LMFDB - Embedded newform 3822.2.a.ca.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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.34975 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.34975 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.34975 q^{10} +5.25858 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.34975 q^{15} +1.00000 q^{16} -3.25858 q^{17} +1.00000 q^{18} +1.34975 q^{19} +1.34975 q^{20} +5.25858 q^{22} +0.650251 q^{23} +1.00000 q^{24} -3.17818 q^{25} +1.00000 q^{26} +1.00000 q^{27} +0.155630 q^{29} +1.34975 q^{30} +1.90883 q^{31} +1.00000 q^{32} +5.25858 q^{33} -3.25858 q^{34} +1.00000 q^{36} +7.59239 q^{37} +1.34975 q^{38} +1.00000 q^{39} +1.34975 q^{40} +3.32305 q^{41} -3.16742 q^{43} +5.25858 q^{44} +1.34975 q^{45} +0.650251 q^{46} -8.15147 q^{47} +1.00000 q^{48} -3.17818 q^{50} -3.25858 q^{51} +1.00000 q^{52} +4.49462 q^{53} +1.00000 q^{54} +7.09777 q^{55} +1.34975 q^{57} +0.155630 q^{58} +1.90883 q^{59} +1.34975 q^{60} -2.26934 q^{61} +1.90883 q^{62} +1.00000 q^{64} +1.34975 q^{65} +5.25858 q^{66} +1.88629 q^{67} -3.25858 q^{68} +0.650251 q^{69} -5.30783 q^{71} +1.00000 q^{72} -5.34975 q^{73} +7.59239 q^{74} -3.17818 q^{75} +1.34975 q^{76} +1.00000 q^{78} +5.74802 q^{79} +1.34975 q^{80} +1.00000 q^{81} +3.32305 q^{82} +2.95736 q^{83} -4.39827 q^{85} -3.16742 q^{86} +0.155630 q^{87} +5.25858 q^{88} -10.7598 q^{89} +1.34975 q^{90} +0.650251 q^{92} +1.90883 q^{93} -8.15147 q^{94} +1.82182 q^{95} +1.00000 q^{96} +11.3456 q^{97} +5.25858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.34975	0.603626	0.301813	−	0.953367i	$-0.402408\pi$
$5$	1.34975	0.603626	0.301813	+	0.953367i	$0.402408\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.34975	0.426828
$11$	5.25858	1.58552	0.792761	−	0.609532i	$-0.208643\pi$
$11$	5.25858	1.58552	0.792761	+	0.609532i	$0.208643\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	1.34975	0.348504
$16$	1.00000	0.250000
$17$	−3.25858	−0.790323	−0.395161	−	0.918612i	$-0.629311\pi$
$17$	−3.25858	−0.790323	−0.395161	+	0.918612i	$0.629311\pi$
$18$	1.00000	0.235702
$19$	1.34975	0.309654	0.154827	−	0.987942i	$-0.450518\pi$
$19$	1.34975	0.309654	0.154827	+	0.987942i	$0.450518\pi$
$20$	1.34975	0.301813
$21$	0	0
$22$	5.25858	1.12113
$23$	0.650251	0.135587	0.0677933	−	0.997699i	$-0.478404\pi$
$23$	0.650251	0.135587	0.0677933	+	0.997699i	$0.478404\pi$
$24$	1.00000	0.204124
$25$	−3.17818	−0.635635
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	0.155630	0.0288998	0.0144499	−	0.999896i	$-0.495400\pi$
$29$	0.155630	0.0288998	0.0144499	+	0.999896i	$0.495400\pi$
$30$	1.34975	0.246429
$31$	1.90883	0.342837	0.171418	−	0.985198i	$-0.445165\pi$
$31$	1.90883	0.342837	0.171418	+	0.985198i	$0.445165\pi$
$32$	1.00000	0.176777
$33$	5.25858	0.915402
$34$	−3.25858	−0.558842
$35$	0	0
$36$	1.00000	0.166667
$37$	7.59239	1.24818	0.624091	−	0.781352i	$-0.285470\pi$
$37$	7.59239	1.24818	0.624091	+	0.781352i	$0.285470\pi$
$38$	1.34975	0.218958
$39$	1.00000	0.160128
$40$	1.34975	0.213414
$41$	3.32305	0.518973	0.259486	−	0.965747i	$-0.416447\pi$
$41$	3.32305	0.518973	0.259486	+	0.965747i	$0.416447\pi$
$42$	0	0
$43$	−3.16742	−0.483027	−0.241513	−	0.970398i	$-0.577644\pi$
$43$	−3.16742	−0.483027	−0.241513	+	0.970398i	$0.577644\pi$
$44$	5.25858	0.792761
$45$	1.34975	0.201209
$46$	0.650251	0.0958742
$47$	−8.15147	−1.18901	−0.594507	−	0.804090i	$-0.702653\pi$
$47$	−8.15147	−1.18901	−0.594507	+	0.804090i	$0.702653\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−3.17818	−0.449462
$51$	−3.25858	−0.456293
$52$	1.00000	0.138675
$53$	4.49462	0.617384	0.308692	−	0.951162i	$-0.400109\pi$
$53$	4.49462	0.617384	0.308692	+	0.951162i	$0.400109\pi$
$54$	1.00000	0.136083
$55$	7.09777	0.957063
$56$	0	0
$57$	1.34975	0.178779
$58$	0.155630	0.0204353
$59$	1.90883	0.248509	0.124255	−	0.992250i	$-0.460346\pi$
$59$	1.90883	0.248509	0.124255	+	0.992250i	$0.460346\pi$
$60$	1.34975	0.174252
$61$	−2.26934	−0.290560	−0.145280	−	0.989391i	$-0.546408\pi$
$61$	−2.26934	−0.290560	−0.145280	+	0.989391i	$0.546408\pi$
$62$	1.90883	0.242422
$63$	0	0
$64$	1.00000	0.125000
$65$	1.34975	0.167416
$66$	5.25858	0.647287
$67$	1.88629	0.230447	0.115223	−	0.993340i	$-0.463242\pi$
$67$	1.88629	0.230447	0.115223	+	0.993340i	$0.463242\pi$
$68$	−3.25858	−0.395161
$69$	0.650251	0.0782810
$70$	0	0
$71$	−5.30783	−0.629924	−0.314962	−	0.949104i	$-0.601992\pi$
$71$	−5.30783	−0.629924	−0.314962	+	0.949104i	$0.601992\pi$
$72$	1.00000	0.117851
$73$	−5.34975	−0.626141	−0.313070	−	0.949730i	$-0.601358\pi$
$73$	−5.34975	−0.626141	−0.313070	+	0.949730i	$0.601358\pi$
$74$	7.59239	0.882597
$75$	−3.17818	−0.366984
$76$	1.34975	0.154827
$77$	0	0
$78$	1.00000	0.113228
$79$	5.74802	0.646703	0.323351	−	0.946279i	$-0.395190\pi$
$79$	5.74802	0.646703	0.323351	+	0.946279i	$0.395190\pi$
$80$	1.34975	0.150907
$81$	1.00000	0.111111
$82$	3.32305	0.366969
$83$	2.95736	0.324612	0.162306	−	0.986740i	$-0.448107\pi$
$83$	2.95736	0.324612	0.162306	+	0.986740i	$0.448107\pi$
$84$	0	0
$85$	−4.39827	−0.477059
$86$	−3.16742	−0.341551
$87$	0.155630	0.0166853
$88$	5.25858	0.560567
$89$	−10.7598	−1.14054	−0.570269	−	0.821458i	$-0.693161\pi$
