LMFDB - Embedded newform 1014.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(1,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	1014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.29590 q^{5} -1.00000 q^{6} +4.35690 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.29590 q^{5} -1.00000 q^{6} +4.35690 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.29590 q^{10} -1.15883 q^{11} -1.00000 q^{12} +4.35690 q^{14} +4.29590 q^{15} +1.00000 q^{16} +0.493959 q^{17} +1.00000 q^{18} -1.78017 q^{19} -4.29590 q^{20} -4.35690 q^{21} -1.15883 q^{22} +3.38404 q^{23} -1.00000 q^{24} +13.4547 q^{25} -1.00000 q^{27} +4.35690 q^{28} +6.93900 q^{29} +4.29590 q^{30} +2.22521 q^{31} +1.00000 q^{32} +1.15883 q^{33} +0.493959 q^{34} -18.7168 q^{35} +1.00000 q^{36} +3.87800 q^{37} -1.78017 q^{38} -4.29590 q^{40} +6.31767 q^{41} -4.35690 q^{42} +7.38404 q^{43} -1.15883 q^{44} -4.29590 q^{45} +3.38404 q^{46} +1.78017 q^{47} -1.00000 q^{48} +11.9825 q^{49} +13.4547 q^{50} -0.493959 q^{51} -2.51573 q^{53} -1.00000 q^{54} +4.97823 q^{55} +4.35690 q^{56} +1.78017 q^{57} +6.93900 q^{58} -6.63102 q^{59} +4.29590 q^{60} +10.4940 q^{61} +2.22521 q^{62} +4.35690 q^{63} +1.00000 q^{64} +1.15883 q^{66} -4.09783 q^{67} +0.493959 q^{68} -3.38404 q^{69} -18.7168 q^{70} -9.38404 q^{71} +1.00000 q^{72} -0.374354 q^{73} +3.87800 q^{74} -13.4547 q^{75} -1.78017 q^{76} -5.04892 q^{77} +2.65519 q^{79} -4.29590 q^{80} +1.00000 q^{81} +6.31767 q^{82} +14.2784 q^{83} -4.35690 q^{84} -2.12200 q^{85} +7.38404 q^{86} -6.93900 q^{87} -1.15883 q^{88} -0.835790 q^{89} -4.29590 q^{90} +3.38404 q^{92} -2.22521 q^{93} +1.78017 q^{94} +7.64742 q^{95} -1.00000 q^{96} -18.3937 q^{97} +11.9825 q^{98} -1.15883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + q^{5} - 3 q^{6} + 9 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + q^5 - 3 * q^6 + 9 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + q^{5} - 3 q^{6} + 9 q^{7} + 3 q^{8} + 3 q^{9} + q^{10} + 5 q^{11} - 3 q^{12} + 9 q^{14} - q^{15} + 3 q^{16} - 8 q^{17} + 3 q^{18} - 4 q^{19} + q^{20} - 9 q^{21} + 5 q^{22} - 3 q^{24} + 18 q^{25} - 3 q^{27} + 9 q^{28} + 11 q^{29} - q^{30} + 5 q^{31} + 3 q^{32} - 5 q^{33} - 8 q^{34} - 4 q^{35} + 3 q^{36} - 8 q^{37} - 4 q^{38} + q^{40} + 2 q^{41} - 9 q^{42} + 12 q^{43} + 5 q^{44} + q^{45} + 4 q^{47} - 3 q^{48} + 20 q^{49} + 18 q^{50} + 8 q^{51} + 5 q^{53} - 3 q^{54} + 18 q^{55} + 9 q^{56} + 4 q^{57} + 11 q^{58} - 5 q^{59} - q^{60} + 22 q^{61} + 5 q^{62} + 9 q^{63} + 3 q^{64} - 5 q^{66} + 6 q^{67} - 8 q^{68} - 4 q^{70} - 18 q^{71} + 3 q^{72} - 13 q^{73} - 8 q^{74} - 18 q^{75} - 4 q^{76} - 6 q^{77} + 31 q^{79} + q^{80} + 3 q^{81} + 2 q^{82} + 13 q^{83} - 9 q^{84} - 26 q^{85} + 12 q^{86} - 11 q^{87} + 5 q^{88} - 14 q^{89} + q^{90} - 5 q^{93} + 4 q^{94} + 8 q^{95} - 3 q^{96} - 23 q^{97} + 20 q^{98} + 5 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + q^5 - 3 * q^6 + 9 * q^7 + 3 * q^8 + 3 * q^9 + q^10 + 5 * q^11 - 3 * q^12 + 9 * q^14 - q^15 + 3 * q^16 - 8 * q^17 + 3 * q^18 - 4 * q^19 + q^20 - 9 * q^21 + 5 * q^22 - 3 * q^24 + 18 * q^25 - 3 * q^27 + 9 * q^28 + 11 * q^29 - q^30 + 5 * q^31 + 3 * q^32 - 5 * q^33 - 8 * q^34 - 4 * q^35 + 3 * q^36 - 8 * q^37 - 4 * q^38 + q^40 + 2 * q^41 - 9 * q^42 + 12 * q^43 + 5 * q^44 + q^45 + 4 * q^47 - 3 * q^48 + 20 * q^49 + 18 * q^50 + 8 * q^51 + 5 * q^53 - 3 * q^54 + 18 * q^55 + 9 * q^56 + 4 * q^57 + 11 * q^58 - 5 * q^59 - q^60 + 22 * q^61 + 5 * q^62 + 9 * q^63 + 3 * q^64 - 5 * q^66 + 6 * q^67 - 8 * q^68 - 4 * q^70 - 18 * q^71 + 3 * q^72 - 13 * q^73 - 8 * q^74 - 18 * q^75 - 4 * q^76 - 6 * q^77 + 31 * q^79 + q^80 + 3 * q^81 + 2 * q^82 + 13 * q^83 - 9 * q^84 - 26 * q^85 + 12 * q^86 - 11 * q^87 + 5 * q^88 - 14 * q^89 + q^90 - 5 * q^93 + 4 * q^94 + 8 * q^95 - 3 * q^96 - 23 * q^97 + 20 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−4.29590	−1.92118	−0.960592	−	0.277963i	$-0.910341\pi$
$5$	−4.29590	−1.92118	−0.960592	+	0.277963i	$0.910341\pi$
$6$	−1.00000	−0.408248
$7$	4.35690	1.64675	0.823376	−	0.567496i	$-0.192088\pi$
$7$	4.35690	1.64675	0.823376	+	0.567496i	$0.192088\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−4.29590	−1.35848
$11$	−1.15883	−0.349401	−0.174701	−	0.984622i	$-0.555896\pi$
$11$	−1.15883	−0.349401	−0.174701	+	0.984622i	$0.555896\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	4.35690	1.16443
$15$	4.29590	1.10920
$16$	1.00000	0.250000
$17$	0.493959	0.119803	0.0599014	−	0.998204i	$-0.480921\pi$
$17$	0.493959	0.119803	0.0599014	+	0.998204i	$0.480921\pi$
$18$	1.00000	0.235702
$19$	−1.78017	−0.408398	−0.204199	−	0.978929i	$-0.565459\pi$
$19$	−1.78017	−0.408398	−0.204199	+	0.978929i	$0.565459\pi$
$20$	−4.29590	−0.960592
$21$	−4.35690	−0.950753
$22$	−1.15883	−0.247064
$23$	3.38404	0.705622	0.352811	−	0.935695i	$-0.385226\pi$
$23$	3.38404	0.705622	0.352811	+	0.935695i	$0.385226\pi$
$24$	−1.00000	−0.204124
$25$	13.4547	2.69095
$26$	0	0
$27$	−1.00000	−0.192450
$28$	4.35690	0.823376
$29$	6.93900	1.28854	0.644270	−	0.764798i	$-0.277161\pi$
$29$	6.93900	1.28854	0.644270	+	0.764798i	$0.277161\pi$
$30$	4.29590	0.784320
$31$	2.22521	0.399659	0.199830	−	0.979831i	$-0.435961\pi$
$31$	2.22521	0.399659	0.199830	+	0.979831i	$0.435961\pi$
$32$	1.00000	0.176777
$33$	1.15883	0.201727
$34$	0.493959	0.0847133
$35$	−18.7168	−3.16371
$36$	1.00000	0.166667
$37$	3.87800	0.637540	0.318770	−	0.947832i	$-0.396730\pi$
$37$	3.87800	0.637540	0.318770	+	0.947832i	$0.396730\pi$
$38$	−1.78017	−0.288781
$39$	0	0
$40$	−4.29590	−0.679241
$41$	6.31767	0.986654	0.493327	−	0.869844i	$-0.335781\pi$
$41$	6.31767	0.986654	0.493327	+	0.869844i	$0.335781\pi$
$42$	−4.35690	−0.672284
$43$	7.38404	1.12606	0.563028	−	0.826438i	$-0.309636\pi$
$43$	7.38404	1.12606	0.563028	+	0.826438i	$0.309636\pi$
$44$	−1.15883	−0.174701
$45$	−4.29590	−0.640395
$46$	3.38404	0.498950
$47$	1.78017	0.259664	0.129832	−	0.991536i	$-0.458556\pi$
$47$	1.78017	0.259664	0.129832	+	0.991536i	$0.458556\pi$
$48$	−1.00000	−0.144338
$49$	11.9825	1.71179
