LMFDB - Embedded newform 1911.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1911,2,Mod(1,1911)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1911, 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("1911.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1911 = 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1911.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:	$15.2594118263$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.470683$ of defining polynomial
Character	$\chi$	$=$	1911.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.529317 q^{2} +1.00000 q^{3} -1.71982 q^{4} -1.77846 q^{5} -0.529317 q^{6} +1.96896 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.529317 q^{2} +1.00000 q^{3} -1.71982 q^{4} -1.77846 q^{5} -0.529317 q^{6} +1.96896 q^{8} +1.00000 q^{9} +0.941367 q^{10} -6.49828 q^{11} -1.71982 q^{12} +1.00000 q^{13} -1.77846 q^{15} +2.39744 q^{16} +2.94137 q^{17} -0.529317 q^{18} +4.83709 q^{19} +3.05863 q^{20} +3.43965 q^{22} -5.77846 q^{23} +1.96896 q^{24} -1.83709 q^{25} -0.529317 q^{26} +1.00000 q^{27} -2.83709 q^{29} +0.941367 q^{30} -6.27674 q^{31} -5.20693 q^{32} -6.49828 q^{33} -1.55691 q^{34} -1.71982 q^{36} +9.55691 q^{37} -2.56035 q^{38} +1.00000 q^{39} -3.50172 q^{40} +3.05863 q^{41} +2.71982 q^{43} +11.1759 q^{44} -1.77846 q^{45} +3.05863 q^{46} +8.71982 q^{47} +2.39744 q^{48} +0.972402 q^{50} +2.94137 q^{51} -1.71982 q^{52} +6.39400 q^{53} -0.529317 q^{54} +11.5569 q^{55} +4.83709 q^{57} +1.50172 q^{58} -1.55691 q^{59} +3.05863 q^{60} -3.88273 q^{61} +3.32238 q^{62} -2.03877 q^{64} -1.77846 q^{65} +3.43965 q^{66} +5.67418 q^{67} -5.05863 q^{68} -5.77846 q^{69} +10.0552 q^{71} +1.96896 q^{72} +15.8337 q^{73} -5.05863 q^{74} -1.83709 q^{75} -8.31894 q^{76} -0.529317 q^{78} -1.28018 q^{79} -4.26375 q^{80} +1.00000 q^{81} -1.61899 q^{82} +2.83709 q^{83} -5.23109 q^{85} -1.43965 q^{86} -2.83709 q^{87} -12.7949 q^{88} +7.66119 q^{89} +0.941367 q^{90} +9.93793 q^{92} -6.27674 q^{93} -4.61555 q^{94} -8.60256 q^{95} -5.20693 q^{96} +17.7164 q^{97} -6.49828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{5} - 2 q^{6} - 12 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^5 - 2 * q^6 - 12 * q^8 + 3 * q^9	$ 3 q - 2 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{5} - 2 q^{6} - 12 q^{8} + 3 q^{9} + 2 q^{10} - 2 q^{11} + 4 q^{12} + 3 q^{13} + 3 q^{15} + 18 q^{16} + 8 q^{17} - 2 q^{18} + 7 q^{19} + 10 q^{20} - 8 q^{22} - 9 q^{23} - 12 q^{24} + 2 q^{25} - 2 q^{26} + 3 q^{27} - q^{29} + 2 q^{30} + 7 q^{31} - 36 q^{32} - 2 q^{33} + 12 q^{34} + 4 q^{36} + 12 q^{37} - 26 q^{38} + 3 q^{39} - 28 q^{40} + 10 q^{41} - q^{43} + 36 q^{44} + 3 q^{45} + 10 q^{46} + 17 q^{47} + 18 q^{48} + 20 q^{50} + 8 q^{51} + 4 q^{52} - 5 q^{53} - 2 q^{54} + 18 q^{55} + 7 q^{57} + 22 q^{58} + 12 q^{59} + 10 q^{60} - 10 q^{61} - 10 q^{62} + 58 q^{64} + 3 q^{65} - 8 q^{66} + 2 q^{67} - 16 q^{68} - 9 q^{69} - 4 q^{71} - 12 q^{72} + 5 q^{73} - 16 q^{74} + 2 q^{75} + 30 q^{76} - 2 q^{78} - 13 q^{79} + 8 q^{80} + 3 q^{81} - 24 q^{82} + q^{83} + 16 q^{85} + 14 q^{86} - q^{87} - 60 q^{88} + 13 q^{89} + 2 q^{90} - 6 q^{92} + 7 q^{93} + 2 q^{94} - 15 q^{95} - 36 q^{96} + 9 q^{97} - 2 q^{99}+O(q^{100}) $ 3 * q - 2 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^5 - 2 * q^6 - 12 * q^8 + 3 * q^9 + 2 * q^10 - 2 * q^11 + 4 * q^12 + 3 * q^13 + 3 * q^15 + 18 * q^16 + 8 * q^17 - 2 * q^18 + 7 * q^19 + 10 * q^20 - 8 * q^22 - 9 * q^23 - 12 * q^24 + 2 * q^25 - 2 * q^26 + 3 * q^27 - q^29 + 2 * q^30 + 7 * q^31 - 36 * q^32 - 2 * q^33 + 12 * q^34 + 4 * q^36 + 12 * q^37 - 26 * q^38 + 3 * q^39 - 28 * q^40 + 10 * q^41 - q^43 + 36 * q^44 + 3 * q^45 + 10 * q^46 + 17 * q^47 + 18 * q^48 + 20 * q^50 + 8 * q^51 + 4 * q^52 - 5 * q^53 - 2 * q^54 + 18 * q^55 + 7 * q^57 + 22 * q^58 + 12 * q^59 + 10 * q^60 - 10 * q^61 - 10 * q^62 + 58 * q^64 + 3 * q^65 - 8 * q^66 + 2 * q^67 - 16 * q^68 - 9 * q^69 - 4 * q^71 - 12 * q^72 + 5 * q^73 - 16 * q^74 + 2 * q^75 + 30 * q^76 - 2 * q^78 - 13 * q^79 + 8 * q^80 + 3 * q^81 - 24 * q^82 + q^83 + 16 * q^85 + 14 * q^86 - q^87 - 60 * q^88 + 13 * q^89 + 2 * q^90 - 6 * q^92 + 7 * q^93 + 2 * q^94 - 15 * q^95 - 36 * q^96 + 9 * q^97 - 2 * 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 $

$2$	−0.529317	−0.374283	−0.187142	−	0.982333i	$-0.559922\pi$
$2$	−0.529317	−0.374283	−0.187142	+	0.982333i	$0.559922\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.71982	−0.859912
$5$	−1.77846	−0.795350	−0.397675	−	0.917526i	$-0.630183\pi$
$5$	−1.77846	−0.795350	−0.397675	+	0.917526i	$0.630183\pi$
$6$	−0.529317	−0.216093
$7$	0	0
$7$	0	0
$8$	1.96896	0.696134
$9$	1.00000	0.333333
$10$	0.941367	0.297686
$11$	−6.49828	−1.95931	−0.979653	−	0.200700i	$-0.935678\pi$
$11$	−6.49828	−1.95931	−0.979653	+	0.200700i	$0.935678\pi$
$12$	−1.71982	−0.496470
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−1.77846	−0.459196
$16$	2.39744	0.599361
$17$	2.94137	0.713386	0.356693	−	0.934222i	$-0.383904\pi$
$17$	2.94137	0.713386	0.356693	+	0.934222i	$0.383904\pi$
$18$	−0.529317	−0.124761
$19$	4.83709	1.10970	0.554852	−	0.831949i	$-0.312775\pi$
$19$	4.83709	1.10970	0.554852	+	0.831949i	$0.312775\pi$
$20$	3.05863	0.683931
$21$	0	0
$22$	3.43965	0.733335
$23$	−5.77846	−1.20489	−0.602446	−	0.798160i	$-0.705807\pi$
$23$	−5.77846	−1.20489	−0.602446	+	0.798160i	$0.705807\pi$
$24$	1.96896	0.401913
$25$	−1.83709	−0.367418
$26$	−0.529317	−0.103808
$27$	1.00000	0.192450
$28$	0	0
$29$	−2.83709	−0.526834	−0.263417	−	0.964682i	$-0.584850\pi$
$29$	−2.83709	−0.526834	−0.263417	+	0.964682i	$0.584850\pi$
$30$	0.941367	0.171869
$31$	−6.27674	−1.12734	−0.563668	−	0.826002i	$-0.690610\pi$
$31$	−6.27674	−1.12734	−0.563668	+	0.826002i	$0.690610\pi$
$32$	−5.20693	−0.920465
$33$	−6.49828	−1.13121
$34$	−1.55691	−0.267009
$35$	0	0
$36$	−1.71982	−0.286637
