LMFDB - Embedded newform 2738.2.a.e.1.2

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:	$2$
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			1.2
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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.732051 q^{3} +1.00000 q^{4} +1.73205 q^{5} -0.732051 q^{6} -2.00000 q^{7} -1.00000 q^{8} -2.46410 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.732051 q^{3} +1.00000 q^{4} +1.73205 q^{5} -0.732051 q^{6} -2.00000 q^{7} -1.00000 q^{8} -2.46410 q^{9} -1.73205 q^{10} +1.26795 q^{11} +0.732051 q^{12} -3.46410 q^{13} +2.00000 q^{14} +1.26795 q^{15} +1.00000 q^{16} +4.26795 q^{17} +2.46410 q^{18} -4.73205 q^{19} +1.73205 q^{20} -1.46410 q^{21} -1.26795 q^{22} +1.26795 q^{23} -0.732051 q^{24} -2.00000 q^{25} +3.46410 q^{26} -4.00000 q^{27} -2.00000 q^{28} +8.66025 q^{29} -1.26795 q^{30} +4.73205 q^{31} -1.00000 q^{32} +0.928203 q^{33} -4.26795 q^{34} -3.46410 q^{35} -2.46410 q^{36} +4.73205 q^{38} -2.53590 q^{39} -1.73205 q^{40} +3.92820 q^{41} +1.46410 q^{42} +12.9282 q^{43} +1.26795 q^{44} -4.26795 q^{45} -1.26795 q^{46} +1.26795 q^{47} +0.732051 q^{48} -3.00000 q^{49} +2.00000 q^{50} +3.12436 q^{51} -3.46410 q^{52} +9.46410 q^{53} +4.00000 q^{54} +2.19615 q^{55} +2.00000 q^{56} -3.46410 q^{57} -8.66025 q^{58} +9.46410 q^{59} +1.26795 q^{60} -1.73205 q^{61} -4.73205 q^{62} +4.92820 q^{63} +1.00000 q^{64} -6.00000 q^{65} -0.928203 q^{66} -0.196152 q^{67} +4.26795 q^{68} +0.928203 q^{69} +3.46410 q^{70} -3.46410 q^{71} +2.46410 q^{72} -4.00000 q^{73} -1.46410 q^{75} -4.73205 q^{76} -2.53590 q^{77} +2.53590 q^{78} +16.7321 q^{79} +1.73205 q^{80} +4.46410 q^{81} -3.92820 q^{82} +11.6603 q^{83} -1.46410 q^{84} +7.39230 q^{85} -12.9282 q^{86} +6.33975 q^{87} -1.26795 q^{88} +17.1962 q^{89} +4.26795 q^{90} +6.92820 q^{91} +1.26795 q^{92} +3.46410 q^{93} -1.26795 q^{94} -8.19615 q^{95} -0.732051 q^{96} +4.26795 q^{97} +3.00000 q^{98} -3.12436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 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 - 4 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9} + 6 q^{11} - 2 q^{12} + 4 q^{14} + 6 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} - 6 q^{19} + 4 q^{21} - 6 q^{22} + 6 q^{23} + 2 q^{24} - 4 q^{25} - 8 q^{27} - 4 q^{28} - 6 q^{30} + 6 q^{31} - 2 q^{32} - 12 q^{33} - 12 q^{34} + 2 q^{36} + 6 q^{38} - 12 q^{39} - 6 q^{41} - 4 q^{42} + 12 q^{43} + 6 q^{44} - 12 q^{45} - 6 q^{46} + 6 q^{47} - 2 q^{48} - 6 q^{49} + 4 q^{50} - 18 q^{51} + 12 q^{53} + 8 q^{54} - 6 q^{55} + 4 q^{56} + 12 q^{59} + 6 q^{60} - 6 q^{62} - 4 q^{63} + 2 q^{64} - 12 q^{65} + 12 q^{66} + 10 q^{67} + 12 q^{68} - 12 q^{69} - 2 q^{72} - 8 q^{73} + 4 q^{75} - 6 q^{76} - 12 q^{77} + 12 q^{78} + 30 q^{79} + 2 q^{81} + 6 q^{82} + 6 q^{83} + 4 q^{84} - 6 q^{85} - 12 q^{86} + 30 q^{87} - 6 q^{88} + 24 q^{89} + 12 q^{90} + 6 q^{92} - 6 q^{94} - 6 q^{95} + 2 q^{96} + 12 q^{97} + 6 q^{98} + 18 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9 + 6 * q^11 - 2 * q^12 + 4 * q^14 + 6 * q^15 + 2 * q^16 + 12 * q^17 - 2 * q^18 - 6 * q^19 + 4 * q^21 - 6 * q^22 + 6 * q^23 + 2 * q^24 - 4 * q^25 - 8 * q^27 - 4 * q^28 - 6 * q^30 + 6 * q^31 - 2 * q^32 - 12 * q^33 - 12 * q^34 + 2 * q^36 + 6 * q^38 - 12 * q^39 - 6 * q^41 - 4 * q^42 + 12 * q^43 + 6 * q^44 - 12 * q^45 - 6 * q^46 + 6 * q^47 - 2 * q^48 - 6 * q^49 + 4 * q^50 - 18 * q^51 + 12 * q^53 + 8 * q^54 - 6 * q^55 + 4 * q^56 + 12 * q^59 + 6 * q^60 - 6 * q^62 - 4 * q^63 + 2 * q^64 - 12 * q^65 + 12 * q^66 + 10 * q^67 + 12 * q^68 - 12 * q^69 - 2 * q^72 - 8 * q^73 + 4 * q^75 - 6 * q^76 - 12 * q^77 + 12 * q^78 + 30 * q^79 + 2 * q^81 + 6 * q^82 + 6 * q^83 + 4 * q^84 - 6 * q^85 - 12 * q^86 + 30 * q^87 - 6 * q^88 + 24 * q^89 + 12 * q^90 + 6 * q^92 - 6 * q^94 - 6 * q^95 + 2 * q^96 + 12 * q^97 + 6 * q^98 + 18 * 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
$3$	0.732051	0.422650	0.211325	−	0.977416i	$-0.432222\pi$
$3$	0.732051	0.422650	0.211325	+	0.977416i	$0.432222\pi$
$4$	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	$0.373408\pi$
$6$	−0.732051	−0.298858
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	−2.46410	−0.821367
$10$	−1.73205	−0.547723
$11$	1.26795	0.382301	0.191151	−	0.981561i	$-0.438778\pi$
$11$	1.26795	0.382301	0.191151	+	0.981561i	$0.438778\pi$
$12$	0.732051	0.211325
$13$	−3.46410	−0.960769	−0.480384	−	0.877058i	$-0.659503\pi$
$13$	−3.46410	−0.960769	−0.480384	+	0.877058i	$0.659503\pi$
$14$	2.00000	0.534522
$15$	1.26795	0.327383
$16$	1.00000	0.250000
$17$	4.26795	1.03513	0.517565	−	0.855644i	$-0.326839\pi$
$17$	4.26795	1.03513	0.517565	+	0.855644i	$0.326839\pi$
$18$	2.46410	0.580794
$19$	−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
$21$	−1.46410	−0.319493
$22$	−1.26795	−0.270328
$23$	1.26795	0.264386	0.132193	−	0.991224i	$-0.457798\pi$
$23$	1.26795	0.264386	0.132193	+	0.991224i	$0.457798\pi$
$24$	−0.732051	−0.149429
$25$	−2.00000	−0.400000
$26$	3.46410	0.679366
$27$	−4.00000	−0.769800
$28$	−2.00000	−0.377964
$29$	8.66025	1.60817	0.804084	−	0.594515i	$-0.202656\pi$
$29$	8.66025	1.60817	0.804084	+	0.594515i	$0.202656\pi$
$30$	−1.26795	−0.231495
$31$	4.73205	0.849901	0.424951	−	0.905216i	$-0.360291\pi$
$31$	4.73205	0.849901	0.424951	+	0.905216i	$0.360291\pi$
$32$	−1.00000	−0.176777
$33$	0.928203	0.161579
$34$	−4.26795	−0.731947
$35$	−3.46410	−0.585540
$36$	−2.46410	−0.410684
$37$	0	0
$37$	0	0
$38$	4.73205	0.767640
$39$	−2.53590	−0.406069
$40$	−1.73205	−0.273861
$41$	3.92820	0.613482	0.306741	−	0.951793i	$-0.400761\pi$
$41$	3.92820	0.613482	0.306741	+	0.951793i	$0.400761\pi$
$42$	1.46410	0.225916
$43$	12.9282	1.97153	0.985766	−	0.168122i	$-0.0537701\pi$
$43$	12.9282	1.97153	0.985766	+	0.168122i	$0.0537701\pi$
$44$	1.26795	0.191151
$45$	−4.26795	−0.636228
$46$	−1.26795	−0.186949
$47$	1.26795	0.184949	0.0924747	−	0.995715i	$-0.470522\pi$
$47$	1.26795	0.184949	0.0924747	+	0.995715i	$0.470522\pi$
$48$	0.732051	0.105662
