LMFDB - Embedded newform 3549.2.a.n.1.3

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:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.87939$ 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)

$f(q)$	$=$	$q+1.87939 q^{2} +1.00000 q^{3} +1.53209 q^{4} -2.34730 q^{5} +1.87939 q^{6} +1.00000 q^{7} -0.879385 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.87939 q^{2} +1.00000 q^{3} +1.53209 q^{4} -2.34730 q^{5} +1.87939 q^{6} +1.00000 q^{7} -0.879385 q^{8} +1.00000 q^{9} -4.41147 q^{10} -4.71688 q^{11} +1.53209 q^{12} +1.87939 q^{14} -2.34730 q^{15} -4.71688 q^{16} +6.24897 q^{17} +1.87939 q^{18} -3.69459 q^{19} -3.59627 q^{20} +1.00000 q^{21} -8.86484 q^{22} +6.98545 q^{23} -0.879385 q^{24} +0.509800 q^{25} +1.00000 q^{27} +1.53209 q^{28} -6.39693 q^{29} -4.41147 q^{30} -1.95811 q^{31} -7.10607 q^{32} -4.71688 q^{33} +11.7442 q^{34} -2.34730 q^{35} +1.53209 q^{36} -8.80066 q^{37} -6.94356 q^{38} +2.06418 q^{40} -6.73917 q^{41} +1.87939 q^{42} -4.66044 q^{43} -7.22668 q^{44} -2.34730 q^{45} +13.1284 q^{46} +3.10607 q^{47} -4.71688 q^{48} +1.00000 q^{49} +0.958111 q^{50} +6.24897 q^{51} -13.3405 q^{53} +1.87939 q^{54} +11.0719 q^{55} -0.879385 q^{56} -3.69459 q^{57} -12.0223 q^{58} -12.3746 q^{59} -3.59627 q^{60} -7.36959 q^{61} -3.68004 q^{62} +1.00000 q^{63} -3.92127 q^{64} -8.86484 q^{66} +13.2199 q^{67} +9.57398 q^{68} +6.98545 q^{69} -4.41147 q^{70} +9.98545 q^{71} -0.879385 q^{72} -9.16250 q^{73} -16.5398 q^{74} +0.509800 q^{75} -5.66044 q^{76} -4.71688 q^{77} -3.58853 q^{79} +11.0719 q^{80} +1.00000 q^{81} -12.6655 q^{82} -0.829755 q^{83} +1.53209 q^{84} -14.6682 q^{85} -8.75877 q^{86} -6.39693 q^{87} +4.14796 q^{88} +2.30541 q^{89} -4.41147 q^{90} +10.7023 q^{92} -1.95811 q^{93} +5.83750 q^{94} +8.67230 q^{95} -7.10607 q^{96} -12.6236 q^{97} +1.87939 q^{98} -4.71688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{3} - 6 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^3 - 6 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{3} - 6 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 6 q^{11} - 6 q^{15} - 6 q^{16} + 6 q^{17} - 9 q^{19} + 3 q^{20} + 3 q^{21} - 3 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} + 3 q^{27} + 9 q^{29} - 3 q^{30} - 9 q^{31} - 9 q^{32} - 6 q^{33} + 6 q^{34} - 6 q^{35} - 12 q^{37} - 6 q^{38} - 3 q^{40} - 6 q^{41} + 9 q^{43} - 15 q^{44} - 6 q^{45} + 21 q^{46} - 3 q^{47} - 6 q^{48} + 3 q^{49} + 6 q^{50} + 6 q^{51} + 3 q^{53} + 3 q^{56} - 9 q^{57} - 30 q^{58} - 15 q^{59} + 3 q^{60} - 15 q^{61} + 9 q^{62} + 3 q^{63} - 3 q^{64} - 3 q^{66} - 9 q^{67} + 21 q^{68} + 3 q^{69} - 3 q^{70} + 12 q^{71} + 3 q^{72} - 30 q^{73} - 21 q^{74} + 3 q^{75} + 6 q^{76} - 6 q^{77} - 21 q^{79} + 3 q^{81} - 24 q^{83} + 3 q^{85} - 15 q^{86} + 9 q^{87} - 3 q^{88} + 9 q^{89} - 3 q^{90} + 6 q^{92} - 9 q^{93} + 15 q^{94} + 30 q^{95} - 9 q^{96} - 3 q^{97} - 6 q^{99}+O(q^{100}) $ 3 * q + 3 * q^3 - 6 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 6 * q^11 - 6 * q^15 - 6 * q^16 + 6 * q^17 - 9 * q^19 + 3 * q^20 + 3 * q^21 - 3 * q^22 + 3 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 + 9 * q^29 - 3 * q^30 - 9 * q^31 - 9 * q^32 - 6 * q^33 + 6 * q^34 - 6 * q^35 - 12 * q^37 - 6 * q^38 - 3 * q^40 - 6 * q^41 + 9 * q^43 - 15 * q^44 - 6 * q^45 + 21 * q^46 - 3 * q^47 - 6 * q^48 + 3 * q^49 + 6 * q^50 + 6 * q^51 + 3 * q^53 + 3 * q^56 - 9 * q^57 - 30 * q^58 - 15 * q^59 + 3 * q^60 - 15 * q^61 + 9 * q^62 + 3 * q^63 - 3 * q^64 - 3 * q^66 - 9 * q^67 + 21 * q^68 + 3 * q^69 - 3 * q^70 + 12 * q^71 + 3 * q^72 - 30 * q^73 - 21 * q^74 + 3 * q^75 + 6 * q^76 - 6 * q^77 - 21 * q^79 + 3 * q^81 - 24 * q^83 + 3 * q^85 - 15 * q^86 + 9 * q^87 - 3 * q^88 + 9 * q^89 - 3 * q^90 + 6 * q^92 - 9 * q^93 + 15 * q^94 + 30 * q^95 - 9 * q^96 - 3 * 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 $

$2$	1.87939	1.32893	0.664463	−	0.747321i	$-0.268660\pi$
$2$	1.87939	1.32893	0.664463	+	0.747321i	$0.268660\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.53209	0.766044
$5$	−2.34730	−1.04974	−0.524871	−	0.851182i	$-0.675887\pi$
$5$	−2.34730	−1.04974	−0.524871	+	0.851182i	$0.675887\pi$
$6$	1.87939	0.767256
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.879385	−0.310910
$9$	1.00000	0.333333
$10$	−4.41147	−1.39503
$11$	−4.71688	−1.42219	−0.711097	−	0.703094i	$-0.751801\pi$
$11$	−4.71688	−1.42219	−0.711097	+	0.703094i	$0.751801\pi$
$12$	1.53209	0.442276
$13$	0	0
$13$	0	0
$14$	1.87939	0.502287
$15$	−2.34730	−0.606069
$16$	−4.71688	−1.17922
$17$	6.24897	1.51560	0.757799	−	0.652488i	$-0.226275\pi$
$17$	6.24897	1.51560	0.757799	+	0.652488i	$0.226275\pi$
$18$	1.87939	0.442975
$19$	−3.69459	−0.847598	−0.423799	−	0.905756i	$-0.639304\pi$
$19$	−3.69459	−0.847598	−0.423799	+	0.905756i	$0.639304\pi$
$20$	−3.59627	−0.804150
$21$	1.00000	0.218218
$22$	−8.86484	−1.88999
$23$	6.98545	1.45657	0.728284	−	0.685276i	$-0.240318\pi$
$23$	6.98545	1.45657	0.728284	+	0.685276i	$0.240318\pi$
$24$	−0.879385	−0.179504
$25$	0.509800	0.101960
$26$	0	0
$27$	1.00000	0.192450
$28$	1.53209	0.289538
$29$	−6.39693	−1.18788	−0.593940	−	0.804510i	$-0.702428\pi$
$29$	−6.39693	−1.18788	−0.593940	+	0.804510i	$0.702428\pi$
$30$	−4.41147	−0.805421
$31$	−1.95811	−0.351687	−0.175844	−	0.984418i	$-0.556265\pi$
$31$	−1.95811	−0.351687	−0.175844	+	0.984418i	$0.556265\pi$
$32$	−7.10607	−1.25619
$33$	−4.71688	−0.821104
$34$	11.7442	2.01412
$35$	−2.34730	−0.396766
$36$	1.53209	0.255348
$37$	−8.80066	−1.44682	−0.723410	−	0.690419i	$-0.757426\pi$
$37$	−8.80066	−1.44682	−0.723410	+	0.690419i	$0.757426\pi$
$38$	−6.94356	−1.12639
$39$	0	0
$40$	2.06418	0.326375
$41$	−6.73917	−1.05248	−0.526241	−	0.850336i	$-0.676399\pi$
$41$	−6.73917	−1.05248	−0.526241	+	0.850336i	$0.676399\pi$
$42$	1.87939	0.289995
$43$	−4.66044	−0.710711	−0.355356	−	0.934731i	$-0.615640\pi$
$43$	−4.66044	−0.710711	−0.355356	+	0.934731i	$0.615640\pi$