$89$	−10.7598	−1.14054	−0.570269	+	0.821458i	$0.693161\pi$
$90$	1.34975	0.142276
$91$	0	0
$92$	0.650251	0.0677933
$93$	1.90883	0.197937
$94$	−8.15147	−0.840760
$95$	1.82182	0.186915
$96$	1.00000	0.102062
$97$	11.3456	1.15197	0.575985	−	0.817460i	$-0.304619\pi$
$97$	11.3456	1.15197	0.575985	+	0.817460i	$0.304619\pi$
$98$	0	0
$99$	5.25858	0.528508
$100$	−3.17818	−0.317818
$101$	−1.77991	−0.177107	−0.0885536	−	0.996071i	$-0.528224\pi$
$101$	−1.77991	−0.177107	−0.0885536	+	0.996071i	$0.528224\pi$
$102$	−3.25858	−0.322648
$103$	−17.9487	−1.76854	−0.884271	−	0.466974i	$-0.845344\pi$
$103$	−17.9487	−1.76854	−0.884271	+	0.466974i	$0.845344\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	4.49462	0.436556
$107$	−11.4593	−1.10781	−0.553906	−	0.832579i	$-0.686863\pi$
$107$	−11.4593	−1.10781	−0.553906	+	0.832579i	$0.686863\pi$
$108$	1.00000	0.0962250
$109$	−1.02182	−0.0978726	−0.0489363	−	0.998802i	$-0.515583\pi$
$109$	−1.02182	−0.0978726	−0.0489363	+	0.998802i	$0.515583\pi$
$110$	7.09777	0.676746
$111$	7.59239	0.720638
$112$	0	0
$113$	15.9539	1.50082	0.750410	−	0.660973i	$-0.229856\pi$
$113$	15.9539	1.50082	0.750410	+	0.660973i	$0.229856\pi$
$114$	1.34975	0.126416
$115$	0.877675	0.0818436
$116$	0.155630	0.0144499
$117$	1.00000	0.0924500
$118$	1.90883	0.175722
$119$	0	0
$120$	1.34975	0.123215
$121$	16.6527	1.51388
$122$	−2.26934	−0.205457
$123$	3.32305	0.299629
$124$	1.90883	0.171418
$125$	−11.0385	−0.987312
$126$	0	0
$127$	−2.03776	−0.180822	−0.0904111	−	0.995905i	$-0.528818\pi$
$127$	−2.03776	−0.180822	−0.0904111	+	0.995905i	$0.528818\pi$
$128$	1.00000	0.0883883
$129$	−3.16742	−0.278876
$130$	1.34975	0.118381
$131$	−15.5615	−1.35962	−0.679809	−	0.733389i	$-0.737937\pi$
$131$	−15.5615	−1.35962	−0.679809	+	0.733389i	$0.737937\pi$
$132$	5.25858	0.457701
$133$	0	0
$134$	1.88629	0.162950
$135$	1.34975	0.116168
$136$	−3.25858	−0.279421
$137$	2.58060	0.220476	0.110238	−	0.993905i	$-0.464839\pi$
$137$	2.58060	0.220476	0.110238	+	0.993905i	$0.464839\pi$
$138$	0.650251	0.0553530
$139$	−18.2059	−1.54420	−0.772102	−	0.635498i	$-0.780795\pi$
$139$	−18.2059	−1.54420	−0.772102	+	0.635498i	$0.780795\pi$
$140$	0	0
$141$	−8.15147	−0.686478
$142$	−5.30783	−0.445423
$143$	5.25858	0.439745
$144$	1.00000	0.0833333
$145$	0.210062	0.0174447
$146$	−5.34975	−0.442748
$147$	0	0
$148$	7.59239	0.624091
$149$	9.50641	0.778795	0.389398	−	0.921070i	$-0.372683\pi$
$149$	9.50641	0.778795	0.389398	+	0.921070i	$0.372683\pi$
$150$	−3.17818	−0.259497
$151$	13.1297	1.06848	0.534238	−	0.845334i	$-0.320599\pi$
$151$	13.1297	1.06848	0.534238	+	0.845334i	$0.320599\pi$
$152$	1.34975	0.109479
$153$	−3.25858	−0.263441
$154$	0	0
$155$	2.57645	0.206945
$156$	1.00000	0.0800641
$157$	−2.32275	−0.185375	−0.0926877	−	0.995695i	$-0.529546\pi$
$157$	−2.32275	−0.185375	−0.0926877	+	0.995695i	$0.529546\pi$
$158$	5.74802	0.457288
$159$	4.49462	0.356447
$160$	1.34975	0.106707
$161$	0	0
$162$	1.00000	0.0785674
$163$	21.5956	1.69150	0.845748	−	0.533583i	$-0.179155\pi$
$163$	21.5956	1.69150	0.845748	+	0.533583i	$0.179155\pi$
$164$	3.32305	0.259486
$165$	7.09777	0.552561
$166$	2.95736	0.229535
$167$	25.3321	1.96026	0.980128	−	0.198364i	$-0.0635629\pi$
$167$	25.3321	1.96026	0.980128	+	0.198364i	$0.0635629\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−4.39827	−0.337332
$171$	1.34975	0.103218
$172$	−3.16742	−0.241513
$173$	−1.80142	−0.136960	−0.0684799	−	0.997652i	$-0.521815\pi$
$173$	−1.80142	−0.136960	−0.0684799	+	0.997652i	$0.521815\pi$
$174$	0.155630	0.0117983
$175$	0	0
$176$	5.25858	0.396381
$177$	1.90883	0.143477
$178$	−10.7598	−0.806482
$179$	−0.274526	−0.0205190	−0.0102595	−	0.999947i	$-0.503266\pi$
$179$	−0.274526	−0.0205190	−0.0102595	+	0.999947i	$0.503266\pi$
$180$	1.34975	0.100604
$181$	12.7750	0.949560	0.474780	−	0.880105i	$-0.342528\pi$
$181$	12.7750	0.949560	0.474780	+	0.880105i	$0.342528\pi$
$182$	0	0
$183$	−2.26934	−0.167755
$184$	0.650251	0.0479371
$185$	10.2478	0.753435
$186$	1.90883	0.139962
$187$	−17.1355	−1.25307
$188$	−8.15147	−0.594507
$189$	0	0
$190$	1.82182	0.132169
$191$	−19.1487	−1.38555	−0.692777	−	0.721152i	$-0.743613\pi$
$191$	−19.1487	−1.38555	−0.692777	+	0.721152i	$0.743613\pi$
$192$	1.00000	0.0721688
$193$	9.49016	0.683117	0.341558	−	0.939861i	$-0.389045\pi$
$193$	9.49016	0.683117	0.341558	+	0.939861i	$0.389045\pi$
$194$	11.3456	0.814566
$195$	1.34975	0.0966576
$196$	0	0
$197$	1.33826	0.0953473	0.0476737	−	0.998863i	$-0.484819\pi$
$197$	1.33826	0.0953473	0.0476737	+	0.998863i	$0.484819\pi$
$198$	5.25858	0.373711
$199$	−21.0988	−1.49565	−0.747827	−	0.663894i	$-0.768903\pi$
$199$	−21.0988	−1.49565	−0.747827	+	0.663894i	$0.768903\pi$
$200$	−3.17818	−0.224731
$201$	1.88629	0.133048
$202$	−1.77991	−0.125234
$203$	0	0
$204$	−3.25858	−0.228146
$205$	4.48528	0.313266
$206$	−17.9487	−1.25055
$207$	0.650251	0.0451955
$208$	1.00000	0.0693375
$209$	7.09777	0.490963
$210$	0	0
$211$	7.16742	0.493425	0.246713	−	0.969089i	$-0.420650\pi$
$211$	7.16742	0.493425	0.246713	+	0.969089i	$0.420650\pi$
$212$	4.49462	0.308692
$213$	−5.30783	−0.363687
$214$	−11.4593	−0.783342
$215$	−4.27522	−0.291568
$216$	1.00000	0.0680414
$217$	0	0