$49$	−3.00000	−0.428571
$50$	2.00000	0.282843
$51$	3.12436	0.437497
$52$	−3.46410	−0.480384
$53$	9.46410	1.29999	0.649997	−	0.759937i	$-0.274770\pi$
$53$	9.46410	1.29999	0.649997	+	0.759937i	$0.274770\pi$
$54$	4.00000	0.544331
$55$	2.19615	0.296129
$56$	2.00000	0.267261
$57$	−3.46410	−0.458831
$58$	−8.66025	−1.13715
$59$	9.46410	1.23212	0.616061	−	0.787699i	$-0.288728\pi$
$59$	9.46410	1.23212	0.616061	+	0.787699i	$0.288728\pi$
$60$	1.26795	0.163692
$61$	−1.73205	−0.221766	−0.110883	−	0.993833i	$-0.535368\pi$
$61$	−1.73205	−0.221766	−0.110883	+	0.993833i	$0.535368\pi$
$62$	−4.73205	−0.600971
$63$	4.92820	0.620895
$64$	1.00000	0.125000
$65$	−6.00000	−0.744208
$66$	−0.928203	−0.114254
$67$	−0.196152	−0.0239638	−0.0119819	−	0.999928i	$-0.503814\pi$
$67$	−0.196152	−0.0239638	−0.0119819	+	0.999928i	$0.503814\pi$
$68$	4.26795	0.517565
$69$	0.928203	0.111743
$70$	3.46410	0.414039
$71$	−3.46410	−0.411113	−0.205557	−	0.978645i	$-0.565900\pi$
$71$	−3.46410	−0.411113	−0.205557	+	0.978645i	$0.565900\pi$
$72$	2.46410	0.290397
$73$	−4.00000	−0.468165	−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000	−0.468165	−0.234082	+	0.972217i	$0.575209\pi$
$74$	0	0
$75$	−1.46410	−0.169060
$76$	−4.73205	−0.542803
$77$	−2.53590	−0.288992
$78$	2.53590	0.287134
$79$	16.7321	1.88250	0.941251	−	0.337707i	$-0.109651\pi$
$79$	16.7321	1.88250	0.941251	+	0.337707i	$0.109651\pi$
$80$	1.73205	0.193649
$81$	4.46410	0.496011
$82$	−3.92820	−0.433797
$83$	11.6603	1.27988	0.639940	−	0.768425i	$-0.278959\pi$
$83$	11.6603	1.27988	0.639940	+	0.768425i	$0.278959\pi$
$84$	−1.46410	−0.159747
$85$	7.39230	0.801808
$86$	−12.9282	−1.39408
$87$	6.33975	0.679692
$88$	−1.26795	−0.135164
$89$	17.1962	1.82279	0.911394	−	0.411534i	$-0.135007\pi$
$89$	17.1962	1.82279	0.911394	+	0.411534i	$0.135007\pi$
$90$	4.26795	0.449881
$91$	6.92820	0.726273
$92$	1.26795	0.132193
$93$	3.46410	0.359211
$94$	−1.26795	−0.130779
$95$	−8.19615	−0.840907
$96$	−0.732051	−0.0747146
$97$	4.26795	0.433345	0.216672	−	0.976244i	$-0.430480\pi$
$97$	4.26795	0.433345	0.216672	+	0.976244i	$0.430480\pi$
$98$	3.00000	0.303046
$99$	−3.12436	−0.314010
$100$	−2.00000	−0.200000
$101$	−5.53590	−0.550842	−0.275421	−	0.961324i	$-0.588817\pi$
$101$	−5.53590	−0.550842	−0.275421	+	0.961324i	$0.588817\pi$
$102$	−3.12436	−0.309357
$103$	15.4641	1.52372	0.761862	−	0.647740i	$-0.224286\pi$
$103$	15.4641	1.52372	0.761862	+	0.647740i	$0.224286\pi$
$104$	3.46410	0.339683
$105$	−2.53590	−0.247478
$106$	−9.46410	−0.919235
$107$	10.3923	1.00466	0.502331	−	0.864675i	$-0.332476\pi$
$107$	10.3923	1.00466	0.502331	+	0.864675i	$0.332476\pi$
$108$	−4.00000	−0.384900
$109$	−14.6603	−1.40420	−0.702099	−	0.712080i	$-0.747754\pi$
$109$	−14.6603	−1.40420	−0.702099	+	0.712080i	$0.747754\pi$
$110$	−2.19615	−0.209395
$111$	0	0
$112$	−2.00000	−0.188982
$113$	−3.46410	−0.325875	−0.162938	−	0.986636i	$-0.552097\pi$
$113$	−3.46410	−0.325875	−0.162938	+	0.986636i	$0.552097\pi$
$114$	3.46410	0.324443
$115$	2.19615	0.204792
$116$	8.66025	0.804084
$117$	8.53590	0.789144
$118$	−9.46410	−0.871241
$119$	−8.53590	−0.782485
$120$	−1.26795	−0.115747
$121$	−9.39230	−0.853846
$122$	1.73205	0.156813
$123$	2.87564	0.259288
$124$	4.73205	0.424951
$125$	−12.1244	−1.08444
$126$	−4.92820	−0.439039
$127$	−18.1962	−1.61465	−0.807324	−	0.590109i	$-0.799085\pi$
$127$	−18.1962	−1.61465	−0.807324	+	0.590109i	$0.799085\pi$
$128$	−1.00000	−0.0883883
$129$	9.46410	0.833268
$130$	6.00000	0.526235
$131$	−20.1962	−1.76455	−0.882273	−	0.470738i	$-0.843988\pi$
$131$	−20.1962	−1.76455	−0.882273	+	0.470738i	$0.843988\pi$
$132$	0.928203	0.0807897
$133$	9.46410	0.820642
$134$	0.196152	0.0169450
$135$	−6.92820	−0.596285
$136$	−4.26795	−0.365974
$137$	19.3923	1.65680	0.828398	−	0.560140i	$-0.189253\pi$
$137$	19.3923	1.65680	0.828398	+	0.560140i	$0.189253\pi$
$138$	−0.928203	−0.0790139
$139$	−10.5885	−0.898101	−0.449051	−	0.893506i	$-0.648238\pi$
$139$	−10.5885	−0.898101	−0.449051	+	0.893506i	$0.648238\pi$
$140$	−3.46410	−0.292770
$141$	0.928203	0.0781688
$142$	3.46410	0.290701
$143$	−4.39230	−0.367303
$144$	−2.46410	−0.205342
$145$	15.0000	1.24568
$146$	4.00000	0.331042
$147$	−2.19615	−0.181136
$148$	0	0
$149$	−2.07180	−0.169728	−0.0848641	−	0.996393i	$-0.527046\pi$
$149$	−2.07180	−0.169728	−0.0848641	+	0.996393i	$0.527046\pi$
$150$	1.46410	0.119543
$151$	6.19615	0.504236	0.252118	−	0.967697i	$-0.418873\pi$
$151$	6.19615	0.504236	0.252118	+	0.967697i	$0.418873\pi$
$152$	4.73205	0.383820
$153$	−10.5167	−0.850222
$154$	2.53590	0.204349
$155$	8.19615	0.658331
$156$	−2.53590	−0.203034
$157$	1.00000	0.0798087	0.0399043	−	0.999204i	$-0.487295\pi$
$157$	1.00000	0.0798087	0.0399043	+	0.999204i	$0.487295\pi$
$158$	−16.7321	−1.33113
$159$	6.92820	0.549442
$160$	−1.73205	−0.136931
$161$	−2.53590	−0.199857
$162$	−4.46410	−0.350733
$163$	0.928203	0.0727025	0.0363512	−	0.999339i	$-0.488426\pi$
$163$	0.928203	0.0727025	0.0363512	+	0.999339i	$0.488426\pi$
$164$	3.92820	0.306741
$165$	1.60770	0.125159
$166$	−11.6603	−0.905011
$167$	−13.8564	−1.07224	−0.536120	−	0.844141i	$-0.680111\pi$
$167$	−13.8564	−1.07224	−0.536120	+	0.844141i	$0.680111\pi$
$168$	1.46410	0.112958
$169$	−1.00000	−0.0769231
$170$	−7.39230	−0.566964
$171$	11.6603	0.891682
$172$	12.9282	0.985766
$173$	−12.4641	−0.947628	−0.473814	−	0.880625i	$-0.657123\pi$
$173$	−12.4641	−0.947628	−0.473814	+	0.880625i	$0.657123\pi$
$174$	−6.33975	−0.480615
$175$	4.00000	0.302372
$176$	1.26795	0.0955753
$177$	6.92820	0.520756
$178$	−17.1962	−1.28891
$179$	2.53590	0.189542	0.0947710	−	0.995499i	$-0.469788\pi$
$179$	2.53590	0.189542	0.0947710	+	0.995499i	$0.469788\pi$
$180$	−4.26795	−0.318114
$181$	11.3923	0.846783	0.423392	−	0.905947i	$-0.360839\pi$
$181$	11.3923	0.846783	0.423392	+	0.905947i	$0.360839\pi$
$182$	−6.92820	−0.513553
$183$	−1.26795	−0.0937295
$184$	−1.26795	−0.0934745
$185$	0	0
$186$	−3.46410	−0.254000
$187$	5.41154	0.395731
$188$	1.26795	0.0924747
$189$	8.00000	0.581914