$37$	9.55691	1.57115	0.785574	−	0.618768i	$-0.212368\pi$
$37$	9.55691	1.57115	0.785574	+	0.618768i	$0.212368\pi$
$38$	−2.56035	−0.415344
$39$	1.00000	0.160128
$40$	−3.50172	−0.553670
$41$	3.05863	0.477678	0.238839	−	0.971059i	$-0.423233\pi$
$41$	3.05863	0.477678	0.238839	+	0.971059i	$0.423233\pi$
$42$	0	0
$43$	2.71982	0.414769	0.207385	−	0.978259i	$-0.433505\pi$
$43$	2.71982	0.414769	0.207385	+	0.978259i	$0.433505\pi$
$44$	11.1759	1.68483
$45$	−1.77846	−0.265117
$46$	3.05863	0.450971
$47$	8.71982	1.27192	0.635959	−	0.771723i	$-0.280605\pi$
$47$	8.71982	1.27192	0.635959	+	0.771723i	$0.280605\pi$
$48$	2.39744	0.346041
$49$	0	0
$50$	0.972402	0.137518
$51$	2.94137	0.411874
$52$	−1.71982	−0.238497
$53$	6.39400	0.878284	0.439142	−	0.898418i	$-0.355282\pi$
$53$	6.39400	0.878284	0.439142	+	0.898418i	$0.355282\pi$
$54$	−0.529317	−0.0720309
$55$	11.5569	1.55833
$56$	0	0
$57$	4.83709	0.640688
$58$	1.50172	0.197185
$59$	−1.55691	−0.202693	−0.101346	−	0.994851i	$-0.532315\pi$
$59$	−1.55691	−0.202693	−0.101346	+	0.994851i	$0.532315\pi$
$60$	3.05863	0.394868
$61$	−3.88273	−0.497133	−0.248567	−	0.968615i	$-0.579959\pi$
$61$	−3.88273	−0.497133	−0.248567	+	0.968615i	$0.579959\pi$
$62$	3.32238	0.421943
$63$	0	0
$64$	−2.03877	−0.254846
$65$	−1.77846	−0.220590
$66$	3.43965	0.423391
$67$	5.67418	0.693211	0.346606	−	0.938011i	$-0.387334\pi$
$67$	5.67418	0.693211	0.346606	+	0.938011i	$0.387334\pi$
$68$	−5.05863	−0.613449
$69$	−5.77846	−0.695644
$70$	0	0
$71$	10.0552	1.19333	0.596666	−	0.802490i	$-0.296492\pi$
$71$	10.0552	1.19333	0.596666	+	0.802490i	$0.296492\pi$
$72$	1.96896	0.232045
$73$	15.8337	1.85319	0.926594	−	0.376062i	$-0.122722\pi$
$73$	15.8337	1.85319	0.926594	+	0.376062i	$0.122722\pi$
$74$	−5.05863	−0.588054
$75$	−1.83709	−0.212129
$76$	−8.31894	−0.954248
$77$	0	0
$78$	−0.529317	−0.0599333
$79$	−1.28018	−0.144031	−0.0720155	−	0.997404i	$-0.522943\pi$
$79$	−1.28018	−0.144031	−0.0720155	+	0.997404i	$0.522943\pi$
$80$	−4.26375	−0.476702
$81$	1.00000	0.111111
$82$	−1.61899	−0.178787
$83$	2.83709	0.311411	0.155706	−	0.987804i	$-0.450235\pi$
$83$	2.83709	0.311411	0.155706	+	0.987804i	$0.450235\pi$
$84$	0	0
$85$	−5.23109	−0.567392
$86$	−1.43965	−0.155241
$87$	−2.83709	−0.304168
$88$	−12.7949	−1.36394
$89$	7.66119	0.812085	0.406042	−	0.913854i	$-0.366909\pi$
$89$	7.66119	0.812085	0.406042	+	0.913854i	$0.366909\pi$
$90$	0.941367	0.0992288
$91$	0	0
$92$	9.93793	1.03610
$93$	−6.27674	−0.650867
$94$	−4.61555	−0.476057
$95$	−8.60256	−0.882604
$96$	−5.20693	−0.531431
$97$	17.7164	1.79883	0.899413	−	0.437099i	$-0.143994\pi$
$97$	17.7164	1.79883	0.899413	+	0.437099i	$0.143994\pi$
$98$	0	0
$99$	−6.49828	−0.653102
$100$	3.15947	0.315947
$101$	−6.73281	−0.669940	−0.334970	−	0.942229i	$-0.608726\pi$
$101$	−6.73281	−0.669940	−0.334970	+	0.942229i	$0.608726\pi$
$102$	−1.55691	−0.154157
$103$	−10.8793	−1.07197	−0.535984	−	0.844228i	$-0.680059\pi$
$103$	−10.8793	−1.07197	−0.535984	+	0.844228i	$0.680059\pi$
$104$	1.96896	0.193073
$105$	0	0
$106$	−3.38445	−0.328727
$107$	−8.49828	−0.821560	−0.410780	−	0.911735i	$-0.634744\pi$
$107$	−8.49828	−0.821560	−0.410780	+	0.911735i	$0.634744\pi$
$108$	−1.71982	−0.165490
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	−6.11727	−0.583258
$111$	9.55691	0.907102
$112$	0	0
$113$	14.6026	1.37369	0.686847	−	0.726802i	$-0.258994\pi$
$113$	14.6026	1.37369	0.686847	+	0.726802i	$0.258994\pi$
$114$	−2.56035	−0.239799
$115$	10.2767	0.958311
$116$	4.87930	0.453031
$117$	1.00000	0.0924500
$118$	0.824101	0.0758646
$119$	0	0
$120$	−3.50172	−0.319662
$121$	31.2277	2.83888
$122$	2.05520	0.186069
$123$	3.05863	0.275788
$124$	10.7949	0.969409
$125$	12.1595	1.08758
$126$	0	0
$127$	−9.88273	−0.876951	−0.438475	−	0.898743i	$-0.644481\pi$
$127$	−9.88273	−0.876951	−0.438475	+	0.898743i	$0.644481\pi$
$128$	11.4930	1.01585
$129$	2.71982	0.239467
$130$	0.941367	0.0825633
$131$	−3.76547	−0.328990	−0.164495	−	0.986378i	$-0.552600\pi$
$131$	−3.76547	−0.328990	−0.164495	+	0.986378i	$0.552600\pi$
$132$	11.1759	0.972737
$133$	0	0
$134$	−3.00344	−0.259458
$135$	−1.77846	−0.153065
$136$	5.79145	0.496612
$137$	−16.9966	−1.45211	−0.726057	−	0.687634i	$-0.758649\pi$
$137$	−16.9966	−1.45211	−0.726057	+	0.687634i	$0.758649\pi$
$138$	3.05863	0.260368
$139$	8.55348	0.725496	0.362748	−	0.931887i	$-0.381839\pi$
$139$	8.55348	0.725496	0.362748	+	0.931887i	$0.381839\pi$
$140$	0	0
$141$	8.71982	0.734342
$142$	−5.32238	−0.446644
$143$	−6.49828	−0.543414
$144$	2.39744	0.199787
$145$	5.04564	0.419018
$146$	−8.38101	−0.693618
$147$	0	0
$148$	−16.4362	−1.35105
$149$	−15.5569	−1.27447	−0.637236	−	0.770669i	$-0.719922\pi$
$149$	−15.5569	−1.27447	−0.637236	+	0.770669i	$0.719922\pi$
$150$	0.972402	0.0793963
$151$	4.99656	0.406614	0.203307	−	0.979115i	$-0.434831\pi$
$151$	4.99656	0.406614	0.203307	+	0.979115i	$0.434831\pi$
$152$	9.52406	0.772503
$153$	2.94137	0.237795
$154$	0	0
$155$	11.1629	0.896626
$156$	−1.71982	−0.137696
$157$	18.7880	1.49945	0.749723	−	0.661752i	$-0.230187\pi$
$157$	18.7880	1.49945	0.749723	+	0.661752i	$0.230187\pi$
$158$	0.677618	0.0539084
$159$	6.39400	0.507078
$160$	9.26031	0.732092
$161$	0	0
$162$	−0.529317	−0.0415870
$163$	−9.88273	−0.774075	−0.387038	−	0.922064i	$-0.626502\pi$
$163$	−9.88273	−0.774075	−0.387038	+	0.922064i	$0.626502\pi$
$164$	−5.26031	−0.410761
$165$	11.5569	0.899705
$166$	−1.50172	−0.116556
$167$	7.04564	0.545208	0.272604	−	0.962126i	$-0.412115\pi$
$167$	7.04564	0.545208	0.272604	+	0.962126i	$0.412115\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	2.76891	0.212365
$171$	4.83709	0.369902
$172$	−4.67762	−0.356665
$173$	14.2897	1.08643	0.543214	−	0.839594i	$-0.317207\pi$
$173$	14.2897	1.08643	0.543214	+	0.839594i	$0.317207\pi$
$174$	1.50172	0.113845
$175$	0	0
$176$	−15.5793	−1.17433
$177$	−1.55691	−0.117025
$178$	−4.05520	−0.303950
$179$	−8.65775	−0.647111	−0.323555	−	0.946209i	$-0.604878\pi$