$44$	−7.22668	−1.08946
$45$	−2.34730	−0.349914
$46$	13.1284	1.93567
$47$	3.10607	0.453066	0.226533	−	0.974003i	$-0.427261\pi$
$47$	3.10607	0.453066	0.226533	+	0.974003i	$0.427261\pi$
$48$	−4.71688	−0.680823
$49$	1.00000	0.142857
$50$	0.958111	0.135497
$51$	6.24897	0.875031
$52$	0	0
$53$	−13.3405	−1.83246	−0.916229	−	0.400656i	$-0.868782\pi$
$53$	−13.3405	−1.83246	−0.916229	+	0.400656i	$0.868782\pi$
$54$	1.87939	0.255752
$55$	11.0719	1.49294
$56$	−0.879385	−0.117513
$57$	−3.69459	−0.489361
$58$	−12.0223	−1.57860
$59$	−12.3746	−1.61104	−0.805520	−	0.592568i	$-0.798114\pi$
$59$	−12.3746	−1.61104	−0.805520	+	0.592568i	$0.798114\pi$
$60$	−3.59627	−0.464276
$61$	−7.36959	−0.943579	−0.471789	−	0.881711i	$-0.656392\pi$
$61$	−7.36959	−0.943579	−0.471789	+	0.881711i	$0.656392\pi$
$62$	−3.68004	−0.467366
$63$	1.00000	0.125988
$64$	−3.92127	−0.490159
$65$	0	0
$66$	−8.86484	−1.09119
$67$	13.2199	1.61506	0.807532	−	0.589823i	$-0.200803\pi$
$67$	13.2199	1.61506	0.807532	+	0.589823i	$0.200803\pi$
$68$	9.57398	1.16102
$69$	6.98545	0.840950
$70$	−4.41147	−0.527272
$71$	9.98545	1.18506	0.592528	−	0.805550i	$-0.298130\pi$
$71$	9.98545	1.18506	0.592528	+	0.805550i	$0.298130\pi$
$72$	−0.879385	−0.103637
$73$	−9.16250	−1.07239	−0.536195	−	0.844094i	$-0.680139\pi$
$73$	−9.16250	−1.07239	−0.536195	+	0.844094i	$0.680139\pi$
$74$	−16.5398	−1.92272
$75$	0.509800	0.0588667
$76$	−5.66044	−0.649298
$77$	−4.71688	−0.537539
$78$	0	0
$79$	−3.58853	−0.403741	−0.201870	−	0.979412i	$-0.564702\pi$
$79$	−3.58853	−0.403741	−0.201870	+	0.979412i	$0.564702\pi$
$80$	11.0719	1.23788
$81$	1.00000	0.111111
$82$	−12.6655	−1.39867
$83$	−0.829755	−0.0910775	−0.0455387	−	0.998963i	$-0.514500\pi$
$83$	−0.829755	−0.0910775	−0.0455387	+	0.998963i	$0.514500\pi$
$84$	1.53209	0.167165
$85$	−14.6682	−1.59099
$86$	−8.75877	−0.944483
$87$	−6.39693	−0.685822
$88$	4.14796	0.442174
$89$	2.30541	0.244373	0.122186	−	0.992507i	$-0.461009\pi$
$89$	2.30541	0.244373	0.122186	+	0.992507i	$0.461009\pi$
$90$	−4.41147	−0.465010
$91$	0	0
$92$	10.7023	1.11580
$93$	−1.95811	−0.203047
$94$	5.83750	0.602092
$95$	8.67230	0.889760
$96$	−7.10607	−0.725260
$97$	−12.6236	−1.28173	−0.640867	−	0.767652i	$-0.721425\pi$
$97$	−12.6236	−1.28173	−0.640867	+	0.767652i	$0.721425\pi$
$98$	1.87939	0.189847
$99$	−4.71688	−0.474064
$100$	0.781059	0.0781059
$101$	−2.40373	−0.239180	−0.119590	−	0.992823i	$-0.538158\pi$
$101$	−2.40373	−0.239180	−0.119590	+	0.992823i	$0.538158\pi$
$102$	11.7442	1.16285
$103$	1.69459	0.166973	0.0834866	−	0.996509i	$-0.473394\pi$
$103$	1.69459	0.166973	0.0834866	+	0.996509i	$0.473394\pi$
$104$	0	0
$105$	−2.34730	−0.229073
$106$	−25.0719	−2.43520
$107$	3.85710	0.372880	0.186440	−	0.982466i	$-0.440305\pi$
$107$	3.85710	0.372880	0.186440	+	0.982466i	$0.440305\pi$
$108$	1.53209	0.147425
$109$	−0.268571	−0.0257244	−0.0128622	−	0.999917i	$-0.504094\pi$
$109$	−0.268571	−0.0257244	−0.0128622	+	0.999917i	$0.504094\pi$
$110$	20.8084	1.98400
$111$	−8.80066	−0.835322
$112$	−4.71688	−0.445703
$113$	7.71688	0.725943	0.362972	−	0.931800i	$-0.381762\pi$
$113$	7.71688	0.725943	0.362972	+	0.931800i	$0.381762\pi$
$114$	−6.94356	−0.650324
$115$	−16.3969	−1.52902
$116$	−9.80066	−0.909968
$117$	0	0
$118$	−23.2567	−2.14095
$119$	6.24897	0.572842
$120$	2.06418	0.188433
$121$	11.2490	1.02263
$122$	−13.8503	−1.25395
$123$	−6.73917	−0.607651
$124$	−3.00000	−0.269408
$125$	10.5398	0.942711
$126$	1.87939	0.167429
$127$	−7.65270	−0.679068	−0.339534	−	0.940594i	$-0.610269\pi$
$127$	−7.65270	−0.679068	−0.339534	+	0.940594i	$0.610269\pi$
$128$	6.84255	0.604802
$129$	−4.66044	−0.410329
$130$	0	0
$131$	−9.25402	−0.808528	−0.404264	−	0.914642i	$-0.632472\pi$
$131$	−9.25402	−0.808528	−0.404264	+	0.914642i	$0.632472\pi$
$132$	−7.22668	−0.629002
$133$	−3.69459	−0.320362
$134$	24.8452	2.14630
$135$	−2.34730	−0.202023
$136$	−5.49525	−0.471214
$137$	17.5817	1.50211	0.751054	−	0.660241i	$-0.229546\pi$
$137$	17.5817	1.50211	0.751054	+	0.660241i	$0.229546\pi$
$138$	13.1284	1.11756
$139$	−3.89899	−0.330708	−0.165354	−	0.986234i	$-0.552877\pi$
$139$	−3.89899	−0.330708	−0.165354	+	0.986234i	$0.552877\pi$
$140$	−3.59627	−0.303940
$141$	3.10607	0.261578
$142$	18.7665	1.57485
$143$	0	0
$144$	−4.71688	−0.393073
$145$	15.0155	1.24697
$146$	−17.2199	−1.42513
$147$	1.00000	0.0824786
$148$	−13.4834	−1.10833
$149$	11.1702	0.915102	0.457551	−	0.889183i	$-0.348727\pi$
$149$	11.1702	0.915102	0.457551	+	0.889183i	$0.348727\pi$
$150$	0.958111	0.0782294
$151$	5.97090	0.485905	0.242953	−	0.970038i	$-0.421884\pi$
$151$	5.97090	0.485905	0.242953	+	0.970038i	$0.421884\pi$
$152$	3.24897	0.263526
$153$	6.24897	0.505199
$154$	−8.86484	−0.714349
$155$	4.59627	0.369181
$156$	0	0
$157$	8.75196	0.698483	0.349241	−	0.937033i	$-0.386439\pi$
$157$	8.75196	0.698483	0.349241	+	0.937033i	$0.386439\pi$
$158$	−6.74422	−0.536542
$159$	−13.3405	−1.05797
$160$	16.6800	1.31867
$161$	6.98545	0.550531
$162$	1.87939	0.147658
$163$	−2.22163	−0.174011	−0.0870057	−	0.996208i	$-0.527730\pi$
$163$	−2.22163	−0.174011	−0.0870057	+	0.996208i	$0.527730\pi$
$164$	−10.3250	−0.806248
$165$	11.0719	0.861948
$166$	−1.55943	−0.121035
$167$	15.9513	1.23435	0.617174	−	0.786826i	$-0.288277\pi$
$167$	15.9513	1.23435	0.617174	+	0.786826i	$0.288277\pi$
$168$	−0.879385	−0.0678460
$169$	0	0
$170$	−27.5672	−2.11431
$171$	−3.69459	−0.282533
$172$	−7.14022	−0.544436
$173$	3.09833	0.235561	0.117781	−	0.993040i	$-0.462422\pi$
$173$	3.09833	0.235561	0.117781	+	0.993040i	$0.462422\pi$
$174$	−12.0223	−0.911407
$175$	0.509800	0.0385373
$176$	22.2490	1.67708
$177$	−12.3746	−0.930135
$178$	4.33275	0.324753
$179$	15.5895	1.16521	0.582605	−	0.812755i	$-0.302033\pi$
$179$	15.5895	1.16521	0.582605	+	0.812755i	$0.302033\pi$
$180$	−3.59627	−0.268050
$181$	18.0942	1.34493	0.672466	−	0.740128i	$-0.265235\pi$
$181$	18.0942	1.34493	0.672466	+	0.740128i	$0.265235\pi$
$182$	0	0
$183$	−7.36959	−0.544775