$218$	−1.02182	−0.0692064
$219$	−5.34975	−0.361503
$220$	7.09777	0.478532
$221$	−3.25858	−0.219196
$222$	7.59239	0.509568
$223$	12.6593	0.847730	0.423865	−	0.905725i	$-0.360673\pi$
$223$	12.6593	0.847730	0.423865	+	0.905725i	$0.360673\pi$
$224$	0	0
$225$	−3.17818	−0.211878
$226$	15.9539	1.06124
$227$	9.77991	0.649115	0.324558	−	0.945866i	$-0.394785\pi$
$227$	9.77991	0.649115	0.324558	+	0.945866i	$0.394785\pi$
$228$	1.34975	0.0893893
$229$	−27.0721	−1.78897	−0.894487	−	0.447094i	$-0.852459\pi$
$229$	−27.0721	−1.78897	−0.894487	+	0.447094i	$0.852459\pi$
$230$	0.877675	0.0578722
$231$	0	0
$232$	0.155630	0.0102176
$233$	−22.5838	−1.47951	−0.739756	−	0.672875i	$-0.765059\pi$
$233$	−22.5838	−1.47951	−0.739756	+	0.672875i	$0.765059\pi$
$234$	1.00000	0.0653720
$235$	−11.0024	−0.717721
$236$	1.90883	0.124255
$237$	5.74802	0.373374
$238$	0	0
$239$	13.0617	0.844893	0.422447	−	0.906388i	$-0.361171\pi$
$239$	13.0617	0.844893	0.422447	+	0.906388i	$0.361171\pi$
$240$	1.34975	0.0871259
$241$	6.04509	0.389399	0.194699	−	0.980863i	$-0.437627\pi$
$241$	6.04509	0.389399	0.194699	+	0.980863i	$0.437627\pi$
$242$	16.6527	1.07048
$243$	1.00000	0.0641500
$244$	−2.26934	−0.145280
$245$	0	0
$246$	3.32305	0.211870
$247$	1.34975	0.0858825
$248$	1.90883	0.121211
$249$	2.95736	0.187415
$250$	−11.0385	−0.698135
$251$	10.7331	0.677468	0.338734	−	0.940882i	$-0.390001\pi$
$251$	10.7331	0.677468	0.338734	+	0.940882i	$0.390001\pi$
$252$	0	0
$253$	3.41940	0.214976
$254$	−2.03776	−0.127861
$255$	−4.39827	−0.275430
$256$	1.00000	0.0625000
$257$	−1.13969	−0.0710918	−0.0355459	−	0.999368i	$-0.511317\pi$
$257$	−1.13969	−0.0710918	−0.0355459	+	0.999368i	$0.511317\pi$
$258$	−3.16742	−0.197195
$259$	0	0
$260$	1.34975	0.0837079
$261$	0.155630	0.00963327
$262$	−15.5615	−0.961395
$263$	25.2922	1.55958	0.779792	−	0.626039i	$-0.215325\pi$
$263$	25.2922	1.55958	0.779792	+	0.626039i	$0.215325\pi$
$264$	5.25858	0.323643
$265$	6.06661	0.372669
$266$	0	0
$267$	−10.7598	−0.658490
$268$	1.88629	0.115223
$269$	4.66174	0.284231	0.142116	−	0.989850i	$-0.454610\pi$
$269$	4.66174	0.284231	0.142116	+	0.989850i	$0.454610\pi$
$270$	1.34975	0.0821431
$271$	−6.70538	−0.407323	−0.203661	−	0.979041i	$-0.565284\pi$
$271$	−6.70538	−0.407323	−0.203661	+	0.979041i	$0.565284\pi$
$272$	−3.25858	−0.197581
$273$	0	0
$274$	2.58060	0.155900
$275$	−16.7127	−1.00781
$276$	0.650251	0.0391405
$277$	−29.1068	−1.74886	−0.874430	−	0.485152i	$-0.838764\pi$
$277$	−29.1068	−1.74886	−0.874430	+	0.485152i	$0.838764\pi$
$278$	−18.2059	−1.09192
$279$	1.90883	0.114279
$280$	0	0
$281$	0.356353	0.0212582	0.0106291	−	0.999944i	$-0.496617\pi$
$281$	0.356353	0.0212582	0.0106291	+	0.999944i	$0.496617\pi$
$282$	−8.15147	−0.485413
$283$	−21.8392	−1.29820	−0.649102	−	0.760701i	$-0.724855\pi$
$283$	−21.8392	−1.29820	−0.649102	+	0.760701i	$0.724855\pi$
$284$	−5.30783	−0.314962
$285$	1.82182	0.107916
$286$	5.25858	0.310947
$287$	0	0
$288$	1.00000	0.0589256
$289$	−6.38163	−0.375390
$290$	0.210062	0.0123353
$291$	11.3456	0.665090
$292$	−5.34975	−0.313070
$293$	9.18478	0.536581	0.268290	−	0.963338i	$-0.413541\pi$
$293$	9.18478	0.536581	0.268290	+	0.963338i	$0.413541\pi$
$294$	0	0
$295$	2.57645	0.150007
$296$	7.59239	0.441299
$297$	5.25858	0.305134
$298$	9.50641	0.550691
$299$	0.650251	0.0376050
$300$	−3.17818	−0.183492
$301$	0	0
$302$	13.1297	0.755527
$303$	−1.77991	−0.102253
$304$	1.34975	0.0774134
$305$	−3.06304	−0.175389
$306$	−3.25858	−0.186281
$307$	6.01321	0.343192	0.171596	−	0.985167i	$-0.445108\pi$
$307$	6.01321	0.343192	0.171596	+	0.985167i	$0.445108\pi$
$308$	0	0
$309$	−17.9487	−1.02107
$310$	2.57645	0.146332
$311$	13.8926	0.787777	0.393888	−	0.919158i	$-0.371130\pi$
$311$	13.8926	0.787777	0.393888	+	0.919158i	$0.371130\pi$
$312$	1.00000	0.0566139
$313$	−12.9206	−0.730317	−0.365158	−	0.930945i	$-0.618985\pi$
$313$	−12.9206	−0.730317	−0.365158	+	0.930945i	$0.618985\pi$
$314$	−2.32275	−0.131080
$315$	0	0
$316$	5.74802	0.323351
$317$	−28.4696	−1.59901	−0.799507	−	0.600657i	$-0.794906\pi$
$317$	−28.4696	−1.59901	−0.799507	+	0.600657i	$0.794906\pi$
$318$	4.49462	0.252046
$319$	0.818395	0.0458213
$320$	1.34975	0.0754533
$321$	−11.4593	−0.639596
$322$	0	0
$323$	−4.39827	−0.244726
$324$	1.00000	0.0555556
$325$	−3.17818	−0.176294
$326$	21.5956	1.19607
$327$	−1.02182	−0.0565068
$328$	3.32305	0.183485
$329$	0	0
$330$	7.09777	0.390719
$331$	−18.7383	−1.02995	−0.514975	−	0.857205i	$-0.672199\pi$
$331$	−18.7383	−1.02995	−0.514975	+	0.857205i	$0.672199\pi$
$332$	2.95736	0.162306
$333$	7.59239	0.416060
$334$	25.3321	1.38611
$335$	2.54602	0.139104
$336$	0	0
$337$	5.30955	0.289230	0.144615	−	0.989488i	$-0.453806\pi$
$337$	5.30955	0.289230	0.144615	+	0.989488i	$0.453806\pi$
$338$	1.00000	0.0543928
$339$	15.9539	0.866498
$340$	−4.39827	−0.238530
$341$	10.0378	0.543575
$342$	1.34975	0.0729861
$343$	0	0
$344$	−3.16742	−0.170776
$345$	0.877675	0.0472525
$346$	−1.80142	−0.0968452
$347$	29.0628	1.56017	0.780085	−	0.625673i	$-0.215176\pi$
$347$	29.0628	1.56017	0.780085	+	0.625673i	$0.215176\pi$
$348$	0.155630	0.00834266
$349$	−8.83576	−0.472967	−0.236484	−	0.971635i	$-0.575995\pi$
