LMFDB - Embedded newform 3822.2.a.bz.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(1,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, 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("3822.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.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:	$30.5188236525$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.31808.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 11x^{2} + 12x + 28 $ x^4 - 2x^3 - 11x^2 + 12*x + 28
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.34975$ of defining polynomial
Character	$\chi$	$=$	3822.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.34975 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.34975 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +2.34975 q^{10} -3.67280 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.34975 q^{15} +1.00000 q^{16} -5.67280 q^{17} +1.00000 q^{18} +2.34975 q^{19} +2.34975 q^{20} -3.67280 q^{22} +4.34975 q^{23} -1.00000 q^{24} +0.521322 q^{25} -1.00000 q^{26} -1.00000 q^{27} +9.08701 q^{29} -2.34975 q^{30} +3.32305 q^{31} +1.00000 q^{32} +3.67280 q^{33} -5.67280 q^{34} +1.00000 q^{36} +3.89289 q^{37} +2.34975 q^{38} +1.00000 q^{39} +2.34975 q^{40} +1.90883 q^{41} +10.9958 q^{43} -3.67280 q^{44} +2.34975 q^{45} +4.34975 q^{46} +2.91959 q^{47} -1.00000 q^{48} +0.521322 q^{50} +5.67280 q^{51} -1.00000 q^{52} -0.737261 q^{53} -1.00000 q^{54} -8.63015 q^{55} -2.34975 q^{57} +9.08701 q^{58} +3.32305 q^{59} -2.34975 q^{60} +3.80173 q^{61} +3.32305 q^{62} +1.00000 q^{64} -2.34975 q^{65} +3.67280 q^{66} +9.28529 q^{67} -5.67280 q^{68} -4.34975 q^{69} +14.7220 q^{71} +1.00000 q^{72} +1.65025 q^{73} +3.89289 q^{74} -0.521322 q^{75} +2.34975 q^{76} +1.00000 q^{78} +10.9799 q^{79} +2.34975 q^{80} +1.00000 q^{81} +1.90883 q^{82} -10.3564 q^{83} -13.3297 q^{85} +10.9958 q^{86} -9.08701 q^{87} -3.67280 q^{88} -7.10295 q^{89} +2.34975 q^{90} +4.34975 q^{92} -3.32305 q^{93} +2.91959 q^{94} +5.52132 q^{95} -1.00000 q^{96} +6.51717 q^{97} -3.67280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 2 q^{10} + 6 q^{11} - 4 q^{12} - 4 q^{13} - 2 q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 2 q^{19} + 2 q^{20} + 6 q^{22} + 10 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} - 4 q^{27} + 10 q^{29} - 2 q^{30} + 4 q^{32} - 6 q^{33} - 2 q^{34} + 4 q^{36} + 6 q^{37} + 2 q^{38} + 4 q^{39} + 2 q^{40} + 10 q^{43} + 6 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 4 q^{48} + 6 q^{50} + 2 q^{51} - 4 q^{52} + 16 q^{53} - 4 q^{54} - 6 q^{55} - 2 q^{57} + 10 q^{58} - 2 q^{60} - 2 q^{61} + 4 q^{64} - 2 q^{65} - 6 q^{66} + 28 q^{67} - 2 q^{68} - 10 q^{69} + 16 q^{71} + 4 q^{72} + 14 q^{73} + 6 q^{74} - 6 q^{75} + 2 q^{76} + 4 q^{78} + 8 q^{79} + 2 q^{80} + 4 q^{81} - 4 q^{83} - 10 q^{85} + 10 q^{86} - 10 q^{87} + 6 q^{88} - 4 q^{89} + 2 q^{90} + 10 q^{92} + 8 q^{94} + 26 q^{95} - 4 q^{96} - 4 q^{97} + 6 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 2 * q^10 + 6 * q^11 - 4 * q^12 - 4 * q^13 - 2 * q^15 + 4 * q^16 - 2 * q^17 + 4 * q^18 + 2 * q^19 + 2 * q^20 + 6 * q^22 + 10 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 - 4 * q^27 + 10 * q^29 - 2 * q^30 + 4 * q^32 - 6 * q^33 - 2 * q^34 + 4 * q^36 + 6 * q^37 + 2 * q^38 + 4 * q^39 + 2 * q^40 + 10 * q^43 + 6 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 4 * q^48 + 6 * q^50 + 2 * q^51 - 4 * q^52 + 16 * q^53 - 4 * q^54 - 6 * q^55 - 2 * q^57 + 10 * q^58 - 2 * q^60 - 2 * q^61 + 4 * q^64 - 2 * q^65 - 6 * q^66 + 28 * q^67 - 2 * q^68 - 10 * q^69 + 16 * q^71 + 4 * q^72 + 14 * q^73 + 6 * q^74 - 6 * q^75 + 2 * q^76 + 4 * q^78 + 8 * q^79 + 2 * q^80 + 4 * q^81 - 4 * q^83 - 10 * q^85 + 10 * q^86 - 10 * q^87 + 6 * q^88 - 4 * q^89 + 2 * q^90 + 10 * q^92 + 8 * q^94 + 26 * q^95 - 4 * q^96 - 4 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.34975	1.05084	0.525420	−	0.850843i	$-0.323908\pi$
$5$	2.34975	1.05084	0.525420	+	0.850843i	$0.323908\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.34975	0.743056
$11$	−3.67280	−1.10739	−0.553695	−	0.832720i	$-0.686783\pi$
$11$	−3.67280	−1.10739	−0.553695	+	0.832720i	$0.686783\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	−2.34975	−0.606703
$16$	1.00000	0.250000
$17$	−5.67280	−1.37586	−0.687928	−	0.725779i	$-0.741479\pi$
$17$	−5.67280	−1.37586	−0.687928	+	0.725779i	$0.741479\pi$
$18$	1.00000	0.235702
$19$	2.34975	0.539069	0.269535	−	0.962991i	$-0.413130\pi$
$19$	2.34975	0.539069	0.269535	+	0.962991i	$0.413130\pi$
$20$	2.34975	0.525420
$21$	0	0
$22$	−3.67280	−0.783043
$23$	4.34975	0.906985	0.453493	−	0.891260i	$-0.350178\pi$
$23$	4.34975	0.906985	0.453493	+	0.891260i	$0.350178\pi$
$24$	−1.00000	−0.204124
$25$	0.521322	0.104264
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	0	0
$29$	9.08701	1.68742	0.843708	−	0.536803i	$-0.180368\pi$
$29$	9.08701	1.68742	0.843708	+	0.536803i	$0.180368\pi$
$30$	−2.34975	−0.429004
$31$	3.32305	0.596837	0.298418	−	0.954435i	$-0.403541\pi$
$31$	3.32305	0.596837	0.298418	+	0.954435i	$0.403541\pi$
$32$	1.00000	0.176777
$33$	3.67280	0.639352
$34$	−5.67280	−0.972877
$35$	0	0
$36$	1.00000	0.166667
$37$	3.89289	0.639987	0.319994	−	0.947420i	$-0.396319\pi$
$37$	3.89289	0.639987	0.319994	+	0.947420i	$0.396319\pi$
$38$	2.34975	0.381180
$39$	1.00000	0.160128
$40$	2.34975	0.371528
$41$	1.90883	0.298110	0.149055	−	0.988829i	$-0.452377\pi$
$41$	1.90883	0.298110	0.149055	+	0.988829i	$0.452377\pi$
$42$	0	0
$43$	10.9958	1.67685	0.838425	−	0.545017i	$-0.183477\pi$
$43$	10.9958	1.67685	0.838425	+	0.545017i	$0.183477\pi$
$44$	−3.67280	−0.553695
$45$	2.34975	0.350280
$46$	4.34975	0.641336
$47$	2.91959	0.425866	0.212933	−	0.977067i	$-0.431698\pi$
