LMFDB - Embedded newform 483.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("483.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.837.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 1 $ x^3 - 6*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.52892$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.52892 q^{2} +1.00000 q^{3} +4.39543 q^{4} -1.52892 q^{5} +2.52892 q^{6} -1.00000 q^{7} +6.05784 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.52892 q^{2} +1.00000 q^{3} +4.39543 q^{4} -1.52892 q^{5} +2.52892 q^{6} -1.00000 q^{7} +6.05784 q^{8} +1.00000 q^{9} -3.86651 q^{10} +1.86651 q^{11} +4.39543 q^{12} +0.604574 q^{13} -2.52892 q^{14} -1.52892 q^{15} +6.52892 q^{16} -2.92434 q^{17} +2.52892 q^{18} -1.86651 q^{19} -6.72025 q^{20} -1.00000 q^{21} +4.72025 q^{22} -1.00000 q^{23} +6.05784 q^{24} -2.66241 q^{25} +1.52892 q^{26} +1.00000 q^{27} -4.39543 q^{28} +7.19133 q^{29} -3.86651 q^{30} -5.86651 q^{31} +4.39543 q^{32} +1.86651 q^{33} -7.39543 q^{34} +1.52892 q^{35} +4.39543 q^{36} -3.19133 q^{37} -4.72025 q^{38} +0.604574 q^{39} -9.26193 q^{40} -6.65736 q^{41} -2.52892 q^{42} -5.66241 q^{43} +8.20410 q^{44} -1.52892 q^{45} -2.52892 q^{46} +10.7909 q^{47} +6.52892 q^{48} +1.00000 q^{49} -6.73302 q^{50} -2.92434 q^{51} +2.65736 q^{52} -1.52892 q^{53} +2.52892 q^{54} -2.85374 q^{55} -6.05784 q^{56} -1.86651 q^{57} +18.1863 q^{58} -6.31977 q^{59} -6.72025 q^{60} -3.66241 q^{61} -14.8359 q^{62} -1.00000 q^{63} -1.94216 q^{64} -0.924344 q^{65} +4.72025 q^{66} +5.37761 q^{67} -12.8537 q^{68} -1.00000 q^{69} +3.86651 q^{70} +15.2441 q^{71} +6.05784 q^{72} +13.9822 q^{73} -8.07061 q^{74} -2.66241 q^{75} -8.20410 q^{76} -1.86651 q^{77} +1.52892 q^{78} +9.19133 q^{79} -9.98218 q^{80} +1.00000 q^{81} -16.8359 q^{82} -0.924344 q^{83} -4.39543 q^{84} +4.47108 q^{85} -14.3198 q^{86} +7.19133 q^{87} +11.3070 q^{88} +7.39543 q^{89} -3.86651 q^{90} -0.604574 q^{91} -4.39543 q^{92} -5.86651 q^{93} +27.2892 q^{94} +2.85374 q^{95} +4.39543 q^{96} +5.98218 q^{97} +2.52892 q^{98} +1.86651 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{3} + 6 q^{4} + 3 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^3 + 6 * q^4 + 3 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{3} + 6 q^{4} + 3 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 12 q^{10} + 6 q^{11} + 6 q^{12} + 9 q^{13} + 3 q^{15} + 12 q^{16} + 6 q^{17} - 6 q^{19} + 3 q^{20} - 3 q^{21} - 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} + 3 q^{27} - 6 q^{28} + 6 q^{29} - 12 q^{30} - 18 q^{31} + 6 q^{32} + 6 q^{33} - 15 q^{34} - 3 q^{35} + 6 q^{36} + 6 q^{37} + 9 q^{38} + 9 q^{39} - 21 q^{40} - 6 q^{41} - 9 q^{43} + 33 q^{44} + 3 q^{45} + 18 q^{47} + 12 q^{48} + 3 q^{49} - 21 q^{50} + 6 q^{51} - 6 q^{52} + 3 q^{53} + 15 q^{55} - 3 q^{56} - 6 q^{57} + 33 q^{58} + 3 q^{59} + 3 q^{60} - 3 q^{61} + 9 q^{62} - 3 q^{63} - 21 q^{64} + 12 q^{65} - 9 q^{66} - 21 q^{67} - 15 q^{68} - 3 q^{69} + 12 q^{70} + 9 q^{71} + 3 q^{72} + 12 q^{73} - 33 q^{74} - 33 q^{76} - 6 q^{77} - 3 q^{78} + 12 q^{79} + 3 q^{81} + 3 q^{82} + 12 q^{83} - 6 q^{84} + 21 q^{85} - 21 q^{86} + 6 q^{87} - 12 q^{88} + 15 q^{89} - 12 q^{90} - 9 q^{91} - 6 q^{92} - 18 q^{93} + 6 q^{94} - 15 q^{95} + 6 q^{96} - 12 q^{97} + 6 q^{99}+O(q^{100}) $ 3 * q + 3 * q^3 + 6 * q^4 + 3 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 12 * q^10 + 6 * q^11 + 6 * q^12 + 9 * q^13 + 3 * q^15 + 12 * q^16 + 6 * q^17 - 6 * q^19 + 3 * q^20 - 3 * q^21 - 9 * q^22 - 3 * q^23 + 3 * q^24 - 3 * q^26 + 3 * q^27 - 6 * q^28 + 6 * q^29 - 12 * q^30 - 18 * q^31 + 6 * q^32 + 6 * q^33 - 15 * q^34 - 3 * q^35 + 6 * q^36 + 6 * q^37 + 9 * q^38 + 9 * q^39 - 21 * q^40 - 6 * q^41 - 9 * q^43 + 33 * q^44 + 3 * q^45 + 18 * q^47 + 12 * q^48 + 3 * q^49 - 21 * q^50 + 6 * q^51 - 6 * q^52 + 3 * q^53 + 15 * q^55 - 3 * q^56 - 6 * q^57 + 33 * q^58 + 3 * q^59 + 3 * q^60 - 3 * q^61 + 9 * q^62 - 3 * q^63 - 21 * q^64 + 12 * q^65 - 9 * q^66 - 21 * q^67 - 15 * q^68 - 3 * q^69 + 12 * q^70 + 9 * q^71 + 3 * q^72 + 12 * q^73 - 33 * q^74 - 33 * q^76 - 6 * q^77 - 3 * q^78 + 12 * q^79 + 3 * q^81 + 3 * q^82 + 12 * q^83 - 6 * q^84 + 21 * q^85 - 21 * q^86 + 6 * q^87 - 12 * q^88 + 15 * q^89 - 12 * q^90 - 9 * q^91 - 6 * q^92 - 18 * q^93 + 6 * q^94 - 15 * q^95 + 6 * q^96 - 12 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.52892	1.78822	0.894108	−	0.447852i	$-0.147811\pi$
$2$	2.52892	1.78822	0.894108	+	0.447852i	$0.147811\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.39543	2.19771
$5$	−1.52892	−0.683753	−0.341876	−	0.939745i	$-0.611062\pi$
$5$	−1.52892	−0.683753	−0.341876	+	0.939745i	$0.611062\pi$
$6$	2.52892	1.03243
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	6.05784	2.14177
$9$	1.00000	0.333333
$10$	−3.86651	−1.22270
$11$	1.86651	0.562773	0.281387	−	0.959594i	$-0.409206\pi$
$11$	1.86651	0.562773	0.281387	+	0.959594i	$0.409206\pi$
$12$	4.39543	1.26885
$13$	0.604574	0.167679	0.0838393	−	0.996479i	$-0.473282\pi$
$13$	0.604574	0.167679	0.0838393	+	0.996479i	$0.473282\pi$
$14$	−2.52892	−0.675882
$15$	−1.52892	−0.394765
$16$	6.52892	1.63223
$17$	−2.92434	−0.709258	−0.354629	−	0.935007i	$-0.615393\pi$
$17$	−2.92434	−0.709258	−0.354629	+	0.935007i	$0.615393\pi$
$18$	2.52892	0.596072
$19$	−1.86651	−0.428206	−0.214103	−	0.976811i	$-0.568683\pi$
$19$	−1.86651	−0.428206	−0.214103	+	0.976811i	$0.568683\pi$
$20$	−6.72025	−1.50269
$21$	−1.00000	−0.218218
$22$	4.72025	1.00636
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	6.05784	1.23655
$25$	−2.66241	−0.532482
$26$	1.52892	0.299845
$27$	1.00000	0.192450
$28$	−4.39543	−0.830657
$29$	7.19133	1.33540	0.667698	−	0.744432i	$-0.267280\pi$
$29$	7.19133	1.33540	0.667698	+	0.744432i	$0.267280\pi$
$30$	−3.86651	−0.705925
$31$	−5.86651	−1.05366	−0.526828	−	0.849972i	$-0.676619\pi$
$31$	−5.86651	−1.05366	−0.526828	+	0.849972i	$0.676619\pi$
$32$	4.39543	0.777009
$33$	1.86651	0.324917
$34$	−7.39543	−1.26831
$35$	1.52892	0.258434
$36$	4.39543	0.732571
$37$	−3.19133	−0.524651	−0.262326	−	0.964979i	$-0.584489\pi$
$37$	−3.19133	−0.524651	−0.262326	+	0.964979i	$0.584489\pi$
$38$	−4.72025	−0.765725
$39$	0.604574	0.0968093
