LMFDB - Embedded newform 2738.2.a.x.1.3

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:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 8 x^{17} - 8 x^{16} + 209 x^{15} - 253 x^{14} - 1996 x^{13} + 4196 x^{12} + 8667 x^{11} + \cdots + 113 $ x^18 - 8x^17 - 8x^16 + 209x^15 - 253x^14 - 1996x^13 + 4196x^12 + 8667x^11 - 24522x^10 - 18284x^9 + 68697x^8 + 20865x^7 - 97011x^6 - 20844x^5 + 64568x^4 + 17499x^3 - 13387x^2 - 3713*x + 113
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.72365$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.88881 q^{3} +1.00000 q^{4} -0.545033 q^{5} -1.88881 q^{6} -1.80620 q^{7} +1.00000 q^{8} +0.567610 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.88881 q^{3} +1.00000 q^{4} -0.545033 q^{5} -1.88881 q^{6} -1.80620 q^{7} +1.00000 q^{8} +0.567610 q^{9} -0.545033 q^{10} -2.25587 q^{11} -1.88881 q^{12} -2.31178 q^{13} -1.80620 q^{14} +1.02947 q^{15} +1.00000 q^{16} +2.80992 q^{17} +0.567610 q^{18} -8.14308 q^{19} -0.545033 q^{20} +3.41157 q^{21} -2.25587 q^{22} +6.33018 q^{23} -1.88881 q^{24} -4.70294 q^{25} -2.31178 q^{26} +4.59433 q^{27} -1.80620 q^{28} +8.96993 q^{29} +1.02947 q^{30} +2.91631 q^{31} +1.00000 q^{32} +4.26091 q^{33} +2.80992 q^{34} +0.984440 q^{35} +0.567610 q^{36} -8.14308 q^{38} +4.36652 q^{39} -0.545033 q^{40} +4.27903 q^{41} +3.41157 q^{42} -11.0612 q^{43} -2.25587 q^{44} -0.309366 q^{45} +6.33018 q^{46} -0.642561 q^{47} -1.88881 q^{48} -3.73764 q^{49} -4.70294 q^{50} -5.30740 q^{51} -2.31178 q^{52} +6.97173 q^{53} +4.59433 q^{54} +1.22952 q^{55} -1.80620 q^{56} +15.3807 q^{57} +8.96993 q^{58} +10.3995 q^{59} +1.02947 q^{60} +14.1246 q^{61} +2.91631 q^{62} -1.02522 q^{63} +1.00000 q^{64} +1.26000 q^{65} +4.26091 q^{66} +7.87525 q^{67} +2.80992 q^{68} -11.9565 q^{69} +0.984440 q^{70} -0.432789 q^{71} +0.567610 q^{72} +0.290772 q^{73} +8.88297 q^{75} -8.14308 q^{76} +4.07455 q^{77} +4.36652 q^{78} -11.8557 q^{79} -0.545033 q^{80} -10.3806 q^{81} +4.27903 q^{82} +4.29617 q^{83} +3.41157 q^{84} -1.53150 q^{85} -11.0612 q^{86} -16.9425 q^{87} -2.25587 q^{88} +10.5014 q^{89} -0.309366 q^{90} +4.17554 q^{91} +6.33018 q^{92} -5.50836 q^{93} -0.642561 q^{94} +4.43825 q^{95} -1.88881 q^{96} +1.28186 q^{97} -3.73764 q^{98} -1.28045 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 18 q^{2} + 8 q^{3} + 18 q^{4} + 9 q^{5} + 8 q^{6} + 18 q^{7} + 18 q^{8} + 26 q^{9}+O(q^{10}) $ 18 * q + 18 * q^2 + 8 * q^3 + 18 * q^4 + 9 * q^5 + 8 * q^6 + 18 * q^7 + 18 * q^8 + 26 * q^9	\( 18 q + 18 q^{2} + 8 q^{3} + 18 q^{4} + 9 q^{5} + 8 q^{6} + 18 q^{7} + 18 q^{8} + 26 q^{9} + 9 q^{10} + 10 q^{11} + 8 q^{12} + 9 q^{13} + 18 q^{14} - 4 q^{15} + 18 q^{16} + 13 q^{17} + 26 q^{18} + 2 q^{19} + 9 q^{20} + 24 q^{21} + 10 q^{22} - 11 q^{23} + 8 q^{24} + 49 q^{25} + 9 q^{26} + 29 q^{27} + 18 q^{28} + 30 q^{29} - 4 q^{30} - 8 q^{31} + 18 q^{32} + 42 q^{33} + 13 q^{34} + 25 q^{35} + 26 q^{36} + 2 q^{38} - 45 q^{39} + 9 q^{40} + 5 q^{41} + 24 q^{42} - 3 q^{43} + 10 q^{44} - 30 q^{45} - 11 q^{46} + 37 q^{47} + 8 q^{48} + 50 q^{49} + 49 q^{50} + 10 q^{51} + 9 q^{52} + 25 q^{53} + 29 q^{54} - 44 q^{55} + 18 q^{56} + 22 q^{57} + 30 q^{58} + 26 q^{59} - 4 q^{60} + 27 q^{61} - 8 q^{62} + 74 q^{63} + 18 q^{64} - 16 q^{65} + 42 q^{66} + 23 q^{67} + 13 q^{68} - 2 q^{69} + 25 q^{70} - 25 q^{71} + 26 q^{72} + 77 q^{73} - q^{75} + 2 q^{76} - 6 q^{77} - 45 q^{78} - 13 q^{79} + 9 q^{80} + 38 q^{81} + 5 q^{82} - 10 q^{83} + 24 q^{84} + 16 q^{85} - 3 q^{86} - 55 q^{87} + 10 q^{88} + 55 q^{89} - 30 q^{90} + 12 q^{91} - 11 q^{92} - 58 q^{93} + 37 q^{94} - 18 q^{95} + 8 q^{96} - 59 q^{97} + 50 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + 18 * q^2 + 8 * q^3 + 18 * q^4 + 9 * q^5 + 8 * q^6 + 18 * q^7 + 18 * q^8 + 26 * q^9 + 9 * q^10 + 10 * q^11 + 8 * q^12 + 9 * q^13 + 18 * q^14 - 4 * q^15 + 18 * q^16 + 13 * q^17 + 26 * q^18 + 2 * q^19 + 9 * q^20 + 24 * q^21 + 10 * q^22 - 11 * q^23 + 8 * q^24 + 49 * q^25 + 9 * q^26 + 29 * q^27 + 18 * q^28 + 30 * q^29 - 4 * q^30 - 8 * q^31 + 18 * q^32 + 42 * q^33 + 13 * q^34 + 25 * q^35 + 26 * q^36 + 2 * q^38 - 45 * q^39 + 9 * q^40 + 5 * q^41 + 24 * q^42 - 3 * q^43 + 10 * q^44 - 30 * q^45 - 11 * q^46 + 37 * q^47 + 8 * q^48 + 50 * q^49 + 49 * q^50 + 10 * q^51 + 9 * q^52 + 25 * q^53 + 29 * q^54 - 44 * q^55 + 18 * q^56 + 22 * q^57 + 30 * q^58 + 26 * q^59 - 4 * q^60 + 27 * q^61 - 8 * q^62 + 74 * q^63 + 18 * q^64 - 16 * q^65 + 42 * q^66 + 23 * q^67 + 13 * q^68 - 2 * q^69 + 25 * q^70 - 25 * q^71 + 26 * q^72 + 77 * q^73 - q^75 + 2 * q^76 - 6 * q^77 - 45 * q^78 - 13 * q^79 + 9 * q^80 + 38 * q^81 + 5 * q^82 - 10 * q^83 + 24 * q^84 + 16 * q^85 - 3 * q^86 - 55 * q^87 + 10 * q^88 + 55 * q^89 - 30 * q^90 + 12 * q^91 - 11 * q^92 - 58 * q^93 + 37 * q^94 - 18 * q^95 + 8 * q^96 - 59 * q^97 + 50 * q^98 + 11 * 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
$3$	−1.88881	−1.09051	−0.545253	−	0.838272i	$-0.683566\pi$
$3$	−1.88881	−1.09051	−0.545253	+	0.838272i	$0.683566\pi$
$4$	1.00000	0.500000
$5$	−0.545033	−0.243746	−0.121873	−	0.992546i	$-0.538890\pi$
$5$	−0.545033	−0.243746	−0.121873	+	0.992546i	$0.538890\pi$
$6$	−1.88881	−0.771104
$7$	−1.80620	−0.682680	−0.341340	−	0.939940i	$-0.610881\pi$
$7$	−1.80620	−0.682680	−0.341340	+	0.939940i	$0.610881\pi$
$8$	1.00000	0.353553
$9$	0.567610	0.189203
$10$	−0.545033	−0.172355
$11$	−2.25587	−0.680169	−0.340085	−	0.940395i	$-0.610456\pi$
$11$	−2.25587	−0.680169	−0.340085	+	0.940395i	$0.610456\pi$
$12$	−1.88881	−0.545253
$13$	−2.31178	−0.641172	−0.320586	−	0.947219i	$-0.603880\pi$
$13$	−2.31178	−0.641172	−0.320586	+	0.947219i	$0.603880\pi$
$14$	−1.80620	−0.482728
$15$	1.02947	0.265807
$16$	1.00000	0.250000
$17$	2.80992	0.681505	0.340753	−	0.940153i	$-0.389318\pi$
$17$	2.80992	0.681505	0.340753	+	0.940153i	$0.389318\pi$
$18$	0.567610	0.133787
$19$	−8.14308	−1.86815	−0.934076	−	0.357075i	$-0.883774\pi$
$19$	−8.14308	−1.86815	−0.934076	+	0.357075i	$0.883774\pi$
$20$	−0.545033	−0.121873
$21$	3.41157	0.744467
$22$	−2.25587	−0.480952
$23$	6.33018	1.31993	0.659967	−	0.751294i	$-0.270570\pi$
$23$	6.33018	1.31993	0.659967	+	0.751294i	$0.270570\pi$
$24$	−1.88881	−0.385552
$25$	−4.70294	−0.940588
$26$	−2.31178	−0.453377