$47$	2.91959	0.425866	0.212933	+	0.977067i	$0.431698\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	0.521322	0.0737261
$51$	5.67280	0.794350
$52$	−1.00000	−0.138675
$53$	−0.737261	−0.101271	−0.0506353	−	0.998717i	$-0.516125\pi$
$53$	−0.737261	−0.101271	−0.0506353	+	0.998717i	$0.516125\pi$
$54$	−1.00000	−0.136083
$55$	−8.63015	−1.16369
$56$	0	0
$57$	−2.34975	−0.311232
$58$	9.08701	1.19318
$59$	3.32305	0.432624	0.216312	−	0.976324i	$-0.430597\pi$
$59$	3.32305	0.432624	0.216312	+	0.976324i	$0.430597\pi$
$60$	−2.34975	−0.303351
$61$	3.80173	0.486761	0.243381	−	0.969931i	$-0.421744\pi$
$61$	3.80173	0.486761	0.243381	+	0.969931i	$0.421744\pi$
$62$	3.32305	0.422027
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.34975	−0.291451
$66$	3.67280	0.452090
$67$	9.28529	1.13438	0.567189	−	0.823588i	$-0.308031\pi$
$67$	9.28529	1.13438	0.567189	+	0.823588i	$0.308031\pi$
$68$	−5.67280	−0.687928
$69$	−4.34975	−0.523648
$70$	0	0
$71$	14.7220	1.74719	0.873593	−	0.486658i	$-0.161784\pi$
$71$	14.7220	1.74719	0.873593	+	0.486658i	$0.161784\pi$
$72$	1.00000	0.117851
$73$	1.65025	0.193147	0.0965736	−	0.995326i	$-0.469212\pi$
$73$	1.65025	0.193147	0.0965736	+	0.995326i	$0.469212\pi$
$74$	3.89289	0.452539
$75$	−0.521322	−0.0601971
$76$	2.34975	0.269535
$77$	0	0
$78$	1.00000	0.113228
$79$	10.9799	1.23534	0.617668	−	0.786439i	$-0.288078\pi$
$79$	10.9799	1.23534	0.617668	+	0.786439i	$0.288078\pi$
$80$	2.34975	0.262710
$81$	1.00000	0.111111
$82$	1.90883	0.210795
$83$	−10.3564	−1.13676	−0.568379	−	0.822767i	$-0.692429\pi$
$83$	−10.3564	−1.13676	−0.568379	+	0.822767i	$0.692429\pi$
$84$	0	0
$85$	−13.3297	−1.44580
$86$	10.9958	1.18571
$87$	−9.08701	−0.974230
$88$	−3.67280	−0.391521
$89$	−7.10295	−0.752912	−0.376456	−	0.926435i	$-0.622857\pi$
$89$	−7.10295	−0.752912	−0.376456	+	0.926435i	$0.622857\pi$
$90$	2.34975	0.247685
$91$	0	0
$92$	4.34975	0.453493
$93$	−3.32305	−0.344584
$94$	2.91959	0.301133
$95$	5.52132	0.566476
$96$	−1.00000	−0.102062
$97$	6.51717	0.661718	0.330859	−	0.943680i	$-0.392662\pi$
$97$	6.51717	0.661718	0.330859	+	0.943680i	$0.392662\pi$
$98$	0	0
$99$	−3.67280	−0.369130
$100$	0.521322	0.0521322
$101$	−10.8510	−1.07971	−0.539856	−	0.841757i	$-0.681521\pi$
$101$	−10.8510	−1.07971	−0.539856	+	0.841757i	$0.681521\pi$
$102$	5.67280	0.561691
$103$	6.85025	0.674975	0.337487	−	0.941330i	$-0.390423\pi$
$103$	6.85025	0.674975	0.337487	+	0.941330i	$0.390423\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	−0.737261	−0.0716091
$107$	13.8025	1.33433	0.667167	−	0.744908i	$-0.267507\pi$
$107$	13.8025	1.33433	0.667167	+	0.744908i	$0.267507\pi$
$108$	−1.00000	−0.0962250
$109$	−12.1203	−1.16092	−0.580458	−	0.814290i	$-0.697126\pi$
$109$	−12.1203	−1.16092	−0.580458	+	0.814290i	$0.697126\pi$
$110$	−8.63015	−0.822853
$111$	−3.89289	−0.369497
$112$	0	0
$113$	−14.5397	−1.36778	−0.683891	−	0.729585i	$-0.739713\pi$
$113$	−14.5397	−1.36778	−0.683891	+	0.729585i	$0.739713\pi$
$114$	−2.34975	−0.220074
$115$	10.2208	0.953096
$116$	9.08701	0.843708
$117$	−1.00000	−0.0924500
$118$	3.32305	0.305911
$119$	0	0
$120$	−2.34975	−0.214502
$121$	2.48944	0.226312
$122$	3.80173	0.344192
$123$	−1.90883	−0.172114
$124$	3.32305	0.298418
$125$	−10.5238	−0.941275
$126$	0	0
$127$	−4.20488	−0.373123	−0.186561	−	0.982443i	$-0.559734\pi$
$127$	−4.20488	−0.373123	−0.186561	+	0.982443i	$0.559734\pi$
$128$	1.00000	0.0883883
$129$	−10.9958	−0.968130
$130$	−2.34975	−0.206087
$131$	−3.83361	−0.334944	−0.167472	−	0.985877i	$-0.553560\pi$
$131$	−3.83361	−0.334944	−0.167472	+	0.985877i	$0.553560\pi$
$132$	3.67280	0.319676
$133$	0	0
$134$	9.28529	0.802126
$135$	−2.34975	−0.202234
$136$	−5.67280	−0.486438
$137$	21.9757	1.87751	0.938757	−	0.344579i	$-0.111978\pi$
$137$	21.9757	1.87751	0.938757	+	0.344579i	$0.111978\pi$
$138$	−4.34975	−0.370275
$139$	−17.5196	−1.48599	−0.742997	−	0.669295i	$-0.766596\pi$
$139$	−17.5196	−1.48599	−0.742997	+	0.669295i	$0.766596\pi$
$140$	0	0
$141$	−2.91959	−0.245874
$142$	14.7220	1.23545
$143$	3.67280	0.307135
$144$	1.00000	0.0833333
$145$	21.3522	1.77320
$146$	1.65025	0.136576
$147$	0	0
$148$	3.89289	0.319994
$149$	−18.8201	−1.54180	−0.770902	−	0.636954i	$-0.780194\pi$
$149$	−18.8201	−1.54180	−0.770902	+	0.636954i	$0.780194\pi$
$150$	−0.521322	−0.0425658
$151$	−3.20072	−0.260471	−0.130236	−	0.991483i	$-0.541573\pi$
$151$	−3.20072	−0.260471	−0.130236	+	0.991483i	$0.541573\pi$
$152$	2.34975	0.190590
$153$	−5.67280	−0.458618
$154$	0	0
$155$	7.80833	0.627180
$156$	1.00000	0.0800641
$157$	6.91989	0.552268	0.276134	−	0.961119i	$-0.410947\pi$
$157$	6.91989	0.552268	0.276134	+	0.961119i	$0.410947\pi$
$158$	10.9799	0.873514
$159$	0.737261	0.0584686
$160$	2.34975	0.185764
$161$	0	0
$162$	1.00000	0.0785674
$163$	−23.6961	−1.85602	−0.928010	−	0.372556i	$-0.878481\pi$
$163$	−23.6961	−1.85602	−0.928010	+	0.372556i	$0.878481\pi$
$164$	1.90883	0.149055
$165$	8.63015	0.671856
$166$	−10.3564	−0.803809
$167$	1.46204	0.113136	0.0565681	−	0.998399i	$-0.481984\pi$
$167$	1.46204	0.113136	0.0565681	+	0.998399i	$0.481984\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−13.3297	−1.02234
$171$	2.34975	0.179690
$172$	10.9958	0.838425
$173$	10.0981	0.767742	0.383871	−	0.923387i	$-0.374591\pi$
$173$	10.0981	0.767742	0.383871	+	0.923387i	$0.374591\pi$
$174$	−9.08701	−0.688884
$175$	0	0
$176$	−3.67280	−0.276847
$177$	−3.32305	−0.249776
$178$	−7.10295	−0.532389
$179$	17.5882	1.31461	0.657303	−	0.753626i	$-0.271697\pi$
$179$	17.5882	1.31461	0.657303	+	0.753626i	$0.271697\pi$
$180$	2.34975	0.175140
$181$	−9.71026	−0.721758	−0.360879	−	0.932613i	$-0.617523\pi$
$181$	−9.71026	−0.721758	−0.360879	+	0.932613i	$0.617523\pi$
$182$	0	0
$183$	−3.80173	−0.281032
