LMFDB - Embedded newform 5929.2.a.bi.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5929,2,Mod(1,5929)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5929, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5929.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.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:	$47.3433033584$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2525.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 5 $ x^4 - 2x^3 - 4x^2 + 5*x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.77748$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.77748 q^{2} -0.618034 q^{3} +1.15945 q^{4} +2.77748 q^{5} -1.09855 q^{6} -1.49406 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q+1.77748 q^{2} -0.618034 q^{3} +1.15945 q^{4} +2.77748 q^{5} -1.09855 q^{6} -1.49406 q^{8} -2.61803 q^{9} +4.93693 q^{10} -0.716580 q^{12} +4.29348 q^{13} -1.71658 q^{15} -4.97458 q^{16} +2.75556 q^{17} -4.65351 q^{18} -1.93910 q^{19} +3.22035 q^{20} +4.37009 q^{23} +0.923382 q^{24} +2.71442 q^{25} +7.63159 q^{26} +3.47214 q^{27} +8.62809 q^{29} -3.05119 q^{30} +0.200588 q^{31} -5.85410 q^{32} +4.89796 q^{34} -3.03548 q^{36} +1.03548 q^{37} -3.44671 q^{38} -2.65351 q^{39} -4.14974 q^{40} -9.60616 q^{41} -4.70820 q^{43} -7.27155 q^{45} +7.76777 q^{46} +13.0455 q^{47} +3.07446 q^{48} +4.82484 q^{50} -1.70303 q^{51} +4.97807 q^{52} -3.90012 q^{53} +6.17167 q^{54} +1.19843 q^{57} +15.3363 q^{58} +8.55713 q^{59} -1.99029 q^{60} +0.988609 q^{61} +0.356542 q^{62} -0.456423 q^{64} +11.9251 q^{65} -5.41745 q^{67} +3.19493 q^{68} -2.70087 q^{69} -2.01705 q^{71} +3.91151 q^{72} +9.97108 q^{73} +1.84055 q^{74} -1.67760 q^{75} -2.24828 q^{76} -4.71658 q^{78} +6.29348 q^{79} -13.8168 q^{80} +5.70820 q^{81} -17.0748 q^{82} +1.72146 q^{83} +7.65351 q^{85} -8.36876 q^{86} -5.33245 q^{87} +15.3035 q^{89} -12.9251 q^{90} +5.06691 q^{92} -0.123970 q^{93} +23.1882 q^{94} -5.38581 q^{95} +3.61803 q^{96} -11.6162 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} + q^{6} + 9 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 + q^6 + 9 * q^8 - 6 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} + q^{6} + 9 q^{8} - 6 q^{9} + 14 q^{10} + 7 q^{12} + 3 q^{15} - 4 q^{16} + 3 q^{17} - 3 q^{18} - 3 q^{19} + 17 q^{20} - 8 q^{23} + 12 q^{24} + 12 q^{26} - 4 q^{27} + 3 q^{29} + 12 q^{30} + 3 q^{31} - 10 q^{32} + 12 q^{34} - q^{36} - 7 q^{37} + 20 q^{38} + 5 q^{39} + 13 q^{40} - 4 q^{41} + 8 q^{43} - 9 q^{45} - 3 q^{46} + 14 q^{47} + 3 q^{48} + 33 q^{50} - 11 q^{51} + 17 q^{52} - 9 q^{53} - 2 q^{54} + 