$27$	4.59433	0.884179
$28$	−1.80620	−0.341340
$29$	8.96993	1.66567	0.832837	−	0.553519i	$-0.186715\pi$
$29$	8.96993	1.66567	0.832837	+	0.553519i	$0.186715\pi$
$30$	1.02947	0.187954
$31$	2.91631	0.523784	0.261892	−	0.965097i	$-0.415654\pi$
$31$	2.91631	0.523784	0.261892	+	0.965097i	$0.415654\pi$
$32$	1.00000	0.176777
$33$	4.26091	0.741729
$34$	2.80992	0.481897
$35$	0.984440	0.166401
$36$	0.567610	0.0946016
$37$	0	0
$37$	0	0
$38$	−8.14308	−1.32098
$39$	4.36652	0.699202
$40$	−0.545033	−0.0861773
$41$	4.27903	0.668272	0.334136	−	0.942525i	$-0.391556\pi$
$41$	4.27903	0.668272	0.334136	+	0.942525i	$0.391556\pi$
$42$	3.41157	0.526417
$43$	−11.0612	−1.68681	−0.843405	−	0.537278i	$-0.819453\pi$
$43$	−11.0612	−1.68681	−0.843405	+	0.537278i	$0.819453\pi$
$44$	−2.25587	−0.340085
$45$	−0.309366	−0.0461176
$46$	6.33018	0.933335
$47$	−0.642561	−0.0937271	−0.0468635	−	0.998901i	$-0.514923\pi$
$47$	−0.642561	−0.0937271	−0.0468635	+	0.998901i	$0.514923\pi$
$48$	−1.88881	−0.272626
$49$	−3.73764	−0.533948
$50$	−4.70294	−0.665096
$51$	−5.30740	−0.743185
$52$	−2.31178	−0.320586
$53$	6.97173	0.957640	0.478820	−	0.877913i	$-0.341065\pi$
$53$	6.97173	0.957640	0.478820	+	0.877913i	$0.341065\pi$
$54$	4.59433	0.625209
$55$	1.22952	0.165789
$56$	−1.80620	−0.241364
$57$	15.3807	2.03723
$58$	8.96993	1.17781
$59$	10.3995	1.35390	0.676951	−	0.736028i	$-0.263301\pi$
$59$	10.3995	1.35390	0.676951	+	0.736028i	$0.263301\pi$
$60$	1.02947	0.132903
$61$	14.1246	1.80847	0.904234	−	0.427038i	$-0.140443\pi$
$61$	14.1246	1.80847	0.904234	+	0.427038i	$0.140443\pi$
$62$	2.91631	0.370371
$63$	−1.02522	−0.129165
$64$	1.00000	0.125000
$65$	1.26000	0.156283
$66$	4.26091	0.524481
$67$	7.87525	0.962114	0.481057	−	0.876689i	$-0.340253\pi$
$67$	7.87525	0.962114	0.481057	+	0.876689i	$0.340253\pi$
$68$	2.80992	0.340753
$69$	−11.9565	−1.43940
$70$	0.984440	0.117663
$71$	−0.432789	−0.0513626	−0.0256813	−	0.999670i	$-0.508176\pi$
$71$	−0.432789	−0.0513626	−0.0256813	+	0.999670i	$0.508176\pi$
$72$	0.567610	0.0668934
$73$	0.290772	0.0340322	0.0170161	−	0.999855i	$-0.494583\pi$
$73$	0.290772	0.0340322	0.0170161	+	0.999855i	$0.494583\pi$
$74$	0	0
$75$	8.88297	1.02572
$76$	−8.14308	−0.934076
$77$	4.07455	0.464338
$78$	4.36652	0.494410
$79$	−11.8557	−1.33387	−0.666936	−	0.745115i	$-0.732395\pi$
$79$	−11.8557	−1.33387	−0.666936	+	0.745115i	$0.732395\pi$
$80$	−0.545033	−0.0609366
$81$	−10.3806	−1.15341
$82$	4.27903	0.472539
$83$	4.29617	0.471566	0.235783	−	0.971806i	$-0.424234\pi$
$83$	4.29617	0.471566	0.235783	+	0.971806i	$0.424234\pi$
$84$	3.41157	0.372233
$85$	−1.53150	−0.166114
$86$	−11.0612	−1.19275
$87$	−16.9425	−1.81643
$88$	−2.25587	−0.240476
$89$	10.5014	1.11314	0.556571	−	0.830800i	$-0.312117\pi$
$89$	10.5014	1.11314	0.556571	+	0.830800i	$0.312117\pi$
$90$	−0.309366	−0.0326100
$91$	4.17554	0.437715
$92$	6.33018	0.659967
$93$	−5.50836	−0.571190
$94$	−0.642561	−0.0662751
$95$	4.43825	0.455355
$96$	−1.88881	−0.192776
$97$	1.28186	0.130153	0.0650763	−	0.997880i	$-0.479271\pi$
$97$	1.28186	0.130153	0.0650763	+	0.997880i	$0.479271\pi$
$98$	−3.73764	−0.377558
$99$	−1.28045	−0.128690
$100$	−4.70294	−0.470294
$101$	6.18950	0.615879	0.307939	−	0.951406i	$-0.400361\pi$
$101$	6.18950	0.615879	0.307939	+	0.951406i	$0.400361\pi$
$102$	−5.30740	−0.525511
$103$	−2.63631	−0.259763	−0.129882	−	0.991529i	$-0.541460\pi$
$103$	−2.63631	−0.259763	−0.129882	+	0.991529i	$0.541460\pi$
$104$	−2.31178	−0.226689
$105$	−1.85942	−0.181461
$106$	6.97173	0.677154
$107$	3.35746	0.324578	0.162289	−	0.986743i	$-0.448112\pi$
$107$	3.35746	0.324578	0.162289	+	0.986743i	$0.448112\pi$
$108$	4.59433	0.442089
$109$	1.33140	0.127525	0.0637624	−	0.997965i	$-0.479690\pi$
$109$	1.33140	0.127525	0.0637624	+	0.997965i	$0.479690\pi$
$110$	1.22952	0.117230
$111$	0	0
$112$	−1.80620	−0.170670
$113$	−12.2983	−1.15692	−0.578462	−	0.815709i	$-0.696347\pi$
$113$	−12.2983	−1.15692	−0.578462	+	0.815709i	$0.696347\pi$
$114$	15.3807	1.44054
$115$	−3.45016	−0.321729
$116$	8.96993	0.832837
$117$	−1.31219	−0.121312
$118$	10.3995	0.957353
$119$	−5.07528	−0.465250
$120$	1.02947	0.0939769
$121$	−5.91106	−0.537369
$122$	14.1246	1.27878
$123$	−8.08228	−0.728754
$124$	2.91631	0.261892
$125$	5.28842	0.473011
$126$	−1.02522	−0.0913336
$127$	7.80943	0.692975	0.346488	−	0.938055i	$-0.387374\pi$
$127$	7.80943	0.692975	0.346488	+	0.938055i	$0.387374\pi$
$128$	1.00000	0.0883883
$129$	20.8924	1.83948
$130$	1.26000	0.110509
$131$	17.6721	1.54402	0.772009	−	0.635611i	$-0.219252\pi$
$131$	17.6721	1.54402	0.772009	+	0.635611i	$0.219252\pi$
$132$	4.26091	0.370864
$133$	14.7080	1.27535
$134$	7.87525	0.680318
$135$	−2.50406	−0.215515
$136$	2.80992	0.240948
$137$	−14.1882	−1.21218	−0.606091	−	0.795396i	$-0.707263\pi$
$137$	−14.1882	−1.21218	−0.606091	+	0.795396i	$0.707263\pi$
$138$	−11.9565	−1.01781
$139$	−0.366366	−0.0310748	−0.0155374	−	0.999879i	$-0.504946\pi$
$139$	−0.366366	−0.0310748	−0.0155374	+	0.999879i	$0.504946\pi$
$140$	0.984440	0.0832003
$141$	1.21368	0.102210
$142$	−0.432789	−0.0363188
$143$	5.21507	0.436106
$144$	0.567610	0.0473008
$145$	−4.88891	−0.406002
$146$	0.290772	0.0240644
$147$	7.05969	0.582274
$148$	0	0
$149$	17.1484	1.40485	0.702425	−	0.711758i	$-0.252101\pi$
$149$	17.1484	1.40485	0.702425	+	0.711758i	$0.252101\pi$
$150$	8.88297	0.725291
$151$	12.8627	1.04676	0.523378	−	0.852101i	$-0.324672\pi$
$151$	12.8627	1.04676	0.523378	+	0.852101i	$0.324672\pi$
$152$	−8.14308	−0.660491
$153$	1.59494	0.128943
$154$	4.07455	0.328337
$155$	−1.58948	−0.127670
$156$	4.36652	0.349601
$157$	8.46273	0.675399	0.337700	−	0.941254i	$-0.390351\pi$
$157$	8.46273	0.675399	0.337700	+	0.941254i	$0.390351\pi$
$158$	−11.8557	−0.943190
$159$	−13.1683	−1.04431
$160$	−0.545033	−0.0430887
$161$	−11.4336	−0.901093
$162$	−10.3806	−0.815581
$163$	−7.46006	−0.584317	−0.292159	−	0.956370i	$-0.594374\pi$
$163$	−7.46006	−0.584317	−0.292159	+	0.956370i	$0.594374\pi$
$164$	4.27903	0.334136
$165$	−2.32234	−0.180794
$166$	4.29617	0.333448
$167$	−0.0698883	−0.00540812	−0.00270406	−	0.999996i	$-0.500861\pi$
$167$	−0.0698883	−0.00540812	−0.00270406	+	0.999996i	$0.500861\pi$
$168$	3.41157	0.263209
$169$	−7.65568	−0.588898
$170$	−1.53150	−0.117461
