LMFDB - Embedded newform 3549.2.a.bh.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, 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("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + \cdots + 281 $ x^15 - 2x^14 - 27x^13 + 51x^12 + 290x^11 - 510x^10 - 1575x^9 + 2522x^8 + 4553x^7 - 6393x^6 - 6785x^5 + 7806x^4 + 4632x^3 - 3811x^2 - 1041x + 281
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.08127$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.08127 q^{2} +1.00000 q^{3} -0.830866 q^{4} -1.66920 q^{5} -1.08127 q^{6} -1.00000 q^{7} +3.06092 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.08127 q^{2} +1.00000 q^{3} -0.830866 q^{4} -1.66920 q^{5} -1.08127 q^{6} -1.00000 q^{7} +3.06092 q^{8} +1.00000 q^{9} +1.80485 q^{10} +4.63545 q^{11} -0.830866 q^{12} +1.08127 q^{14} -1.66920 q^{15} -1.64793 q^{16} +4.03225 q^{17} -1.08127 q^{18} +0.793678 q^{19} +1.38688 q^{20} -1.00000 q^{21} -5.01215 q^{22} +4.31595 q^{23} +3.06092 q^{24} -2.21376 q^{25} +1.00000 q^{27} +0.830866 q^{28} +4.61741 q^{29} +1.80485 q^{30} -5.75711 q^{31} -4.33998 q^{32} +4.63545 q^{33} -4.35994 q^{34} +1.66920 q^{35} -0.830866 q^{36} -5.73497 q^{37} -0.858176 q^{38} -5.10929 q^{40} -7.33613 q^{41} +1.08127 q^{42} +11.4344 q^{43} -3.85144 q^{44} -1.66920 q^{45} -4.66668 q^{46} +5.10901 q^{47} -1.64793 q^{48} +1.00000 q^{49} +2.39366 q^{50} +4.03225 q^{51} -6.41614 q^{53} -1.08127 q^{54} -7.73752 q^{55} -3.06092 q^{56} +0.793678 q^{57} -4.99264 q^{58} -12.2304 q^{59} +1.38688 q^{60} +10.3412 q^{61} +6.22497 q^{62} -1.00000 q^{63} +7.98853 q^{64} -5.01215 q^{66} +1.86971 q^{67} -3.35026 q^{68} +4.31595 q^{69} -1.80485 q^{70} -6.08759 q^{71} +3.06092 q^{72} +3.11657 q^{73} +6.20102 q^{74} -2.21376 q^{75} -0.659440 q^{76} -4.63545 q^{77} +2.28592 q^{79} +2.75073 q^{80} +1.00000 q^{81} +7.93230 q^{82} -0.655507 q^{83} +0.830866 q^{84} -6.73066 q^{85} -12.3636 q^{86} +4.61741 q^{87} +14.1887 q^{88} +10.8262 q^{89} +1.80485 q^{90} -3.58597 q^{92} -5.75711 q^{93} -5.52419 q^{94} -1.32481 q^{95} -4.33998 q^{96} +14.7169 q^{97} -1.08127 q^{98} +4.63545 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9} + 21 q^{10} + 5 q^{11} + 28 q^{12} - 2 q^{14} - 9 q^{15} + 50 q^{16} - q^{17} + 2 q^{18} + 3 q^{19} - 23 q^{20} - 15 q^{21} + 21 q^{22} + 4 q^{23} + 9 q^{24} + 50 q^{25} + 15 q^{27} - 28 q^{28} + 9 q^{29} + 21 q^{30} + 7 q^{31} + 35 q^{32} + 5 q^{33} - 2 q^{34} + 9 q^{35} + 28 q^{36} + 17 q^{37} - 12 q^{38} + 46 q^{40} - 22 q^{41} - 2 q^{42} + 36 q^{43} + 29 q^{44} - 9 q^{45} - q^{46} - 12 q^{47} + 50 q^{48} + 15 q^{49} + 53 q^{50} - q^{51} - 5 q^{53} + 2 q^{54} + 43 q^{55} - 9 q^{56} + 3 q^{57} + 29 q^{58} - 29 q^{59} - 23 q^{60} + 12 q^{61} + 14 q^{62} - 15 q^{63} + 95 q^{64} + 21 q^{66} - 12 q^{67} - 16 q^{68} + 4 q^{69} - 21 q^{70} + 36 q^{71} + 9 q^{72} - 29 q^{73} - 5 q^{74} + 50 q^{75} + 25 q^{76} - 5 q^{77} + 35 q^{79} - 89 q^{80} + 15 q^{81} + 51 q^{82} - 10 q^{83} - 28 q^{84} + 23 q^{85} + 19 q^{86} + 9 q^{87} + 73 q^{88} + 25 q^{89} + 21 q^{90} - 31 q^{92} + 7 q^{93} - 19 q^{94} - 7 q^{95} + 35 q^{96} - 26 q^{97} + 2 q^{98} + 5 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9 + 21 * q^10 + 5 * q^11 + 28 * q^12 - 2 * q^14 - 9 * q^15 + 50 * q^16 - q^17 + 2 * q^18 + 3 * q^19 - 23 * q^20 - 15 * q^21 + 21 * q^22 + 4 * q^23 + 9 * q^24 + 50 * q^25 + 15 * q^27 - 28 * q^28 + 9 * q^29 + 21 * q^30 + 7 * q^31 + 35 * q^32 + 5 * q^33 - 2 * q^34 + 9 * q^35 + 28 * q^36 + 17 * q^37 - 12 * q^38 + 46 * q^40 - 22 * q^41 - 2 * q^42 + 36 * q^43 + 29 * q^44 - 9 * q^45 - q^46 - 12 * q^47 + 50 * q^48 + 15 * q^49 + 53 * q^50 - q^51 - 5 * q^53 + 2 * q^54 + 43 * q^55 - 9 * q^56 + 3 * q^57 + 29 * q^58 - 29 * q^59 - 23 * q^60 + 12 * q^61 + 14 * q^62 - 15 * q^63 + 95 * q^64 + 21 * q^66 - 12 * q^67 - 16 * q^68 + 4 * q^69 - 21 * q^70 + 36 * q^71 + 9 * q^72 - 29 * q^73 - 5 * q^74 + 50 * q^75 + 25 * q^76 - 5 * q^77 + 35 * q^79 - 89 * q^80 + 15 * q^81 + 51 * q^82 - 10 * q^83 - 28 * q^84 + 23 * q^85 + 19 * q^86 + 9 * q^87 + 73 * q^88 + 25 * q^89 + 21 * q^90 - 31 * q^92 + 7 * q^93 - 19 * q^94 - 7 * q^95 + 35 * q^96 - 26 * q^97 + 2 * 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 $

$2$	−1.08127	−0.764570	−0.382285	−	0.924044i	$-0.624863\pi$
$2$	−1.08127	−0.764570	−0.382285	+	0.924044i	$0.624863\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.830866	−0.415433
$5$	−1.66920	−0.746491	−0.373245	−	0.927733i	$-0.621755\pi$
$5$	−1.66920	−0.746491	−0.373245	+	0.927733i	$0.621755\pi$
$6$	−1.08127	−0.441425
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.06092	1.08220
$9$	1.00000	0.333333
$10$	1.80485	0.570744
$11$	4.63545	1.39764	0.698821	−	0.715297i	$-0.253709\pi$
$11$	4.63545	1.39764	0.698821	+	0.715297i	$0.253709\pi$
$12$	−0.830866	−0.239850
$13$	0	0
$13$	0	0
$14$	1.08127	0.288980
$15$	−1.66920	−0.430987
$16$	−1.64793	−0.411983
$17$	4.03225	0.977965	0.488983	−	0.872294i	$-0.337368\pi$
$17$	4.03225	0.977965	0.488983	+	0.872294i	$0.337368\pi$
$18$	−1.08127	−0.254857
$19$	0.793678	0.182082	0.0910411	−	0.995847i	$-0.470981\pi$
$19$	0.793678	0.182082	0.0910411	+	0.995847i	$0.470981\pi$
$20$	1.38688	0.310117
$21$	−1.00000	−0.218218
$22$	−5.01215	−1.06859
$23$	4.31595	0.899937	0.449969	−	0.893044i	$-0.351435\pi$
$23$	4.31595	0.899937	0.449969	+	0.893044i	$0.351435\pi$
$24$	3.06092	0.624807
$25$	−2.21376	−0.442752
$26$	0	0
$27$	1.00000	0.192450
$28$	0.830866	0.157019
$29$	4.61741	0.857431	0.428716	−	0.903439i	$-0.358966\pi$
$29$	4.61741	0.857431	0.428716	+	0.903439i	$0.358966\pi$
$30$	1.80485	0.329519
$31$	−5.75711	−1.03401	−0.517004	−	0.855983i	$-0.672953\pi$
$31$	−5.75711	−1.03401	−0.517004	+	0.855983i	$0.672953\pi$
$32$	−4.33998	−0.767208
$33$	4.63545	0.806929
$34$	−4.35994	−0.747723
$35$	1.66920	0.282147
$36$	−0.830866	−0.138478
$37$	−5.73497	−0.942823	−0.471412	−	0.881913i	$-0.656255\pi$
$37$	−5.73497	−0.942823	−0.471412	+	0.881913i	$0.656255\pi$