$184$	−6.14290	−0.452861
$185$	20.6578	1.51879
$186$	−3.68004	−0.269834
$187$	−29.4757	−2.15547
$188$	4.75877	0.347069
$189$	1.00000	0.0727393
$190$	16.2986	1.18242
$191$	−12.9017	−0.933532	−0.466766	−	0.884381i	$-0.654581\pi$
$191$	−12.9017	−0.933532	−0.466766	+	0.884381i	$0.654581\pi$
$192$	−3.92127	−0.282994
$193$	12.6313	0.909224	0.454612	−	0.890689i	$-0.349778\pi$
$193$	12.6313	0.909224	0.454612	+	0.890689i	$0.349778\pi$
$194$	−23.7246	−1.70333
$195$	0	0
$196$	1.53209	0.109435
$197$	4.72462	0.336615	0.168308	−	0.985735i	$-0.446170\pi$
$197$	4.72462	0.336615	0.168308	+	0.985735i	$0.446170\pi$
$198$	−8.86484	−0.629997
$199$	−15.6604	−1.11014	−0.555070	−	0.831804i	$-0.687308\pi$
$199$	−15.6604	−1.11014	−0.555070	+	0.831804i	$0.687308\pi$
$200$	−0.448311	−0.0317004
$201$	13.2199	0.932458
$202$	−4.51754	−0.317853
$203$	−6.39693	−0.448976
$204$	9.57398	0.670313
$205$	15.8188	1.10483
$206$	3.18479	0.221895
$207$	6.98545	0.485522
$208$	0	0
$209$	17.4270	1.20545
$210$	−4.41147	−0.304421
$211$	6.13341	0.422241	0.211121	−	0.977460i	$-0.432289\pi$
$211$	6.13341	0.422241	0.211121	+	0.977460i	$0.432289\pi$
$212$	−20.4388	−1.40374
$213$	9.98545	0.684192
$214$	7.24897	0.495529
$215$	10.9394	0.746064
$216$	−0.879385	−0.0598346
$217$	−1.95811	−0.132925
$218$	−0.504748	−0.0341858
$219$	−9.16250	−0.619145
$220$	16.9632	1.14366
$221$	0	0
$222$	−16.5398	−1.11008
$223$	1.36959	0.0917142	0.0458571	−	0.998948i	$-0.485398\pi$
$223$	1.36959	0.0917142	0.0458571	+	0.998948i	$0.485398\pi$
$224$	−7.10607	−0.474794
$225$	0.509800	0.0339867
$226$	14.5030	0.964725
$227$	7.34730	0.487657	0.243829	−	0.969818i	$-0.421597\pi$
$227$	7.34730	0.487657	0.243829	+	0.969818i	$0.421597\pi$
$228$	−5.66044	−0.374872
$229$	−15.1976	−1.00428	−0.502142	−	0.864785i	$-0.667455\pi$
$229$	−15.1976	−1.00428	−0.502142	+	0.864785i	$0.667455\pi$
$230$	−30.8161	−2.03196
$231$	−4.71688	−0.310348
$232$	5.62536	0.369323
$233$	13.6263	0.892688	0.446344	−	0.894861i	$-0.352726\pi$
$233$	13.6263	0.892688	0.446344	+	0.894861i	$0.352726\pi$
$234$	0	0
$235$	−7.29086	−0.475603
$236$	−18.9590	−1.23413
$237$	−3.58853	−0.233100
$238$	11.7442	0.761265
$239$	2.36959	0.153276	0.0766379	−	0.997059i	$-0.475581\pi$
$239$	2.36959	0.153276	0.0766379	+	0.997059i	$0.475581\pi$
$240$	11.0719	0.714689
$241$	21.0378	1.35516	0.677581	−	0.735448i	$-0.263028\pi$
$241$	21.0378	1.35516	0.677581	+	0.735448i	$0.263028\pi$
$242$	21.1411	1.35900
$243$	1.00000	0.0641500
$244$	−11.2909	−0.722823
$245$	−2.34730	−0.149963
$246$	−12.6655	−0.807523
$247$	0	0
$248$	1.72193	0.109343
$249$	−0.829755	−0.0525836
$250$	19.8084	1.25279
$251$	7.10607	0.448531	0.224265	−	0.974528i	$-0.428002\pi$
$251$	7.10607	0.448531	0.224265	+	0.974528i	$0.428002\pi$
$252$	1.53209	0.0965125
$253$	−32.9495	−2.07152
$254$	−14.3824	−0.902431
$255$	−14.6682	−0.918557
$256$	20.7023	1.29390
$257$	−15.2071	−0.948592	−0.474296	−	0.880366i	$-0.657297\pi$
$257$	−15.2071	−0.948592	−0.474296	+	0.880366i	$0.657297\pi$
$258$	−8.75877	−0.545297
$259$	−8.80066	−0.546846
$260$	0	0
$261$	−6.39693	−0.395960
$262$	−17.3919	−1.07447
$263$	12.8375	0.791594	0.395797	−	0.918338i	$-0.370468\pi$
$263$	12.8375	0.791594	0.395797	+	0.918338i	$0.370468\pi$
$264$	4.14796	0.255289
$265$	31.3141	1.92361
$266$	−6.94356	−0.425737
$267$	2.30541	0.141089
$268$	20.2540	1.23721
$269$	−17.8007	−1.08533	−0.542663	−	0.839951i	$-0.682584\pi$
$269$	−17.8007	−1.08533	−0.542663	+	0.839951i	$0.682584\pi$
$270$	−4.41147	−0.268474
$271$	0.702333	0.0426637	0.0213319	−	0.999772i	$-0.493209\pi$
$271$	0.702333	0.0426637	0.0213319	+	0.999772i	$0.493209\pi$
$272$	−29.4757	−1.78722
$273$	0	0
$274$	33.0428	1.99619
$275$	−2.40467	−0.145007
$276$	10.7023	0.644205
$277$	−0.453363	−0.0272400	−0.0136200	−	0.999907i	$-0.504336\pi$
$277$	−0.453363	−0.0272400	−0.0136200	+	0.999907i	$0.504336\pi$
$278$	−7.32770	−0.439486
$279$	−1.95811	−0.117229
$280$	2.06418	0.123358
$281$	−25.3628	−1.51302	−0.756508	−	0.653984i	$-0.773096\pi$
$281$	−25.3628	−1.51302	−0.756508	+	0.653984i	$0.773096\pi$
$282$	5.83750	0.347618
$283$	−12.7956	−0.760620	−0.380310	−	0.924859i	$-0.624183\pi$
$283$	−12.7956	−0.760620	−0.380310	+	0.924859i	$0.624183\pi$
$284$	15.2986	0.907805
$285$	8.67230	0.513703
$286$	0	0
$287$	−6.73917	−0.397801
$288$	−7.10607	−0.418729
$289$	22.0496	1.29704
$290$	28.2199	1.65713
$291$	−12.6236	−0.740009
$292$	−14.0378	−0.821498
$293$	−8.06687	−0.471271	−0.235636	−	0.971841i	$-0.575717\pi$
$293$	−8.06687	−0.471271	−0.235636	+	0.971841i	$0.575717\pi$
$294$	1.87939	0.109608
$295$	29.0469	1.69118
$296$	7.73917	0.449830
$297$	−4.71688	−0.273701
$298$	20.9932	1.21610
$299$	0	0
$300$	0.781059	0.0450945
$301$	−4.66044	−0.268624
$302$	11.2216	0.645732
$303$	−2.40373	−0.138091
$304$	17.4270	0.999504
$305$	17.2986	0.990515
$306$	11.7442	0.671373
$307$	−10.6536	−0.608035	−0.304018	−	0.952666i	$-0.598328\pi$
$307$	−10.6536	−0.608035	−0.304018	+	0.952666i	$0.598328\pi$
$308$	−7.22668	−0.411778
$309$	1.69459	0.0964020
$310$	8.63816	0.490614
$311$	1.83481	0.104042	0.0520212	−	0.998646i	$-0.483434\pi$
$311$	1.83481	0.104042	0.0520212	+	0.998646i	$0.483434\pi$
$312$	0	0
$313$	−25.9094	−1.46449	−0.732243	−	0.681043i	$-0.761527\pi$
$313$	−25.9094	−1.46449	−0.732243	+	0.681043i	$0.761527\pi$
$314$	16.4483	0.928232
$315$	−2.34730	−0.132255
$316$	−5.49794	−0.309283
$317$	14.6186	0.821060	0.410530	−	0.911847i	$-0.365344\pi$
$317$	14.6186	0.821060	0.410530	+	0.911847i	$0.365344\pi$
$318$	−25.0719	−1.40596
$319$	30.1735	1.68939
$320$	9.20439	0.514541
$321$	3.85710	0.215282
$322$	13.1284	0.731615
$323$	−23.0874	−1.28462
$324$	1.53209	0.0851160
$325$	0	0
$326$	−4.17530	−0.231248
$327$	−0.268571	−0.0148520
$328$	5.92633	0.327227
$329$	3.10607	0.171243
$330$	20.8084	1.14546
$331$	−9.52940	−0.523783	−0.261892	−	0.965097i	$-0.584346\pi$
$331$	−9.52940	−0.523783	−0.261892	+	0.965097i	$0.584346\pi$