$50$	13.4547	1.90279
$51$	−0.493959	−0.0691681
$52$	0	0
$53$	−2.51573	−0.345562	−0.172781	−	0.984960i	$-0.555275\pi$
$53$	−2.51573	−0.345562	−0.172781	+	0.984960i	$0.555275\pi$
$54$	−1.00000	−0.136083
$55$	4.97823	0.671264
$56$	4.35690	0.582215
$57$	1.78017	0.235789
$58$	6.93900	0.911135
$59$	−6.63102	−0.863286	−0.431643	−	0.902045i	$-0.642066\pi$
$59$	−6.63102	−0.863286	−0.431643	+	0.902045i	$0.642066\pi$
$60$	4.29590	0.554598
$61$	10.4940	1.34361	0.671807	−	0.740726i	$-0.265518\pi$
$61$	10.4940	1.34361	0.671807	+	0.740726i	$0.265518\pi$
$62$	2.22521	0.282602
$63$	4.35690	0.548917
$64$	1.00000	0.125000
$65$	0	0
$66$	1.15883	0.142643
$67$	−4.09783	−0.500630	−0.250315	−	0.968164i	$-0.580534\pi$
$67$	−4.09783	−0.500630	−0.250315	+	0.968164i	$0.580534\pi$
$68$	0.493959	0.0599014
$69$	−3.38404	−0.407391
$70$	−18.7168	−2.23708
$71$	−9.38404	−1.11368	−0.556841	−	0.830619i	$-0.687987\pi$
$71$	−9.38404	−1.11368	−0.556841	+	0.830619i	$0.687987\pi$
$72$	1.00000	0.117851
$73$	−0.374354	−0.0438149	−0.0219074	−	0.999760i	$-0.506974\pi$
$73$	−0.374354	−0.0438149	−0.0219074	+	0.999760i	$0.506974\pi$
$74$	3.87800	0.450809
$75$	−13.4547	−1.55362
$76$	−1.78017	−0.204199
$77$	−5.04892	−0.575378
$78$	0	0
$79$	2.65519	0.298732	0.149366	−	0.988782i	$-0.452277\pi$
$79$	2.65519	0.298732	0.149366	+	0.988782i	$0.452277\pi$
$80$	−4.29590	−0.480296
$81$	1.00000	0.111111
$82$	6.31767	0.697670
$83$	14.2784	1.56726	0.783631	−	0.621226i	$-0.213365\pi$
$83$	14.2784	1.56726	0.783631	+	0.621226i	$0.213365\pi$
$84$	−4.35690	−0.475376
$85$	−2.12200	−0.230163
$86$	7.38404	0.796242
$87$	−6.93900	−0.743939
$88$	−1.15883	−0.123532
$89$	−0.835790	−0.0885935	−0.0442968	−	0.999018i	$-0.514105\pi$
$89$	−0.835790	−0.0885935	−0.0442968	+	0.999018i	$0.514105\pi$
$90$	−4.29590	−0.452827
$91$	0	0
$92$	3.38404	0.352811
$93$	−2.22521	−0.230743
$94$	1.78017	0.183610
$95$	7.64742	0.784608
$96$	−1.00000	−0.102062
$97$	−18.3937	−1.86760	−0.933800	−	0.357795i	$-0.883529\pi$
$97$	−18.3937	−1.86760	−0.933800	+	0.357795i	$0.883529\pi$
$98$	11.9825	1.21042
$99$	−1.15883	−0.116467
$100$	13.4547	1.34547
$101$	−5.46681	−0.543968	−0.271984	−	0.962302i	$-0.587680\pi$
$101$	−5.46681	−0.543968	−0.271984	+	0.962302i	$0.587680\pi$
$102$	−0.493959	−0.0489092
$103$	7.00969	0.690685	0.345343	−	0.938477i	$-0.387763\pi$
$103$	7.00969	0.690685	0.345343	+	0.938477i	$0.387763\pi$
$104$	0	0
$105$	18.7168	1.82657
$106$	−2.51573	−0.244349
$107$	−1.91723	−0.185346	−0.0926728	−	0.995697i	$-0.529541\pi$
$107$	−1.91723	−0.185346	−0.0926728	+	0.995697i	$0.529541\pi$
$108$	−1.00000	−0.0962250
$109$	−18.7681	−1.79766	−0.898828	−	0.438301i	$-0.855580\pi$
$109$	−18.7681	−1.79766	−0.898828	+	0.438301i	$0.855580\pi$
$110$	4.97823	0.474656
$111$	−3.87800	−0.368084
$112$	4.35690	0.411688
$113$	10.4155	0.979808	0.489904	−	0.871776i	$-0.337032\pi$
$113$	10.4155	0.979808	0.489904	+	0.871776i	$0.337032\pi$
$114$	1.78017	0.166728
$115$	−14.5375	−1.35563
$116$	6.93900	0.644270
$117$	0	0
$118$	−6.63102	−0.610435
$119$	2.15213	0.197285
$120$	4.29590	0.392160
$121$	−9.65710	−0.877919
$122$	10.4940	0.950078
$123$	−6.31767	−0.569645
$124$	2.22521	0.199830
$125$	−36.3207	−3.24862
$126$	4.35690	0.388143
$127$	8.39373	0.744823	0.372412	−	0.928068i	$-0.378531\pi$
$127$	8.39373	0.744823	0.372412	+	0.928068i	$0.378531\pi$
$128$	1.00000	0.0883883
$129$	−7.38404	−0.650129
$130$	0	0
$131$	−13.5036	−1.17982	−0.589910	−	0.807469i	$-0.700837\pi$
$131$	−13.5036	−1.17982	−0.589910	+	0.807469i	$0.700837\pi$
$132$	1.15883	0.100864
$133$	−7.75600	−0.672531
$134$	−4.09783	−0.353999
$135$	4.29590	0.369732
$136$	0.493959	0.0423567
$137$	−4.00000	−0.341743	−0.170872	−	0.985293i	$-0.554658\pi$
$137$	−4.00000	−0.341743	−0.170872	+	0.985293i	$0.554658\pi$
$138$	−3.38404	−0.288069
$139$	−15.0315	−1.27495	−0.637476	−	0.770470i	$-0.720021\pi$
$139$	−15.0315	−1.27495	−0.637476	+	0.770470i	$0.720021\pi$
$140$	−18.7168	−1.58186
$141$	−1.78017	−0.149917
$142$	−9.38404	−0.787491
$143$	0	0
$144$	1.00000	0.0833333
$145$	−29.8092	−2.47552
$146$	−0.374354	−0.0309818
$147$	−11.9825	−0.988303
$148$	3.87800	0.318770
$149$	3.92692	0.321706	0.160853	−	0.986978i	$-0.448576\pi$
$149$	3.92692	0.321706	0.160853	+	0.986978i	$0.448576\pi$
$150$	−13.4547	−1.09857
$151$	−9.62863	−0.783567	−0.391783	−	0.920057i	$-0.628142\pi$
$151$	−9.62863	−0.783567	−0.391783	+	0.920057i	$0.628142\pi$
$152$	−1.78017	−0.144391
$153$	0.493959	0.0399342
$154$	−5.04892	−0.406853
$155$	−9.55927	−0.767819
$156$	0	0
$157$	−17.3840	−1.38740	−0.693699	−	0.720265i	$-0.744020\pi$
$157$	−17.3840	−1.38740	−0.693699	+	0.720265i	$0.744020\pi$
$158$	2.65519	0.211235
$159$	2.51573	0.199510
$160$	−4.29590	−0.339620
$161$	14.7439	1.16198
$162$	1.00000	0.0785674
$163$	22.4698	1.75997	0.879985	−	0.475001i	$-0.157552\pi$
$163$	22.4698	1.75997	0.879985	+	0.475001i	$0.157552\pi$
$164$	6.31767	0.493327
$165$	−4.97823	−0.387555
$166$	14.2784	1.10822
$167$	0.835790	0.0646753	0.0323377	−	0.999477i	$-0.489705\pi$
$167$	0.835790	0.0646753	0.0323377	+	0.999477i	$0.489705\pi$
$168$	−4.35690	−0.336142
$169$	0	0
$170$	−2.12200	−0.162750
$171$	−1.78017	−0.136133
$172$	7.38404	0.563028
$173$	−4.17092	−0.317109	−0.158554	−	0.987350i	$-0.550683\pi$
$173$	−4.17092	−0.317109	−0.158554	+	0.987350i	$0.550683\pi$
$174$	−6.93900	−0.526044
$175$	58.6209	4.43132
$176$	−1.15883	−0.0873504
$177$	6.63102	0.498418
$178$	−0.835790	−0.0626451
$179$	22.8877	1.71071	0.855353	−	0.518045i	$-0.173340\pi$
$179$	22.8877	1.71071	0.855353	+	0.518045i	$0.173340\pi$
$180$	−4.29590	−0.320197
$181$	11.6039	0.862509	0.431255	−	0.902230i	$-0.358071\pi$
$181$	11.6039	0.862509	0.431255	+	0.902230i	$0.358071\pi$
$182$	0	0
$183$	−10.4940	−0.775736
$184$	3.38404	0.249475
$185$	−16.6595	−1.22483
$186$	−2.22521	−0.163160
$187$	−0.572417	−0.0418592
$188$	1.78017	0.129832
$189$	−4.35690	−0.316918
$190$	7.64742	0.554802
$191$	16.6896	1.20762	0.603810	−	0.797129i	$-0.293649\pi$
$191$	16.6896	1.20762	0.603810	+	0.797129i	$0.293649\pi$