$38$	−0.858176	−0.139215
$39$	0	0
$40$	−5.10929	−0.807850
$41$	−7.33613	−1.14571	−0.572855	−	0.819657i	$-0.694164\pi$
$41$	−7.33613	−1.14571	−0.572855	+	0.819657i	$0.694164\pi$
$42$	1.08127	0.166843
$43$	11.4344	1.74373	0.871863	−	0.489750i	$-0.162912\pi$
$43$	11.4344	1.74373	0.871863	+	0.489750i	$0.162912\pi$
$44$	−3.85144	−0.580626
$45$	−1.66920	−0.248830
$46$	−4.66668	−0.688065
$47$	5.10901	0.745226	0.372613	−	0.927987i	$-0.378462\pi$
$47$	5.10901	0.745226	0.372613	+	0.927987i	$0.378462\pi$
$48$	−1.64793	−0.237858
$49$	1.00000	0.142857
$50$	2.39366	0.338514
$51$	4.03225	0.564629
$52$	0	0
$53$	−6.41614	−0.881325	−0.440663	−	0.897673i	$-0.645256\pi$
$53$	−6.41614	−0.881325	−0.440663	+	0.897673i	$0.645256\pi$
$54$	−1.08127	−0.147142
$55$	−7.73752	−1.04333
$56$	−3.06092	−0.409032
$57$	0.793678	0.105125
$58$	−4.99264	−0.655566
$59$	−12.2304	−1.59227	−0.796133	−	0.605122i	$-0.793124\pi$
$59$	−12.2304	−1.59227	−0.796133	+	0.605122i	$0.793124\pi$
$60$	1.38688	0.179046
$61$	10.3412	1.32406	0.662029	−	0.749478i	$-0.269695\pi$
$61$	10.3412	1.32406	0.662029	+	0.749478i	$0.269695\pi$
$62$	6.22497	0.790571
$63$	−1.00000	−0.125988
$64$	7.98853	0.998567
$65$	0	0
$66$	−5.01215	−0.616953
$67$	1.86971	0.228422	0.114211	−	0.993457i	$-0.463566\pi$
$67$	1.86971	0.228422	0.114211	+	0.993457i	$0.463566\pi$
$68$	−3.35026	−0.406279
$69$	4.31595	0.519579
$70$	−1.80485	−0.215721
$71$	−6.08759	−0.722464	−0.361232	−	0.932476i	$-0.617644\pi$
$71$	−6.08759	−0.722464	−0.361232	+	0.932476i	$0.617644\pi$
$72$	3.06092	0.360732
$73$	3.11657	0.364767	0.182384	−	0.983227i	$-0.441619\pi$
$73$	3.11657	0.364767	0.182384	+	0.983227i	$0.441619\pi$
$74$	6.20102	0.720854
$75$	−2.21376	−0.255623
$76$	−0.659440	−0.0756429
$77$	−4.63545	−0.528259
$78$	0	0
$79$	2.28592	0.257186	0.128593	−	0.991697i	$-0.458954\pi$
$79$	2.28592	0.257186	0.128593	+	0.991697i	$0.458954\pi$
$80$	2.75073	0.307541
$81$	1.00000	0.111111
$82$	7.93230	0.875976
$83$	−0.655507	−0.0719513	−0.0359756	−	0.999353i	$-0.511454\pi$
$83$	−0.655507	−0.0719513	−0.0359756	+	0.999353i	$0.511454\pi$
$84$	0.830866	0.0906549
$85$	−6.73066	−0.730042
$86$	−12.3636	−1.33320
$87$	4.61741	0.495038
$88$	14.1887	1.51252
$89$	10.8262	1.14758	0.573788	−	0.819004i	$-0.305473\pi$
$89$	10.8262	1.14758	0.573788	+	0.819004i	$0.305473\pi$
$90$	1.80485	0.190248
$91$	0	0
$92$	−3.58597	−0.373864
$93$	−5.75711	−0.596985
$94$	−5.52419	−0.569777
$95$	−1.32481	−0.135923
$96$	−4.33998	−0.442948
$97$	14.7169	1.49427	0.747136	−	0.664671i	$-0.231428\pi$
$97$	14.7169	1.49427	0.747136	+	0.664671i	$0.231428\pi$
$98$	−1.08127	−0.109224
$99$	4.63545	0.465880
$100$	1.83934	0.183934
$101$	−7.83185	−0.779298	−0.389649	−	0.920963i	$-0.627404\pi$
$101$	−7.83185	−0.779298	−0.389649	+	0.920963i	$0.627404\pi$
$102$	−4.35994	−0.431698
$103$	−14.2990	−1.40892	−0.704461	−	0.709743i	$-0.748811\pi$
$103$	−14.2990	−1.40892	−0.704461	+	0.709743i	$0.748811\pi$
$104$	0	0
$105$	1.66920	0.162898
$106$	6.93755	0.673835
$107$	−13.6120	−1.31592	−0.657960	−	0.753053i	$-0.728580\pi$
$107$	−13.6120	−1.31592	−0.657960	+	0.753053i	$0.728580\pi$
$108$	−0.830866	−0.0799501
$109$	1.08293	0.103726	0.0518631	−	0.998654i	$-0.483484\pi$
$109$	1.08293	0.103726	0.0518631	+	0.998654i	$0.483484\pi$
$110$	8.36630	0.797696
$111$	−5.73497	−0.544339
$112$	1.64793	0.155715
$113$	14.7313	1.38581	0.692903	−	0.721031i	$-0.256331\pi$
$113$	14.7313	1.38581	0.692903	+	0.721031i	$0.256331\pi$
$114$	−0.858176	−0.0803755
$115$	−7.20420	−0.671795
$116$	−3.83645	−0.356205
$117$	0	0
$118$	13.2243	1.21740
$119$	−4.03225	−0.369636
$120$	−5.10929	−0.466413
$121$	10.4874	0.953401
$122$	−11.1816	−1.01234
$123$	−7.33613	−0.661476
$124$	4.78339	0.429561
$125$	12.0412	1.07700
$126$	1.08127	0.0963267
$127$	19.2838	1.71116	0.855582	−	0.517667i	$-0.173199\pi$
$127$	19.2838	1.71116	0.855582	+	0.517667i	$0.173199\pi$
$128$	0.0422458	0.00373404
$129$	11.4344	1.00674
$130$	0	0
$131$	0.626566	0.0547433	0.0273717	−	0.999625i	$-0.491286\pi$
$131$	0.626566	0.0547433	0.0273717	+	0.999625i	$0.491286\pi$
$132$	−3.85144	−0.335225
$133$	−0.793678	−0.0688206
$134$	−2.02166	−0.174644
$135$	−1.66920	−0.143662
$136$	12.3424	1.05835
$137$	−1.27827	−0.109210	−0.0546052	−	0.998508i	$-0.517390\pi$
$137$	−1.27827	−0.109210	−0.0546052	+	0.998508i	$0.517390\pi$
$138$	−4.66668	−0.397254
$139$	17.3701	1.47331	0.736656	−	0.676268i	$-0.236404\pi$
$139$	17.3701	1.47331	0.736656	+	0.676268i	$0.236404\pi$
$140$	−1.38688	−0.117213
$141$	5.10901	0.430256
$142$	6.58230	0.552375
$143$	0	0
$144$	−1.64793	−0.137328
$145$	−7.70740	−0.640065
$146$	−3.36984	−0.278890
$147$	1.00000	0.0824786
$148$	4.76499	0.391680
$149$	2.06250	0.168967	0.0844834	−	0.996425i	$-0.473076\pi$
$149$	2.06250	0.168967	0.0844834	+	0.996425i	$0.473076\pi$
$150$	2.39366	0.195441
$151$	−10.6932	−0.870199	−0.435100	−	0.900382i	$-0.643287\pi$
$151$	−10.6932	−0.870199	−0.435100	+	0.900382i	$0.643287\pi$
$152$	2.42938	0.197049
$153$	4.03225	0.325988
$154$	5.01215	0.403891
$155$	9.60980	0.771878
$156$	0	0
$157$	−9.91978	−0.791685	−0.395842	−	0.918318i	$-0.629547\pi$
$157$	−9.91978	−0.791685	−0.395842	+	0.918318i	$0.629547\pi$
$158$	−2.47169	−0.196637
$159$	−6.41614	−0.508833
$160$	7.24432	0.572714
$161$	−4.31595	−0.340144
$162$	−1.08127	−0.0849522
$163$	20.9575	1.64152	0.820759	−	0.571275i	$-0.193551\pi$
$163$	20.9575	1.64152	0.820759	+	0.571275i	$0.193551\pi$
$164$	6.09534	0.475966
$165$	−7.73752	−0.602365
$166$	0.708777	0.0550118
$167$	8.36605	0.647384	0.323692	−	0.946162i	$-0.395076\pi$
$167$	8.36605	0.647384	0.323692	+	0.946162i	$0.395076\pi$
$168$	−3.06092	−0.236155
$169$	0	0
$170$	7.27762	0.558168
$171$	0.793678	0.0606940
$172$	−9.50043	−0.724401
$173$	5.93501	0.451230	0.225615	−	0.974217i	$-0.427561\pi$
$173$	5.93501	0.451230	0.225615	+	0.974217i	$0.427561\pi$
$174$	−4.99264	−0.378491
$175$	2.21376	0.167344
$176$	−7.63890	−0.575804
$177$	−12.2304	−0.919295
$178$	−11.7060	−0.877403