$40$	−9.26193	−1.46444
$41$	−6.65736	−1.03970	−0.519852	−	0.854256i	$-0.674013\pi$
$41$	−6.65736	−1.03970	−0.519852	+	0.854256i	$0.674013\pi$
$42$	−2.52892	−0.390221
$43$	−5.66241	−0.863509	−0.431755	−	0.901991i	$-0.642105\pi$
$43$	−5.66241	−0.863509	−0.431755	+	0.901991i	$0.642105\pi$
$44$	8.20410	1.23681
$45$	−1.52892	−0.227918
$46$	−2.52892	−0.372869
$47$	10.7909	1.57401	0.787004	−	0.616948i	$-0.211631\pi$
$47$	10.7909	1.57401	0.787004	+	0.616948i	$0.211631\pi$
$48$	6.52892	0.942368
$49$	1.00000	0.142857
$50$	−6.73302	−0.952192
$51$	−2.92434	−0.409490
$52$	2.65736	0.368510
$53$	−1.52892	−0.210013	−0.105007	−	0.994472i	$-0.533486\pi$
$53$	−1.52892	−0.210013	−0.105007	+	0.994472i	$0.533486\pi$
$54$	2.52892	0.344142
$55$	−2.85374	−0.384798
$56$	−6.05784	−0.809512
$57$	−1.86651	−0.247225
$58$	18.1863	2.38798
$59$	−6.31977	−0.822764	−0.411382	−	0.911463i	$-0.634954\pi$
$59$	−6.31977	−0.822764	−0.411382	+	0.911463i	$0.634954\pi$
$60$	−6.72025	−0.867580
$61$	−3.66241	−0.468924	−0.234462	−	0.972125i	$-0.575333\pi$
$61$	−3.66241	−0.468924	−0.234462	+	0.972125i	$0.575333\pi$
$62$	−14.8359	−1.88416
$63$	−1.00000	−0.125988
$64$	−1.94216	−0.242771
$65$	−0.924344	−0.114651
$66$	4.72025	0.581022
$67$	5.37761	0.656979	0.328490	−	0.944508i	$-0.393460\pi$
$67$	5.37761	0.656979	0.328490	+	0.944508i	$0.393460\pi$
$68$	−12.8537	−1.55874
$69$	−1.00000	−0.120386
$70$	3.86651	0.462136
$71$	15.2441	1.80914	0.904572	−	0.426321i	$-0.140191\pi$
$71$	15.2441	1.80914	0.904572	+	0.426321i	$0.140191\pi$
$72$	6.05784	0.713923
$73$	13.9822	1.63649	0.818245	−	0.574869i	$-0.194947\pi$
$73$	13.9822	1.63649	0.818245	+	0.574869i	$0.194947\pi$
$74$	−8.07061	−0.938189
$75$	−2.66241	−0.307429
$76$	−8.20410	−0.941075
$77$	−1.86651	−0.212708
$78$	1.52892	0.173116
$79$	9.19133	1.03411	0.517053	−	0.855954i	$-0.327029\pi$
$79$	9.19133	1.03411	0.517053	+	0.855954i	$0.327029\pi$
$80$	−9.98218	−1.11604
$81$	1.00000	0.111111
$82$	−16.8359	−1.85922
$83$	−0.924344	−0.101460	−0.0507300	−	0.998712i	$-0.516155\pi$
$83$	−0.924344	−0.101460	−0.0507300	+	0.998712i	$0.516155\pi$
$84$	−4.39543	−0.479580
$85$	4.47108	0.484957
$86$	−14.3198	−1.54414
$87$	7.19133	0.770991
$88$	11.3070	1.20533
$89$	7.39543	0.783914	0.391957	−	0.919984i	$-0.371798\pi$
$89$	7.39543	0.783914	0.391957	+	0.919984i	$0.371798\pi$
$90$	−3.86651	−0.407566
$91$	−0.604574	−0.0633766
$92$	−4.39543	−0.458255
$93$	−5.86651	−0.608329
$94$	27.2892	2.81466
$95$	2.85374	0.292787
$96$	4.39543	0.448606
$97$	5.98218	0.607398	0.303699	−	0.952768i	$-0.401778\pi$
$97$	5.98218	0.607398	0.303699	+	0.952768i	$0.401778\pi$
$98$	2.52892	0.255459
$99$	1.86651	0.187591
$100$	−11.7024	−1.17024
$101$	4.05279	0.403267	0.201634	−	0.979461i	$-0.435375\pi$
$101$	4.05279	0.403267	0.201634	+	0.979461i	$0.435375\pi$
$102$	−7.39543	−0.732256
$103$	−6.11567	−0.602595	−0.301298	−	0.953530i	$-0.597420\pi$
$103$	−6.11567	−0.602595	−0.301298	+	0.953530i	$0.597420\pi$
$104$	3.66241	0.359129
$105$	1.52892	0.149207
$106$	−3.86651	−0.375548
$107$	−2.33759	−0.225983	−0.112992	−	0.993596i	$-0.536043\pi$
$107$	−2.33759	−0.225983	−0.112992	+	0.993596i	$0.536043\pi$
$108$	4.39543	0.422950
$109$	−8.58675	−0.822462	−0.411231	−	0.911531i	$-0.634901\pi$
$109$	−8.58675	−0.822462	−0.411231	+	0.911531i	$0.634901\pi$
$110$	−7.21687	−0.688101
$111$	−3.19133	−0.302907
$112$	−6.52892	−0.616925
$113$	19.3776	1.82289	0.911446	−	0.411420i	$-0.134967\pi$
$113$	19.3776	1.82289	0.911446	+	0.411420i	$0.134967\pi$
$114$	−4.72025	−0.442092
$115$	1.52892	0.142572
$116$	31.6089	2.93482
$117$	0.604574	0.0558929
$118$	−15.9822	−1.47128
$119$	2.92434	0.268074
$120$	−9.26193	−0.845495
$121$	−7.51615	−0.683286
$122$	−9.26193	−0.838536
$123$	−6.65736	−0.600274
$124$	−25.7858	−2.31563
$125$	11.7152	1.04784
$126$	−2.52892	−0.225294
$127$	4.98723	0.442545	0.221273	−	0.975212i	$-0.428979\pi$
$127$	4.98723	0.442545	0.221273	+	0.975212i	$0.428979\pi$
$128$	−13.7024	−1.21113
$129$	−5.66241	−0.498547
$130$	−2.33759	−0.205020
$131$	−1.86651	−0.163078	−0.0815388	−	0.996670i	$-0.525983\pi$
$131$	−1.86651	−0.163078	−0.0815388	+	0.996670i	$0.525983\pi$
$132$	8.20410	0.714075
$133$	1.86651	0.161847
$134$	13.5995	1.17482
$135$	−1.52892	−0.131588
$136$	−17.7152	−1.51907
$137$	−15.1913	−1.29788	−0.648941	−	0.760838i	$-0.724788\pi$
$137$	−15.1913	−1.29788	−0.648941	+	0.760838i	$0.724788\pi$
$138$	−2.52892	−0.215276
$139$	−12.4711	−1.05778	−0.528892	−	0.848689i	$-0.677392\pi$
$139$	−12.4711	−1.05778	−0.528892	+	0.848689i	$0.677392\pi$
$140$	6.72025	0.567964
$141$	10.7909	0.908754
$142$	38.5511	3.23514
$143$	1.12844	0.0943651
$144$	6.52892	0.544076
$145$	−10.9950	−0.913081
$146$	35.3598	2.92640
$147$	1.00000	0.0824786
$148$	−14.0272	−1.15303
$149$	−0.523868	−0.0429170	−0.0214585	−	0.999770i	$-0.506831\pi$
$149$	−0.523868	−0.0429170	−0.0214585	+	0.999770i	$0.506831\pi$
$150$	−6.73302	−0.549748
$151$	−11.3248	−0.921601	−0.460800	−	0.887504i	$-0.652438\pi$
$151$	−11.3248	−0.921601	−0.460800	+	0.887504i	$0.652438\pi$
$152$	−11.3070	−0.917119
$153$	−2.92434	−0.236419
$154$	−4.72025	−0.380368
$155$	8.96941	0.720440
$156$	2.65736	0.212759
$157$	21.0222	1.67775	0.838877	−	0.544321i	$-0.183213\pi$
$157$	21.0222	1.67775	0.838877	+	0.544321i	$0.183213\pi$
$158$	23.2441	1.84920
$159$	−1.52892	−0.121251
$160$	−6.72025	−0.531282
$161$	1.00000	0.0788110
$162$	2.52892	0.198691
$163$	−13.3776	−1.04781	−0.523907	−	0.851775i	$-0.675526\pi$
$163$	−13.3776	−1.04781	−0.523907	+	0.851775i	$0.675526\pi$
$164$	−29.2619	−2.28497
$165$	−2.85374	−0.222163
$166$	−2.33759	−0.181432
$167$	20.5161	1.58759	0.793794	−	0.608187i	$-0.208103\pi$
$167$	20.5161	1.58759	0.793794	+	0.608187i	$0.208103\pi$
$168$	−6.05784	−0.467372
$169$	−12.6345	−0.971884
$170$	11.3070	0.867207
$171$	−1.86651	−0.142735
$172$	−24.8887	−1.89775
$173$	−1.34264	−0.102079	−0.0510395	−	0.998697i	$-0.516253\pi$
$173$	−1.34264	−0.102079	−0.0510395	+	0.998697i	$0.516253\pi$
$174$	18.1863	1.37870
$175$	2.66241	0.201259
$176$	12.1863	0.918575
$177$	−6.31977	−0.475023
$178$	18.7024	1.40181
$179$	−0.204098	−0.0152550	−0.00762751	−	0.999971i	$-0.502428\pi$