$171$	−4.62209	−0.353460
$172$	−11.0612	−0.843405
$173$	22.9464	1.74458	0.872291	−	0.488987i	$-0.162634\pi$
$173$	22.9464	1.74458	0.872291	+	0.488987i	$0.162634\pi$
$174$	−16.9425	−1.28441
$175$	8.49445	0.642120
$176$	−2.25587	−0.170042
$177$	−19.6427	−1.47644
$178$	10.5014	0.787111
$179$	−22.4514	−1.67809	−0.839047	−	0.544060i	$-0.816887\pi$
$179$	−22.4514	−1.67809	−0.839047	+	0.544060i	$0.816887\pi$
$180$	−0.309366	−0.0230588
$181$	16.1239	1.19848	0.599239	−	0.800570i	$-0.295470\pi$
$181$	16.1239	1.19848	0.599239	+	0.800570i	$0.295470\pi$
$182$	4.17554	0.309512
$183$	−26.6787	−1.97214
$184$	6.33018	0.466667
$185$	0	0
$186$	−5.50836	−0.403892
$187$	−6.33880	−0.463539
$188$	−0.642561	−0.0468635
$189$	−8.29828	−0.603611
$190$	4.43825	0.321985
$191$	−9.69164	−0.701263	−0.350631	−	0.936514i	$-0.614033\pi$
$191$	−9.69164	−0.701263	−0.350631	+	0.936514i	$0.614033\pi$
$192$	−1.88881	−0.136313
$193$	25.3690	1.82610	0.913050	−	0.407848i	$-0.133721\pi$
$193$	25.3690	1.82610	0.913050	+	0.407848i	$0.133721\pi$
$194$	1.28186	0.0920318
$195$	−2.37990	−0.170428
$196$	−3.73764	−0.266974
$197$	23.1864	1.65196	0.825981	−	0.563697i	$-0.190622\pi$
$197$	23.1864	1.65196	0.825981	+	0.563697i	$0.190622\pi$
$198$	−1.28045	−0.0909977
$199$	5.73000	0.406189	0.203094	−	0.979159i	$-0.434900\pi$
$199$	5.73000	0.406189	0.203094	+	0.979159i	$0.434900\pi$
$200$	−4.70294	−0.332548
$201$	−14.8749	−1.04919
$202$	6.18950	0.435492
$203$	−16.2015	−1.13712
$204$	−5.30740	−0.371593
$205$	−2.33221	−0.162889
$206$	−2.63631	−0.183681
$207$	3.59307	0.249736
$208$	−2.31178	−0.160293
$209$	18.3697	1.27066
$210$	−1.85942	−0.128312
$211$	21.2666	1.46405	0.732027	−	0.681275i	$-0.238574\pi$
$211$	21.2666	1.46405	0.732027	+	0.681275i	$0.238574\pi$
$212$	6.97173	0.478820
$213$	0.817457	0.0560112
$214$	3.35746	0.229511
$215$	6.02870	0.411154
$216$	4.59433	0.312604
$217$	−5.26744	−0.357577
$218$	1.33140	0.0901737
$219$	−0.549213	−0.0371124
$220$	1.22952	0.0828944
$221$	−6.49591	−0.436962
$222$	0	0
$223$	22.5132	1.50759	0.753796	−	0.657108i	$-0.228221\pi$
$223$	22.5132	1.50759	0.753796	+	0.657108i	$0.228221\pi$
$224$	−1.80620	−0.120682
$225$	−2.66943	−0.177962
$226$	−12.2983	−0.818069
$227$	−8.42449	−0.559153	−0.279577	−	0.960123i	$-0.590194\pi$
$227$	−8.42449	−0.559153	−0.279577	+	0.960123i	$0.590194\pi$
$228$	15.3807	1.01861
$229$	21.5928	1.42689	0.713445	−	0.700711i	$-0.247134\pi$
$229$	21.5928	1.42689	0.713445	+	0.700711i	$0.247134\pi$
$230$	−3.45016	−0.227497
$231$	−7.69606	−0.506363
$232$	8.96993	0.588905
$233$	−4.00050	−0.262082	−0.131041	−	0.991377i	$-0.541832\pi$
$233$	−4.00050	−0.262082	−0.131041	+	0.991377i	$0.541832\pi$
$234$	−1.31219	−0.0857804
$235$	0.350217	0.0228456
$236$	10.3995	0.676951
$237$	22.3932	1.45460
$238$	−5.07528	−0.328981
$239$	−14.1689	−0.916513	−0.458256	−	0.888820i	$-0.651526\pi$
$239$	−14.1689	−0.916513	−0.458256	+	0.888820i	$0.651526\pi$
$240$	1.02947	0.0664517
$241$	−9.20130	−0.592708	−0.296354	−	0.955078i	$-0.595771\pi$
$241$	−9.20130	−0.592708	−0.296354	+	0.955078i	$0.595771\pi$
$242$	−5.91106	−0.379978
$243$	5.82411	0.373617
$244$	14.1246	0.904234
$245$	2.03714	0.130148
$246$	−8.08228	−0.515307
$247$	18.8250	1.19781
$248$	2.91631	0.185186
$249$	−8.11466	−0.514246
$250$	5.28842	0.334469
$251$	−15.4284	−0.973830	−0.486915	−	0.873449i	$-0.661878\pi$
$251$	−15.4284	−0.973830	−0.486915	+	0.873449i	$0.661878\pi$
$252$	−1.02522	−0.0645826
$253$	−14.2801	−0.897779
$254$	7.80943	0.490007
$255$	2.89271	0.181149
$256$	1.00000	0.0625000
$257$	−9.93434	−0.619687	−0.309844	−	0.950788i	$-0.600277\pi$
$257$	−9.93434	−0.619687	−0.309844	+	0.950788i	$0.600277\pi$
$258$	20.8924	1.30071
$259$	0	0
$260$	1.26000	0.0781417
$261$	5.09142	0.315151
$262$	17.6721	1.09179
$263$	−5.62230	−0.346686	−0.173343	−	0.984862i	$-0.555457\pi$
$263$	−5.62230	−0.346686	−0.173343	+	0.984862i	$0.555457\pi$
$264$	4.26091	0.262241
$265$	−3.79982	−0.233421
$266$	14.7080	0.901808
$267$	−19.8351	−1.21389
$268$	7.87525	0.481057
$269$	−20.8984	−1.27420	−0.637100	−	0.770781i	$-0.719866\pi$
$269$	−20.8984	−1.27420	−0.637100	+	0.770781i	$0.719866\pi$
$270$	−2.50406	−0.152392
$271$	−29.7114	−1.80484	−0.902420	−	0.430857i	$-0.858211\pi$
$271$	−29.7114	−1.80484	−0.902420	+	0.430857i	$0.858211\pi$
$272$	2.80992	0.170376
$273$	−7.88681	−0.477331
$274$	−14.1882	−0.857141
$275$	10.6092	0.639759
$276$	−11.9565	−0.719698
$277$	−10.0889	−0.606181	−0.303090	−	0.952962i	$-0.598018\pi$
$277$	−10.0889	−0.606181	−0.303090	+	0.952962i	$0.598018\pi$
$278$	−0.366366	−0.0219732
$279$	1.65532	0.0991016
$280$	0.984440	0.0588315
$281$	−15.1931	−0.906341	−0.453171	−	0.891424i	$-0.649707\pi$
$281$	−15.1931	−0.906341	−0.453171	+	0.891424i	$0.649707\pi$
$282$	1.21368	0.0722733
$283$	−9.71446	−0.577465	−0.288732	−	0.957410i	$-0.593234\pi$
$283$	−9.71446	−0.577465	−0.288732	+	0.957410i	$0.593234\pi$
$284$	−0.432789	−0.0256813
$285$	−8.38302	−0.496567
$286$	5.21507	0.308373
$287$	−7.72878	−0.456216
$288$	0.567610	0.0334467
$289$	−9.10436	−0.535551
$290$	−4.88891	−0.287087
$291$	−2.42118	−0.141932
$292$	0.290772	0.0170161
$293$	29.2117	1.70657	0.853283	−	0.521447i	$-0.174608\pi$
$293$	29.2117	1.70657	0.853283	+	0.521447i	$0.174608\pi$
$294$	7.05969	0.411730
$295$	−5.66808	−0.330009
$296$	0	0
$297$	−10.3642	−0.601391
$298$	17.1484	0.993378
$299$	−14.6340	−0.846305
$300$	8.88297	0.512858
$301$	19.9787	1.15155
$302$	12.8627	0.740168
$303$	−11.6908	−0.671619
$304$	−8.14308	−0.467038
$305$	−7.69837	−0.440807
$306$	1.59494	0.0911764
$307$	13.4047	0.765045	0.382522	−	0.923946i	$-0.375055\pi$
$307$	13.4047	0.765045	0.382522	+	0.923946i	$0.375055\pi$
$308$	4.07455	0.232169
$309$	4.97950	0.283274
$310$	−1.58948	−0.0902766
$311$	−9.57909	−0.543180	−0.271590	−	0.962413i	$-0.587549\pi$
$311$	−9.57909	−0.543180	−0.271590	+	0.962413i	$0.587549\pi$
$312$	4.36652	0.247205
$313$	6.04152	0.341487	0.170744	−	0.985316i	$-0.445383\pi$
$313$	6.04152	0.341487	0.170744	+	0.985316i	$0.445383\pi$
$314$	8.46273	0.477579
$315$	0.558777	0.0314835
$316$	−11.8557	−0.666936
$317$	−12.7432	−0.715730	−0.357865	−	0.933773i	$-0.616495\pi$
$317$	−12.7432	−0.715730	−0.357865	+	0.933773i	$0.616495\pi$