$179$	−8.65775	−0.647111	−0.323555	+	0.946209i	$0.604878\pi$
$180$	3.05863	0.227977
$181$	−26.3449	−1.95820	−0.979101	−	0.203373i	$-0.934810\pi$
$181$	−26.3449	−1.95820	−0.979101	+	0.203373i	$0.934810\pi$
$182$	0	0
$183$	−3.88273	−0.287020
$184$	−11.3776	−0.838766
$185$	−16.9966	−1.24961
$186$	3.32238	0.243609
$187$	−19.1138	−1.39774
$188$	−14.9966	−1.09374
$189$	0	0
$190$	4.55348	0.330344
$191$	6.61555	0.478684	0.239342	−	0.970935i	$-0.423068\pi$
$191$	6.61555	0.478684	0.239342	+	0.970935i	$0.423068\pi$
$192$	−2.03877	−0.147135
$193$	11.8827	0.855338	0.427669	−	0.903935i	$-0.359335\pi$
$193$	11.8827	0.855338	0.427669	+	0.903935i	$0.359335\pi$
$194$	−9.37758	−0.673271
$195$	−1.77846	−0.127358
$196$	0	0
$197$	11.5569	0.823396	0.411698	−	0.911320i	$-0.364936\pi$
$197$	11.5569	0.823396	0.411698	+	0.911320i	$0.364936\pi$
$198$	3.43965	0.244445
$199$	−0.996562	−0.0706444	−0.0353222	−	0.999376i	$-0.511246\pi$
$199$	−0.996562	−0.0706444	−0.0353222	+	0.999376i	$0.511246\pi$
$200$	−3.61717	−0.255772
$201$	5.67418	0.400226
$202$	3.56379	0.250747
$203$	0	0
$204$	−5.05863	−0.354175
$205$	−5.43965	−0.379921
$206$	5.75859	0.401220
$207$	−5.77846	−0.401631
$208$	2.39744	0.166233
$209$	−31.4328	−2.17425
$210$	0	0
$211$	26.8302	1.84707	0.923534	−	0.383516i	$-0.125287\pi$
$211$	26.8302	1.84707	0.923534	+	0.383516i	$0.125287\pi$
$212$	−10.9966	−0.755247
$213$	10.0552	0.688971
$214$	4.49828	0.307496
$215$	−4.83709	−0.329887
$216$	1.96896	0.133971
$217$	0	0
$218$	−5.29317	−0.358498
$219$	15.8337	1.06994
$220$	−19.8759	−1.34003
$221$	2.94137	0.197858
$222$	−5.05863	−0.339513
$223$	2.92838	0.196099	0.0980493	−	0.995182i	$-0.468740\pi$
$223$	2.92838	0.196099	0.0980493	+	0.995182i	$0.468740\pi$
$224$	0	0
$225$	−1.83709	−0.122473
$226$	−7.72938	−0.514150
$227$	9.79145	0.649881	0.324941	−	0.945734i	$-0.394656\pi$
$227$	9.79145	0.649881	0.324941	+	0.945734i	$0.394656\pi$
$228$	−8.31894	−0.550936
$229$	−3.88273	−0.256578	−0.128289	−	0.991737i	$-0.540949\pi$
$229$	−3.88273	−0.256578	−0.128289	+	0.991737i	$0.540949\pi$
$230$	−5.43965	−0.358680
$231$	0	0
$232$	−5.58613	−0.366747
$233$	−15.8337	−1.03730	−0.518649	−	0.854988i	$-0.673565\pi$
$233$	−15.8337	−1.03730	−0.518649	+	0.854988i	$0.673565\pi$
$234$	−0.529317	−0.0346025
$235$	−15.5078	−1.01162
$236$	2.67762	0.174298
$237$	−1.28018	−0.0831564
$238$	0	0
$239$	−6.94137	−0.449000	−0.224500	−	0.974474i	$-0.572075\pi$
$239$	−6.94137	−0.449000	−0.224500	+	0.974474i	$0.572075\pi$
$240$	−4.26375	−0.275224
$241$	−7.28018	−0.468957	−0.234479	−	0.972121i	$-0.575338\pi$
$241$	−7.28018	−0.468957	−0.234479	+	0.972121i	$0.575338\pi$
$242$	−16.5293	−1.06254
$243$	1.00000	0.0641500
$244$	6.67762	0.427491
$245$	0	0
$246$	−1.61899	−0.103223
$247$	4.83709	0.307777
$248$	−12.3587	−0.784777
$249$	2.83709	0.179793
$250$	−6.43621	−0.407062
$251$	−23.3224	−1.47210	−0.736048	−	0.676930i	$-0.763310\pi$
$251$	−23.3224	−1.47210	−0.736048	+	0.676930i	$0.763310\pi$
$252$	0	0
$253$	37.5500	2.36075
$254$	5.23109	0.328228
$255$	−5.23109	−0.327584
$256$	−2.00591	−0.125370
$257$	−15.4948	−0.966542	−0.483271	−	0.875471i	$-0.660551\pi$
$257$	−15.4948	−0.966542	−0.483271	+	0.875471i	$0.660551\pi$
$258$	−1.43965	−0.0896286
$259$	0	0
$260$	3.05863	0.189688
$261$	−2.83709	−0.175611
$262$	1.99312	0.123136
$263$	3.42666	0.211297	0.105648	−	0.994404i	$-0.466308\pi$
$263$	3.42666	0.211297	0.105648	+	0.994404i	$0.466308\pi$
$264$	−12.7949	−0.787471
$265$	−11.3715	−0.698543
$266$	0	0
$267$	7.66119	0.468857
$268$	−9.75859	−0.596101
$269$	0.172462	0.0105152	0.00525759	−	0.999986i	$-0.498326\pi$
$269$	0.172462	0.0105152	0.00525759	+	0.999986i	$0.498326\pi$
$270$	0.941367	0.0572898
$271$	25.9931	1.57897	0.789485	−	0.613770i	$-0.210348\pi$
$271$	25.9931	1.57897	0.789485	+	0.613770i	$0.210348\pi$
$272$	7.05176	0.427576
$273$	0	0
$274$	8.99656	0.543502
$275$	11.9379	0.719884
$276$	9.93793	0.598193
$277$	3.72326	0.223709	0.111855	−	0.993725i	$-0.464321\pi$
$277$	3.72326	0.223709	0.111855	+	0.993725i	$0.464321\pi$
$278$	−4.52750	−0.271541
$279$	−6.27674	−0.375778
$280$	0	0
$281$	−21.5500	−1.28557	−0.642784	−	0.766048i	$-0.722221\pi$
$281$	−21.5500	−1.28557	−0.642784	+	0.766048i	$0.722221\pi$
$282$	−4.61555	−0.274852
$283$	31.8759	1.89482	0.947412	−	0.320018i	$-0.103689\pi$
$283$	31.8759	1.89482	0.947412	+	0.320018i	$0.103689\pi$
$284$	−17.2932	−1.02616
$285$	−8.60256	−0.509572
$286$	3.43965	0.203391
$287$	0	0
$288$	−5.20693	−0.306822
$289$	−8.34836	−0.491080
$290$	−2.67074	−0.156831
$291$	17.7164	1.03855
$292$	−27.2311	−1.59358
$293$	−3.42666	−0.200188	−0.100094	−	0.994978i	$-0.531914\pi$
$293$	−3.42666	−0.200188	−0.100094	+	0.994978i	$0.531914\pi$
$294$	0	0
$295$	2.76891	0.161212
$296$	18.8172	1.09373
$297$	−6.49828	−0.377069
$298$	8.23453	0.477014
$299$	−5.77846	−0.334177
$300$	3.15947	0.182412
$301$	0	0
$302$	−2.64476	−0.152189
$303$	−6.73281	−0.386790
$304$	11.5966	0.665113
$305$	6.90528	0.395395
$306$	−1.55691	−0.0890029
$307$	3.39744	0.193902	0.0969511	−	0.995289i	$-0.469091\pi$
$307$	3.39744	0.193902	0.0969511	+	0.995289i	$0.469091\pi$
$308$	0	0
$309$	−10.8793	−0.618902
$310$	−5.90871	−0.335592
$311$	0.443086	0.0251251	0.0125625	−	0.999921i	$-0.496001\pi$
$311$	0.443086	0.0251251	0.0125625	+	0.999921i	$0.496001\pi$
$312$	1.96896	0.111471
$313$	19.8827	1.12384	0.561919	−	0.827192i	$-0.310063\pi$
$313$	19.8827	1.12384	0.561919	+	0.827192i	$0.310063\pi$
$314$	−9.94480	−0.561218
$315$	0	0
$316$	2.20168	0.123854
$317$	9.46563	0.531643	0.265821	−	0.964022i	$-0.414357\pi$
$317$	9.46563	0.531643	0.265821	+	0.964022i	$0.414357\pi$
$318$	−3.38445	−0.189791
$319$	18.4362	1.03223
$320$	3.62586	0.202692
$321$	−8.49828	−0.474328
$322$	0	0
$323$	14.2277	0.791648
$324$	−1.71982	−0.0955458
$325$	−1.83709	−0.101903
$326$	5.23109	0.289724
$327$	10.0000	0.553001
$328$	6.02234	0.332528