$332$	−1.27126	−0.0697694
$333$	−8.80066	−0.482273
$334$	29.9786	1.64036
$335$	−31.0310	−1.69540
$336$	−4.71688	−0.257327
$337$	−17.2790	−0.941247	−0.470624	−	0.882334i	$-0.655971\pi$
$337$	−17.2790	−0.941247	−0.470624	+	0.882334i	$0.655971\pi$
$338$	0	0
$339$	7.71688	0.419123
$340$	−22.4730	−1.21877
$341$	9.23618	0.500167
$342$	−6.94356	−0.375465
$343$	1.00000	0.0539949
$344$	4.09833	0.220967
$345$	−16.3969	−0.882781
$346$	5.82295	0.313044
$347$	19.4320	1.04316	0.521582	−	0.853201i	$-0.325342\pi$
$347$	19.4320	1.04316	0.521582	+	0.853201i	$0.325342\pi$
$348$	−9.80066	−0.525370
$349$	−28.9786	−1.55119	−0.775596	−	0.631230i	$-0.782550\pi$
$349$	−28.9786	−1.55119	−0.775596	+	0.631230i	$0.782550\pi$
$350$	0.958111	0.0512132
$351$	0	0
$352$	33.5185	1.78654
$353$	−2.53983	−0.135181	−0.0675907	−	0.997713i	$-0.521531\pi$
$353$	−2.53983	−0.135181	−0.0675907	+	0.997713i	$0.521531\pi$
$354$	−23.2567	−1.23608
$355$	−23.4388	−1.24400
$356$	3.53209	0.187200
$357$	6.24897	0.330731
$358$	29.2986	1.54848
$359$	−26.4243	−1.39462	−0.697310	−	0.716770i	$-0.745620\pi$
$359$	−26.4243	−1.39462	−0.697310	+	0.716770i	$0.745620\pi$
$360$	2.06418	0.108792
$361$	−5.34998	−0.281578
$362$	34.0060	1.78731
$363$	11.2490	0.590418
$364$	0	0
$365$	21.5071	1.12573
$366$	−13.8503	−0.723966
$367$	−2.70502	−0.141201	−0.0706005	−	0.997505i	$-0.522492\pi$
$367$	−2.70502	−0.141201	−0.0706005	+	0.997505i	$0.522492\pi$
$368$	−32.9495	−1.71761
$369$	−6.73917	−0.350827
$370$	38.8239	2.01836
$371$	−13.3405	−0.692604
$372$	−3.00000	−0.155543
$373$	−30.2071	−1.56406	−0.782032	−	0.623239i	$-0.785817\pi$
$373$	−30.2071	−1.56406	−0.782032	+	0.623239i	$0.785817\pi$
$374$	−55.3961	−2.86446
$375$	10.5398	0.544274
$376$	−2.73143	−0.140863
$377$	0	0
$378$	1.87939	0.0966651
$379$	−23.8871	−1.22700	−0.613500	−	0.789695i	$-0.710239\pi$
$379$	−23.8871	−1.22700	−0.613500	+	0.789695i	$0.710239\pi$
$380$	13.2867	0.681595
$381$	−7.65270	−0.392060
$382$	−24.2472	−1.24060
$383$	−34.5526	−1.76556	−0.882778	−	0.469790i	$-0.844330\pi$
$383$	−34.5526	−1.76556	−0.882778	+	0.469790i	$0.844330\pi$
$384$	6.84255	0.349182
$385$	11.0719	0.564277
$386$	23.7392	1.20829
$387$	−4.66044	−0.236904
$388$	−19.3405	−0.981865
$389$	24.3114	1.23264	0.616318	−	0.787497i	$-0.288623\pi$
$389$	24.3114	1.23264	0.616318	+	0.787497i	$0.288623\pi$
$390$	0	0
$391$	43.6519	2.20757
$392$	−0.879385	−0.0444157
$393$	−9.25402	−0.466804
$394$	8.87939	0.447337
$395$	8.42333	0.423824
$396$	−7.22668	−0.363154
$397$	−17.2831	−0.867415	−0.433707	−	0.901054i	$-0.642795\pi$
$397$	−17.2831	−0.867415	−0.433707	+	0.901054i	$0.642795\pi$
$398$	−29.4320	−1.47529
$399$	−3.69459	−0.184961
$400$	−2.40467	−0.120233
$401$	4.35773	0.217614	0.108807	−	0.994063i	$-0.465297\pi$
$401$	4.35773	0.217614	0.108807	+	0.994063i	$0.465297\pi$
$402$	24.8452	1.23917
$403$	0	0
$404$	−3.68273	−0.183223
$405$	−2.34730	−0.116638
$406$	−12.0223	−0.596656
$407$	41.5117	2.05766
$408$	−5.49525	−0.272056
$409$	−31.8307	−1.57393	−0.786963	−	0.617000i	$-0.788348\pi$
$409$	−31.8307	−1.57393	−0.786963	+	0.617000i	$0.788348\pi$
$410$	29.7297	1.46824
$411$	17.5817	0.867242
$412$	2.59627	0.127909
$413$	−12.3746	−0.608916
$414$	13.1284	0.645223
$415$	1.94768	0.0956079
$416$	0	0
$417$	−3.89899	−0.190934
$418$	32.7520	1.60195
$419$	23.4953	1.14782	0.573909	−	0.818919i	$-0.305426\pi$
$419$	23.4953	1.14782	0.573909	+	0.818919i	$0.305426\pi$
$420$	−3.59627	−0.175480
$421$	9.07697	0.442384	0.221192	−	0.975230i	$-0.429005\pi$
$421$	9.07697	0.442384	0.221192	+	0.975230i	$0.429005\pi$
$422$	11.5270	0.561127
$423$	3.10607	0.151022
$424$	11.7314	0.569729
$425$	3.18573	0.154530
$426$	18.7665	0.909240
$427$	−7.36959	−0.356639
$428$	5.90941	0.285642
$429$	0	0
$430$	20.5594	0.991464
$431$	23.4020	1.12723	0.563617	−	0.826036i	$-0.309409\pi$
$431$	23.4020	1.12723	0.563617	+	0.826036i	$0.309409\pi$
$432$	−4.71688	−0.226941
$433$	9.14384	0.439425	0.219712	−	0.975565i	$-0.429488\pi$
$433$	9.14384	0.439425	0.219712	+	0.975565i	$0.429488\pi$
$434$	−3.68004	−0.176648
$435$	15.0155	0.719937
$436$	−0.411474	−0.0197060
$437$	−25.8084	−1.23458
$438$	−17.2199	−0.822797
$439$	40.8212	1.94829	0.974145	−	0.225925i	$-0.0725405\pi$
$439$	40.8212	1.94829	0.974145	+	0.225925i	$0.0725405\pi$
$440$	−9.73648	−0.464169
$441$	1.00000	0.0476190
$442$	0	0
$443$	−11.0838	−0.526606	−0.263303	−	0.964713i	$-0.584812\pi$
$443$	−11.0838	−0.526606	−0.263303	+	0.964713i	$0.584812\pi$
$444$	−13.4834	−0.639893
$445$	−5.41147	−0.256528
$446$	2.57398	0.121881
$447$	11.1702	0.528334
$448$	−3.92127	−0.185263
$449$	1.47977	0.0698347	0.0349173	−	0.999390i	$-0.488883\pi$
$449$	1.47977	0.0698347	0.0349173	+	0.999390i	$0.488883\pi$
$450$	0.958111	0.0451658
$451$	31.7879	1.49683
$452$	11.8229	0.556105
$453$	5.97090	0.280538
$454$	13.8084	0.648060
$455$	0	0
$456$	3.24897	0.152147
$457$	10.0341	0.469378	0.234689	−	0.972071i	$-0.424593\pi$
$457$	10.0341	0.469378	0.234689	+	0.972071i	$0.424593\pi$
$458$	−28.5621	−1.33462
$459$	6.24897	0.291677
$460$	−25.1215	−1.17130
$461$	−4.45605	−0.207539	−0.103770	−	0.994601i	$-0.533090\pi$
$461$	−4.45605	−0.207539	−0.103770	+	0.994601i	$0.533090\pi$
$462$	−8.86484	−0.412430
$463$	−26.3901	−1.22645	−0.613226	−	0.789907i	$-0.710129\pi$
$463$	−26.3901	−1.22645	−0.613226	+	0.789907i	$0.710129\pi$
$464$	30.1735	1.40077
$465$	4.59627	0.213147
$466$	25.6091	1.18632
$467$	−19.3037	−0.893267	−0.446633	−	0.894717i	$-0.647377\pi$
$467$	−19.3037	−0.893267	−0.446633	+	0.894717i	$0.647377\pi$
$468$	0	0
$469$	13.2199	0.610437
$470$	−13.7023	−0.632042
$471$	8.75196	0.403269
$472$	10.8821	0.500888
$473$	21.9828	1.01077
$474$	−6.74422	−0.309772
$475$	−1.88350	−0.0864211
$476$	9.57398	0.438823
$477$	−13.3405	−0.610819
$478$	4.45336	0.203692
$479$	−1.30634	−0.0596882	−0.0298441	−	0.999555i	$-0.509501\pi$
$479$	−1.30634	−0.0596882	−0.0298441	+	0.999555i	$0.509501\pi$
$480$	16.6800	0.761336
$481$	0	0