$318$	−13.1683	−0.738440
$319$	−20.2350	−1.13294
$320$	−0.545033	−0.0304683
$321$	−6.34161	−0.353954
$322$	−11.4336	−0.637169
$323$	−22.8814	−1.27315
$324$	−10.3806	−0.576703
$325$	10.8722	0.603079
$326$	−7.46006	−0.413175
$327$	−2.51476	−0.139067
$328$	4.27903	0.236270
$329$	1.16059	0.0639856
$330$	−2.32234	−0.127840
$331$	3.14720	0.172986	0.0864930	−	0.996252i	$-0.472434\pi$
$331$	3.14720	0.172986	0.0864930	+	0.996252i	$0.472434\pi$
$332$	4.29617	0.235783
$333$	0	0
$334$	−0.0698883	−0.00382412
$335$	−4.29227	−0.234512
$336$	3.41157	0.186117
$337$	13.3502	0.727233	0.363617	−	0.931549i	$-0.381542\pi$
$337$	13.3502	0.727233	0.363617	+	0.931549i	$0.381542\pi$
$338$	−7.65568	−0.416414
$339$	23.2291	1.26163
$340$	−1.53150	−0.0830571
$341$	−6.57880	−0.356262
$342$	−4.62209	−0.249934
$343$	19.3943	1.04720
$344$	−11.0612	−0.596377
$345$	6.51670	0.350848
$346$	22.9464	1.23361
$347$	−17.2879	−0.928061	−0.464030	−	0.885819i	$-0.653597\pi$
$347$	−17.2879	−0.928061	−0.464030	+	0.885819i	$0.653597\pi$
$348$	−16.9425	−0.908214
$349$	−16.5296	−0.884811	−0.442405	−	0.896815i	$-0.645875\pi$
$349$	−16.5296	−0.884811	−0.442405	+	0.896815i	$0.645875\pi$
$350$	8.49445	0.454048
$351$	−10.6211	−0.566911
$352$	−2.25587	−0.120238
$353$	−14.9020	−0.793155	−0.396577	−	0.918001i	$-0.629802\pi$
$353$	−14.9020	−0.793155	−0.396577	+	0.918001i	$0.629802\pi$
$354$	−19.6427	−1.04400
$355$	0.235884	0.0125194
$356$	10.5014	0.556571
$357$	9.58624	0.507358
$358$	−22.4514	−1.18659
$359$	26.9184	1.42070	0.710349	−	0.703849i	$-0.248537\pi$
$359$	26.9184	1.42070	0.710349	+	0.703849i	$0.248537\pi$
$360$	−0.309366	−0.0163050
$361$	47.3098	2.48999
$362$	16.1239	0.847452
$363$	11.1649	0.586005
$364$	4.17554	0.218858
$365$	−0.158480	−0.00829523
$366$	−26.6787	−1.39452
$367$	−28.8555	−1.50625	−0.753123	−	0.657880i	$-0.771453\pi$
$367$	−28.8555	−1.50625	−0.753123	+	0.657880i	$0.771453\pi$
$368$	6.33018	0.329984
$369$	2.42882	0.126439
$370$	0	0
$371$	−12.5923	−0.653762
$372$	−5.50836	−0.285595
$373$	−14.9712	−0.775182	−0.387591	−	0.921832i	$-0.626693\pi$
$373$	−14.9712	−0.775182	−0.387591	+	0.921832i	$0.626693\pi$
$374$	−6.33880	−0.327772
$375$	−9.98884	−0.515821
$376$	−0.642561	−0.0331375
$377$	−20.7365	−1.06798
$378$	−8.29828	−0.426817
$379$	−15.4300	−0.792587	−0.396294	−	0.918124i	$-0.629704\pi$
$379$	−15.4300	−0.792587	−0.396294	+	0.918124i	$0.629704\pi$
$380$	4.43825	0.227677
$381$	−14.7505	−0.755693
$382$	−9.69164	−0.495868
$383$	7.88746	0.403031	0.201515	−	0.979485i	$-0.435413\pi$
$383$	7.88746	0.403031	0.201515	+	0.979485i	$0.435413\pi$
$384$	−1.88881	−0.0963880
$385$	−2.22076	−0.113181
$386$	25.3690	1.29125
$387$	−6.27842	−0.319150
$388$	1.28186	0.0650763
$389$	21.7840	1.10449	0.552246	−	0.833681i	$-0.313771\pi$
$389$	21.7840	1.10449	0.552246	+	0.833681i	$0.313771\pi$
$390$	−2.37990	−0.120511
$391$	17.7873	0.899542
$392$	−3.73764	−0.188779
$393$	−33.3793	−1.68376
$394$	23.1864	1.16811
$395$	6.46176	0.325126
$396$	−1.28045	−0.0643451
$397$	17.3822	0.872386	0.436193	−	0.899853i	$-0.356326\pi$
$397$	17.3822	0.872386	0.436193	+	0.899853i	$0.356326\pi$
$398$	5.73000	0.287219
$399$	−27.7807	−1.39078
$400$	−4.70294	−0.235147
$401$	17.7577	0.886776	0.443388	−	0.896330i	$-0.353776\pi$
$401$	17.7577	0.886776	0.443388	+	0.896330i	$0.353776\pi$
$402$	−14.8749	−0.741890
$403$	−6.74186	−0.335836
$404$	6.18950	0.307939
$405$	5.65780	0.281138
$406$	−16.2015	−0.804067
$407$	0	0
$408$	−5.30740	−0.262756
$409$	−34.5910	−1.71042	−0.855208	−	0.518286i	$-0.826570\pi$
$409$	−34.5910	−1.71042	−0.855208	+	0.518286i	$0.826570\pi$
$410$	−2.33221	−0.115180
$411$	26.7989	1.32189
$412$	−2.63631	−0.129882
$413$	−18.7836	−0.924282
$414$	3.59307	0.176590
$415$	−2.34156	−0.114943
$416$	−2.31178	−0.113344
$417$	0.691997	0.0338872
$418$	18.3697	0.898492
$419$	−2.52509	−0.123359	−0.0616793	−	0.998096i	$-0.519646\pi$
$419$	−2.52509	−0.123359	−0.0616793	+	0.998096i	$0.519646\pi$
$420$	−1.85942	−0.0907305
$421$	10.4459	0.509102	0.254551	−	0.967059i	$-0.418072\pi$
$421$	10.4459	0.509102	0.254551	+	0.967059i	$0.418072\pi$
$422$	21.2666	1.03524
$423$	−0.364723	−0.0177335
$424$	6.97173	0.338577
$425$	−13.2149	−0.641015
$426$	0.817457	0.0396059
$427$	−25.5118	−1.23460
$428$	3.35746	0.162289
$429$	−9.85028	−0.475576
$430$	6.02870	0.290730
$431$	14.6132	0.703893	0.351946	−	0.936020i	$-0.385520\pi$
$431$	14.6132	0.703893	0.351946	+	0.936020i	$0.385520\pi$
$432$	4.59433	0.221045
$433$	20.6365	0.991726	0.495863	−	0.868401i	$-0.334852\pi$
$433$	20.6365	0.991726	0.495863	+	0.868401i	$0.334852\pi$
$434$	−5.26744	−0.252845
$435$	9.23423	0.442747
$436$	1.33140	0.0637624
$437$	−51.5472	−2.46584
$438$	−0.549213	−0.0262424
$439$	8.63827	0.412282	0.206141	−	0.978522i	$-0.433909\pi$
$439$	8.63827	0.412282	0.206141	+	0.978522i	$0.433909\pi$
$440$	1.22952	0.0586152
$441$	−2.12152	−0.101025
$442$	−6.49591	−0.308979
$443$	−17.6883	−0.840396	−0.420198	−	0.907432i	$-0.638039\pi$
$443$	−17.6883	−0.840396	−0.420198	+	0.907432i	$0.638039\pi$
$444$	0	0
$445$	−5.72359	−0.271324
$446$	22.5132	1.06603
$447$	−32.3900	−1.53200
$448$	−1.80620	−0.0853350
$449$	14.1914	0.669735	0.334868	−	0.942265i	$-0.391308\pi$
$449$	14.1914	0.669735	0.334868	+	0.942265i	$0.391308\pi$
$450$	−2.66943	−0.125838
$451$	−9.65291	−0.454538
$452$	−12.2983	−0.578462
$453$	−24.2953	−1.14149
$454$	−8.42449	−0.395381
$455$	−2.27581	−0.106691
$456$	15.3807	0.720270
$457$	21.1339	0.988603	0.494301	−	0.869291i	$-0.335424\pi$
$457$	21.1339	0.988603	0.494301	+	0.869291i	$0.335424\pi$
$458$	21.5928	1.00896
$459$	12.9097	0.602572
$460$	−3.45016	−0.160865
$461$	−11.9560	−0.556845	−0.278423	−	0.960459i	$-0.589812\pi$
$461$	−11.9560	−0.556845	−0.278423	+	0.960459i	$0.589812\pi$
$462$	−7.69606	−0.358053
$463$	−8.46127	−0.393228	−0.196614	−	0.980481i	$-0.562995\pi$
$463$	−8.46127	−0.393228	−0.196614	+	0.980481i	$0.562995\pi$
$464$	8.96993	0.416418
$465$	3.00224	0.139225
$466$	−4.00050	−0.185320
$467$	42.3768	1.96096	0.980482	−	0.196609i	$-0.0629931\pi$
$467$	42.3768	1.96096	0.980482	+	0.196609i	$0.0629931\pi$
$468$	−1.31219	−0.0606559
$469$	−14.2243	−0.656816
$470$	0.350217	0.0161543
$471$	−15.9845	−0.736527
$472$	10.3995	0.478677
$473$	24.9525	1.14732