$349$	−8.83576	−0.472967	−0.236484	+	0.971635i	$0.575995\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	5.25858	0.280283
$353$	−25.7030	−1.36803	−0.684016	−	0.729467i	$-0.739768\pi$
$353$	−25.7030	−1.36803	−0.684016	+	0.729467i	$0.739768\pi$
$354$	1.90883	0.101453
$355$	−7.16424	−0.380239
$356$	−10.7598	−0.570269
$357$	0	0
$358$	−0.274526	−0.0145091
$359$	−23.4211	−1.23612	−0.618060	−	0.786131i	$-0.712081\pi$
$359$	−23.4211	−1.23612	−0.618060	+	0.786131i	$0.712081\pi$
$360$	1.34975	0.0711380
$361$	−17.1782	−0.904115
$362$	12.7750	0.671440
$363$	16.6527	0.874040
$364$	0	0
$365$	−7.22082	−0.377955
$366$	−2.26934	−0.118620
$367$	−18.7442	−0.978437	−0.489219	−	0.872161i	$-0.662718\pi$
$367$	−18.7442	−0.978437	−0.489219	+	0.872161i	$0.662718\pi$
$368$	0.650251	0.0338967
$369$	3.32305	0.172991
$370$	10.2478	0.532759
$371$	0	0
$372$	1.90883	0.0989684
$373$	−19.9005	−1.03041	−0.515205	−	0.857067i	$-0.672284\pi$
$373$	−19.9005	−1.03041	−0.515205	+	0.857067i	$0.672284\pi$
$374$	−17.1355	−0.886057
$375$	−11.0385	−0.570025
$376$	−8.15147	−0.420380
$377$	0.155630	0.00801536
$378$	0	0
$379$	−24.6760	−1.26752	−0.633760	−	0.773530i	$-0.718489\pi$
$379$	−24.6760	−1.26752	−0.633760	+	0.773530i	$0.718489\pi$
$380$	1.82182	0.0934576
$381$	−2.03776	−0.104398
$382$	−19.1487	−0.979735
$383$	21.2115	1.08386	0.541928	−	0.840425i	$-0.317695\pi$
$383$	21.2115	1.08386	0.541928	+	0.840425i	$0.317695\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	9.49016	0.483037
$387$	−3.16742	−0.161009
$388$	11.3456	0.575985
$389$	−33.2073	−1.68368	−0.841839	−	0.539729i	$-0.818527\pi$
$389$	−33.2073	−1.68368	−0.841839	+	0.539729i	$0.818527\pi$
$390$	1.34975	0.0683472
$391$	−2.11890	−0.107157
$392$	0	0
$393$	−15.5615	−0.784975
$394$	1.33826	0.0674207
$395$	7.75839	0.390367
$396$	5.25858	0.264254
$397$	−21.3907	−1.07357	−0.536784	−	0.843720i	$-0.680361\pi$
$397$	−21.3907	−1.07357	−0.536784	+	0.843720i	$0.680361\pi$
$398$	−21.0988	−1.05759
$399$	0	0
$400$	−3.17818	−0.158909
$401$	−21.4745	−1.07239	−0.536193	−	0.844095i	$-0.680138\pi$
$401$	−21.4745	−1.07239	−0.536193	+	0.844095i	$0.680138\pi$
$402$	1.88629	0.0940795
$403$	1.90883	0.0950858
$404$	−1.77991	−0.0885536
$405$	1.34975	0.0670696
$406$	0	0
$407$	39.9252	1.97902
$408$	−3.25858	−0.161324
$409$	4.18854	0.207110	0.103555	−	0.994624i	$-0.466978\pi$
$409$	4.18854	0.207110	0.103555	+	0.994624i	$0.466978\pi$
$410$	4.48528	0.221512
$411$	2.58060	0.127292
$412$	−17.9487	−0.884271
$413$	0	0
$414$	0.650251	0.0319581
$415$	3.99169	0.195944
$416$	1.00000	0.0490290
$417$	−18.2059	−0.891547
$418$	7.09777	0.347163
$419$	−8.88501	−0.434061	−0.217030	−	0.976165i	$-0.569637\pi$
$419$	−8.88501	−0.434061	−0.217030	+	0.976165i	$0.569637\pi$
$420$	0	0
$421$	9.59411	0.467588	0.233794	−	0.972286i	$-0.424886\pi$
$421$	9.59411	0.467588	0.233794	+	0.972286i	$0.424886\pi$
$422$	7.16742	0.348904
$423$	−8.15147	−0.396338
$424$	4.49462	0.218278
$425$	10.3564	0.502357
$426$	−5.30783	−0.257165
$427$	0	0
$428$	−11.4593	−0.553906
$429$	5.25858	0.253887
$430$	−4.27522	−0.206169
$431$	16.6897	0.803916	0.401958	−	0.915658i	$-0.368330\pi$
$431$	16.6897	0.803916	0.401958	+	0.915658i	$0.368330\pi$
$432$	1.00000	0.0481125
$433$	12.8613	0.618077	0.309038	−	0.951050i	$-0.399993\pi$
$433$	12.8613	0.618077	0.309038	+	0.951050i	$0.399993\pi$
$434$	0	0
$435$	0.210062	0.0100717
$436$	−1.02182	−0.0489363
$437$	0.877675	0.0419849
$438$	−5.34975	−0.255621
$439$	−2.23359	−0.106603	−0.0533017	−	0.998578i	$-0.516975\pi$
$439$	−2.23359	−0.106603	−0.0533017	+	0.998578i	$0.516975\pi$
$440$	7.09777	0.338373
$441$	0	0
$442$	−3.25858	−0.154995
$443$	26.5093	1.25949	0.629747	−	0.776800i	$-0.283159\pi$
$443$	26.5093	1.25949	0.629747	+	0.776800i	$0.283159\pi$
$444$	7.59239	0.360319
$445$	−14.5230	−0.688458
$446$	12.6593	0.599435
$447$	9.50641	0.449638
$448$	0	0
$449$	−28.1306	−1.32757	−0.663784	−	0.747925i	$-0.731050\pi$
$449$	−28.1306	−1.32757	−0.663784	+	0.747925i	$0.731050\pi$
$450$	−3.17818	−0.149821
$451$	17.4745	0.822843
$452$	15.9539	0.750410
$453$	13.1297	0.616885
$454$	9.77991	0.458994
$455$	0	0
$456$	1.34975	0.0632078
$457$	−15.0715	−0.705015	−0.352507	−	0.935809i	$-0.614671\pi$
$457$	−15.0715	−0.705015	−0.352507	+	0.935809i	$0.614671\pi$
$458$	−27.0721	−1.26500
$459$	−3.25858	−0.152098
$460$	0.877675	0.0409218
$461$	−10.4492	−0.486670	−0.243335	−	0.969942i	$-0.578241\pi$
$461$	−10.4492	−0.486670	−0.243335	+	0.969942i	$0.578241\pi$
$462$	0	0
$463$	12.0115	0.558221	0.279111	−	0.960259i	$-0.409960\pi$
$463$	12.0115	0.558221	0.279111	+	0.960259i	$0.409960\pi$
$464$	0.155630	0.00722495
$465$	2.57645	0.119480
$466$	−22.5838	−1.04617
$467$	21.6468	1.00170	0.500848	−	0.865535i	$-0.333022\pi$
$467$	21.6468	1.00170	0.500848	+	0.865535i	$0.333022\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	−11.0024	−0.507505
$471$	−2.32275	−0.107027
$472$	1.90883	0.0878612
$473$	−16.6561	−0.765850
$474$	5.74802	0.264015
$475$	−4.28974	−0.196827
$476$	0	0
$477$	4.49462	0.205795
$478$	13.0617	0.597430
$479$	3.28211	0.149963	0.0749817	−	0.997185i	$-0.476110\pi$
$479$	3.28211	0.149963	0.0749817	+	0.997185i	$0.476110\pi$
$480$	1.34975	0.0616073
$481$	7.59239	0.346183
$482$	6.04509	0.275346