$329$	0	0
$330$	−6.11727	−0.336744
$331$	−27.4328	−1.50784	−0.753921	−	0.656965i	$-0.771840\pi$
$331$	−27.4328	−1.50784	−0.753921	+	0.656965i	$0.771840\pi$
$332$	−4.87930	−0.267786
$333$	9.55691	0.523716
$334$	−3.72938	−0.204062
$335$	−10.0913	−0.551346
$336$	0	0
$337$	−20.2767	−1.10454	−0.552272	−	0.833664i	$-0.686239\pi$
$337$	−20.2767	−1.10454	−0.552272	+	0.833664i	$0.686239\pi$
$338$	−0.529317	−0.0287910
$339$	14.6026	0.793102
$340$	8.99656	0.487907
$341$	40.7880	2.20879
$342$	−2.56035	−0.138448
$343$	0	0
$344$	5.35524	0.288735
$345$	10.2767	0.553281
$346$	−7.56379	−0.406632
$347$	16.7328	0.898265	0.449132	−	0.893465i	$-0.351733\pi$
$347$	16.7328	0.898265	0.449132	+	0.893465i	$0.351733\pi$
$348$	4.87930	0.261558
$349$	−22.3940	−1.19872	−0.599362	−	0.800478i	$-0.704579\pi$
$349$	−22.3940	−1.19872	−0.599362	+	0.800478i	$0.704579\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	33.8361	1.80347
$353$	27.1690	1.44606	0.723031	−	0.690816i	$-0.242749\pi$
$353$	27.1690	1.44606	0.723031	+	0.690816i	$0.242749\pi$
$354$	0.824101	0.0438004
$355$	−17.8827	−0.949117
$356$	−13.1759	−0.698321
$357$	0	0
$358$	4.58269	0.242203
$359$	−29.0586	−1.53366	−0.766828	−	0.641853i	$-0.778166\pi$
$359$	−29.0586	−1.53366	−0.766828	+	0.641853i	$0.778166\pi$
$360$	−3.50172	−0.184557
$361$	4.39744	0.231444
$362$	13.9448	0.732923
$363$	31.2277	1.63903
$364$	0	0
$365$	−28.1595	−1.47393
$366$	2.05520	0.107427
$367$	4.44309	0.231927	0.115964	−	0.993253i	$-0.463004\pi$
$367$	4.44309	0.231927	0.115964	+	0.993253i	$0.463004\pi$
$368$	−13.8535	−0.722165
$369$	3.05863	0.159226
$370$	8.99656	0.467709
$371$	0	0
$372$	10.7949	0.559689
$373$	31.3415	1.62280	0.811400	−	0.584491i	$-0.198706\pi$
$373$	31.3415	1.62280	0.811400	+	0.584491i	$0.198706\pi$
$374$	10.1173	0.523151
$375$	12.1595	0.627912
$376$	17.1690	0.885425
$377$	−2.83709	−0.146118
$378$	0	0
$379$	−11.5569	−0.593639	−0.296819	−	0.954934i	$-0.595926\pi$
$379$	−11.5569	−0.593639	−0.296819	+	0.954934i	$0.595926\pi$
$380$	14.7949	0.758962
$381$	−9.88273	−0.506308
$382$	−3.50172	−0.179164
$383$	25.6673	1.31154	0.655769	−	0.754962i	$-0.272345\pi$
$383$	25.6673	1.31154	0.655769	+	0.754962i	$0.272345\pi$
$384$	11.4930	0.586501
$385$	0	0
$386$	−6.28973	−0.320139
$387$	2.71982	0.138256
$388$	−30.4691	−1.54683
$389$	−24.2277	−1.22839	−0.614195	−	0.789154i	$-0.710519\pi$
$389$	−24.2277	−1.22839	−0.614195	+	0.789154i	$0.710519\pi$
$390$	0.941367	0.0476680
$391$	−16.9966	−0.859553
$392$	0	0
$393$	−3.76547	−0.189943
$394$	−6.11727	−0.308183
$395$	2.27674	0.114555
$396$	11.1759	0.561610
$397$	14.3680	0.721111	0.360555	−	0.932738i	$-0.382587\pi$
$397$	14.3680	0.721111	0.360555	+	0.932738i	$0.382587\pi$
$398$	0.527497	0.0264410
$399$	0	0
$400$	−4.40432	−0.220216
$401$	−21.8827	−1.09277	−0.546386	−	0.837534i	$-0.683997\pi$
$401$	−21.8827	−1.09277	−0.546386	+	0.837534i	$0.683997\pi$
$402$	−3.00344	−0.149798
$403$	−6.27674	−0.312667
$404$	11.5793	0.576089
$405$	−1.77846	−0.0883722
$406$	0	0
$407$	−62.1035	−3.07836
$408$	5.79145	0.286719
$409$	−7.39057	−0.365440	−0.182720	−	0.983165i	$-0.558490\pi$
$409$	−7.39057	−0.365440	−0.182720	+	0.983165i	$0.558490\pi$
$410$	2.87930	0.142198
$411$	−16.9966	−0.838379
$412$	18.7105	0.921799
$413$	0	0
$414$	3.05863	0.150324
$415$	−5.04564	−0.247681
$416$	−5.20693	−0.255291
$417$	8.55348	0.418866
$418$	16.6379	0.813786
$419$	−33.7846	−1.65048	−0.825242	−	0.564779i	$-0.808961\pi$
$419$	−33.7846	−1.65048	−0.825242	+	0.564779i	$0.808961\pi$
$420$	0	0
$421$	−35.5500	−1.73260	−0.866301	−	0.499522i	$-0.833509\pi$
$421$	−35.5500	−1.73260	−0.866301	+	0.499522i	$0.833509\pi$
$422$	−14.2017	−0.691327
$423$	8.71982	0.423972
$424$	12.5896	0.611403
$425$	−5.40356	−0.262111
$426$	−5.32238	−0.257870
$427$	0	0
$428$	14.6155	0.706469
$429$	−6.49828	−0.313740
$430$	2.56035	0.123471
$431$	23.7294	1.14300	0.571502	−	0.820601i	$-0.306361\pi$
$431$	23.7294	1.14300	0.571502	+	0.820601i	$0.306361\pi$
$432$	2.39744	0.115347
$433$	5.55691	0.267048	0.133524	−	0.991046i	$-0.457371\pi$
$433$	5.55691	0.267048	0.133524	+	0.991046i	$0.457371\pi$
$434$	0	0
$435$	5.04564	0.241920
$436$	−17.1982	−0.823646
$437$	−27.9509	−1.33707
$438$	−8.38101	−0.400460
$439$	−5.32926	−0.254352	−0.127176	−	0.991880i	$-0.540591\pi$
$439$	−5.32926	−0.254352	−0.127176	+	0.991880i	$0.540591\pi$
$440$	22.7552	1.08481
$441$	0	0
$442$	−1.55691	−0.0740549
$443$	5.33537	0.253491	0.126746	−	0.991935i	$-0.459547\pi$
$443$	5.33537	0.253491	0.126746	+	0.991935i	$0.459547\pi$
$444$	−16.4362	−0.780028
$445$	−13.6251	−0.645892
$446$	−1.55004	−0.0733965
$447$	−15.5569	−0.735817
$448$	0	0
$449$	26.2277	1.23776	0.618880	−	0.785486i	$-0.287587\pi$
$449$	26.2277	1.23776	0.618880	+	0.785486i	$0.287587\pi$
$450$	0.972402	0.0458395
$451$	−19.8759	−0.935918
$452$	−25.1138	−1.18126
$453$	4.99656	0.234759
$454$	−5.18278	−0.243240
$455$	0	0
$456$	9.52406	0.446005
$457$	11.4396	0.535124	0.267562	−	0.963541i	$-0.413782\pi$
$457$	11.4396	0.535124	0.267562	+	0.963541i	$0.413782\pi$
$458$	2.05520	0.0960330
$459$	2.94137	0.137291
$460$	−17.6742	−0.824063
$461$	28.0552	1.30666	0.653330	−	0.757073i	$-0.273371\pi$
$461$	28.0552	1.30666	0.653330	+	0.757073i	$0.273371\pi$
$462$	0	0
$463$	−10.5604	−0.490781	−0.245391	−	0.969424i	$-0.578916\pi$
$463$	−10.5604	−0.490781	−0.245391	+	0.969424i	$0.578916\pi$
$464$	−6.80176	−0.315764
$465$	11.1629	0.517668
$466$	8.38101	0.388243
$467$	−16.6776	−0.771748	−0.385874	−	0.922551i	$-0.626100\pi$
$467$	−16.6776	−0.771748	−0.385874	+	0.922551i	$0.626100\pi$
$468$	−1.71982	−0.0794989
$469$	0	0
$470$	8.20855	0.378632
$471$	18.7880	0.865706
$472$	−3.06551	−0.141101
$473$	−17.6742	−0.812660
$474$	0.677618	0.0311240
$475$	−8.88617	−0.407726
$476$	0	0
$477$	6.39400	0.292761
$478$	3.67418	0.168053
$479$	−4.06819	−0.185880	−0.0929401	−	0.995672i	$-0.529626\pi$