$179$	14.5930	1.09073	0.545365	−	0.838199i	$-0.316391\pi$
$179$	14.5930	1.09073	0.545365	+	0.838199i	$0.316391\pi$
$180$	1.38688	0.103372
$181$	−2.33617	−0.173646	−0.0868232	−	0.996224i	$-0.527672\pi$
$181$	−2.33617	−0.173646	−0.0868232	+	0.996224i	$0.527672\pi$
$182$	0	0
$183$	10.3412	0.764446
$184$	13.2108	0.973910
$185$	9.57283	0.703809
$186$	6.22497	0.456437
$187$	18.6913	1.36684
$188$	−4.24490	−0.309591
$189$	−1.00000	−0.0727393
$190$	1.43247	0.103922
$191$	2.92459	0.211616	0.105808	−	0.994387i	$-0.466257\pi$
$191$	2.92459	0.211616	0.105808	+	0.994387i	$0.466257\pi$
$192$	7.98853	0.576523
$193$	24.0430	1.73065	0.865327	−	0.501207i	$-0.167111\pi$
$193$	24.0430	1.73065	0.865327	+	0.501207i	$0.167111\pi$
$194$	−15.9128	−1.14248
$195$	0	0
$196$	−0.830866	−0.0593476
$197$	14.6055	1.04060	0.520299	−	0.853984i	$-0.325820\pi$
$197$	14.6055	1.04060	0.520299	+	0.853984i	$0.325820\pi$
$198$	−5.01215	−0.356198
$199$	−15.4843	−1.09765	−0.548827	−	0.835936i	$-0.684925\pi$
$199$	−15.4843	−1.09765	−0.548827	+	0.835936i	$0.684925\pi$
$200$	−6.77613	−0.479145
$201$	1.86971	0.131879
$202$	8.46830	0.595828
$203$	−4.61741	−0.324079
$204$	−3.35026	−0.234565
$205$	12.2455	0.855262
$206$	15.4610	1.07722
$207$	4.31595	0.299979
$208$	0	0
$209$	3.67905	0.254486
$210$	−1.80485	−0.124547
$211$	19.8268	1.36493	0.682467	−	0.730917i	$-0.260907\pi$
$211$	19.8268	1.36493	0.682467	+	0.730917i	$0.260907\pi$
$212$	5.33095	0.366131
$213$	−6.08759	−0.417115
$214$	14.7182	1.00611
$215$	−19.0863	−1.30168
$216$	3.06092	0.208269
$217$	5.75711	0.390818
$218$	−1.17094	−0.0793059
$219$	3.11657	0.210599
$220$	6.42884	0.433432
$221$	0	0
$222$	6.20102	0.416185
$223$	−27.3639	−1.83242	−0.916211	−	0.400695i	$-0.868769\pi$
$223$	−27.3639	−1.83242	−0.916211	+	0.400695i	$0.868769\pi$
$224$	4.33998	0.289977
$225$	−2.21376	−0.147584
$226$	−15.9285	−1.05955
$227$	15.1297	1.00419	0.502096	−	0.864812i	$-0.332562\pi$
$227$	15.1297	1.00419	0.502096	+	0.864812i	$0.332562\pi$
$228$	−0.659440	−0.0436725
$229$	10.6735	0.705322	0.352661	−	0.935751i	$-0.385277\pi$
$229$	10.6735	0.705322	0.352661	+	0.935751i	$0.385277\pi$
$230$	7.78965	0.513634
$231$	−4.63545	−0.304990
$232$	14.1335	0.927910
$233$	−10.6341	−0.696660	−0.348330	−	0.937372i	$-0.613251\pi$
$233$	−10.6341	−0.696660	−0.348330	+	0.937372i	$0.613251\pi$
$234$	0	0
$235$	−8.52798	−0.556304
$236$	10.1618	0.661479
$237$	2.28592	0.148487
$238$	4.35994	0.282613
$239$	14.5524	0.941315	0.470658	−	0.882316i	$-0.344017\pi$
$239$	14.5524	0.941315	0.470658	+	0.882316i	$0.344017\pi$
$240$	2.75073	0.177559
$241$	21.0486	1.35586	0.677929	−	0.735127i	$-0.262877\pi$
$241$	21.0486	1.35586	0.677929	+	0.735127i	$0.262877\pi$
$242$	−11.3397	−0.728942
$243$	1.00000	0.0641500
$244$	−8.59218	−0.550058
$245$	−1.66920	−0.106642
$246$	7.93230	0.505745
$247$	0	0
$248$	−17.6220	−1.11900
$249$	−0.655507	−0.0415411
$250$	−13.0198	−0.823442
$251$	−16.3957	−1.03489	−0.517443	−	0.855718i	$-0.673116\pi$
$251$	−16.3957	−1.03489	−0.517443	+	0.855718i	$0.673116\pi$
$252$	0.830866	0.0523396
$253$	20.0064	1.25779
$254$	−20.8509	−1.30830
$255$	−6.73066	−0.421490
$256$	−16.0227	−1.00142
$257$	−14.2261	−0.887400	−0.443700	−	0.896175i	$-0.646334\pi$
$257$	−14.2261	−0.887400	−0.443700	+	0.896175i	$0.646334\pi$
$258$	−12.3636	−0.769724
$259$	5.73497	0.356354
$260$	0	0
$261$	4.61741	0.285810
$262$	−0.677484	−0.0418551
$263$	17.0566	1.05175	0.525876	−	0.850561i	$-0.323737\pi$
$263$	17.0566	1.05175	0.525876	+	0.850561i	$0.323737\pi$
$264$	14.1887	0.873256
$265$	10.7099	0.657901
$266$	0.858176	0.0526181
$267$	10.8262	0.662554
$268$	−1.55348	−0.0948940
$269$	17.2732	1.05317	0.526583	−	0.850124i	$-0.323473\pi$
$269$	17.2732	1.05317	0.526583	+	0.850124i	$0.323473\pi$
$270$	1.80485	0.109840
$271$	−7.90154	−0.479985	−0.239992	−	0.970775i	$-0.577145\pi$
$271$	−7.90154	−0.479985	−0.239992	+	0.970775i	$0.577145\pi$
$272$	−6.64487	−0.402905
$273$	0	0
$274$	1.38215	0.0834990
$275$	−10.2618	−0.618808
$276$	−3.58597	−0.215850
$277$	4.50995	0.270977	0.135488	−	0.990779i	$-0.456740\pi$
$277$	4.50995	0.270977	0.135488	+	0.990779i	$0.456740\pi$
$278$	−18.7817	−1.12645
$279$	−5.75711	−0.344669
$280$	5.10929	0.305339
$281$	−20.7726	−1.23919	−0.619594	−	0.784922i	$-0.712703\pi$
$281$	−20.7726	−1.23919	−0.619594	+	0.784922i	$0.712703\pi$
$282$	−5.52419	−0.328961
$283$	−2.02320	−0.120267	−0.0601335	−	0.998190i	$-0.519153\pi$
$283$	−2.02320	−0.120267	−0.0601335	+	0.998190i	$0.519153\pi$
$284$	5.05797	0.300136
$285$	−1.32481	−0.0784750
$286$	0	0
$287$	7.33613	0.433038
$288$	−4.33998	−0.255736
$289$	−0.740925	−0.0435838
$290$	8.33374	0.489374
$291$	14.7169	0.862719
$292$	−2.58946	−0.151536
$293$	−25.9848	−1.51805	−0.759024	−	0.651063i	$-0.774323\pi$
$293$	−25.9848	−1.51805	−0.759024	+	0.651063i	$0.774323\pi$
$294$	−1.08127	−0.0630607
$295$	20.4151	1.18861
$296$	−17.5543	−1.02032
$297$	4.63545	0.268976
$298$	−2.23011	−0.129187
$299$	0	0
$300$	1.83934	0.106194
$301$	−11.4344	−0.659067
$302$	11.5622	0.665328
$303$	−7.83185	−0.449928
$304$	−1.30793	−0.0750147
$305$	−17.2616	−0.988398
$306$	−4.35994	−0.249241
$307$	−24.6185	−1.40505	−0.702526	−	0.711658i	$-0.747945\pi$
$307$	−24.6185	−1.40505	−0.702526	+	0.711658i	$0.747945\pi$
$308$	3.85144	0.219456
$309$	−14.2990	−0.813441
$310$	−10.3907	−0.590154
$311$	33.1216	1.87815	0.939076	−	0.343711i	$-0.111684\pi$
$311$	33.1216	1.87815	0.939076	+	0.343711i	$0.111684\pi$
$312$	0	0
$313$	−7.05477	−0.398759	−0.199380	−	0.979922i	$-0.563893\pi$
$313$	−7.05477	−0.398759	−0.199380	+	0.979922i	$0.563893\pi$
$314$	10.7259	0.605298
$315$	1.66920	0.0940490
$316$	−1.89930	−0.106844
$317$	−13.0084	−0.730622	−0.365311	−	0.930886i	$-0.619037\pi$
$317$	−13.0084	−0.730622	−0.365311	+	0.930886i	$0.619037\pi$
$318$	6.93755	0.389039
$319$	21.4038	1.19838
$320$	−13.3345	−0.745421
$321$	−13.6120	−0.759747
$322$	4.66668	0.260064
$323$	3.20031	0.178070
$324$	−0.830866	−0.0461592
$325$	0	0