$192$	−1.00000	−0.0721688
$193$	9.64742	0.694436	0.347218	−	0.937784i	$-0.387126\pi$
$193$	9.64742	0.694436	0.347218	+	0.937784i	$0.387126\pi$
$194$	−18.3937	−1.32059
$195$	0	0
$196$	11.9825	0.855896
$197$	19.6383	1.39917	0.699586	−	0.714548i	$-0.253368\pi$
$197$	19.6383	1.39917	0.699586	+	0.714548i	$0.253368\pi$
$198$	−1.15883	−0.0823547
$199$	−18.4209	−1.30582	−0.652911	−	0.757435i	$-0.726452\pi$
$199$	−18.4209	−1.30582	−0.652911	+	0.757435i	$0.726452\pi$
$200$	13.4547	0.951393
$201$	4.09783	0.289039
$202$	−5.46681	−0.384644
$203$	30.2325	2.12191
$204$	−0.493959	−0.0345841
$205$	−27.1400	−1.89554
$206$	7.00969	0.488388
$207$	3.38404	0.235207
$208$	0	0
$209$	2.06292	0.142695
$210$	18.7168	1.29158
$211$	15.9215	1.09608	0.548042	−	0.836451i	$-0.315373\pi$
$211$	15.9215	1.09608	0.548042	+	0.836451i	$0.315373\pi$
$212$	−2.51573	−0.172781
$213$	9.38404	0.642984
$214$	−1.91723	−0.131059
$215$	−31.7211	−2.16336
$216$	−1.00000	−0.0680414
$217$	9.69501	0.658140
$218$	−18.7681	−1.27114
$219$	0.374354	0.0252965
$220$	4.97823	0.335632
$221$	0	0
$222$	−3.87800	−0.260274
$223$	−5.18359	−0.347119	−0.173559	−	0.984823i	$-0.555527\pi$
$223$	−5.18359	−0.347119	−0.173559	+	0.984823i	$0.555527\pi$
$224$	4.35690	0.291107
$225$	13.4547	0.896982
$226$	10.4155	0.692829
$227$	14.8877	0.988131	0.494065	−	0.869425i	$-0.335510\pi$
$227$	14.8877	0.988131	0.494065	+	0.869425i	$0.335510\pi$
$228$	1.78017	0.117894
$229$	23.4577	1.55013	0.775065	−	0.631882i	$-0.217717\pi$
$229$	23.4577	1.55013	0.775065	+	0.631882i	$0.217717\pi$
$230$	−14.5375	−0.958574
$231$	5.04892	0.332194
$232$	6.93900	0.455568
$233$	−11.8780	−0.778154	−0.389077	−	0.921205i	$-0.627206\pi$
$233$	−11.8780	−0.778154	−0.389077	+	0.921205i	$0.627206\pi$
$234$	0	0
$235$	−7.64742	−0.498862
$236$	−6.63102	−0.431643
$237$	−2.65519	−0.172473
$238$	2.15213	0.139502
$239$	−25.3599	−1.64039	−0.820197	−	0.572081i	$-0.806136\pi$
$239$	−25.3599	−1.64039	−0.820197	+	0.572081i	$0.806136\pi$
$240$	4.29590	0.277299
$241$	12.0218	0.774390	0.387195	−	0.921998i	$-0.373444\pi$
$241$	12.0218	0.774390	0.387195	+	0.921998i	$0.373444\pi$
$242$	−9.65710	−0.620782
$243$	−1.00000	−0.0641500
$244$	10.4940	0.671807
$245$	−51.4758	−3.28867
$246$	−6.31767	−0.402800
$247$	0	0
$248$	2.22521	0.141301
$249$	−14.2784	−0.904859
$250$	−36.3207	−2.29712
$251$	−15.3448	−0.968556	−0.484278	−	0.874914i	$-0.660918\pi$
$251$	−15.3448	−0.968556	−0.484278	+	0.874914i	$0.660918\pi$
$252$	4.35690	0.274459
$253$	−3.92154	−0.246545
$254$	8.39373	0.526670
$255$	2.12200	0.132885
$256$	1.00000	0.0625000
$257$	−7.50604	−0.468214	−0.234107	−	0.972211i	$-0.575217\pi$
$257$	−7.50604	−0.468214	−0.234107	+	0.972211i	$0.575217\pi$
$258$	−7.38404	−0.459710
$259$	16.8961	1.04987
$260$	0	0
$261$	6.93900	0.429513
$262$	−13.5036	−0.834258
$263$	−12.2306	−0.754170	−0.377085	−	0.926179i	$-0.623074\pi$
$263$	−12.2306	−0.754170	−0.377085	+	0.926179i	$0.623074\pi$
$264$	1.15883	0.0713213
$265$	10.8073	0.663888
$266$	−7.75600	−0.475551
$267$	0.835790	0.0511495
$268$	−4.09783	−0.250315
$269$	2.71618	0.165609	0.0828044	−	0.996566i	$-0.473612\pi$
$269$	2.71618	0.165609	0.0828044	+	0.996566i	$0.473612\pi$
$270$	4.29590	0.261440
$271$	12.3937	0.752866	0.376433	−	0.926444i	$-0.377151\pi$
$271$	12.3937	0.752866	0.376433	+	0.926444i	$0.377151\pi$
$272$	0.493959	0.0299507
$273$	0	0
$274$	−4.00000	−0.241649
$275$	−15.5918	−0.940221
$276$	−3.38404	−0.203695
$277$	−24.1280	−1.44971	−0.724854	−	0.688902i	$-0.758093\pi$
$277$	−24.1280	−1.44971	−0.724854	+	0.688902i	$0.758093\pi$
$278$	−15.0315	−0.901527
$279$	2.22521	0.133220
$280$	−18.7168	−1.11854
$281$	12.8358	0.765719	0.382860	−	0.923807i	$-0.374939\pi$
$281$	12.8358	0.765719	0.382860	+	0.923807i	$0.374939\pi$
$282$	−1.78017	−0.106007
$283$	5.64742	0.335704	0.167852	−	0.985812i	$-0.446317\pi$
$283$	5.64742	0.335704	0.167852	+	0.985812i	$0.446317\pi$
$284$	−9.38404	−0.556841
$285$	−7.64742	−0.452994
$286$	0	0
$287$	27.5254	1.62477
$288$	1.00000	0.0589256
$289$	−16.7560	−0.985647
$290$	−29.8092	−1.75046
$291$	18.3937	1.07826
$292$	−0.374354	−0.0219074
$293$	21.3653	1.24817	0.624086	−	0.781356i	$-0.285472\pi$
$293$	21.3653	1.24817	0.624086	+	0.781356i	$0.285472\pi$
$294$	−11.9825	−0.698836
$295$	28.4862	1.65853
$296$	3.87800	0.225404
$297$	1.15883	0.0672423
$298$	3.92692	0.227480
$299$	0	0
$300$	−13.4547	−0.776809
$301$	32.1715	1.85433
$302$	−9.62863	−0.554065
$303$	5.46681	0.314060
$304$	−1.78017	−0.102100
$305$	−45.0810	−2.58133
$306$	0.493959	0.0282378
$307$	−28.8853	−1.64857	−0.824286	−	0.566174i	$-0.808423\pi$
$307$	−28.8853	−1.64857	−0.824286	+	0.566174i	$0.808423\pi$
$308$	−5.04892	−0.287689
$309$	−7.00969	−0.398767
$310$	−9.55927	−0.542930
$311$	3.38404	0.191891	0.0959457	−	0.995387i	$-0.469412\pi$
$311$	3.38404	0.191891	0.0959457	+	0.995387i	$0.469412\pi$
$312$	0	0
$313$	14.3502	0.811121	0.405560	−	0.914068i	$-0.367076\pi$
$313$	14.3502	0.811121	0.405560	+	0.914068i	$0.367076\pi$
$314$	−17.3840	−0.981038
$315$	−18.7168	−1.05457
$316$	2.65519	0.149366
$317$	−18.5332	−1.04093	−0.520464	−	0.853884i	$-0.674241\pi$
$317$	−18.5332	−1.04093	−0.520464	+	0.853884i	$0.674241\pi$
$318$	2.51573	0.141075
$319$	−8.04115	−0.450218
$320$	−4.29590	−0.240148
$321$	1.91723	0.107009
$322$	14.7439	0.821647
$323$	−0.879330	−0.0489272
$324$	1.00000	0.0555556
$325$	0	0
$326$	22.4698	1.24449
$327$	18.7681	1.03788
$328$	6.31767	0.348835
$329$	7.75600	0.427602
$330$	−4.97823	−0.274043
$331$	7.87800	0.433014	0.216507	−	0.976281i	$-0.430534\pi$
$331$	7.87800	0.433014	0.216507	+	0.976281i	$0.430534\pi$
$332$	14.2784	0.783631
$333$	3.87800	0.212513
$334$	0.835790	0.0457324
$335$	17.6039	0.961802
$336$	−4.35690	−0.237688
$337$	−13.7265	−0.747728	−0.373864	−	0.927484i	$-0.621967\pi$
$337$	−13.7265	−0.747728	−0.373864	+	0.927484i	$0.621967\pi$
$338$	0	0
$339$	−10.4155	−0.565692
$340$	−2.12200	−0.115081
$341$	−2.57865	−0.139642
$342$	−1.78017	−0.0962604
$343$	21.7084	1.17214
$344$	7.38404	0.398121
$345$	14.5375	0.782673