$483$	0	0
$484$	16.6527	0.756941
$485$	15.3137	0.695360
$486$	1.00000	0.0453609
$487$	25.3907	1.15056	0.575281	−	0.817956i	$-0.304893\pi$
$487$	25.3907	1.15056	0.575281	+	0.817956i	$0.304893\pi$
$488$	−2.26934	−0.102728
$489$	21.5956	0.976585
$490$	0	0
$491$	−16.6368	−0.750806	−0.375403	−	0.926862i	$-0.622496\pi$
$491$	−16.6368	−0.750806	−0.375403	+	0.926862i	$0.622496\pi$
$492$	3.32305	0.149815
$493$	−0.507134	−0.0228402
$494$	1.34975	0.0607281
$495$	7.09777	0.319021
$496$	1.90883	0.0857092
$497$	0	0
$498$	2.95736	0.132522
$499$	−15.0495	−0.673710	−0.336855	−	0.941556i	$-0.609363\pi$
$499$	−15.0495	−0.673710	−0.336855	+	0.941556i	$0.609363\pi$
$500$	−11.0385	−0.493656
$501$	25.3321	1.13175
$502$	10.7331	0.479042
$503$	23.3529	1.04126	0.520628	−	0.853784i	$-0.325698\pi$
$503$	23.3529	1.04126	0.520628	+	0.853784i	$0.325698\pi$
$504$	0	0
$505$	−2.40243	−0.106907
$506$	3.41940	0.152011
$507$	1.00000	0.0444116
$508$	−2.03776	−0.0904111
$509$	6.67237	0.295748	0.147874	−	0.989006i	$-0.452757\pi$
$509$	6.67237	0.295748	0.147874	+	0.989006i	$0.452757\pi$
$510$	−4.39827	−0.194759
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.34975	0.0595929
$514$	−1.13969	−0.0502695
$515$	−24.2263	−1.06754
$516$	−3.16742	−0.139438
$517$	−42.8652	−1.88521
$518$	0	0
$519$	−1.80142	−0.0790737
$520$	1.34975	0.0591904
$521$	13.4846	0.590769	0.295385	−	0.955378i	$-0.404552\pi$
$521$	13.4846	0.590769	0.295385	+	0.955378i	$0.404552\pi$
$522$	0.155630	0.00681175
$523$	36.5162	1.59674	0.798371	−	0.602166i	$-0.205696\pi$
$523$	36.5162	1.59674	0.798371	+	0.602166i	$0.205696\pi$
$524$	−15.5615	−0.679809
$525$	0	0
$526$	25.2922	1.10279
$527$	−6.22009	−0.270952
$528$	5.25858	0.228850
$529$	−22.5772	−0.981616
$530$	6.06661	0.263517
$531$	1.90883	0.0828363
$532$	0	0
$533$	3.32305	0.143937
$534$	−10.7598	−0.465622
$535$	−15.4672	−0.668705
$536$	1.88629	0.0814752
$537$	−0.274526	−0.0118467
$538$	4.66174	0.200982
$539$	0	0
$540$	1.34975	0.0580840
$541$	31.7130	1.36345	0.681724	−	0.731609i	$-0.261230\pi$
$541$	31.7130	1.36345	0.681724	+	0.731609i	$0.261230\pi$
$542$	−6.70538	−0.288021
$543$	12.7750	0.548229
$544$	−3.25858	−0.139711
$545$	−1.37920	−0.0590785
$546$	0	0
$547$	11.1848	0.478227	0.239113	−	0.970992i	$-0.423143\pi$
$547$	11.1848	0.478227	0.239113	+	0.970992i	$0.423143\pi$
$548$	2.58060	0.110238
$549$	−2.26934	−0.0968532
$550$	−16.7127	−0.712632
$551$	0.210062	0.00894893
$552$	0.650251	0.0276765
$553$	0	0
$554$	−29.1068	−1.23663
$555$	10.2478	0.434996
$556$	−18.2059	−0.772102
$557$	44.9103	1.90291	0.951455	−	0.307787i	$-0.0995884\pi$
$557$	44.9103	1.90291	0.951455	+	0.307787i	$0.0995884\pi$
$558$	1.90883	0.0808074
$559$	−3.16742	−0.133967
$560$	0	0
$561$	−17.1355	−0.723463
$562$	0.356353	0.0150318
$563$	−18.9910	−0.800374	−0.400187	−	0.916434i	$-0.631055\pi$
$563$	−18.9910	−0.800374	−0.400187	+	0.916434i	$0.631055\pi$
$564$	−8.15147	−0.343239
$565$	21.5338	0.905934
$566$	−21.8392	−0.917969
$567$	0	0
$568$	−5.30783	−0.222712
$569$	22.1657	0.929235	0.464617	−	0.885512i	$-0.346192\pi$
$569$	22.1657	0.929235	0.464617	+	0.885512i	$0.346192\pi$
$570$	1.82182	0.0763078
$571$	−37.3269	−1.56208	−0.781041	−	0.624479i	$-0.785311\pi$
$571$	−37.3269	−1.56208	−0.781041	+	0.624479i	$0.785311\pi$
$572$	5.25858	0.219872
$573$	−19.1487	−0.799950
$574$	0	0
$575$	−2.06661	−0.0861836
$576$	1.00000	0.0416667
$577$	27.2084	1.13270	0.566349	−	0.824165i	$-0.308355\pi$
$577$	27.2084	1.13270	0.566349	+	0.824165i	$0.308355\pi$
$578$	−6.38163	−0.265441
$579$	9.49016	0.394398
$580$	0.210062	0.00872234
$581$	0	0
$582$	11.3456	0.470290
$583$	23.6353	0.978876
$584$	−5.34975	−0.221374
$585$	1.34975	0.0558053
$586$	9.18478	0.379420
$587$	−30.5623	−1.26144	−0.630720	−	0.776011i	$-0.717240\pi$
$587$	−30.5623	−1.26144	−0.630720	+	0.776011i	$0.717240\pi$
$588$	0	0
$589$	2.57645	0.106161
$590$	2.57645	0.106071
$591$	1.33826	0.0550488
$592$	7.59239	0.312045
$593$	16.4167	0.674151	0.337076	−	0.941478i	$-0.390562\pi$
$593$	16.4167	0.674151	0.337076	+	0.941478i	$0.390562\pi$
$594$	5.25858	0.215762
$595$	0	0
$596$	9.50641	0.389398
$597$	−21.0988	−0.863516
$598$	0.650251	0.0265907
$599$	2.96296	0.121063	0.0605317	−	0.998166i	$-0.480720\pi$
$599$	2.96296	0.121063	0.0605317	+	0.998166i	$0.480720\pi$
$600$	−3.17818	−0.129749
$601$	19.7966	0.807519	0.403760	−	0.914865i	$-0.367703\pi$
$601$	19.7966	0.807519	0.403760	+	0.914865i	$0.367703\pi$
$602$	0	0
$603$	1.88629	0.0768156
$604$	13.1297	0.534238
$605$	22.4770	0.913819
$606$	−1.77991	−0.0723037
$607$	−29.0150	−1.17768	−0.588840	−	0.808249i	$-0.700415\pi$
$607$	−29.0150	−1.17768	−0.588840	+	0.808249i	$0.700415\pi$
$608$	1.34975	0.0547396
$609$	0	0
$610$	−3.06304	−0.124019
$611$	−8.15147	−0.329773
$612$	−3.25858	−0.131720
$613$	−21.2826	−0.859595	−0.429798	−	0.902925i	$-0.641415\pi$
$613$	−21.2826	−0.859595	−0.429798	+	0.902925i	$0.641415\pi$
$614$	6.01321	0.242673
$615$	4.48528	0.180864
$616$	0	0
$617$	−46.3601	−1.86639	−0.933194	−	0.359372i	$-0.882991\pi$
$617$	−46.3601	−1.86639	−0.933194	+	0.359372i	$0.882991\pi$
$618$	−17.9487	−0.722004
$619$	−33.2340	−1.33579	−0.667894	−	0.744256i	$-0.732804\pi$