$326$	−22.6606	−1.25506
$327$	1.08293	0.0598863
$328$	−22.4553	−1.23988
$329$	−5.10901	−0.281669
$330$	8.36630	0.460550
$331$	−17.9368	−0.985894	−0.492947	−	0.870059i	$-0.664080\pi$
$331$	−17.9368	−0.985894	−0.492947	+	0.870059i	$0.664080\pi$
$332$	0.544638	0.0298909
$333$	−5.73497	−0.314274
$334$	−9.04592	−0.494970
$335$	−3.12093	−0.170515
$336$	1.64793	0.0899020
$337$	28.3388	1.54371	0.771856	−	0.635797i	$-0.219328\pi$
$337$	28.3388	1.54371	0.771856	+	0.635797i	$0.219328\pi$
$338$	0	0
$339$	14.7313	0.800095
$340$	5.59227	0.303284
$341$	−26.6868	−1.44517
$342$	−0.858176	−0.0464048
$343$	−1.00000	−0.0539949
$344$	34.9997	1.88706
$345$	−7.20420	−0.387861
$346$	−6.41732	−0.344997
$347$	−8.49524	−0.456048	−0.228024	−	0.973655i	$-0.573227\pi$
$347$	−8.49524	−0.456048	−0.228024	+	0.973655i	$0.573227\pi$
$348$	−3.83645	−0.205655
$349$	11.0479	0.591381	0.295691	−	0.955284i	$-0.404450\pi$
$349$	11.0479	0.591381	0.295691	+	0.955284i	$0.404450\pi$
$350$	−2.39366	−0.127946
$351$	0	0
$352$	−20.1178	−1.07228
$353$	−11.0968	−0.590621	−0.295310	−	0.955401i	$-0.595423\pi$
$353$	−11.0968	−0.590621	−0.295310	+	0.955401i	$0.595423\pi$
$354$	13.2243	0.702865
$355$	10.1614	0.539313
$356$	−8.99514	−0.476741
$357$	−4.03225	−0.213410
$358$	−15.7789	−0.833940
$359$	16.3104	0.860830	0.430415	−	0.902631i	$-0.358367\pi$
$359$	16.3104	0.860830	0.430415	+	0.902631i	$0.358367\pi$
$360$	−5.10929	−0.269283
$361$	−18.3701	−0.966846
$362$	2.52602	0.132765
$363$	10.4874	0.550446
$364$	0	0
$365$	−5.20220	−0.272296
$366$	−11.1816	−0.584472
$367$	15.3843	0.803056	0.401528	−	0.915847i	$-0.368479\pi$
$367$	15.3843	0.803056	0.401528	+	0.915847i	$0.368479\pi$
$368$	−7.11238	−0.370758
$369$	−7.33613	−0.381903
$370$	−10.3508	−0.538111
$371$	6.41614	0.333110
$372$	4.78339	0.248007
$373$	21.1348	1.09432	0.547160	−	0.837028i	$-0.315709\pi$
$373$	21.1348	1.09432	0.547160	+	0.837028i	$0.315709\pi$
$374$	−20.2103	−1.04505
$375$	12.0412	0.621807
$376$	15.6382	0.806481
$377$	0	0
$378$	1.08127	0.0556143
$379$	27.2340	1.39892	0.699458	−	0.714674i	$-0.253425\pi$
$379$	27.2340	1.39892	0.699458	+	0.714674i	$0.253425\pi$
$380$	1.10074	0.0564667
$381$	19.2838	0.987941
$382$	−3.16226	−0.161795
$383$	−15.5635	−0.795257	−0.397629	−	0.917546i	$-0.630167\pi$
$383$	−15.5635	−0.795257	−0.397629	+	0.917546i	$0.630167\pi$
$384$	0.0422458	0.00215585
$385$	7.73752	0.394340
$386$	−25.9969	−1.32321
$387$	11.4344	0.581242
$388$	−12.2278	−0.620770
$389$	−25.1109	−1.27317	−0.636586	−	0.771206i	$-0.719654\pi$
$389$	−25.1109	−1.27317	−0.636586	+	0.771206i	$0.719654\pi$
$390$	0	0
$391$	17.4030	0.880107
$392$	3.06092	0.154600
$393$	0.626566	0.0316061
$394$	−15.7924	−0.795610
$395$	−3.81567	−0.191987
$396$	−3.85144	−0.193542
$397$	−3.55580	−0.178461	−0.0892304	−	0.996011i	$-0.528441\pi$
$397$	−3.55580	−0.178461	−0.0892304	+	0.996011i	$0.528441\pi$
$398$	16.7426	0.839233
$399$	−0.793678	−0.0397336
$400$	3.64812	0.182406
$401$	31.3198	1.56403	0.782017	−	0.623257i	$-0.214191\pi$
$401$	31.3198	1.56403	0.782017	+	0.623257i	$0.214191\pi$
$402$	−2.02166	−0.100831
$403$	0	0
$404$	6.50721	0.323746
$405$	−1.66920	−0.0829434
$406$	4.99264	0.247781
$407$	−26.5842	−1.31773
$408$	12.3424	0.611040
$409$	10.2735	0.507991	0.253996	−	0.967205i	$-0.418255\pi$
$409$	10.2735	0.507991	0.253996	+	0.967205i	$0.418255\pi$
$410$	−13.2406	−0.653908
$411$	−1.27827	−0.0630527
$412$	11.8805	0.585312
$413$	12.2304	0.601820
$414$	−4.66668	−0.229355
$415$	1.09418	0.0537109
$416$	0	0
$417$	17.3701	0.850617
$418$	−3.97803	−0.194572
$419$	5.29913	0.258879	0.129440	−	0.991587i	$-0.458682\pi$
$419$	5.29913	0.258879	0.129440	+	0.991587i	$0.458682\pi$
$420$	−1.38688	−0.0676730
$421$	17.2903	0.842677	0.421339	−	0.906903i	$-0.361560\pi$
$421$	17.2903	0.842677	0.421339	+	0.906903i	$0.361560\pi$
$422$	−21.4380	−1.04359
$423$	5.10901	0.248409
$424$	−19.6393	−0.953768
$425$	−8.92643	−0.432996
$426$	6.58230	0.318914
$427$	−10.3412	−0.500447
$428$	11.3097	0.546676
$429$	0	0
$430$	20.6374	0.995222
$431$	19.2244	0.926008	0.463004	−	0.886356i	$-0.346771\pi$
$431$	19.2244	0.926008	0.463004	+	0.886356i	$0.346771\pi$
$432$	−1.64793	−0.0792861
$433$	−9.23571	−0.443840	−0.221920	−	0.975065i	$-0.571232\pi$
$433$	−9.23571	−0.443840	−0.221920	+	0.975065i	$0.571232\pi$
$434$	−6.22497	−0.298808
$435$	−7.70740	−0.369542
$436$	−0.899772	−0.0430912
$437$	3.42547	0.163862
$438$	−3.36984	−0.161017
$439$	36.8646	1.75945	0.879726	−	0.475480i	$-0.157726\pi$
$439$	36.8646	1.75945	0.879726	+	0.475480i	$0.157726\pi$
$440$	−23.6839	−1.12909
$441$	1.00000	0.0476190
$442$	0	0
$443$	−20.1394	−0.956850	−0.478425	−	0.878128i	$-0.658792\pi$
$443$	−20.1394	−0.956850	−0.478425	+	0.878128i	$0.658792\pi$
$444$	4.76499	0.226136
$445$	−18.0712	−0.856656
$446$	29.5876	1.40102
$447$	2.06250	0.0975530
$448$	−7.98853	−0.377423
$449$	−33.2197	−1.56774	−0.783868	−	0.620927i	$-0.786756\pi$
$449$	−33.2197	−1.56774	−0.783868	+	0.620927i	$0.786756\pi$
$450$	2.39366	0.112838
$451$	−34.0063	−1.60129
$452$	−12.2398	−0.575709
$453$	−10.6932	−0.502410
$454$	−16.3592	−0.767776
$455$	0	0
$456$	2.42938	0.113766
$457$	25.1540	1.17665	0.588327	−	0.808623i	$-0.299787\pi$
$457$	25.1540	1.17665	0.588327	+	0.808623i	$0.299787\pi$
$458$	−11.5408	−0.539268
$459$	4.03225	0.188210
$460$	5.98572	0.279086
$461$	23.1849	1.07983	0.539915	−	0.841720i	$-0.318457\pi$
$461$	23.1849	1.07983	0.539915	+	0.841720i	$0.318457\pi$
$462$	5.01215	0.233186
$463$	−12.8679	−0.598022	−0.299011	−	0.954250i	$-0.596657\pi$
$463$	−12.8679	−0.598022	−0.299011	+	0.954250i	$0.596657\pi$
$464$	−7.60917	−0.353247
$465$	9.60980	0.445644
$466$	11.4982	0.532645
$467$	−25.5865	−1.18400	−0.592000	−	0.805938i	$-0.701661\pi$
$467$	−25.5865	−1.18400	−0.592000	+	0.805938i	$0.701661\pi$
$468$	0	0
$469$	−1.86971	−0.0863353
$470$	9.22101	0.425333
$471$	−9.91978	−0.457079
$472$	−37.4363	−1.72315
$473$	53.0035	2.43710
$474$	−2.47169	−0.113528
$475$	−1.75701	−0.0806171