$184$	4.34975	0.320668
$185$	9.14732	0.672524
$186$	−3.32305	−0.243658
$187$	20.8350	1.52361
$188$	2.91959	0.212933
$189$	0	0
$190$	5.52132	0.400559
$191$	−15.4492	−1.11787	−0.558934	−	0.829212i	$-0.688789\pi$
$191$	−15.4492	−1.11787	−0.558934	+	0.829212i	$0.688789\pi$
$192$	−1.00000	−0.0721688
$193$	−0.0759502	−0.00546701	−0.00273351	−	0.999996i	$-0.500870\pi$
$193$	−0.0759502	−0.00546701	−0.00273351	+	0.999996i	$0.500870\pi$
$194$	6.51717	0.467905
$195$	2.34975	0.168269
$196$	0	0
$197$	10.9044	0.776905	0.388452	−	0.921469i	$-0.373010\pi$
$197$	10.9044	0.776905	0.388452	+	0.921469i	$0.373010\pi$
$198$	−3.67280	−0.261014
$199$	−10.9272	−0.774610	−0.387305	−	0.921952i	$-0.626594\pi$
$199$	−10.9272	−0.774610	−0.387305	+	0.921952i	$0.626594\pi$
$200$	0.521322	0.0368631
$201$	−9.28529	−0.654934
$202$	−10.8510	−0.763472
$203$	0	0
$204$	5.67280	0.397175
$205$	4.48528	0.313266
$206$	6.85025	0.477279
$207$	4.34975	0.302328
$208$	−1.00000	−0.0693375
$209$	−8.63015	−0.596960
$210$	0	0
$211$	−6.99584	−0.481614	−0.240807	−	0.970573i	$-0.577412\pi$
$211$	−6.99584	−0.481614	−0.240807	+	0.970573i	$0.577412\pi$
$212$	−0.737261	−0.0506353
$213$	−14.7220	−1.00874
$214$	13.8025	0.943516
$215$	25.8375	1.76210
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−12.1203	−0.820891
$219$	−1.65025	−0.111514
$220$	−8.63015	−0.581845
$221$	5.67280	0.381594
$222$	−3.89289	−0.261274
$223$	5.20346	0.348449	0.174225	−	0.984706i	$-0.444258\pi$
$223$	5.20346	0.348449	0.174225	+	0.984706i	$0.444258\pi$
$224$	0	0
$225$	0.521322	0.0347548
$226$	−14.5397	−0.967167
$227$	2.85097	0.189226	0.0946129	−	0.995514i	$-0.469839\pi$
$227$	2.85097	0.189226	0.0946129	+	0.995514i	$0.469839\pi$
$228$	−2.34975	−0.155616
$229$	−6.48631	−0.428627	−0.214314	−	0.976765i	$-0.568751\pi$
$229$	−6.48631	−0.428627	−0.214314	+	0.976765i	$0.568751\pi$
$230$	10.2208	0.673941
$231$	0	0
$232$	9.08701	0.596591
$233$	−0.386785	−0.0253391	−0.0126696	−	0.999920i	$-0.504033\pi$
$233$	−0.386785	−0.0253391	−0.0126696	+	0.999920i	$0.504033\pi$
$234$	−1.00000	−0.0653720
$235$	6.86031	0.447517
$236$	3.32305	0.216312
$237$	−10.9799	−0.713221
$238$	0	0
$239$	18.2936	1.18332	0.591658	−	0.806189i	$-0.298474\pi$
$239$	18.2936	1.18332	0.591658	+	0.806189i	$0.298474\pi$
$240$	−2.34975	−0.151676
$241$	19.2167	1.23785	0.618927	−	0.785448i	$-0.287568\pi$
$241$	19.2167	1.23785	0.618927	+	0.785448i	$0.287568\pi$
$242$	2.48944	0.160027
$243$	−1.00000	−0.0641500
$244$	3.80173	0.243381
$245$	0	0
$246$	−1.90883	−0.121703
$247$	−2.34975	−0.149511
$248$	3.32305	0.211014
$249$	10.3564	0.656307
$250$	−10.5238	−0.665582
$251$	8.66204	0.546743	0.273371	−	0.961909i	$-0.411861\pi$
$251$	8.66204	0.546743	0.273371	+	0.961909i	$0.411861\pi$
$252$	0	0
$253$	−15.9757	−1.00439
$254$	−4.20488	−0.263838
$255$	13.3297	0.834735
$256$	1.00000	0.0625000
$257$	19.0024	1.18534	0.592670	−	0.805445i	$-0.298074\pi$
$257$	19.0024	1.18534	0.592670	+	0.805445i	$0.298074\pi$
$258$	−10.9958	−0.684571
$259$	0	0
$260$	−2.34975	−0.145725
$261$	9.08701	0.562472
$262$	−3.83361	−0.236841
$263$	4.36466	0.269137	0.134568	−	0.990904i	$-0.457035\pi$
$263$	4.36466	0.269137	0.134568	+	0.990904i	$0.457035\pi$
$264$	3.67280	0.226045
$265$	−1.73238	−0.106419
$266$	0	0
$267$	7.10295	0.434694
$268$	9.28529	0.567189
$269$	4.90438	0.299025	0.149513	−	0.988760i	$-0.452230\pi$
$269$	4.90438	0.299025	0.149513	+	0.988760i	$0.452230\pi$
$270$	−2.34975	−0.143001
$271$	19.3363	1.17459	0.587297	−	0.809372i	$-0.300192\pi$
$271$	19.3363	1.17459	0.587297	+	0.809372i	$0.300192\pi$
$272$	−5.67280	−0.343964
$273$	0	0
$274$	21.9757	1.32760
$275$	−1.91471	−0.115461
$276$	−4.34975	−0.261824
$277$	−9.07694	−0.545381	−0.272690	−	0.962102i	$-0.587913\pi$
$277$	−9.07694	−0.545381	−0.272690	+	0.962102i	$0.587913\pi$
$278$	−17.5196	−1.05076
$279$	3.32305	0.198946
$280$	0	0
$281$	−7.04264	−0.420129	−0.210064	−	0.977688i	$-0.567367\pi$
$281$	−7.04264	−0.420129	−0.210064	+	0.977688i	$0.567367\pi$
$282$	−2.91959	−0.173859
$283$	32.3029	1.92021	0.960106	−	0.279638i	$-0.0902144\pi$
$283$	32.3029	1.92021	0.960106	+	0.279638i	$0.0902144\pi$
$284$	14.7220	0.873593
$285$	−5.52132	−0.327055
$286$	3.67280	0.217177
$287$	0	0
$288$	1.00000	0.0589256
$289$	15.1806	0.892978
$290$	21.3522	1.25384
$291$	−6.51717	−0.382043
$292$	1.65025	0.0965736
$293$	−1.78578	−0.104327	−0.0521633	−	0.998639i	$-0.516612\pi$
$293$	−1.78578	−0.104327	−0.0521633	+	0.998639i	$0.516612\pi$
$294$	0	0
$295$	7.80833	0.454618
$296$	3.89289	0.226270
$297$	3.67280	0.213117
$298$	−18.8201	−1.09022
$299$	−4.34975	−0.251553
$300$	−0.521322	−0.0300986
$301$	0	0
$302$	−3.20072	−0.184181
$303$	10.8510	0.623372
$304$	2.34975	0.134767
$305$	8.93310	0.511508
$306$	−5.67280	−0.324292
$307$	1.38579	0.0790912	0.0395456	−	0.999218i	$-0.487409\pi$
$307$	1.38579	0.0790912	0.0395456	+	0.999218i	$0.487409\pi$
$308$	0	0
$309$	−6.85025	−0.389697
$310$	7.80833	0.443483
$311$	−27.4211	−1.55491	−0.777454	−	0.628939i	$-0.783489\pi$
$311$	−27.4211	−1.55491	−0.777454	+	0.628939i	$0.783489\pi$
$312$	1.00000	0.0566139
$313$	−15.4059	−0.870793	−0.435397	−	0.900239i	$-0.643392\pi$
$313$	−15.4059	−0.870793	−0.435397	+	0.900239i	$0.643392\pi$
$314$	6.91989	0.390512
$315$	0	0
$316$	10.9799	0.617668
$317$	−27.5720	−1.54860	−0.774299	−	0.632820i	$-0.781897\pi$
$317$	−27.5720	−1.54860	−0.774299	+	0.632820i	$0.781897\pi$
$318$	0.737261	0.0413435
$319$	−33.3747	−1.86863
$320$	2.34975	0.131355
$321$	−13.8025	−0.770378
$322$	0	0
$323$	−13.3297	−0.741682
$324$	1.00000	0.0555556
$325$	−0.521322	−0.0289178
$326$	−23.6961	−1.31240
$327$	12.1203	0.670255
$328$	1.90883	0.105398
$329$	0	0
$330$	8.63015	0.475074
$331$	20.0520	1.10216	0.551079	−	0.834453i	$-0.314216\pi$