$619$	−33.2340	−1.33579	−0.667894	+	0.744256i	$0.732804\pi$
$620$	2.57645	0.103473
$621$	0.650251	0.0260937
$622$	13.8926	0.557042
$623$	0	0
$624$	1.00000	0.0400320
$625$	0.991689	0.0396675
$626$	−12.9206	−0.516412
$627$	7.09777	0.283458
$628$	−2.32275	−0.0926877
$629$	−24.7404	−0.986466
$630$	0	0
$631$	−31.4007	−1.25004	−0.625021	−	0.780608i	$-0.714910\pi$
$631$	−31.4007	−1.25004	−0.625021	+	0.780608i	$0.714910\pi$
$632$	5.74802	0.228644
$633$	7.16742	0.284879
$634$	−28.4696	−1.13067
$635$	−2.75047	−0.109149
$636$	4.49462	0.178223
$637$	0	0
$638$	0.818395	0.0324006
$639$	−5.30783	−0.209975
$640$	1.34975	0.0533535
$641$	−39.3432	−1.55396	−0.776981	−	0.629524i	$-0.783250\pi$
$641$	−39.3432	−1.55396	−0.776981	+	0.629524i	$0.783250\pi$
$642$	−11.4593	−0.452263
$643$	−25.9120	−1.02187	−0.510935	−	0.859619i	$-0.670701\pi$
$643$	−25.9120	−1.02187	−0.510935	+	0.859619i	$0.670701\pi$
$644$	0	0
$645$	−4.27522	−0.168337
$646$	−4.39827	−0.173048
$647$	−1.30881	−0.0514547	−0.0257274	−	0.999669i	$-0.508190\pi$
$647$	−1.30881	−0.0514547	−0.0257274	+	0.999669i	$0.508190\pi$
$648$	1.00000	0.0392837
$649$	10.0378	0.394017
$650$	−3.17818	−0.124658
$651$	0	0
$652$	21.5956	0.845748
$653$	43.0639	1.68522	0.842610	−	0.538525i	$-0.181018\pi$
$653$	43.0639	1.68522	0.842610	+	0.538525i	$0.181018\pi$
$654$	−1.02182	−0.0399563
$655$	−21.0042	−0.820701
$656$	3.32305	0.129743
$657$	−5.34975	−0.208714
$658$	0	0
$659$	22.6583	0.882641	0.441321	−	0.897350i	$-0.354510\pi$
$659$	22.6583	0.882641	0.441321	+	0.897350i	$0.354510\pi$
$660$	7.09777	0.276280
$661$	35.9411	1.39795	0.698974	−	0.715147i	$-0.253640\pi$
$661$	35.9411	1.39795	0.698974	+	0.715147i	$0.253640\pi$
$662$	−18.7383	−0.728284
$663$	−3.25858	−0.126553
$664$	2.95736	0.114768
$665$	0	0
$666$	7.59239	0.294199
$667$	0.101199	0.00391843
$668$	25.3321	0.980128
$669$	12.6593	0.489437
$670$	2.54602	0.0983612
$671$	−11.9335	−0.460689
$672$	0	0
$673$	−31.4296	−1.21152	−0.605760	−	0.795647i	$-0.707131\pi$
$673$	−31.4296	−1.21152	−0.605760	+	0.795647i	$0.707131\pi$
$674$	5.30955	0.204516
$675$	−3.17818	−0.122328
$676$	1.00000	0.0384615
$677$	−11.8524	−0.455524	−0.227762	−	0.973717i	$-0.573141\pi$
$677$	−11.8524	−0.455524	−0.227762	+	0.973717i	$0.573141\pi$
$678$	15.9539	0.612707
$679$	0	0
$680$	−4.39827	−0.168666
$681$	9.77991	0.374767
$682$	10.0378	0.384366
$683$	25.0576	0.958801	0.479401	−	0.877596i	$-0.340854\pi$
$683$	25.0576	0.958801	0.479401	+	0.877596i	$0.340854\pi$
$684$	1.34975	0.0516090
$685$	3.48317	0.133085
$686$	0	0
$687$	−27.0721	−1.03286
$688$	−3.16742	−0.120757
$689$	4.49462	0.171231
$690$	0.877675	0.0334125
$691$	−36.9935	−1.40730	−0.703650	−	0.710547i	$-0.748448\pi$
$691$	−36.9935	−1.40730	−0.703650	+	0.710547i	$0.748448\pi$
$692$	−1.80142	−0.0684799
$693$	0	0
$694$	29.0628	1.10321
$695$	−24.5734	−0.932123
$696$	0.155630	0.00589915
$697$	−10.8284	−0.410156
$698$	−8.83576	−0.334438
$699$	−22.5838	−0.854197
$700$	0	0
$701$	−12.9986	−0.490950	−0.245475	−	0.969403i	$-0.578944\pi$
$701$	−12.9986	−0.490950	−0.245475	+	0.969403i	$0.578944\pi$
$702$	1.00000	0.0377426
$703$	10.2478	0.386504
$704$	5.25858	0.198190
$705$	−11.0024	−0.414376
$706$	−25.7030	−0.967344
$707$	0	0
$708$	1.90883	0.0717384
$709$	−37.1873	−1.39660	−0.698298	−	0.715807i	$-0.746059\pi$
$709$	−37.1873	−1.39660	−0.698298	+	0.715807i	$0.746059\pi$
$710$	−7.16424	−0.268869
$711$	5.74802	0.215568
$712$	−10.7598	−0.403241
$713$	1.24122	0.0464841
$714$	0	0
$715$	7.09777	0.265442
$716$	−0.274526	−0.0102595
$717$	13.0617	0.487799
$718$	−23.4211	−0.874068
$719$	6.51268	0.242882	0.121441	−	0.992599i	$-0.461248\pi$
$719$	6.51268	0.242882	0.121441	+	0.992599i	$0.461248\pi$
$720$	1.34975	0.0503022
$721$	0	0
$722$	−17.1782	−0.639306
$723$	6.04509	0.224819
$724$	12.7750	0.474780
$725$	−0.494620	−0.0183697
$726$	16.6527	0.618040
$727$	25.7968	0.956752	0.478376	−	0.878155i	$-0.341226\pi$
$727$	25.7968	0.956752	0.478376	+	0.878155i	$0.341226\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−7.22082	−0.267255
$731$	10.3213	0.381747
$732$	−2.26934	−0.0838773
$733$	−46.2888	−1.70971	−0.854857	−	0.518863i	$-0.826355\pi$
$733$	−46.2888	−1.70971	−0.854857	+	0.518863i	$0.826355\pi$
$734$	−18.7442	−0.691860
$735$	0	0
$736$	0.650251	0.0239686
$737$	9.91920	0.365378
$738$	3.32305	0.122323
$739$	−1.87210	−0.0688663	−0.0344331	−	0.999407i	$-0.510963\pi$
$739$	−1.87210	−0.0688663	−0.0344331	+	0.999407i	$0.510963\pi$
$740$	10.2478	0.376718
$741$	1.34975	0.0495843
$742$	0	0
$743$	11.0211	0.404326	0.202163	−	0.979352i	$-0.435203\pi$
$743$	11.0211	0.404326	0.202163	+	0.979352i	$0.435203\pi$
$744$	1.90883	0.0699812
$745$	12.8313	0.470101
$746$	−19.9005	−0.728610
$747$	2.95736	0.108204
$748$	−17.1355	−0.626537
$749$	0	0
$750$	−11.0385	−0.403069
$751$	27.2892	0.995795	0.497898	−	0.867236i	$-0.334106\pi$
$751$	27.2892	0.995795	0.497898	+	0.867236i	$0.334106\pi$
$752$	−8.15147	−0.297254
$753$	10.7331	0.391136
$754$	0.155630	0.00566772
$755$	17.7217	0.644960
$756$	0	0
$757$	−13.9754	−0.507946	−0.253973	−	0.967211i	$-0.581737\pi$
$757$	−13.9754	−0.507946	−0.253973	+	0.967211i	$0.581737\pi$
$758$	−24.6760	−0.896272
$759$	3.41940	0.124116
