LMFDB - Embedded newform 2738.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} -2.73205 q^{6} -2.00000 q^{7} +1.00000 q^{8} +4.46410 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} -2.73205 q^{6} -2.00000 q^{7} +1.00000 q^{8} +4.46410 q^{9} +1.73205 q^{10} +4.73205 q^{11} -2.73205 q^{12} -3.46410 q^{13} -2.00000 q^{14} -4.73205 q^{15} +1.00000 q^{16} -7.73205 q^{17} +4.46410 q^{18} +1.26795 q^{19} +1.73205 q^{20} +5.46410 q^{21} +4.73205 q^{22} -4.73205 q^{23} -2.73205 q^{24} -2.00000 q^{25} -3.46410 q^{26} -4.00000 q^{27} -2.00000 q^{28} +8.66025 q^{29} -4.73205 q^{30} -1.26795 q^{31} +1.00000 q^{32} -12.9282 q^{33} -7.73205 q^{34} -3.46410 q^{35} +4.46410 q^{36} +1.26795 q^{38} +9.46410 q^{39} +1.73205 q^{40} -9.92820 q^{41} +5.46410 q^{42} +0.928203 q^{43} +4.73205 q^{44} +7.73205 q^{45} -4.73205 q^{46} +4.73205 q^{47} -2.73205 q^{48} -3.00000 q^{49} -2.00000 q^{50} +21.1244 q^{51} -3.46410 q^{52} +2.53590 q^{53} -4.00000 q^{54} +8.19615 q^{55} -2.00000 q^{56} -3.46410 q^{57} +8.66025 q^{58} -2.53590 q^{59} -4.73205 q^{60} -1.73205 q^{61} -1.26795 q^{62} -8.92820 q^{63} +1.00000 q^{64} -6.00000 q^{65} -12.9282 q^{66} +10.1962 q^{67} -7.73205 q^{68} +12.9282 q^{69} -3.46410 q^{70} +3.46410 q^{71} +4.46410 q^{72} -4.00000 q^{73} +5.46410 q^{75} +1.26795 q^{76} -9.46410 q^{77} +9.46410 q^{78} -13.2679 q^{79} +1.73205 q^{80} -2.46410 q^{81} -9.92820 q^{82} -5.66025 q^{83} +5.46410 q^{84} -13.3923 q^{85} +0.928203 q^{86} -23.6603 q^{87} +4.73205 q^{88} -6.80385 q^{89} +7.73205 q^{90} +6.92820 q^{91} -4.73205 q^{92} +3.46410 q^{93} +4.73205 q^{94} +2.19615 q^{95} -2.73205 q^{96} -7.73205 q^{97} -3.00000 q^{98} +21.1244 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.73205	−1.57735	−0.788675	−	0.614810i	$-0.789233\pi$
$3$	−2.73205	−1.57735	−0.788675	+	0.614810i	$0.789233\pi$
$4$	1.00000	0.500000
$5$	1.73205	0.774597	0.387298	−	0.921954i	$-0.373408\pi$
$5$	1.73205	0.774597	0.387298	+	0.921954i	$0.373408\pi$
$6$	−2.73205	−1.11536
$7$	−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
$9$	4.46410	1.48803
$10$	1.73205	0.547723
$11$	4.73205	1.42677	0.713384	−	0.700774i	$-0.247162\pi$
$11$	4.73205	1.42677	0.713384	+	0.700774i	$0.247162\pi$
$12$	−2.73205	−0.788675
$13$	−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
$15$	−4.73205	−1.22181
$16$	1.00000	0.250000
$17$	−7.73205	−1.87530	−0.937649	−	0.347584i	$-0.887002\pi$
$17$	−7.73205	−1.87530	−0.937649	+	0.347584i	$0.887002\pi$
$18$	4.46410	1.05220
$19$	1.26795	0.290887	0.145444	−	0.989367i	$-0.453539\pi$
$19$	1.26795	0.290887	0.145444	+	0.989367i	$0.453539\pi$
$20$	1.73205	0.387298
$21$	5.46410	1.19236
$22$	4.73205	1.00888
$23$	−4.73205	−0.986701	−0.493350	−	0.869831i	$-0.664228\pi$
$23$	−4.73205	−0.986701	−0.493350	+	0.869831i	$0.664228\pi$
$24$	−2.73205	−0.557678
$25$	−2.00000	−0.400000
$26$	−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	$0.202656\pi$
$30$	−4.73205	−0.863950
$31$	−1.26795	−0.227730	−0.113865	−	0.993496i	$-0.536323\pi$
$31$	−1.26795	−0.227730	−0.113865	+	0.993496i	$0.536323\pi$
$32$	1.00000	0.176777
$33$	−12.9282	−2.25051
$34$	−7.73205	−1.32604
$35$	−3.46410	−0.585540
$36$	4.46410	0.744017
$37$	0	0
$37$	0	0
$38$	1.26795	0.205689
$39$	9.46410	1.51547
$40$	1.73205	0.273861
$41$	−9.92820	−1.55052	−0.775262	−	0.631639i	$-0.782382\pi$
$41$	−9.92820	−1.55052	−0.775262	+	0.631639i	$0.782382\pi$
$42$	5.46410	0.843129
$43$	0.928203	0.141550	0.0707748	−	0.997492i	$-0.477453\pi$
$43$	0.928203	0.141550	0.0707748	+	0.997492i	$0.477453\pi$
$44$	4.73205	0.713384
$45$	7.73205	1.15263
$46$	−4.73205	−0.697703
$47$	4.73205	0.690241	0.345120	−	0.938558i	$-0.387838\pi$
$47$	4.73205	0.690241	0.345120	+	0.938558i	$0.387838\pi$
$48$	−2.73205	−0.394338
$49$	−3.00000	−0.428571
$50$	−2.00000	−0.282843
$51$	21.1244	2.95800
$52$	−3.46410	−0.480384
$53$	2.53590	0.348332	0.174166	−	0.984716i	$-0.444277\pi$
$53$	2.53590	0.348332	0.174166	+	0.984716i	$0.444277\pi$
$54$	−4.00000	−0.544331
$55$	8.19615	1.10517
$56$	−2.00000	−0.267261
$57$	−3.46410	−0.458831
$58$	8.66025	1.13715
$59$	−2.53590	−0.330146	−0.165073	−	0.986281i	$-0.552786\pi$
$59$	−2.53590	−0.330146	−0.165073	+	0.986281i	$0.552786\pi$
$60$	−4.73205	−0.610905
$61$	−1.73205	−0.221766	−0.110883	−	0.993833i	$-0.535368\pi$
$61$	−1.73205	−0.221766	−0.110883	+	0.993833i	$0.535368\pi$
$62$	−1.26795	−0.161030
$63$	−8.92820	−1.12485
$64$	1.00000	0.125000
$65$	−6.00000	−0.744208
$66$	−12.9282	−1.59135
$67$	10.1962	1.24566	0.622829	−	0.782358i	$-0.285983\pi$
$67$	10.1962	1.24566	0.622829	+	0.782358i	$0.285983\pi$
$68$	−7.73205	−0.937649
$69$	12.9282	1.55637
$70$	−3.46410	−0.414039
$71$	3.46410	0.411113	0.205557	−	0.978645i	$-0.434100\pi$
$71$	3.46410	0.411113	0.205557	+	0.978645i	$0.434100\pi$
$72$	4.46410	0.526099
$73$	−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
$75$	5.46410	0.630940
$76$	1.26795	0.145444
$77$	−9.46410	−1.07853
$78$	9.46410	1.07160
$79$	−13.2679	−1.49276	−0.746380	−	0.665520i	$-0.768210\pi$
$79$	−13.2679	−1.49276	−0.746380	+	0.665520i	$0.768210\pi$
$80$	1.73205	0.193649
$81$	−2.46410	−0.273789
$82$	−9.92820	−1.09639
$83$	−5.66025	−0.621294	−0.310647	−	0.950525i	$-0.600546\pi$
$83$	−5.66025	−0.621294	−0.310647	+	0.950525i	$0.600546\pi$
$84$	5.46410	0.596182
$85$	−13.3923	−1.45260
$86$	0.928203	0.100091