$331$	20.0520	1.10216	0.551079	+	0.834453i	$0.314216\pi$
$332$	−10.3564	−0.568379
$333$	3.89289	0.213329
$334$	1.46204	0.0799994
$335$	21.8181	1.19205
$336$	0	0
$337$	−8.85371	−0.482292	−0.241146	−	0.970489i	$-0.577523\pi$
$337$	−8.85371	−0.482292	−0.241146	+	0.970489i	$0.577523\pi$
$338$	1.00000	0.0543928
$339$	14.5397	0.789689
$340$	−13.3297	−0.722902
$341$	−12.2049	−0.660931
$342$	2.34975	0.127060
$343$	0	0
$344$	10.9958	0.592856
$345$	−10.2208	−0.550271
$346$	10.0981	0.542876
$347$	0.736233	0.0395231	0.0197615	−	0.999805i	$-0.493709\pi$
$347$	0.736233	0.0395231	0.0197615	+	0.999805i	$0.493709\pi$
$348$	−9.08701	−0.487115
$349$	−18.5931	−0.995267	−0.497633	−	0.867387i	$-0.665797\pi$
$349$	−18.5931	−0.995267	−0.497633	+	0.867387i	$0.665797\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	−3.67280	−0.195761
$353$	−33.1172	−1.76265	−0.881325	−	0.472511i	$-0.843348\pi$
$353$	−33.1172	−1.76265	−0.881325	+	0.472511i	$0.843348\pi$
$354$	−3.32305	−0.176618
$355$	34.5931	1.83601
$356$	−7.10295	−0.376456
$357$	0	0
$358$	17.5882	0.929567
$359$	−9.89259	−0.522111	−0.261055	−	0.965324i	$-0.584071\pi$
$359$	−9.89259	−0.522111	−0.261055	+	0.965324i	$0.584071\pi$
$360$	2.34975	0.123843
$361$	−13.4787	−0.709404
$362$	−9.71026	−0.510360
$363$	−2.48944	−0.130662
$364$	0	0
$365$	3.87768	0.202967
$366$	−3.80173	−0.198719
$367$	−0.0162437	−0.000847912 0	−0.000423956	−	1.00000i	$-0.500135\pi$
$367$	−0.0162437	−0.000847912 0	−0.000423956		1.00000i	$0.500135\pi$
$368$	4.34975	0.226746
$369$	1.90883	0.0993699
$370$	9.14732	0.475546
$371$	0	0
$372$	−3.32305	−0.172292
$373$	13.6579	0.707178	0.353589	−	0.935401i	$-0.384961\pi$
$373$	13.6579	0.707178	0.353589	+	0.935401i	$0.384961\pi$
$374$	20.8350	1.07735
$375$	10.5238	0.543445
$376$	2.91959	0.150567
$377$	−9.08701	−0.468005
$378$	0	0
$379$	25.8475	1.32770	0.663850	−	0.747866i	$-0.268922\pi$
$379$	25.8475	1.32770	0.663850	+	0.747866i	$0.268922\pi$
$380$	5.52132	0.283238
$381$	4.20488	0.215422
$382$	−15.4492	−0.790452
$383$	−15.3449	−0.784086	−0.392043	−	0.919947i	$-0.628232\pi$
$383$	−15.3449	−0.784086	−0.392043	+	0.919947i	$0.628232\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−0.0759502	−0.00386576
$387$	10.9958	0.558950
$388$	6.51717	0.330859
$389$	−13.1774	−0.668123	−0.334062	−	0.942551i	$-0.608419\pi$
$389$	−13.1774	−0.668123	−0.334062	+	0.942551i	$0.608419\pi$
$390$	2.34975	0.118984
$391$	−24.6752	−1.24788
$392$	0	0
$393$	3.83361	0.193380
$394$	10.9044	0.549355
$395$	25.8000	1.29814
$396$	−3.67280	−0.184565
$397$	−21.7338	−1.09079	−0.545395	−	0.838179i	$-0.683620\pi$
$397$	−21.7338	−1.09079	−0.545395	+	0.838179i	$0.683620\pi$
$398$	−10.9272	−0.547732
$399$	0	0
$400$	0.521322	0.0260661
$401$	−11.0108	−0.549851	−0.274926	−	0.961466i	$-0.588653\pi$
$401$	−11.0108	−0.549851	−0.274926	+	0.961466i	$0.588653\pi$
$402$	−9.28529	−0.463108
$403$	−3.32305	−0.165533
$404$	−10.8510	−0.539856
$405$	2.34975	0.116760
$406$	0	0
$407$	−14.2978	−0.708716
$408$	5.67280	0.280845
$409$	38.3012	1.89387	0.946937	−	0.321418i	$-0.104160\pi$
$409$	38.3012	1.89387	0.946937	+	0.321418i	$0.104160\pi$
$410$	4.48528	0.221512
$411$	−21.9757	−1.08398
$412$	6.85025	0.337487
$413$	0	0
$414$	4.34975	0.213779
$415$	−24.3348	−1.19455
$416$	−1.00000	−0.0490290
$417$	17.5196	0.857939
$418$	−8.63015	−0.422115
$419$	−29.6424	−1.44812	−0.724062	−	0.689735i	$-0.757727\pi$
$419$	−29.6424	−1.44812	−0.724062	+	0.689735i	$0.757727\pi$
$420$	0	0
$421$	11.7612	0.573207	0.286604	−	0.958049i	$-0.407474\pi$
$421$	11.7612	0.573207	0.286604	+	0.958049i	$0.407474\pi$
$422$	−6.99584	−0.340552
$423$	2.91959	0.141955
$424$	−0.737261	−0.0358046
$425$	−2.95736	−0.143453
$426$	−14.7220	−0.713285
$427$	0	0
$428$	13.8025	0.667167
$429$	−3.67280	−0.177324
$430$	25.8375	1.24599
$431$	28.4230	1.36909	0.684543	−	0.728972i	$-0.260002\pi$
$431$	28.4230	1.36909	0.684543	+	0.728972i	$0.260002\pi$
$432$	−1.00000	−0.0481125
$433$	38.5598	1.85307	0.926533	−	0.376212i	$-0.122774\pi$
$433$	38.5598	1.85307	0.926533	+	0.376212i	$0.122774\pi$
$434$	0	0
$435$	−21.3522	−1.02376
$436$	−12.1203	−0.580458
$437$	10.2208	0.488928
$438$	−1.65025	−0.0788520
$439$	23.7958	1.13571	0.567857	−	0.823127i	$-0.307773\pi$
$439$	23.7958	1.13571	0.567857	+	0.823127i	$0.307773\pi$
$440$	−8.63015	−0.411426
$441$	0	0
$442$	5.67280	0.269827
$443$	−33.5803	−1.59545	−0.797725	−	0.603021i	$-0.793963\pi$
$443$	−33.5803	−1.59545	−0.797725	+	0.603021i	$0.793963\pi$
$444$	−3.89289	−0.184748
$445$	−16.6902	−0.791189
$446$	5.20346	0.246391
$447$	18.8201	0.890161
$448$	0	0
$449$	−41.3963	−1.95361	−0.976805	−	0.214130i	$-0.931308\pi$
$449$	−41.3963	−1.95361	−0.976805	+	0.214130i	$0.931308\pi$
$450$	0.521322	0.0245754
$451$	−7.01076	−0.330124
$452$	−14.5397	−0.683891
$453$	3.20072	0.150383
$454$	2.85097	0.133803
$455$	0	0
$456$	−2.34975	−0.110037
$457$	−1.17115	−0.0547840	−0.0273920	−	0.999625i	$-0.508720\pi$
$457$	−1.17115	−0.0547840	−0.0273920	+	0.999625i	$0.508720\pi$
$458$	−6.48631	−0.303085
$459$	5.67280	0.264783
$460$	10.2208	0.476548
$461$	14.1487	0.658972	0.329486	−	0.944160i	$-0.393124\pi$
$461$	14.1487	0.658972	0.329486	+	0.944160i	$0.393124\pi$
$462$	0	0
$463$	−1.25413	−0.0582842	−0.0291421	−	0.999575i	$-0.509278\pi$
$463$	−1.25413	−0.0582842	−0.0291421	+	0.999575i	$0.509278\pi$
$464$	9.08701	0.421854
$465$	−7.80833	−0.362103
$466$	−0.386785	−0.0179175
$467$	12.5463	0.580574	0.290287	−	0.956940i	$-0.406249\pi$
$467$	12.5463	0.580574	0.290287	+	0.956940i	$0.406249\pi$
$468$	−1.00000	−0.0462250
$469$	0	0
$470$	6.86031	0.316443
$471$	−6.91989	−0.318852
$472$	3.32305	0.152956
$473$	−40.3855	−1.85693
$474$	−10.9799	−0.504324
$475$	1.22498	0.0562058