$760$	1.82182	0.0660845
$761$	−6.01424	−0.218016	−0.109008	−	0.994041i	$-0.534767\pi$
$761$	−6.01424	−0.218016	−0.109008	+	0.994041i	$0.534767\pi$
$762$	−2.03776	−0.0738203
$763$	0	0
$764$	−19.1487	−0.692777
$765$	−4.39827	−0.159020
$766$	21.2115	0.766402
$767$	1.90883	0.0689240
$768$	1.00000	0.0360844
$769$	−9.25125	−0.333609	−0.166804	−	0.985990i	$-0.553345\pi$
$769$	−9.25125	−0.333609	−0.166804	+	0.985990i	$0.553345\pi$
$770$	0	0
$771$	−1.13969	−0.0410448
$772$	9.49016	0.341558
$773$	22.2218	0.799263	0.399632	−	0.916676i	$-0.369138\pi$
$773$	22.2218	0.799263	0.399632	+	0.916676i	$0.369138\pi$
$774$	−3.16742	−0.113850
$775$	−6.06661	−0.217919
$776$	11.3456	0.407283
$777$	0	0
$778$	−33.2073	−1.19054
$779$	4.48528	0.160702
$780$	1.34975	0.0483288
$781$	−27.9117	−0.998758
$782$	−2.11890	−0.0757716
$783$	0.155630	0.00556177
$784$	0	0
$785$	−3.13513	−0.111897
$786$	−15.5615	−0.555061
$787$	−29.5786	−1.05436	−0.527182	−	0.849752i	$-0.676751\pi$
$787$	−29.5786	−1.05436	−0.527182	+	0.849752i	$0.676751\pi$
$788$	1.33826	0.0476737
$789$	25.2922	0.900426
$790$	7.75839	0.276031
$791$	0	0
$792$	5.25858	0.186856
$793$	−2.26934	−0.0805867
$794$	−21.3907	−0.759127
$795$	6.06661	0.215161
$796$	−21.0988	−0.747827
$797$	5.40203	0.191350	0.0956749	−	0.995413i	$-0.469499\pi$
$797$	5.40203	0.191350	0.0956749	+	0.995413i	$0.469499\pi$
$798$	0	0
$799$	26.5623	0.939705
$800$	−3.17818	−0.112366
$801$	−10.7598	−0.380179
$802$	−21.4745	−0.758292
$803$	−28.1321	−0.992760
$804$	1.88629	0.0665242
$805$	0	0
$806$	1.90883	0.0672358
$807$	4.66174	0.164101
$808$	−1.77991	−0.0626169
$809$	−44.1176	−1.55109	−0.775546	−	0.631291i	$-0.782525\pi$
$809$	−44.1176	−1.55109	−0.775546	+	0.631291i	$0.782525\pi$
$810$	1.34975	0.0474254
$811$	2.21006	0.0776058	0.0388029	−	0.999247i	$-0.487646\pi$
$811$	2.21006	0.0776058	0.0388029	+	0.999247i	$0.487646\pi$
$812$	0	0
$813$	−6.70538	−0.235168
$814$	39.9252	1.39938
$815$	29.1486	1.02103
$816$	−3.25858	−0.114073
$817$	−4.27522	−0.149571
$818$	4.18854	0.146449
$819$	0	0
$820$	4.48528	0.156633
$821$	−27.5113	−0.960151	−0.480076	−	0.877227i	$-0.659391\pi$
$821$	−27.5113	−0.960151	−0.480076	+	0.877227i	$0.659391\pi$
$822$	2.58060	0.0900089
$823$	16.0711	0.560203	0.280102	−	0.959970i	$-0.409632\pi$
$823$	16.0711	0.560203	0.280102	+	0.959970i	$0.409632\pi$
$824$	−17.9487	−0.625274
$825$	−16.7127	−0.581862
$826$	0	0
$827$	−53.9526	−1.87612	−0.938058	−	0.346478i	$-0.887377\pi$
$827$	−53.9526	−1.87612	−0.938058	+	0.346478i	$0.887377\pi$
$828$	0.650251	0.0225978
$829$	−24.6125	−0.854827	−0.427414	−	0.904056i	$-0.640575\pi$
$829$	−24.6125	−0.854827	−0.427414	+	0.904056i	$0.640575\pi$
$830$	3.99169	0.138554
$831$	−29.1068	−1.00970
$832$	1.00000	0.0346688
$833$	0	0
$834$	−18.2059	−0.630419
$835$	34.1920	1.18326
$836$	7.09777	0.245481
$837$	1.90883	0.0659790
$838$	−8.88501	−0.306927
$839$	24.6672	0.851606	0.425803	−	0.904816i	$-0.359992\pi$
$839$	24.6672	0.851606	0.425803	+	0.904816i	$0.359992\pi$
$840$	0	0
$841$	−28.9758	−0.999165
$842$	9.59411	0.330635
$843$	0.356353	0.0122735
$844$	7.16742	0.246713
$845$	1.34975	0.0464328
$846$	−8.15147	−0.280253
$847$	0	0
$848$	4.49462	0.154346
$849$	−21.8392	−0.749519
$850$	10.3564	0.355220
$851$	4.93696	0.169237
$852$	−5.30783	−0.181843
$853$	−22.0347	−0.754455	−0.377227	−	0.926121i	$-0.623122\pi$
$853$	−22.0347	−0.754455	−0.377227	+	0.926121i	$0.623122\pi$
$854$	0	0
$855$	1.82182	0.0623050
$856$	−11.4593	−0.391671
$857$	57.3284	1.95830	0.979150	−	0.203139i	$-0.0651144\pi$
$857$	57.3284	1.95830	0.979150	+	0.203139i	$0.0651144\pi$
$858$	5.25858	0.179525
$859$	8.34804	0.284832	0.142416	−	0.989807i	$-0.454513\pi$
$859$	8.34804	0.284832	0.142416	+	0.989807i	$0.454513\pi$
$860$	−4.27522	−0.145784
$861$	0	0
$862$	16.6897	0.568455
$863$	−8.06661	−0.274591	−0.137295	−	0.990530i	$-0.543841\pi$
$863$	−8.06661	−0.274591	−0.137295	+	0.990530i	$0.543841\pi$
$864$	1.00000	0.0340207
$865$	−2.43147	−0.0826725
$866$	12.8613	0.437046
$867$	−6.38163	−0.216732
$868$	0	0
$869$	30.2264	1.02536
$870$	0.210062	0.00712176
$871$	1.88629	0.0639144
$872$	−1.02182	−0.0346032
$873$	11.3456	0.383990
$874$	0.877675	0.0296878
$875$	0	0
$876$	−5.34975	−0.180751
$877$	26.4857	0.894359	0.447179	−	0.894444i	$-0.352429\pi$
$877$	26.4857	0.894359	0.447179	+	0.894444i	$0.352429\pi$
$878$	−2.23359	−0.0753800
$879$	9.18478	0.309795
$880$	7.09777	0.239266
$881$	−9.38606	−0.316224	−0.158112	−	0.987421i	$-0.550541\pi$
$881$	−9.38606	−0.316224	−0.158112	+	0.987421i	$0.550541\pi$
$882$	0	0
$883$	0.824271	0.0277389	0.0138695	−	0.999904i	$-0.495585\pi$
$883$	0.824271	0.0277389	0.0138695	+	0.999904i	$0.495585\pi$
$884$	−3.25858	−0.109598
$885$	2.57645	0.0866063
$886$	26.5093	0.890597
$887$	19.4079	0.651654	0.325827	−	0.945429i	$-0.394357\pi$
$887$	19.4079	0.651654	0.325827	+	0.945429i	$0.394357\pi$
$888$	7.59239	0.254784
$889$	0	0
$890$	−14.5230	−0.486814
$891$	5.25858	0.176169
$892$	12.6593	0.423865
$893$	−11.0024	−0.368183
$894$	9.50641	0.317942
$895$	−0.370541	−0.0123858
$896$	0	0
$897$	0.650251	0.0217112
$898$	−28.1306	−0.938732
$899$	0.297072	0.00990791
$900$	−3.17818	−0.105939
$901$	−14.6461	−0.487932
$902$	17.4745	0.581838