$87$	−23.6603	−2.53665
$88$	4.73205	0.504438
$89$	−6.80385	−0.721206	−0.360603	−	0.932719i	$-0.617429\pi$
$89$	−6.80385	−0.721206	−0.360603	+	0.932719i	$0.617429\pi$
$90$	7.73205	0.815030
$91$	6.92820	0.726273
$92$	−4.73205	−0.493350
$93$	3.46410	0.359211
$94$	4.73205	0.488074
$95$	2.19615	0.225320
$96$	−2.73205	−0.278839
$97$	−7.73205	−0.785071	−0.392535	−	0.919737i	$-0.628402\pi$
$97$	−7.73205	−0.785071	−0.392535	+	0.919737i	$0.628402\pi$
$98$	−3.00000	−0.303046
$99$	21.1244	2.12308
$100$	−2.00000	−0.200000
$101$	−12.4641	−1.24022	−0.620112	−	0.784513i	$-0.712913\pi$
$101$	−12.4641	−1.24022	−0.620112	+	0.784513i	$0.712913\pi$
$102$	21.1244	2.09162
$103$	−8.53590	−0.841067	−0.420534	−	0.907277i	$-0.638157\pi$
$103$	−8.53590	−0.841067	−0.420534	+	0.907277i	$0.638157\pi$
$104$	−3.46410	−0.339683
$105$	9.46410	0.923602
$106$	2.53590	0.246308
$107$	−10.3923	−1.00466	−0.502331	−	0.864675i	$-0.667524\pi$
$107$	−10.3923	−1.00466	−0.502331	+	0.864675i	$0.667524\pi$
$108$	−4.00000	−0.384900
$109$	−2.66025	−0.254806	−0.127403	−	0.991851i	$-0.540664\pi$
$109$	−2.66025	−0.254806	−0.127403	+	0.991851i	$0.540664\pi$
$110$	8.19615	0.781472
$111$	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
$115$	−8.19615	−0.764295
$116$	8.66025	0.804084
$117$	−15.4641	−1.42966
$118$	−2.53590	−0.233448
$119$	15.4641	1.41759
$120$	−4.73205	−0.431975
$121$	11.3923	1.03566
$122$	−1.73205	−0.156813
$123$	27.1244	2.44572
$124$	−1.26795	−0.113865
$125$	−12.1244	−1.08444
$126$	−8.92820	−0.795388
$127$	−7.80385	−0.692479	−0.346240	−	0.938146i	$-0.612542\pi$
$127$	−7.80385	−0.692479	−0.346240	+	0.938146i	$0.612542\pi$
$128$	1.00000	0.0883883
$129$	−2.53590	−0.223273
$130$	−6.00000	−0.526235
$131$	9.80385	0.856566	0.428283	−	0.903645i	$-0.359119\pi$
$131$	9.80385	0.856566	0.428283	+	0.903645i	$0.359119\pi$
$132$	−12.9282	−1.12526
$133$	−2.53590	−0.219890
$134$	10.1962	0.880813
$135$	−6.92820	−0.596285
$136$	−7.73205	−0.663018
$137$	−1.39230	−0.118953	−0.0594763	−	0.998230i	$-0.518943\pi$
$137$	−1.39230	−0.118953	−0.0594763	+	0.998230i	$0.518943\pi$
$138$	12.9282	1.10052
$139$	20.5885	1.74629	0.873145	−	0.487460i	$-0.162077\pi$
$139$	20.5885	1.74629	0.873145	+	0.487460i	$0.162077\pi$
$140$	−3.46410	−0.292770
$141$	−12.9282	−1.08875
$142$	3.46410	0.290701
$143$	−16.3923	−1.37079
$144$	4.46410	0.372008
$145$	15.0000	1.24568
$146$	−4.00000	−0.331042
$147$	8.19615	0.676007
$148$	0	0
$149$	−15.9282	−1.30489	−0.652445	−	0.757836i	$-0.726257\pi$
$149$	−15.9282	−1.30489	−0.652445	+	0.757836i	$0.726257\pi$
$150$	5.46410	0.446142
$151$	−4.19615	−0.341478	−0.170739	−	0.985316i	$-0.554616\pi$
$151$	−4.19615	−0.341478	−0.170739	+	0.985316i	$0.554616\pi$
$152$	1.26795	0.102844
$153$	−34.5167	−2.79051
$154$	−9.46410	−0.762639
$155$	−2.19615	−0.176399
$156$	9.46410	0.757735
$157$	1.00000	0.0798087	0.0399043	−	0.999204i	$-0.487295\pi$
$157$	1.00000	0.0798087	0.0399043	+	0.999204i	$0.487295\pi$
$158$	−13.2679	−1.05554
$159$	−6.92820	−0.549442
$160$	1.73205	0.136931
$161$	9.46410	0.745876
$162$	−2.46410	−0.193598
$163$	12.9282	1.01262	0.506308	−	0.862353i	$-0.331010\pi$
$163$	12.9282	1.01262	0.506308	+	0.862353i	$0.331010\pi$
$164$	−9.92820	−0.775262
$165$	−22.3923	−1.74324
$166$	−5.66025	−0.439321
$167$	−13.8564	−1.07224	−0.536120	−	0.844141i	$-0.680111\pi$
$167$	−13.8564	−1.07224	−0.536120	+	0.844141i	$0.680111\pi$
$168$	5.46410	0.421565
$169$	−1.00000	−0.0769231
$170$	−13.3923	−1.02714
$171$	5.66025	0.432850
$172$	0.928203	0.0707748
$173$	−5.53590	−0.420887	−0.210443	−	0.977606i	$-0.567491\pi$
$173$	−5.53590	−0.420887	−0.210443	+	0.977606i	$0.567491\pi$
$174$	−23.6603	−1.79368
$175$	4.00000	0.302372
$176$	4.73205	0.356692
$177$	6.92820	0.520756
$178$	−6.80385	−0.509970
$179$	−9.46410	−0.707380	−0.353690	−	0.935363i	$-0.615073\pi$
$179$	−9.46410	−0.707380	−0.353690	+	0.935363i	$0.615073\pi$
$180$	7.73205	0.576313
$181$	−9.39230	−0.698125	−0.349062	−	0.937100i	$-0.613500\pi$
$181$	−9.39230	−0.698125	−0.349062	+	0.937100i	$0.613500\pi$
$182$	6.92820	0.513553
$183$	4.73205	0.349803
$184$	−4.73205	−0.348851
$185$	0	0
$186$	3.46410	0.254000
$187$	−36.5885	−2.67561
$188$	4.73205	0.345120
$189$	8.00000	0.581914
$190$	2.19615	0.159326
$191$	−2.19615	−0.158908	−0.0794540	−	0.996839i	$-0.525318\pi$
$191$	−2.19615	−0.158908	−0.0794540	+	0.996839i	$0.525318\pi$
$192$	−2.73205	−0.197169
$193$	−11.1962	−0.805917	−0.402958	−	0.915218i	$-0.632018\pi$
$193$	−11.1962	−0.805917	−0.402958	+	0.915218i	$0.632018\pi$
$194$	−7.73205	−0.555129
$195$	16.3923	1.17388
$196$	−3.00000	−0.214286
$197$	6.46410	0.460548	0.230274	−	0.973126i	$-0.426038\pi$
$197$	6.46410	0.460548	0.230274	+	0.973126i	$0.426038\pi$
$198$	21.1244	1.50124
$199$	−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
$201$	−27.8564	−1.96484
$202$	−12.4641	−0.876971
$203$	−17.3205	−1.21566
$204$	21.1244	1.47900
$205$	−17.1962	−1.20103
$206$	−8.53590	−0.594724
$207$	−21.1244	−1.46824
$208$	−3.46410	−0.240192
$209$	6.00000	0.415029
$210$	9.46410	0.653085
$211$	−2.39230	−0.164693	−0.0823465	−	0.996604i	$-0.526241\pi$
$211$	−2.39230	−0.164693	−0.0823465	+	0.996604i	$0.526241\pi$
$212$	2.53590	0.174166
$213$	−9.46410	−0.648470
$214$	−10.3923	−0.710403
$215$	1.60770	0.109644
$216$	−4.00000	−0.272166
$217$	2.53590	0.172148
$218$	−2.66025	−0.180175