$479$	−4.06819	−0.185880	−0.0929401	+	0.995672i	$0.529626\pi$
$480$	9.26031	0.422673
$481$	9.55691	0.435758
$482$	3.85352	0.175523
$483$	0	0
$484$	−53.7061	−2.44119
$485$	−31.5078	−1.43070
$486$	−0.529317	−0.0240103
$487$	−0.443086	−0.0200781	−0.0100391	−	0.999950i	$-0.503196\pi$
$487$	−0.443086	−0.0200781	−0.0100391	+	0.999950i	$0.503196\pi$
$488$	−7.64496	−0.346071
$489$	−9.88273	−0.446913
$490$	0	0
$491$	20.7328	0.935659	0.467829	−	0.883819i	$-0.345036\pi$
$491$	20.7328	0.935659	0.467829	+	0.883819i	$0.345036\pi$
$492$	−5.26031	−0.237153
$493$	−8.34492	−0.375836
$494$	−2.56035	−0.115196
$495$	11.5569	0.519445
$496$	−15.0481	−0.675680
$497$	0	0
$498$	−1.50172	−0.0672936
$499$	−13.9931	−0.626418	−0.313209	−	0.949684i	$-0.601404\pi$
$499$	−13.9931	−0.626418	−0.313209	+	0.949684i	$0.601404\pi$
$500$	−20.9122	−0.935220
$501$	7.04564	0.314776
$502$	12.3449	0.550981
$503$	−5.67418	−0.252999	−0.126500	−	0.991967i	$-0.540374\pi$
$503$	−5.67418	−0.252999	−0.126500	+	0.991967i	$0.540374\pi$
$504$	0	0
$505$	11.9740	0.532837
$506$	−19.8759	−0.883590
$507$	1.00000	0.0444116
$508$	16.9966	0.754101
$509$	6.22154	0.275765	0.137883	−	0.990449i	$-0.455970\pi$
$509$	6.22154	0.275765	0.137883	+	0.990449i	$0.455970\pi$
$510$	2.76891	0.122609
$511$	0	0
$512$	−21.9243	−0.968926
$513$	4.83709	0.213563
$514$	8.20168	0.361760
$515$	19.3484	0.852591
$516$	−4.67762	−0.205921
$517$	−56.6639	−2.49207
$518$	0	0
$519$	14.2897	0.627249
$520$	−3.50172	−0.153561
$521$	10.2897	0.450801	0.225401	−	0.974266i	$-0.427631\pi$
$521$	10.2897	0.450801	0.225401	+	0.974266i	$0.427631\pi$
$522$	1.50172	0.0657285
$523$	2.32582	0.101701	0.0508505	−	0.998706i	$-0.483807\pi$
$523$	2.32582	0.101701	0.0508505	+	0.998706i	$0.483807\pi$
$524$	6.47594	0.282903
$525$	0	0
$526$	−1.81379	−0.0790849
$527$	−18.4622	−0.804226
$528$	−15.5793	−0.678000
$529$	10.3906	0.451764
$530$	6.01910	0.261453
$531$	−1.55691	−0.0675643
$532$	0	0
$533$	3.05863	0.132484
$534$	−4.05520	−0.175485
$535$	15.1138	0.653428
$536$	11.1723	0.482568
$537$	−8.65775	−0.373610
$538$	−0.0912868	−0.00393565
$539$	0	0
$540$	3.05863	0.131623
$541$	5.55691	0.238910	0.119455	−	0.992840i	$-0.461885\pi$
$541$	5.55691	0.238910	0.119455	+	0.992840i	$0.461885\pi$
$542$	−13.7586	−0.590982
$543$	−26.3449	−1.13057
$544$	−15.3155	−0.656647
$545$	−17.7846	−0.761807
$546$	0	0
$547$	−5.48873	−0.234681	−0.117341	−	0.993092i	$-0.537437\pi$
$547$	−5.48873	−0.234681	−0.117341	+	0.993092i	$0.537437\pi$
$548$	29.2311	1.24869
$549$	−3.88273	−0.165711
$550$	−6.31894	−0.269441
$551$	−13.7233	−0.584631
$552$	−11.3776	−0.484262
$553$	0	0
$554$	−1.97078	−0.0837306
$555$	−16.9966	−0.721464
$556$	−14.7105	−0.623863
$557$	−22.9897	−0.974104	−0.487052	−	0.873373i	$-0.661928\pi$
$557$	−22.9897	−0.974104	−0.487052	+	0.873373i	$0.661928\pi$
$558$	3.32238	0.140648
$559$	2.71982	0.115036
$560$	0	0
$561$	−19.1138	−0.806986
$562$	11.4068	0.481167
$563$	32.7620	1.38075	0.690377	−	0.723449i	$-0.257444\pi$
$563$	32.7620	1.38075	0.690377	+	0.723449i	$0.257444\pi$
$564$	−14.9966	−0.631469
$565$	−25.9700	−1.09257
$566$	−16.8724	−0.709201
$567$	0	0
$568$	19.7983	0.830719
$569$	36.1526	1.51560	0.757798	−	0.652489i	$-0.226275\pi$
$569$	36.1526	1.51560	0.757798	+	0.652489i	$0.226275\pi$
$570$	4.55348	0.190724
$571$	6.48529	0.271401	0.135700	−	0.990750i	$-0.456672\pi$
$571$	6.48529	0.271401	0.135700	+	0.990750i	$0.456672\pi$
$572$	11.1759	0.467288
$573$	6.61555	0.276368
$574$	0	0
$575$	10.6155	0.442699
$576$	−2.03877	−0.0849487
$577$	−3.99312	−0.166236	−0.0831180	−	0.996540i	$-0.526488\pi$
$577$	−3.99312	−0.166236	−0.0831180	+	0.996540i	$0.526488\pi$
$578$	4.41893	0.183803
$579$	11.8827	0.493830
$580$	−8.67762	−0.360318
$581$	0	0
$582$	−9.37758	−0.388713
$583$	−41.5500	−1.72083
$584$	31.1759	1.29007
$585$	−1.77846	−0.0735302
$586$	1.81379	0.0749268
$587$	−4.16635	−0.171964	−0.0859818	−	0.996297i	$-0.527403\pi$
$587$	−4.16635	−0.171964	−0.0859818	+	0.996297i	$0.527403\pi$
$588$	0	0
$589$	−30.3611	−1.25101
$590$	−1.46563	−0.0603389
$591$	11.5569	0.475388
$592$	22.9122	0.941684
$593$	−16.1303	−0.662390	−0.331195	−	0.943562i	$-0.607452\pi$
$593$	−16.1303	−0.662390	−0.331195	+	0.943562i	$0.607452\pi$
$594$	3.43965	0.141130
$595$	0	0
$596$	26.7552	1.09593
$597$	−0.996562	−0.0407866
$598$	3.05863	0.125077
$599$	−33.2372	−1.35804	−0.679018	−	0.734122i	$-0.737594\pi$
$599$	−33.2372	−1.35804	−0.679018	+	0.734122i	$0.737594\pi$
$600$	−3.61717	−0.147670
$601$	28.9897	1.18251	0.591257	−	0.806483i	$-0.298632\pi$
$601$	28.9897	1.18251	0.591257	+	0.806483i	$0.298632\pi$
$602$	0	0
$603$	5.67418	0.231070
$604$	−8.59321	−0.349653
$605$	−55.5370	−2.25790
$606$	3.56379	0.144769
$607$	25.7846	1.04656	0.523282	−	0.852160i	$-0.324708\pi$
$607$	25.7846	1.04656	0.523282	+	0.852160i	$0.324708\pi$
$608$	−25.1864	−1.02144
$609$	0	0
$610$	−3.65508	−0.147990
$611$	8.71982	0.352766
$612$	−5.05863	−0.204483
$613$	−7.43965	−0.300485	−0.150242	−	0.988649i	$-0.548005\pi$
$613$	−7.43965	−0.300485	−0.150242	+	0.988649i	$0.548005\pi$
$614$	−1.79832	−0.0725744
$615$	−5.43965	−0.219348
$616$	0	0
$617$	−2.67074	−0.107520	−0.0537600	−	0.998554i	$-0.517121\pi$
$617$	−2.67074	−0.107520	−0.0537600	+	0.998554i	$0.517121\pi$
$618$	5.75859	0.231645
$619$	4.46907	0.179627	0.0898134	−	0.995959i	$-0.471373\pi$
$619$	4.46907	0.179627	0.0898134	+	0.995959i	$0.471373\pi$
$620$	−19.1982	−0.771020
$621$	−5.77846	−0.231881
$622$	−0.234533	−0.00940390
$623$	0	0
$624$	2.39744	0.0959745
$625$	−12.4396	−0.497586
$626$	−10.5243	−0.420634
$627$	−31.4328	−1.25530
$628$	−32.3121	−1.28939
$629$	28.1104	1.12083
$630$	0	0
$631$	23.0878	0.919113	0.459556	−	0.888149i	$-0.348008\pi$
$631$	23.0878	0.919113	0.459556	+	0.888149i	$0.348008\pi$
$632$	−2.52062	−0.100265
$633$	26.8302	1.06641
$634$	−5.01031	−0.198985
$635$	17.5760	0.697483
$636$	−10.9966	−0.436042
$637$	0	0