$179$	−0.204098	−0.0152550	−0.00762751	+	0.999971i	$0.502428\pi$
$180$	−6.72025	−0.500898
$181$	17.4482	1.29692	0.648458	−	0.761251i	$-0.275414\pi$
$181$	17.4482	1.29692	0.648458	+	0.761251i	$0.275414\pi$
$182$	−1.52892	−0.113331
$183$	−3.66241	−0.270733
$184$	−6.05784	−0.446590
$185$	4.87928	0.358732
$186$	−14.8359	−1.08782
$187$	−5.45831	−0.399151
$188$	47.4304	3.45922
$189$	−1.00000	−0.0727393
$190$	7.21687	0.523567
$191$	19.3248	1.39829	0.699147	−	0.714978i	$-0.253563\pi$
$191$	19.3248	1.39829	0.699147	+	0.714978i	$0.253563\pi$
$192$	−1.94216	−0.140164
$193$	−1.32482	−0.0953626	−0.0476813	−	0.998863i	$-0.515183\pi$
$193$	−1.32482	−0.0953626	−0.0476813	+	0.998863i	$0.515183\pi$
$194$	15.1284	1.08616
$195$	−0.924344	−0.0661936
$196$	4.39543	0.313959
$197$	17.5111	1.24761	0.623807	−	0.781578i	$-0.285585\pi$
$197$	17.5111	1.24761	0.623807	+	0.781578i	$0.285585\pi$
$198$	4.72025	0.335453
$199$	−22.1786	−1.57220	−0.786098	−	0.618102i	$-0.787902\pi$
$199$	−22.1786	−1.57220	−0.786098	+	0.618102i	$0.787902\pi$
$200$	−16.1284	−1.14045
$201$	5.37761	0.379307
$202$	10.2492	0.721129
$203$	−7.19133	−0.504732
$204$	−12.8537	−0.899942
$205$	10.1786	0.710901
$206$	−15.4660	−1.07757
$207$	−1.00000	−0.0695048
$208$	3.94721	0.273690
$209$	−3.48385	−0.240983
$210$	3.86651	0.266814
$211$	2.40048	0.165256	0.0826278	−	0.996580i	$-0.473669\pi$
$211$	2.40048	0.165256	0.0826278	+	0.996580i	$0.473669\pi$
$212$	−6.72025	−0.461548
$213$	15.2441	1.04451
$214$	−5.91157	−0.404107
$215$	8.65736	0.590427
$216$	6.05784	0.412184
$217$	5.86651	0.398245
$218$	−21.7152	−1.47074
$219$	13.9822	0.944828
$220$	−12.5434	−0.845675
$221$	−1.76798	−0.118927
$222$	−8.07061	−0.541664
$223$	−14.0528	−0.941044	−0.470522	−	0.882388i	$-0.655934\pi$
$223$	−14.0528	−0.941044	−0.470522	+	0.882388i	$0.655934\pi$
$224$	−4.39543	−0.293682
$225$	−2.66241	−0.177494
$226$	49.0044	3.25972
$227$	14.8537	0.985877	0.492939	−	0.870064i	$-0.335923\pi$
$227$	14.8537	0.985877	0.492939	+	0.870064i	$0.335923\pi$
$228$	−8.20410	−0.543330
$229$	−23.1106	−1.52719	−0.763596	−	0.645694i	$-0.776568\pi$
$229$	−23.1106	−1.52719	−0.763596	+	0.645694i	$0.776568\pi$
$230$	3.86651	0.254950
$231$	−1.86651	−0.122807
$232$	43.5639	2.86011
$233$	−21.1207	−1.38366	−0.691832	−	0.722058i	$-0.743196\pi$
$233$	−21.1207	−1.38366	−0.691832	+	0.722058i	$0.743196\pi$
$234$	1.52892	0.0999485
$235$	−16.4983	−1.07623
$236$	−27.7781	−1.80820
$237$	9.19133	0.597041
$238$	7.39543	0.479374
$239$	−5.64459	−0.365118	−0.182559	−	0.983195i	$-0.558438\pi$
$239$	−5.64459	−0.365118	−0.182559	+	0.983195i	$0.558438\pi$
$240$	−9.98218	−0.644347
$241$	−9.44821	−0.608613	−0.304306	−	0.952574i	$-0.598425\pi$
$241$	−9.44821	−0.608613	−0.304306	+	0.952574i	$0.598425\pi$
$242$	−19.0077	−1.22186
$243$	1.00000	0.0641500
$244$	−16.0979	−1.03056
$245$	−1.52892	−0.0976790
$246$	−16.8359	−1.07342
$247$	−1.12844	−0.0718011
$248$	−35.5383	−2.25669
$249$	−0.924344	−0.0585779
$250$	29.6268	1.87376
$251$	0.639540	0.0403674	0.0201837	−	0.999796i	$-0.493575\pi$
$251$	0.639540	0.0403674	0.0201837	+	0.999796i	$0.493575\pi$
$252$	−4.39543	−0.276886
$253$	−1.86651	−0.117346
$254$	12.6123	0.791366
$255$	4.47108	0.279990
$256$	−30.7680	−1.92300
$257$	−18.6395	−1.16270	−0.581351	−	0.813653i	$-0.697476\pi$
$257$	−18.6395	−1.16270	−0.581351	+	0.813653i	$0.697476\pi$
$258$	−14.3198	−0.891510
$259$	3.19133	0.198299
$260$	−4.06289	−0.251969
$261$	7.19133	0.445132
$262$	−4.72025	−0.291618
$263$	−25.1557	−1.55117	−0.775583	−	0.631246i	$-0.782544\pi$
$263$	−25.1557	−1.55117	−0.775583	+	0.631246i	$0.782544\pi$
$264$	11.3070	0.695898
$265$	2.33759	0.143597
$266$	4.72025	0.289417
$267$	7.39543	0.452593
$268$	23.6369	1.44385
$269$	−4.97713	−0.303461	−0.151730	−	0.988422i	$-0.548485\pi$
$269$	−4.97713	−0.303461	−0.151730	+	0.988422i	$0.548485\pi$
$270$	−3.86651	−0.235308
$271$	4.92434	0.299133	0.149566	−	0.988752i	$-0.452212\pi$
$271$	4.92434	0.299133	0.149566	+	0.988752i	$0.452212\pi$
$272$	−19.0928	−1.15767
$273$	−0.604574	−0.0365905
$274$	−38.4176	−2.32089
$275$	−4.96941	−0.299667
$276$	−4.39543	−0.264574
$277$	25.1029	1.50829	0.754144	−	0.656710i	$-0.228052\pi$
$277$	25.1029	1.50829	0.754144	+	0.656710i	$0.228052\pi$
$278$	−31.5383	−1.89154
$279$	−5.86651	−0.351219
$280$	9.26193	0.553506
$281$	26.3726	1.57325	0.786627	−	0.617428i	$-0.211825\pi$
$281$	26.3726	1.57325	0.786627	+	0.617428i	$0.211825\pi$
$282$	27.2892	1.62505
$283$	12.4354	0.739210	0.369605	−	0.929189i	$-0.379493\pi$
$283$	12.4354	0.739210	0.369605	+	0.929189i	$0.379493\pi$
$284$	67.0044	3.97598
$285$	2.85374	0.169041
$286$	2.85374	0.168745
$287$	6.65736	0.392972
$288$	4.39543	0.259003
$289$	−8.44821	−0.496954
$290$	−27.8053	−1.63279
$291$	5.98218	0.350682
$292$	61.4576	3.59654
$293$	24.3827	1.42445	0.712225	−	0.701951i	$-0.247688\pi$
$293$	24.3827	1.42445	0.712225	+	0.701951i	$0.247688\pi$
$294$	2.52892	0.147489
$295$	9.66241	0.562567
$296$	−19.3325	−1.12368
$297$	1.86651	0.108306
$298$	−1.32482	−0.0767447
$299$	−0.604574	−0.0349634
$300$	−11.7024	−0.675640
$301$	5.66241	0.326376
$302$	−28.6395	−1.64802
$303$	4.05279	0.232826
$304$	−12.1863	−0.698931
$305$	5.59952	0.320628
$306$	−7.39543	−0.422768
$307$	−6.13349	−0.350057	−0.175028	−	0.984563i	$-0.556002\pi$
$307$	−6.13349	−0.350057	−0.175028	+	0.984563i	$0.556002\pi$
$308$	−8.20410	−0.467472
$309$	−6.11567	−0.347908
$310$	22.6829	1.28830
$311$	−1.12844	−0.0639881	−0.0319940	−	0.999488i	$-0.510186\pi$
$311$	−1.12844	−0.0639881	−0.0319940	+	0.999488i	$0.510186\pi$
$312$	3.66241	0.207343
$313$	25.4304	1.43741	0.718705	−	0.695315i	$-0.244735\pi$
$313$	25.4304	1.43741	0.718705	+	0.695315i	$0.244735\pi$
$314$	53.1634	3.00018
$315$	1.52892	0.0861448
$316$	40.3998	2.27267
$317$	−7.64459	−0.429363	−0.214681	−	0.976684i	$-0.568871\pi$
$317$	−7.64459	−0.429363	−0.214681	+	0.976684i	$0.568871\pi$
$318$	−3.86651	−0.216823
$319$	13.4227	0.751525
$320$	2.96941	0.165995
$321$	−2.33759	−0.130472
$322$	2.52892	0.140931
$323$	5.45831	0.303709
$324$	4.39543	0.244190
$325$	−1.60962	−0.0892859
$326$	−33.8309	−1.87372
$327$	−8.58675	−0.474849
$328$	−40.3292	−2.22681
$329$	−10.7909	−0.594919