$219$	10.9282	0.738460
$220$	8.19615	0.552584
$221$	26.7846	1.80173
$222$	0	0
$223$	16.1962	1.08457	0.542287	−	0.840193i	$-0.317558\pi$
$223$	16.1962	1.08457	0.542287	+	0.840193i	$0.317558\pi$
$224$	−2.00000	−0.133631
$225$	−8.92820	−0.595214
$226$	−3.46410	−0.230429
$227$	1.26795	0.0841567	0.0420784	−	0.999114i	$-0.486602\pi$
$227$	1.26795	0.0841567	0.0420784	+	0.999114i	$0.486602\pi$
$228$	−3.46410	−0.229416
$229$	27.3923	1.81013	0.905067	−	0.425269i	$-0.139820\pi$
$229$	27.3923	1.81013	0.905067	+	0.425269i	$0.139820\pi$
$230$	−8.19615	−0.540438
$231$	25.8564	1.70123
$232$	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	$0.663493\pi$
$234$	−15.4641	−1.01092
$235$	8.19615	0.534658
$236$	−2.53590	−0.165073
$237$	36.2487	2.35461
$238$	15.4641	1.00239
$239$	17.3205	1.12037	0.560185	−	0.828367i	$-0.310730\pi$
$239$	17.3205	1.12037	0.560185	+	0.828367i	$0.310730\pi$
$240$	−4.73205	−0.305453
$241$	15.4641	0.996130	0.498065	−	0.867140i	$-0.334044\pi$
$241$	15.4641	0.996130	0.498065	+	0.867140i	$0.334044\pi$
$242$	11.3923	0.732325
$243$	18.7321	1.20166
$244$	−1.73205	−0.110883
$245$	−5.19615	−0.331970
$246$	27.1244	1.72939
$247$	−4.39230	−0.279476
$248$	−1.26795	−0.0805149
$249$	15.4641	0.979998
$250$	−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	$0.684090\pi$
$252$	−8.92820	−0.562424
$253$	−22.3923	−1.40779
$254$	−7.80385	−0.489657
$255$	36.5885	2.29126
$256$	1.00000	0.0625000
$257$	−6.80385	−0.424412	−0.212206	−	0.977225i	$-0.568065\pi$
$257$	−6.80385	−0.424412	−0.212206	+	0.977225i	$0.568065\pi$
$258$	−2.53590	−0.157878
$259$	0	0
$260$	−6.00000	−0.372104
$261$	38.6603	2.39301
$262$	9.80385	0.605684
$263$	−21.4641	−1.32353	−0.661767	−	0.749710i	$-0.730193\pi$
$263$	−21.4641	−1.32353	−0.661767	+	0.749710i	$0.730193\pi$
$264$	−12.9282	−0.795676
$265$	4.39230	0.269817
$266$	−2.53590	−0.155486
$267$	18.5885	1.13760
$268$	10.1962	0.622829
$269$	−4.39230	−0.267804	−0.133902	−	0.990995i	$-0.542751\pi$
$269$	−4.39230	−0.267804	−0.133902	+	0.990995i	$0.542751\pi$
$270$	−6.92820	−0.421637
$271$	−2.58846	−0.157238	−0.0786188	−	0.996905i	$-0.525051\pi$
$271$	−2.58846	−0.157238	−0.0786188	+	0.996905i	$0.525051\pi$
$272$	−7.73205	−0.468824
$273$	−18.9282	−1.14559
$274$	−1.39230	−0.0841122
$275$	−9.46410	−0.570707
$276$	12.9282	0.778186
$277$	−11.1962	−0.672712	−0.336356	−	0.941735i	$-0.609194\pi$
$277$	−11.1962	−0.672712	−0.336356	+	0.941735i	$0.609194\pi$
$278$	20.5885	1.23481
$279$	−5.66025	−0.338871
$280$	−3.46410	−0.207020
$281$	27.5885	1.64579	0.822895	−	0.568194i	$-0.192358\pi$
$281$	27.5885	1.64579	0.822895	+	0.568194i	$0.192358\pi$
$282$	−12.9282	−0.769863
$283$	7.85641	0.467015	0.233507	−	0.972355i	$-0.424980\pi$
$283$	7.85641	0.467015	0.233507	+	0.972355i	$0.424980\pi$
$284$	3.46410	0.205557
$285$	−6.00000	−0.355409
$286$	−16.3923	−0.969297
$287$	19.8564	1.17209
$288$	4.46410	0.263050
$289$	42.7846	2.51674
$290$	15.0000	0.880830
$291$	21.1244	1.23833
$292$	−4.00000	−0.234082
$293$	−1.39230	−0.0813393	−0.0406697	−	0.999173i	$-0.512949\pi$
$293$	−1.39230	−0.0813393	−0.0406697	+	0.999173i	$0.512949\pi$
$294$	8.19615	0.478009
$295$	−4.39230	−0.255730
$296$	0	0
$297$	−18.9282	−1.09833
$298$	−15.9282	−0.922696
$299$	16.3923	0.947991
$300$	5.46410	0.315470
$301$	−1.85641	−0.107001
$302$	−4.19615	−0.241461
$303$	34.0526	1.95627
$304$	1.26795	0.0727219
$305$	−3.00000	−0.171780
$306$	−34.5167	−1.97319
$307$	22.0000	1.25561	0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000	1.25561	0.627803	+	0.778372i	$0.283954\pi$
$308$	−9.46410	−0.539267
$309$	23.3205	1.32666
$310$	−2.19615	−0.124733
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	9.46410	0.535799
$313$	−24.1244	−1.36359	−0.681795	−	0.731544i	$-0.738800\pi$
$313$	−24.1244	−1.36359	−0.681795	+	0.731544i	$0.738800\pi$
$314$	1.00000	0.0564333
$315$	−15.4641	−0.871303
$316$	−13.2679	−0.746380
$317$	−7.39230	−0.415193	−0.207597	−	0.978215i	$-0.566564\pi$
$317$	−7.39230	−0.415193	−0.207597	+	0.978215i	$0.566564\pi$
$318$	−6.92820	−0.388514
$319$	40.9808	2.29448
$320$	1.73205	0.0968246
$321$	28.3923	1.58470
$322$	9.46410	0.527414
$323$	−9.80385	−0.545501
$324$	−2.46410	−0.136895
$325$	6.92820	0.384308
$326$	12.9282	0.716027
$327$	7.26795	0.401919
$328$	−9.92820	−0.548193
$329$	−9.46410	−0.521773
$330$	−22.3923	−1.23266
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	−5.66025	−0.310647
$333$	0	0
$334$	−13.8564	−0.758189
$335$	17.6603	0.964883
$336$	5.46410	0.298091
$337$	32.1769	1.75279	0.876394	−	0.481595i	$-0.159942\pi$
$337$	32.1769	1.75279	0.876394	+	0.481595i	$0.159942\pi$
$338$	−1.00000	−0.0543928
$339$	9.46410	0.514019
$340$	−13.3923	−0.726300
$341$	−6.00000	−0.324918
$342$	5.66025	0.306071
$343$	20.0000	1.07990
$344$	0.928203	0.0500454
$345$	22.3923	1.20556
$346$	−5.53590	−0.297612
$347$	9.12436	0.489821	0.244911	−	0.969546i	$-0.421241\pi$
$347$	9.12436	0.489821	0.244911	+	0.969546i	$0.421241\pi$
$348$	−23.6603	−1.26832
$349$	11.3923	0.609816	0.304908	−	0.952382i	$-0.401374\pi$
$349$	11.3923	0.609816	0.304908	+	0.952382i	$0.401374\pi$
$350$	4.00000	0.213809
$351$	13.8564	0.739600
$352$	4.73205	0.252219
$353$	−19.7321	−1.05023	−0.525116	−	0.851031i	$-0.675978\pi$
$353$	−19.7321	−1.05023	−0.525116	+	0.851031i	$0.675978\pi$
$354$	6.92820	0.368230
$355$	6.00000	0.318447
$356$	−6.80385	−0.360603