$476$	3.35026	0.153559
$477$	−6.41614	−0.293775
$478$	−15.7350	−0.719701
$479$	25.2752	1.15485	0.577426	−	0.816443i	$-0.304057\pi$
$479$	25.2752	1.15485	0.577426	+	0.816443i	$0.304057\pi$
$480$	7.24432	0.330656
$481$	0	0
$482$	−22.7591	−1.03665
$483$	−4.31595	−0.196382
$484$	−8.71363	−0.396074
$485$	−24.5655	−1.11546
$486$	−1.08127	−0.0490472
$487$	−42.4961	−1.92568	−0.962841	−	0.270068i	$-0.912954\pi$
$487$	−42.4961	−1.92568	−0.962841	+	0.270068i	$0.912954\pi$
$488$	31.6536	1.43289
$489$	20.9575	0.947731
$490$	1.80485	0.0815349
$491$	−40.3541	−1.82116	−0.910578	−	0.413337i	$-0.864363\pi$
$491$	−40.3541	−1.82116	−0.910578	+	0.413337i	$0.864363\pi$
$492$	6.09534	0.274799
$493$	18.6186	0.838538
$494$	0	0
$495$	−7.73752	−0.347775
$496$	9.48732	0.425993
$497$	6.08759	0.273066
$498$	0.708777	0.0317611
$499$	5.56698	0.249212	0.124606	−	0.992206i	$-0.460233\pi$
$499$	5.56698	0.249212	0.124606	+	0.992206i	$0.460233\pi$
$500$	−10.0047	−0.447422
$501$	8.36605	0.373767
$502$	17.7281	0.791242
$503$	18.0562	0.805085	0.402542	−	0.915401i	$-0.368127\pi$
$503$	18.0562	0.805085	0.402542	+	0.915401i	$0.368127\pi$
$504$	−3.06092	−0.136344
$505$	13.0729	0.581739
$506$	−21.6322	−0.961668
$507$	0	0
$508$	−16.0223	−0.710874
$509$	9.76430	0.432795	0.216397	−	0.976305i	$-0.430569\pi$
$509$	9.76430	0.432795	0.216397	+	0.976305i	$0.430569\pi$
$510$	7.27762	0.322259
$511$	−3.11657	−0.137869
$512$	17.2403	0.761923
$513$	0.793678	0.0350417
$514$	15.3822	0.678480
$515$	23.8679	1.05175
$516$	−9.50043	−0.418233
$517$	23.6826	1.04156
$518$	−6.20102	−0.272457
$519$	5.93501	0.260518
$520$	0	0
$521$	19.4225	0.850914	0.425457	−	0.904979i	$-0.360113\pi$
$521$	19.4225	0.850914	0.425457	+	0.904979i	$0.360113\pi$
$522$	−4.99264	−0.218522
$523$	15.4560	0.675845	0.337923	−	0.941174i	$-0.390276\pi$
$523$	15.4560	0.675845	0.337923	+	0.941174i	$0.390276\pi$
$524$	−0.520592	−0.0227422
$525$	2.21376	0.0966163
$526$	−18.4427	−0.804138
$527$	−23.2141	−1.01122
$528$	−7.63890	−0.332440
$529$	−4.37260	−0.190113
$530$	−11.5802	−0.503011
$531$	−12.2304	−0.530755
$532$	0.659440	0.0285903
$533$	0	0
$534$	−11.7060	−0.506569
$535$	22.7212	0.982322
$536$	5.72304	0.247197
$537$	14.5930	0.629733
$538$	−18.6769	−0.805219
$539$	4.63545	0.199663
$540$	1.38688	0.0596820
$541$	3.65437	0.157114	0.0785569	−	0.996910i	$-0.474969\pi$
$541$	3.65437	0.157114	0.0785569	+	0.996910i	$0.474969\pi$
$542$	8.54366	0.366982
$543$	−2.33617	−0.100255
$544$	−17.4999	−0.750303
$545$	−1.80764	−0.0774306
$546$	0	0
$547$	41.0035	1.75318	0.876592	−	0.481235i	$-0.159812\pi$
$547$	41.0035	1.75318	0.876592	+	0.481235i	$0.159812\pi$
$548$	1.06208	0.0453696
$549$	10.3412	0.441353
$550$	11.0957	0.473122
$551$	3.66473	0.156123
$552$	13.2108	0.562287
$553$	−2.28592	−0.0972074
$554$	−4.87645	−0.207181
$555$	9.57283	0.406344
$556$	−14.4322	−0.612062
$557$	6.55475	0.277734	0.138867	−	0.990311i	$-0.455654\pi$
$557$	6.55475	0.277734	0.138867	+	0.990311i	$0.455654\pi$
$558$	6.22497	0.263524
$559$	0	0
$560$	−2.75073	−0.116240
$561$	18.6913	0.789148
$562$	22.4607	0.947446
$563$	−25.4130	−1.07103	−0.535516	−	0.844525i	$-0.679883\pi$
$563$	−25.4130	−1.07103	−0.535516	+	0.844525i	$0.679883\pi$
$564$	−4.24490	−0.178743
$565$	−24.5896	−1.03449
$566$	2.18762	0.0919526
$567$	−1.00000	−0.0419961
$568$	−18.6336	−0.781849
$569$	21.8432	0.915713	0.457857	−	0.889026i	$-0.348617\pi$
$569$	21.8432	0.915713	0.457857	+	0.889026i	$0.348617\pi$
$570$	1.43247	0.0599996
$571$	28.7510	1.20319	0.601596	−	0.798800i	$-0.294532\pi$
$571$	28.7510	1.20319	0.601596	+	0.798800i	$0.294532\pi$
$572$	0	0
$573$	2.92459	0.122177
$574$	−7.93230	−0.331088
$575$	−9.55446	−0.398449
$576$	7.98853	0.332856
$577$	46.2811	1.92671	0.963353	−	0.268238i	$-0.0864414\pi$
$577$	46.2811	1.92671	0.963353	+	0.268238i	$0.0864414\pi$
$578$	0.801136	0.0333229
$579$	24.0430	0.999194
$580$	6.40382	0.265904
$581$	0.655507	0.0271950
$582$	−15.9128	−0.659609
$583$	−29.7417	−1.23178
$584$	9.53957	0.394750
$585$	0	0
$586$	28.0965	1.16065
$587$	−1.61084	−0.0664866	−0.0332433	−	0.999447i	$-0.510584\pi$
$587$	−1.61084	−0.0664866	−0.0332433	+	0.999447i	$0.510584\pi$
$588$	−0.830866	−0.0342643
$589$	−4.56929	−0.188274
$590$	−22.0741	−0.908776
$591$	14.6055	0.600790
$592$	9.45083	0.388427
$593$	36.9127	1.51582	0.757912	−	0.652357i	$-0.226220\pi$
$593$	36.9127	1.51582	0.757912	+	0.652357i	$0.226220\pi$
$594$	−5.01215	−0.205651
$595$	6.73066	0.275930
$596$	−1.71366	−0.0701944
$597$	−15.4843	−0.633730
$598$	0	0
$599$	−13.4868	−0.551054	−0.275527	−	0.961293i	$-0.588852\pi$
$599$	−13.4868	−0.551054	−0.275527	+	0.961293i	$0.588852\pi$
$600$	−6.77613	−0.276634
$601$	47.7912	1.94945	0.974723	−	0.223418i	$-0.0717214\pi$
$601$	47.7912	1.94945	0.974723	+	0.223418i	$0.0717214\pi$
$602$	12.3636	0.503902
$603$	1.86971	0.0761406
$604$	8.88460	0.361509
$605$	−17.5056	−0.711705
$606$	8.46830	0.344001
$607$	−31.8176	−1.29144	−0.645718	−	0.763576i	$-0.723442\pi$
$607$	−31.8176	−1.29144	−0.645718	+	0.763576i	$0.723442\pi$
$608$	−3.44455	−0.139695
$609$	−4.61741	−0.187107
$610$	18.6644	0.755699
$611$	0	0
$612$	−3.35026	−0.135426
$613$	−35.4524	−1.43191	−0.715955	−	0.698146i	$-0.754009\pi$
$613$	−35.4524	−1.43191	−0.715955	+	0.698146i	$0.754009\pi$
$614$	26.6191	1.07426
$615$	12.2455	0.493786
$616$	−14.1887	−0.571680
$617$	49.4752	1.99180	0.995899	−	0.0904759i	$-0.0288388\pi$
$617$	49.4752	1.99180	0.995899	+	0.0904759i	$0.0288388\pi$
$618$	15.4610	0.621933
$619$	−11.7993	−0.474253	−0.237126	−	0.971479i	$-0.576206\pi$
$619$	−11.7993	−0.474253	−0.237126	+	0.971479i	$0.576206\pi$
$620$	−7.98445	−0.320663
$621$	4.31595	0.173193
$622$	−35.8132	−1.43598
$623$	−10.8262	−0.433743
$624$	0	0
$625$	−9.03049	−0.361220
$626$	7.62807	0.304879
$627$	3.67905	0.146927
$628$	8.24201	0.328892
$629$	−23.1249	−0.922048
$630$	−1.80485	−0.0719070
$631$	5.14719	0.204906	0.102453	−	0.994738i	$-0.467331\pi$
$631$	5.14719	0.204906	0.102453	+	0.994738i	$0.467331\pi$