$346$	−4.17092	−0.224230
$347$	−4.85086	−0.260408	−0.130204	−	0.991487i	$-0.541563\pi$
$347$	−4.85086	−0.260408	−0.130204	+	0.991487i	$0.541563\pi$
$348$	−6.93900	−0.371970
$349$	−28.3478	−1.51742	−0.758711	−	0.651427i	$-0.774171\pi$
$349$	−28.3478	−1.51742	−0.758711	+	0.651427i	$0.774171\pi$
$350$	58.6209	3.13342
$351$	0	0
$352$	−1.15883	−0.0617660
$353$	−28.4456	−1.51401	−0.757004	−	0.653410i	$-0.773338\pi$
$353$	−28.4456	−1.51401	−0.757004	+	0.653410i	$0.773338\pi$
$354$	6.63102	0.352435
$355$	40.3129	2.13959
$356$	−0.835790	−0.0442968
$357$	−2.15213	−0.113903
$358$	22.8877	1.20965
$359$	11.2271	0.592545	0.296273	−	0.955103i	$-0.404256\pi$
$359$	11.2271	0.592545	0.296273	+	0.955103i	$0.404256\pi$
$360$	−4.29590	−0.226414
$361$	−15.8310	−0.833211
$362$	11.6039	0.609886
$363$	9.65710	0.506867
$364$	0	0
$365$	1.60819	0.0841764
$366$	−10.4940	−0.548528
$367$	16.8267	0.878346	0.439173	−	0.898402i	$-0.355271\pi$
$367$	16.8267	0.878346	0.439173	+	0.898402i	$0.355271\pi$
$368$	3.38404	0.176405
$369$	6.31767	0.328885
$370$	−16.6595	−0.866086
$371$	−10.9608	−0.569055
$372$	−2.22521	−0.115372
$373$	−26.5327	−1.37381	−0.686906	−	0.726746i	$-0.741032\pi$
$373$	−26.5327	−1.37381	−0.686906	+	0.726746i	$0.741032\pi$
$374$	−0.572417	−0.0295990
$375$	36.3207	1.87559
$376$	1.78017	0.0918051
$377$	0	0
$378$	−4.35690	−0.224095
$379$	21.9758	1.12882	0.564411	−	0.825494i	$-0.309103\pi$
$379$	21.9758	1.12882	0.564411	+	0.825494i	$0.309103\pi$
$380$	7.64742	0.392304
$381$	−8.39373	−0.430024
$382$	16.6896	0.853916
$383$	−0.615957	−0.0314739	−0.0157370	−	0.999876i	$-0.505009\pi$
$383$	−0.615957	−0.0314739	−0.0157370	+	0.999876i	$0.505009\pi$
$384$	−1.00000	−0.0510310
$385$	21.6896	1.10541
$386$	9.64742	0.491041
$387$	7.38404	0.375352
$388$	−18.3937	−0.933800
$389$	−35.5260	−1.80124	−0.900620	−	0.434607i	$-0.856887\pi$
$389$	−35.5260	−1.80124	−0.900620	+	0.434607i	$0.856887\pi$
$390$	0	0
$391$	1.67158	0.0845354
$392$	11.9825	0.605210
$393$	13.5036	0.681169
$394$	19.6383	0.989364
$395$	−11.4064	−0.573918
$396$	−1.15883	−0.0582336
$397$	−16.0785	−0.806955	−0.403477	−	0.914990i	$-0.632199\pi$
$397$	−16.0785	−0.806955	−0.403477	+	0.914990i	$0.632199\pi$
$398$	−18.4209	−0.923355
$399$	7.75600	0.388286
$400$	13.4547	0.672737
$401$	22.9095	1.14404	0.572022	−	0.820238i	$-0.306159\pi$
$401$	22.9095	1.14404	0.572022	+	0.820238i	$0.306159\pi$
$402$	4.09783	0.204381
$403$	0	0
$404$	−5.46681	−0.271984
$405$	−4.29590	−0.213465
$406$	30.2325	1.50041
$407$	−4.49396	−0.222757
$408$	−0.493959	−0.0244546
$409$	−1.24698	−0.0616592	−0.0308296	−	0.999525i	$-0.509815\pi$
$409$	−1.24698	−0.0616592	−0.0308296	+	0.999525i	$0.509815\pi$
$410$	−27.1400	−1.34035
$411$	4.00000	0.197305
$412$	7.00969	0.345343
$413$	−28.8907	−1.42162
$414$	3.38404	0.166317
$415$	−61.3387	−3.01100
$416$	0	0
$417$	15.0315	0.736094
$418$	2.06292	0.100901
$419$	29.4631	1.43937	0.719683	−	0.694303i	$-0.244287\pi$
$419$	29.4631	1.43937	0.719683	+	0.694303i	$0.244287\pi$
$420$	18.7168	0.913285
$421$	−17.3491	−0.845545	−0.422772	−	0.906236i	$-0.638943\pi$
$421$	−17.3491	−0.845545	−0.422772	+	0.906236i	$0.638943\pi$
$422$	15.9215	0.775049
$423$	1.78017	0.0865547
$424$	−2.51573	−0.122175
$425$	6.64609	0.322383
$426$	9.38404	0.454658
$427$	45.7211	2.21260
$428$	−1.91723	−0.0926728
$429$	0	0
$430$	−31.7211	−1.52973
$431$	25.3840	1.22271	0.611353	−	0.791358i	$-0.290626\pi$
$431$	25.3840	1.22271	0.611353	+	0.791358i	$0.290626\pi$
$432$	−1.00000	−0.0481125
$433$	20.0054	0.961397	0.480699	−	0.876886i	$-0.340383\pi$
$433$	20.0054	0.961397	0.480699	+	0.876886i	$0.340383\pi$
$434$	9.69501	0.465375
$435$	29.8092	1.42924
$436$	−18.7681	−0.898828
$437$	−6.02416	−0.288175
$438$	0.374354	0.0178873
$439$	0.543941	0.0259609	0.0129805	−	0.999916i	$-0.495868\pi$
$439$	0.543941	0.0259609	0.0129805	+	0.999916i	$0.495868\pi$
$440$	4.97823	0.237328
$441$	11.9825	0.570597
$442$	0	0
$443$	−18.1360	−0.861667	−0.430834	−	0.902431i	$-0.641780\pi$
$443$	−18.1360	−0.861667	−0.430834	+	0.902431i	$0.641780\pi$
$444$	−3.87800	−0.184042
$445$	3.59047	0.170204
$446$	−5.18359	−0.245450
$447$	−3.92692	−0.185737
$448$	4.35690	0.205844
$449$	29.3793	1.38649	0.693246	−	0.720701i	$-0.256180\pi$
$449$	29.3793	1.38649	0.693246	+	0.720701i	$0.256180\pi$
$450$	13.4547	0.634262
$451$	−7.32113	−0.344738
$452$	10.4155	0.489904
$453$	9.62863	0.452392
$454$	14.8877	0.698714
$455$	0	0
$456$	1.78017	0.0833640
$457$	−8.34721	−0.390466	−0.195233	−	0.980757i	$-0.562546\pi$
$457$	−8.34721	−0.390466	−0.195233	+	0.980757i	$0.562546\pi$
$458$	23.4577	1.09611
$459$	−0.493959	−0.0230560
$460$	−14.5375	−0.677814
$461$	21.4969	1.00121	0.500606	−	0.865675i	$-0.333110\pi$
$461$	21.4969	1.00121	0.500606	+	0.865675i	$0.333110\pi$
$462$	5.04892	0.234897
$463$	26.1715	1.21629	0.608147	−	0.793825i	$-0.291913\pi$
$463$	26.1715	1.21629	0.608147	+	0.793825i	$0.291913\pi$
$464$	6.93900	0.322135
$465$	9.55927	0.443301
$466$	−11.8780	−0.550238
$467$	−9.81269	−0.454077	−0.227039	−	0.973886i	$-0.572904\pi$
$467$	−9.81269	−0.454077	−0.227039	+	0.973886i	$0.572904\pi$
$468$	0	0
$469$	−17.8538	−0.824414
$470$	−7.64742	−0.352749
$471$	17.3840	0.801014
$472$	−6.63102	−0.305218
$473$	−8.55688	−0.393446
$474$	−2.65519	−0.121957
$475$	−23.9517	−1.09898
$476$	2.15213	0.0986427
$477$	−2.51573	−0.115187
$478$	−25.3599	−1.15993
$479$	17.2814	0.789608	0.394804	−	0.918765i	$-0.370812\pi$
$479$	17.2814	0.789608	0.394804	+	0.918765i	$0.370812\pi$
$480$	4.29590	0.196080
$481$	0	0
$482$	12.0218	0.547577
$483$	−14.7439	−0.670872
$484$	−9.65710	−0.438959
$485$	79.0176	3.58800
$486$	−1.00000	−0.0453609
$487$	−31.6886	−1.43595	−0.717973	−	0.696071i	$-0.754930\pi$
$487$	−31.6886	−1.43595	−0.717973	+	0.696071i	$0.754930\pi$
$488$	10.4940	0.475039
$489$	−22.4698	−1.01612
$490$	−51.4758	−2.32544
$491$	2.30367	0.103963	0.0519815	−	0.998648i	$-0.483446\pi$
$491$	2.30367	0.103963	0.0519815	+	0.998648i	$0.483446\pi$
$492$	−6.31767	−0.284822
$493$	3.42758	0.154371
$494$	0	0