$476$	0	0
$477$	−0.737261	−0.0337569
$478$	18.2936	0.836730
$479$	−37.4752	−1.71229	−0.856144	−	0.516737i	$-0.827146\pi$
$479$	−37.4752	−1.71229	−0.856144	+	0.516737i	$0.827146\pi$
$480$	−2.34975	−0.107251
$481$	−3.89289	−0.177501
$482$	19.2167	0.875295
$483$	0	0
$484$	2.48944	0.113156
$485$	15.3137	0.695360
$486$	−1.00000	−0.0453609
$487$	−17.7338	−0.803597	−0.401798	−	0.915728i	$-0.631615\pi$
$487$	−17.7338	−0.803597	−0.401798	+	0.915728i	$0.631615\pi$
$488$	3.80173	0.172096
$489$	23.6961	1.07157
$490$	0	0
$491$	−11.4049	−0.514695	−0.257347	−	0.966319i	$-0.582848\pi$
$491$	−11.4049	−0.514695	−0.257347	+	0.966319i	$0.582848\pi$
$492$	−1.90883	−0.0860569
$493$	−51.5488	−2.32164
$494$	−2.34975	−0.105720
$495$	−8.63015	−0.387897
$496$	3.32305	0.149209
$497$	0	0
$498$	10.3564	0.464079
$499$	5.87798	0.263134	0.131567	−	0.991307i	$-0.457999\pi$
$499$	5.87798	0.263134	0.131567	+	0.991307i	$0.457999\pi$
$500$	−10.5238	−0.470637
$501$	−1.46204	−0.0653192
$502$	8.66204	0.386606
$503$	21.9387	0.978199	0.489099	−	0.872228i	$-0.337326\pi$
$503$	21.9387	0.978199	0.489099	+	0.872228i	$0.337326\pi$
$504$	0	0
$505$	−25.4971	−1.13460
$506$	−15.9757	−0.710209
$507$	−1.00000	−0.0444116
$508$	−4.20488	−0.186561
$509$	−11.6413	−0.515993	−0.257997	−	0.966146i	$-0.583062\pi$
$509$	−11.6413	−0.515993	−0.257997	+	0.966146i	$0.583062\pi$
$510$	13.3297	0.590247
$511$	0	0
$512$	1.00000	0.0441942
$513$	−2.34975	−0.103744
$514$	19.0024	0.838162
$515$	16.0964	0.709291
$516$	−10.9958	−0.484065
$517$	−10.7231	−0.471600
$518$	0	0
$519$	−10.0981	−0.443256
$520$	−2.34975	−0.103043
$521$	−37.2139	−1.63037	−0.815186	−	0.579199i	$-0.803365\pi$
$521$	−37.2139	−1.63037	−0.815186	+	0.579199i	$0.803365\pi$
$522$	9.08701	0.397728
$523$	37.1020	1.62236	0.811178	−	0.584799i	$-0.198827\pi$
$523$	37.1020	1.62236	0.811178	+	0.584799i	$0.198827\pi$
$524$	−3.83361	−0.167472
$525$	0	0
$526$	4.36466	0.190308
$527$	−18.8510	−0.821161
$528$	3.67280	0.159838
$529$	−4.07968	−0.177377
$530$	−1.73238	−0.0752497
$531$	3.32305	0.144208
$532$	0	0
$533$	−1.90883	−0.0826808
$534$	7.10295	0.307375
$535$	32.4323	1.40217
$536$	9.28529	0.401063
$537$	−17.5882	−0.758988
$538$	4.90438	0.211443
$539$	0	0
$540$	−2.34975	−0.101117
$541$	7.08598	0.304650	0.152325	−	0.988330i	$-0.451324\pi$
$541$	7.08598	0.304650	0.152325	+	0.988330i	$0.451324\pi$
$542$	19.3363	0.830563
$543$	9.71026	0.416707
$544$	−5.67280	−0.243219
$545$	−28.4797	−1.21994
$546$	0	0
$547$	3.78578	0.161868	0.0809342	−	0.996719i	$-0.474210\pi$
$547$	3.78578	0.161868	0.0809342	+	0.996719i	$0.474210\pi$
$548$	21.9757	0.938757
$549$	3.80173	0.162254
$550$	−1.91471	−0.0816435
$551$	21.3522	0.909634
$552$	−4.34975	−0.185138
$553$	0	0
$554$	−9.07694	−0.385642
$555$	−9.14732	−0.388282
$556$	−17.5196	−0.742997
$557$	−33.9397	−1.43807	−0.719036	−	0.694972i	$-0.755417\pi$
$557$	−33.9397	−1.43807	−0.719036	+	0.694972i	$0.755417\pi$
$558$	3.32305	0.140676
$559$	−10.9958	−0.465075
$560$	0	0
$561$	−20.8350	−0.879656
$562$	−7.04264	−0.297076
$563$	14.3938	0.606627	0.303313	−	0.952891i	$-0.401907\pi$
$563$	14.3938	0.606627	0.303313	+	0.952891i	$0.401907\pi$
$564$	−2.91959	−0.122937
$565$	−34.1647	−1.43732
$566$	32.3029	1.35779
$567$	0	0
$568$	14.7220	0.617723
$569$	−24.0236	−1.00712	−0.503560	−	0.863960i	$-0.667977\pi$
$569$	−24.0236	−1.00712	−0.503560	+	0.863960i	$0.667977\pi$
$570$	−5.52132	−0.231263
$571$	−29.9279	−1.25244	−0.626222	−	0.779645i	$-0.715400\pi$
$571$	−29.9279	−1.25244	−0.626222	+	0.779645i	$0.715400\pi$
$572$	3.67280	0.153567
$573$	15.4492	0.645401
$574$	0	0
$575$	2.26762	0.0945663
$576$	1.00000	0.0416667
$577$	26.3799	1.09821	0.549105	−	0.835753i	$-0.314969\pi$
$577$	26.3799	1.09821	0.549105	+	0.835753i	$0.314969\pi$
$578$	15.1806	0.631431
$579$	0.0759502	0.00315638
$580$	21.3522	0.886602
$581$	0	0
$582$	−6.51717	−0.270145
$583$	2.70781	0.112146
$584$	1.65025	0.0682879
$585$	−2.34975	−0.0971502
$586$	−1.78578	−0.0737700
$587$	−12.5623	−0.518500	−0.259250	−	0.965810i	$-0.583475\pi$
$587$	−12.5623	−0.518500	−0.259250	+	0.965810i	$0.583475\pi$
$588$	0	0
$589$	7.80833	0.321737
$590$	7.80833	0.321464
$591$	−10.9044	−0.448546
$592$	3.89289	0.159997
$593$	1.44610	0.0593842	0.0296921	−	0.999559i	$-0.490547\pi$
$593$	1.44610	0.0593842	0.0296921	+	0.999559i	$0.490547\pi$
$594$	3.67280	0.150697
$595$	0	0
$596$	−18.8201	−0.770902
$597$	10.9272	0.447222
$598$	−4.34975	−0.177874
$599$	−22.9335	−0.937039	−0.468519	−	0.883453i	$-0.655212\pi$
$599$	−22.9335	−0.937039	−0.468519	+	0.883453i	$0.655212\pi$
$600$	−0.521322	−0.0212829
$601$	25.4951	1.03997	0.519983	−	0.854177i	$-0.325938\pi$
$601$	25.4951	1.03997	0.519983	+	0.854177i	$0.325938\pi$
$602$	0	0
$603$	9.28529	0.378126
$604$	−3.20072	−0.130236
$605$	5.84955	0.237818
$606$	10.8510	0.440791
$607$	−35.6718	−1.44787	−0.723937	−	0.689866i	$-0.757669\pi$
$607$	−35.6718	−1.44787	−0.723937	+	0.689866i	$0.757669\pi$
$608$	2.34975	0.0952949
$609$	0	0
$610$	8.93310	0.361691
$611$	−2.91959	−0.118114
$612$	−5.67280	−0.229309
$613$	47.7384	1.92814	0.964068	−	0.265654i	$-0.0855879\pi$
$613$	47.7384	1.92814	0.964068	+	0.265654i	$0.0855879\pi$
$614$	1.38579	0.0559259
$615$	−4.48528	−0.180864
$616$	0	0
$617$	22.2891	0.897324	0.448662	−	0.893702i	$-0.351901\pi$
$617$	22.2891	0.897324	0.448662	+	0.893702i	$0.351901\pi$
$618$	−6.85025	−0.275557
$619$	14.7365	0.592311	0.296156	−	0.955140i	$-0.404295\pi$
$619$	14.7365	0.592311	0.296156	+	0.955140i	$0.404295\pi$
$620$	7.80833	0.313590
$621$	−4.34975	−0.174549
$622$	−27.4211	−1.09949
$623$	0	0
$624$	1.00000	0.0400320
$625$	−27.3348	−1.09339
$626$	−15.4059	−0.615744
$627$	8.63015	0.344655
$628$	6.91989	0.276134
$629$	−22.0836	−0.880530