$482$	39.5381	1.80091
$483$	6.98545	0.317849
$484$	17.2344	0.783383
$485$	29.6313	1.34549
$486$	1.87939	0.0852506
$487$	−5.16519	−0.234057	−0.117029	−	0.993129i	$-0.537337\pi$
$487$	−5.16519	−0.234057	−0.117029	+	0.993129i	$0.537337\pi$
$488$	6.48070	0.293368
$489$	−2.22163	−0.100466
$490$	−4.41147	−0.199290
$491$	22.2739	1.00521	0.502605	−	0.864516i	$-0.332375\pi$
$491$	22.2739	1.00521	0.502605	+	0.864516i	$0.332375\pi$
$492$	−10.3250	−0.465487
$493$	−39.9742	−1.80035
$494$	0	0
$495$	11.0719	0.497646
$496$	9.23618	0.414717
$497$	9.98545	0.447909
$498$	−1.55943	−0.0698797
$499$	−29.6091	−1.32548	−0.662742	−	0.748848i	$-0.730607\pi$
$499$	−29.6091	−1.32548	−0.662742	+	0.748848i	$0.730607\pi$
$500$	16.1480	0.722159
$501$	15.9513	0.712652
$502$	13.3550	0.596064
$503$	−18.3054	−0.816198	−0.408099	−	0.912938i	$-0.633808\pi$
$503$	−18.3054	−0.816198	−0.408099	+	0.912938i	$0.633808\pi$
$504$	−0.879385	−0.0391709
$505$	5.64227	0.251078
$506$	−61.9249	−2.75290
$507$	0	0
$508$	−11.7246	−0.520196
$509$	38.9513	1.72649	0.863243	−	0.504788i	$-0.168429\pi$
$509$	38.9513	1.72649	0.863243	+	0.504788i	$0.168429\pi$
$510$	−27.5672	−1.22069
$511$	−9.16250	−0.405325
$512$	25.2226	1.11469
$513$	−3.69459	−0.163120
$514$	−28.5800	−1.26061
$515$	−3.97771	−0.175279
$516$	−7.14022	−0.314330
$517$	−14.6509	−0.644348
$518$	−16.5398	−0.726718
$519$	3.09833	0.136001
$520$	0	0
$521$	18.4415	0.807937	0.403968	−	0.914773i	$-0.367631\pi$
$521$	18.4415	0.807937	0.403968	+	0.914773i	$0.367631\pi$
$522$	−12.0223	−0.526201
$523$	19.7425	0.863278	0.431639	−	0.902046i	$-0.357935\pi$
$523$	19.7425	0.863278	0.431639	+	0.902046i	$0.357935\pi$
$524$	−14.1780	−0.619368
$525$	0.509800	0.0222495
$526$	24.1266	1.05197
$527$	−12.2362	−0.533016
$528$	22.2490	0.968262
$529$	25.7965	1.12159
$530$	58.8512	2.55633
$531$	−12.3746	−0.537014
$532$	−5.66044	−0.245411
$533$	0	0
$534$	4.33275	0.187496
$535$	−9.05375	−0.391428
$536$	−11.6254	−0.502139
$537$	15.5895	0.672735
$538$	−33.4543	−1.44232
$539$	−4.71688	−0.203170
$540$	−3.59627	−0.154759
$541$	30.7766	1.32319	0.661595	−	0.749861i	$-0.269880\pi$
$541$	30.7766	1.32319	0.661595	+	0.749861i	$0.269880\pi$
$542$	1.31996	0.0566969
$543$	18.0942	0.776497
$544$	−44.4056	−1.90387
$545$	0.630415	0.0270040
$546$	0	0
$547$	−14.3874	−0.615162	−0.307581	−	0.951522i	$-0.599520\pi$
$547$	−14.3874	−0.615162	−0.307581	+	0.951522i	$0.599520\pi$
$548$	26.9368	1.15068
$549$	−7.36959	−0.314526
$550$	−4.51930	−0.192703
$551$	23.6340	1.00684
$552$	−6.14290	−0.261459
$553$	−3.58853	−0.152600
$554$	−0.852044	−0.0361999
$555$	20.6578	0.876873
$556$	−5.97359	−0.253337
$557$	13.5841	0.575576	0.287788	−	0.957694i	$-0.407080\pi$
$557$	13.5841	0.575576	0.287788	+	0.957694i	$0.407080\pi$
$558$	−3.68004	−0.155789
$559$	0	0
$560$	11.0719	0.467874
$561$	−29.4757	−1.24446
$562$	−47.6664	−2.01069
$563$	−26.7469	−1.12725	−0.563624	−	0.826032i	$-0.690593\pi$
$563$	−26.7469	−1.12725	−0.563624	+	0.826032i	$0.690593\pi$
$564$	4.75877	0.200380
$565$	−18.1138	−0.762054
$566$	−24.0479	−1.01081
$567$	1.00000	0.0419961
$568$	−8.78106	−0.368445
$569$	−2.56118	−0.107370	−0.0536852	−	0.998558i	$-0.517097\pi$
$569$	−2.56118	−0.107370	−0.0536852	+	0.998558i	$0.517097\pi$
$570$	16.2986	0.682673
$571$	−20.7415	−0.868006	−0.434003	−	0.900911i	$-0.642899\pi$
$571$	−20.7415	−0.868006	−0.434003	+	0.900911i	$0.642899\pi$
$572$	0	0
$573$	−12.9017	−0.538975
$574$	−12.6655	−0.528648
$575$	3.56118	0.148512
$576$	−3.92127	−0.163386
$577$	0.615867	0.0256389	0.0128194	−	0.999918i	$-0.495919\pi$
$577$	0.615867	0.0256389	0.0128194	+	0.999918i	$0.495919\pi$
$578$	41.4397	1.72367
$579$	12.6313	0.524941
$580$	23.0051	0.955233
$581$	−0.829755	−0.0344241
$582$	−23.7246	−0.983417
$583$	62.9255	2.60611
$584$	8.05737	0.333416
$585$	0	0
$586$	−15.1607	−0.626285
$587$	−13.4175	−0.553798	−0.276899	−	0.960899i	$-0.589307\pi$
$587$	−13.4175	−0.553798	−0.276899	+	0.960899i	$0.589307\pi$
$588$	1.53209	0.0631823
$589$	7.23442	0.298089
$590$	54.5904	2.24745
$591$	4.72462	0.194345
$592$	41.5117	1.70612
$593$	−12.7665	−0.524258	−0.262129	−	0.965033i	$-0.584425\pi$
$593$	−12.7665	−0.524258	−0.262129	+	0.965033i	$0.584425\pi$
$594$	−8.86484	−0.363729
$595$	−14.6682	−0.601337
$596$	17.1138	0.701009
$597$	−15.6604	−0.640939
$598$	0	0
$599$	−1.22762	−0.0501590	−0.0250795	−	0.999685i	$-0.507984\pi$
$599$	−1.22762	−0.0501590	−0.0250795	+	0.999685i	$0.507984\pi$
$600$	−0.448311	−0.0183022
$601$	22.0823	0.900758	0.450379	−	0.892838i	$-0.351289\pi$
$601$	22.0823	0.900758	0.450379	+	0.892838i	$0.351289\pi$
$602$	−8.75877	−0.356981
$603$	13.2199	0.538355
$604$	9.14796	0.372225
$605$	−26.4047	−1.07350
$606$	−4.51754	−0.183513
$607$	35.8057	1.45331	0.726655	−	0.687003i	$-0.241074\pi$
$607$	35.8057	1.45331	0.726655	+	0.687003i	$0.241074\pi$
$608$	26.2540	1.06474
$609$	−6.39693	−0.259217
$610$	32.5107	1.31632
$611$	0	0
$612$	9.57398	0.387005
$613$	−10.4911	−0.423733	−0.211866	−	0.977299i	$-0.567954\pi$
$613$	−10.4911	−0.423733	−0.211866	+	0.977299i	$0.567954\pi$
$614$	−20.0223	−0.808034
$615$	15.8188	0.637877
$616$	4.14796	0.167126
$617$	7.10195	0.285914	0.142957	−	0.989729i	$-0.454339\pi$
$617$	7.10195	0.285914	0.142957	+	0.989729i	$0.454339\pi$
$618$	3.18479	0.128111
$619$	10.1438	0.407715	0.203858	−	0.979001i	$-0.434652\pi$
$619$	10.1438	0.407715	0.203858	+	0.979001i	$0.434652\pi$
$620$	7.04189	0.282809
$621$	6.98545	0.280317
$622$	3.44831	0.138265
$623$	2.30541	0.0923642
$624$	0	0
$625$	−27.2891	−1.09156
$626$	−48.6938	−1.94619
$627$	17.4270	0.695966
$628$	13.4088	0.535069
$629$	−54.9951	−2.19280
$630$	−4.41147	−0.175757
$631$	−20.0624	−0.798672	−0.399336	−	0.916805i	$-0.630759\pi$
$631$	−20.0624	−0.798672	−0.399336	+	0.916805i	$0.630759\pi$
$632$	3.15570	0.125527
$633$	6.13341	0.243781
$634$	27.4739	1.09113
$635$	17.9632	0.712846
$636$	−20.4388	−0.810452
$637$	0	0
$638$	56.7077	2.24508