$474$	22.3932	1.02855
$475$	38.2964	1.75716
$476$	−5.07528	−0.232625
$477$	3.95722	0.181189
$478$	−14.1689	−0.648072
$479$	17.8784	0.816884	0.408442	−	0.912784i	$-0.366072\pi$
$479$	17.8784	0.816884	0.408442	+	0.912784i	$0.366072\pi$
$480$	1.02947	0.0469884
$481$	0	0
$482$	−9.20130	−0.419108
$483$	21.5959	0.982647
$484$	−5.91106	−0.268685
$485$	−0.698654	−0.0317242
$486$	5.82411	0.264187
$487$	−6.92527	−0.313814	−0.156907	−	0.987613i	$-0.550152\pi$
$487$	−6.92527	−0.313814	−0.156907	+	0.987613i	$0.550152\pi$
$488$	14.1246	0.639390
$489$	14.0907	0.637201
$490$	2.03714	0.0920284
$491$	−2.42015	−0.109220	−0.0546100	−	0.998508i	$-0.517392\pi$
$491$	−2.42015	−0.109220	−0.0546100	+	0.998508i	$0.517392\pi$
$492$	−8.08228	−0.364377
$493$	25.2048	1.13517
$494$	18.8250	0.846977
$495$	0.697889	0.0313678
$496$	2.91631	0.130946
$497$	0.781704	0.0350642
$498$	−8.11466	−0.363627
$499$	−36.4959	−1.63378	−0.816890	−	0.576793i	$-0.804304\pi$
$499$	−36.4959	−1.63378	−0.816890	+	0.576793i	$0.804304\pi$
$500$	5.28842	0.236505
$501$	0.132006	0.00589758
$502$	−15.4284	−0.688601
$503$	−0.620544	−0.0276687	−0.0138344	−	0.999904i	$-0.504404\pi$
$503$	−0.620544	−0.0276687	−0.0138344	+	0.999904i	$0.504404\pi$
$504$	−1.02522	−0.0456668
$505$	−3.37348	−0.150118
$506$	−14.2801	−0.634826
$507$	14.4601	0.642197
$508$	7.80943	0.346488
$509$	−21.2550	−0.942113	−0.471057	−	0.882103i	$-0.656127\pi$
$509$	−21.2550	−0.942113	−0.471057	+	0.882103i	$0.656127\pi$
$510$	2.89271	0.128091
$511$	−0.525192	−0.0232331
$512$	1.00000	0.0441942
$513$	−37.4120	−1.65178
$514$	−9.93434	−0.438185
$515$	1.43688	0.0633164
$516$	20.8924	0.919738
$517$	1.44953	0.0637503
$518$	0	0
$519$	−43.3414	−1.90248
$520$	1.26000	0.0552545
$521$	−4.81237	−0.210834	−0.105417	−	0.994428i	$-0.533618\pi$
$521$	−4.81237	−0.210834	−0.105417	+	0.994428i	$0.533618\pi$
$522$	5.09142	0.222845
$523$	−3.13830	−0.137228	−0.0686141	−	0.997643i	$-0.521858\pi$
$523$	−3.13830	−0.137228	−0.0686141	+	0.997643i	$0.521858\pi$
$524$	17.6721	0.772009
$525$	−16.0444	−0.700236
$526$	−5.62230	−0.245144
$527$	8.19458	0.356962
$528$	4.26091	0.185432
$529$	17.0712	0.742228
$530$	−3.79982	−0.165054
$531$	5.90287	0.256163
$532$	14.7080	0.637675
$533$	−9.89216	−0.428477
$534$	−19.8351	−0.858349
$535$	−1.82993	−0.0791147
$536$	7.87525	0.340159
$537$	42.4064	1.82997
$538$	−20.8984	−0.900996
$539$	8.43161	0.363175
$540$	−2.50406	−0.107758
$541$	−23.1072	−0.993455	−0.496728	−	0.867906i	$-0.665465\pi$
$541$	−23.1072	−0.993455	−0.496728	+	0.867906i	$0.665465\pi$
$542$	−29.7114	−1.27622
$543$	−30.4550	−1.30695
$544$	2.80992	0.120474
$545$	−0.725657	−0.0310837
$546$	−7.88681	−0.337524
$547$	−5.73611	−0.245258	−0.122629	−	0.992453i	$-0.539133\pi$
$547$	−5.73611	−0.245258	−0.122629	+	0.992453i	$0.539133\pi$
$548$	−14.1882	−0.606091
$549$	8.01725	0.342168
$550$	10.6092	0.452378
$551$	−73.0429	−3.11173
$552$	−11.9565	−0.508904
$553$	21.4138	0.910608
$554$	−10.0889	−0.428634
$555$	0	0
$556$	−0.366366	−0.0155374
$557$	30.2128	1.28016	0.640080	−	0.768309i	$-0.278901\pi$
$557$	30.2128	1.28016	0.640080	+	0.768309i	$0.278901\pi$
$558$	1.65532	0.0700754
$559$	25.5709	1.08154
$560$	0.984440	0.0416002
$561$	11.9728	0.505492
$562$	−15.1931	−0.640880
$563$	2.71084	0.114248	0.0571242	−	0.998367i	$-0.481807\pi$
$563$	2.71084	0.114248	0.0571242	+	0.998367i	$0.481807\pi$
$564$	1.21368	0.0511050
$565$	6.70296	0.281996
$566$	−9.71446	−0.408329
$567$	18.7495	0.787407
$568$	−0.432789	−0.0181594
$569$	−13.3429	−0.559365	−0.279683	−	0.960093i	$-0.590229\pi$
$569$	−13.3429	−0.559365	−0.279683	+	0.960093i	$0.590229\pi$
$570$	−8.38302	−0.351126
$571$	−17.7394	−0.742370	−0.371185	−	0.928559i	$-0.621048\pi$
$571$	−17.7394	−0.742370	−0.371185	+	0.928559i	$0.621048\pi$
$572$	5.21507	0.218053
$573$	18.3057	0.764731
$574$	−7.72878	−0.322593
$575$	−29.7705	−1.24151
$576$	0.567610	0.0236504
$577$	−24.9713	−1.03957	−0.519785	−	0.854297i	$-0.673988\pi$
$577$	−24.9713	−1.03957	−0.519785	+	0.854297i	$0.673988\pi$
$578$	−9.10436	−0.378692
$579$	−47.9172	−1.99137
$580$	−4.88891	−0.203001
$581$	−7.75976	−0.321929
$582$	−2.42118	−0.100361
$583$	−15.7273	−0.651358
$584$	0.290772	0.0120322
$585$	0.715186	0.0295693
$586$	29.2117	1.20673
$587$	23.2219	0.958470	0.479235	−	0.877687i	$-0.340914\pi$
$587$	23.2219	0.958470	0.479235	+	0.877687i	$0.340914\pi$
$588$	7.05969	0.291137
$589$	−23.7477	−0.978508
$590$	−5.66808	−0.233351
$591$	−43.7947	−1.80148
$592$	0	0
$593$	−13.3834	−0.549592	−0.274796	−	0.961503i	$-0.588610\pi$
$593$	−13.3834	−0.549592	−0.274796	+	0.961503i	$0.588610\pi$
$594$	−10.3642	−0.425248
$595$	2.76619	0.113403
$596$	17.1484	0.702425
$597$	−10.8229	−0.442951
$598$	−14.6340	−0.598428
$599$	25.6839	1.04942	0.524708	−	0.851282i	$-0.324174\pi$
$599$	25.6839	1.04942	0.524708	+	0.851282i	$0.324174\pi$
$600$	8.88297	0.362646
$601$	19.5201	0.796243	0.398121	−	0.917333i	$-0.369662\pi$
$601$	19.5201	0.796243	0.398121	+	0.917333i	$0.369662\pi$
$602$	19.9787	0.814270
$603$	4.47006	0.182035
$604$	12.8627	0.523378
$605$	3.22173	0.130982
$606$	−11.6908	−0.474907
$607$	−12.8725	−0.522479	−0.261240	−	0.965274i	$-0.584131\pi$
$607$	−12.8725	−0.522479	−0.261240	+	0.965274i	$0.584131\pi$
$608$	−8.14308	−0.330246
$609$	30.6016	1.24004
$610$	−7.69837	−0.311698
$611$	1.48546	0.0600952
$612$	1.59494	0.0644715
$613$	−17.7962	−0.718780	−0.359390	−	0.933187i	$-0.617015\pi$
$613$	−17.7962	−0.718780	−0.359390	+	0.933187i	$0.617015\pi$
$614$	13.4047	0.540968
$615$	4.40511	0.177631
$616$	4.07455	0.164168
$617$	10.0414	0.404253	0.202126	−	0.979359i	$-0.435215\pi$
$617$	10.0414	0.404253	0.202126	+	0.979359i	$0.435215\pi$
$618$	4.97950	0.200305
$619$	−5.39043	−0.216660	−0.108330	−	0.994115i	$-0.534550\pi$
$619$	−5.39043	−0.216660	−0.108330	+	0.994115i	$0.534550\pi$
$620$	−1.58948	−0.0638352
$621$	29.0829	1.16706
$622$	−9.57909	−0.384086
$623$	−18.9676	−0.759920
$624$	4.36652	0.174801
$625$	20.6323	0.825293
$626$	6.04152	0.241468
$627$	−34.6969	−1.38566
$628$	8.46273	0.337700
$629$	0	0
$630$	0.558777	0.0222622
$631$	9.36510	0.372819	0.186409	−	0.982472i	$-0.440315\pi$
$631$	9.36510	0.372819	0.186409	+	0.982472i	$0.440315\pi$
$632$	−11.8557	−0.471595