$190$	8.19615	0.594611
$191$	−8.19615	−0.593053	−0.296526	−	0.955025i	$-0.595828\pi$
$191$	−8.19615	−0.593053	−0.296526	+	0.955025i	$0.595828\pi$
$192$	0.732051	0.0528312
$193$	0.803848	0.0578622	0.0289311	−	0.999581i	$-0.490790\pi$
$193$	0.803848	0.0578622	0.0289311	+	0.999581i	$0.490790\pi$
$194$	−4.26795	−0.306421
$195$	−4.39230	−0.314539
$196$	−3.00000	−0.214286
$197$	−0.464102	−0.0330659	−0.0165329	−	0.999863i	$-0.505263\pi$
$197$	−0.464102	−0.0330659	−0.0165329	+	0.999863i	$0.505263\pi$
$198$	3.12436	0.222038
$199$	−10.3923	−0.736691	−0.368345	−	0.929689i	$-0.620076\pi$
$199$	−10.3923	−0.736691	−0.368345	+	0.929689i	$0.620076\pi$
$200$	2.00000	0.141421
$201$	−0.143594	−0.0101283
$202$	5.53590	0.389504
$203$	−17.3205	−1.21566
$204$	3.12436	0.218749
$205$	6.80385	0.475201
$206$	−15.4641	−1.07744
$207$	−3.12436	−0.217158
$208$	−3.46410	−0.240192
$209$	−6.00000	−0.415029
$210$	2.53590	0.174994
$211$	18.3923	1.26618	0.633089	−	0.774079i	$-0.281787\pi$
$211$	18.3923	1.26618	0.633089	+	0.774079i	$0.281787\pi$
$212$	9.46410	0.649997
$213$	−2.53590	−0.173757
$214$	−10.3923	−0.710403
$215$	22.3923	1.52714
$216$	4.00000	0.272166
$217$	−9.46410	−0.642465
$218$	14.6603	0.992918
$219$	−2.92820	−0.197870
$220$	2.19615	0.148065
$221$	−14.7846	−0.994520
$222$	0	0
$223$	5.80385	0.388654	0.194327	−	0.980937i	$-0.437748\pi$
$223$	5.80385	0.388654	0.194327	+	0.980937i	$0.437748\pi$
$224$	2.00000	0.133631
$225$	4.92820	0.328547
$226$	3.46410	0.230429
$227$	−4.73205	−0.314077	−0.157039	−	0.987592i	$-0.550195\pi$
$227$	−4.73205	−0.314077	−0.157039	+	0.987592i	$0.550195\pi$
$228$	−3.46410	−0.229416
$229$	6.60770	0.436649	0.218324	−	0.975876i	$-0.429941\pi$
$229$	6.60770	0.436649	0.218324	+	0.975876i	$0.429941\pi$
$230$	−2.19615	−0.144810
$231$	−1.85641	−0.122143
$232$	−8.66025	−0.568574
$233$	−15.0000	−0.982683	−0.491341	−	0.870967i	$-0.663493\pi$
$233$	−15.0000	−0.982683	−0.491341	+	0.870967i	$0.663493\pi$
$234$	−8.53590	−0.558009
$235$	2.19615	0.143261
$236$	9.46410	0.616061
$237$	12.2487	0.795639
$238$	8.53590	0.553300
$239$	17.3205	1.12037	0.560185	−	0.828367i	$-0.310730\pi$
$239$	17.3205	1.12037	0.560185	+	0.828367i	$0.310730\pi$
$240$	1.26795	0.0818458
$241$	−8.53590	−0.549846	−0.274923	−	0.961466i	$-0.588652\pi$
$241$	−8.53590	−0.549846	−0.274923	+	0.961466i	$0.588652\pi$
$242$	9.39230	0.603760
$243$	15.2679	0.979439
$244$	−1.73205	−0.110883
$245$	−5.19615	−0.331970
$246$	−2.87564	−0.183344
$247$	16.3923	1.04302
$248$	−4.73205	−0.300486
$249$	8.53590	0.540941
$250$	12.1244	0.766812
$251$	−17.3205	−1.09326	−0.546630	−	0.837374i	$-0.684090\pi$
$251$	−17.3205	−1.09326	−0.546630	+	0.837374i	$0.684090\pi$
$252$	4.92820	0.310448
$253$	1.60770	0.101075
$254$	18.1962	1.14173
$255$	5.41154	0.338884
$256$	1.00000	0.0625000
$257$	17.1962	1.07267	0.536333	−	0.844006i	$-0.319809\pi$
$257$	17.1962	1.07267	0.536333	+	0.844006i	$0.319809\pi$
$258$	−9.46410	−0.589209
$259$	0	0
$260$	−6.00000	−0.372104
$261$	−21.3397	−1.32090
$262$	20.1962	1.24772
$263$	−14.5359	−0.896322	−0.448161	−	0.893953i	$-0.647921\pi$
$263$	−14.5359	−0.896322	−0.448161	+	0.893953i	$0.647921\pi$
$264$	−0.928203	−0.0571270
$265$	16.3923	1.00697
$266$	−9.46410	−0.580281
$267$	12.5885	0.770401
$268$	−0.196152	−0.0119819
$269$	16.3923	0.999456	0.499728	−	0.866182i	$-0.333433\pi$
$269$	16.3923	0.999456	0.499728	+	0.866182i	$0.333433\pi$
$270$	6.92820	0.421637
$271$	28.5885	1.73663	0.868313	−	0.496017i	$-0.165205\pi$
$271$	28.5885	1.73663	0.868313	+	0.496017i	$0.165205\pi$
$272$	4.26795	0.258782
$273$	5.07180	0.306959
$274$	−19.3923	−1.17153
$275$	−2.53590	−0.152920
$276$	0.928203	0.0558713
$277$	0.803848	0.0482985	0.0241493	−	0.999708i	$-0.492312\pi$
$277$	0.803848	0.0482985	0.0241493	+	0.999708i	$0.492312\pi$
$278$	10.5885	0.635053
$279$	−11.6603	−0.698081
$280$	3.46410	0.207020
$281$	3.58846	0.214069	0.107035	−	0.994255i	$-0.465864\pi$
$281$	3.58846	0.214069	0.107035	+	0.994255i	$0.465864\pi$
$282$	−0.928203	−0.0552737
$283$	19.8564	1.18034	0.590170	−	0.807279i	$-0.299061\pi$
$283$	19.8564	1.18034	0.590170	+	0.807279i	$0.299061\pi$
$284$	−3.46410	−0.205557
$285$	−6.00000	−0.355409
$286$	4.39230	0.259722
$287$	−7.85641	−0.463749
$288$	2.46410	0.145199
$289$	1.21539	0.0714935
$290$	−15.0000	−0.880830
$291$	3.12436	0.183153
$292$	−4.00000	−0.234082
$293$	19.3923	1.13291	0.566455	−	0.824092i	$-0.308314\pi$
$293$	19.3923	1.13291	0.566455	+	0.824092i	$0.308314\pi$
$294$	2.19615	0.128082
$295$	16.3923	0.954397
$296$	0	0
$297$	−5.07180	−0.294295
$298$	2.07180	0.120016
$299$	−4.39230	−0.254014
$300$	−1.46410	−0.0845299
$301$	−25.8564	−1.49034
$302$	−6.19615	−0.356549
$303$	−4.05256	−0.232813
$304$	−4.73205	−0.271402
$305$	−3.00000	−0.171780
$306$	10.5167	0.601197
$307$	22.0000	1.25561	0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000	1.25561	0.627803	+	0.778372i	$0.283954\pi$
$308$	−2.53590	−0.144496
$309$	11.3205	0.644001
$310$	−8.19615	−0.465510
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	2.53590	0.143567
$313$	−0.124356	−0.00702900	−0.00351450	−	0.999994i	$-0.501119\pi$
$313$	−0.124356	−0.00702900	−0.00351450	+	0.999994i	$0.501119\pi$
$314$	−1.00000	−0.0564333
$315$	8.53590	0.480943
$316$	16.7321	0.941251
$317$	13.3923	0.752187	0.376093	−	0.926582i	$-0.377267\pi$
$317$	13.3923	0.752187	0.376093	+	0.926582i	$0.377267\pi$
$318$	−6.92820	−0.388514
$319$	10.9808	0.614805
$320$	1.73205	0.0968246
$321$	7.60770	0.424620
$322$	2.53590	0.141320
$323$	−20.1962	−1.12374
$324$	4.46410	0.248006
$325$	6.92820	0.384308
$326$	−0.928203	−0.0514084
$327$	−10.7321	−0.593484
$328$	−3.92820	−0.216899
$329$	−2.53590	−0.139809
$330$	−1.60770	−0.0885007
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	11.6603	0.639940
$333$	0	0
$334$	13.8564	0.758189
$335$	−0.339746	−0.0185623
$336$	−1.46410	−0.0798733
$337$	−30.1769	−1.64384	−0.821921	−	0.569602i	$-0.807097\pi$
$337$	−30.1769	−1.64384	−0.821921	+	0.569602i	$0.807097\pi$