$639$	9.98545	0.395018
$640$	−16.0615	−0.634886
$641$	−44.4056	−1.75392	−0.876958	−	0.480567i	$-0.840431\pi$
$641$	−44.4056	−1.75392	−0.876958	+	0.480567i	$0.840431\pi$
$642$	7.24897	0.286094
$643$	−30.1735	−1.18993	−0.594964	−	0.803752i	$-0.702834\pi$
$643$	−30.1735	−1.18993	−0.594964	+	0.803752i	$0.702834\pi$
$644$	10.7023	0.421731
$645$	10.9394	0.430740
$646$	−43.3901	−1.70716
$647$	−6.59896	−0.259432	−0.129716	−	0.991551i	$-0.541407\pi$
$647$	−6.59896	−0.259432	−0.129716	+	0.991551i	$0.541407\pi$
$648$	−0.879385	−0.0345455
$649$	58.3697	2.29121
$650$	0	0
$651$	−1.95811	−0.0767444
$652$	−3.40373	−0.133300
$653$	8.56212	0.335062	0.167531	−	0.985867i	$-0.446421\pi$
$653$	8.56212	0.335062	0.167531	+	0.985867i	$0.446421\pi$
$654$	−0.504748	−0.0197372
$655$	21.7219	0.848746
$656$	31.7879	1.24111
$657$	−9.16250	−0.357463
$658$	5.83750	0.227569
$659$	32.1702	1.25317	0.626587	−	0.779351i	$-0.284451\pi$
$659$	32.1702	1.25317	0.626587	+	0.779351i	$0.284451\pi$
$660$	16.9632	0.660290
$661$	7.43645	0.289244	0.144622	−	0.989487i	$-0.453803\pi$
$661$	7.43645	0.289244	0.144622	+	0.989487i	$0.453803\pi$
$662$	−17.9094	−0.696069
$663$	0	0
$664$	0.729675	0.0283169
$665$	8.67230	0.336298
$666$	−16.5398	−0.640905
$667$	−44.6854	−1.73023
$668$	24.4388	0.945566
$669$	1.36959	0.0529512
$670$	−58.3191	−2.25306
$671$	34.7615	1.34195
$672$	−7.10607	−0.274122
$673$	−46.8827	−1.80719	−0.903597	−	0.428383i	$-0.859083\pi$
$673$	−46.8827	−1.80719	−0.903597	+	0.428383i	$0.859083\pi$
$674$	−32.4739	−1.25085
$675$	0.509800	0.0196222
$676$	0	0
$677$	−35.1206	−1.34979	−0.674897	−	0.737912i	$-0.735812\pi$
$677$	−35.1206	−1.34979	−0.674897	+	0.737912i	$0.735812\pi$
$678$	14.5030	0.556984
$679$	−12.6236	−0.484450
$680$	12.8990	0.494654
$681$	7.34730	0.281549
$682$	17.3583	0.664685
$683$	−32.2327	−1.23335	−0.616674	−	0.787218i	$-0.711520\pi$
$683$	−32.2327	−1.23335	−0.616674	+	0.787218i	$0.711520\pi$
$684$	−5.66044	−0.216433
$685$	−41.2695	−1.57683
$686$	1.87939	0.0717553
$687$	−15.1976	−0.579824
$688$	21.9828	0.838085
$689$	0	0
$690$	−30.8161	−1.17315
$691$	−27.4442	−1.04403	−0.522013	−	0.852937i	$-0.674819\pi$
$691$	−27.4442	−1.04403	−0.522013	+	0.852937i	$0.674819\pi$
$692$	4.74691	0.180450
$693$	−4.71688	−0.179180
$694$	36.5202	1.38629
$695$	9.15207	0.347158
$696$	5.62536	0.213229
$697$	−42.1129	−1.59514
$698$	−54.4620	−2.06142
$699$	13.6263	0.515394
$700$	0.781059	0.0295213
$701$	−21.4611	−0.810575	−0.405287	−	0.914189i	$-0.632829\pi$
$701$	−21.4611	−0.810575	−0.405287	+	0.914189i	$0.632829\pi$
$702$	0	0
$703$	32.5149	1.22632
$704$	18.4962	0.697101
$705$	−7.29086	−0.274590
$706$	−4.77332	−0.179646
$707$	−2.40373	−0.0904017
$708$	−18.9590	−0.712525
$709$	36.2422	1.36110	0.680552	−	0.732700i	$-0.261740\pi$
$709$	36.2422	1.36110	0.680552	+	0.732700i	$0.261740\pi$
$710$	−44.0506	−1.65319
$711$	−3.58853	−0.134580
$712$	−2.02734	−0.0759778
$713$	−13.6783	−0.512256
$714$	11.7442	0.439516
$715$	0	0
$716$	23.8844	0.892603
$717$	2.36959	0.0884938
$718$	−49.6614	−1.85335
$719$	−27.6996	−1.03302	−0.516511	−	0.856280i	$-0.672770\pi$
$719$	−27.6996	−1.03302	−0.516511	+	0.856280i	$0.672770\pi$
$720$	11.0719	0.412626
$721$	1.69459	0.0631099
$722$	−10.0547	−0.374197
$723$	21.0378	0.782403
$724$	27.7219	1.03028
$725$	−3.26115	−0.121116
$726$	21.1411	0.784622
$727$	−11.1516	−0.413589	−0.206795	−	0.978384i	$-0.566303\pi$
$727$	−11.1516	−0.413589	−0.206795	+	0.978384i	$0.566303\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	40.4201	1.49602
$731$	−29.1230	−1.07715
$732$	−11.2909	−0.417322
$733$	18.4219	0.680429	0.340214	−	0.940348i	$-0.389500\pi$
$733$	18.4219	0.680429	0.340214	+	0.940348i	$0.389500\pi$
$734$	−5.08378	−0.187646
$735$	−2.34730	−0.0865813
$736$	−49.6391	−1.82972
$737$	−62.3566	−2.29693
$738$	−12.6655	−0.466223
$739$	26.8435	0.987453	0.493727	−	0.869617i	$-0.335634\pi$
$739$	26.8435	0.987453	0.493727	+	0.869617i	$0.335634\pi$
$740$	31.6495	1.16346
$741$	0	0
$742$	−25.0719	−0.920419
$743$	15.9590	0.585481	0.292740	−	0.956192i	$-0.405433\pi$
$743$	15.9590	0.585481	0.292740	+	0.956192i	$0.405433\pi$
$744$	1.72193	0.0631292
$745$	−26.2199	−0.960622
$746$	−56.7707	−2.07852
$747$	−0.829755	−0.0303592
$748$	−45.1593	−1.65119
$749$	3.85710	0.140935
$750$	19.8084	0.723301
$751$	−21.4766	−0.783692	−0.391846	−	0.920031i	$-0.628163\pi$
$751$	−21.4766	−0.783692	−0.391846	+	0.920031i	$0.628163\pi$
$752$	−14.6509	−0.534265
$753$	7.10607	0.258959
$754$	0	0
$755$	−14.0155	−0.510076
$756$	1.53209	0.0557215
$757$	17.5672	0.638490	0.319245	−	0.947672i	$-0.396571\pi$
$757$	17.5672	0.638490	0.319245	+	0.947672i	$0.396571\pi$
$758$	−44.8931	−1.63059
$759$	−32.9495	−1.19599
$760$	−7.62630	−0.276635
$761$	27.4567	0.995303	0.497652	−	0.867377i	$-0.334196\pi$
$761$	27.4567	0.995303	0.497652	+	0.867377i	$0.334196\pi$
$762$	−14.3824	−0.521019
$763$	−0.268571	−0.00972291
$764$	−19.7665	−0.715127
$765$	−14.6682	−0.530329
$766$	−64.9377	−2.34629
$767$	0	0
$768$	20.7023	0.747031
$769$	26.9905	0.973302	0.486651	−	0.873596i	$-0.338218\pi$
$769$	26.9905	0.973302	0.486651	+	0.873596i	$0.338218\pi$
$770$	20.8084	0.749883
$771$	−15.2071	−0.547670
$772$	19.3523	0.696506
$773$	7.56799	0.272202	0.136101	−	0.990695i	$-0.456543\pi$
$773$	7.56799	0.272202	0.136101	+	0.990695i	$0.456543\pi$
$774$	−8.75877	−0.314828
$775$	−0.998245	−0.0358580
$776$	11.1010	0.398503
$777$	−8.80066	−0.315722
$778$	45.6905	1.63808
$779$	24.8985	0.892081
$780$	0	0
$781$	−47.1002	−1.68538
$782$	82.0387	2.93370
$783$	−6.39693	−0.228607
$784$	−4.71688	−0.168460
$785$	−20.5435	−0.733227
$786$	−17.3919	−0.620348
$787$	3.64227	0.129833	0.0649165	−	0.997891i	$-0.479322\pi$
$787$	3.64227	0.129833	0.0649165	+	0.997891i	$0.479322\pi$
$788$	7.23854	0.257862
$789$	12.8375	0.457027
$790$	15.8307	0.563231
$791$	7.71688	0.274381
$792$	4.14796	0.147391
$793$	0	0
$794$	−32.4816	−1.15273
$795$	31.3141	1.11060