$633$	−40.1686	−1.59656
$634$	−12.7432	−0.506097
$635$	−4.25640	−0.168910
$636$	−13.1683	−0.522156
$637$	8.64059	0.342353
$638$	−20.2350	−0.801110
$639$	−0.245655	−0.00971797
$640$	−0.545033	−0.0215443
$641$	26.9211	1.06332	0.531661	−	0.846958i	$-0.321568\pi$
$641$	26.9211	1.06332	0.531661	+	0.846958i	$0.321568\pi$
$642$	−6.34161	−0.250284
$643$	37.9354	1.49603	0.748013	−	0.663684i	$-0.231008\pi$
$643$	37.9354	1.49603	0.748013	+	0.663684i	$0.231008\pi$
$644$	−11.4336	−0.450546
$645$	−11.3871	−0.448366
$646$	−22.8814	−0.900256
$647$	4.32863	0.170176	0.0850879	−	0.996373i	$-0.472883\pi$
$647$	4.32863	0.170176	0.0850879	+	0.996373i	$0.472883\pi$
$648$	−10.3806	−0.407790
$649$	−23.4599	−0.920883
$650$	10.8722	0.426441
$651$	9.94920	0.389940
$652$	−7.46006	−0.292159
$653$	8.57060	0.335394	0.167697	−	0.985839i	$-0.446367\pi$
$653$	8.57060	0.335394	0.167697	+	0.985839i	$0.446367\pi$
$654$	−2.51476	−0.0983350
$655$	−9.63188	−0.376349
$656$	4.27903	0.167068
$657$	0.165045	0.00643901
$658$	1.16059	0.0452447
$659$	1.99449	0.0776942	0.0388471	−	0.999245i	$-0.487631\pi$
$659$	1.99449	0.0776942	0.0388471	+	0.999245i	$0.487631\pi$
$660$	−2.32234	−0.0903968
$661$	22.8731	0.889661	0.444831	−	0.895615i	$-0.353264\pi$
$661$	22.8731	0.889661	0.444831	+	0.895615i	$0.353264\pi$
$662$	3.14720	0.122320
$663$	12.2695	0.476510
$664$	4.29617	0.166724
$665$	−8.01637	−0.310862
$666$	0	0
$667$	56.7813	2.19858
$668$	−0.0698883	−0.00270406
$669$	−42.5231	−1.64404
$670$	−4.29227	−0.165825
$671$	−31.8632	−1.23006
$672$	3.41157	0.131604
$673$	16.7255	0.644721	0.322361	−	0.946617i	$-0.395524\pi$
$673$	16.7255	0.644721	0.322361	+	0.946617i	$0.395524\pi$
$674$	13.3502	0.514232
$675$	−21.6068	−0.831648
$676$	−7.65568	−0.294449
$677$	31.2844	1.20236	0.601178	−	0.799115i	$-0.294698\pi$
$677$	31.2844	1.20236	0.601178	+	0.799115i	$0.294698\pi$
$678$	23.2291	0.892109
$679$	−2.31529	−0.0888526
$680$	−1.53150	−0.0587303
$681$	15.9123	0.609760
$682$	−6.57880	−0.251915
$683$	−9.85607	−0.377132	−0.188566	−	0.982061i	$-0.560384\pi$
$683$	−9.85607	−0.377132	−0.188566	+	0.982061i	$0.560384\pi$
$684$	−4.62209	−0.176730
$685$	7.73305	0.295465
$686$	19.3943	0.740479
$687$	−40.7847	−1.55603
$688$	−11.0612	−0.421703
$689$	−16.1171	−0.614012
$690$	6.51670	0.248087
$691$	−31.1854	−1.18635	−0.593175	−	0.805074i	$-0.702126\pi$
$691$	−31.1854	−1.18635	−0.593175	+	0.805074i	$0.702126\pi$
$692$	22.9464	0.872291
$693$	2.31275	0.0878542
$694$	−17.2879	−0.656238
$695$	0.199682	0.00757436
$696$	−16.9425	−0.642204
$697$	12.0237	0.455431
$698$	−16.5296	−0.625656
$699$	7.55619	0.285802
$700$	8.49445	0.321060
$701$	50.0941	1.89203	0.946013	−	0.324127i	$-0.105071\pi$
$701$	50.0941	1.89203	0.946013	+	0.324127i	$0.105071\pi$
$702$	−10.6211	−0.400866
$703$	0	0
$704$	−2.25587	−0.0850212
$705$	−0.661494	−0.0249133
$706$	−14.9020	−0.560845
$707$	−11.1795	−0.420448
$708$	−19.6427	−0.738219
$709$	−41.2376	−1.54871	−0.774355	−	0.632751i	$-0.781926\pi$
$709$	−41.2376	−1.54871	−0.774355	+	0.632751i	$0.781926\pi$
$710$	0.235884	0.00885258
$711$	−6.72942	−0.252373
$712$	10.5014	0.393555
$713$	18.4608	0.691361
$714$	9.58624	0.358756
$715$	−2.84238	−0.106299
$716$	−22.4514	−0.839047
$717$	26.7625	0.999462
$718$	26.9184	1.00459
$719$	−1.90891	−0.0711904	−0.0355952	−	0.999366i	$-0.511333\pi$
$719$	−1.90891	−0.0711904	−0.0355952	+	0.999366i	$0.511333\pi$
$720$	−0.309366	−0.0115294
$721$	4.76171	0.177335
$722$	47.3098	1.76069
$723$	17.3795	0.646351
$724$	16.1239	0.599239
$725$	−42.1850	−1.56671
$726$	11.1649	0.414368
$727$	−33.0668	−1.22638	−0.613189	−	0.789936i	$-0.710114\pi$
$727$	−33.0668	−1.22638	−0.613189	+	0.789936i	$0.710114\pi$
$728$	4.17554	0.154756
$729$	20.1413	0.745974
$730$	−0.158480	−0.00586561
$731$	−31.0809	−1.14957
$732$	−26.6787	−0.986072
$733$	−1.82686	−0.0674768	−0.0337384	−	0.999431i	$-0.510741\pi$
$733$	−1.82686	−0.0674768	−0.0337384	+	0.999431i	$0.510741\pi$
$734$	−28.8555	−1.06508
$735$	−3.84777	−0.141927
$736$	6.33018	0.233334
$737$	−17.7655	−0.654401
$738$	2.42882	0.0894060
$739$	−14.4698	−0.532281	−0.266140	−	0.963934i	$-0.585748\pi$
$739$	−14.4698	−0.532281	−0.266140	+	0.963934i	$0.585748\pi$
$740$	0	0
$741$	−35.5569	−1.30622
$742$	−12.5923	−0.462279
$743$	−27.2721	−1.00052	−0.500258	−	0.865877i	$-0.666761\pi$
$743$	−27.2721	−1.00052	−0.500258	+	0.865877i	$0.666761\pi$
$744$	−5.50836	−0.201946
$745$	−9.34643	−0.342427
$746$	−14.9712	−0.548136
$747$	2.43855	0.0892219
$748$	−6.33880	−0.231769
$749$	−6.06425	−0.221583
$750$	−9.98884	−0.364741
$751$	10.9469	0.399457	0.199728	−	0.979851i	$-0.435994\pi$
$751$	10.9469	0.399457	0.199728	+	0.979851i	$0.435994\pi$
$752$	−0.642561	−0.0234318
$753$	29.1413	1.06197
$754$	−20.7365	−0.755178
$755$	−7.01063	−0.255143
$756$	−8.29828	−0.301806
$757$	−25.5826	−0.929815	−0.464908	−	0.885359i	$-0.653912\pi$
$757$	−25.5826	−0.929815	−0.464908	+	0.885359i	$0.653912\pi$
$758$	−15.4300	−0.560444
$759$	26.9723	0.979034
$760$	4.43825	0.160992
$761$	−21.9079	−0.794159	−0.397080	−	0.917784i	$-0.629976\pi$
$761$	−21.9079	−0.794159	−0.397080	+	0.917784i	$0.629976\pi$
$762$	−14.7505	−0.534356
$763$	−2.40477	−0.0870587
$764$	−9.69164	−0.350631
$765$	−0.869293	−0.0314294
$766$	7.88746	0.284986
$767$	−24.0414	−0.868084
$768$	−1.88881	−0.0681566
$769$	−18.7616	−0.676562	−0.338281	−	0.941045i	$-0.609845\pi$
$769$	−18.7616	−0.676562	−0.338281	+	0.941045i	$0.609845\pi$
$770$	−2.22076	−0.0800308
$771$	18.7641	0.675773
$772$	25.3690	0.913050
$773$	−0.239630	−0.00861890	−0.00430945	−	0.999991i	$-0.501372\pi$
$773$	−0.239630	−0.00861890	−0.00430945	+	0.999991i	$0.501372\pi$
$774$	−6.27842	−0.225673
$775$	−13.7152	−0.492665
$776$	1.28186	0.0460159
$777$	0	0
$778$	21.7840	0.780994
$779$	−34.8445	−1.24843
$780$	−2.37990	−0.0852139
$781$	0.976314	0.0349353
$782$	17.7873	0.636072
$783$	41.2108	1.47275
$784$	−3.73764	−0.133487
$785$	−4.61247	−0.164626
$786$	−33.3793	−1.19060
$787$	54.4542	1.94108	0.970542	−	0.240933i	$-0.0774535\pi$
$787$	54.4542	1.94108	0.970542	+	0.240933i	$0.0774535\pi$
$788$	23.1864	0.825981
$789$	10.6195	0.378063
$790$	6.46176	0.229899
$791$	22.2132	0.789809
$792$	−1.28045	−0.0454989
$793$	−32.6529	−1.15954
$794$	17.3822	0.616870