$338$	1.00000	0.0543928
$339$	−2.53590	−0.137731
$340$	7.39230	0.400904
$341$	6.00000	0.324918
$342$	−11.6603	−0.630514
$343$	20.0000	1.07990
$344$	−12.9282	−0.697042
$345$	1.60770	0.0865554
$346$	12.4641	0.670074
$347$	15.1244	0.811918	0.405959	−	0.913891i	$-0.366938\pi$
$347$	15.1244	0.811918	0.405959	+	0.913891i	$0.366938\pi$
$348$	6.33975	0.339846
$349$	−9.39230	−0.502759	−0.251379	−	0.967889i	$-0.580884\pi$
$349$	−9.39230	−0.502759	−0.251379	+	0.967889i	$0.580884\pi$
$350$	−4.00000	−0.213809
$351$	13.8564	0.739600
$352$	−1.26795	−0.0675819
$353$	16.2679	0.865856	0.432928	−	0.901429i	$-0.357481\pi$
$353$	16.2679	0.865856	0.432928	+	0.901429i	$0.357481\pi$
$354$	−6.92820	−0.368230
$355$	−6.00000	−0.318447
$356$	17.1962	0.911394
$357$	−6.24871	−0.330717
$358$	−2.53590	−0.134026
$359$	0.679492	0.0358622	0.0179311	−	0.999839i	$-0.494292\pi$
$359$	0.679492	0.0358622	0.0179311	+	0.999839i	$0.494292\pi$
$360$	4.26795	0.224941
$361$	3.39230	0.178542
$362$	−11.3923	−0.598766
$363$	−6.87564	−0.360878
$364$	6.92820	0.363137
$365$	−6.92820	−0.362639
$366$	1.26795	0.0662768
$367$	−8.39230	−0.438075	−0.219037	−	0.975716i	$-0.570292\pi$
$367$	−8.39230	−0.438075	−0.219037	+	0.975716i	$0.570292\pi$
$368$	1.26795	0.0660964
$369$	−9.67949	−0.503894
$370$	0	0
$371$	−18.9282	−0.982703
$372$	3.46410	0.179605
$373$	−7.00000	−0.362446	−0.181223	−	0.983442i	$-0.558006\pi$
$373$	−7.00000	−0.362446	−0.181223	+	0.983442i	$0.558006\pi$
$374$	−5.41154	−0.279824
$375$	−8.87564	−0.458336
$376$	−1.26795	−0.0653895
$377$	−30.0000	−1.54508
$378$	−8.00000	−0.411476
$379$	6.78461	0.348502	0.174251	−	0.984701i	$-0.444250\pi$
$379$	6.78461	0.348502	0.174251	+	0.984701i	$0.444250\pi$
$380$	−8.19615	−0.420454
$381$	−13.3205	−0.682430
$382$	8.19615	0.419352
$383$	−3.46410	−0.177007	−0.0885037	−	0.996076i	$-0.528208\pi$
$383$	−3.46410	−0.177007	−0.0885037	+	0.996076i	$0.528208\pi$
$384$	−0.732051	−0.0373573
$385$	−4.39230	−0.223853
$386$	−0.803848	−0.0409148
$387$	−31.8564	−1.61935
$388$	4.26795	0.216672
$389$	−25.9808	−1.31728	−0.658638	−	0.752460i	$-0.728867\pi$
$389$	−25.9808	−1.31728	−0.658638	+	0.752460i	$0.728867\pi$
$390$	4.39230	0.222413
$391$	5.41154	0.273673
$392$	3.00000	0.151523
$393$	−14.7846	−0.745785
$394$	0.464102	0.0233811
$395$	28.9808	1.45818
$396$	−3.12436	−0.157005
$397$	23.0000	1.15434	0.577168	−	0.816625i	$-0.304158\pi$
$397$	23.0000	1.15434	0.577168	+	0.816625i	$0.304158\pi$
$398$	10.3923	0.520919
$399$	6.92820	0.346844
$400$	−2.00000	−0.100000
$401$	−10.3923	−0.518967	−0.259483	−	0.965748i	$-0.583552\pi$
$401$	−10.3923	−0.518967	−0.259483	+	0.965748i	$0.583552\pi$
$402$	0.143594	0.00716179
$403$	−16.3923	−0.816559
$404$	−5.53590	−0.275421
$405$	7.73205	0.384209
$406$	17.3205	0.859602
$407$	0	0
$408$	−3.12436	−0.154679
$409$	34.5167	1.70674	0.853370	−	0.521307i	$-0.174555\pi$
$409$	34.5167	1.70674	0.853370	+	0.521307i	$0.174555\pi$
$410$	−6.80385	−0.336018
$411$	14.1962	0.700245
$412$	15.4641	0.761862
$413$	−18.9282	−0.931396
$414$	3.12436	0.153554
$415$	20.1962	0.991390
$416$	3.46410	0.169842
$417$	−7.75129	−0.379582
$418$	6.00000	0.293470
$419$	−31.8564	−1.55629	−0.778144	−	0.628086i	$-0.783838\pi$
$419$	−31.8564	−1.55629	−0.778144	+	0.628086i	$0.783838\pi$
$420$	−2.53590	−0.123739
$421$	−12.1244	−0.590905	−0.295452	−	0.955357i	$-0.595470\pi$
$421$	−12.1244	−0.590905	−0.295452	+	0.955357i	$0.595470\pi$
$422$	−18.3923	−0.895323
$423$	−3.12436	−0.151911
$424$	−9.46410	−0.459617
$425$	−8.53590	−0.414052
$426$	2.53590	0.122865
$427$	3.46410	0.167640
$428$	10.3923	0.502331
$429$	−3.21539	−0.155241
$430$	−22.3923	−1.07985
$431$	−0.339746	−0.0163650	−0.00818249	−	0.999967i	$-0.502605\pi$
$431$	−0.339746	−0.0163650	−0.00818249	+	0.999967i	$0.502605\pi$
$432$	−4.00000	−0.192450
$433$	−25.7846	−1.23913	−0.619565	−	0.784946i	$-0.712691\pi$
$433$	−25.7846	−1.23913	−0.619565	+	0.784946i	$0.712691\pi$
$434$	9.46410	0.454291
$435$	10.9808	0.526487
$436$	−14.6603	−0.702099
$437$	−6.00000	−0.287019
$438$	2.92820	0.139915
$439$	30.2487	1.44369	0.721846	−	0.692054i	$-0.243294\pi$
$439$	30.2487	1.44369	0.721846	+	0.692054i	$0.243294\pi$
$440$	−2.19615	−0.104697
$441$	7.39230	0.352015
$442$	14.7846	0.703232
$443$	21.4641	1.01979	0.509895	−	0.860237i	$-0.329684\pi$
$443$	21.4641	1.01979	0.509895	+	0.860237i	$0.329684\pi$
$444$	0	0
$445$	29.7846	1.41193
$446$	−5.80385	−0.274820
$447$	−1.51666	−0.0717356
$448$	−2.00000	−0.0944911
$449$	−27.4641	−1.29611	−0.648056	−	0.761593i	$-0.724418\pi$
$449$	−27.4641	−1.29611	−0.648056	+	0.761593i	$0.724418\pi$
$450$	−4.92820	−0.232318
$451$	4.98076	0.234535
$452$	−3.46410	−0.162938
$453$	4.53590	0.213115
$454$	4.73205	0.222086
$455$	12.0000	0.562569
$456$	3.46410	0.162221
$457$	−13.9808	−0.653992	−0.326996	−	0.945026i	$-0.606036\pi$
$457$	−13.9808	−0.653992	−0.326996	+	0.945026i	$0.606036\pi$
$458$	−6.60770	−0.308757
$459$	−17.0718	−0.796843
$460$	2.19615	0.102396
$461$	−32.5359	−1.51535	−0.757674	−	0.652633i	$-0.773664\pi$
$461$	−32.5359	−1.51535	−0.757674	+	0.652633i	$0.773664\pi$
$462$	1.85641	0.0863678
$463$	30.0000	1.39422	0.697109	−	0.716965i	$-0.254469\pi$
$463$	30.0000	1.39422	0.697109	+	0.716965i	$0.254469\pi$
$464$	8.66025	0.402042
$465$	6.00000	0.278243
$466$	15.0000	0.694862
$467$	−9.46410	−0.437946	−0.218973	−	0.975731i	$-0.570271\pi$
$467$	−9.46410	−0.437946	−0.218973	+	0.975731i	$0.570271\pi$
$468$	8.53590	0.394572
$469$	0.392305	0.0181150
$470$	−2.19615	−0.101301
$471$	0.732051	0.0337311
$472$	−9.46410	−0.435621
$473$	16.3923	0.753719
$474$	−12.2487	−0.562602
$475$	9.46410	0.434243
$476$	−8.53590	−0.391242
$477$	−23.3205	−1.06777
$478$	−17.3205	−0.792222
$479$	2.53590	0.115868	0.0579341	−	0.998320i	$-0.481549\pi$
$479$	2.53590	0.115868	0.0579341	+	0.998320i	$0.481549\pi$
$480$	−1.26795	−0.0578737
$481$	0	0
$482$	8.53590	0.388800
$483$	−1.85641	−0.0844694
$484$	−9.39230	−0.426923
$485$	7.39230	0.335667
$486$	−15.2679	−0.692568