$630$	0	0
$631$	−22.4693	−0.894490	−0.447245	−	0.894411i	$-0.647595\pi$
$631$	−22.4693	−0.894490	−0.447245	+	0.894411i	$0.647595\pi$
$632$	10.9799	0.436757
$633$	6.99584	0.278060
$634$	−27.5720	−1.09502
$635$	−9.88041	−0.392092
$636$	0.737261	0.0292343
$637$	0	0
$638$	−33.3747	−1.32132
$639$	14.7220	0.582395
$640$	2.34975	0.0928820
$641$	−13.1838	−0.520727	−0.260363	−	0.965511i	$-0.583842\pi$
$641$	−13.1838	−0.520727	−0.260363	+	0.965511i	$0.583842\pi$
$642$	−13.8025	−0.544739
$643$	−20.9120	−0.824689	−0.412345	−	0.911028i	$-0.635290\pi$
$643$	−20.9120	−0.824689	−0.412345	+	0.911028i	$0.635290\pi$
$644$	0	0
$645$	−25.8375	−1.01735
$646$	−13.3297	−0.524448
$647$	37.0343	1.45597	0.727985	−	0.685593i	$-0.240457\pi$
$647$	37.0343	1.45597	0.727985	+	0.685593i	$0.240457\pi$
$648$	1.00000	0.0392837
$649$	−12.2049	−0.479083
$650$	−0.521322	−0.0204479
$651$	0	0
$652$	−23.6961	−0.928010
$653$	40.2620	1.57557	0.787787	−	0.615947i	$-0.211227\pi$
$653$	40.2620	1.57557	0.787787	+	0.615947i	$0.211227\pi$
$654$	12.1203	0.473942
$655$	−9.00802	−0.351973
$656$	1.90883	0.0745274
$657$	1.65025	0.0643824
$658$	0	0
$659$	38.3539	1.49406	0.747028	−	0.664792i	$-0.231480\pi$
$659$	38.3539	1.49406	0.747028	+	0.664792i	$0.231480\pi$
$660$	8.63015	0.335928
$661$	−35.9411	−1.39795	−0.698974	−	0.715147i	$-0.746360\pi$
$661$	−35.9411	−1.39795	−0.698974	+	0.715147i	$0.746360\pi$
$662$	20.0520	0.779343
$663$	−5.67280	−0.220313
$664$	−10.3564	−0.401904
$665$	0	0
$666$	3.89289	0.150846
$667$	39.5262	1.53046
$668$	1.46204	0.0565681
$669$	−5.20346	−0.201177
$670$	21.8181	0.842906
$671$	−13.9630	−0.539034
$672$	0	0
$673$	−15.9968	−0.616633	−0.308316	−	0.951284i	$-0.599766\pi$
$673$	−15.9968	−0.616633	−0.308316	+	0.951284i	$0.599766\pi$
$674$	−8.85371	−0.341032
$675$	−0.521322	−0.0200657
$676$	1.00000	0.0384615
$677$	14.9172	0.573313	0.286656	−	0.958033i	$-0.407456\pi$
$677$	14.9172	0.573313	0.286656	+	0.958033i	$0.407456\pi$
$678$	14.5397	0.558394
$679$	0	0
$680$	−13.3297	−0.511169
$681$	−2.85097	−0.109250
$682$	−12.2049	−0.467349
$683$	16.1262	0.617052	0.308526	−	0.951216i	$-0.400164\pi$
$683$	16.1262	0.617052	0.308526	+	0.951216i	$0.400164\pi$
$684$	2.34975	0.0898449
$685$	51.6375	1.97297
$686$	0	0
$687$	6.48631	0.247468
$688$	10.9958	0.419213
$689$	0.737261	0.0280874
$690$	−10.2208	−0.389100
$691$	10.4623	0.398005	0.199003	−	0.979999i	$-0.436230\pi$
$691$	10.4623	0.398005	0.199003	+	0.979999i	$0.436230\pi$
$692$	10.0981	0.383871
$693$	0	0
$694$	0.736233	0.0279470
$695$	−41.1667	−1.56154
$696$	−9.08701	−0.344442
$697$	−10.8284	−0.410156
$698$	−18.5931	−0.703760
$699$	0.386785	0.0146295
$700$	0	0
$701$	2.69706	0.101867	0.0509334	−	0.998702i	$-0.483780\pi$
$701$	2.69706	0.101867	0.0509334	+	0.998702i	$0.483780\pi$
$702$	1.00000	0.0377426
$703$	9.14732	0.344998
$704$	−3.67280	−0.138424
$705$	−6.86031	−0.258374
$706$	−33.1172	−1.24638
$707$	0	0
$708$	−3.32305	−0.124888
$709$	51.2289	1.92394	0.961971	−	0.273153i	$-0.0880664\pi$
$709$	51.2289	1.92394	0.961971	+	0.273153i	$0.0880664\pi$
$710$	34.5931	1.29826
$711$	10.9799	0.411778
$712$	−7.10295	−0.266194
$713$	14.4544	0.541322
$714$	0	0
$715$	8.63015	0.322749
$716$	17.5882	0.657303
$717$	−18.2936	−0.683187
$718$	−9.89259	−0.369188
$719$	−47.4701	−1.77034	−0.885168	−	0.465272i	$-0.845956\pi$
$719$	−47.4701	−1.77034	−0.885168	+	0.465272i	$0.845956\pi$
$720$	2.34975	0.0875700
$721$	0	0
$722$	−13.4787	−0.501624
$723$	−19.2167	−0.714675
$724$	−9.71026	−0.360879
$725$	4.73726	0.175937
$726$	−2.48944	−0.0923917
$727$	−33.8306	−1.25471	−0.627353	−	0.778735i	$-0.715862\pi$
$727$	−33.8306	−1.25471	−0.627353	+	0.778735i	$0.715862\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	3.87768	0.143519
$731$	−62.3772	−2.30710
$732$	−3.80173	−0.140516
$733$	−12.5314	−0.462858	−0.231429	−	0.972852i	$-0.574340\pi$
$733$	−12.5314	−0.462858	−0.231429	+	0.972852i	$0.574340\pi$
$734$	−0.0162437	−0.000599564 0
$735$	0	0
$736$	4.34975	0.160334
$737$	−34.1030	−1.25620
$738$	1.90883	0.0702651
$739$	39.0853	1.43778	0.718888	−	0.695126i	$-0.244651\pi$
$739$	39.0853	1.43778	0.718888	+	0.695126i	$0.244651\pi$
$740$	9.14732	0.336262
$741$	2.34975	0.0863202
$742$	0	0
$743$	−17.3054	−0.634873	−0.317437	−	0.948279i	$-0.602822\pi$
$743$	−17.3054	−0.634873	−0.317437	+	0.948279i	$0.602822\pi$
$744$	−3.32305	−0.121829
$745$	−44.2226	−1.62019
$746$	13.6579	0.500051
$747$	−10.3564	−0.378919
$748$	20.8350	0.761804
$749$	0	0
$750$	10.5238	0.384274
$751$	17.7230	0.646723	0.323361	−	0.946276i	$-0.395187\pi$
$751$	17.7230	0.646723	0.323361	+	0.946276i	$0.395187\pi$
$752$	2.91959	0.106467
$753$	−8.66204	−0.315662
$754$	−9.08701	−0.330929
$755$	−7.52090	−0.273713
$756$	0	0
$757$	−4.40933	−0.160260	−0.0801299	−	0.996784i	$-0.525534\pi$
$757$	−4.40933	−0.160260	−0.0801299	+	0.996784i	$0.525534\pi$
$758$	25.8475	0.938825
$759$	15.9757	0.579883
$760$	5.52132	0.200279
$761$	−34.9432	−1.26669	−0.633344	−	0.773870i	$-0.718318\pi$
$761$	−34.9432	−1.26669	−0.633344	+	0.773870i	$0.718318\pi$
$762$	4.20488	0.152327
$763$	0	0
$764$	−15.4492	−0.558934
$765$	−13.3297	−0.481935
$766$	−15.3449	−0.554433
$767$	−3.32305	−0.119988
$768$	−1.00000	−0.0360844
$769$	27.7487	1.00065	0.500323	−	0.865839i	$-0.333215\pi$
$769$	27.7487	1.00065	0.500323	+	0.865839i	$0.333215\pi$
$770$	0	0
$771$	−19.0024	−0.684356
$772$	−0.0759502	−0.00273351
$773$	−40.7193	−1.46457	−0.732286	−	0.680997i	$-0.761547\pi$
$773$	−40.7193	−1.46457	−0.732286	+	0.680997i	$0.761547\pi$
$774$	10.9958	0.395237
$775$	1.73238	0.0622289
$776$	6.51717	0.233953
$777$	0	0
$778$	−13.1774	−0.472434
$779$	4.48528	0.160702
$780$	2.34975	0.0841345
$781$	−54.0711	−1.93482
$782$	−24.6752	−0.882385