$357$	−42.2487	−2.23604
$358$	−9.46410	−0.500193
$359$	35.3205	1.86415	0.932073	−	0.362272i	$-0.117999\pi$
$359$	35.3205	1.86415	0.932073	+	0.362272i	$0.117999\pi$
$360$	7.73205	0.407515
$361$	−17.3923	−0.915384
$362$	−9.39230	−0.493649
$363$	−31.1244	−1.63361
$364$	6.92820	0.363137
$365$	−6.92820	−0.362639
$366$	4.73205	0.247348
$367$	12.3923	0.646873	0.323437	−	0.946250i	$-0.395162\pi$
$367$	12.3923	0.646873	0.323437	+	0.946250i	$0.395162\pi$
$368$	−4.73205	−0.246675
$369$	−44.3205	−2.30723
$370$	0	0
$371$	−5.07180	−0.263315
$372$	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	$0.558006\pi$
$374$	−36.5885	−1.89194
$375$	33.1244	1.71053
$376$	4.73205	0.244037
$377$	−30.0000	−1.54508
$378$	8.00000	0.411476
$379$	−34.7846	−1.78677	−0.893383	−	0.449297i	$-0.851675\pi$
$379$	−34.7846	−1.78677	−0.893383	+	0.449297i	$0.851675\pi$
$380$	2.19615	0.112660
$381$	21.3205	1.09228
$382$	−2.19615	−0.112365
$383$	−3.46410	−0.177007	−0.0885037	−	0.996076i	$-0.528208\pi$
$383$	−3.46410	−0.177007	−0.0885037	+	0.996076i	$0.528208\pi$
$384$	−2.73205	−0.139419
$385$	−16.3923	−0.835429
$386$	−11.1962	−0.569869
$387$	4.14359	0.210631
$388$	−7.73205	−0.392535
$389$	−25.9808	−1.31728	−0.658638	−	0.752460i	$-0.728867\pi$
$389$	−25.9808	−1.31728	−0.658638	+	0.752460i	$0.728867\pi$
$390$	16.3923	0.830057
$391$	36.5885	1.85036
$392$	−3.00000	−0.151523
$393$	−26.7846	−1.35110
$394$	6.46410	0.325657
$395$	−22.9808	−1.15629
$396$	21.1244	1.06154
$397$	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	$0.583552\pi$
$402$	−27.8564	−1.38935
$403$	4.39230	0.218796
$404$	−12.4641	−0.620112
$405$	−4.26795	−0.212076
$406$	−17.3205	−0.859602
$407$	0	0
$408$	21.1244	1.04581
$409$	10.5167	0.520015	0.260008	−	0.965607i	$-0.416275\pi$
$409$	10.5167	0.520015	0.260008	+	0.965607i	$0.416275\pi$
$410$	−17.1962	−0.849257
$411$	3.80385	0.187630
$412$	−8.53590	−0.420534
$413$	5.07180	0.249567
$414$	−21.1244	−1.03821
$415$	−9.80385	−0.481252
$416$	−3.46410	−0.169842
$417$	−56.2487	−2.75451
$418$	6.00000	0.293470
$419$	−4.14359	−0.202428	−0.101214	−	0.994865i	$-0.532273\pi$
$419$	−4.14359	−0.202428	−0.101214	+	0.994865i	$0.532273\pi$
$420$	9.46410	0.461801
$421$	−12.1244	−0.590905	−0.295452	−	0.955357i	$-0.595470\pi$
$421$	−12.1244	−0.590905	−0.295452	+	0.955357i	$0.595470\pi$
$422$	−2.39230	−0.116456
$423$	21.1244	1.02710
$424$	2.53590	0.123154
$425$	15.4641	0.750119
$426$	−9.46410	−0.458537
$427$	3.46410	0.167640
$428$	−10.3923	−0.502331
$429$	44.7846	2.16222
$430$	1.60770	0.0775299
$431$	17.6603	0.850665	0.425332	−	0.905037i	$-0.360157\pi$
$431$	17.6603	0.850665	0.425332	+	0.905037i	$0.360157\pi$
$432$	−4.00000	−0.192450
$433$	15.7846	0.758560	0.379280	−	0.925282i	$-0.376172\pi$
$433$	15.7846	0.758560	0.379280	+	0.925282i	$0.376172\pi$
$434$	2.53590	0.121727
$435$	−40.9808	−1.96488
$436$	−2.66025	−0.127403
$437$	−6.00000	−0.287019
$438$	10.9282	0.522170
$439$	18.2487	0.870963	0.435482	−	0.900198i	$-0.356578\pi$
$439$	18.2487	0.870963	0.435482	+	0.900198i	$0.356578\pi$
$440$	8.19615	0.390736
$441$	−13.3923	−0.637729
$442$	26.7846	1.27401
$443$	14.5359	0.690621	0.345311	−	0.938488i	$-0.387774\pi$
$443$	14.5359	0.690621	0.345311	+	0.938488i	$0.387774\pi$
$444$	0	0
$445$	−11.7846	−0.558644
$446$	16.1962	0.766910
$447$	43.5167	2.05827
$448$	−2.00000	−0.0944911
$449$	20.5359	0.969149	0.484574	−	0.874750i	$-0.338974\pi$
$449$	20.5359	0.969149	0.484574	+	0.874750i	$0.338974\pi$
$450$	−8.92820	−0.420880
$451$	−46.9808	−2.21224
$452$	−3.46410	−0.162938
$453$	11.4641	0.538630
$454$	1.26795	0.0595078
$455$	12.0000	0.562569
$456$	−3.46410	−0.162221
$457$	−37.9808	−1.77667	−0.888333	−	0.459201i	$-0.848136\pi$
$457$	−37.9808	−1.77667	−0.888333	+	0.459201i	$0.848136\pi$
$458$	27.3923	1.27996
$459$	30.9282	1.44360
$460$	−8.19615	−0.382148
$461$	39.4641	1.83803	0.919013	−	0.394227i	$-0.128988\pi$
$461$	39.4641	1.83803	0.919013	+	0.394227i	$0.128988\pi$
$462$	25.8564	1.20295
$463$	−30.0000	−1.39422	−0.697109	−	0.716965i	$-0.745531\pi$
$463$	−30.0000	−1.39422	−0.697109	+	0.716965i	$0.745531\pi$
$464$	8.66025	0.402042
$465$	6.00000	0.278243
$466$	−15.0000	−0.694862
$467$	2.53590	0.117347	0.0586737	−	0.998277i	$-0.481313\pi$
$467$	2.53590	0.117347	0.0586737	+	0.998277i	$0.481313\pi$
$468$	−15.4641	−0.714828
$469$	−20.3923	−0.941629
$470$	8.19615	0.378060
$471$	−2.73205	−0.125886
$472$	−2.53590	−0.116724
$473$	4.39230	0.201958
$474$	36.2487	1.66496
$475$	−2.53590	−0.116355
$476$	15.4641	0.708796
$477$	11.3205	0.518330
$478$	17.3205	0.792222
$479$	−9.46410	−0.432426	−0.216213	−	0.976346i	$-0.569371\pi$
$479$	−9.46410	−0.432426	−0.216213	+	0.976346i	$0.569371\pi$
$480$	−4.73205	−0.215988
$481$	0	0
$482$	15.4641	0.704371
$483$	−25.8564	−1.17651
$484$	11.3923	0.517832
$485$	−13.3923	−0.608113
$486$	18.7321	0.849703
$487$	−16.0526	−0.727411	−0.363705	−	0.931514i	$-0.618489\pi$
$487$	−16.0526	−0.727411	−0.363705	+	0.931514i	$0.618489\pi$
$488$	−1.73205	−0.0784063
$489$	−35.3205	−1.59725
$490$	−5.19615	−0.234738
$491$	26.1962	1.18222	0.591108	−	0.806592i	$-0.298691\pi$
$491$	26.1962	1.18222	0.591108	+	0.806592i	$0.298691\pi$
$492$	27.1244	1.22286
$493$	−66.9615	−3.01580
$494$	−4.39230	−0.197619
$495$	36.5885	1.64453
$496$	−1.26795	−0.0569326
$497$	−6.92820	−0.310772
$498$	15.4641	0.692963