$632$	6.99702	0.278327
$633$	19.8268	0.788045
$634$	14.0655	0.558611
$635$	−32.1887	−1.27737
$636$	5.33095	0.211386
$637$	0	0
$638$	−23.1432	−0.916246
$639$	−6.08759	−0.240821
$640$	−0.0705168	−0.00278742
$641$	−13.5685	−0.535924	−0.267962	−	0.963429i	$-0.586350\pi$
$641$	−13.5685	−0.535924	−0.267962	+	0.963429i	$0.586350\pi$
$642$	14.7182	0.580879
$643$	11.1073	0.438030	0.219015	−	0.975721i	$-0.429716\pi$
$643$	11.1073	0.438030	0.219015	+	0.975721i	$0.429716\pi$
$644$	3.58597	0.141307
$645$	−19.0863	−0.751523
$646$	−3.46038	−0.136147
$647$	−9.09478	−0.357553	−0.178776	−	0.983890i	$-0.557214\pi$
$647$	−9.09478	−0.357553	−0.178776	+	0.983890i	$0.557214\pi$
$648$	3.06092	0.120244
$649$	−56.6935	−2.22542
$650$	0	0
$651$	5.75711	0.225639
$652$	−17.4129	−0.681941
$653$	3.37219	0.131964	0.0659819	−	0.997821i	$-0.478982\pi$
$653$	3.37219	0.131964	0.0659819	+	0.997821i	$0.478982\pi$
$654$	−1.17094	−0.0457873
$655$	−1.04587	−0.0408654
$656$	12.0894	0.472013
$657$	3.11657	0.121589
$658$	5.52419	0.215355
$659$	−20.0281	−0.780185	−0.390092	−	0.920776i	$-0.627557\pi$
$659$	−20.0281	−0.780185	−0.390092	+	0.920776i	$0.627557\pi$
$660$	6.42884	0.250242
$661$	−25.9859	−1.01073	−0.505367	−	0.862905i	$-0.668643\pi$
$661$	−25.9859	−1.01073	−0.505367	+	0.862905i	$0.668643\pi$
$662$	19.3944	0.753785
$663$	0	0
$664$	−2.00645	−0.0778655
$665$	1.32481	0.0513739
$666$	6.20102	0.240285
$667$	19.9285	0.771634
$668$	−6.95106	−0.268945
$669$	−27.3639	−1.05795
$670$	3.37456	0.130370
$671$	47.9363	1.85056
$672$	4.33998	0.167418
$673$	−26.8919	−1.03661	−0.518303	−	0.855197i	$-0.673436\pi$
$673$	−26.8919	−1.03661	−0.518303	+	0.855197i	$0.673436\pi$
$674$	−30.6417	−1.18028
$675$	−2.21376	−0.0852076
$676$	0	0
$677$	−23.0492	−0.885853	−0.442927	−	0.896558i	$-0.646060\pi$
$677$	−23.0492	−0.885853	−0.442927	+	0.896558i	$0.646060\pi$
$678$	−15.9285	−0.611729
$679$	−14.7169	−0.564782
$680$	−20.6020	−0.790050
$681$	15.1297	0.579771
$682$	28.8555	1.10494
$683$	35.3125	1.35119	0.675597	−	0.737271i	$-0.263886\pi$
$683$	35.3125	1.35119	0.675597	+	0.737271i	$0.263886\pi$
$684$	−0.659440	−0.0252143
$685$	2.13370	0.0815246
$686$	1.08127	0.0412829
$687$	10.6735	0.407218
$688$	−18.8431	−0.718385
$689$	0	0
$690$	7.78965	0.296547
$691$	−29.9975	−1.14116	−0.570580	−	0.821242i	$-0.693282\pi$
$691$	−29.9975	−1.14116	−0.570580	+	0.821242i	$0.693282\pi$
$692$	−4.93120	−0.187456
$693$	−4.63545	−0.176086
$694$	9.18560	0.348681
$695$	−28.9942	−1.09981
$696$	14.1335	0.535729
$697$	−29.5811	−1.12046
$698$	−11.9457	−0.452152
$699$	−10.6341	−0.402217
$700$	−1.83934	−0.0695204
$701$	−32.8331	−1.24009	−0.620045	−	0.784566i	$-0.712886\pi$
$701$	−32.8331	−1.24009	−0.620045	+	0.784566i	$0.712886\pi$
$702$	0	0
$703$	−4.55172	−0.171671
$704$	37.0305	1.39564
$705$	−8.52798	−0.321182
$706$	11.9985	0.451571
$707$	7.83185	0.294547
$708$	10.1618	0.381905
$709$	0.735973	0.0276400	0.0138200	−	0.999904i	$-0.495601\pi$
$709$	0.735973	0.0276400	0.0138200	+	0.999904i	$0.495601\pi$
$710$	−10.9872	−0.412343
$711$	2.28592	0.0857288
$712$	33.1382	1.24190
$713$	−24.8474	−0.930542
$714$	4.35994	0.163166
$715$	0	0
$716$	−12.1248	−0.453125
$717$	14.5524	0.543469
$718$	−17.6359	−0.658165
$719$	−12.0005	−0.447544	−0.223772	−	0.974642i	$-0.571837\pi$
$719$	−12.0005	−0.447544	−0.223772	+	0.974642i	$0.571837\pi$
$720$	2.75073	0.102514
$721$	14.2990	0.532522
$722$	19.8629	0.739221
$723$	21.0486	0.782805
$724$	1.94105	0.0721384
$725$	−10.2218	−0.379629
$726$	−11.3397	−0.420855
$727$	−37.0876	−1.37550	−0.687751	−	0.725947i	$-0.741402\pi$
$727$	−37.0876	−1.37550	−0.687751	+	0.725947i	$0.741402\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	5.62496	0.208189
$731$	46.1063	1.70530
$732$	−8.59218	−0.317576
$733$	29.3473	1.08397	0.541983	−	0.840390i	$-0.317674\pi$
$733$	29.3473	1.08397	0.541983	+	0.840390i	$0.317674\pi$
$734$	−16.6345	−0.613992
$735$	−1.66920	−0.0615695
$736$	−18.7311	−0.690439
$737$	8.66697	0.319252
$738$	7.93230	0.291992
$739$	−14.5291	−0.534463	−0.267231	−	0.963632i	$-0.586109\pi$
$739$	−14.5291	−0.534463	−0.267231	+	0.963632i	$0.586109\pi$
$740$	−7.95374	−0.292385
$741$	0	0
$742$	−6.93755	−0.254686
$743$	17.9329	0.657896	0.328948	−	0.944348i	$-0.393306\pi$
$743$	17.9329	0.657896	0.328948	+	0.944348i	$0.393306\pi$
$744$	−17.6220	−0.646055
$745$	−3.44274	−0.126132
$746$	−22.8523	−0.836684
$747$	−0.655507	−0.0239838
$748$	−15.5300	−0.567832
$749$	13.6120	0.497371
$750$	−13.0198	−0.475415
$751$	−21.4043	−0.781055	−0.390527	−	0.920591i	$-0.627707\pi$
$751$	−21.4043	−0.781055	−0.390527	+	0.920591i	$0.627707\pi$
$752$	−8.41929	−0.307020
$753$	−16.3957	−0.597491
$754$	0	0
$755$	17.8491	0.649596
$756$	0.830866	0.0302183
$757$	43.6768	1.58746	0.793730	−	0.608270i	$-0.208136\pi$
$757$	43.6768	1.58746	0.793730	+	0.608270i	$0.208136\pi$
$758$	−29.4472	−1.06957
$759$	20.0064	0.726185
$760$	−4.05513	−0.147095
$761$	−31.4196	−1.13896	−0.569479	−	0.822006i	$-0.692855\pi$
$761$	−31.4196	−1.13896	−0.569479	+	0.822006i	$0.692855\pi$
$762$	−20.8509	−0.755350
$763$	−1.08293	−0.0392048
$764$	−2.42994	−0.0879122
$765$	−6.73066	−0.243347
$766$	16.8283	0.608030
$767$	0	0
$768$	−16.0227	−0.578171
$769$	5.48923	0.197947	0.0989733	−	0.995090i	$-0.468444\pi$
$769$	5.48923	0.197947	0.0989733	+	0.995090i	$0.468444\pi$
$770$	−8.36630	−0.301501
$771$	−14.2261	−0.512341
$772$	−19.9765	−0.718971
$773$	−31.3794	−1.12864	−0.564319	−	0.825557i	$-0.690861\pi$
$773$	−31.3794	−1.12864	−0.564319	+	0.825557i	$0.690861\pi$
$774$	−12.3636	−0.444400
$775$	12.7449	0.457809
$776$	45.0471	1.61710
$777$	5.73497	0.205741
$778$	27.1515	0.973429
$779$	−5.82252	−0.208613
$780$	0	0
$781$	−28.2187	−1.00975
$782$	−18.8173	−0.672904
$783$	4.61741	0.165013
$784$	−1.64793	−0.0588546
$785$	16.5581	0.590985
$786$	−0.677484	−0.0241651
$787$	7.84245	0.279553	0.139777	−	0.990183i	$-0.455362\pi$
$787$	7.84245	0.279553	0.139777	+	0.990183i	$0.455362\pi$