$638$	−9.75859	−0.386346
$639$	10.0552	0.397777
$640$	−20.4398	−0.807956
$641$	41.8268	1.65206	0.826029	−	0.563627i	$-0.190595\pi$
$641$	41.8268	1.65206	0.826029	+	0.563627i	$0.190595\pi$
$642$	4.49828	0.177533
$643$	−3.11383	−0.122797	−0.0613987	−	0.998113i	$-0.519556\pi$
$643$	−3.11383	−0.122797	−0.0613987	+	0.998113i	$0.519556\pi$
$644$	0	0
$645$	−4.83709	−0.190460
$646$	−7.53093	−0.296301
$647$	−30.4362	−1.19657	−0.598285	−	0.801283i	$-0.704151\pi$
$647$	−30.4362	−1.19657	−0.598285	+	0.801283i	$0.704151\pi$
$648$	1.96896	0.0773482
$649$	10.1173	0.397137
$650$	0.972402	0.0381408
$651$	0	0
$652$	16.9966	0.665637
$653$	3.99312	0.156263	0.0781315	−	0.996943i	$-0.475105\pi$
$653$	3.99312	0.156263	0.0781315	+	0.996943i	$0.475105\pi$
$654$	−5.29317	−0.206979
$655$	6.69672	0.261663
$656$	7.33290	0.286302
$657$	15.8337	0.617730
$658$	0	0
$659$	32.6578	1.27217	0.636083	−	0.771621i	$-0.280554\pi$
$659$	32.6578	1.27217	0.636083	+	0.771621i	$0.280554\pi$
$660$	−19.8759	−0.773667
$661$	−43.7355	−1.70111	−0.850557	−	0.525883i	$-0.823735\pi$
$661$	−43.7355	−1.70111	−0.850557	+	0.525883i	$0.823735\pi$
$662$	14.5206	0.564360
$663$	2.94137	0.114233
$664$	5.58613	0.216784
$665$	0	0
$666$	−5.05863	−0.196018
$667$	16.3940	0.634778
$668$	−12.1173	−0.468831
$669$	2.92838	0.113218
$670$	5.34149	0.206360
$671$	25.2311	0.974036
$672$	0	0
$673$	−9.63198	−0.371285	−0.185643	−	0.982617i	$-0.559437\pi$
$673$	−9.63198	−0.371285	−0.185643	+	0.982617i	$0.559437\pi$
$674$	10.7328	0.413413
$675$	−1.83709	−0.0707096
$676$	−1.71982	−0.0661471
$677$	−16.4914	−0.633816	−0.316908	−	0.948456i	$-0.602645\pi$
$677$	−16.4914	−0.633816	−0.316908	+	0.948456i	$0.602645\pi$
$678$	−7.72938	−0.296845
$679$	0	0
$680$	−10.2998	−0.394981
$681$	9.79145	0.375209
$682$	−21.5898	−0.826715
$683$	41.9311	1.60445	0.802224	−	0.597024i	$-0.203650\pi$
$683$	41.9311	1.60445	0.802224	+	0.597024i	$0.203650\pi$
$684$	−8.31894	−0.318083
$685$	30.2277	1.15494
$686$	0	0
$687$	−3.88273	−0.148136
$688$	6.52062	0.248596
$689$	6.39400	0.243592
$690$	−5.43965	−0.207084
$691$	−38.1786	−1.45238	−0.726191	−	0.687493i	$-0.758711\pi$
$691$	−38.1786	−1.45238	−0.726191	+	0.687493i	$0.758711\pi$
$692$	−24.5758	−0.934232
$693$	0	0
$694$	−8.85696	−0.336205
$695$	−15.2120	−0.577024
$696$	−5.58613	−0.211742
$697$	8.99656	0.340769
$698$	11.8535	0.448662
$699$	−15.8337	−0.598884
$700$	0	0
$701$	16.5957	0.626810	0.313405	−	0.949620i	$-0.398530\pi$
$701$	16.5957	0.626810	0.313405	+	0.949620i	$0.398530\pi$
$702$	−0.529317	−0.0199778
$703$	46.2277	1.74351
$704$	13.2485	0.499321
$705$	−15.5078	−0.584059
$706$	−14.3810	−0.541237
$707$	0	0
$708$	2.67762	0.100631
$709$	21.7655	0.817419	0.408710	−	0.912664i	$-0.365979\pi$
$709$	21.7655	0.817419	0.408710	+	0.912664i	$0.365979\pi$
$710$	9.46563	0.355239
$711$	−1.28018	−0.0480104
$712$	15.0846	0.565320
$713$	36.2699	1.35832
$714$	0	0
$715$	11.5569	0.432204
$716$	14.8898	0.556458
$717$	−6.94137	−0.259230
$718$	15.3812	0.574022
$719$	−36.7880	−1.37196	−0.685981	−	0.727620i	$-0.740627\pi$
$719$	−36.7880	−1.37196	−0.685981	+	0.727620i	$0.740627\pi$
$720$	−4.26375	−0.158901
$721$	0	0
$722$	−2.32764	−0.0866258
$723$	−7.28018	−0.270753
$724$	45.3086	1.68388
$725$	5.21199	0.193568
$726$	−16.5293	−0.613460
$727$	32.3189	1.19864	0.599322	−	0.800508i	$-0.295437\pi$
$727$	32.3189	1.19864	0.599322	+	0.800508i	$0.295437\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	14.9053	0.551669
$731$	8.00000	0.295891
$732$	6.67762	0.246812
$733$	12.7198	0.469817	0.234909	−	0.972017i	$-0.424521\pi$
$733$	12.7198	0.469817	0.234909	+	0.972017i	$0.424521\pi$
$734$	−2.35180	−0.0868065
$735$	0	0
$736$	30.0881	1.10906
$737$	−36.8724	−1.35821
$738$	−1.61899	−0.0595957
$739$	23.1982	0.853361	0.426681	−	0.904402i	$-0.359683\pi$
$739$	23.1982	0.853361	0.426681	+	0.904402i	$0.359683\pi$
$740$	29.2311	1.07456
$741$	4.83709	0.177695
$742$	0	0
$743$	31.8138	1.16713	0.583567	−	0.812065i	$-0.301656\pi$
$743$	31.8138	1.16713	0.583567	+	0.812065i	$0.301656\pi$
$744$	−12.3587	−0.453091
$745$	27.6673	1.01365
$746$	−16.5896	−0.607387
$747$	2.83709	0.103804
$748$	32.8724	1.20193
$749$	0	0
$750$	−6.43621	−0.235017
$751$	−0.863070	−0.0314939	−0.0157469	−	0.999876i	$-0.505013\pi$
$751$	−0.863070	−0.0314939	−0.0157469	+	0.999876i	$0.505013\pi$
$752$	20.9053	0.762337
$753$	−23.3224	−0.849915
$754$	1.50172	0.0546894
$755$	−8.88617	−0.323401
$756$	0	0
$757$	−13.3974	−0.486938	−0.243469	−	0.969909i	$-0.578285\pi$
$757$	−13.3974	−0.486938	−0.243469	+	0.969909i	$0.578285\pi$
$758$	6.11727	0.222189
$759$	37.5500	1.36298
$760$	−16.9381	−0.614411
$761$	35.5630	1.28916	0.644579	−	0.764537i	$-0.277033\pi$
$761$	35.5630	1.28916	0.644579	+	0.764537i	$0.277033\pi$
$762$	5.23109	0.189503
$763$	0	0
$764$	−11.3776	−0.411626
$765$	−5.23109	−0.189131
$766$	−13.5861	−0.490887
$767$	−1.55691	−0.0562169
$768$	−2.00591	−0.0723821
$769$	48.3871	1.74488	0.872442	−	0.488717i	$-0.162535\pi$
$769$	48.3871	1.74488	0.872442	+	0.488717i	$0.162535\pi$
$770$	0	0
$771$	−15.4948	−0.558033
$772$	−20.4362	−0.735515
$773$	−17.9379	−0.645182	−0.322591	−	0.946538i	$-0.604554\pi$
$773$	−17.9379	−0.645182	−0.322591	+	0.946538i	$0.604554\pi$
$774$	−1.43965	−0.0517471
$775$	11.5309	0.414203
$776$	34.8829	1.25222
$777$	0	0
$778$	12.8241	0.459766
$779$	14.7949	0.530082
$780$	3.05863	0.109517
$781$	−65.3415	−2.33810
$782$	8.99656	0.321716
$783$	−2.83709	−0.101389
$784$	0	0
$785$	−33.4137	−1.19258
$786$	1.99312	0.0710924
$787$	3.71639	0.132475	0.0662374	−	0.997804i	$-0.478901\pi$
$787$	3.71639	0.132475	0.0662374	+	0.997804i	$0.478901\pi$
$788$	−19.8759	−0.708048
$789$	3.42666	0.121992
$790$	−1.20512	−0.0428761
$791$	0	0
$792$	−12.7949	−0.454646
$793$	−3.88273	−0.137880
$794$	−7.60523	−0.269900
$795$	−11.3715	−0.403304
$796$	1.71391	0.0607480
$797$	−14.9673	−0.530171	−0.265085	−	0.964225i	$-0.585400\pi$