$499$	20.1962	0.904104	0.452052	−	0.891992i	$-0.350692\pi$
$499$	20.1962	0.904104	0.452052	+	0.891992i	$0.350692\pi$
$500$	−12.1244	−0.542218
$501$	37.8564	1.69130
$502$	−17.3205	−0.773052
$503$	20.1962	0.900502	0.450251	−	0.892902i	$-0.351335\pi$
$503$	20.1962	0.900502	0.450251	+	0.892902i	$0.351335\pi$
$504$	−8.92820	−0.397694
$505$	−21.5885	−0.960674
$506$	−22.3923	−0.995459
$507$	2.73205	0.121335
$508$	−7.80385	−0.346240
$509$	6.46410	0.286516	0.143258	−	0.989685i	$-0.454242\pi$
$509$	6.46410	0.286516	0.143258	+	0.989685i	$0.454242\pi$
$510$	36.5885	1.62016
$511$	8.00000	0.353899
$512$	1.00000	0.0441942
$513$	−5.07180	−0.223925
$514$	−6.80385	−0.300105
$515$	−14.7846	−0.651488
$516$	−2.53590	−0.111637
$517$	22.3923	0.984812
$518$	0	0
$519$	15.1244	0.663886
$520$	−6.00000	−0.263117
$521$	−5.07180	−0.222199	−0.111100	−	0.993809i	$-0.535437\pi$
$521$	−5.07180	−0.222199	−0.111100	+	0.993809i	$0.535437\pi$
$522$	38.6603	1.69211
$523$	20.4449	0.893991	0.446996	−	0.894536i	$-0.352494\pi$
$523$	20.4449	0.893991	0.446996	+	0.894536i	$0.352494\pi$
$524$	9.80385	0.428283
$525$	−10.9282	−0.476946
$526$	−21.4641	−0.935879
$527$	9.80385	0.427062
$528$	−12.9282	−0.562628
$529$	−0.607695	−0.0264215
$530$	4.39230	0.190790
$531$	−11.3205	−0.491268
$532$	−2.53590	−0.109945
$533$	34.3923	1.48970
$534$	18.5885	0.804401
$535$	−18.0000	−0.778208
$536$	10.1962	0.440407
$537$	25.8564	1.11579
$538$	−4.39230	−0.189366
$539$	−14.1962	−0.611472
$540$	−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	$0.634320\pi$
$542$	−2.58846	−0.111184
$543$	25.6603	1.10119
$544$	−7.73205	−0.331509
$545$	−4.60770	−0.197372
$546$	−18.9282	−0.810052
$547$	41.6603	1.78126	0.890632	−	0.454725i	$-0.150262\pi$
$547$	41.6603	1.78126	0.890632	+	0.454725i	$0.150262\pi$
$548$	−1.39230	−0.0594763
$549$	−7.73205	−0.329996
$550$	−9.46410	−0.403551
$551$	10.9808	0.467796
$552$	12.9282	0.550261
$553$	26.5359	1.12842
$554$	−11.1962	−0.475679
$555$	0	0
$556$	20.5885	0.873145
$557$	23.4449	0.993391	0.496695	−	0.867925i	$-0.334547\pi$
$557$	23.4449	0.993391	0.496695	+	0.867925i	$0.334547\pi$
$558$	−5.66025	−0.239618
$559$	−3.21539	−0.135997
$560$	−3.46410	−0.146385
$561$	99.9615	4.22038
$562$	27.5885	1.16375
$563$	18.5885	0.783410	0.391705	−	0.920091i	$-0.371885\pi$
$563$	18.5885	0.783410	0.391705	+	0.920091i	$0.371885\pi$
$564$	−12.9282	−0.544376
$565$	−6.00000	−0.252422
$566$	7.85641	0.330229
$567$	4.92820	0.206965
$568$	3.46410	0.145350
$569$	−5.87564	−0.246320	−0.123160	−	0.992387i	$-0.539303\pi$
$569$	−5.87564	−0.246320	−0.123160	+	0.992387i	$0.539303\pi$
$570$	−6.00000	−0.251312
$571$	37.3731	1.56401	0.782007	−	0.623270i	$-0.214196\pi$
$571$	37.3731	1.56401	0.782007	+	0.623270i	$0.214196\pi$
$572$	−16.3923	−0.685397
$573$	6.00000	0.250654
$574$	19.8564	0.828790
$575$	9.46410	0.394680
$576$	4.46410	0.186004
$577$	0.928203	0.0386416	0.0193208	−	0.999813i	$-0.493850\pi$
$577$	0.928203	0.0386416	0.0193208	+	0.999813i	$0.493850\pi$
$578$	42.7846	1.77961
$579$	30.5885	1.27121
$580$	15.0000	0.622841
$581$	11.3205	0.469654
$582$	21.1244	0.875633
$583$	12.0000	0.496989
$584$	−4.00000	−0.165521
$585$	−26.7846	−1.10741
$586$	−1.39230	−0.0575156
$587$	−33.1244	−1.36719	−0.683594	−	0.729862i	$-0.739584\pi$
$587$	−33.1244	−1.36719	−0.683594	+	0.729862i	$0.739584\pi$
$588$	8.19615	0.338004
$589$	−1.60770	−0.0662439
$590$	−4.39230	−0.180828
$591$	−17.6603	−0.726446
$592$	0	0
$593$	43.6410	1.79212	0.896061	−	0.443931i	$-0.146417\pi$
$593$	43.6410	1.79212	0.896061	+	0.443931i	$0.146417\pi$
$594$	−18.9282	−0.776634
$595$	26.7846	1.09806
$596$	−15.9282	−0.652445
$597$	28.3923	1.16202
$598$	16.3923	0.670331
$599$	47.6603	1.94735	0.973673	−	0.227951i	$-0.0732026\pi$
$599$	47.6603	1.94735	0.973673	+	0.227951i	$0.0732026\pi$
$600$	5.46410	0.223071
$601$	−12.6077	−0.514279	−0.257139	−	0.966374i	$-0.582780\pi$
$601$	−12.6077	−0.514279	−0.257139	+	0.966374i	$0.582780\pi$
$602$	−1.85641	−0.0756615
$603$	45.5167	1.85358
$604$	−4.19615	−0.170739
$605$	19.7321	0.802222
$606$	34.0526	1.38329
$607$	−23.9090	−0.970435	−0.485217	−	0.874394i	$-0.661260\pi$
$607$	−23.9090	−0.970435	−0.485217	+	0.874394i	$0.661260\pi$
$608$	1.26795	0.0514221
$609$	47.3205	1.91752
$610$	−3.00000	−0.121466
$611$	−16.3923	−0.663162
$612$	−34.5167	−1.39525
$613$	−7.78461	−0.314417	−0.157209	−	0.987565i	$-0.550250\pi$
$613$	−7.78461	−0.314417	−0.157209	+	0.987565i	$0.550250\pi$
$614$	22.0000	0.887848
$615$	46.9808	1.89445
$616$	−9.46410	−0.381320
$617$	−12.6795	−0.510457	−0.255229	−	0.966881i	$-0.582151\pi$
$617$	−12.6795	−0.510457	−0.255229	+	0.966881i	$0.582151\pi$
$618$	23.3205	0.938088
$619$	−30.3923	−1.22157	−0.610785	−	0.791797i	$-0.709146\pi$
$619$	−30.3923	−1.22157	−0.610785	+	0.791797i	$0.709146\pi$
$620$	−2.19615	−0.0881996
$621$	18.9282	0.759563
$622$	−18.0000	−0.721734
$623$	13.6077	0.545181
$624$	9.46410	0.378867
$625$	−11.0000	−0.440000
$626$	−24.1244	−0.964203
$627$	−16.3923	−0.654646
$628$	1.00000	0.0399043
$629$	0	0
$630$	−15.4641	−0.616105
$631$	−34.9808	−1.39256	−0.696281	−	0.717769i	$-0.745163\pi$
$631$	−34.9808	−1.39256	−0.696281	+	0.717769i	$0.745163\pi$
$632$	−13.2679	−0.527771
$633$	6.53590	0.259779
$634$	−7.39230	−0.293586
$635$	−13.5167	−0.536392
$636$	−6.92820	−0.274721
$637$	10.3923	0.411758
$638$	40.9808	1.62244