$330$	−7.21687	−0.397276
$331$	−10.1513	−0.557967	−0.278983	−	0.960296i	$-0.589997\pi$
$331$	−10.1513	−0.557967	−0.278983	+	0.960296i	$0.589997\pi$
$332$	−4.06289	−0.222980
$333$	−3.19133	−0.174884
$334$	51.8837	2.83895
$335$	−8.22192	−0.449211
$336$	−6.52892	−0.356182
$337$	4.60457	0.250827	0.125414	−	0.992105i	$-0.459974\pi$
$337$	4.60457	0.250827	0.125414	+	0.992105i	$0.459974\pi$
$338$	−31.9516	−1.73794
$339$	19.3776	1.05245
$340$	19.6523	1.06580
$341$	−10.9499	−0.592970
$342$	−4.72025	−0.255242
$343$	−1.00000	−0.0539949
$344$	−34.3019	−1.84944
$345$	1.52892	0.0823142
$346$	−3.39543	−0.182539
$347$	−15.5740	−0.836055	−0.418028	−	0.908434i	$-0.637278\pi$
$347$	−15.5740	−0.836055	−0.418028	+	0.908434i	$0.637278\pi$
$348$	31.6089	1.69442
$349$	25.2263	1.35033	0.675166	−	0.737666i	$-0.264072\pi$
$349$	25.2263	1.35033	0.675166	+	0.737666i	$0.264072\pi$
$350$	6.73302	0.359895
$351$	0.604574	0.0322698
$352$	8.20410	0.437280
$353$	28.5060	1.51722	0.758612	−	0.651543i	$-0.225878\pi$
$353$	28.5060	1.51722	0.758612	+	0.651543i	$0.225878\pi$
$354$	−15.9822	−0.849443
$355$	−23.3070	−1.23701
$356$	32.5060	1.72282
$357$	2.92434	0.154773
$358$	−0.516148	−0.0272792
$359$	−32.4711	−1.71376	−0.856879	−	0.515517i	$-0.827600\pi$
$359$	−32.4711	−1.71376	−0.856879	+	0.515517i	$0.827600\pi$
$360$	−9.26193	−0.488147
$361$	−15.5161	−0.816639
$362$	44.1251	2.31916
$363$	−7.51615	−0.394495
$364$	−2.65736	−0.139284
$365$	−21.3776	−1.11896
$366$	−9.26193	−0.484129
$367$	−6.87156	−0.358692	−0.179346	−	0.983786i	$-0.557398\pi$
$367$	−6.87156	−0.358692	−0.179346	+	0.983786i	$0.557398\pi$
$368$	−6.52892	−0.340343
$369$	−6.65736	−0.346568
$370$	12.3393	0.641489
$371$	1.52892	0.0793775
$372$	−25.7858	−1.33693
$373$	−10.6574	−0.551817	−0.275909	−	0.961184i	$-0.588979\pi$
$373$	−10.6574	−0.551817	−0.275909	+	0.961184i	$0.588979\pi$
$374$	−13.8036	−0.713768
$375$	11.7152	0.604970
$376$	65.3692	3.37116
$377$	4.34769	0.223917
$378$	−2.52892	−0.130074
$379$	−35.9287	−1.84553	−0.922767	−	0.385358i	$-0.874078\pi$
$379$	−35.9287	−1.84553	−0.922767	+	0.385358i	$0.874078\pi$
$380$	12.5434	0.643462
$381$	4.98723	0.255504
$382$	48.8709	2.50045
$383$	−0.657360	−0.0335895	−0.0167948	−	0.999859i	$-0.505346\pi$
$383$	−0.657360	−0.0335895	−0.0167948	+	0.999859i	$0.505346\pi$
$384$	−13.7024	−0.699249
$385$	2.85374	0.145440
$386$	−3.35036	−0.170529
$387$	−5.66241	−0.287836
$388$	26.2942	1.33489
$389$	25.4126	1.28847	0.644234	−	0.764828i	$-0.277176\pi$
$389$	25.4126	1.28847	0.644234	+	0.764828i	$0.277176\pi$
$390$	−2.33759	−0.118368
$391$	2.92434	0.147890
$392$	6.05784	0.305967
$393$	−1.86651	−0.0941529
$394$	44.2841	2.23100
$395$	−14.0528	−0.707072
$396$	8.20410	0.412271
$397$	35.7075	1.79211	0.896053	−	0.443946i	$-0.146422\pi$
$397$	35.7075	1.79211	0.896053	+	0.443946i	$0.146422\pi$
$398$	−56.0878	−2.81142
$399$	1.86651	0.0934423
$400$	−17.3827	−0.869133
$401$	19.0299	0.950309	0.475154	−	0.879902i	$-0.342392\pi$
$401$	19.0299	0.950309	0.475154	+	0.879902i	$0.342392\pi$
$402$	13.5995	0.678283
$403$	−3.54674	−0.176676
$404$	17.8137	0.886266
$405$	−1.52892	−0.0759725
$406$	−18.1863	−0.902570
$407$	−5.95664	−0.295260
$408$	−17.7152	−0.877033
$409$	−4.77303	−0.236011	−0.118006	−	0.993013i	$-0.537650\pi$
$409$	−4.77303	−0.236011	−0.118006	+	0.993013i	$0.537650\pi$
$410$	25.7407	1.27124
$411$	−15.1913	−0.749333
$412$	−26.8810	−1.32433
$413$	6.31977	0.310976
$414$	−2.52892	−0.124290
$415$	1.41325	0.0693735
$416$	2.65736	0.130288
$417$	−12.4711	−0.610712
$418$	−8.81038	−0.430930
$419$	17.6089	0.860253	0.430127	−	0.902769i	$-0.358469\pi$
$419$	17.6089	0.860253	0.430127	+	0.902769i	$0.358469\pi$
$420$	6.72025	0.327914
$421$	40.4075	1.96934	0.984671	−	0.174422i	$-0.0558056\pi$
$421$	40.4075	1.96934	0.984671	+	0.174422i	$0.0558056\pi$
$422$	6.07061	0.295512
$423$	10.7909	0.524669
$424$	−9.26193	−0.449799
$425$	7.78580	0.377667
$426$	38.5511	1.86781
$427$	3.66241	0.177236
$428$	−10.2747	−0.496647
$429$	1.12844	0.0544817
$430$	21.8938	1.05581
$431$	−28.0094	−1.34917	−0.674583	−	0.738199i	$-0.735677\pi$
$431$	−28.0094	−1.34917	−0.674583	+	0.738199i	$0.735677\pi$
$432$	6.52892	0.314123
$433$	−30.3726	−1.45961	−0.729806	−	0.683654i	$-0.760390\pi$
$433$	−30.3726	−1.45961	−0.729806	+	0.683654i	$0.760390\pi$
$434$	14.8359	0.712147
$435$	−10.9950	−0.527168
$436$	−37.7424	−1.80754
$437$	1.86651	0.0892872
$438$	35.3598	1.68956
$439$	−5.33254	−0.254508	−0.127254	−	0.991870i	$-0.540616\pi$
$439$	−5.33254	−0.254508	−0.127254	+	0.991870i	$0.540616\pi$
$440$	−17.2875	−0.824148
$441$	1.00000	0.0476190
$442$	−4.47108	−0.212668
$443$	−18.1157	−0.860702	−0.430351	−	0.902662i	$-0.641610\pi$
$443$	−18.1157	−0.860702	−0.430351	+	0.902662i	$0.641610\pi$
$444$	−14.0272	−0.665704
$445$	−11.3070	−0.536003
$446$	−35.5383	−1.68279
$447$	−0.523868	−0.0247781
$448$	1.94216	0.0917586
$449$	−33.7603	−1.59325	−0.796623	−	0.604477i	$-0.793382\pi$
$449$	−33.7603	−1.59325	−0.796623	+	0.604477i	$0.793382\pi$
$450$	−6.73302	−0.317397
$451$	−12.4260	−0.585118
$452$	85.1728	4.00619
$453$	−11.3248	−0.532086
$454$	37.5639	1.76296
$455$	0.924344	0.0433339
$456$	−11.3070	−0.529499
$457$	−1.29757	−0.0606980	−0.0303490	−	0.999539i	$-0.509662\pi$
$457$	−1.29757	−0.0606980	−0.0303490	+	0.999539i	$0.509662\pi$
$458$	−58.4449	−2.73095
$459$	−2.92434	−0.136497
$460$	6.72025	0.313333
$461$	−27.3420	−1.27344	−0.636721	−	0.771094i	$-0.719710\pi$
$461$	−27.3420	−1.27344	−0.636721	+	0.771094i	$0.719710\pi$
$462$	−4.72025	−0.219606
$463$	−24.6217	−1.14427	−0.572134	−	0.820160i	$-0.693884\pi$
$463$	−24.6217	−1.14427	−0.572134	+	0.820160i	$0.693884\pi$
$464$	46.9516	2.17967
$465$	8.96941	0.415946
$466$	−53.4126	−2.47429
$467$	−12.6574	−0.585713	−0.292856	−	0.956156i	$-0.594606\pi$
$467$	−12.6574	−0.585713	−0.292856	+	0.956156i	$0.594606\pi$
$468$	2.65736	0.122837
$469$	−5.37761	−0.248315
$470$	−41.7229	−1.92453
$471$	21.0222	0.968652
$472$	−38.2841	−1.76217
$473$	−10.5689	−0.485960
$474$	23.2441	1.06764
$475$	4.96941	0.228012
$476$	12.8537	0.589150
$477$	−1.52892	−0.0700043
$478$	−14.2747	−0.652910
$479$	7.18123	0.328119	0.164059	−	0.986450i	$-0.447541\pi$