$795$	7.17715	0.254547
$796$	5.73000	0.203094
$797$	47.9777	1.69946	0.849728	−	0.527221i	$-0.176766\pi$
$797$	47.9777	1.69946	0.849728	+	0.527221i	$0.176766\pi$
$798$	−27.7807	−0.983427
$799$	−1.80554	−0.0638755
$800$	−4.70294	−0.166274
$801$	5.96068	0.210610
$802$	17.7577	0.627045
$803$	−0.655942	−0.0231477
$804$	−14.8749	−0.524596
$805$	6.23168	0.219638
$806$	−6.74186	−0.237472
$807$	39.4732	1.38952
$808$	6.18950	0.217746
$809$	10.3661	0.364451	0.182226	−	0.983257i	$-0.441670\pi$
$809$	10.3661	0.364451	0.182226	+	0.983257i	$0.441670\pi$
$810$	5.65780	0.198795
$811$	−8.25750	−0.289960	−0.144980	−	0.989435i	$-0.546312\pi$
$811$	−8.25750	−0.289960	−0.144980	+	0.989435i	$0.546312\pi$
$812$	−16.2015	−0.568561
$813$	56.1193	1.96819
$814$	0	0
$815$	4.06598	0.142425
$816$	−5.30740	−0.185796
$817$	90.0719	3.15122
$818$	−34.5910	−1.20945
$819$	2.37008	0.0828171
$820$	−2.33221	−0.0814444
$821$	0.0973428	0.00339729	0.00169864	−	0.999999i	$-0.499459\pi$
$821$	0.0973428	0.00339729	0.00169864	+	0.999999i	$0.499459\pi$
$822$	26.7989	0.934718
$823$	23.9126	0.833539	0.416770	−	0.909012i	$-0.363162\pi$
$823$	23.9126	0.833539	0.416770	+	0.909012i	$0.363162\pi$
$824$	−2.63631	−0.0918403
$825$	−20.0388	−0.697661
$826$	−18.7836	−0.653566
$827$	−4.41702	−0.153595	−0.0767974	−	0.997047i	$-0.524469\pi$
$827$	−4.41702	−0.153595	−0.0767974	+	0.997047i	$0.524469\pi$
$828$	3.59307	0.124868
$829$	−15.3925	−0.534604	−0.267302	−	0.963613i	$-0.586132\pi$
$829$	−15.3925	−0.534604	−0.267302	+	0.963613i	$0.586132\pi$
$830$	−2.34156	−0.0812767
$831$	19.0560	0.661044
$832$	−2.31178	−0.0801465
$833$	−10.5024	−0.363888
$834$	0.691997	0.0239619
$835$	0.0380914	0.00131821
$836$	18.3697	0.635330
$837$	13.3985	0.463119
$838$	−2.52509	−0.0872277
$839$	−7.45938	−0.257526	−0.128763	−	0.991675i	$-0.541101\pi$
$839$	−7.45938	−0.257526	−0.128763	+	0.991675i	$0.541101\pi$
$840$	−1.85942	−0.0641561
$841$	51.4596	1.77447
$842$	10.4459	0.359990
$843$	28.6968	0.988371
$844$	21.2666	0.732027
$845$	4.17260	0.143542
$846$	−0.364723	−0.0125395
$847$	10.6766	0.366851
$848$	6.97173	0.239410
$849$	18.3488	0.629729
$850$	−13.2149	−0.453266
$851$	0	0
$852$	0.817457	0.0280056
$853$	35.3824	1.21147	0.605735	−	0.795667i	$-0.292879\pi$
$853$	35.3824	1.21147	0.605735	+	0.795667i	$0.292879\pi$
$854$	−25.5118	−0.872997
$855$	2.51919	0.0861546
$856$	3.35746	0.114756
$857$	52.4235	1.79075	0.895377	−	0.445310i	$-0.146906\pi$
$857$	52.4235	1.79075	0.895377	+	0.445310i	$0.146906\pi$
$858$	−9.85028	−0.336283
$859$	−7.93318	−0.270677	−0.135338	−	0.990799i	$-0.543212\pi$
$859$	−7.93318	−0.270677	−0.135338	+	0.990799i	$0.543212\pi$
$860$	6.02870	0.205577
$861$	14.5982	0.497506
$862$	14.6132	0.497727
$863$	19.3823	0.659780	0.329890	−	0.944019i	$-0.392988\pi$
$863$	19.3823	0.659780	0.329890	+	0.944019i	$0.392988\pi$
$864$	4.59433	0.156302
$865$	−12.5065	−0.425235
$866$	20.6365	0.701256
$867$	17.1964	0.584021
$868$	−5.26744	−0.178789
$869$	26.7449	0.907259
$870$	9.23423	0.313070
$871$	−18.2058	−0.616881
$872$	1.33140	0.0450869
$873$	0.727593	0.0246253
$874$	−51.5472	−1.74361
$875$	−9.55196	−0.322915
$876$	−0.549213	−0.0185562
$877$	−44.2077	−1.49279	−0.746394	−	0.665505i	$-0.768216\pi$
$877$	−44.2077	−1.49279	−0.746394	+	0.665505i	$0.768216\pi$
$878$	8.63827	0.291527
$879$	−55.1754	−1.86102
$880$	1.22952	0.0414472
$881$	8.62949	0.290735	0.145367	−	0.989378i	$-0.453564\pi$
$881$	8.62949	0.290735	0.145367	+	0.989378i	$0.453564\pi$
$882$	−2.12152	−0.0714352
$883$	20.2388	0.681091	0.340546	−	0.940228i	$-0.389388\pi$
$883$	20.2388	0.681091	0.340546	+	0.940228i	$0.389388\pi$
$884$	−6.49591	−0.218481
$885$	10.7059	0.359876
$886$	−17.6883	−0.594250
$887$	49.2658	1.65418	0.827092	−	0.562066i	$-0.189993\pi$
$887$	49.2658	1.65418	0.827092	+	0.562066i	$0.189993\pi$
$888$	0	0
$889$	−14.1054	−0.473080
$890$	−5.72359	−0.191855
$891$	23.4174	0.784511
$892$	22.5132	0.753796
$893$	5.23242	0.175096
$894$	−32.3900	−1.08328
$895$	12.2367	0.409029
$896$	−1.80620	−0.0603410
$897$	27.6408	0.922901
$898$	14.1914	0.473575
$899$	26.1591	0.872454
$900$	−2.66943	−0.0889811
$901$	19.5900	0.652637
$902$	−9.65291	−0.321407
$903$	−37.7360	−1.25577
$904$	−12.2983	−0.409034
$905$	−8.78805	−0.292125
$906$	−24.2953	−0.807158
$907$	30.9021	1.02609	0.513044	−	0.858362i	$-0.328518\pi$
$907$	30.9021	1.02609	0.513044	+	0.858362i	$0.328518\pi$
$908$	−8.42449	−0.279577
$909$	3.51322	0.116526
$910$	−2.27581	−0.0754423
$911$	39.0266	1.29301	0.646504	−	0.762911i	$-0.276230\pi$
$911$	39.0266	1.29301	0.646504	+	0.762911i	$0.276230\pi$
$912$	15.3807	0.509307
$913$	−9.69160	−0.320745
$914$	21.1339	0.699048
$915$	14.5408	0.480703
$916$	21.5928	0.713445
$917$	−31.9194	−1.05407
$918$	12.9097	0.426083
$919$	−53.9025	−1.77808	−0.889040	−	0.457830i	$-0.848627\pi$
$919$	−53.9025	−1.77808	−0.889040	+	0.457830i	$0.848627\pi$
$920$	−3.45016	−0.113748
$921$	−25.3189	−0.834286
$922$	−11.9560	−0.393749
$923$	1.00051	0.0329323
$924$	−7.69606	−0.253182
$925$	0	0
$926$	−8.46127	−0.278055
$927$	−1.49640	−0.0491481
$928$	8.96993	0.294452
$929$	−43.7795	−1.43636	−0.718179	−	0.695859i	$-0.755024\pi$
$929$	−43.7795	−1.43636	−0.718179	+	0.695859i	$0.755024\pi$
$930$	3.00224	0.0984472
$931$	30.4359	0.997496
$932$	−4.00050	−0.131041
$933$	18.0931	0.592341
$934$	42.3768	1.38661
$935$	3.45486	0.112986
$936$	−1.31219	−0.0428902
$937$	6.32554	0.206646	0.103323	−	0.994648i	$-0.467052\pi$
$937$	6.32554	0.206646	0.103323	+	0.994648i	$0.467052\pi$
$938$	−14.2243	−0.464439
$939$	−11.4113	−0.372394
$940$	0.350217	0.0114228
$941$	58.2334	1.89836	0.949178	−	0.314740i	$-0.101917\pi$
$941$	58.2334	1.89836	0.949178	+	0.314740i	$0.101917\pi$
$942$	−15.9845	−0.520803
$943$	27.0870	0.882075
$944$	10.3995	0.338476
$945$	4.52284	0.147128
$946$	24.9525	0.811276
$947$	29.9108	0.971969	0.485984	−	0.873967i	$-0.338461\pi$
$947$	29.9108	0.971969	0.485984	+	0.873967i	$0.338461\pi$
$948$	22.3932	0.727298
$949$	−0.672200	−0.0218205
$950$	38.2964	1.24250
$951$	24.0695	0.780508
$952$	−5.07528	−0.164491
$953$	−3.66170	−0.118614	−0.0593070	−	0.998240i	$-0.518889\pi$
$953$	−3.66170	−0.118614	−0.0593070	+	0.998240i	$0.518889\pi$
$954$	3.95722	0.128120
$955$	5.28227	0.170930