$639$	15.4641	0.611750
$640$	1.73205	0.0684653
$641$	1.14359	0.0451692	0.0225846	−	0.999745i	$-0.492810\pi$
$641$	1.14359	0.0451692	0.0225846	+	0.999745i	$0.492810\pi$
$642$	28.3923	1.12055
$643$	−13.2679	−0.523237	−0.261618	−	0.965171i	$-0.584256\pi$
$643$	−13.2679	−0.523237	−0.261618	+	0.965171i	$0.584256\pi$
$644$	9.46410	0.372938
$645$	−4.39230	−0.172947
$646$	−9.80385	−0.385727
$647$	−23.0718	−0.907046	−0.453523	−	0.891245i	$-0.649833\pi$
$647$	−23.0718	−0.907046	−0.453523	+	0.891245i	$0.649833\pi$
$648$	−2.46410	−0.0967991
$649$	−12.0000	−0.471041
$650$	6.92820	0.271746
$651$	−6.92820	−0.271538
$652$	12.9282	0.506308
$653$	43.9808	1.72110	0.860550	−	0.509366i	$-0.170120\pi$
$653$	43.9808	1.72110	0.860550	+	0.509366i	$0.170120\pi$
$654$	7.26795	0.284199
$655$	16.9808	0.663493
$656$	−9.92820	−0.387631
$657$	−17.8564	−0.696645
$658$	−9.46410	−0.368949
$659$	9.46410	0.368669	0.184335	−	0.982864i	$-0.440987\pi$
$659$	9.46410	0.368669	0.184335	+	0.982864i	$0.440987\pi$
$660$	−22.3923	−0.871619
$661$	−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
$663$	−73.1769	−2.84196
$664$	−5.66025	−0.219660
$665$	−4.39230	−0.170326
$666$	0	0
$667$	−40.9808	−1.58678
$668$	−13.8564	−0.536120
$669$	−44.2487	−1.71075
$670$	17.6603	0.682275
$671$	−8.19615	−0.316409
$672$	5.46410	0.210782
$673$	16.0000	0.616755	0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000	0.616755	0.308377	+	0.951264i	$0.400214\pi$
$674$	32.1769	1.23941
$675$	8.00000	0.307920
$676$	−1.00000	−0.0384615
$677$	−33.9282	−1.30397	−0.651983	−	0.758233i	$-0.726063\pi$
$677$	−33.9282	−1.30397	−0.651983	+	0.758233i	$0.726063\pi$
$678$	9.46410	0.363467
$679$	15.4641	0.593458
$680$	−13.3923	−0.513571
$681$	−3.46410	−0.132745
$682$	−6.00000	−0.229752
$683$	20.5359	0.785784	0.392892	−	0.919585i	$-0.371475\pi$
$683$	20.5359	0.785784	0.392892	+	0.919585i	$0.371475\pi$
$684$	5.66025	0.216425
$685$	−2.41154	−0.0921403
$686$	20.0000	0.763604
$687$	−74.8372	−2.85522
$688$	0.928203	0.0353874
$689$	−8.78461	−0.334667
$690$	22.3923	0.852460
$691$	−26.9808	−1.02640	−0.513198	−	0.858270i	$-0.671539\pi$
$691$	−26.9808	−1.02640	−0.513198	+	0.858270i	$0.671539\pi$
$692$	−5.53590	−0.210443
$693$	−42.2487	−1.60490
$694$	9.12436	0.346356
$695$	35.6603	1.35267
$696$	−23.6603	−0.896840
$697$	76.7654	2.90770
$698$	11.3923	0.431205
$699$	40.9808	1.55003
$700$	4.00000	0.151186
$701$	−18.9282	−0.714908	−0.357454	−	0.933931i	$-0.616355\pi$
$701$	−18.9282	−0.714908	−0.357454	+	0.933931i	$0.616355\pi$
$702$	13.8564	0.522976
$703$	0	0
$704$	4.73205	0.178346
$705$	−22.3923	−0.843343
$706$	−19.7321	−0.742626
$707$	24.9282	0.937522
$708$	6.92820	0.260378
$709$	9.71281	0.364772	0.182386	−	0.983227i	$-0.441618\pi$
$709$	9.71281	0.364772	0.182386	+	0.983227i	$0.441618\pi$
$710$	6.00000	0.225176
$711$	−59.2295	−2.22128
$712$	−6.80385	−0.254985
$713$	6.00000	0.224702
$714$	−42.2487	−1.58112
$715$	−28.3923	−1.06181
$716$	−9.46410	−0.353690
$717$	−47.3205	−1.76722
$718$	35.3205	1.31815
$719$	37.2679	1.38986	0.694930	−	0.719077i	$-0.255435\pi$
$719$	37.2679	1.38986	0.694930	+	0.719077i	$0.255435\pi$
$720$	7.73205	0.288157
$721$	17.0718	0.635787
$722$	−17.3923	−0.647275
$723$	−42.2487	−1.57125
$724$	−9.39230	−0.349062
$725$	−17.3205	−0.643268
$726$	−31.1244	−1.15513
$727$	−39.7128	−1.47287	−0.736433	−	0.676510i	$-0.763492\pi$
$727$	−39.7128	−1.47287	−0.736433	+	0.676510i	$0.763492\pi$
$728$	6.92820	0.256776
$729$	−43.7846	−1.62165
$730$	−6.92820	−0.256424
$731$	−7.17691	−0.265448
$732$	4.73205	0.174902
$733$	33.5692	1.23991	0.619954	−	0.784638i	$-0.287151\pi$
$733$	33.5692	1.23991	0.619954	+	0.784638i	$0.287151\pi$
$734$	12.3923	0.457408
$735$	14.1962	0.523633
$736$	−4.73205	−0.174426
$737$	48.2487	1.77726
$738$	−44.3205	−1.63146
$739$	−32.5885	−1.19879	−0.599393	−	0.800455i	$-0.704591\pi$
$739$	−32.5885	−1.19879	−0.599393	+	0.800455i	$0.704591\pi$
$740$	0	0
$741$	12.0000	0.440831
$742$	−5.07180	−0.186192
$743$	−1.51666	−0.0556409	−0.0278204	−	0.999613i	$-0.508857\pi$
$743$	−1.51666	−0.0556409	−0.0278204	+	0.999613i	$0.508857\pi$
$744$	3.46410	0.127000
$745$	−27.5885	−1.01076
$746$	−7.00000	−0.256288
$747$	−25.2679	−0.924506
$748$	−36.5885	−1.33781
$749$	20.7846	0.759453
$750$	33.1244	1.20953
$751$	−29.6077	−1.08040	−0.540200	−	0.841537i	$-0.681651\pi$
$751$	−29.6077	−1.08040	−0.540200	+	0.841537i	$0.681651\pi$
$752$	4.73205	0.172560
$753$	47.3205	1.72446
$754$	−30.0000	−1.09254
$755$	−7.26795	−0.264508
$756$	8.00000	0.290957
$757$	−17.1962	−0.625005	−0.312502	−	0.949917i	$-0.601167\pi$
$757$	−17.1962	−0.625005	−0.312502	+	0.949917i	$0.601167\pi$
$758$	−34.7846	−1.26343
$759$	61.1769	2.22058
$760$	2.19615	0.0796628
$761$	2.32051	0.0841184	0.0420592	−	0.999115i	$-0.486608\pi$
$761$	2.32051	0.0841184	0.0420592	+	0.999115i	$0.486608\pi$
$762$	21.3205	0.772361
$763$	5.32051	0.192615
$764$	−2.19615	−0.0794540
$765$	−59.7846	−2.16152
$766$	−3.46410	−0.125163
$767$	8.78461	0.317194
$768$	−2.73205	−0.0985844
$769$	13.6077	0.490706	0.245353	−	0.969434i	$-0.421096\pi$
$769$	13.6077	0.490706	0.245353	+	0.969434i	$0.421096\pi$
$770$	−16.3923	−0.590738
$771$	18.5885	0.669447
$772$	−11.1962	−0.402958
$773$	33.9282	1.22031	0.610156	−	0.792281i	$-0.291107\pi$
$773$	33.9282	1.22031	0.610156	+	0.792281i	$0.291107\pi$
$774$	4.14359	0.148938