$479$	7.18123	0.328119	0.164059	+	0.986450i	$0.447541\pi$
$480$	−6.72025	−0.306736
$481$	−1.92939	−0.0879728
$482$	−23.8938	−1.08833
$483$	1.00000	0.0455016
$484$	−33.0367	−1.50167
$485$	−9.14626	−0.415310
$486$	2.52892	0.114714
$487$	−20.8887	−0.946558	−0.473279	−	0.880913i	$-0.656930\pi$
$487$	−20.8887	−0.946558	−0.473279	+	0.880913i	$0.656930\pi$
$488$	−22.1863	−1.00433
$489$	−13.3776	−0.604956
$490$	−3.86651	−0.174671
$491$	−20.7202	−0.935092	−0.467546	−	0.883969i	$-0.654862\pi$
$491$	−20.7202	−0.935092	−0.467546	+	0.883969i	$0.654862\pi$
$492$	−29.2619	−1.31923
$493$	−21.0299	−0.947140
$494$	−2.85374	−0.128396
$495$	−2.85374	−0.128266
$496$	−38.3019	−1.71981
$497$	−15.2441	−0.683792
$498$	−2.33759	−0.104750
$499$	−7.22629	−0.323493	−0.161747	−	0.986832i	$-0.551713\pi$
$499$	−7.22629	−0.323493	−0.161747	+	0.986832i	$0.551713\pi$
$500$	51.4933	2.30285
$501$	20.5161	0.916594
$502$	1.61734	0.0721856
$503$	−32.0272	−1.42802	−0.714012	−	0.700133i	$-0.753124\pi$
$503$	−32.0272	−1.42802	−0.714012	+	0.700133i	$0.753124\pi$
$504$	−6.05784	−0.269837
$505$	−6.19638	−0.275735
$506$	−4.72025	−0.209841
$507$	−12.6345	−0.561117
$508$	21.9210	0.972587
$509$	38.3369	1.69925	0.849627	−	0.527384i	$-0.176827\pi$
$509$	38.3369	1.69925	0.849627	+	0.527384i	$0.176827\pi$
$510$	11.3070	0.500682
$511$	−13.9822	−0.618535
$512$	−50.4049	−2.22760
$513$	−1.86651	−0.0824083
$514$	−47.1379	−2.07916
$515$	9.35036	0.412026
$516$	−24.8887	−1.09566
$517$	20.1412	0.885810
$518$	8.07061	0.354602
$519$	−1.34264	−0.0589353
$520$	−5.59952	−0.245555
$521$	−31.2791	−1.37036	−0.685181	−	0.728373i	$-0.740277\pi$
$521$	−31.2791	−1.37036	−0.685181	+	0.728373i	$0.740277\pi$
$522$	18.1863	0.795992
$523$	−29.0323	−1.26949	−0.634747	−	0.772720i	$-0.718896\pi$
$523$	−29.0323	−1.26949	−0.634747	+	0.772720i	$0.718896\pi$
$524$	−8.20410	−0.358398
$525$	2.66241	0.116197
$526$	−63.6167	−2.77382
$527$	17.1557	0.747313
$528$	12.1863	0.530340
$529$	1.00000	0.0434783
$530$	5.91157	0.256782
$531$	−6.31977	−0.274255
$532$	8.20410	0.355693
$533$	−4.02487	−0.174336
$534$	18.7024	0.809333
$535$	3.57398	0.154517
$536$	32.5767	1.40710
$537$	−0.204098	−0.00880749
$538$	−12.5868	−0.542653
$539$	1.86651	0.0803962
$540$	−6.72025	−0.289193
$541$	−21.8231	−0.938250	−0.469125	−	0.883132i	$-0.655431\pi$
$541$	−21.8231	−0.938250	−0.469125	+	0.883132i	$0.655431\pi$
$542$	12.4533	0.534913
$543$	17.4482	0.748774
$544$	−12.8537	−0.551099
$545$	13.1284	0.562361
$546$	−1.52892	−0.0654316
$547$	37.7502	1.61408	0.807040	−	0.590497i	$-0.201068\pi$
$547$	37.7502	1.61408	0.807040	+	0.590497i	$0.201068\pi$
$548$	−66.7724	−2.85237
$549$	−3.66241	−0.156308
$550$	−12.5672	−0.535868
$551$	−13.4227	−0.571825
$552$	−6.05784	−0.257839
$553$	−9.19133	−0.390855
$554$	63.4832	2.69714
$555$	4.87928	0.207114
$556$	−54.8157	−2.32470
$557$	−13.8588	−0.587216	−0.293608	−	0.955926i	$-0.594856\pi$
$557$	−13.8588	−0.587216	−0.293608	+	0.955926i	$0.594856\pi$
$558$	−14.8359	−0.628054
$559$	−3.42335	−0.144792
$560$	9.98218	0.421824
$561$	−5.45831	−0.230450
$562$	66.6940	2.81332
$563$	−36.5588	−1.54077	−0.770386	−	0.637578i	$-0.779936\pi$
$563$	−36.5588	−1.54077	−0.770386	+	0.637578i	$0.779936\pi$
$564$	47.4304	1.99718
$565$	−29.6268	−1.24641
$566$	31.4482	1.32187
$567$	−1.00000	−0.0419961
$568$	92.3463	3.87477
$569$	11.3147	0.474338	0.237169	−	0.971468i	$-0.423781\pi$
$569$	11.3147	0.474338	0.237169	+	0.971468i	$0.423781\pi$
$570$	7.21687	0.302281
$571$	27.2714	1.14127	0.570635	−	0.821204i	$-0.306697\pi$
$571$	27.2714	1.14127	0.570635	+	0.821204i	$0.306697\pi$
$572$	4.95998	0.207387
$573$	19.3248	0.807306
$574$	16.8359	0.702718
$575$	2.66241	0.111030
$576$	−1.94216	−0.0809235
$577$	25.4660	1.06016	0.530082	−	0.847946i	$-0.322161\pi$
$577$	25.4660	1.06016	0.530082	+	0.847946i	$0.322161\pi$
$578$	−21.3648	−0.888660
$579$	−1.32482	−0.0550576
$580$	−48.3275	−2.00669
$581$	0.924344	0.0383483
$582$	15.1284	0.627094
$583$	−2.85374	−0.118190
$584$	84.7018	3.50498
$585$	−0.924344	−0.0382169
$586$	61.6617	2.54722
$587$	−5.16408	−0.213144	−0.106572	−	0.994305i	$-0.533988\pi$
$587$	−5.16408	−0.213144	−0.106572	+	0.994305i	$0.533988\pi$
$588$	4.39543	0.181264
$589$	10.9499	0.451182
$590$	24.4354	1.00599
$591$	17.5111	0.720310
$592$	−20.8359	−0.856351
$593$	−3.20915	−0.131784	−0.0658920	−	0.997827i	$-0.520989\pi$
$593$	−3.20915	−0.131784	−0.0658920	+	0.997827i	$0.520989\pi$
$594$	4.72025	0.193674
$595$	−4.47108	−0.183296
$596$	−2.30262	−0.0943192
$597$	−22.1786	−0.907708
$598$	−1.52892	−0.0625221
$599$	−0.186278	−0.00761112	−0.00380556	−	0.999993i	$-0.501211\pi$
$599$	−0.186278	−0.00761112	−0.00380556	+	0.999993i	$0.501211\pi$
$600$	−16.1284	−0.658441
$601$	14.1328	0.576490	0.288245	−	0.957557i	$-0.406928\pi$
$601$	14.1328	0.576490	0.288245	+	0.957557i	$0.406928\pi$
$602$	14.3198	0.583630
$603$	5.37761	0.218993
$604$	−49.7774	−2.02541
$605$	11.4916	0.467199
$606$	10.2492	0.416344
$607$	−29.8938	−1.21335	−0.606675	−	0.794950i	$-0.707497\pi$
$607$	−29.8938	−1.21335	−0.606675	+	0.794950i	$0.707497\pi$
$608$	−8.20410	−0.332720
$609$	−7.19133	−0.291407
$610$	14.1607	0.573351
$611$	6.52387	0.263927
$612$	−12.8537	−0.519582
$613$	−27.5282	−1.11186	−0.555928	−	0.831231i	$-0.687637\pi$
$613$	−27.5282	−1.11186	−0.555928	+	0.831231i	$0.687637\pi$
$614$	−15.5111	−0.625977
$615$	10.1786	0.410439
$616$	−11.3070	−0.455572
$617$	35.0572	1.41135	0.705674	−	0.708537i	$-0.250644\pi$
$617$	35.0572	1.41135	0.705674	+	0.708537i	$0.250644\pi$
$618$	−15.4660	−0.622135
$619$	21.1284	0.849224	0.424612	−	0.905375i	$-0.360411\pi$
$619$	21.1284	0.849224	0.424612	+	0.905375i	$0.360411\pi$
$620$	39.4244	1.58332
$621$	−1.00000	−0.0401286
$622$	−2.85374	−0.114424
$623$	−7.39543	−0.296291
$624$	3.94721	0.158015
$625$	−4.59952	−0.183981
$626$	64.3114	2.57040
$627$	−3.48385	−0.139132
$628$	92.4015	3.68722
$629$	9.33254	0.372113
$630$	3.86651	0.154045
$631$	37.0145	1.47352	0.736761	−	0.676153i	$-0.236354\pi$
$631$	37.0145	1.47352	0.736761	+	0.676153i	$0.236354\pi$
$632$	55.6796	2.21481
$633$	2.40048	0.0954103
$634$	−19.3325	−0.767793
$635$	−7.62506	−0.302591
$636$	−6.72025	−0.266475