$487$	−22.0526	−0.999297	−0.499648	−	0.866228i	$-0.666537\pi$
$487$	−22.0526	−0.999297	−0.499648	+	0.866228i	$0.666537\pi$
$488$	1.73205	0.0784063
$489$	0.679492	0.0307277
$490$	5.19615	0.234738
$491$	15.8038	0.713218	0.356609	−	0.934254i	$-0.383933\pi$
$491$	15.8038	0.713218	0.356609	+	0.934254i	$0.383933\pi$
$492$	2.87564	0.129644
$493$	36.9615	1.66466
$494$	−16.3923	−0.737525
$495$	−5.41154	−0.243231
$496$	4.73205	0.212475
$497$	6.92820	0.310772
$498$	−8.53590	−0.382503
$499$	−9.80385	−0.438880	−0.219440	−	0.975626i	$-0.570423\pi$
$499$	−9.80385	−0.438880	−0.219440	+	0.975626i	$0.570423\pi$
$500$	−12.1244	−0.542218
$501$	−10.1436	−0.453182
$502$	17.3205	0.773052
$503$	−9.80385	−0.437132	−0.218566	−	0.975822i	$-0.570138\pi$
$503$	−9.80385	−0.437132	−0.218566	+	0.975822i	$0.570138\pi$
$504$	−4.92820	−0.219520
$505$	−9.58846	−0.426681
$506$	−1.60770	−0.0714708
$507$	−0.732051	−0.0325115
$508$	−18.1962	−0.807324
$509$	−0.464102	−0.0205709	−0.0102855	−	0.999947i	$-0.503274\pi$
$509$	−0.464102	−0.0205709	−0.0102855	+	0.999947i	$0.503274\pi$
$510$	−5.41154	−0.239627
$511$	8.00000	0.353899
$512$	−1.00000	−0.0441942
$513$	18.9282	0.835701
$514$	−17.1962	−0.758490
$515$	26.7846	1.18027
$516$	9.46410	0.416634
$517$	1.60770	0.0707064
$518$	0	0
$519$	−9.12436	−0.400515
$520$	6.00000	0.263117
$521$	−18.9282	−0.829260	−0.414630	−	0.909990i	$-0.636089\pi$
$521$	−18.9282	−0.829260	−0.414630	+	0.909990i	$0.636089\pi$
$522$	21.3397	0.934015
$523$	38.4449	1.68108	0.840538	−	0.541752i	$-0.182239\pi$
$523$	38.4449	1.68108	0.840538	+	0.541752i	$0.182239\pi$
$524$	−20.1962	−0.882273
$525$	2.92820	0.127797
$526$	14.5359	0.633795
$527$	20.1962	0.879758
$528$	0.928203	0.0403949
$529$	−21.3923	−0.930100
$530$	−16.3923	−0.712036
$531$	−23.3205	−1.01202
$532$	9.46410	0.410321
$533$	−13.6077	−0.589415
$534$	−12.5885	−0.544756
$535$	18.0000	0.778208
$536$	0.196152	0.00847249
$537$	1.85641	0.0801099
$538$	−16.3923	−0.706722
$539$	−3.80385	−0.163843
$540$	−6.92820	−0.298142
$541$	−19.0526	−0.819133	−0.409567	−	0.912280i	$-0.634320\pi$
$541$	−19.0526	−0.819133	−0.409567	+	0.912280i	$0.634320\pi$
$542$	−28.5885	−1.22798
$543$	8.33975	0.357893
$544$	−4.26795	−0.182987
$545$	−25.3923	−1.08769
$546$	−5.07180	−0.217053
$547$	−24.3397	−1.04069	−0.520346	−	0.853955i	$-0.674197\pi$
$547$	−24.3397	−1.04069	−0.520346	+	0.853955i	$0.674197\pi$
$548$	19.3923	0.828398
$549$	4.26795	0.182152
$550$	2.53590	0.108131
$551$	−40.9808	−1.74584
$552$	−0.928203	−0.0395070
$553$	−33.4641	−1.42304
$554$	−0.803848	−0.0341522
$555$	0	0
$556$	−10.5885	−0.449051
$557$	35.4449	1.50185	0.750924	−	0.660389i	$-0.229609\pi$
$557$	35.4449	1.50185	0.750924	+	0.660389i	$0.229609\pi$
$558$	11.6603	0.493618
$559$	−44.7846	−1.89419
$560$	−3.46410	−0.146385
$561$	3.96152	0.167256
$562$	−3.58846	−0.151370
$563$	12.5885	0.530540	0.265270	−	0.964174i	$-0.414539\pi$
$563$	12.5885	0.530540	0.265270	+	0.964174i	$0.414539\pi$
$564$	0.928203	0.0390844
$565$	−6.00000	−0.252422
$566$	−19.8564	−0.834627
$567$	−8.92820	−0.374949
$568$	3.46410	0.145350
$569$	30.1244	1.26288	0.631439	−	0.775425i	$-0.282464\pi$
$569$	30.1244	1.26288	0.631439	+	0.775425i	$0.282464\pi$
$570$	6.00000	0.251312
$571$	−35.3731	−1.48032	−0.740158	−	0.672433i	$-0.765249\pi$
$571$	−35.3731	−1.48032	−0.740158	+	0.672433i	$0.765249\pi$
$572$	−4.39230	−0.183651
$573$	−6.00000	−0.250654
$574$	7.85641	0.327920
$575$	−2.53590	−0.105754
$576$	−2.46410	−0.102671
$577$	12.9282	0.538208	0.269104	−	0.963111i	$-0.413272\pi$
$577$	12.9282	0.538208	0.269104	+	0.963111i	$0.413272\pi$
$578$	−1.21539	−0.0505536
$579$	0.588457	0.0244554
$580$	15.0000	0.622841
$581$	−23.3205	−0.967498
$582$	−3.12436	−0.129509
$583$	12.0000	0.496989
$584$	4.00000	0.165521
$585$	14.7846	0.611268
$586$	−19.3923	−0.801089
$587$	8.87564	0.366337	0.183169	−	0.983082i	$-0.441365\pi$
$587$	8.87564	0.366337	0.183169	+	0.983082i	$0.441365\pi$
$588$	−2.19615	−0.0905678
$589$	−22.3923	−0.922659
$590$	−16.3923	−0.674861
$591$	−0.339746	−0.0139753
$592$	0	0
$593$	−25.6410	−1.05295	−0.526475	−	0.850191i	$-0.676487\pi$
$593$	−25.6410	−1.05295	−0.526475	+	0.850191i	$0.676487\pi$
$594$	5.07180	0.208098
$595$	−14.7846	−0.606110
$596$	−2.07180	−0.0848641
$597$	−7.60770	−0.311362
$598$	4.39230	0.179615
$599$	30.3397	1.23965	0.619824	−	0.784741i	$-0.287204\pi$
$599$	30.3397	1.23965	0.619824	+	0.784741i	$0.287204\pi$
$600$	1.46410	0.0597717
$601$	−33.3923	−1.36210	−0.681050	−	0.732237i	$-0.738476\pi$
$601$	−33.3923	−1.36210	−0.681050	+	0.732237i	$0.738476\pi$
$602$	25.8564	1.05383
$603$	0.483340	0.0196831
$604$	6.19615	0.252118
$605$	−16.2679	−0.661386
$606$	4.05256	0.164624
$607$	−41.9090	−1.70103	−0.850516	−	0.525949i	$-0.823710\pi$
$607$	−41.9090	−1.70103	−0.850516	+	0.525949i	$0.823710\pi$
$608$	4.73205	0.191910
$609$	−12.6795	−0.513799
$610$	3.00000	0.121466
$611$	−4.39230	−0.177694
$612$	−10.5167	−0.425111
$613$	33.7846	1.36455	0.682274	−	0.731097i	$-0.260991\pi$
$613$	33.7846	1.36455	0.682274	+	0.731097i	$0.260991\pi$
$614$	−22.0000	−0.887848
$615$	4.98076	0.200844
$616$	2.53590	0.102174
$617$	−47.3205	−1.90505	−0.952526	−	0.304457i	$-0.901525\pi$
$617$	−47.3205	−1.90505	−0.952526	+	0.304457i	$0.901525\pi$
$618$	−11.3205	−0.455378
$619$	−9.60770	−0.386166	−0.193083	−	0.981182i	$-0.561849\pi$
$619$	−9.60770	−0.386166	−0.193083	+	0.981182i	$0.561849\pi$
$620$	8.19615	0.329165
$621$	−5.07180	−0.203524
$622$	−18.0000	−0.721734
$623$	−34.3923	−1.37790
$624$	−2.53590	−0.101517
$625$	−11.0000	−0.440000
$626$	0.124356	0.00497025
$627$	−4.39230	−0.175412
$628$	1.00000	0.0399043
$629$	0	0
$630$	−8.53590	−0.340078
$631$	−16.9808	−0.675993	−0.337997	−	0.941147i	$-0.609749\pi$
$631$	−16.9808	−0.675993	−0.337997	+	0.941147i	$0.609749\pi$
$632$	−16.7321	−0.665565
$633$	13.4641	0.535150
$634$	−13.3923	−0.531876
$635$	−31.5167	−1.25070
$636$	6.92820	0.274721
$637$	10.3923	0.411758
$638$	−10.9808	−0.434733
$639$	8.53590	0.337675
$640$	−1.73205	−0.0684653