$797$	−14.9673	−0.530171	−0.265085	+	0.964225i	$0.585400\pi$
$798$	0	0
$799$	25.6482	0.907368
$800$	9.56561	0.338195
$801$	7.66119	0.270695
$802$	11.5829	0.409006
$803$	−102.892	−3.63096
$804$	−9.75859	−0.344159
$805$	0	0
$806$	3.32238	0.117026
$807$	0.172462	0.00607094
$808$	−13.2567	−0.466368
$809$	11.7233	0.412168	0.206084	−	0.978534i	$-0.433928\pi$
$809$	11.7233	0.412168	0.206084	+	0.978534i	$0.433928\pi$
$810$	0.941367	0.0330763
$811$	0.886172	0.0311177	0.0155588	−	0.999879i	$-0.495047\pi$
$811$	0.886172	0.0311177	0.0155588	+	0.999879i	$0.495047\pi$
$812$	0	0
$813$	25.9931	0.911619
$814$	32.8724	1.15218
$815$	17.5760	0.615661
$816$	7.05176	0.246861
$817$	13.1560	0.460271
$818$	3.91195	0.136778
$819$	0	0
$820$	9.35524	0.326699
$821$	−53.7846	−1.87709	−0.938547	−	0.345151i	$-0.887828\pi$
$821$	−53.7846	−1.87709	−0.938547	+	0.345151i	$0.887828\pi$
$822$	8.99656	0.313791
$823$	−35.7655	−1.24671	−0.623353	−	0.781941i	$-0.714230\pi$
$823$	−35.7655	−1.24671	−0.623353	+	0.781941i	$0.714230\pi$
$824$	−21.4209	−0.746234
$825$	11.9379	0.415625
$826$	0	0
$827$	7.41043	0.257686	0.128843	−	0.991665i	$-0.458874\pi$
$827$	7.41043	0.257686	0.128843	+	0.991665i	$0.458874\pi$
$828$	9.93793	0.345367
$829$	31.9931	1.11117	0.555584	−	0.831461i	$-0.312495\pi$
$829$	31.9931	1.11117	0.555584	+	0.831461i	$0.312495\pi$
$830$	2.67074	0.0927028
$831$	3.72326	0.129159
$832$	−2.03877	−0.0706816
$833$	0	0
$834$	−4.52750	−0.156774
$835$	−12.5304	−0.433631
$836$	54.0588	1.86966
$837$	−6.27674	−0.216956
$838$	17.8827	0.617749
$839$	1.55691	0.0537506	0.0268753	−	0.999639i	$-0.491444\pi$
$839$	1.55691	0.0537506	0.0268753	+	0.999639i	$0.491444\pi$
$840$	0	0
$841$	−20.9509	−0.722445
$842$	18.8172	0.648484
$843$	−21.5500	−0.742223
$844$	−46.1432	−1.58832
$845$	−1.77846	−0.0611808
$846$	−4.61555	−0.158686
$847$	0	0
$848$	15.3293	0.526409
$849$	31.8759	1.09398
$850$	2.86019	0.0981038
$851$	−55.2242	−1.89306
$852$	−17.2932	−0.592454
$853$	−35.4750	−1.21464	−0.607320	−	0.794457i	$-0.707755\pi$
$853$	−35.4750	−1.21464	−0.607320	+	0.794457i	$0.707755\pi$
$854$	0	0
$855$	−8.60256	−0.294201
$856$	−16.7328	−0.571916
$857$	2.49828	0.0853397	0.0426698	−	0.999089i	$-0.486414\pi$
$857$	2.49828	0.0853397	0.0426698	+	0.999089i	$0.486414\pi$
$858$	3.43965	0.117428
$859$	−52.0122	−1.77463	−0.887317	−	0.461160i	$-0.847434\pi$
$859$	−52.0122	−1.77463	−0.887317	+	0.461160i	$0.847434\pi$
$860$	8.31894	0.283674
$861$	0	0
$862$	−12.5604	−0.427807
$863$	34.8172	1.18519	0.592596	−	0.805500i	$-0.298103\pi$
$863$	34.8172	1.18519	0.592596	+	0.805500i	$0.298103\pi$
$864$	−5.20693	−0.177144
$865$	−25.4137	−0.864091
$866$	−2.94137	−0.0999517
$867$	−8.34836	−0.283525
$868$	0	0
$869$	8.31894	0.282201
$870$	−2.67074	−0.0905467
$871$	5.67418	0.192262
$872$	19.6896	0.666776
$873$	17.7164	0.599609
$874$	14.7949	0.500444
$875$	0	0
$876$	−27.2311	−0.920053
$877$	−11.2571	−0.380124	−0.190062	−	0.981772i	$-0.560869\pi$
$877$	−11.2571	−0.380124	−0.190062	+	0.981772i	$0.560869\pi$
$878$	2.82086	0.0951996
$879$	−3.42666	−0.115578
$880$	27.7070	0.934004
$881$	9.50172	0.320121	0.160061	−	0.987107i	$-0.448831\pi$
$881$	9.50172	0.320121	0.160061	+	0.987107i	$0.448831\pi$
$882$	0	0
$883$	23.7655	0.799772	0.399886	−	0.916565i	$-0.369050\pi$
$883$	23.7655	0.799772	0.399886	+	0.916565i	$0.369050\pi$
$884$	−5.05863	−0.170140
$885$	2.76891	0.0930757
$886$	−2.82410	−0.0948775
$887$	−18.3518	−0.616193	−0.308097	−	0.951355i	$-0.599692\pi$
$887$	−18.3518	−0.616193	−0.308097	+	0.951355i	$0.599692\pi$
$888$	18.8172	0.631465
$889$	0	0
$890$	7.21199	0.241746
$891$	−6.49828	−0.217701
$892$	−5.03629	−0.168628
$893$	42.1786	1.41145
$894$	8.23453	0.275404
$895$	15.3974	0.514680
$896$	0	0
$897$	−5.77846	−0.192937
$898$	−13.8827	−0.463273
$899$	17.8077	0.593919
$900$	3.15947	0.105316
$901$	18.8071	0.626556
$902$	10.5206	0.350298
$903$	0	0
$904$	28.7519	0.956275
$905$	46.8533	1.55746
$906$	−2.64476	−0.0878664
$907$	35.7164	1.18594	0.592972	−	0.805223i	$-0.297955\pi$
$907$	35.7164	1.18594	0.592972	+	0.805223i	$0.297955\pi$
$908$	−16.8396	−0.558841
$909$	−6.73281	−0.223313
$910$	0	0
$911$	−16.2147	−0.537216	−0.268608	−	0.963250i	$-0.586564\pi$
$911$	−16.2147	−0.537216	−0.268608	+	0.963250i	$0.586564\pi$
$912$	11.5966	0.384003
$913$	−18.4362	−0.610149
$914$	−6.05520	−0.200288
$915$	6.90528	0.228281
$916$	6.67762	0.220635
$917$	0	0
$918$	−1.55691	−0.0513858
$919$	−34.4622	−1.13680	−0.568401	−	0.822751i	$-0.692438\pi$
$919$	−34.4622	−1.13680	−0.568401	+	0.822751i	$0.692438\pi$
$920$	20.2345	0.667113
$921$	3.39744	0.111950
$922$	−14.8501	−0.489061
$923$	10.0552	0.330971
$924$	0	0
$925$	−17.5569	−0.577268
$926$	5.58977	0.183691
$927$	−10.8793	−0.357323
$928$	14.7725	0.484933
$929$	28.4492	0.933388	0.466694	−	0.884419i	$-0.345445\pi$
$929$	28.4492	0.933388	0.466694	+	0.884419i	$0.345445\pi$
$930$	−5.90871	−0.193754
$931$	0	0
$932$	27.2311	0.891984
$933$	0.443086	0.0145060
$934$	8.82774	0.288852
$935$	33.9931	1.11169
$936$	1.96896	0.0643576
$937$	−2.91215	−0.0951358	−0.0475679	−	0.998868i	$-0.515147\pi$
$937$	−2.91215	−0.0951358	−0.0475679	+	0.998868i	$0.515147\pi$
$938$	0	0
$939$	19.8827	0.648848
$940$	26.6707	0.869904
$941$	59.0096	1.92366	0.961828	−	0.273654i	$-0.0882323\pi$
$941$	59.0096	1.92366	0.961828	+	0.273654i	$0.0882323\pi$
$942$	−9.94480	−0.324019
$943$	−17.6742	−0.575551
$944$	−3.73261	−0.121486
$945$	0	0
$946$	9.35524	0.304165
$947$	34.8432	1.13225	0.566126	−	0.824319i	$-0.308442\pi$
$947$	34.8432	1.13225	0.566126	+	0.824319i	$0.308442\pi$
$948$	2.20168	0.0715072
$949$	15.8337	0.513982
$950$	4.70360	0.152605
$951$	9.46563	0.306944
$952$	0	0
$953$	23.9578	0.776069	0.388035	−	0.921645i	$-0.373154\pi$
$953$	23.9578	0.776069	0.388035	+	0.921645i	$0.373154\pi$
$954$	−3.38445	−0.109576
$955$	−11.7655	−0.380722
$956$	11.9379	0.386100
$957$	18.4362	0.595958