$495$	4.97823	0.223755
$496$	2.22521	0.0999148
$497$	−40.8853	−1.83396
$498$	−14.2784	−0.639832
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	−36.3207	−1.62431
$501$	−0.835790	−0.0373403
$502$	−15.3448	−0.684873
$503$	−35.3685	−1.57700	−0.788502	−	0.615032i	$-0.789143\pi$
$503$	−35.3685	−1.57700	−0.788502	+	0.615032i	$0.789143\pi$
$504$	4.35690	0.194072
$505$	23.4849	1.04506
$506$	−3.92154	−0.174334
$507$	0	0
$508$	8.39373	0.372412
$509$	28.6112	1.26817	0.634084	−	0.773264i	$-0.281377\pi$
$509$	28.6112	1.26817	0.634084	+	0.773264i	$0.281377\pi$
$510$	2.12200	0.0939636
$511$	−1.63102	−0.0721522
$512$	1.00000	0.0441942
$513$	1.78017	0.0785963
$514$	−7.50604	−0.331077
$515$	−30.1129	−1.32693
$516$	−7.38404	−0.325064
$517$	−2.06292	−0.0907270
$518$	16.8961	0.742370
$519$	4.17092	0.183083
$520$	0	0
$521$	−17.1594	−0.751768	−0.375884	−	0.926667i	$-0.622661\pi$
$521$	−17.1594	−0.751768	−0.375884	+	0.926667i	$0.622661\pi$
$522$	6.93900	0.303712
$523$	16.5133	0.722078	0.361039	−	0.932551i	$-0.382422\pi$
$523$	16.5133	0.722078	0.361039	+	0.932551i	$0.382422\pi$
$524$	−13.5036	−0.589910
$525$	−58.6209	−2.55842
$526$	−12.2306	−0.533279
$527$	1.09916	0.0478803
$528$	1.15883	0.0504318
$529$	−11.5483	−0.502098
$530$	10.8073	0.469440
$531$	−6.63102	−0.287762
$532$	−7.75600	−0.336265
$533$	0	0
$534$	0.835790	0.0361682
$535$	8.23623	0.356083
$536$	−4.09783	−0.176999
$537$	−22.8877	−0.987677
$538$	2.71618	0.117103
$539$	−13.8858	−0.598103
$540$	4.29590	0.184866
$541$	−25.0858	−1.07852	−0.539260	−	0.842139i	$-0.681296\pi$
$541$	−25.0858	−1.07852	−0.539260	+	0.842139i	$0.681296\pi$
$542$	12.3937	0.532356
$543$	−11.6039	−0.497970
$544$	0.493959	0.0211783
$545$	80.6258	3.45363
$546$	0	0
$547$	31.1594	1.33228	0.666140	−	0.745826i	$-0.267945\pi$
$547$	31.1594	1.33228	0.666140	+	0.745826i	$0.267945\pi$
$548$	−4.00000	−0.170872
$549$	10.4940	0.447871
$550$	−15.5918	−0.664836
$551$	−12.3526	−0.526238
$552$	−3.38404	−0.144034
$553$	11.5684	0.491937
$554$	−24.1280	−1.02510
$555$	16.6595	0.707156
$556$	−15.0315	−0.637476
$557$	3.97584	0.168462	0.0842308	−	0.996446i	$-0.473157\pi$
$557$	3.97584	0.168462	0.0842308	+	0.996446i	$0.473157\pi$
$558$	2.22521	0.0942006
$559$	0	0
$560$	−18.7168	−0.790928
$561$	0.572417	0.0241674
$562$	12.8358	0.541445
$563$	0.602811	0.0254054	0.0127027	−	0.999919i	$-0.495956\pi$
$563$	0.602811	0.0254054	0.0127027	+	0.999919i	$0.495956\pi$
$564$	−1.78017	−0.0749586
$565$	−44.7439	−1.88239
$566$	5.64742	0.237379
$567$	4.35690	0.182972
$568$	−9.38404	−0.393746
$569$	2.21983	0.0930602	0.0465301	−	0.998917i	$-0.485184\pi$
$569$	2.21983	0.0930602	0.0465301	+	0.998917i	$0.485184\pi$
$570$	−7.64742	−0.320315
$571$	24.4155	1.02176	0.510878	−	0.859653i	$-0.329320\pi$
$571$	24.4155	1.02176	0.510878	+	0.859653i	$0.329320\pi$
$572$	0	0
$573$	−16.6896	−0.697219
$574$	27.5254	1.14889
$575$	45.5314	1.89879
$576$	1.00000	0.0416667
$577$	−20.7375	−0.863313	−0.431656	−	0.902038i	$-0.642071\pi$
$577$	−20.7375	−0.863313	−0.431656	+	0.902038i	$0.642071\pi$
$578$	−16.7560	−0.696958
$579$	−9.64742	−0.400933
$580$	−29.8092	−1.23776
$581$	62.2097	2.58089
$582$	18.3937	0.762445
$583$	2.91531	0.120740
$584$	−0.374354	−0.0154909
$585$	0	0
$586$	21.3653	0.882591
$587$	−11.3679	−0.469204	−0.234602	−	0.972092i	$-0.575379\pi$
$587$	−11.3679	−0.469204	−0.234602	+	0.972092i	$0.575379\pi$
$588$	−11.9825	−0.494152
$589$	−3.96125	−0.163220
$590$	28.4862	1.17276
$591$	−19.6383	−0.807812
$592$	3.87800	0.159385
$593$	36.7198	1.50790	0.753950	−	0.656932i	$-0.228146\pi$
$593$	36.7198	1.50790	0.753950	+	0.656932i	$0.228146\pi$
$594$	1.15883	0.0475475
$595$	−9.24532	−0.379021
$596$	3.92692	0.160853
$597$	18.4209	0.753916
$598$	0	0
$599$	−47.4965	−1.94065	−0.970327	−	0.241798i	$-0.922263\pi$
$599$	−47.4965	−1.94065	−0.970327	+	0.241798i	$0.922263\pi$
$600$	−13.4547	−0.549287
$601$	7.75063	0.316155	0.158077	−	0.987427i	$-0.449470\pi$
$601$	7.75063	0.316155	0.158077	+	0.987427i	$0.449470\pi$
$602$	32.1715	1.31121
$603$	−4.09783	−0.166877
$604$	−9.62863	−0.391783
$605$	41.4859	1.68664
$606$	5.46681	0.222074
$607$	3.64310	0.147869	0.0739345	−	0.997263i	$-0.476444\pi$
$607$	3.64310	0.147869	0.0739345	+	0.997263i	$0.476444\pi$
$608$	−1.78017	−0.0721953
$609$	−30.2325	−1.22508
$610$	−45.0810	−1.82528
$611$	0	0
$612$	0.493959	0.0199671
$613$	−30.4263	−1.22890	−0.614452	−	0.788954i	$-0.710623\pi$
$613$	−30.4263	−1.22890	−0.614452	+	0.788954i	$0.710623\pi$
$614$	−28.8853	−1.16572
$615$	27.1400	1.09439
$616$	−5.04892	−0.203427
$617$	8.16554	0.328732	0.164366	−	0.986399i	$-0.447442\pi$
$617$	8.16554	0.328732	0.164366	+	0.986399i	$0.447442\pi$
$618$	−7.00969	−0.281971
$619$	7.95646	0.319797	0.159899	−	0.987133i	$-0.448883\pi$
$619$	7.95646	0.319797	0.159899	+	0.987133i	$0.448883\pi$
$620$	−9.55927	−0.383910
$621$	−3.38404	−0.135797
$622$	3.38404	0.135688
$623$	−3.64145	−0.145892
$624$	0	0
$625$	88.7561	3.55024
$626$	14.3502	0.573549
$627$	−2.06292	−0.0823850
$628$	−17.3840	−0.693699
$629$	1.91557	0.0763790
$630$	−18.7168	−0.745694
$631$	−15.2336	−0.606439	−0.303219	−	0.952921i	$-0.598062\pi$
$631$	−15.2336	−0.606439	−0.303219	+	0.952921i	$0.598062\pi$
$632$	2.65519	0.105618
$633$	−15.9215	−0.632825
$634$	−18.5332	−0.736047
$635$	−36.0586	−1.43094
$636$	2.51573	0.0997552
$637$	0	0
$638$	−8.04115	−0.318352
$639$	−9.38404	−0.371227
$640$	−4.29590	−0.169810
$641$	−14.1909	−0.560506	−0.280253	−	0.959926i	$-0.590418\pi$
$641$	−14.1909	−0.560506	−0.280253	+	0.959926i	$0.590418\pi$
$642$	1.91723	0.0756671
$643$	−22.5569	−0.889556	−0.444778	−	0.895641i	$-0.646717\pi$
$643$	−22.5569	−0.889556	−0.444778	+	0.895641i	$0.646717\pi$
$644$	14.7439	0.580992
$645$	31.7211	1.24902
$646$	−0.879330	−0.0345968
$647$	−36.9047	−1.45087	−0.725436	−	0.688289i	$-0.758362\pi$
$647$	−36.9047	−1.45087	−0.725436	+	0.688289i	$0.758362\pi$
$648$	1.00000	0.0392837
$649$	7.68425	0.301633
$650$	0	0
$651$	−9.69501	−0.379977
$652$	22.4698	0.879985
$653$	−1.84953	−0.0723776	−0.0361888	−	0.999345i	$-0.511522\pi$