$775$	2.53590	0.0910922
$776$	−7.73205	−0.277564
$777$	0	0
$778$	−25.9808	−0.931455
$779$	−12.5885	−0.451028
$780$	16.3923	0.586939
$781$	16.3923	0.586563
$782$	36.5885	1.30840
$783$	−34.6410	−1.23797
$784$	−3.00000	−0.107143
$785$	1.73205	0.0618195
$786$	−26.7846	−0.955375
$787$	−41.1769	−1.46780	−0.733899	−	0.679258i	$-0.762302\pi$
$787$	−41.1769	−1.46780	−0.733899	+	0.679258i	$0.762302\pi$
$788$	6.46410	0.230274
$789$	58.6410	2.08768
$790$	−22.9808	−0.817619
$791$	6.92820	0.246339
$792$	21.1244	0.750621
$793$	6.00000	0.213066
$794$	23.0000	0.816239
$795$	−12.0000	−0.425596
$796$	−10.3923	−0.368345
$797$	8.78461	0.311167	0.155583	−	0.987823i	$-0.450274\pi$
$797$	8.78461	0.311167	0.155583	+	0.987823i	$0.450274\pi$
$798$	6.92820	0.245256
$799$	−36.5885	−1.29441
$800$	−2.00000	−0.0707107
$801$	−30.3731	−1.07318
$802$	−10.3923	−0.366965
$803$	−18.9282	−0.667962
$804$	−27.8564	−0.982420
$805$	16.3923	0.577753
$806$	4.39230	0.154712
$807$	12.0000	0.422420
$808$	−12.4641	−0.438486
$809$	−15.7128	−0.552433	−0.276217	−	0.961095i	$-0.589081\pi$
$809$	−15.7128	−0.552433	−0.276217	+	0.961095i	$0.589081\pi$
$810$	−4.26795	−0.149960
$811$	20.3923	0.716071	0.358035	−	0.933708i	$-0.383447\pi$
$811$	20.3923	0.716071	0.358035	+	0.933708i	$0.383447\pi$
$812$	−17.3205	−0.607831
$813$	7.07180	0.248019
$814$	0	0
$815$	22.3923	0.784368
$816$	21.1244	0.739500
$817$	1.17691	0.0411750
$818$	10.5167	0.367706
$819$	30.9282	1.08072
$820$	−17.1962	−0.600516
$821$	2.53590	0.0885035	0.0442517	−	0.999020i	$-0.485910\pi$
$821$	2.53590	0.0885035	0.0442517	+	0.999020i	$0.485910\pi$
$822$	3.80385	0.132674
$823$	23.8038	0.829750	0.414875	−	0.909878i	$-0.363825\pi$
$823$	23.8038	0.829750	0.414875	+	0.909878i	$0.363825\pi$
$824$	−8.53590	−0.297362
$825$	25.8564	0.900205
$826$	5.07180	0.176470
$827$	−1.85641	−0.0645536	−0.0322768	−	0.999479i	$-0.510276\pi$
$827$	−1.85641	−0.0645536	−0.0322768	+	0.999479i	$0.510276\pi$
$828$	−21.1244	−0.734122
$829$	10.3923	0.360940	0.180470	−	0.983581i	$-0.442238\pi$
$829$	10.3923	0.360940	0.180470	+	0.983581i	$0.442238\pi$
$830$	−9.80385	−0.340297
$831$	30.5885	1.06110
$832$	−3.46410	−0.120096
$833$	23.1962	0.803699
$834$	−56.2487	−1.94773
$835$	−24.0000	−0.830554
$836$	6.00000	0.207514
$837$	5.07180	0.175307
$838$	−4.14359	−0.143138
$839$	52.9808	1.82910	0.914550	−	0.404474i	$-0.132545\pi$
$839$	52.9808	1.82910	0.914550	+	0.404474i	$0.132545\pi$
$840$	9.46410	0.326543
$841$	46.0000	1.58621
$842$	−12.1244	−0.417833
$843$	−75.3731	−2.59599
$844$	−2.39230	−0.0823465
$845$	−1.73205	−0.0595844
$846$	21.1244	0.726270
$847$	−22.7846	−0.782888
$848$	2.53590	0.0870831
$849$	−21.4641	−0.736646
$850$	15.4641	0.530414
$851$	0	0
$852$	−9.46410	−0.324235
$853$	−10.2679	−0.351568	−0.175784	−	0.984429i	$-0.556246\pi$
$853$	−10.2679	−0.351568	−0.175784	+	0.984429i	$0.556246\pi$
$854$	3.46410	0.118539
$855$	9.80385	0.335285
$856$	−10.3923	−0.355202
$857$	−2.66025	−0.0908725	−0.0454363	−	0.998967i	$-0.514468\pi$
$857$	−2.66025	−0.0908725	−0.0454363	+	0.998967i	$0.514468\pi$
$858$	44.7846	1.52892
$859$	−30.0000	−1.02359	−0.511793	−	0.859109i	$-0.671019\pi$
$859$	−30.0000	−1.02359	−0.511793	+	0.859109i	$0.671019\pi$
$860$	1.60770	0.0548219
$861$	−54.2487	−1.84879
$862$	17.6603	0.601511
$863$	4.39230	0.149516	0.0747579	−	0.997202i	$-0.476182\pi$
$863$	4.39230	0.149516	0.0747579	+	0.997202i	$0.476182\pi$
$864$	−4.00000	−0.136083
$865$	−9.58846	−0.326017
$866$	15.7846	0.536383
$867$	−116.890	−3.96978
$868$	2.53590	0.0860740
$869$	−62.7846	−2.12982
$870$	−40.9808	−1.38938
$871$	−35.3205	−1.19679
$872$	−2.66025	−0.0900876
$873$	−34.5167	−1.16821
$874$	−6.00000	−0.202953
$875$	24.2487	0.819756
$876$	10.9282	0.369230
$877$	38.1769	1.28914	0.644571	−	0.764544i	$-0.277036\pi$
$877$	38.1769	1.28914	0.644571	+	0.764544i	$0.277036\pi$
$878$	18.2487	0.615864
$879$	3.80385	0.128301
$880$	8.19615	0.276292
$881$	−28.6077	−0.963818	−0.481909	−	0.876221i	$-0.660056\pi$
$881$	−28.6077	−0.963818	−0.481909	+	0.876221i	$0.660056\pi$
$882$	−13.3923	−0.450942
$883$	16.0526	0.540212	0.270106	−	0.962831i	$-0.412941\pi$
$883$	16.0526	0.540212	0.270106	+	0.962831i	$0.412941\pi$
$884$	26.7846	0.900864
$885$	12.0000	0.403376
$886$	14.5359	0.488343
$887$	46.0526	1.54629	0.773147	−	0.634227i	$-0.218682\pi$
$887$	46.0526	1.54629	0.773147	+	0.634227i	$0.218682\pi$
$888$	0	0
$889$	15.6077	0.523465
$890$	−11.7846	−0.395021
$891$	−11.6603	−0.390633
$892$	16.1962	0.542287
$893$	6.00000	0.200782
$894$	43.5167	1.45541
$895$	−16.3923	−0.547934
$896$	−2.00000	−0.0668153
$897$	−44.7846	−1.49531
$898$	20.5359	0.685292
$899$	−10.9808	−0.366229
$900$	−8.92820	−0.297607
$901$	−19.6077	−0.653227
$902$	−46.9808	−1.56429
$903$	5.07180	0.168779
$904$	−3.46410	−0.115214
$905$	−16.2679	−0.540765
$906$	11.4641	0.380869
$907$	11.4115	0.378914	0.189457	−	0.981889i	$-0.439327\pi$
$907$	11.4115	0.378914	0.189457	+	0.981889i	$0.439327\pi$
$908$	1.26795	0.0420784
$909$	−55.6410	−1.84550
$910$	12.0000	0.397796
$911$	−35.6603	−1.18148	−0.590738	−	0.806863i	$-0.701163\pi$
$911$	−35.6603	−1.18148	−0.590738	+	0.806863i	$0.701163\pi$
$912$	−3.46410	−0.114708
$913$	−26.7846	−0.886441
$914$	−37.9808	−1.25629
$915$	8.19615	0.270956
$916$	27.3923	0.905067
$917$	−19.6077	−0.647503
$918$	30.9282	1.02078
$919$	−21.1244	−0.696828	−0.348414	−	0.937341i	$-0.613280\pi$