$641$	28.8564	1.13976	0.569880	−	0.821728i	$-0.306990\pi$
$641$	28.8564	1.13976	0.569880	+	0.821728i	$0.306990\pi$
$642$	−7.60770	−0.300252
$643$	16.7321	0.659848	0.329924	−	0.944008i	$-0.392977\pi$
$643$	16.7321	0.659848	0.329924	+	0.944008i	$0.392977\pi$
$644$	−2.53590	−0.0999284
$645$	16.3923	0.645446
$646$	20.1962	0.794607
$647$	36.9282	1.45180	0.725899	−	0.687802i	$-0.241424\pi$
$647$	36.9282	1.45180	0.725899	+	0.687802i	$0.241424\pi$
$648$	−4.46410	−0.175366
$649$	12.0000	0.471041
$650$	−6.92820	−0.271746
$651$	−6.92820	−0.271538
$652$	0.928203	0.0363512
$653$	7.98076	0.312311	0.156156	−	0.987732i	$-0.450090\pi$
$653$	7.98076	0.312311	0.156156	+	0.987732i	$0.450090\pi$
$654$	10.7321	0.419656
$655$	−34.9808	−1.36681
$656$	3.92820	0.153371
$657$	9.85641	0.384535
$658$	2.53590	0.0988596
$659$	2.53590	0.0987846	0.0493923	−	0.998779i	$-0.484272\pi$
$659$	2.53590	0.0987846	0.0493923	+	0.998779i	$0.484272\pi$
$660$	1.60770	0.0625794
$661$	−1.73205	−0.0673690	−0.0336845	−	0.999433i	$-0.510724\pi$
$661$	−1.73205	−0.0673690	−0.0336845	+	0.999433i	$0.510724\pi$
$662$	0	0
$663$	−10.8231	−0.420334
$664$	−11.6603	−0.452506
$665$	16.3923	0.635666
$666$	0	0
$667$	10.9808	0.425177
$668$	−13.8564	−0.536120
$669$	4.24871	0.164265
$670$	0.339746	0.0131255
$671$	−2.19615	−0.0847815
$672$	1.46410	0.0564789
$673$	16.0000	0.616755	0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000	0.616755	0.308377	+	0.951264i	$0.400214\pi$
$674$	30.1769	1.16237
$675$	8.00000	0.307920
$676$	−1.00000	−0.0384615
$677$	−20.0718	−0.771422	−0.385711	−	0.922620i	$-0.626044\pi$
$677$	−20.0718	−0.771422	−0.385711	+	0.922620i	$0.626044\pi$
$678$	2.53590	0.0973906
$679$	−8.53590	−0.327578
$680$	−7.39230	−0.283482
$681$	−3.46410	−0.132745
$682$	−6.00000	−0.229752
$683$	−27.4641	−1.05088	−0.525442	−	0.850829i	$-0.676100\pi$
$683$	−27.4641	−1.05088	−0.525442	+	0.850829i	$0.676100\pi$
$684$	11.6603	0.445841
$685$	33.5885	1.28335
$686$	−20.0000	−0.763604
$687$	4.83717	0.184549
$688$	12.9282	0.492883
$689$	−32.7846	−1.24899
$690$	−1.60770	−0.0612039
$691$	24.9808	0.950313	0.475156	−	0.879901i	$-0.342391\pi$
$691$	24.9808	0.950313	0.475156	+	0.879901i	$0.342391\pi$
$692$	−12.4641	−0.473814
$693$	6.24871	0.237369
$694$	−15.1244	−0.574113
$695$	−18.3397	−0.695666
$696$	−6.33975	−0.240307
$697$	16.7654	0.635034
$698$	9.39230	0.355504
$699$	−10.9808	−0.415331
$700$	4.00000	0.151186
$701$	5.07180	0.191559	0.0957796	−	0.995403i	$-0.469466\pi$
$701$	5.07180	0.191559	0.0957796	+	0.995403i	$0.469466\pi$
$702$	−13.8564	−0.522976
$703$	0	0
$704$	1.26795	0.0477876
$705$	1.60770	0.0605493
$706$	−16.2679	−0.612252
$707$	11.0718	0.416398
$708$	6.92820	0.260378
$709$	45.7128	1.71678	0.858390	−	0.512997i	$-0.171465\pi$
$709$	45.7128	1.71678	0.858390	+	0.512997i	$0.171465\pi$
$710$	6.00000	0.225176
$711$	−41.2295	−1.54623
$712$	−17.1962	−0.644453
$713$	6.00000	0.224702
$714$	6.24871	0.233852
$715$	−7.60770	−0.284512
$716$	2.53590	0.0947710
$717$	12.6795	0.473524
$718$	−0.679492	−0.0253584
$719$	40.7321	1.51905	0.759525	−	0.650479i	$-0.225432\pi$
$719$	40.7321	1.51905	0.759525	+	0.650479i	$0.225432\pi$
$720$	−4.26795	−0.159057
$721$	−30.9282	−1.15183
$722$	−3.39230	−0.126249
$723$	−6.24871	−0.232392
$724$	11.3923	0.423392
$725$	−17.3205	−0.643268
$726$	6.87564	0.255179
$727$	−15.7128	−0.582756	−0.291378	−	0.956608i	$-0.594114\pi$
$727$	−15.7128	−0.582756	−0.291378	+	0.956608i	$0.594114\pi$
$728$	−6.92820	−0.256776
$729$	−2.21539	−0.0820515
$730$	6.92820	0.256424
$731$	55.1769	2.04079
$732$	−1.26795	−0.0468648
$733$	−49.5692	−1.83088	−0.915440	−	0.402453i	$-0.868158\pi$
$733$	−49.5692	−1.83088	−0.915440	+	0.402453i	$0.868158\pi$
$734$	8.39230	0.309766
$735$	−3.80385	−0.140307
$736$	−1.26795	−0.0467372
$737$	−0.248711	−0.00916140
$738$	9.67949	0.356307
$739$	−1.41154	−0.0519244	−0.0259622	−	0.999663i	$-0.508265\pi$
$739$	−1.41154	−0.0519244	−0.0259622	+	0.999663i	$0.508265\pi$
$740$	0	0
$741$	12.0000	0.440831
$742$	18.9282	0.694876
$743$	43.5167	1.59647	0.798236	−	0.602345i	$-0.205767\pi$
$743$	43.5167	1.59647	0.798236	+	0.602345i	$0.205767\pi$
$744$	−3.46410	−0.127000
$745$	−3.58846	−0.131471
$746$	7.00000	0.256288
$747$	−28.7321	−1.05125
$748$	5.41154	0.197866
$749$	−20.7846	−0.759453
$750$	8.87564	0.324093
$751$	−50.3923	−1.83884	−0.919421	−	0.393276i	$-0.871342\pi$
$751$	−50.3923	−1.83884	−0.919421	+	0.393276i	$0.871342\pi$
$752$	1.26795	0.0462373
$753$	−12.6795	−0.462066
$754$	30.0000	1.09254
$755$	10.7321	0.390579
$756$	8.00000	0.290957
$757$	6.80385	0.247290	0.123645	−	0.992327i	$-0.460542\pi$
$757$	6.80385	0.247290	0.123645	+	0.992327i	$0.460542\pi$
$758$	−6.78461	−0.246428
$759$	1.17691	0.0427193
$760$	8.19615	0.297306
$761$	−32.3205	−1.17162	−0.585809	−	0.810449i	$-0.699223\pi$
$761$	−32.3205	−1.17162	−0.585809	+	0.810449i	$0.699223\pi$
$762$	13.3205	0.482551
$763$	29.3205	1.06147
$764$	−8.19615	−0.296526
$765$	−18.2154	−0.658579
$766$	3.46410	0.125163
$767$	−32.7846	−1.18378
$768$	0.732051	0.0264156
$769$	−34.3923	−1.24022	−0.620109	−	0.784516i	$-0.712912\pi$
$769$	−34.3923	−1.24022	−0.620109	+	0.784516i	$0.712912\pi$
$770$	4.39230	0.158288
$771$	12.5885	0.453362
$772$	0.803848	0.0289311
$773$	20.0718	0.721932	0.360966	−	0.932579i	$-0.382447\pi$
$773$	20.0718	0.721932	0.360966	+	0.932579i	$0.382447\pi$
$774$	31.8564	1.14505
$775$	−9.46410	−0.339961
$776$	−4.26795	−0.153210
$777$	0	0
$778$	25.9808	0.931455
$779$	−18.5885	−0.666001
$780$	−4.39230	−0.157270
$781$	−4.39230	−0.157169
$782$	−5.41154	−0.193516
$783$	−34.6410	−1.23797
$784$	−3.00000	−0.107143
$785$	1.73205	0.0618195
$786$	14.7846	0.527350
$787$	21.1769	0.754875	0.377438	−	0.926035i	$-0.376805\pi$
$787$	21.1769	0.754875	0.377438	+	0.926035i	$0.376805\pi$
$788$	−0.464102	−0.0165329
$789$	−10.6410	−0.378830
$790$	−28.9808	−1.03109
$791$	6.92820	0.246339
$792$	3.12436	0.111019
$793$	6.00000	0.213066
$794$	−23.0000	−0.816239
$795$	12.0000	0.425596