$956$	−14.1689	−0.458256
$957$	38.2200	1.23548
$958$	17.8784	0.577624
$959$	25.6268	0.827532
$960$	1.02947	0.0332258
$961$	−22.4952	−0.725650
$962$	0	0
$963$	1.90573	0.0614112
$964$	−9.20130	−0.296354
$965$	−13.8269	−0.445105
$966$	21.5959	0.694836
$967$	33.1864	1.06720	0.533601	−	0.845736i	$-0.320838\pi$
$967$	33.1864	1.06720	0.533601	+	0.845736i	$0.320838\pi$
$968$	−5.91106	−0.189989
$969$	43.2186	1.38838
$970$	−0.698654	−0.0224324
$971$	−19.0862	−0.612505	−0.306252	−	0.951950i	$-0.599075\pi$
$971$	−19.0862	−0.612505	−0.306252	+	0.951950i	$0.599075\pi$
$972$	5.82411	0.186808
$973$	0.661731	0.0212141
$974$	−6.92527	−0.221900
$975$	−20.5355	−0.657661
$976$	14.1246	0.452117
$977$	52.3650	1.67530	0.837652	−	0.546204i	$-0.183928\pi$
$977$	52.3650	1.67530	0.837652	+	0.546204i	$0.183928\pi$
$978$	14.0907	0.450569
$979$	−23.6897	−0.757126
$980$	2.03714	0.0650739
$981$	0.755715	0.0241281
$982$	−2.42015	−0.0772302
$983$	0.810028	0.0258359	0.0129179	−	0.999917i	$-0.495888\pi$
$983$	0.810028	0.0258359	0.0129179	+	0.999917i	$0.495888\pi$
$984$	−8.08228	−0.257654
$985$	−12.6374	−0.402660
$986$	25.2048	0.802683
$987$	−2.19214	−0.0697767
$988$	18.8250	0.598903
$989$	−70.0191	−2.22648
$990$	0.697889	0.0221804
$991$	0.480082	0.0152503	0.00762515	−	0.999971i	$-0.497573\pi$
$991$	0.480082	0.0152503	0.00762515	+	0.999971i	$0.497573\pi$
$992$	2.91631	0.0925928
$993$	−5.94447	−0.188642
$994$	0.781704	0.0247941
$995$	−3.12304	−0.0990070
$996$	−8.11466	−0.257123
$997$	4.86248	0.153996	0.0769981	−	0.997031i	$-0.475466\pi$
$997$	4.86248	0.153996	0.0769981	+	0.997031i	$0.475466\pi$
$998$	−36.4959	−1.15526
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.x.1.3	yes	18
37.36	even	2		2738.2.a.w.1.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2738.2.a.w.1.3	✓	18	37.36	even	2
2738.2.a.x.1.3	yes	18	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.88881 q^{3} +1.00000 q^{4} -0.545033 q^{5} -1.88881 q^{6} -1.80620 q^{7} +1.00000 q^{8} +0.567610 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.88881 q^{3} +1.00000 q^{4} -0.545033 q^{5} -1.88881 q^{6} -1.80620 q^{7} +1.00000 q^{8} +0.567610 q^{9} -0.545033 q^{10} -2.25587 q^{11} -1.88881 q^{12} -2.31178 q^{13} -1.80620 q^{14} +1.02947 q^{15} +1.00000 q^{16} +2.80992 q^{17} +0.567610 q^{18} -8.14308 q^{19} -0.545033 q^{20} +3.41157 q^{21} -2.25587 q^{22} +6.33018 q^{23} -1.88881 q^{24} -4.70294 q^{25} -2.31178 q^{26} +4.59433 q^{27} -1.80620 q^{28} +8.96993 q^{29} +1.02947 q^{30} +2.91631 q^{31} +1.00000 q^{32} +4.26091 q^{33} +2.80992 q^{34} +0.984440 q^{35} +0.567610 q^{36} -8.14308 q^{38} +4.36652 q^{39} -0.545033 q^{40} +4.27903 q^{41} +3.41157 q^{42} -11.0612 q^{43} -2.25587 q^{44} -0.309366 q^{45} +6.33018 q^{46} -0.642561 q^{47} -1.88881 q^{48} -3.73764 q^{49} -4.70294 q^{50} -5.30740 q^{51} -2.31178 q^{52} +6.97173 q^{53} +4.59433 q^{54} +1.22952 q^{55} -1.80620 q^{56} +15.3807 q^{57} +8.96993 q^{58} +10.3995 q^{59} +1.02947 q^{60} +14.1246 q^{61} +2.91631 q^{62} -1.02522 q^{63} +1.00000 q^{64} +1.26000 q^{65} +4.26091 q^{66} +7.87525 q^{67} +2.80992 q^{68} -11.9565 q^{69} +0.984440 q^{70} -0.432789 q^{71} +0.567610 q^{72} +0.290772 q^{73} +8.88297 q^{75} -8.14308 q^{76} +4.07455 q^{77} +4.36652 q^{78} -11.8557 q^{79} -0.545033 q^{80} -10.3806 q^{81} +4.27903 q^{82} +4.29617 q^{83} +3.41157 q^{84} -1.53150 q^{85} -11.0612 q^{86} -16.9425 q^{87} -2.25587 q^{88} +10.5014 q^{89} -0.309366 q^{90} +4.17554 q^{91} +6.33018 q^{92} -5.50836 q^{93} -0.642561 q^{94} +4.43825 q^{95} -1.88881 q^{96} +1.28186 q^{97} -3.73764 q^{98} -1.28045 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 18 q^{2} + 8 q^{3} + 18 q^{4} + 9 q^{5} + 8 q^{6} + 18 q^{7} + 18 q^{8} + 26 q^{9}+O(q^{10}) \) 18 * q + 18 * q^2 + 8 * q^3 + 18 * q^4 + 9 * q^5 + 8 * q^6 + 18 * q^7 + 18 * q^8 + 26 * q^9	\( 18 q + 18 q^{2} + 8 q^{3} + 18 q^{4} + 9 q^{5} + 8 q^{6} + 18 q^{7} + 18 q^{8} + 26 q^{9} + 9 q^{10} + 10 q^{11} + 8 q^{12} + 9 q^{13} + 18 q^{14} - 4 q^{15} + 18 q^{16} + 13 q^{17} + 26 q^{18} + 2 q^{19} + 9 q^{20} + 24 q^{21} + 10 q^{22} - 11 q^{23} + 8 q^{24} + 49 q^{25} + 9 q^{26} + 29 q^{27} + 18 q^{28} + 30 q^{29} - 4 q^{30} - 8 q^{31} + 18 q^{32} + 42 q^{33} + 13 q^{34} + 25 q^{35} + 26 q^{36} + 2 q^{38} - 45 q^{39} + 9 q^{40} + 5 q^{41} + 24 q^{42} - 3 q^{43} + 10 q^{44} - 30 q^{45} - 11 q^{46} + 37 q^{47} + 8 q^{48} + 50 q^{49} + 49 q^{50} + 10 q^{51} + 9 q^{52} + 25 q^{53} + 29 q^{54} - 44 q^{55} + 18 q^{56} + 22 q^{57} + 30 q^{58} + 26 q^{59} - 4 q^{60} + 27 q^{61} - 8 q^{62} + 74 q^{63} + 18 q^{64} - 16 q^{65} + 42 q^{66} + 23 q^{67} + 13 q^{68} - 2 q^{69} + 25 q^{70} - 25 q^{71} + 26 q^{72} + 77 q^{73} - q^{75} + 2 q^{76} - 6 q^{77} - 45 q^{78} - 13 q^{79} + 9 q^{80} + 38 q^{81} + 5 q^{82} - 10 q^{83} + 24 q^{84} + 16 q^{85} - 3 q^{86} - 55 q^{87} + 10 q^{88} + 55 q^{89} - 30 q^{90} + 12 q^{91} - 11 q^{92} - 58 q^{93} + 37 q^{94} - 18 q^{95} + 8 q^{96} - 59 q^{97} + 50 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + 18 * q^2 + 8 * q^3 + 18 * q^4 + 9 * q^5 + 8 * q^6 + 18 * q^7 + 18 * q^8 + 26 * q^9 + 9 * q^10 + 10 * q^11 + 8 * q^12 + 9 * q^13 + 18 * q^14 - 4 * q^15 + 18 * q^16 + 13 * q^17 + 26 * q^18 + 2 * q^19 + 9 * q^20 + 24 * q^21 + 10 * q^22 - 11 * q^23 + 8 * q^24 + 49 * q^25 + 9 * q^26 + 29 * q^27 + 18 * q^28 + 30 * q^29 - 4 * q^30 - 8 * q^31 + 18 * q^32 + 42 * q^33 + 13 * q^34 + 25 * q^35 + 26 * q^36 + 2 * q^38 - 45 * q^39 + 9 * q^40 + 5 * q^41 + 24 * q^42 - 3 * q^43 + 10 * q^44 - 30 * q^45 - 11 * q^46 + 37 * q^47 + 8 * q^48 + 50 * q^49 + 49 * q^50 + 10 * q^51 + 9 * q^52 + 25 * q^53 + 29 * q^54 - 44 * q^55 + 18 * q^56 + 22 * q^57 + 30 * q^58 + 26 * q^59 - 4 * q^60 + 27 * q^61 - 8 * q^62 + 74 * q^63 + 18 * q^64 - 16 * q^65 + 42 * q^66 + 23 * q^67 + 13 * q^68 - 2 * q^69 + 25 * q^70 - 25 * q^71 + 26 * q^72 + 77 * q^73 - q^75 + 2 * q^76 - 6 * q^77 - 45 * q^78 - 13 * q^79 + 9 * q^80 + 38 * q^81 + 5 * q^82 - 10 * q^83 + 24 * q^84 + 16 * q^85 - 3 * q^86 - 55 * q^87 + 10 * q^88 + 55 * q^89 - 30 * q^90 + 12 * q^91 - 11 * q^92 - 58 * q^93 + 37 * q^94 - 18 * q^95 + 8 * q^96 - 59 * q^97 + 50 * q^98 + 11 * q^99

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