$653$	−1.84953	−0.0723776	−0.0361888	+	0.999345i	$0.511522\pi$
$654$	18.7681	0.733890
$655$	58.0103	2.26665
$656$	6.31767	0.246663
$657$	−0.374354	−0.0146050
$658$	7.75600	0.302361
$659$	18.2784	0.712027	0.356013	−	0.934481i	$-0.384136\pi$
$659$	18.2784	0.712027	0.356013	+	0.934481i	$0.384136\pi$
$660$	−4.97823	−0.193777
$661$	−3.63401	−0.141346	−0.0706732	−	0.997500i	$-0.522515\pi$
$661$	−3.63401	−0.141346	−0.0706732	+	0.997500i	$0.522515\pi$
$662$	7.87800	0.306187
$663$	0	0
$664$	14.2784	0.554111
$665$	33.3190	1.29206
$666$	3.87800	0.150270
$667$	23.4819	0.909222
$668$	0.835790	0.0323377
$669$	5.18359	0.200409
$670$	17.6039	0.680097
$671$	−12.1608	−0.469461
$672$	−4.35690	−0.168071
$673$	−6.14782	−0.236981	−0.118490	−	0.992955i	$-0.537806\pi$
$673$	−6.14782	−0.236981	−0.118490	+	0.992955i	$0.537806\pi$
$674$	−13.7265	−0.528724
$675$	−13.4547	−0.517873
$676$	0	0
$677$	−18.2892	−0.702911	−0.351455	−	0.936205i	$-0.614313\pi$
$677$	−18.2892	−0.702911	−0.351455	+	0.936205i	$0.614313\pi$
$678$	−10.4155	−0.400005
$679$	−80.1396	−3.07547
$680$	−2.12200	−0.0813749
$681$	−14.8877	−0.570498
$682$	−2.57865	−0.0987415
$683$	−3.59286	−0.137477	−0.0687385	−	0.997635i	$-0.521897\pi$
$683$	−3.59286	−0.137477	−0.0687385	+	0.997635i	$0.521897\pi$
$684$	−1.78017	−0.0680664
$685$	17.1836	0.656551
$686$	21.7084	0.828831
$687$	−23.4577	−0.894968
$688$	7.38404	0.281514
$689$	0	0
$690$	14.5375	0.553433
$691$	19.8189	0.753947	0.376974	−	0.926224i	$-0.376965\pi$
$691$	19.8189	0.753947	0.376974	+	0.926224i	$0.376965\pi$
$692$	−4.17092	−0.158554
$693$	−5.04892	−0.191793
$694$	−4.85086	−0.184136
$695$	64.5736	2.44942
$696$	−6.93900	−0.263022
$697$	3.12067	0.118204
$698$	−28.3478	−1.07298
$699$	11.8780	0.449267
$700$	58.6209	2.21566
$701$	5.25608	0.198519	0.0992596	−	0.995062i	$-0.468353\pi$
$701$	5.25608	0.198519	0.0992596	+	0.995062i	$0.468353\pi$
$702$	0	0
$703$	−6.90349	−0.260370
$704$	−1.15883	−0.0436752
$705$	7.64742	0.288018
$706$	−28.4456	−1.07057
$707$	−23.8183	−0.895781
$708$	6.63102	0.249209
$709$	−26.0978	−0.980125	−0.490062	−	0.871687i	$-0.663026\pi$
$709$	−26.0978	−0.980125	−0.490062	+	0.871687i	$0.663026\pi$
$710$	40.3129	1.51292
$711$	2.65519	0.0995772
$712$	−0.835790	−0.0313225
$713$	7.53020	0.282008
$714$	−2.15213	−0.0805414
$715$	0	0
$716$	22.8877	0.855353
$717$	25.3599	0.947082
$718$	11.2271	0.418993
$719$	50.8310	1.89568	0.947838	−	0.318752i	$-0.103264\pi$
$719$	50.8310	1.89568	0.947838	+	0.318752i	$0.103264\pi$
$720$	−4.29590	−0.160099
$721$	30.5405	1.13739
$722$	−15.8310	−0.589169
$723$	−12.0218	−0.447094
$724$	11.6039	0.431255
$725$	93.3624	3.46739
$726$	9.65710	0.358409
$727$	−20.5042	−0.760460	−0.380230	−	0.924892i	$-0.624155\pi$
$727$	−20.5042	−0.760460	−0.380230	+	0.924892i	$0.624155\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.60819	0.0595217
$731$	3.64742	0.134905
$732$	−10.4940	−0.387868
$733$	−3.26205	−0.120486	−0.0602432	−	0.998184i	$-0.519188\pi$
$733$	−3.26205	−0.120486	−0.0602432	+	0.998184i	$0.519188\pi$
$734$	16.8267	0.621085
$735$	51.4758	1.89871
$736$	3.38404	0.124737
$737$	4.74871	0.174921
$738$	6.31767	0.232557
$739$	32.8203	1.20731	0.603656	−	0.797245i	$-0.293710\pi$
$739$	32.8203	1.20731	0.603656	+	0.797245i	$0.293710\pi$
$740$	−16.6595	−0.612415
$741$	0	0
$742$	−10.9608	−0.402383
$743$	−34.9530	−1.28230	−0.641151	−	0.767415i	$-0.721543\pi$
$743$	−34.9530	−1.28230	−0.641151	+	0.767415i	$0.721543\pi$
$744$	−2.22521	−0.0815801
$745$	−16.8696	−0.618056
$746$	−26.5327	−0.971432
$747$	14.2784	0.522421
$748$	−0.572417	−0.0209296
$749$	−8.35317	−0.305218
$750$	36.3207	1.32624
$751$	−10.1661	−0.370967	−0.185484	−	0.982647i	$-0.559385\pi$
$751$	−10.1661	−0.370967	−0.185484	+	0.982647i	$0.559385\pi$
$752$	1.78017	0.0649160
$753$	15.3448	0.559196
$754$	0	0
$755$	41.3636	1.50538
$756$	−4.35690	−0.158459
$757$	−2.46383	−0.0895494	−0.0447747	−	0.998997i	$-0.514257\pi$
$757$	−2.46383	−0.0895494	−0.0447747	+	0.998997i	$0.514257\pi$
$758$	21.9758	0.798198
$759$	3.92154	0.142343
$760$	7.64742	0.277401
$761$	−42.8068	−1.55175	−0.775873	−	0.630889i	$-0.782690\pi$
$761$	−42.8068	−1.55175	−0.775873	+	0.630889i	$0.782690\pi$
$762$	−8.39373	−0.304073
$763$	−81.7706	−2.96029
$764$	16.6896	0.603810
$765$	−2.12200	−0.0767210
$766$	−0.615957	−0.0222554
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	25.4034	0.916071	0.458035	−	0.888934i	$-0.348553\pi$
$769$	25.4034	0.916071	0.458035	+	0.888934i	$0.348553\pi$
$770$	21.6896	0.781640
$771$	7.50604	0.270323
$772$	9.64742	0.347218
$773$	4.47889	0.161095	0.0805473	−	0.996751i	$-0.474333\pi$
$773$	4.47889	0.161095	0.0805473	+	0.996751i	$0.474333\pi$
$774$	7.38404	0.265414
$775$	29.9396	1.07546
$776$	−18.3937	−0.660296
$777$	−16.8961	−0.606142
$778$	−35.5260	−1.27367
$779$	−11.2465	−0.402948
$780$	0	0
$781$	10.8745	0.389122
$782$	1.67158	0.0597755
$783$	−6.93900	−0.247980
$784$	11.9825	0.427948
$785$	74.6801	2.66545
$786$	13.5036	0.481659
$787$	9.43834	0.336440	0.168220	−	0.985749i	$-0.446198\pi$
$787$	9.43834	0.336440	0.168220	+	0.985749i	$0.446198\pi$
$788$	19.6383	0.699586
$789$	12.2306	0.435420
$790$	−11.4064	−0.405822
$791$	45.3793	1.61350
$792$	−1.15883	−0.0411774
$793$	0	0
$794$	−16.0785	−0.570603
$795$	−10.8073	−0.383296
$796$	−18.4209	−0.652911
$797$	−25.2459	−0.894256	−0.447128	−	0.894470i	$-0.647553\pi$
$797$	−25.2459	−0.894256	−0.447128	+	0.894470i	$0.647553\pi$
$798$	7.75600	0.274560
$799$	0.879330	0.0311085
$800$	13.4547	0.475697
$801$	−0.835790	−0.0295312
$802$	22.9095	0.808961
$803$	0.433814	0.0153090
$804$	4.09783	0.144519
$805$	−63.3384	−2.23238
$806$	0	0
$807$	−2.71618	−0.0956142
$808$	−5.46681	−0.192322
$809$	11.7065	0.411578	0.205789	−	0.978596i	$-0.434024\pi$
$809$	11.7065	0.411578	0.205789	+	0.978596i	$0.434024\pi$
$810$	−4.29590	−0.150942
$811$	30.5628	1.07321	0.536603	−	0.843835i	$-0.319707\pi$
$811$	30.5628	1.07321	0.536603	+	0.843835i	$0.319707\pi$
$812$	30.2325	1.06095
$813$	−12.3937	−0.434667
$814$	−4.49396	−0.157513