$637$	0.604574	0.0239541
$638$	33.9448	1.34389
$639$	15.2441	0.603048
$640$	20.9499	0.828117
$641$	−39.9993	−1.57988	−0.789939	−	0.613185i	$-0.789888\pi$
$641$	−39.9993	−1.57988	−0.789939	+	0.613185i	$0.789888\pi$
$642$	−5.91157	−0.233311
$643$	−31.9193	−1.25877	−0.629387	−	0.777092i	$-0.716694\pi$
$643$	−31.9193	−1.25877	−0.629387	+	0.777092i	$0.716694\pi$
$644$	4.39543	0.173204
$645$	8.65736	0.340883
$646$	13.8036	0.543096
$647$	−19.1005	−0.750919	−0.375460	−	0.926839i	$-0.622515\pi$
$647$	−19.1005	−0.750919	−0.375460	+	0.926839i	$0.622515\pi$
$648$	6.05784	0.237974
$649$	−11.7959	−0.463030
$650$	−4.07061	−0.159662
$651$	5.86651	0.229927
$652$	−58.8003	−2.30280
$653$	−26.3998	−1.03310	−0.516552	−	0.856256i	$-0.672785\pi$
$653$	−26.3998	−1.03310	−0.516552	+	0.856256i	$0.672785\pi$
$654$	−21.7152	−0.849131
$655$	2.85374	0.111505
$656$	−43.4654	−1.69704
$657$	13.9822	0.545497
$658$	−27.2892	−1.06384
$659$	7.98218	0.310942	0.155471	−	0.987840i	$-0.450311\pi$
$659$	7.98218	0.310942	0.155471	+	0.987840i	$0.450311\pi$
$660$	−12.5434	−0.488251
$661$	45.6796	1.77673	0.888364	−	0.459139i	$-0.151842\pi$
$661$	45.6796	1.77673	0.888364	+	0.459139i	$0.151842\pi$
$662$	−25.6718	−0.997764
$663$	−1.76798	−0.0686627
$664$	−5.59952	−0.217304
$665$	−2.85374	−0.110663
$666$	−8.07061	−0.312730
$667$	−7.19133	−0.278449
$668$	90.1772	3.48906
$669$	−14.0528	−0.543312
$670$	−20.7926	−0.803287
$671$	−6.83592	−0.263898
$672$	−4.39543	−0.169557
$673$	23.0501	0.888517	0.444258	−	0.895899i	$-0.353467\pi$
$673$	23.0501	0.888517	0.444258	+	0.895899i	$0.353467\pi$
$674$	11.6446	0.448533
$675$	−2.66241	−0.102476
$676$	−55.5340	−2.13592
$677$	24.0350	0.923739	0.461869	−	0.886948i	$-0.347179\pi$
$677$	24.0350	0.923739	0.461869	+	0.886948i	$0.347179\pi$
$678$	49.0044	1.88200
$679$	−5.98218	−0.229575
$680$	27.0851	1.03867
$681$	14.8537	0.569196
$682$	−27.6914	−1.06036
$683$	23.5740	0.902033	0.451017	−	0.892516i	$-0.351061\pi$
$683$	23.5740	0.902033	0.451017	+	0.892516i	$0.351061\pi$
$684$	−8.20410	−0.313692
$685$	23.2263	0.887431
$686$	−2.52892	−0.0965545
$687$	−23.1106	−0.881725
$688$	−36.9694	−1.40945
$689$	−0.924344	−0.0352147
$690$	3.86651	0.147195
$691$	−26.2663	−0.999218	−0.499609	−	0.866251i	$-0.666523\pi$
$691$	−26.2663	−0.999218	−0.499609	+	0.866251i	$0.666523\pi$
$692$	−5.90147	−0.224340
$693$	−1.86651	−0.0709028
$694$	−39.3853	−1.49505
$695$	19.0673	0.723262
$696$	43.5639	1.65128
$697$	19.4684	0.737419
$698$	63.7952	2.41468
$699$	−21.1207	−0.798859
$700$	11.7024	0.442310
$701$	34.8282	1.31544	0.657721	−	0.753261i	$-0.271520\pi$
$701$	34.8282	1.31544	0.657721	+	0.753261i	$0.271520\pi$
$702$	1.52892	0.0577053
$703$	5.95664	0.224659
$704$	−3.62506	−0.136625
$705$	−16.4983	−0.621363
$706$	72.0895	2.71312
$707$	−4.05279	−0.152421
$708$	−27.7781	−1.04396
$709$	10.4176	0.391242	0.195621	−	0.980680i	$-0.437328\pi$
$709$	10.4176	0.391242	0.195621	+	0.980680i	$0.437328\pi$
$710$	−58.9415	−2.21203
$711$	9.19133	0.344702
$712$	44.8003	1.67896
$713$	5.86651	0.219702
$714$	7.39543	0.276767
$715$	−1.72530	−0.0645224
$716$	−0.897099	−0.0335261
$717$	−5.64459	−0.210801
$718$	−82.1167	−3.06457
$719$	10.2593	0.382606	0.191303	−	0.981531i	$-0.438729\pi$
$719$	10.2593	0.382606	0.191303	+	0.981531i	$0.438729\pi$
$720$	−9.98218	−0.372014
$721$	6.11567	0.227760
$722$	−39.2391	−1.46033
$723$	−9.44821	−0.351383
$724$	76.6923	2.85025
$725$	−19.1463	−0.711074
$726$	−19.0077	−0.705443
$727$	−31.4328	−1.16578	−0.582888	−	0.812552i	$-0.698078\pi$
$727$	−31.4328	−1.16578	−0.582888	+	0.812552i	$0.698078\pi$
$728$	−3.66241	−0.135738
$729$	1.00000	0.0370370
$730$	−54.0622	−2.00093
$731$	16.5588	0.612451
$732$	−16.0979	−0.594994
$733$	1.32482	0.0489333	0.0244667	−	0.999701i	$-0.492211\pi$
$733$	1.32482	0.0489333	0.0244667	+	0.999701i	$0.492211\pi$
$734$	−17.3776	−0.641419
$735$	−1.52892	−0.0563950
$736$	−4.39543	−0.162018
$737$	10.0373	0.369730
$738$	−16.8359	−0.619739
$739$	1.33254	0.0490183	0.0245091	−	0.999700i	$-0.492198\pi$
$739$	1.33254	0.0490183	0.0245091	+	0.999700i	$0.492198\pi$
$740$	21.4465	0.788389
$741$	−1.12844	−0.0414544
$742$	3.86651	0.141944
$743$	8.06289	0.295799	0.147899	−	0.989002i	$-0.452749\pi$
$743$	8.06289	0.295799	0.147899	+	0.989002i	$0.452749\pi$
$744$	−35.5383	−1.30290
$745$	0.800952	0.0293446
$746$	−26.9516	−0.986768
$747$	−0.924344	−0.0338200
$748$	−23.9916	−0.877220
$749$	2.33759	0.0854137
$750$	29.6268	1.08182
$751$	8.39980	0.306513	0.153257	−	0.988186i	$-0.451024\pi$
$751$	8.39980	0.306513	0.153257	+	0.988186i	$0.451024\pi$
$752$	70.4526	2.56914
$753$	0.639540	0.0233061
$754$	10.9950	0.400412
$755$	17.3147	0.630147
$756$	−4.39543	−0.159860
$757$	2.95998	0.107582	0.0537912	−	0.998552i	$-0.482869\pi$
$757$	2.95998	0.107582	0.0537912	+	0.998552i	$0.482869\pi$
$758$	−90.8608	−3.30021
$759$	−1.86651	−0.0677500
$760$	17.2875	0.627083
$761$	−47.7774	−1.73193	−0.865965	−	0.500105i	$-0.833295\pi$
$761$	−47.7774	−1.73193	−0.865965	+	0.500105i	$0.833295\pi$
$762$	12.6123	0.456895
$763$	8.58675	0.310861
$764$	84.9408	3.07305
$765$	4.47108	0.161652
$766$	−1.66241	−0.0600653
$767$	−3.82077	−0.137960
$768$	−30.7680	−1.11024
$769$	44.7196	1.61263	0.806315	−	0.591487i	$-0.201459\pi$
$769$	44.7196	1.61263	0.806315	+	0.591487i	$0.201459\pi$
$770$	7.21687	0.260078
$771$	−18.6395	−0.671287
$772$	−5.82315	−0.209580
$773$	22.2848	0.801529	0.400764	−	0.916181i	$-0.368745\pi$
$773$	22.2848	0.801529	0.400764	+	0.916181i	$0.368745\pi$
$774$	−14.3198	−0.514714
$775$	15.6190	0.561053
$776$	36.2391	1.30091
$777$	3.19133	0.114488
$778$	64.2663	2.30406
$779$	12.4260	0.445208
$780$	−4.06289	−0.145475
$781$	28.4533	1.01814
$782$	7.39543	0.264460
$783$	7.19133	0.256997
$784$	6.52892	0.233176
$785$	−32.1412	−1.14717
$786$	−4.72025	−0.168366
$787$	−13.9472	−0.497164	−0.248582	−	0.968611i	$-0.579965\pi$
$787$	−13.9472	−0.497164	−0.248582	+	0.968611i	$0.579965\pi$
$788$	76.9687	2.74190
$789$	−25.1557	−0.895566
$790$	−35.5383	−1.26440
$791$	−19.3776	−0.688988
$792$	11.3070	0.401777
$793$	−2.21420	−0.0786285
$794$	90.3013	3.20467
$795$	2.33759	0.0829058
$796$	−97.4842	−3.45524