$788$	−12.1352	−0.432299
$789$	17.0566	0.607230
$790$	4.12575	0.146788
$791$	−14.7313	−0.523785
$792$	14.1887	0.504175
$793$	0	0
$794$	3.84477	0.136446
$795$	10.7099	0.379839
$796$	12.8654	0.456001
$797$	5.01412	0.177609	0.0888047	−	0.996049i	$-0.471695\pi$
$797$	5.01412	0.177609	0.0888047	+	0.996049i	$0.471695\pi$
$798$	0.858176	0.0303791
$799$	20.6008	0.728805
$800$	9.60767	0.339682
$801$	10.8262	0.382526
$802$	−33.8650	−1.19581
$803$	14.4467	0.509814
$804$	−1.55348	−0.0547870
$805$	7.20420	0.253915
$806$	0	0
$807$	17.2732	0.608046
$808$	−23.9726	−0.843354
$809$	−30.4281	−1.06980	−0.534898	−	0.844917i	$-0.679650\pi$
$809$	−30.4281	−1.06980	−0.534898	+	0.844917i	$0.679650\pi$
$810$	1.80485	0.0634160
$811$	−49.4527	−1.73652	−0.868260	−	0.496109i	$-0.834762\pi$
$811$	−49.4527	−1.73652	−0.868260	+	0.496109i	$0.834762\pi$
$812$	3.83645	0.134633
$813$	−7.90154	−0.277119
$814$	28.7445	1.00750
$815$	−34.9823	−1.22538
$816$	−6.64487	−0.232617
$817$	9.07521	0.317501
$818$	−11.1084	−0.388395
$819$	0	0
$820$	−10.1744	−0.355304
$821$	−15.7133	−0.548398	−0.274199	−	0.961673i	$-0.588413\pi$
$821$	−15.7133	−0.548398	−0.274199	+	0.961673i	$0.588413\pi$
$822$	1.38215	0.0482082
$823$	9.09400	0.316997	0.158499	−	0.987359i	$-0.449335\pi$
$823$	9.09400	0.316997	0.158499	+	0.987359i	$0.449335\pi$
$824$	−43.7680	−1.52473
$825$	−10.2618	−0.357269
$826$	−13.2243	−0.460133
$827$	−8.35927	−0.290680	−0.145340	−	0.989382i	$-0.546428\pi$
$827$	−8.35927	−0.290680	−0.145340	+	0.989382i	$0.546428\pi$
$828$	−3.58597	−0.124621
$829$	−6.13514	−0.213082	−0.106541	−	0.994308i	$-0.533978\pi$
$829$	−6.13514	−0.213082	−0.106541	+	0.994308i	$0.533978\pi$
$830$	−1.18309	−0.0410658
$831$	4.50995	0.156449
$832$	0	0
$833$	4.03225	0.139709
$834$	−18.7817	−0.650356
$835$	−13.9646	−0.483266
$836$	−3.05680	−0.105722
$837$	−5.75711	−0.198995
$838$	−5.72976	−0.197931
$839$	38.5294	1.33018	0.665091	−	0.746762i	$-0.268393\pi$
$839$	38.5294	1.33018	0.665091	+	0.746762i	$0.268393\pi$
$840$	5.10929	0.176287
$841$	−7.67953	−0.264811
$842$	−18.6954	−0.644286
$843$	−20.7726	−0.715446
$844$	−16.4734	−0.567038
$845$	0	0
$846$	−5.52419	−0.189926
$847$	−10.4874	−0.360352
$848$	10.5734	0.363091
$849$	−2.02320	−0.0694362
$850$	9.65184	0.331055
$851$	−24.7518	−0.848482
$852$	5.05797	0.173283
$853$	27.8326	0.952969	0.476485	−	0.879183i	$-0.341911\pi$
$853$	27.8326	0.952969	0.476485	+	0.879183i	$0.341911\pi$
$854$	11.1816	0.382627
$855$	−1.32481	−0.0453075
$856$	−41.6651	−1.42408
$857$	−24.6902	−0.843400	−0.421700	−	0.906735i	$-0.638566\pi$
$857$	−24.6902	−0.843400	−0.421700	+	0.906735i	$0.638566\pi$
$858$	0	0
$859$	31.2546	1.06639	0.533197	−	0.845991i	$-0.320990\pi$
$859$	31.2546	1.06639	0.533197	+	0.845991i	$0.320990\pi$
$860$	15.8582	0.540759
$861$	7.33613	0.250014
$862$	−20.7867	−0.707998
$863$	4.20143	0.143018	0.0715091	−	0.997440i	$-0.477218\pi$
$863$	4.20143	0.143018	0.0715091	+	0.997440i	$0.477218\pi$
$864$	−4.33998	−0.147649
$865$	−9.90674	−0.336839
$866$	9.98625	0.339346
$867$	−0.740925	−0.0251631
$868$	−4.78339	−0.162359
$869$	10.5963	0.359454
$870$	8.33374	0.282540
$871$	0	0
$872$	3.31477	0.112252
$873$	14.7169	0.498091
$874$	−3.70384	−0.125284
$875$	−12.0412	−0.407068
$876$	−2.58946	−0.0874896
$877$	−46.1765	−1.55927	−0.779635	−	0.626234i	$-0.784596\pi$
$877$	−46.1765	−1.55927	−0.779635	+	0.626234i	$0.784596\pi$
$878$	−39.8604	−1.34522
$879$	−25.9848	−0.876445
$880$	12.7509	0.429832
$881$	23.6571	0.797028	0.398514	−	0.917162i	$-0.369526\pi$
$881$	23.6571	0.797028	0.398514	+	0.917162i	$0.369526\pi$
$882$	−1.08127	−0.0364081
$883$	28.4713	0.958134	0.479067	−	0.877778i	$-0.340975\pi$
$883$	28.4713	0.958134	0.479067	+	0.877778i	$0.340975\pi$
$884$	0	0
$885$	20.4151	0.686245
$886$	21.7760	0.731579
$887$	−9.79667	−0.328940	−0.164470	−	0.986382i	$-0.552591\pi$
$887$	−9.79667	−0.328940	−0.164470	+	0.986382i	$0.552591\pi$
$888$	−17.5543	−0.589082
$889$	−19.2838	−0.646759
$890$	19.5397	0.654973
$891$	4.63545	0.155293
$892$	22.7357	0.761249
$893$	4.05491	0.135692
$894$	−2.23011	−0.0745861
$895$	−24.3587	−0.814220
$896$	−0.0422458	−0.00141133
$897$	0	0
$898$	35.9194	1.19864
$899$	−26.5830	−0.886591
$900$	1.83934	0.0613112
$901$	−25.8715	−0.861905
$902$	36.7698	1.22430
$903$	−11.4344	−0.380512
$904$	45.0913	1.49972
$905$	3.89955	0.129625
$906$	11.5622	0.384127
$907$	−32.9274	−1.09334	−0.546669	−	0.837349i	$-0.684104\pi$
$907$	−32.9274	−1.09334	−0.546669	+	0.837349i	$0.684104\pi$
$908$	−12.5707	−0.417175
$909$	−7.83185	−0.259766
$910$	0	0
$911$	−19.3453	−0.640940	−0.320470	−	0.947259i	$-0.603841\pi$
$911$	−19.3453	−0.640940	−0.320470	+	0.947259i	$0.603841\pi$
$912$	−1.30793	−0.0433097
$913$	−3.03857	−0.100562
$914$	−27.1981	−0.899635
$915$	−17.2616	−0.570652
$916$	−8.86822	−0.293014
$917$	−0.626566	−0.0206910
$918$	−4.35994	−0.143899
$919$	−26.9673	−0.889568	−0.444784	−	0.895638i	$-0.646720\pi$
$919$	−26.9673	−0.889568	−0.444784	+	0.895638i	$0.646720\pi$
$920$	−22.0514	−0.727015
$921$	−24.6185	−0.811208
$922$	−25.0690	−0.825605
$923$	0	0
$924$	3.85144	0.126703
$925$	12.6958	0.417436
$926$	13.9136	0.457229
$927$	−14.2990	−0.469640
$928$	−20.0395	−0.657828
$929$	−37.9175	−1.24403	−0.622017	−	0.783004i	$-0.713687\pi$
$929$	−37.9175	−1.24403	−0.622017	+	0.783004i	$0.713687\pi$
$930$	−10.3907	−0.340726
$931$	0.793678	0.0260117
$932$	8.83547	0.289415
$933$	33.1216	1.08435
$934$	27.6657	0.905251
$935$	−31.1996	−1.02034
$936$	0	0
$937$	33.3091	1.08816	0.544080	−	0.839033i	$-0.316879\pi$
$937$	33.3091	1.08816	0.544080	+	0.839033i	$0.316879\pi$
$938$	2.02166	0.0660094
$939$	−7.05477	−0.230224
$940$	7.08561	0.231107
$941$	−9.43451	−0.307556	−0.153778	−	0.988105i	$-0.549144\pi$
$941$	−9.43451	−0.307556	−0.153778	+	0.988105i	$0.549144\pi$
$942$	10.7259	0.349469
$943$	−31.6623	−1.03107
$944$	20.1549	0.655985
$945$	1.66920	0.0542992
$946$	−57.3108	−1.86334
$947$	8.18143	0.265861	0.132930	−	0.991125i	$-0.457561\pi$