$815$	−96.5279	−3.38123
$816$	−0.493959	−0.0172920
$817$	−13.1448	−0.459879
$818$	−1.24698	−0.0435996
$819$	0	0
$820$	−27.1400	−0.947772
$821$	−22.5593	−0.787324	−0.393662	−	0.919255i	$-0.628792\pi$
$821$	−22.5593	−0.787324	−0.393662	+	0.919255i	$0.628792\pi$
$822$	4.00000	0.139516
$823$	−14.5767	−0.508113	−0.254056	−	0.967189i	$-0.581765\pi$
$823$	−14.5767	−0.508113	−0.254056	+	0.967189i	$0.581765\pi$
$824$	7.00969	0.244194
$825$	15.5918	0.542837
$826$	−28.8907	−1.00524
$827$	20.3666	0.708216	0.354108	−	0.935205i	$-0.384785\pi$
$827$	20.3666	0.708216	0.354108	+	0.935205i	$0.384785\pi$
$828$	3.38404	0.117604
$829$	32.4107	1.12567	0.562835	−	0.826569i	$-0.309711\pi$
$829$	32.4107	1.12567	0.562835	+	0.826569i	$0.309711\pi$
$830$	−61.3387	−2.12910
$831$	24.1280	0.836990
$832$	0	0
$833$	5.91889	0.205077
$834$	15.0315	0.520497
$835$	−3.59047	−0.124253
$836$	2.06292	0.0713475
$837$	−2.22521	−0.0769145
$838$	29.4631	1.01779
$839$	−29.9409	−1.03368	−0.516838	−	0.856083i	$-0.672891\pi$
$839$	−29.9409	−1.03368	−0.516838	+	0.856083i	$0.672891\pi$
$840$	18.7168	0.645790
$841$	19.1497	0.660336
$842$	−17.3491	−0.597890
$843$	−12.8358	−0.442088
$844$	15.9215	0.548042
$845$	0	0
$846$	1.78017	0.0612034
$847$	−42.0750	−1.44571
$848$	−2.51573	−0.0863905
$849$	−5.64742	−0.193819
$850$	6.64609	0.227959
$851$	13.1233	0.449862
$852$	9.38404	0.321492
$853$	−41.8780	−1.43388	−0.716938	−	0.697137i	$-0.754457\pi$
$853$	−41.8780	−1.43388	−0.716938	+	0.697137i	$0.754457\pi$
$854$	45.7211	1.56454
$855$	7.64742	0.261536
$856$	−1.91723	−0.0655296
$857$	25.2137	0.861284	0.430642	−	0.902523i	$-0.358287\pi$
$857$	25.2137	0.861284	0.430642	+	0.902523i	$0.358287\pi$
$858$	0	0
$859$	−46.9939	−1.60341	−0.801705	−	0.597719i	$-0.796074\pi$
$859$	−46.9939	−1.60341	−0.801705	+	0.597719i	$0.796074\pi$
$860$	−31.7211	−1.08168
$861$	−27.5254	−0.938064
$862$	25.3840	0.864584
$863$	−43.6969	−1.48746	−0.743730	−	0.668480i	$-0.766945\pi$
$863$	−43.6969	−1.48746	−0.743730	+	0.668480i	$0.766945\pi$
$864$	−1.00000	−0.0340207
$865$	17.9178	0.609224
$866$	20.0054	0.679810
$867$	16.7560	0.569064
$868$	9.69501	0.329070
$869$	−3.07692	−0.104377
$870$	29.8092	1.01063
$871$	0	0
$872$	−18.7681	−0.635568
$873$	−18.3937	−0.622533
$874$	−6.02416	−0.203770
$875$	−158.245	−5.34967
$876$	0.374354	0.0126483
$877$	−12.8901	−0.435267	−0.217634	−	0.976031i	$-0.569834\pi$
$877$	−12.8901	−0.435267	−0.217634	+	0.976031i	$0.569834\pi$
$878$	0.543941	0.0183571
$879$	−21.3653	−0.720632
$880$	4.97823	0.167816
$881$	−14.9578	−0.503941	−0.251970	−	0.967735i	$-0.581079\pi$
$881$	−14.9578	−0.503941	−0.251970	+	0.967735i	$0.581079\pi$
$882$	11.9825	0.403473
$883$	−20.6896	−0.696261	−0.348131	−	0.937446i	$-0.613183\pi$
$883$	−20.6896	−0.696261	−0.348131	+	0.937446i	$0.613183\pi$
$884$	0	0
$885$	−28.4862	−0.957553
$886$	−18.1360	−0.609291
$887$	24.1849	0.812050	0.406025	−	0.913862i	$-0.366915\pi$
$887$	24.1849	0.812050	0.406025	+	0.913862i	$0.366915\pi$
$888$	−3.87800	−0.130137
$889$	36.5706	1.22654
$890$	3.59047	0.120353
$891$	−1.15883	−0.0388224
$892$	−5.18359	−0.173559
$893$	−3.16900	−0.106046
$894$	−3.92692	−0.131336
$895$	−98.3232	−3.28658
$896$	4.35690	0.145554
$897$	0	0
$898$	29.3793	0.980399
$899$	15.4407	0.514977
$900$	13.4547	0.448491
$901$	−1.24267	−0.0413993
$902$	−7.32113	−0.243767
$903$	−32.1715	−1.07060
$904$	10.4155	0.346414
$905$	−49.8491	−1.65704
$906$	9.62863	0.319890
$907$	27.2707	0.905508	0.452754	−	0.891636i	$-0.350442\pi$
$907$	27.2707	0.905508	0.452754	+	0.891636i	$0.350442\pi$
$908$	14.8877	0.494065
$909$	−5.46681	−0.181323
$910$	0	0
$911$	45.2766	1.50008	0.750041	−	0.661391i	$-0.230034\pi$
$911$	45.2766	1.50008	0.750041	+	0.661391i	$0.230034\pi$
$912$	1.78017	0.0589472
$913$	−16.5463	−0.547604
$914$	−8.34721	−0.276101
$915$	45.0810	1.49033
$916$	23.4577	0.775065
$917$	−58.8340	−1.94287
$918$	−0.493959	−0.0163031
$919$	4.68127	0.154421	0.0772104	−	0.997015i	$-0.475399\pi$
$919$	4.68127	0.154421	0.0772104	+	0.997015i	$0.475399\pi$
$920$	−14.5375	−0.479287
$921$	28.8853	0.951803
$922$	21.4969	0.707964
$923$	0	0
$924$	5.04892	0.166097
$925$	52.1775	1.71558
$926$	26.1715	0.860049
$927$	7.00969	0.230228
$928$	6.93900	0.227784
$929$	3.29099	0.107974	0.0539870	−	0.998542i	$-0.482807\pi$
$929$	3.29099	0.107974	0.0539870	+	0.998542i	$0.482807\pi$
$930$	9.55927	0.313461
$931$	−21.3309	−0.699093
$932$	−11.8780	−0.389077
$933$	−3.38404	−0.110789
$934$	−9.81269	−0.321081
$935$	2.45904	0.0804193
$936$	0	0
$937$	6.67563	0.218083	0.109042	−	0.994037i	$-0.465222\pi$
$937$	6.67563	0.218083	0.109042	+	0.994037i	$0.465222\pi$
$938$	−17.8538	−0.582949
$939$	−14.3502	−0.468301
$940$	−7.64742	−0.249431
$941$	38.9778	1.27064	0.635319	−	0.772250i	$-0.280869\pi$
$941$	38.9778	1.27064	0.635319	+	0.772250i	$0.280869\pi$
$942$	17.3840	0.566403
$943$	21.3793	0.696204
$944$	−6.63102	−0.215821
$945$	18.7168	0.608857
$946$	−8.55688	−0.278208
$947$	−40.6679	−1.32153	−0.660764	−	0.750594i	$-0.729768\pi$
$947$	−40.6679	−1.32153	−0.660764	+	0.750594i	$0.729768\pi$
$948$	−2.65519	−0.0862364
$949$	0	0
$950$	−23.9517	−0.777095
$951$	18.5332	0.600980
$952$	2.15213	0.0697509
$953$	−44.8504	−1.45285	−0.726423	−	0.687248i	$-0.758819\pi$
$953$	−44.8504	−1.45285	−0.726423	+	0.687248i	$0.758819\pi$
$954$	−2.51573	−0.0814497
$955$	−71.6969	−2.32006
$956$	−25.3599	−0.820197
$957$	8.04115	0.259933
$958$	17.2814	0.558337
$959$	−17.4276	−0.562766
$960$	4.29590	0.138649
$961$	−26.0484	−0.840272
$962$	0	0
$963$	−1.91723	−0.0617819
$964$	12.0218	0.387195
$965$	−41.4443	−1.33414
$966$	−14.7439	−0.474378
$967$	−22.4704	−0.722599	−0.361299	−	0.932450i	$-0.617667\pi$
$967$	−22.4704	−0.722599	−0.361299	+	0.932450i	$0.617667\pi$
$968$	−9.65710	−0.310391
$969$	0.879330	0.0282482
$970$	79.0176	2.53710
$971$	33.8437	1.08610	0.543048	−	0.839702i	$-0.317270\pi$
$971$	33.8437	1.08610	0.543048	+	0.839702i	$0.317270\pi$
$972$	−1.00000	−0.0320750
$973$	−65.4905	−2.09953
$974$	−31.6886	−1.01537
$975$	0	0