$797$	−26.3369	−0.932901	−0.466451	−	0.884547i	$-0.654468\pi$
$797$	−26.3369	−0.932901	−0.466451	+	0.884547i	$0.654468\pi$
$798$	4.72025	0.167095
$799$	−31.5562	−1.11638
$800$	−11.7024	−0.413743
$801$	7.39543	0.261305
$802$	48.1251	1.69936
$803$	26.0979	0.920973
$804$	23.6369	0.833608
$805$	−1.52892	−0.0538873
$806$	−8.96941	−0.315934
$807$	−4.97713	−0.175203
$808$	24.5511	0.863705
$809$	−36.7101	−1.29066	−0.645330	−	0.763904i	$-0.723280\pi$
$809$	−36.7101	−1.29066	−0.645330	+	0.763904i	$0.723280\pi$
$810$	−3.86651	−0.135855
$811$	10.7730	0.378292	0.189146	−	0.981949i	$-0.439428\pi$
$811$	10.7730	0.378292	0.189146	+	0.981949i	$0.439428\pi$
$812$	−31.6089	−1.10926
$813$	4.92434	0.172704
$814$	−15.0639	−0.527988
$815$	20.4533	0.716447
$816$	−19.0928	−0.668382
$817$	10.5689	0.369760
$818$	−12.0706	−0.422039
$819$	−0.604574	−0.0211255
$820$	44.7391	1.56236
$821$	−10.1258	−0.353392	−0.176696	−	0.984265i	$-0.556541\pi$
$821$	−10.1258	−0.353392	−0.176696	+	0.984265i	$0.556541\pi$
$822$	−38.4176	−1.33997
$823$	29.6446	1.03335	0.516673	−	0.856183i	$-0.327170\pi$
$823$	29.6446	1.03335	0.516673	+	0.856183i	$0.327170\pi$
$824$	−37.0477	−1.29062
$825$	−4.96941	−0.173013
$826$	15.9822	0.556091
$827$	42.4253	1.47527	0.737637	−	0.675198i	$-0.235942\pi$
$827$	42.4253	1.47527	0.737637	+	0.675198i	$0.235942\pi$
$828$	−4.39543	−0.152752
$829$	−3.97208	−0.137956	−0.0689780	−	0.997618i	$-0.521974\pi$
$829$	−3.97208	−0.137956	−0.0689780	+	0.997618i	$0.521974\pi$
$830$	3.57398	0.124055
$831$	25.1029	0.870810
$832$	−1.17418	−0.0407074
$833$	−2.92434	−0.101323
$834$	−31.5383	−1.09208
$835$	−31.3675	−1.08552
$836$	−15.3130	−0.529612
$837$	−5.86651	−0.202776
$838$	44.5316	1.53832
$839$	−21.8938	−0.755856	−0.377928	−	0.925835i	$-0.623363\pi$
$839$	−21.8938	−0.755856	−0.377928	+	0.925835i	$0.623363\pi$
$840$	9.26193	0.319567
$841$	22.7152	0.783283
$842$	102.187	3.52161
$843$	26.3726	0.908319
$844$	10.5511	0.363184
$845$	19.3171	0.664528
$846$	27.2892	0.938221
$847$	7.51615	0.258258
$848$	−9.98218	−0.342789
$849$	12.4354	0.426783
$850$	19.6897	0.675350
$851$	3.19133	0.109397
$852$	67.0044	2.29553
$853$	−1.02220	−0.0349993	−0.0174997	−	0.999847i	$-0.505571\pi$
$853$	−1.02220	−0.0349993	−0.0174997	+	0.999847i	$0.505571\pi$
$854$	9.26193	0.316937
$855$	2.85374	0.0975958
$856$	−14.1607	−0.484004
$857$	39.6718	1.35516	0.677582	−	0.735447i	$-0.263028\pi$
$857$	39.6718	1.35516	0.677582	+	0.735447i	$0.263028\pi$
$858$	2.85374	0.0974250
$859$	47.1278	1.60798	0.803989	−	0.594644i	$-0.202707\pi$
$859$	47.1278	1.60798	0.803989	+	0.594644i	$0.202707\pi$
$860$	38.0528	1.29759
$861$	6.65736	0.226882
$862$	−70.8335	−2.41260
$863$	−16.1258	−0.548928	−0.274464	−	0.961597i	$-0.588500\pi$
$863$	−16.1258	−0.548928	−0.274464	+	0.961597i	$0.588500\pi$
$864$	4.39543	0.149535
$865$	2.05279	0.0697968
$866$	−76.8097	−2.61010
$867$	−8.44821	−0.286916
$868$	25.7858	0.875227
$869$	17.1557	0.581967
$870$	−27.8053	−0.942689
$871$	3.25116	0.110161
$872$	−52.0171	−1.76152
$873$	5.98218	0.202466
$874$	4.72025	0.159665
$875$	−11.7152	−0.396046
$876$	61.4576	2.07646
$877$	34.2670	1.15711	0.578557	−	0.815642i	$-0.303616\pi$
$877$	34.2670	1.15711	0.578557	+	0.815642i	$0.303616\pi$
$878$	−13.4856	−0.455116
$879$	24.3827	0.822407
$880$	−18.6318	−0.628079
$881$	−19.2091	−0.647173	−0.323586	−	0.946199i	$-0.604889\pi$
$881$	−19.2091	−0.647173	−0.323586	+	0.946199i	$0.604889\pi$
$882$	2.52892	0.0851531
$883$	46.4432	1.56294	0.781468	−	0.623945i	$-0.214471\pi$
$883$	46.4432	1.56294	0.781468	+	0.623945i	$0.214471\pi$
$884$	−7.77104	−0.261368
$885$	9.66241	0.324798
$886$	−45.8130	−1.53912
$887$	42.0350	1.41140	0.705698	−	0.708513i	$-0.250634\pi$
$887$	42.0350	1.41140	0.705698	+	0.708513i	$0.250634\pi$
$888$	−19.3325	−0.648758
$889$	−4.98723	−0.167266
$890$	−28.5945	−0.958489
$891$	1.86651	0.0625304
$892$	−61.7680	−2.06815
$893$	−20.1412	−0.674000
$894$	−1.32482	−0.0443086
$895$	0.312049	0.0104307
$896$	13.7024	0.457766
$897$	−0.604574	−0.0201861
$898$	−85.3769	−2.84907
$899$	−42.1880	−1.40705
$900$	−11.7024	−0.390081
$901$	4.47108	0.148953
$902$	−31.4244	−1.04632
$903$	5.66241	0.188433
$904$	117.386	3.90421
$905$	−26.6769	−0.886770
$906$	−28.6395	−0.951485
$907$	35.6547	1.18389	0.591947	−	0.805977i	$-0.298359\pi$
$907$	35.6547	1.18389	0.591947	+	0.805977i	$0.298359\pi$
$908$	65.2885	2.16668
$909$	4.05279	0.134422
$910$	2.33759	0.0774904
$911$	−3.32482	−0.110156	−0.0550781	−	0.998482i	$-0.517541\pi$
$911$	−3.32482	−0.110156	−0.0550781	+	0.998482i	$0.517541\pi$
$912$	−12.1863	−0.403528
$913$	−1.72530	−0.0570989
$914$	−3.28146	−0.108541
$915$	5.59952	0.185115
$916$	−101.581	−3.35633
$917$	1.86651	0.0616375
$918$	−7.39543	−0.244085
$919$	−29.8665	−0.985205	−0.492603	−	0.870254i	$-0.663954\pi$
$919$	−29.8665	−0.985205	−0.492603	+	0.870254i	$0.663954\pi$
$920$	9.26193	0.305357
$921$	−6.13349	−0.202105
$922$	−69.1456	−2.27719
$923$	9.21619	0.303355
$924$	−8.20410	−0.269895
$925$	8.49662	0.279367
$926$	−62.2663	−2.04620
$927$	−6.11567	−0.200865
$928$	31.6089	1.03761
$929$	−5.15636	−0.169175	−0.0845874	−	0.996416i	$-0.526957\pi$
$929$	−5.15636	−0.169175	−0.0845874	+	0.996416i	$0.526957\pi$
$930$	22.6829	0.743802
$931$	−1.86651	−0.0611723
$932$	−92.8346	−3.04090
$933$	−1.12844	−0.0369435
$934$	−32.0094	−1.04738
$935$	8.34531	0.272921
$936$	3.66241	0.119710
$937$	−47.1200	−1.53934	−0.769672	−	0.638439i	$-0.779580\pi$
$937$	−47.1200	−1.53934	−0.769672	+	0.638439i	$0.779580\pi$
$938$	−13.5995	−0.444040
$939$	25.4304	0.829889
$940$	−72.5172	−2.36525
$941$	−10.7808	−0.351442	−0.175721	−	0.984440i	$-0.556226\pi$
$941$	−10.7808	−0.351442	−0.175721	+	0.984440i	$0.556226\pi$
$942$	53.1634	1.73216
$943$	6.65736	0.216793
$944$	−41.2613	−1.34294
$945$	1.52892	0.0497357
$946$	−26.7280	−0.869001
$947$	42.0800	1.36742	0.683709	−	0.729755i	$-0.260366\pi$
$947$	42.0800	1.36742	0.683709	+	0.729755i	$0.260366\pi$
$948$	40.3998	1.31212
$949$	8.45326	0.274404
$950$	12.5672	0.407735
$951$	−7.64459	−0.247893
$952$	17.7152	0.574153
$953$	−28.8716	−0.935241	−0.467621	−	0.883929i	$-0.654889\pi$
$953$	−28.8716	−0.935241	−0.467621	+	0.883929i	$0.654889\pi$
$954$	−3.86651	−0.125183