$958$	2.15336	0.0695718
$959$	0	0
$960$	3.62586	0.117024
$961$	8.39744	0.270885
$962$	−5.05863	−0.163097
$963$	−8.49828	−0.273853
$964$	12.5206	0.403262
$965$	−21.1329	−0.680293
$966$	0	0
$967$	−37.3155	−1.19999	−0.599993	−	0.800005i	$-0.704830\pi$
$967$	−37.3155	−1.19999	−0.599993	+	0.800005i	$0.704830\pi$
$968$	61.4861	1.97624
$969$	14.2277	0.457058
$970$	16.6776	0.535486
$971$	−20.7880	−0.667119	−0.333559	−	0.942729i	$-0.608250\pi$
$971$	−20.7880	−0.667119	−0.333559	+	0.942729i	$0.608250\pi$
$972$	−1.71982	−0.0551634
$973$	0	0
$974$	0.234533	0.00751491
$975$	−1.83709	−0.0588340
$976$	−9.30863	−0.297962
$977$	49.0810	1.57024	0.785120	−	0.619344i	$-0.212601\pi$
$977$	49.0810	1.57024	0.785120	+	0.619344i	$0.212601\pi$
$978$	5.23109	0.167272
$979$	−49.7846	−1.59112
$980$	0	0
$981$	10.0000	0.319275
$982$	−10.9742	−0.350201
$983$	−10.1855	−0.324865	−0.162433	−	0.986720i	$-0.551934\pi$
$983$	−10.1855	−0.324865	−0.162433	+	0.986720i	$0.551934\pi$
$984$	6.02234	0.191985
$985$	−20.5535	−0.654888
$986$	4.41711	0.140669
$987$	0	0
$988$	−8.31894	−0.264661
$989$	−15.7164	−0.499752
$990$	−6.11727	−0.194419
$991$	4.34492	0.138021	0.0690105	−	0.997616i	$-0.478016\pi$
$991$	4.34492	0.138021	0.0690105	+	0.997616i	$0.478016\pi$
$992$	32.6826	1.03767
$993$	−27.4328	−0.870553
$994$	0	0
$995$	1.77234	0.0561871
$996$	−4.87930	−0.154606
$997$	−44.9637	−1.42401	−0.712007	−	0.702172i	$-0.752214\pi$
$997$	−44.9637	−1.42401	−0.712007	+	0.702172i	$0.752214\pi$
$998$	7.40679	0.234458
$999$	9.55691	0.302367

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.2.a.n.1.2		3
3.2	odd	2		5733.2.a.bc.1.2		3
7.6	odd	2		273.2.a.d.1.2	✓	3
21.20	even	2		819.2.a.j.1.2		3
28.27	even	2		4368.2.a.bq.1.3		3
35.34	odd	2		6825.2.a.bd.1.2		3
91.90	odd	2		3549.2.a.t.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.a.d.1.2	✓	3	7.6	odd	2
819.2.a.j.1.2		3	21.20	even	2
1911.2.a.n.1.2		3	1.1	even	1	trivial
3549.2.a.t.1.2		3	91.90	odd	2
4368.2.a.bq.1.3		3	28.27	even	2
5733.2.a.bc.1.2		3	3.2	odd	2
6825.2.a.bd.1.2		3	35.34	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:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)

\(f(q)\)	\(=\)	\(q-0.529317 q^{2} +1.00000 q^{3} -1.71982 q^{4} -1.77846 q^{5} -0.529317 q^{6} +1.96896 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.529317 q^{2} +1.00000 q^{3} -1.71982 q^{4} -1.77846 q^{5} -0.529317 q^{6} +1.96896 q^{8} +1.00000 q^{9} +0.941367 q^{10} -6.49828 q^{11} -1.71982 q^{12} +1.00000 q^{13} -1.77846 q^{15} +2.39744 q^{16} +2.94137 q^{17} -0.529317 q^{18} +4.83709 q^{19} +3.05863 q^{20} +3.43965 q^{22} -5.77846 q^{23} +1.96896 q^{24} -1.83709 q^{25} -0.529317 q^{26} +1.00000 q^{27} -2.83709 q^{29} +0.941367 q^{30} -6.27674 q^{31} -5.20693 q^{32} -6.49828 q^{33} -1.55691 q^{34} -1.71982 q^{36} +9.55691 q^{37} -2.56035 q^{38} +1.00000 q^{39} -3.50172 q^{40} +3.05863 q^{41} +2.71982 q^{43} +11.1759 q^{44} -1.77846 q^{45} +3.05863 q^{46} +8.71982 q^{47} +2.39744 q^{48} +0.972402 q^{50} +2.94137 q^{51} -1.71982 q^{52} +6.39400 q^{53} -0.529317 q^{54} +11.5569 q^{55} +4.83709 q^{57} +1.50172 q^{58} -1.55691 q^{59} +3.05863 q^{60} -3.88273 q^{61} +3.32238 q^{62} -2.03877 q^{64} -1.77846 q^{65} +3.43965 q^{66} +5.67418 q^{67} -5.05863 q^{68} -5.77846 q^{69} +10.0552 q^{71} +1.96896 q^{72} +15.8337 q^{73} -5.05863 q^{74} -1.83709 q^{75} -8.31894 q^{76} -0.529317 q^{78} -1.28018 q^{79} -4.26375 q^{80} +1.00000 q^{81} -1.61899 q^{82} +2.83709 q^{83} -5.23109 q^{85} -1.43965 q^{86} -2.83709 q^{87} -12.7949 q^{88} +7.66119 q^{89} +0.941367 q^{90} +9.93793 q^{92} -6.27674 q^{93} -4.61555 q^{94} -8.60256 q^{95} -5.20693 q^{96} +17.7164 q^{97} -6.49828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{5} - 2 q^{6} - 12 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^5 - 2 * q^6 - 12 * q^8 + 3 * q^9	\( 3 q - 2 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{5} - 2 q^{6} - 12 q^{8} + 3 q^{9} + 2 q^{10} - 2 q^{11} + 4 q^{12} + 3 q^{13} + 3 q^{15} + 18 q^{16} + 8 q^{17} - 2 q^{18} + 7 q^{19} + 10 q^{20} - 8 q^{22} - 9 q^{23} - 12 q^{24} + 2 q^{25} - 2 q^{26} + 3 q^{27} - q^{29} + 2 q^{30} + 7 q^{31} - 36 q^{32} - 2 q^{33} + 12 q^{34} + 4 q^{36} + 12 q^{37} - 26 q^{38} + 3 q^{39} - 28 q^{40} + 10 q^{41} - q^{43} + 36 q^{44} + 3 q^{45} + 10 q^{46} + 17 q^{47} + 18 q^{48} + 20 q^{50} + 8 q^{51} + 4 q^{52} - 5 q^{53} - 2 q^{54} + 18 q^{55} + 7 q^{57} + 22 q^{58} + 12 q^{59} + 10 q^{60} - 10 q^{61} - 10 q^{62} + 58 q^{64} + 3 q^{65} - 8 q^{66} + 2 q^{67} - 16 q^{68} - 9 q^{69} - 4 q^{71} - 12 q^{72} + 5 q^{73} - 16 q^{74} + 2 q^{75} + 30 q^{76} - 2 q^{78} - 13 q^{79} + 8 q^{80} + 3 q^{81} - 24 q^{82} + q^{83} + 16 q^{85} + 14 q^{86} - q^{87} - 60 q^{88} + 13 q^{89} + 2 q^{90} - 6 q^{92} + 7 q^{93} + 2 q^{94} - 15 q^{95} - 36 q^{96} + 9 q^{97} - 2 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^5 - 2 * q^6 - 12 * q^8 + 3 * q^9 + 2 * q^10 - 2 * q^11 + 4 * q^12 + 3 * q^13 + 3 * q^15 + 18 * q^16 + 8 * q^17 - 2 * q^18 + 7 * q^19 + 10 * q^20 - 8 * q^22 - 9 * q^23 - 12 * q^24 + 2 * q^25 - 2 * q^26 + 3 * q^27 - q^29 + 2 * q^30 + 7 * q^31 - 36 * q^32 - 2 * q^33 + 12 * q^34 + 4 * q^36 + 12 * q^37 - 26 * q^38 + 3 * q^39 - 28 * q^40 + 10 * q^41 - q^43 + 36 * q^44 + 3 * q^45 + 10 * q^46 + 17 * q^47 + 18 * q^48 + 20 * q^50 + 8 * q^51 + 4 * q^52 - 5 * q^53 - 2 * q^54 + 18 * q^55 + 7 * q^57 + 22 * q^58 + 12 * q^59 + 10 * q^60 - 10 * q^61 - 10 * q^62 + 58 * q^64 + 3 * q^65 - 8 * q^66 + 2 * q^67 - 16 * q^68 - 9 * q^69 - 4 * q^71 - 12 * q^72 + 5 * q^73 - 16 * q^74 + 2 * q^75 + 30 * q^76 - 2 * q^78 - 13 * q^79 + 8 * q^80 + 3 * q^81 - 24 * q^82 + q^83 + 16 * q^85 + 14 * q^86 - q^87 - 60 * q^88 + 13 * q^89 + 2 * q^90 - 6 * q^92 + 7 * q^93 + 2 * q^94 - 15 * q^95 - 36 * q^96 + 9 * q^97 - 2 * q^99

Introduction

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