$796$	−23.9932	−0.850416
$797$	−24.9949	−0.885366	−0.442683	−	0.896678i	$-0.645973\pi$
$797$	−24.9949	−0.885366	−0.442683	+	0.896678i	$0.645973\pi$
$798$	−6.94356	−0.245799
$799$	19.4097	0.686667
$800$	−3.62267	−0.128081
$801$	2.30541	0.0814576
$802$	8.18984	0.289193
$803$	43.2184	1.52515
$804$	20.2540	0.714304
$805$	−16.3969	−0.577916
$806$	0	0
$807$	−17.8007	−0.626613
$808$	2.11381	0.0743635
$809$	31.2240	1.09778	0.548889	−	0.835896i	$-0.315051\pi$
$809$	31.2240	1.09778	0.548889	+	0.835896i	$0.315051\pi$
$810$	−4.41147	−0.155003
$811$	23.1780	0.813889	0.406945	−	0.913453i	$-0.366594\pi$
$811$	23.1780	0.813889	0.406945	+	0.913453i	$0.366594\pi$
$812$	−9.80066	−0.343936
$813$	0.702333	0.0246319
$814$	78.0164	2.73447
$815$	5.21482	0.182667
$816$	−29.4757	−1.03185
$817$	17.2184	0.602397
$818$	−59.8221	−2.09163
$819$	0	0
$820$	24.2359	0.846353
$821$	53.1688	1.85560	0.927802	−	0.373072i	$-0.121696\pi$
$821$	53.1688	1.85560	0.927802	+	0.373072i	$0.121696\pi$
$822$	33.0428	1.15250
$823$	−13.7047	−0.477716	−0.238858	−	0.971055i	$-0.576773\pi$
$823$	−13.7047	−0.477716	−0.238858	+	0.971055i	$0.576773\pi$
$824$	−1.49020	−0.0519136
$825$	−2.40467	−0.0837198
$826$	−23.2567	−0.809204
$827$	29.0137	1.00891	0.504453	−	0.863439i	$-0.331694\pi$
$827$	29.0137	1.00891	0.504453	+	0.863439i	$0.331694\pi$
$828$	10.7023	0.371932
$829$	53.2526	1.84954	0.924769	−	0.380528i	$-0.124258\pi$
$829$	53.2526	1.84954	0.924769	+	0.380528i	$0.124258\pi$
$830$	3.66044	0.127056
$831$	−0.453363	−0.0157270
$832$	0	0
$833$	6.24897	0.216514
$834$	−7.32770	−0.253737
$835$	−37.4424	−1.29575
$836$	26.6996	0.923427
$837$	−1.95811	−0.0676822
$838$	44.1566	1.52537
$839$	−50.1111	−1.73003	−0.865014	−	0.501748i	$-0.832691\pi$
$839$	−50.1111	−1.73003	−0.865014	+	0.501748i	$0.832691\pi$
$840$	2.06418	0.0712209
$841$	11.9207	0.411057
$842$	17.0591	0.587896
$843$	−25.3628	−0.873540
$844$	9.39693	0.323456
$845$	0	0
$846$	5.83750	0.200697
$847$	11.2490	0.386519
$848$	62.9255	2.16087
$849$	−12.7956	−0.439144
$850$	5.98721	0.205359
$851$	−61.4766	−2.10739
$852$	15.2986	0.524121
$853$	−30.5090	−1.04461	−0.522304	−	0.852760i	$-0.674927\pi$
$853$	−30.5090	−1.04461	−0.522304	+	0.852760i	$0.674927\pi$
$854$	−13.8503	−0.473947
$855$	8.67230	0.296587
$856$	−3.39187	−0.115932
$857$	−4.86390	−0.166148	−0.0830739	−	0.996543i	$-0.526474\pi$
$857$	−4.86390	−0.166148	−0.0830739	+	0.996543i	$0.526474\pi$
$858$	0	0
$859$	−36.8066	−1.25583	−0.627913	−	0.778283i	$-0.716091\pi$
$859$	−36.8066	−1.25583	−0.627913	+	0.778283i	$0.716091\pi$
$860$	16.7602	0.571518
$861$	−6.73917	−0.229670
$862$	43.9813	1.49801
$863$	−39.3414	−1.33920	−0.669599	−	0.742723i	$-0.733534\pi$
$863$	−39.3414	−1.33920	−0.669599	+	0.742723i	$0.733534\pi$
$864$	−7.10607	−0.241753
$865$	−7.27269	−0.247279
$866$	17.1848	0.583963
$867$	22.0496	0.748845
$868$	−3.00000	−0.101827
$869$	16.9267	0.574197
$870$	28.2199	0.956743
$871$	0	0
$872$	0.236177	0.00799797
$873$	−12.6236	−0.427244
$874$	−48.5039	−1.64067
$875$	10.5398	0.356311
$876$	−14.0378	−0.474292
$877$	30.4570	1.02846	0.514230	−	0.857653i	$-0.328078\pi$
$877$	30.4570	1.02846	0.514230	+	0.857653i	$0.328078\pi$
$878$	76.7187	2.58913
$879$	−8.06687	−0.272089
$880$	−52.2249	−1.76050
$881$	1.20439	0.0405770	0.0202885	−	0.999794i	$-0.493542\pi$
$881$	1.20439	0.0405770	0.0202885	+	0.999794i	$0.493542\pi$
$882$	1.87939	0.0632822
$883$	36.8648	1.24060	0.620300	−	0.784364i	$-0.287011\pi$
$883$	36.8648	1.24060	0.620300	+	0.784364i	$0.287011\pi$
$884$	0	0
$885$	29.0469	0.976402
$886$	−20.8307	−0.699821
$887$	−22.4243	−0.752933	−0.376467	−	0.926430i	$-0.622861\pi$
$887$	−22.4243	−0.752933	−0.376467	+	0.926430i	$0.622861\pi$
$888$	7.73917	0.259710
$889$	−7.65270	−0.256663
$890$	−10.1702	−0.340907
$891$	−4.71688	−0.158021
$892$	2.09833	0.0702572
$893$	−11.4757	−0.384018
$894$	20.9932	0.702117
$895$	−36.5931	−1.22317
$896$	6.84255	0.228594
$897$	0	0
$898$	2.78106	0.0928051
$899$	12.5259	0.417762
$900$	0.781059	0.0260353
$901$	−83.3643	−2.77727
$902$	59.7416	1.98918
$903$	−4.66044	−0.155090
$904$	−6.78611	−0.225703
$905$	−42.4725	−1.41183
$906$	11.2216	0.372814
$907$	38.3391	1.27303	0.636514	−	0.771265i	$-0.280376\pi$
$907$	38.3391	1.27303	0.636514	+	0.771265i	$0.280376\pi$
$908$	11.2567	0.373567
$909$	−2.40373	−0.0797268
$910$	0	0
$911$	10.3000	0.341255	0.170628	−	0.985336i	$-0.445420\pi$
$911$	10.3000	0.341255	0.170628	+	0.985336i	$0.445420\pi$
$912$	17.4270	0.577064
$913$	3.91386	0.129530
$914$	18.8580	0.623768
$915$	17.2986	0.571874
$916$	−23.2841	−0.769327
$917$	−9.25402	−0.305595
$918$	11.7442	0.387617
$919$	9.59390	0.316474	0.158237	−	0.987401i	$-0.449419\pi$
$919$	9.59390	0.316474	0.158237	+	0.987401i	$0.449419\pi$
$920$	14.4192	0.475387
$921$	−10.6536	−0.351049
$922$	−8.37464	−0.275804
$923$	0	0
$924$	−7.22668	−0.237740
$925$	−4.48658	−0.147518
$926$	−49.5972	−1.62987
$927$	1.69459	0.0556577
$928$	45.4570	1.49220
$929$	11.3301	0.371727	0.185864	−	0.982576i	$-0.440492\pi$
$929$	11.3301	0.371727	0.185864	+	0.982576i	$0.440492\pi$
$930$	8.63816	0.283256
$931$	−3.69459	−0.121085
$932$	20.8767	0.683839
$933$	1.83481	0.0600689
$934$	−36.2790	−1.18709
$935$	69.1881	2.26269
$936$	0	0
$937$	−48.7749	−1.59341	−0.796703	−	0.604372i	$-0.793424\pi$
$937$	−48.7749	−1.59341	−0.796703	+	0.604372i	$0.793424\pi$
$938$	24.8452	0.811226
$939$	−25.9094	−0.845522
$940$	−11.1702	−0.364333
$941$	8.55943	0.279029	0.139515	−	0.990220i	$-0.455446\pi$
$941$	8.55943	0.279029	0.139515	+	0.990220i	$0.455446\pi$
$942$	16.4483	0.535915
$943$	−47.0761	−1.53301
$944$	58.3697	1.89977
$945$	−2.34730	−0.0763576
$946$	41.3141	1.34324
$947$	2.53983	0.0825334	0.0412667	−	0.999148i	$-0.486861\pi$
$947$	2.53983	0.0825334	0.0412667	+	0.999148i	$0.486861\pi$
$948$	−5.49794	−0.178565
$949$	0	0
$950$	−3.53983	−0.114847
$951$	14.6186	0.474039
$952$	−5.49525	−0.178102
$953$	−53.5954	−1.73613	−0.868063	−	0.496453i	$-0.834635\pi$