$796$	−10.3923	−0.368345
$797$	32.7846	1.16129	0.580645	−	0.814157i	$-0.302800\pi$
$797$	32.7846	1.16129	0.580645	+	0.814157i	$0.302800\pi$
$798$	−6.92820	−0.245256
$799$	5.41154	0.191447
$800$	2.00000	0.0707107
$801$	−42.3731	−1.49718
$802$	10.3923	0.366965
$803$	−5.07180	−0.178980
$804$	−0.143594	−0.00506415
$805$	−4.39230	−0.154808
$806$	16.3923	0.577394
$807$	12.0000	0.422420
$808$	5.53590	0.194752
$809$	−39.7128	−1.39623	−0.698114	−	0.715987i	$-0.745977\pi$
$809$	−39.7128	−1.39623	−0.698114	+	0.715987i	$0.745977\pi$
$810$	−7.73205	−0.271677
$811$	−0.392305	−0.0137757	−0.00688784	−	0.999976i	$-0.502192\pi$
$811$	−0.392305	−0.0137757	−0.00688784	+	0.999976i	$0.502192\pi$
$812$	−17.3205	−0.607831
$813$	20.9282	0.733984
$814$	0	0
$815$	1.60770	0.0563151
$816$	3.12436	0.109374
$817$	−61.1769	−2.14031
$818$	−34.5167	−1.20685
$819$	−17.0718	−0.596537
$820$	6.80385	0.237601
$821$	9.46410	0.330299	0.165150	−	0.986269i	$-0.447189\pi$
$821$	9.46410	0.330299	0.165150	+	0.986269i	$0.447189\pi$
$822$	−14.1962	−0.495148
$823$	34.1962	1.19200	0.596001	−	0.802983i	$-0.296755\pi$
$823$	34.1962	1.19200	0.596001	+	0.802983i	$0.296755\pi$
$824$	−15.4641	−0.538718
$825$	−1.85641	−0.0646318
$826$	18.9282	0.658596
$827$	−25.8564	−0.899115	−0.449558	−	0.893251i	$-0.648418\pi$
$827$	−25.8564	−0.899115	−0.449558	+	0.893251i	$0.648418\pi$
$828$	−3.12436	−0.108579
$829$	10.3923	0.360940	0.180470	−	0.983581i	$-0.442238\pi$
$829$	10.3923	0.360940	0.180470	+	0.983581i	$0.442238\pi$
$830$	−20.1962	−0.701019
$831$	0.588457	0.0204134
$832$	−3.46410	−0.120096
$833$	−12.8038	−0.443627
$834$	7.75129	0.268405
$835$	−24.0000	−0.830554
$836$	−6.00000	−0.207514
$837$	−18.9282	−0.654254
$838$	31.8564	1.10046
$839$	1.01924	0.0351880	0.0175940	−	0.999845i	$-0.494399\pi$
$839$	1.01924	0.0351880	0.0175940	+	0.999845i	$0.494399\pi$
$840$	2.53590	0.0874968
$841$	46.0000	1.58621
$842$	12.1244	0.417833
$843$	2.62693	0.0904764
$844$	18.3923	0.633089
$845$	−1.73205	−0.0595844
$846$	3.12436	0.107418
$847$	18.7846	0.645447
$848$	9.46410	0.324999
$849$	14.5359	0.498871
$850$	8.53590	0.292779
$851$	0	0
$852$	−2.53590	−0.0868784
$853$	13.7321	0.470176	0.235088	−	0.971974i	$-0.424462\pi$
$853$	13.7321	0.470176	0.235088	+	0.971974i	$0.424462\pi$
$854$	−3.46410	−0.118539
$855$	20.1962	0.690694
$856$	−10.3923	−0.355202
$857$	−14.6603	−0.500785	−0.250392	−	0.968144i	$-0.580560\pi$
$857$	−14.6603	−0.500785	−0.250392	+	0.968144i	$0.580560\pi$
$858$	3.21539	0.109772
$859$	30.0000	1.02359	0.511793	−	0.859109i	$-0.328981\pi$
$859$	30.0000	1.02359	0.511793	+	0.859109i	$0.328981\pi$
$860$	22.3923	0.763571
$861$	−5.75129	−0.196003
$862$	0.339746	0.0115718
$863$	−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
$865$	−21.5885	−0.734030
$866$	25.7846	0.876197
$867$	0.889727	0.0302167
$868$	−9.46410	−0.321233
$869$	21.2154	0.719683
$870$	−10.9808	−0.372283
$871$	0.679492	0.0230237
$872$	14.6603	0.496459
$873$	−10.5167	−0.355935
$874$	6.00000	0.202953
$875$	24.2487	0.819756
$876$	−2.92820	−0.0989348
$877$	−24.1769	−0.816396	−0.408198	−	0.912893i	$-0.633843\pi$
$877$	−24.1769	−0.816396	−0.408198	+	0.912893i	$0.633843\pi$
$878$	−30.2487	−1.02084
$879$	14.1962	0.478824
$880$	2.19615	0.0740323
$881$	−49.3923	−1.66407	−0.832035	−	0.554724i	$-0.812824\pi$
$881$	−49.3923	−1.66407	−0.832035	+	0.554724i	$0.812824\pi$
$882$	−7.39230	−0.248912
$883$	22.0526	0.742128	0.371064	−	0.928607i	$-0.378993\pi$
$883$	22.0526	0.742128	0.371064	+	0.928607i	$0.378993\pi$
$884$	−14.7846	−0.497260
$885$	12.0000	0.403376
$886$	−21.4641	−0.721101
$887$	7.94744	0.266849	0.133424	−	0.991059i	$-0.457403\pi$
$887$	7.94744	0.266849	0.133424	+	0.991059i	$0.457403\pi$
$888$	0	0
$889$	36.3923	1.22056
$890$	−29.7846	−0.998382
$891$	5.66025	0.189626
$892$	5.80385	0.194327
$893$	−6.00000	−0.200782
$894$	1.51666	0.0507247
$895$	4.39230	0.146819
$896$	2.00000	0.0668153
$897$	−3.21539	−0.107359
$898$	27.4641	0.916489
$899$	40.9808	1.36678
$900$	4.92820	0.164273
$901$	40.3923	1.34566
$902$	−4.98076	−0.165841
$903$	−18.9282	−0.629891
$904$	3.46410	0.115214
$905$	19.7321	0.655916
$906$	−4.53590	−0.150695
$907$	−42.5885	−1.41413	−0.707063	−	0.707150i	$-0.749980\pi$
$907$	−42.5885	−1.41413	−0.707063	+	0.707150i	$0.749980\pi$
$908$	−4.73205	−0.157039
$909$	13.6410	0.452444
$910$	−12.0000	−0.397796
$911$	18.3397	0.607623	0.303811	−	0.952732i	$-0.401741\pi$
$911$	18.3397	0.607623	0.303811	+	0.952732i	$0.401741\pi$
$912$	−3.46410	−0.114708
$913$	14.7846	0.489299
$914$	13.9808	0.462443
$915$	−2.19615	−0.0726026
$916$	6.60770	0.218324
$917$	40.3923	1.33387
$918$	17.0718	0.563453
$919$	−3.12436	−0.103063	−0.0515315	−	0.998671i	$-0.516410\pi$
$919$	−3.12436	−0.103063	−0.0515315	+	0.998671i	$0.516410\pi$
$920$	−2.19615	−0.0724050
$921$	16.1051	0.530682
$922$	32.5359	1.07151
$923$	12.0000	0.394985
$924$	−1.85641	−0.0610713
$925$	0	0
$926$	−30.0000	−0.985861
$927$	−38.1051	−1.25154
$928$	−8.66025	−0.284287
$929$	4.60770	0.151174	0.0755868	−	0.997139i	$-0.475917\pi$
$929$	4.60770	0.151174	0.0755868	+	0.997139i	$0.475917\pi$
$930$	−6.00000	−0.196748
$931$	14.1962	0.465260
$932$	−15.0000	−0.491341
$933$	13.1769	0.431393
$934$	9.46410	0.309675
$935$	9.37307	0.306532
$936$	−8.53590	−0.279005
$937$	6.60770	0.215864	0.107932	−	0.994158i	$-0.465577\pi$
$937$	6.60770	0.215864	0.107932	+	0.994158i	$0.465577\pi$
$938$	−0.392305	−0.0128092
$939$	−0.0910347	−0.00297080
$940$	2.19615	0.0716306
$941$	−11.7846	−0.384167	−0.192084	−	0.981379i	$-0.561524\pi$
$941$	−11.7846	−0.384167	−0.192084	+	0.981379i	$0.561524\pi$
$942$	−0.732051	−0.0238515
$943$	4.98076	0.162196
$944$	9.46410	0.308030
$945$	13.8564	0.450749
$946$	−16.3923	−0.532960
$947$	−25.1769	−0.818140	−0.409070	−	0.912503i	$-0.634147\pi$
$947$	−25.1769	−0.818140	−0.409070	+	0.912503i	$0.634147\pi$
$948$	12.2487	0.397820
$949$	13.8564	0.449798
$950$	−9.46410	−0.307056
$951$	9.80385	0.317912
$952$	8.53590	0.276650