$947$	8.18143	0.265861	0.132930	+	0.991125i	$0.457561\pi$
$948$	−1.89930	−0.0616863
$949$	0	0
$950$	1.89979	0.0616374
$951$	−13.0084	−0.421825
$952$	−12.3424	−0.400019
$953$	−35.7424	−1.15781	−0.578905	−	0.815395i	$-0.696520\pi$
$953$	−35.7424	−1.15781	−0.578905	+	0.815395i	$0.696520\pi$
$954$	6.93755	0.224612
$955$	−4.88174	−0.157969
$956$	−12.0911	−0.391053
$957$	21.4038	0.691886
$958$	−27.3291	−0.882964
$959$	1.27827	0.0412777
$960$	−13.3345	−0.430369
$961$	2.14436	0.0691728
$962$	0	0
$963$	−13.6120	−0.438640
$964$	−17.4886	−0.563268
$965$	−40.1327	−1.29192
$966$	4.66668	0.150148
$967$	33.9787	1.09268	0.546341	−	0.837563i	$-0.316020\pi$
$967$	33.9787	1.09268	0.546341	+	0.837563i	$0.316020\pi$
$968$	32.1011	1.03177
$969$	3.20031	0.102809
$970$	26.5618	0.852848
$971$	37.6727	1.20897	0.604487	−	0.796615i	$-0.293378\pi$
$971$	37.6727	1.20897	0.604487	+	0.796615i	$0.293378\pi$
$972$	−0.830866	−0.0266500
$973$	−17.3701	−0.556860
$974$	45.9496	1.47232
$975$	0	0
$976$	−17.0416	−0.545489
$977$	25.7786	0.824730	0.412365	−	0.911019i	$-0.364703\pi$
$977$	25.7786	0.824730	0.412365	+	0.911019i	$0.364703\pi$
$978$	−22.6606	−0.724606
$979$	50.1844	1.60390
$980$	1.38688	0.0443024
$981$	1.08293	0.0345754
$982$	43.6335	1.39240
$983$	−31.8264	−1.01510	−0.507552	−	0.861621i	$-0.669450\pi$
$983$	−31.8264	−1.01510	−0.507552	+	0.861621i	$0.669450\pi$
$984$	−22.4553	−0.715848
$985$	−24.3795	−0.776797
$986$	−20.1316	−0.641121
$987$	−5.10901	−0.162622
$988$	0	0
$989$	49.3502	1.56924
$990$	8.36630	0.265899
$991$	22.3388	0.709616	0.354808	−	0.934939i	$-0.384546\pi$
$991$	22.3388	0.709616	0.354808	+	0.934939i	$0.384546\pi$
$992$	24.9858	0.793299
$993$	−17.9368	−0.569206
$994$	−6.58230	−0.208778
$995$	25.8465	0.819388
$996$	0.544638	0.0172575
$997$	22.7194	0.719532	0.359766	−	0.933043i	$-0.382857\pi$
$997$	22.7194	0.719532	0.359766	+	0.933043i	$0.382857\pi$
$998$	−6.01938	−0.190540
$999$	−5.73497	−0.181446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bh.1.6	yes	15
13.12	even	2		3549.2.a.bg.1.10	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.bg.1.10	✓	15	13.12	even	2
3549.2.a.bh.1.6	yes	15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-1.08127 q^{2} +1.00000 q^{3} -0.830866 q^{4} -1.66920 q^{5} -1.08127 q^{6} -1.00000 q^{7} +3.06092 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.08127 q^{2} +1.00000 q^{3} -0.830866 q^{4} -1.66920 q^{5} -1.08127 q^{6} -1.00000 q^{7} +3.06092 q^{8} +1.00000 q^{9} +1.80485 q^{10} +4.63545 q^{11} -0.830866 q^{12} +1.08127 q^{14} -1.66920 q^{15} -1.64793 q^{16} +4.03225 q^{17} -1.08127 q^{18} +0.793678 q^{19} +1.38688 q^{20} -1.00000 q^{21} -5.01215 q^{22} +4.31595 q^{23} +3.06092 q^{24} -2.21376 q^{25} +1.00000 q^{27} +0.830866 q^{28} +4.61741 q^{29} +1.80485 q^{30} -5.75711 q^{31} -4.33998 q^{32} +4.63545 q^{33} -4.35994 q^{34} +1.66920 q^{35} -0.830866 q^{36} -5.73497 q^{37} -0.858176 q^{38} -5.10929 q^{40} -7.33613 q^{41} +1.08127 q^{42} +11.4344 q^{43} -3.85144 q^{44} -1.66920 q^{45} -4.66668 q^{46} +5.10901 q^{47} -1.64793 q^{48} +1.00000 q^{49} +2.39366 q^{50} +4.03225 q^{51} -6.41614 q^{53} -1.08127 q^{54} -7.73752 q^{55} -3.06092 q^{56} +0.793678 q^{57} -4.99264 q^{58} -12.2304 q^{59} +1.38688 q^{60} +10.3412 q^{61} +6.22497 q^{62} -1.00000 q^{63} +7.98853 q^{64} -5.01215 q^{66} +1.86971 q^{67} -3.35026 q^{68} +4.31595 q^{69} -1.80485 q^{70} -6.08759 q^{71} +3.06092 q^{72} +3.11657 q^{73} +6.20102 q^{74} -2.21376 q^{75} -0.659440 q^{76} -4.63545 q^{77} +2.28592 q^{79} +2.75073 q^{80} +1.00000 q^{81} +7.93230 q^{82} -0.655507 q^{83} +0.830866 q^{84} -6.73066 q^{85} -12.3636 q^{86} +4.61741 q^{87} +14.1887 q^{88} +10.8262 q^{89} +1.80485 q^{90} -3.58597 q^{92} -5.75711 q^{93} -5.52419 q^{94} -1.32481 q^{95} -4.33998 q^{96} +14.7169 q^{97} -1.08127 q^{98} +4.63545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9} + 21 q^{10} + 5 q^{11} + 28 q^{12} - 2 q^{14} - 9 q^{15} + 50 q^{16} - q^{17} + 2 q^{18} + 3 q^{19} - 23 q^{20} - 15 q^{21} + 21 q^{22} + 4 q^{23} + 9 q^{24} + 50 q^{25} + 15 q^{27} - 28 q^{28} + 9 q^{29} + 21 q^{30} + 7 q^{31} + 35 q^{32} + 5 q^{33} - 2 q^{34} + 9 q^{35} + 28 q^{36} + 17 q^{37} - 12 q^{38} + 46 q^{40} - 22 q^{41} - 2 q^{42} + 36 q^{43} + 29 q^{44} - 9 q^{45} - q^{46} - 12 q^{47} + 50 q^{48} + 15 q^{49} + 53 q^{50} - q^{51} - 5 q^{53} + 2 q^{54} + 43 q^{55} - 9 q^{56} + 3 q^{57} + 29 q^{58} - 29 q^{59} - 23 q^{60} + 12 q^{61} + 14 q^{62} - 15 q^{63} + 95 q^{64} + 21 q^{66} - 12 q^{67} - 16 q^{68} + 4 q^{69} - 21 q^{70} + 36 q^{71} + 9 q^{72} - 29 q^{73} - 5 q^{74} + 50 q^{75} + 25 q^{76} - 5 q^{77} + 35 q^{79} - 89 q^{80} + 15 q^{81} + 51 q^{82} - 10 q^{83} - 28 q^{84} + 23 q^{85} + 19 q^{86} + 9 q^{87} + 73 q^{88} + 25 q^{89} + 21 q^{90} - 31 q^{92} + 7 q^{93} - 19 q^{94} - 7 q^{95} + 35 q^{96} - 26 q^{97} + 2 q^{98} + 5 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9 + 21 * q^10 + 5 * q^11 + 28 * q^12 - 2 * q^14 - 9 * q^15 + 50 * q^16 - q^17 + 2 * q^18 + 3 * q^19 - 23 * q^20 - 15 * q^21 + 21 * q^22 + 4 * q^23 + 9 * q^24 + 50 * q^25 + 15 * q^27 - 28 * q^28 + 9 * q^29 + 21 * q^30 + 7 * q^31 + 35 * q^32 + 5 * q^33 - 2 * q^34 + 9 * q^35 + 28 * q^36 + 17 * q^37 - 12 * q^38 + 46 * q^40 - 22 * q^41 - 2 * q^42 + 36 * q^43 + 29 * q^44 - 9 * q^45 - q^46 - 12 * q^47 + 50 * q^48 + 15 * q^49 + 53 * q^50 - q^51 - 5 * q^53 + 2 * q^54 + 43 * q^55 - 9 * q^56 + 3 * q^57 + 29 * q^58 - 29 * q^59 - 23 * q^60 + 12 * q^61 + 14 * q^62 - 15 * q^63 + 95 * q^64 + 21 * q^66 - 12 * q^67 - 16 * q^68 + 4 * q^69 - 21 * q^70 + 36 * q^71 + 9 * q^72 - 29 * q^73 - 5 * q^74 + 50 * q^75 + 25 * q^76 - 5 * q^77 + 35 * q^79 - 89 * q^80 + 15 * q^81 + 51 * q^82 - 10 * q^83 - 28 * q^84 + 23 * q^85 + 19 * q^86 + 9 * q^87 + 73 * q^88 + 25 * q^89 + 21 * q^90 - 31 * q^92 + 7 * q^93 - 19 * q^94 - 7 * q^95 + 35 * q^96 - 26 * q^97 + 2 * q^98 + 5 * q^99

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