$955$	−29.5461	−0.956088
$956$	−24.8104	−0.802425
$957$	13.4227	0.433893
$958$	18.1607	0.586747
$959$	15.1913	0.490554
$960$	2.96941	0.0958373
$961$	3.41592	0.110191
$962$	−4.87928	−0.157314
$963$	−2.33759	−0.0753278
$964$	−41.5289	−1.33756
$965$	2.02554	0.0652045
$966$	2.52892	0.0813666
$967$	30.8964	0.993562	0.496781	−	0.867876i	$-0.334515\pi$
$967$	30.8964	0.993562	0.496781	+	0.867876i	$0.334515\pi$
$968$	−45.5316	−1.46344
$969$	5.45831	0.175346
$970$	−23.1301	−0.742664
$971$	−24.4176	−0.783599	−0.391799	−	0.920051i	$-0.628147\pi$
$971$	−24.4176	−0.783599	−0.391799	+	0.920051i	$0.628147\pi$
$972$	4.39543	0.140983
$973$	12.4711	0.399805
$974$	−52.8258	−1.69265
$975$	−1.60962	−0.0515492
$976$	−23.9116	−0.765391
$977$	6.86146	0.219518	0.109759	−	0.993958i	$-0.464992\pi$
$977$	6.86146	0.219518	0.109759	+	0.993958i	$0.464992\pi$
$978$	−33.8309	−1.08179
$979$	13.8036	0.441166
$980$	−6.72025	−0.214670
$981$	−8.58675	−0.274154
$982$	−52.3998	−1.67214
$983$	44.9243	1.43286	0.716432	−	0.697657i	$-0.245774\pi$
$983$	44.9243	1.43286	0.716432	+	0.697657i	$0.245774\pi$
$984$	−40.3292	−1.28565
$985$	−26.7730	−0.853060
$986$	−53.1829	−1.69369
$987$	−10.7909	−0.343477
$988$	−4.95998	−0.157798
$989$	5.66241	0.180054
$990$	−7.21687	−0.229367
$991$	8.31205	0.264041	0.132020	−	0.991247i	$-0.457854\pi$
$991$	8.31205	0.264041	0.132020	+	0.991247i	$0.457854\pi$
$992$	−25.7858	−0.818700
$993$	−10.1513	−0.322142
$994$	−38.5511	−1.22277
$995$	33.9092	1.07499
$996$	−4.06289	−0.128737
$997$	−22.3191	−0.706853	−0.353426	−	0.935462i	$-0.614984\pi$
$997$	−22.3191	−0.706853	−0.353426	+	0.935462i	$0.614984\pi$
$998$	−18.2747	−0.578476
$999$	−3.19133	−0.100969

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.a.h.1.3	✓	3
3.2	odd	2		1449.2.a.l.1.1		3
4.3	odd	2		7728.2.a.bt.1.1		3
7.6	odd	2		3381.2.a.v.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.h.1.3	✓	3	1.1	even	1	trivial
1449.2.a.l.1.1		3	3.2	odd	2
3381.2.a.v.1.3		3	7.6	odd	2
7728.2.a.bt.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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q+2.52892 q^{2} +1.00000 q^{3} +4.39543 q^{4} -1.52892 q^{5} +2.52892 q^{6} -1.00000 q^{7} +6.05784 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.52892 q^{2} +1.00000 q^{3} +4.39543 q^{4} -1.52892 q^{5} +2.52892 q^{6} -1.00000 q^{7} +6.05784 q^{8} +1.00000 q^{9} -3.86651 q^{10} +1.86651 q^{11} +4.39543 q^{12} +0.604574 q^{13} -2.52892 q^{14} -1.52892 q^{15} +6.52892 q^{16} -2.92434 q^{17} +2.52892 q^{18} -1.86651 q^{19} -6.72025 q^{20} -1.00000 q^{21} +4.72025 q^{22} -1.00000 q^{23} +6.05784 q^{24} -2.66241 q^{25} +1.52892 q^{26} +1.00000 q^{27} -4.39543 q^{28} +7.19133 q^{29} -3.86651 q^{30} -5.86651 q^{31} +4.39543 q^{32} +1.86651 q^{33} -7.39543 q^{34} +1.52892 q^{35} +4.39543 q^{36} -3.19133 q^{37} -4.72025 q^{38} +0.604574 q^{39} -9.26193 q^{40} -6.65736 q^{41} -2.52892 q^{42} -5.66241 q^{43} +8.20410 q^{44} -1.52892 q^{45} -2.52892 q^{46} +10.7909 q^{47} +6.52892 q^{48} +1.00000 q^{49} -6.73302 q^{50} -2.92434 q^{51} +2.65736 q^{52} -1.52892 q^{53} +2.52892 q^{54} -2.85374 q^{55} -6.05784 q^{56} -1.86651 q^{57} +18.1863 q^{58} -6.31977 q^{59} -6.72025 q^{60} -3.66241 q^{61} -14.8359 q^{62} -1.00000 q^{63} -1.94216 q^{64} -0.924344 q^{65} +4.72025 q^{66} +5.37761 q^{67} -12.8537 q^{68} -1.00000 q^{69} +3.86651 q^{70} +15.2441 q^{71} +6.05784 q^{72} +13.9822 q^{73} -8.07061 q^{74} -2.66241 q^{75} -8.20410 q^{76} -1.86651 q^{77} +1.52892 q^{78} +9.19133 q^{79} -9.98218 q^{80} +1.00000 q^{81} -16.8359 q^{82} -0.924344 q^{83} -4.39543 q^{84} +4.47108 q^{85} -14.3198 q^{86} +7.19133 q^{87} +11.3070 q^{88} +7.39543 q^{89} -3.86651 q^{90} -0.604574 q^{91} -4.39543 q^{92} -5.86651 q^{93} +27.2892 q^{94} +2.85374 q^{95} +4.39543 q^{96} +5.98218 q^{97} +2.52892 q^{98} +1.86651 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} + 6 q^{4} + 3 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^3 + 6 * q^4 + 3 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{3} + 6 q^{4} + 3 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 12 q^{10} + 6 q^{11} + 6 q^{12} + 9 q^{13} + 3 q^{15} + 12 q^{16} + 6 q^{17} - 6 q^{19} + 3 q^{20} - 3 q^{21} - 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} + 3 q^{27} - 6 q^{28} + 6 q^{29} - 12 q^{30} - 18 q^{31} + 6 q^{32} + 6 q^{33} - 15 q^{34} - 3 q^{35} + 6 q^{36} + 6 q^{37} + 9 q^{38} + 9 q^{39} - 21 q^{40} - 6 q^{41} - 9 q^{43} + 33 q^{44} + 3 q^{45} + 18 q^{47} + 12 q^{48} + 3 q^{49} - 21 q^{50} + 6 q^{51} - 6 q^{52} + 3 q^{53} + 15 q^{55} - 3 q^{56} - 6 q^{57} + 33 q^{58} + 3 q^{59} + 3 q^{60} - 3 q^{61} + 9 q^{62} - 3 q^{63} - 21 q^{64} + 12 q^{65} - 9 q^{66} - 21 q^{67} - 15 q^{68} - 3 q^{69} + 12 q^{70} + 9 q^{71} + 3 q^{72} + 12 q^{73} - 33 q^{74} - 33 q^{76} - 6 q^{77} - 3 q^{78} + 12 q^{79} + 3 q^{81} + 3 q^{82} + 12 q^{83} - 6 q^{84} + 21 q^{85} - 21 q^{86} + 6 q^{87} - 12 q^{88} + 15 q^{89} - 12 q^{90} - 9 q^{91} - 6 q^{92} - 18 q^{93} + 6 q^{94} - 15 q^{95} + 6 q^{96} - 12 q^{97} + 6 q^{99}+O(q^{100}) \) 3 * q + 3 * q^3 + 6 * q^4 + 3 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 12 * q^10 + 6 * q^11 + 6 * q^12 + 9 * q^13 + 3 * q^15 + 12 * q^16 + 6 * q^17 - 6 * q^19 + 3 * q^20 - 3 * q^21 - 9 * q^22 - 3 * q^23 + 3 * q^24 - 3 * q^26 + 3 * q^27 - 6 * q^28 + 6 * q^29 - 12 * q^30 - 18 * q^31 + 6 * q^32 + 6 * q^33 - 15 * q^34 - 3 * q^35 + 6 * q^36 + 6 * q^37 + 9 * q^38 + 9 * q^39 - 21 * q^40 - 6 * q^41 - 9 * q^43 + 33 * q^44 + 3 * q^45 + 18 * q^47 + 12 * q^48 + 3 * q^49 - 21 * q^50 + 6 * q^51 - 6 * q^52 + 3 * q^53 + 15 * q^55 - 3 * q^56 - 6 * q^57 + 33 * q^58 + 3 * q^59 + 3 * q^60 - 3 * q^61 + 9 * q^62 - 3 * q^63 - 21 * q^64 + 12 * q^65 - 9 * q^66 - 21 * q^67 - 15 * q^68 - 3 * q^69 + 12 * q^70 + 9 * q^71 + 3 * q^72 + 12 * q^73 - 33 * q^74 - 33 * q^76 - 6 * q^77 - 3 * q^78 + 12 * q^79 + 3 * q^81 + 3 * q^82 + 12 * q^83 - 6 * q^84 + 21 * q^85 - 21 * q^86 + 6 * q^87 - 12 * q^88 + 15 * q^89 - 12 * q^90 - 9 * q^91 - 6 * q^92 - 18 * q^93 + 6 * q^94 - 15 * q^95 + 6 * q^96 - 12 * q^97 + 6 * q^99

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