$976$	10.4940	0.335903
$977$	−27.2137	−0.870644	−0.435322	−	0.900275i	$-0.643365\pi$
$977$	−27.2137	−0.870644	−0.435322	+	0.900275i	$0.643365\pi$
$978$	−22.4698	−0.718505
$979$	0.968541	0.0309547
$980$	−51.4758	−1.64433
$981$	−18.7681	−0.599219
$982$	2.30367	0.0735130
$983$	50.9965	1.62654	0.813269	−	0.581889i	$-0.197686\pi$
$983$	50.9965	1.62654	0.813269	+	0.581889i	$0.197686\pi$
$984$	−6.31767	−0.201400
$985$	−84.3642	−2.68807
$986$	3.42758	0.109156
$987$	−7.75600	−0.246876
$988$	0	0
$989$	24.9879	0.794570
$990$	4.97823	0.158219
$991$	−24.2804	−0.771291	−0.385645	−	0.922647i	$-0.626021\pi$
$991$	−24.2804	−0.771291	−0.385645	+	0.922647i	$0.626021\pi$
$992$	2.22521	0.0706505
$993$	−7.87800	−0.250001
$994$	−40.8853	−1.29680
$995$	79.1342	2.50872
$996$	−14.2784	−0.452430
$997$	−4.06505	−0.128741	−0.0643707	−	0.997926i	$-0.520504\pi$
$997$	−4.06505	−0.128741	−0.0643707	+	0.997926i	$0.520504\pi$
$998$	0	0
$999$	−3.87800	−0.122695

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.a.n.1.1	yes	3
3.2	odd	2		3042.2.a.ba.1.3		3
4.3	odd	2		8112.2.a.cm.1.1		3
13.2	odd	12		1014.2.i.h.823.6		12
13.3	even	3		1014.2.e.l.529.1		6
13.4	even	6		1014.2.e.n.991.3		6
13.5	odd	4		1014.2.b.f.337.3		6
13.6	odd	12		1014.2.i.h.361.3		12
13.7	odd	12		1014.2.i.h.361.4		12
13.8	odd	4		1014.2.b.f.337.4		6
13.9	even	3		1014.2.e.l.991.1		6
13.10	even	6		1014.2.e.n.529.3		6
13.11	odd	12		1014.2.i.h.823.1		12
13.12	even	2		1014.2.a.l.1.3	✓	3
39.5	even	4		3042.2.b.o.1351.4		6
39.8	even	4		3042.2.b.o.1351.3		6
39.38	odd	2		3042.2.a.bh.1.1		3
52.51	odd	2		8112.2.a.cj.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.l.1.3	✓	3	13.12	even	2
1014.2.a.n.1.1	yes	3	1.1	even	1	trivial
1014.2.b.f.337.3		6	13.5	odd	4
1014.2.b.f.337.4		6	13.8	odd	4
1014.2.e.l.529.1		6	13.3	even	3
1014.2.e.l.991.1		6	13.9	even	3
1014.2.e.n.529.3		6	13.10	even	6
1014.2.e.n.991.3		6	13.4	even	6
1014.2.i.h.361.3		12	13.6	odd	12
1014.2.i.h.361.4		12	13.7	odd	12
1014.2.i.h.823.1		12	13.11	odd	12
1014.2.i.h.823.6		12	13.2	odd	12
3042.2.a.ba.1.3		3	3.2	odd	2
3042.2.a.bh.1.1		3	39.38	odd	2
3042.2.b.o.1351.3		6	39.8	even	4
3042.2.b.o.1351.4		6	39.5	even	4
8112.2.a.cj.1.3		3	52.51	odd	2
8112.2.a.cm.1.1		3	4.3	odd	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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.29590 q^{5} -1.00000 q^{6} +4.35690 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.29590 q^{5} -1.00000 q^{6} +4.35690 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.29590 q^{10} -1.15883 q^{11} -1.00000 q^{12} +4.35690 q^{14} +4.29590 q^{15} +1.00000 q^{16} +0.493959 q^{17} +1.00000 q^{18} -1.78017 q^{19} -4.29590 q^{20} -4.35690 q^{21} -1.15883 q^{22} +3.38404 q^{23} -1.00000 q^{24} +13.4547 q^{25} -1.00000 q^{27} +4.35690 q^{28} +6.93900 q^{29} +4.29590 q^{30} +2.22521 q^{31} +1.00000 q^{32} +1.15883 q^{33} +0.493959 q^{34} -18.7168 q^{35} +1.00000 q^{36} +3.87800 q^{37} -1.78017 q^{38} -4.29590 q^{40} +6.31767 q^{41} -4.35690 q^{42} +7.38404 q^{43} -1.15883 q^{44} -4.29590 q^{45} +3.38404 q^{46} +1.78017 q^{47} -1.00000 q^{48} +11.9825 q^{49} +13.4547 q^{50} -0.493959 q^{51} -2.51573 q^{53} -1.00000 q^{54} +4.97823 q^{55} +4.35690 q^{56} +1.78017 q^{57} +6.93900 q^{58} -6.63102 q^{59} +4.29590 q^{60} +10.4940 q^{61} +2.22521 q^{62} +4.35690 q^{63} +1.00000 q^{64} +1.15883 q^{66} -4.09783 q^{67} +0.493959 q^{68} -3.38404 q^{69} -18.7168 q^{70} -9.38404 q^{71} +1.00000 q^{72} -0.374354 q^{73} +3.87800 q^{74} -13.4547 q^{75} -1.78017 q^{76} -5.04892 q^{77} +2.65519 q^{79} -4.29590 q^{80} +1.00000 q^{81} +6.31767 q^{82} +14.2784 q^{83} -4.35690 q^{84} -2.12200 q^{85} +7.38404 q^{86} -6.93900 q^{87} -1.15883 q^{88} -0.835790 q^{89} -4.29590 q^{90} +3.38404 q^{92} -2.22521 q^{93} +1.78017 q^{94} +7.64742 q^{95} -1.00000 q^{96} -18.3937 q^{97} +11.9825 q^{98} -1.15883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + q^{5} - 3 q^{6} + 9 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + q^5 - 3 * q^6 + 9 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + q^{5} - 3 q^{6} + 9 q^{7} + 3 q^{8} + 3 q^{9} + q^{10} + 5 q^{11} - 3 q^{12} + 9 q^{14} - q^{15} + 3 q^{16} - 8 q^{17} + 3 q^{18} - 4 q^{19} + q^{20} - 9 q^{21} + 5 q^{22} - 3 q^{24} + 18 q^{25} - 3 q^{27} + 9 q^{28} + 11 q^{29} - q^{30} + 5 q^{31} + 3 q^{32} - 5 q^{33} - 8 q^{34} - 4 q^{35} + 3 q^{36} - 8 q^{37} - 4 q^{38} + q^{40} + 2 q^{41} - 9 q^{42} + 12 q^{43} + 5 q^{44} + q^{45} + 4 q^{47} - 3 q^{48} + 20 q^{49} + 18 q^{50} + 8 q^{51} + 5 q^{53} - 3 q^{54} + 18 q^{55} + 9 q^{56} + 4 q^{57} + 11 q^{58} - 5 q^{59} - q^{60} + 22 q^{61} + 5 q^{62} + 9 q^{63} + 3 q^{64} - 5 q^{66} + 6 q^{67} - 8 q^{68} - 4 q^{70} - 18 q^{71} + 3 q^{72} - 13 q^{73} - 8 q^{74} - 18 q^{75} - 4 q^{76} - 6 q^{77} + 31 q^{79} + q^{80} + 3 q^{81} + 2 q^{82} + 13 q^{83} - 9 q^{84} - 26 q^{85} + 12 q^{86} - 11 q^{87} + 5 q^{88} - 14 q^{89} + q^{90} - 5 q^{93} + 4 q^{94} + 8 q^{95} - 3 q^{96} - 23 q^{97} + 20 q^{98} + 5 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + q^5 - 3 * q^6 + 9 * q^7 + 3 * q^8 + 3 * q^9 + q^10 + 5 * q^11 - 3 * q^12 + 9 * q^14 - q^15 + 3 * q^16 - 8 * q^17 + 3 * q^18 - 4 * q^19 + q^20 - 9 * q^21 + 5 * q^22 - 3 * q^24 + 18 * q^25 - 3 * q^27 + 9 * q^28 + 11 * q^29 - q^30 + 5 * q^31 + 3 * q^32 - 5 * q^33 - 8 * q^34 - 4 * q^35 + 3 * q^36 - 8 * q^37 - 4 * q^38 + q^40 + 2 * q^41 - 9 * q^42 + 12 * q^43 + 5 * q^44 + q^45 + 4 * q^47 - 3 * q^48 + 20 * q^49 + 18 * q^50 + 8 * q^51 + 5 * q^53 - 3 * q^54 + 18 * q^55 + 9 * q^56 + 4 * q^57 + 11 * q^58 - 5 * q^59 - q^60 + 22 * q^61 + 5 * q^62 + 9 * q^63 + 3 * q^64 - 5 * q^66 + 6 * q^67 - 8 * q^68 - 4 * q^70 - 18 * q^71 + 3 * q^72 - 13 * q^73 - 8 * q^74 - 18 * q^75 - 4 * q^76 - 6 * q^77 + 31 * q^79 + q^80 + 3 * q^81 + 2 * q^82 + 13 * q^83 - 9 * q^84 - 26 * q^85 + 12 * q^86 - 11 * q^87 + 5 * q^88 - 14 * q^89 + q^90 - 5 * q^93 + 4 * q^94 + 8 * q^95 - 3 * q^96 - 23 * q^97 + 20 * q^98 + 5 * q^99

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