$919$	−21.1244	−0.696828	−0.348414	+	0.937341i	$0.613280\pi$
$920$	−8.19615	−0.270219
$921$	−60.1051	−1.98053
$922$	39.4641	1.29968
$923$	−12.0000	−0.394985
$924$	25.8564	0.850613
$925$	0	0
$926$	−30.0000	−0.985861
$927$	−38.1051	−1.25154
$928$	8.66025	0.284287
$929$	25.3923	0.833094	0.416547	−	0.909114i	$-0.363240\pi$
$929$	25.3923	0.833094	0.416547	+	0.909114i	$0.363240\pi$
$930$	6.00000	0.196748
$931$	−3.80385	−0.124666
$932$	−15.0000	−0.491341
$933$	49.1769	1.60998
$934$	2.53590	0.0829771
$935$	−63.3731	−2.07252
$936$	−15.4641	−0.505460
$937$	27.3923	0.894868	0.447434	−	0.894317i	$-0.352338\pi$
$937$	27.3923	0.894868	0.447434	+	0.894317i	$0.352338\pi$
$938$	−20.3923	−0.665832
$939$	65.9090	2.15086
$940$	8.19615	0.267329
$941$	29.7846	0.970951	0.485475	−	0.874250i	$-0.338647\pi$
$941$	29.7846	0.970951	0.485475	+	0.874250i	$0.338647\pi$
$942$	−2.73205	−0.0890150
$943$	46.9808	1.52990
$944$	−2.53590	−0.0825365
$945$	13.8564	0.450749
$946$	4.39230	0.142806
$947$	−37.1769	−1.20809	−0.604044	−	0.796951i	$-0.706445\pi$
$947$	−37.1769	−1.20809	−0.604044	+	0.796951i	$0.706445\pi$
$948$	36.2487	1.17730
$949$	13.8564	0.449798
$950$	−2.53590	−0.0822754
$951$	20.1962	0.654905
$952$	15.4641	0.501194
$953$	−19.8564	−0.643212	−0.321606	−	0.946874i	$-0.604223\pi$
$953$	−19.8564	−0.643212	−0.321606	+	0.946874i	$0.604223\pi$
$954$	11.3205	0.366515
$955$	−3.80385	−0.123090
$956$	17.3205	0.560185
$957$	−111.962	−3.61920
$958$	−9.46410	−0.305771
$959$	2.78461	0.0899197
$960$	−4.73205	−0.152726
$961$	−29.3923	−0.948139
$962$	0	0
$963$	−46.3923	−1.49497
$964$	15.4641	0.498065
$965$	−19.3923	−0.624260
$966$	−25.8564	−0.831916
$967$	−48.0000	−1.54358	−0.771788	−	0.635880i	$-0.780637\pi$
$967$	−48.0000	−1.54358	−0.771788	+	0.635880i	$0.780637\pi$
$968$	11.3923	0.366163
$969$	26.7846	0.860446
$970$	−13.3923	−0.430001
$971$	−7.01924	−0.225258	−0.112629	−	0.993637i	$-0.535927\pi$
$971$	−7.01924	−0.225258	−0.112629	+	0.993637i	$0.535927\pi$
$972$	18.7321	0.600831
$973$	−41.1769	−1.32007
$974$	−16.0526	−0.514357
$975$	−18.9282	−0.606188
$976$	−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	$0.517648\pi$
$978$	−35.3205	−1.12943
$979$	−32.1962	−1.02899
$980$	−5.19615	−0.165985
$981$	−11.8756	−0.379160
$982$	26.1962	0.835953
$983$	−45.1244	−1.43924	−0.719622	−	0.694366i	$-0.755685\pi$
$983$	−45.1244	−1.43924	−0.719622	+	0.694366i	$0.755685\pi$
$984$	27.1244	0.864693
$985$	11.1962	0.356739
$986$	−66.9615	−2.13249
$987$	25.8564	0.823018
$988$	−4.39230	−0.139738
$989$	−4.39230	−0.139667
$990$	36.5885	1.16286
$991$	−16.6410	−0.528619	−0.264310	−	0.964438i	$-0.585144\pi$
$991$	−16.6410	−0.528619	−0.264310	+	0.964438i	$0.585144\pi$
$992$	−1.26795	−0.0402574
$993$	0	0
$994$	−6.92820	−0.219749
$995$	−18.0000	−0.570638
$996$	15.4641	0.489999
$997$	10.3923	0.329128	0.164564	−	0.986366i	$-0.447378\pi$
$997$	10.3923	0.329128	0.164564	+	0.986366i	$0.447378\pi$
$998$	20.1962	0.639298
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.i.1.1		2
37.8	odd	12		74.2.e.b.27.2	yes	4
37.14	odd	12		74.2.e.b.11.2	✓	4
37.36	even	2		2738.2.a.e.1.1		2
111.8	even	12		666.2.s.a.397.1		4
111.14	even	12		666.2.s.a.307.1		4
148.51	even	12		592.2.w.e.529.2		4
148.119	even	12		592.2.w.e.545.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.e.b.11.2	✓	4	37.14	odd	12
74.2.e.b.27.2	yes	4	37.8	odd	12
592.2.w.e.529.2		4	148.51	even	12
592.2.w.e.545.2		4	148.119	even	12
666.2.s.a.307.1		4	111.14	even	12
666.2.s.a.397.1		4	111.8	even	12
2738.2.a.e.1.1		2	37.36	even	2
2738.2.a.i.1.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} -2.73205 q^{6} -2.00000 q^{7} +1.00000 q^{8} +4.46410 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} -2.73205 q^{6} -2.00000 q^{7} +1.00000 q^{8} +4.46410 q^{9} +1.73205 q^{10} +4.73205 q^{11} -2.73205 q^{12} -3.46410 q^{13} -2.00000 q^{14} -4.73205 q^{15} +1.00000 q^{16} -7.73205 q^{17} +4.46410 q^{18} +1.26795 q^{19} +1.73205 q^{20} +5.46410 q^{21} +4.73205 q^{22} -4.73205 q^{23} -2.73205 q^{24} -2.00000 q^{25} -3.46410 q^{26} -4.00000 q^{27} -2.00000 q^{28} +8.66025 q^{29} -4.73205 q^{30} -1.26795 q^{31} +1.00000 q^{32} -12.9282 q^{33} -7.73205 q^{34} -3.46410 q^{35} +4.46410 q^{36} +1.26795 q^{38} +9.46410 q^{39} +1.73205 q^{40} -9.92820 q^{41} +5.46410 q^{42} +0.928203 q^{43} +4.73205 q^{44} +7.73205 q^{45} -4.73205 q^{46} +4.73205 q^{47} -2.73205 q^{48} -3.00000 q^{49} -2.00000 q^{50} +21.1244 q^{51} -3.46410 q^{52} +2.53590 q^{53} -4.00000 q^{54} +8.19615 q^{55} -2.00000 q^{56} -3.46410 q^{57} +8.66025 q^{58} -2.53590 q^{59} -4.73205 q^{60} -1.73205 q^{61} -1.26795 q^{62} -8.92820 q^{63} +1.00000 q^{64} -6.00000 q^{65} -12.9282 q^{66} +10.1962 q^{67} -7.73205 q^{68} +12.9282 q^{69} -3.46410 q^{70} +3.46410 q^{71} +4.46410 q^{72} -4.00000 q^{73} +5.46410 q^{75} +1.26795 q^{76} -9.46410 q^{77} +9.46410 q^{78} -13.2679 q^{79} +1.73205 q^{80} -2.46410 q^{81} -9.92820 q^{82} -5.66025 q^{83} +5.46410 q^{84} -13.3923 q^{85} +0.928203 q^{86} -23.6603 q^{87} +4.73205 q^{88} -6.80385 q^{89} +7.73205 q^{90} +6.92820 q^{91} -4.73205 q^{92} +3.46410 q^{93} +4.73205 q^{94} +2.19615 q^{95} -2.73205 q^{96} -7.73205 q^{97} -3.00000 q^{98} +21.1244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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