$783$	−9.08701	−0.324743
$784$	0	0
$785$	16.2600	0.580345
$786$	3.83361	0.136740
$787$	−36.3776	−1.29672	−0.648361	−	0.761333i	$-0.724545\pi$
$787$	−36.3776	−1.29672	−0.648361	+	0.761333i	$0.724545\pi$
$788$	10.9044	0.388452
$789$	−4.36466	−0.155386
$790$	25.8000	0.917923
$791$	0	0
$792$	−3.67280	−0.130507
$793$	−3.80173	−0.135003
$794$	−21.7338	−0.771305
$795$	1.73238	0.0614411
$796$	−10.9272	−0.387305
$797$	20.7574	0.735264	0.367632	−	0.929971i	$-0.380169\pi$
$797$	20.7574	0.735264	0.367632	+	0.929971i	$0.380169\pi$
$798$	0	0
$799$	−16.5623	−0.585931
$800$	0.521322	0.0184315
$801$	−7.10295	−0.250971
$802$	−11.0108	−0.388803
$803$	−6.06104	−0.213889
$804$	−9.28529	−0.327467
$805$	0	0
$806$	−3.32305	−0.117049
$807$	−4.90438	−0.172642
$808$	−10.8510	−0.381736
$809$	−34.5515	−1.21476	−0.607382	−	0.794410i	$-0.707780\pi$
$809$	−34.5515	−1.21476	−0.607382	+	0.794410i	$0.707780\pi$
$810$	2.34975	0.0825618
$811$	19.3522	0.679548	0.339774	−	0.940507i	$-0.389649\pi$
$811$	19.3522	0.679548	0.339774	+	0.940507i	$0.389649\pi$
$812$	0	0
$813$	−19.3363	−0.678152
$814$	−14.2978	−0.501138
$815$	−55.6798	−1.95038
$816$	5.67280	0.198588
$817$	25.8375	0.903939
$818$	38.3012	1.33917
$819$	0	0
$820$	4.48528	0.156633
$821$	36.5407	1.27528	0.637640	−	0.770334i	$-0.279911\pi$
$821$	36.5407	1.27528	0.637640	+	0.770334i	$0.279911\pi$
$822$	−21.9757	−0.766492
$823$	−47.0833	−1.64122	−0.820610	−	0.571488i	$-0.806366\pi$
$823$	−47.0833	−1.64122	−0.820610	+	0.571488i	$0.806366\pi$
$824$	6.85025	0.238640
$825$	1.91471	0.0666617
$826$	0	0
$827$	−40.6870	−1.41483	−0.707413	−	0.706801i	$-0.750138\pi$
$827$	−40.6870	−1.41483	−0.707413	+	0.706801i	$0.750138\pi$
$828$	4.34975	0.151164
$829$	26.1449	0.908049	0.454024	−	0.890989i	$-0.349988\pi$
$829$	26.1449	0.908049	0.454024	+	0.890989i	$0.349988\pi$
$830$	−24.3348	−0.844674
$831$	9.07694	0.314876
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	17.5196	0.606655
$835$	3.43543	0.118888
$836$	−8.63015	−0.298480
$837$	−3.32305	−0.114861
$838$	−29.6424	−1.02398
$839$	−49.0313	−1.69275	−0.846374	−	0.532589i	$-0.821219\pi$
$839$	−49.0313	−1.69275	−0.846374	+	0.532589i	$0.821219\pi$
$840$	0	0
$841$	53.5738	1.84737
$842$	11.7612	0.405319
$843$	7.04264	0.242562
$844$	−6.99584	−0.240807
$845$	2.34975	0.0808338
$846$	2.91959	0.100378
$847$	0	0
$848$	−0.737261	−0.0253176
$849$	−32.3029	−1.10863
$850$	−2.95736	−0.101436
$851$	16.9331	0.580459
$852$	−14.7220	−0.504369
$853$	35.5633	1.21766	0.608831	−	0.793300i	$-0.291639\pi$
$853$	35.5633	1.21766	0.608831	+	0.793300i	$0.291639\pi$
$854$	0	0
$855$	5.52132	0.188825
$856$	13.8025	0.471758
$857$	−2.47062	−0.0843948	−0.0421974	−	0.999109i	$-0.513436\pi$
$857$	−2.47062	−0.0843948	−0.0421974	+	0.999109i	$0.513436\pi$
$858$	−3.67280	−0.125387
$859$	27.3775	0.934108	0.467054	−	0.884229i	$-0.345315\pi$
$859$	27.3775	0.934108	0.467054	+	0.884229i	$0.345315\pi$
$860$	25.8375	0.881051
$861$	0	0
$862$	28.4230	0.968090
$863$	−3.73238	−0.127052	−0.0635258	−	0.997980i	$-0.520235\pi$
$863$	−3.73238	−0.127052	−0.0635258	+	0.997980i	$0.520235\pi$
$864$	−1.00000	−0.0340207
$865$	23.7279	0.806774
$866$	38.5598	1.31032
$867$	−15.1806	−0.515561
$868$	0	0
$869$	−40.3269	−1.36800
$870$	−21.3522	−0.723907
$871$	−9.28529	−0.314620
$872$	−12.1203	−0.410446
$873$	6.51717	0.220573
$874$	10.2208	0.345724
$875$	0	0
$876$	−1.65025	−0.0557568
$877$	12.5854	0.424977	0.212489	−	0.977164i	$-0.431843\pi$
$877$	12.5854	0.424977	0.212489	+	0.977164i	$0.431843\pi$
$878$	23.7958	0.803071
$879$	1.78578	0.0602330
$880$	−8.63015	−0.290922
$881$	55.3124	1.86352	0.931762	−	0.363071i	$-0.118272\pi$
$881$	55.3124	1.86352	0.931762	+	0.363071i	$0.118272\pi$
$882$	0	0
$883$	−13.3390	−0.448893	−0.224446	−	0.974486i	$-0.572057\pi$
$883$	−13.3390	−0.448893	−0.224446	+	0.974486i	$0.572057\pi$
$884$	5.67280	0.190797
$885$	−7.80833	−0.262474
$886$	−33.5803	−1.12815
$887$	−13.2784	−0.445844	−0.222922	−	0.974836i	$-0.571560\pi$
$887$	−13.2784	−0.445844	−0.222922	+	0.974836i	$0.571560\pi$
$888$	−3.89289	−0.130637
$889$	0	0
$890$	−16.6902	−0.559455
$891$	−3.67280	−0.123043
$892$	5.20346	0.174225
$893$	6.86031	0.229572
$894$	18.8201	0.629439
$895$	41.3279	1.38144
$896$	0	0
$897$	4.34975	0.145234
$898$	−41.3963	−1.38141
$899$	30.1966	1.00711
$900$	0.521322	0.0173774
$901$	4.18233	0.139334
$902$	−7.01076	−0.233433
$903$	0	0
$904$	−14.5397	−0.483584
$905$	−22.8167	−0.758452
$906$	3.20072	0.106337
$907$	−2.20445	−0.0731977	−0.0365988	−	0.999330i	$-0.511652\pi$
$907$	−2.20445	−0.0731977	−0.0365988	+	0.999330i	$0.511652\pi$
$908$	2.85097	0.0946129
$909$	−10.8510	−0.359904
$910$	0	0
$911$	12.5570	0.416033	0.208017	−	0.978125i	$-0.433299\pi$
$911$	12.5570	0.416033	0.208017	+	0.978125i	$0.433299\pi$
$912$	−2.34975	−0.0778080
$913$	38.0368	1.25883
$914$	−1.17115	−0.0387381
$915$	−8.93310	−0.295319
$916$	−6.48631	−0.214314
$917$	0	0
$918$	5.67280	0.187230
$919$	−36.8548	−1.21573	−0.607865	−	0.794041i	$-0.707974\pi$
$919$	−36.8548	−1.21573	−0.607865	+	0.794041i	$0.707974\pi$
$920$	10.2208	0.336970
$921$	−1.38579	−0.0456633
$922$	14.1487	0.465964
$923$	−14.7220	−0.484582
$924$	0	0
$925$	2.02945	0.0667279
$926$	−1.25413	−0.0412132
$927$	6.85025	0.224992
$928$	9.08701	0.298296
$929$	−9.92059	−0.325484	−0.162742	−	0.986669i	$-0.552034\pi$
$929$	−9.92059	−0.325484	−0.162742	+	0.986669i	$0.552034\pi$
$930$	−7.80833	−0.256045
$931$	0	0
$932$	−0.386785	−0.0126696
$933$	27.4211	0.897727
$934$	12.5463	0.410528
$935$	48.9571	1.60107
$936$	−1.00000	−0.0326860
$937$	−41.0191	−1.34004	−0.670018	−	0.742345i	$-0.733714\pi$
$937$	−41.0191	−1.34004	−0.670018	+	0.742345i	$0.733714\pi$
$938$	0	0
$939$	15.4059	0.502753
$940$	6.86031	0.223759