$953$	−53.5954	−1.73613	−0.868063	+	0.496453i	$0.834635\pi$
$954$	−25.0719	−0.811733
$955$	30.2841	0.979969
$956$	3.63041	0.117416
$957$	30.1735	0.975372
$958$	−2.45512	−0.0793213
$959$	17.5817	0.567743
$960$	9.20439	0.297071
$961$	−27.1658	−0.876316
$962$	0	0
$963$	3.85710	0.124293
$964$	32.2317	1.03811
$965$	−29.6495	−0.954452
$966$	13.1284	0.422398
$967$	13.5953	0.437196	0.218598	−	0.975815i	$-0.429852\pi$
$967$	13.5953	0.437196	0.218598	+	0.975815i	$0.429852\pi$
$968$	−9.89218	−0.317947
$969$	−23.0874	−0.741674
$970$	55.6887	1.78806
$971$	−48.1397	−1.54488	−0.772439	−	0.635090i	$-0.780963\pi$
$971$	−48.1397	−1.54488	−0.772439	+	0.635090i	$0.780963\pi$
$972$	1.53209	0.0491418
$973$	−3.89899	−0.124996
$974$	−9.70739	−0.311045
$975$	0	0
$976$	34.7615	1.11269
$977$	34.9017	1.11660	0.558302	−	0.829638i	$-0.311453\pi$
$977$	34.9017	1.11660	0.558302	+	0.829638i	$0.311453\pi$
$978$	−4.17530	−0.133511
$979$	−10.8743	−0.347545
$980$	−3.59627	−0.114879
$981$	−0.268571	−0.00857480
$982$	41.8613	1.33585
$983$	58.3465	1.86096	0.930482	−	0.366338i	$-0.119389\pi$
$983$	58.3465	1.86096	0.930482	+	0.366338i	$0.119389\pi$
$984$	5.92633	0.188924
$985$	−11.0901	−0.353360
$986$	−75.1269	−2.39253
$987$	3.10607	0.0988672
$988$	0	0
$989$	−32.5553	−1.03520
$990$	20.8084	0.661334
$991$	−60.3988	−1.91863	−0.959315	−	0.282336i	$-0.908891\pi$
$991$	−60.3988	−1.91863	−0.959315	+	0.282336i	$0.908891\pi$
$992$	13.9145	0.441785
$993$	−9.52940	−0.302406
$994$	18.7665	0.595238
$995$	36.7597	1.16536
$996$	−1.27126	−0.0402814
$997$	−24.5134	−0.776348	−0.388174	−	0.921586i	$-0.626894\pi$
$997$	−24.5134	−0.776348	−0.388174	+	0.921586i	$0.626894\pi$
$998$	−55.6468	−1.76147
$999$	−8.80066	−0.278441

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.n.1.3		3
13.4	even	6		273.2.k.a.211.3	yes	6
13.10	even	6		273.2.k.a.22.3	✓	6
13.12	even	2		3549.2.a.o.1.1		3
39.17	odd	6		819.2.o.g.757.1		6
39.23	odd	6		819.2.o.g.568.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.a.22.3	✓	6	13.10	even	6
273.2.k.a.211.3	yes	6	13.4	even	6
819.2.o.g.568.1		6	39.23	odd	6
819.2.o.g.757.1		6	39.17	odd	6
3549.2.a.n.1.3		3	1.1	even	1	trivial
3549.2.a.o.1.1		3	13.12	even	2

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q+1.87939 q^{2} +1.00000 q^{3} +1.53209 q^{4} -2.34730 q^{5} +1.87939 q^{6} +1.00000 q^{7} -0.879385 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.87939 q^{2} +1.00000 q^{3} +1.53209 q^{4} -2.34730 q^{5} +1.87939 q^{6} +1.00000 q^{7} -0.879385 q^{8} +1.00000 q^{9} -4.41147 q^{10} -4.71688 q^{11} +1.53209 q^{12} +1.87939 q^{14} -2.34730 q^{15} -4.71688 q^{16} +6.24897 q^{17} +1.87939 q^{18} -3.69459 q^{19} -3.59627 q^{20} +1.00000 q^{21} -8.86484 q^{22} +6.98545 q^{23} -0.879385 q^{24} +0.509800 q^{25} +1.00000 q^{27} +1.53209 q^{28} -6.39693 q^{29} -4.41147 q^{30} -1.95811 q^{31} -7.10607 q^{32} -4.71688 q^{33} +11.7442 q^{34} -2.34730 q^{35} +1.53209 q^{36} -8.80066 q^{37} -6.94356 q^{38} +2.06418 q^{40} -6.73917 q^{41} +1.87939 q^{42} -4.66044 q^{43} -7.22668 q^{44} -2.34730 q^{45} +13.1284 q^{46} +3.10607 q^{47} -4.71688 q^{48} +1.00000 q^{49} +0.958111 q^{50} +6.24897 q^{51} -13.3405 q^{53} +1.87939 q^{54} +11.0719 q^{55} -0.879385 q^{56} -3.69459 q^{57} -12.0223 q^{58} -12.3746 q^{59} -3.59627 q^{60} -7.36959 q^{61} -3.68004 q^{62} +1.00000 q^{63} -3.92127 q^{64} -8.86484 q^{66} +13.2199 q^{67} +9.57398 q^{68} +6.98545 q^{69} -4.41147 q^{70} +9.98545 q^{71} -0.879385 q^{72} -9.16250 q^{73} -16.5398 q^{74} +0.509800 q^{75} -5.66044 q^{76} -4.71688 q^{77} -3.58853 q^{79} +11.0719 q^{80} +1.00000 q^{81} -12.6655 q^{82} -0.829755 q^{83} +1.53209 q^{84} -14.6682 q^{85} -8.75877 q^{86} -6.39693 q^{87} +4.14796 q^{88} +2.30541 q^{89} -4.41147 q^{90} +10.7023 q^{92} -1.95811 q^{93} +5.83750 q^{94} +8.67230 q^{95} -7.10607 q^{96} -12.6236 q^{97} +1.87939 q^{98} -4.71688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} - 6 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^3 - 6 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{3} - 6 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 6 q^{11} - 6 q^{15} - 6 q^{16} + 6 q^{17} - 9 q^{19} + 3 q^{20} + 3 q^{21} - 3 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} + 3 q^{27} + 9 q^{29} - 3 q^{30} - 9 q^{31} - 9 q^{32} - 6 q^{33} + 6 q^{34} - 6 q^{35} - 12 q^{37} - 6 q^{38} - 3 q^{40} - 6 q^{41} + 9 q^{43} - 15 q^{44} - 6 q^{45} + 21 q^{46} - 3 q^{47} - 6 q^{48} + 3 q^{49} + 6 q^{50} + 6 q^{51} + 3 q^{53} + 3 q^{56} - 9 q^{57} - 30 q^{58} - 15 q^{59} + 3 q^{60} - 15 q^{61} + 9 q^{62} + 3 q^{63} - 3 q^{64} - 3 q^{66} - 9 q^{67} + 21 q^{68} + 3 q^{69} - 3 q^{70} + 12 q^{71} + 3 q^{72} - 30 q^{73} - 21 q^{74} + 3 q^{75} + 6 q^{76} - 6 q^{77} - 21 q^{79} + 3 q^{81} - 24 q^{83} + 3 q^{85} - 15 q^{86} + 9 q^{87} - 3 q^{88} + 9 q^{89} - 3 q^{90} + 6 q^{92} - 9 q^{93} + 15 q^{94} + 30 q^{95} - 9 q^{96} - 3 q^{97} - 6 q^{99}+O(q^{100}) \) 3 * q + 3 * q^3 - 6 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 6 * q^11 - 6 * q^15 - 6 * q^16 + 6 * q^17 - 9 * q^19 + 3 * q^20 + 3 * q^21 - 3 * q^22 + 3 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 + 9 * q^29 - 3 * q^30 - 9 * q^31 - 9 * q^32 - 6 * q^33 + 6 * q^34 - 6 * q^35 - 12 * q^37 - 6 * q^38 - 3 * q^40 - 6 * q^41 + 9 * q^43 - 15 * q^44 - 6 * q^45 + 21 * q^46 - 3 * q^47 - 6 * q^48 + 3 * q^49 + 6 * q^50 + 6 * q^51 + 3 * q^53 + 3 * q^56 - 9 * q^57 - 30 * q^58 - 15 * q^59 + 3 * q^60 - 15 * q^61 + 9 * q^62 + 3 * q^63 - 3 * q^64 - 3 * q^66 - 9 * q^67 + 21 * q^68 + 3 * q^69 - 3 * q^70 + 12 * q^71 + 3 * q^72 - 30 * q^73 - 21 * q^74 + 3 * q^75 + 6 * q^76 - 6 * q^77 - 21 * q^79 + 3 * q^81 - 24 * q^83 + 3 * q^85 - 15 * q^86 + 9 * q^87 - 3 * q^88 + 9 * q^89 - 3 * q^90 + 6 * q^92 - 9 * q^93 + 15 * q^94 + 30 * q^95 - 9 * q^96 - 3 * q^97 - 6 * q^99

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