$953$	7.85641	0.254494	0.127247	−	0.991871i	$-0.459386\pi$
$953$	7.85641	0.254494	0.127247	+	0.991871i	$0.459386\pi$
$954$	23.3205	0.755029
$955$	−14.1962	−0.459377
$956$	17.3205	0.560185
$957$	8.03848	0.259847
$958$	−2.53590	−0.0819312
$959$	−38.7846	−1.25242
$960$	1.26795	0.0409229
$961$	−8.60770	−0.277668
$962$	0	0
$963$	−25.6077	−0.825196
$964$	−8.53590	−0.274923
$965$	1.39230	0.0448199
$966$	1.85641	0.0597289
$967$	48.0000	1.54358	0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000	1.54358	0.771788	+	0.635880i	$0.219363\pi$
$968$	9.39230	0.301880
$969$	−14.7846	−0.474950
$970$	−7.39230	−0.237353
$971$	−58.9808	−1.89278	−0.946391	−	0.323022i	$-0.895301\pi$
$971$	−58.9808	−1.89278	−0.946391	+	0.323022i	$0.895301\pi$
$972$	15.2679	0.489720
$973$	21.1769	0.678901
$974$	22.0526	0.706610
$975$	5.07180	0.162427
$976$	−1.73205	−0.0554416
$977$	−3.46410	−0.110826	−0.0554132	−	0.998464i	$-0.517648\pi$
$977$	−3.46410	−0.110826	−0.0554132	+	0.998464i	$0.517648\pi$
$978$	−0.679492	−0.0217278
$979$	21.8038	0.696854
$980$	−5.19615	−0.165985
$981$	36.1244	1.15336
$982$	−15.8038	−0.504321
$983$	−20.8756	−0.665830	−0.332915	−	0.942957i	$-0.608032\pi$
$983$	−20.8756	−0.665830	−0.332915	+	0.942957i	$0.608032\pi$
$984$	−2.87564	−0.0916722
$985$	−0.803848	−0.0256127
$986$	−36.9615	−1.17709
$987$	−1.85641	−0.0590901
$988$	16.3923	0.521509
$989$	16.3923	0.521245
$990$	5.41154	0.171990
$991$	−52.6410	−1.67220	−0.836098	−	0.548579i	$-0.815169\pi$
$991$	−52.6410	−1.67220	−0.836098	+	0.548579i	$0.815169\pi$
$992$	−4.73205	−0.150243
$993$	0	0
$994$	−6.92820	−0.219749
$995$	−18.0000	−0.570638
$996$	8.53590	0.270470
$997$	10.3923	0.329128	0.164564	−	0.986366i	$-0.447378\pi$
$997$	10.3923	0.329128	0.164564	+	0.986366i	$0.447378\pi$
$998$	9.80385	0.310335
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.e.1.2		2
37.8	odd	12		74.2.e.b.27.1	yes	4
37.14	odd	12		74.2.e.b.11.1	✓	4
37.36	even	2		2738.2.a.i.1.2		2
111.8	even	12		666.2.s.a.397.2		4
111.14	even	12		666.2.s.a.307.2		4
148.51	even	12		592.2.w.e.529.1		4
148.119	even	12		592.2.w.e.545.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.e.b.11.1	✓	4	37.14	odd	12
74.2.e.b.27.1	yes	4	37.8	odd	12
592.2.w.e.529.1		4	148.51	even	12
592.2.w.e.545.1		4	148.119	even	12
666.2.s.a.307.2		4	111.14	even	12
666.2.s.a.397.2		4	111.8	even	12
2738.2.a.e.1.2		2	1.1	even	1	trivial
2738.2.a.i.1.2		2	37.36	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.732051 q^{3} +1.00000 q^{4} +1.73205 q^{5} -0.732051 q^{6} -2.00000 q^{7} -1.00000 q^{8} -2.46410 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.732051 q^{3} +1.00000 q^{4} +1.73205 q^{5} -0.732051 q^{6} -2.00000 q^{7} -1.00000 q^{8} -2.46410 q^{9} -1.73205 q^{10} +1.26795 q^{11} +0.732051 q^{12} -3.46410 q^{13} +2.00000 q^{14} +1.26795 q^{15} +1.00000 q^{16} +4.26795 q^{17} +2.46410 q^{18} -4.73205 q^{19} +1.73205 q^{20} -1.46410 q^{21} -1.26795 q^{22} +1.26795 q^{23} -0.732051 q^{24} -2.00000 q^{25} +3.46410 q^{26} -4.00000 q^{27} -2.00000 q^{28} +8.66025 q^{29} -1.26795 q^{30} +4.73205 q^{31} -1.00000 q^{32} +0.928203 q^{33} -4.26795 q^{34} -3.46410 q^{35} -2.46410 q^{36} +4.73205 q^{38} -2.53590 q^{39} -1.73205 q^{40} +3.92820 q^{41} +1.46410 q^{42} +12.9282 q^{43} +1.26795 q^{44} -4.26795 q^{45} -1.26795 q^{46} +1.26795 q^{47} +0.732051 q^{48} -3.00000 q^{49} +2.00000 q^{50} +3.12436 q^{51} -3.46410 q^{52} +9.46410 q^{53} +4.00000 q^{54} +2.19615 q^{55} +2.00000 q^{56} -3.46410 q^{57} -8.66025 q^{58} +9.46410 q^{59} +1.26795 q^{60} -1.73205 q^{61} -4.73205 q^{62} +4.92820 q^{63} +1.00000 q^{64} -6.00000 q^{65} -0.928203 q^{66} -0.196152 q^{67} +4.26795 q^{68} +0.928203 q^{69} +3.46410 q^{70} -3.46410 q^{71} +2.46410 q^{72} -4.00000 q^{73} -1.46410 q^{75} -4.73205 q^{76} -2.53590 q^{77} +2.53590 q^{78} +16.7321 q^{79} +1.73205 q^{80} +4.46410 q^{81} -3.92820 q^{82} +11.6603 q^{83} -1.46410 q^{84} +7.39230 q^{85} -12.9282 q^{86} +6.33975 q^{87} -1.26795 q^{88} +17.1962 q^{89} +4.26795 q^{90} +6.92820 q^{91} +1.26795 q^{92} +3.46410 q^{93} -1.26795 q^{94} -8.19615 q^{95} -0.732051 q^{96} +4.26795 q^{97} +3.00000 q^{98} -3.12436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9} + 6 q^{11} - 2 q^{12} + 4 q^{14} + 6 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} - 6 q^{19} + 4 q^{21} - 6 q^{22} + 6 q^{23} + 2 q^{24} - 4 q^{25} - 8 q^{27} - 4 q^{28} - 6 q^{30} + 6 q^{31} - 2 q^{32} - 12 q^{33} - 12 q^{34} + 2 q^{36} + 6 q^{38} - 12 q^{39} - 6 q^{41} - 4 q^{42} + 12 q^{43} + 6 q^{44} - 12 q^{45} - 6 q^{46} + 6 q^{47} - 2 q^{48} - 6 q^{49} + 4 q^{50} - 18 q^{51} + 12 q^{53} + 8 q^{54} - 6 q^{55} + 4 q^{56} + 12 q^{59} + 6 q^{60} - 6 q^{62} - 4 q^{63} + 2 q^{64} - 12 q^{65} + 12 q^{66} + 10 q^{67} + 12 q^{68} - 12 q^{69} - 2 q^{72} - 8 q^{73} + 4 q^{75} - 6 q^{76} - 12 q^{77} + 12 q^{78} + 30 q^{79} + 2 q^{81} + 6 q^{82} + 6 q^{83} + 4 q^{84} - 6 q^{85} - 12 q^{86} + 30 q^{87} - 6 q^{88} + 24 q^{89} + 12 q^{90} + 6 q^{92} - 6 q^{94} - 6 q^{95} + 2 q^{96} + 12 q^{97} + 6 q^{98} + 18 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9 + 6 * q^11 - 2 * q^12 + 4 * q^14 + 6 * q^15 + 2 * q^16 + 12 * q^17 - 2 * q^18 - 6 * q^19 + 4 * q^21 - 6 * q^22 + 6 * q^23 + 2 * q^24 - 4 * q^25 - 8 * q^27 - 4 * q^28 - 6 * q^30 + 6 * q^31 - 2 * q^32 - 12 * q^33 - 12 * q^34 + 2 * q^36 + 6 * q^38 - 12 * q^39 - 6 * q^41 - 4 * q^42 + 12 * q^43 + 6 * q^44 - 12 * q^45 - 6 * q^46 + 6 * q^47 - 2 * q^48 - 6 * q^49 + 4 * q^50 - 18 * q^51 + 12 * q^53 + 8 * q^54 - 6 * q^55 + 4 * q^56 + 12 * q^59 + 6 * q^60 - 6 * q^62 - 4 * q^63 + 2 * q^64 - 12 * q^65 + 12 * q^66 + 10 * q^67 + 12 * q^68 - 12 * q^69 - 2 * q^72 - 8 * q^73 + 4 * q^75 - 6 * q^76 - 12 * q^77 + 12 * q^78 + 30 * q^79 + 2 * q^81 + 6 * q^82 + 6 * q^83 + 4 * q^84 - 6 * q^85 - 12 * q^86 + 30 * q^87 - 6 * q^88 + 24 * q^89 + 12 * q^90 + 6 * q^92 - 6 * q^94 - 6 * q^95 + 2 * q^96 + 12 * q^97 + 6 * q^98 + 18 * q^99

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