$941$	−51.5009	−1.67888	−0.839441	−	0.543450i	$-0.817118\pi$
$941$	−51.5009	−1.67888	−0.839441	+	0.543450i	$0.817118\pi$
$942$	−6.91989	−0.225462
$943$	8.30295	0.270381
$944$	3.32305	0.108156
$945$	0	0
$946$	−40.3855	−1.31305
$947$	−10.1796	−0.330792	−0.165396	−	0.986227i	$-0.552890\pi$
$947$	−10.1796	−0.330792	−0.165396	+	0.986227i	$0.552890\pi$
$948$	−10.9799	−0.356611
$949$	−1.65025	−0.0535694
$950$	1.22498	0.0397435
$951$	27.5720	0.894083
$952$	0	0
$953$	41.9377	1.35849	0.679247	−	0.733909i	$-0.262306\pi$
$953$	41.9377	1.35849	0.679247	+	0.733909i	$0.262306\pi$
$954$	−0.737261	−0.0238697
$955$	−36.3018	−1.17470
$956$	18.2936	0.591658
$957$	33.3747	1.07885
$958$	−37.4752	−1.21077
$959$	0	0
$960$	−2.34975	−0.0758378
$961$	−19.9574	−0.643786
$962$	−3.89289	−0.125512
$963$	13.8025	0.444778
$964$	19.2167	0.618927
$965$	−0.178464	−0.00574495
$966$	0	0
$967$	16.0624	0.516533	0.258266	−	0.966074i	$-0.416849\pi$
$967$	16.0624	0.516533	0.258266	+	0.966074i	$0.416849\pi$
$968$	2.48944	0.0800135
$969$	13.3297	0.428210
$970$	15.3137	0.491694
$971$	−28.1289	−0.902700	−0.451350	−	0.892347i	$-0.649057\pi$
$971$	−28.1289	−0.902700	−0.451350	+	0.892347i	$0.649057\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−17.7338	−0.568229
$975$	0.521322	0.0166957
$976$	3.80173	0.121690
$977$	−43.3213	−1.38597	−0.692986	−	0.720951i	$-0.743705\pi$
$977$	−43.3213	−1.38597	−0.692986	+	0.720951i	$0.743705\pi$
$978$	23.6961	0.757717
$979$	26.0877	0.833767
$980$	0	0
$981$	−12.1203	−0.386972
$982$	−11.4049	−0.363944
$983$	15.6797	0.500105	0.250052	−	0.968232i	$-0.419552\pi$
$983$	15.6797	0.500105	0.250052	+	0.968232i	$0.419552\pi$
$984$	−1.90883	−0.0608514
$985$	25.6226	0.816402
$986$	−51.5488	−1.64165
$987$	0	0
$988$	−2.34975	−0.0747555
$989$	47.8292	1.52088
$990$	−8.63015	−0.274284
$991$	−3.99024	−0.126754	−0.0633770	−	0.997990i	$-0.520187\pi$
$991$	−3.99024	−0.126754	−0.0633770	+	0.997990i	$0.520187\pi$
$992$	3.32305	0.105507
$993$	−20.0520	−0.636331
$994$	0	0
$995$	−25.6762	−0.813992
$996$	10.3564	0.328154
$997$	−53.7373	−1.70188	−0.850938	−	0.525266i	$-0.823966\pi$
$997$	−53.7373	−1.70188	−0.850938	+	0.525266i	$0.823966\pi$
$998$	5.87798	0.186064
$999$	−3.89289	−0.123166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.bz.1.3	✓	4
7.6	odd	2		3822.2.a.ca.1.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3822.2.a.bz.1.3	✓	4	1.1	even	1	trivial
3822.2.a.ca.1.2	yes	4	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.34975 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.34975 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +2.34975 q^{10} -3.67280 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.34975 q^{15} +1.00000 q^{16} -5.67280 q^{17} +1.00000 q^{18} +2.34975 q^{19} +2.34975 q^{20} -3.67280 q^{22} +4.34975 q^{23} -1.00000 q^{24} +0.521322 q^{25} -1.00000 q^{26} -1.00000 q^{27} +9.08701 q^{29} -2.34975 q^{30} +3.32305 q^{31} +1.00000 q^{32} +3.67280 q^{33} -5.67280 q^{34} +1.00000 q^{36} +3.89289 q^{37} +2.34975 q^{38} +1.00000 q^{39} +2.34975 q^{40} +1.90883 q^{41} +10.9958 q^{43} -3.67280 q^{44} +2.34975 q^{45} +4.34975 q^{46} +2.91959 q^{47} -1.00000 q^{48} +0.521322 q^{50} +5.67280 q^{51} -1.00000 q^{52} -0.737261 q^{53} -1.00000 q^{54} -8.63015 q^{55} -2.34975 q^{57} +9.08701 q^{58} +3.32305 q^{59} -2.34975 q^{60} +3.80173 q^{61} +3.32305 q^{62} +1.00000 q^{64} -2.34975 q^{65} +3.67280 q^{66} +9.28529 q^{67} -5.67280 q^{68} -4.34975 q^{69} +14.7220 q^{71} +1.00000 q^{72} +1.65025 q^{73} +3.89289 q^{74} -0.521322 q^{75} +2.34975 q^{76} +1.00000 q^{78} +10.9799 q^{79} +2.34975 q^{80} +1.00000 q^{81} +1.90883 q^{82} -10.3564 q^{83} -13.3297 q^{85} +10.9958 q^{86} -9.08701 q^{87} -3.67280 q^{88} -7.10295 q^{89} +2.34975 q^{90} +4.34975 q^{92} -3.32305 q^{93} +2.91959 q^{94} +5.52132 q^{95} -1.00000 q^{96} +6.51717 q^{97} -3.67280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 2 q^{10} + 6 q^{11} - 4 q^{12} - 4 q^{13} - 2 q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 2 q^{19} + 2 q^{20} + 6 q^{22} + 10 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} - 4 q^{27} + 10 q^{29} - 2 q^{30} + 4 q^{32} - 6 q^{33} - 2 q^{34} + 4 q^{36} + 6 q^{37} + 2 q^{38} + 4 q^{39} + 2 q^{40} + 10 q^{43} + 6 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 4 q^{48} + 6 q^{50} + 2 q^{51} - 4 q^{52} + 16 q^{53} - 4 q^{54} - 6 q^{55} - 2 q^{57} + 10 q^{58} - 2 q^{60} - 2 q^{61} + 4 q^{64} - 2 q^{65} - 6 q^{66} + 28 q^{67} - 2 q^{68} - 10 q^{69} + 16 q^{71} + 4 q^{72} + 14 q^{73} + 6 q^{74} - 6 q^{75} + 2 q^{76} + 4 q^{78} + 8 q^{79} + 2 q^{80} + 4 q^{81} - 4 q^{83} - 10 q^{85} + 10 q^{86} - 10 q^{87} + 6 q^{88} - 4 q^{89} + 2 q^{90} + 10 q^{92} + 8 q^{94} + 26 q^{95} - 4 q^{96} - 4 q^{97} + 6 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 2 * q^10 + 6 * q^11 - 4 * q^12 - 4 * q^13 - 2 * q^15 + 4 * q^16 - 2 * q^17 + 4 * q^18 + 2 * q^19 + 2 * q^20 + 6 * q^22 + 10 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 - 4 * q^27 + 10 * q^29 - 2 * q^30 + 4 * q^32 - 6 * q^33 - 2 * q^34 + 4 * q^36 + 6 * q^37 + 2 * q^38 + 4 * q^39 + 2 * q^40 + 10 * q^43 + 6 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 4 * q^48 + 6 * q^50 + 2 * q^51 - 4 * q^52 + 16 * q^53 - 4 * q^54 - 6 * q^55 - 2 * q^57 + 10 * q^58 - 2 * q^60 - 2 * q^61 + 4 * q^64 - 2 * q^65 - 6 * q^66 + 28 * q^67 - 2 * q^68 - 10 * q^69 + 16 * q^71 + 4 * q^72 + 14 * q^73 + 6 * q^74 - 6 * q^75 + 2 * q^76 + 4 * q^78 + 8 * q^79 + 2 * q^80 + 4 * q^81 - 4 * q^83 - 10 * q^85 + 10 * q^86 - 10 * q^87 + 6 * q^88 - 4 * q^89 + 2 * q^90 + 10 * q^92 + 8 * q^94 + 26 * q^95 - 4 * q^96 - 4 * q^97 + 6 * q^99

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