1.40105	0.700523	−	0.713630i	$-0.252950\pi$
$991$	44.1051	1.40105	0.700523	+	0.713630i	$0.252950\pi$
$992$	−4.73205	−0.150243
$993$	−46.6410	−1.48011
$994$	37.8564	1.20073
$995$	−32.7846	−1.03934
$996$	15.4641	0.489999
$997$	−23.5692	−0.746445	−0.373222	−	0.927742i	$-0.621747\pi$
$997$	−23.5692	−0.746445	−0.373222	+	0.927742i	$0.621747\pi$
$998$	2.19615	0.0695180
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.j.1.1		2
37.23	odd	12		74.2.e.a.11.1	✓	4
37.29	odd	12		74.2.e.a.27.1	yes	4
37.36	even	2		2738.2.a.f.1.1		2
111.23	even	12		666.2.s.e.307.2		4
111.29	even	12		666.2.s.e.397.2		4
148.23	even	12		592.2.w.d.529.2		4
148.103	even	12		592.2.w.d.545.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.e.a.11.1	✓	4	37.23	odd	12
74.2.e.a.27.1	yes	4	37.29	odd	12
592.2.w.d.529.2		4	148.23	even	12
592.2.w.d.545.2		4	148.103	even	12
666.2.s.e.307.2		4	111.23	even	12
666.2.s.e.397.2		4	111.29	even	12
2738.2.a.f.1.1		2	37.36	even	2
2738.2.a.j.1.1		2	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:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} -2.73205 q^{6} +4.00000 q^{7} +1.00000 q^{8} +4.46410 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} -2.73205 q^{6} +4.00000 q^{7} +1.00000 q^{8} +4.46410 q^{9} +1.73205 q^{10} -1.26795 q^{11} -2.73205 q^{12} -6.00000 q^{13} +4.00000 q^{14} -4.73205 q^{15} +1.00000 q^{16} -1.73205 q^{17} +4.46410 q^{18} -4.73205 q^{19} +1.73205 q^{20} -10.9282 q^{21} -1.26795 q^{22} -4.73205 q^{23} -2.73205 q^{24} -2.00000 q^{25} -6.00000 q^{26} -4.00000 q^{27} +4.00000 q^{28} -7.73205 q^{29} -4.73205 q^{30} -4.73205 q^{31} +1.00000 q^{32} +3.46410 q^{33} -1.73205 q^{34} +6.92820 q^{35} +4.46410 q^{36} -4.73205 q^{38} +16.3923 q^{39} +1.73205 q^{40} +6.46410 q^{41} -10.9282 q^{42} -2.53590 q^{43} -1.26795 q^{44} +7.73205 q^{45} -4.73205 q^{46} -5.66025 q^{47} -2.73205 q^{48} +9.00000 q^{49} -2.00000 q^{50} +4.73205 q^{51} -6.00000 q^{52} -9.46410 q^{53} -4.00000 q^{54} -2.19615 q^{55} +4.00000 q^{56} +12.9282 q^{57} -7.73205 q^{58} +9.46410 q^{59} -4.73205 q^{60} +2.66025 q^{61} -4.73205 q^{62} +17.8564 q^{63} +1.00000 q^{64} -10.3923 q^{65} +3.46410 q^{66} +4.19615 q^{67} -1.73205 q^{68} +12.9282 q^{69} +6.92820 q^{70} +9.46410 q^{71} +4.46410 q^{72} -8.39230 q^{73} +5.46410 q^{75} -4.73205 q^{76} -5.07180 q^{77} +16.3923 q^{78} +2.19615 q^{79} +1.73205 q^{80} -2.46410 q^{81} +6.46410 q^{82} -5.66025 q^{83} -10.9282 q^{84} -3.00000 q^{85} -2.53590 q^{86} +21.1244 q^{87} -1.26795 q^{88} -5.19615 q^{89} +7.73205 q^{90} -24.0000 q^{91} -4.73205 q^{92} +12.9282 q^{93} -5.66025 q^{94} -8.19615 q^{95} -2.73205 q^{96} +5.19615 q^{97} +9.00000 q^{98} -5.66025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 8 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 8 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 8 q^{7} + 2 q^{8} + 2 q^{9} - 6 q^{11} - 2 q^{12} - 12 q^{13} + 8 q^{14} - 6 q^{15} + 2 q^{16} + 2 q^{18} - 6 q^{19} - 8 q^{21} - 6 q^{22} - 6 q^{23} - 2 q^{24} - 4 q^{25} - 12 q^{26} - 8 q^{27} + 8 q^{28} - 12 q^{29} - 6 q^{30} - 6 q^{31} + 2 q^{32} + 2 q^{36} - 6 q^{38} + 12 q^{39} + 6 q^{41} - 8 q^{42} - 12 q^{43} - 6 q^{44} + 12 q^{45} - 6 q^{46} + 6 q^{47} - 2 q^{48} + 18 q^{49} - 4 q^{50} + 6 q^{51} - 12 q^{52} - 12 q^{53} - 8 q^{54} + 6 q^{55} + 8 q^{56} + 12 q^{57} - 12 q^{58} + 12 q^{59} - 6 q^{60} - 12 q^{61} - 6 q^{62} + 8 q^{63} + 2 q^{64} - 2 q^{67} + 12 q^{69} + 12 q^{71} + 2 q^{72} + 4 q^{73} + 4 q^{75} - 6 q^{76} - 24 q^{77} + 12 q^{78} - 6 q^{79} + 2 q^{81} + 6 q^{82} + 6 q^{83} - 8 q^{84} - 6 q^{85} - 12 q^{86} + 18 q^{87} - 6 q^{88} + 12 q^{90} - 48 q^{91} - 6 q^{92} + 12 q^{93} + 6 q^{94} - 6 q^{95} - 2 q^{96} + 18 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 8 * q^7 + 2 * q^8 + 2 * q^9 - 6 * q^11 - 2 * q^12 - 12 * q^13 + 8 * q^14 - 6 * q^15 + 2 * q^16 + 2 * q^18 - 6 * q^19 - 8 * q^21 - 6 * q^22 - 6 * q^23 - 2 * q^24 - 4 * q^25 - 12 * q^26 - 8 * q^27 + 8 * q^28 - 12 * q^29 - 6 * q^30 - 6 * q^31 + 2 * q^32 + 2 * q^36 - 6 * q^38 + 12 * q^39 + 6 * q^41 - 8 * q^42 - 12 * q^43 - 6 * q^44 + 12 * q^45 - 6 * q^46 + 6 * q^47 - 2 * q^48 + 18 * q^49 - 4 * q^50 + 6 * q^51 - 12 * q^52 - 12 * q^53 - 8 * q^54 + 6 * q^55 + 8 * q^56 + 12 * q^57 - 12 * q^58 + 12 * q^59 - 6 * q^60 - 12 * q^61 - 6 * q^62 + 8 * q^63 + 2 * q^64 - 2 * q^67 + 12 * q^69 + 12 * q^71 + 2 * q^72 + 4 * q^73 + 4 * q^75 - 6 * q^76 - 24 * q^77 + 12 * q^78 - 6 * q^79 + 2 * q^81 + 6 * q^82 + 6 * q^83 - 8 * q^84 - 6 * q^85 - 12 * q^86 + 18 * q^87 - 6 * q^88 + 12 * q^90 - 48 * q^91 - 6 * q^92 + 12 * q^93 + 6 * q^94 - 6 * q^95 - 2 * q^96 + 18 * q^98 + 6 * q^99

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