$903$	0	0
$904$	15.9539	0.530620
$905$	17.2431	0.573179
$906$	13.1297	0.436204
$907$	−13.9377	−0.462793	−0.231397	−	0.972860i	$-0.574329\pi$
$907$	−13.9377	−0.462793	−0.231397	+	0.972860i	$0.574329\pi$
$908$	9.77991	0.324558
$909$	−1.77991	−0.0590357
$910$	0	0
$911$	51.9821	1.72224	0.861121	−	0.508400i	$-0.169763\pi$
$911$	51.9821	1.72224	0.861121	+	0.508400i	$0.169763\pi$
$912$	1.34975	0.0446947
$913$	15.5515	0.514680
$914$	−15.0715	−0.498521
$915$	−3.06304	−0.101261
$916$	−27.0721	−0.894487
$917$	0	0
$918$	−3.25858	−0.107549
$919$	−22.0568	−0.727588	−0.363794	−	0.931479i	$-0.618519\pi$
$919$	−22.0568	−0.727588	−0.363794	+	0.931479i	$0.618519\pi$
$920$	0.877675	0.0289361
$921$	6.01321	0.198142
$922$	−10.4492	−0.344127
$923$	−5.30783	−0.174709
$924$	0	0
$925$	−24.1300	−0.793388
$926$	12.0115	0.394722
$927$	−17.9487	−0.589514
$928$	0.155630	0.00510881
$929$	44.7485	1.46815	0.734075	−	0.679069i	$-0.237616\pi$
$929$	44.7485	1.46815	0.734075	+	0.679069i	$0.237616\pi$
$930$	2.57645	0.0844850
$931$	0	0
$932$	−22.5838	−0.739756
$933$	13.8926	0.454823
$934$	21.6468	0.708306
$935$	−23.1287	−0.756389
$936$	1.00000	0.0326860
$937$	−9.50440	−0.310495	−0.155248	−	0.987876i	$-0.549618\pi$
$937$	−9.50440	−0.310495	−0.155248	+	0.987876i	$0.549618\pi$
$938$	0	0
$939$	−12.9206	−0.421649
$940$	−11.0024	−0.358860
$941$	26.2392	0.855373	0.427686	−	0.903927i	$-0.359329\pi$
$941$	26.2392	0.855373	0.427686	+	0.903927i	$0.359329\pi$
$942$	−2.32275	−0.0756792
$943$	2.16081	0.0703658
$944$	1.90883	0.0621273
$945$	0	0
$946$	−16.6561	−0.541537
$947$	−22.1757	−0.720615	−0.360307	−	0.932834i	$-0.617328\pi$
$947$	−22.1757	−0.720615	−0.360307	+	0.932834i	$0.617328\pi$
$948$	5.74802	0.186687
$949$	−5.34975	−0.173660
$950$	−4.28974	−0.139178
$951$	−28.4696	−0.923191
$952$	0	0
$953$	30.2045	0.978418	0.489209	−	0.872167i	$-0.337285\pi$
$953$	30.2045	0.978418	0.489209	+	0.872167i	$0.337285\pi$
$954$	4.49462	0.145519
$955$	−25.8460	−0.836357
$956$	13.0617	0.422447
$957$	0.818395	0.0264549
$958$	3.28211	0.106040
$959$	0	0
$960$	1.34975	0.0435630
$961$	−27.3564	−0.882463
$962$	7.59239	0.244788
$963$	−11.4593	−0.369271
$964$	6.04509	0.194699
$965$	12.8093	0.412347
$966$	0	0
$967$	60.7193	1.95260	0.976301	−	0.216418i	$-0.0694372\pi$
$967$	60.7193	1.95260	0.976301	+	0.216418i	$0.0694372\pi$
$968$	16.6527	0.535238
$969$	−4.39827	−0.141293
$970$	15.3137	0.491694
$971$	35.5279	1.14015	0.570073	−	0.821594i	$-0.306915\pi$
$971$	35.5279	1.14015	0.570073	+	0.821594i	$0.306915\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	25.3907	0.813570
$975$	−3.17818	−0.101783
$976$	−2.26934	−0.0726399
$977$	−6.06344	−0.193987	−0.0969933	−	0.995285i	$-0.530923\pi$
$977$	−6.06344	−0.193987	−0.0969933	+	0.995285i	$0.530923\pi$
$978$	21.5956	0.690550
$979$	−56.5813	−1.80835
$980$	0	0
$981$	−1.02182	−0.0326242
$982$	−16.6368	−0.530900
$983$	6.78021	0.216255	0.108128	−	0.994137i	$-0.465515\pi$
$983$	6.78021	0.216255	0.108128	+	0.994137i	$0.465515\pi$
$984$	3.32305	0.105935
$985$	1.80632	0.0575541
$986$	−0.507134	−0.0161504
$987$	0	0
$988$	1.34975	0.0429412
$989$	−2.05961	−0.0654919
$990$	7.09777	0.225582
$991$	−23.1225	−0.734509	−0.367255	−	0.930120i	$-0.619702\pi$
$991$	−23.1225	−0.734509	−0.367255	+	0.930120i	$0.619702\pi$
$992$	1.90883	0.0606055
$993$	−18.7383	−0.594642
$994$	0	0
$995$	−28.4781	−0.902816
$996$	2.95736	0.0937074
$997$	22.3460	0.707704	0.353852	−	0.935301i	$-0.384872\pi$
$997$	22.3460	0.707704	0.353852	+	0.935301i	$0.384872\pi$
$998$	−15.0495	−0.476385
$999$	7.59239	0.240213

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.34975 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.34975 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.34975 q^{10} +5.25858 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.34975 q^{15} +1.00000 q^{16} -3.25858 q^{17} +1.00000 q^{18} +1.34975 q^{19} +1.34975 q^{20} +5.25858 q^{22} +0.650251 q^{23} +1.00000 q^{24} -3.17818 q^{25} +1.00000 q^{26} +1.00000 q^{27} +0.155630 q^{29} +1.34975 q^{30} +1.90883 q^{31} +1.00000 q^{32} +5.25858 q^{33} -3.25858 q^{34} +1.00000 q^{36} +7.59239 q^{37} +1.34975 q^{38} +1.00000 q^{39} +1.34975 q^{40} +3.32305 q^{41} -3.16742 q^{43} +5.25858 q^{44} +1.34975 q^{45} +0.650251 q^{46} -8.15147 q^{47} +1.00000 q^{48} -3.17818 q^{50} -3.25858 q^{51} +1.00000 q^{52} +4.49462 q^{53} +1.00000 q^{54} +7.09777 q^{55} +1.34975 q^{57} +0.155630 q^{58} +1.90883 q^{59} +1.34975 q^{60} -2.26934 q^{61} +1.90883 q^{62} +1.00000 q^{64} +1.34975 q^{65} +5.25858 q^{66} +1.88629 q^{67} -3.25858 q^{68} +0.650251 q^{69} -5.30783 q^{71} +1.00000 q^{72} -5.34975 q^{73} +7.59239 q^{74} -3.17818 q^{75} +1.34975 q^{76} +1.00000 q^{78} +5.74802 q^{79} +1.34975 q^{80} +1.00000 q^{81} +3.32305 q^{82} +2.95736 q^{83} -4.39827 q^{85} -3.16742 q^{86} +0.155630 q^{87} +5.25858 q^{88} -10.7598 q^{89} +1.34975 q^{90} +0.650251 q^{92} +1.90883 q^{93} -8.15147 q^{94} +1.82182 q^{95} +1.00000 q^{96} +11.3456 q^{97} +5.25858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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

Introduction

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