6 q^{57} + 3 q^{58} + 25 q^{59} + 21 q^{60} + 19 q^{61} - 10 q^{62} + 3 q^{64} + 12 q^{65} - 15 q^{67} + q^{68} - 14 q^{69} - 7 q^{71} - 6 q^{72} + 11 q^{73} + 8 q^{74} + 5 q^{75} + 26 q^{76} - 9 q^{78} + 8 q^{79} + 4 q^{80} - 4 q^{81} - 3 q^{82} + q^{83} + 15 q^{85} + 4 q^{86} - 6 q^{87} + 17 q^{89} - 16 q^{90} - 17 q^{92} - 11 q^{93} + 20 q^{94} + 17 q^{95} + 10 q^{96} + 15 q^{97}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 + q^6 + 9 * q^8 - 6 * q^9 + 14 * q^10 + 7 * q^12 + 3 * q^15 - 4 * q^16 + 3 * q^17 - 3 * q^18 - 3 * q^19 + 17 * q^20 - 8 * q^23 + 12 * q^24 + 12 * q^26 - 4 * q^27 + 3 * q^29 + 12 * q^30 + 3 * q^31 - 10 * q^32 + 12 * q^34 - q^36 - 7 * q^37 + 20 * q^38 + 5 * q^39 + 13 * q^40 - 4 * q^41 + 8 * q^43 - 9 * q^45 - 3 * q^46 + 14 * q^47 + 3 * q^48 + 33 * q^50 - 11 * q^51 + 17 * q^52 - 9 * q^53 - 2 * q^54 + 6 * q^57 + 3 * q^58 + 25 * q^59 + 21 * q^60 + 19 * q^61 - 10 * q^62 + 3 * q^64 + 12 * q^65 - 15 * q^67 + q^68 - 14 * q^69 - 7 * q^71 - 6 * q^72 + 11 * q^73 + 8 * q^74 + 5 * q^75 + 26 * q^76 - 9 * q^78 + 8 * q^79 + 4 * q^80 - 4 * q^81 - 3 * q^82 + q^83 + 15 * q^85 + 4 * q^86 - 6 * q^87 + 17 * q^89 - 16 * q^90 - 17 * q^92 - 11 * q^93 + 20 * q^94 + 17 * q^95 + 10 * q^96 + 15 * q^97

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 $

$2$	1.77748	1.25687	0.628436	−	0.777862i	$-0.283696\pi$
$2$	1.77748	1.25687	0.628436	+	0.777862i	$0.283696\pi$
$3$	−0.618034	−0.356822	−0.178411	−	0.983956i	$-0.557096\pi$
$3$	−0.618034	−0.356822	−0.178411	+	0.983956i	$0.557096\pi$
$4$	1.15945	0.579725
$5$	2.77748	1.24213	0.621064	−	0.783760i	$-0.286701\pi$
$5$	2.77748	1.24213	0.621064	+	0.783760i	$0.286701\pi$
$6$	−1.09855	−0.448479
$7$	0	0
$7$	0	0
$8$	−1.49406	−0.528231
$9$	−2.61803	−0.872678
$10$	4.93693	1.56120
$11$	0	0
$11$	0	0
$12$	−0.716580	−0.206859
$13$	4.29348	1.19080	0.595398	−	0.803431i	$-0.296994\pi$
$13$	4.29348	1.19080	0.595398	+	0.803431i	$0.296994\pi$
$14$	0	0
$15$	−1.71658	−0.443219
$16$	−4.97458	−1.24364
$17$	2.75556	0.668321	0.334160	−	0.942516i	$-0.391547\pi$
$17$	2.75556	0.668321	0.334160	+	0.942516i	$0.391547\pi$
$18$	−4.65351	−1.09684
$19$	−1.93910	−0.444859	−0.222429	−	0.974949i	$-0.571399\pi$
$19$	−1.93910	−0.444859	−0.222429	+	0.974949i	$0.571399\pi$
$20$	3.22035	0.720093
$21$	0	0
$22$	0	0
$23$	4.37009	0.911228	0.455614	−	0.890178i	$-0.349420\pi$
$23$	4.37009	0.911228	0.455614	+	0.890178i	$0.349420\pi$
$24$	0.923382	0.188485
$25$	2.71442	0.542884
$26$	7.63159	1.49668
$27$	3.47214	0.668213
$28$	0	0
$29$	8.62809	1.60220	0.801098	−	0.598533i	$-0.204250\pi$
$29$	8.62809	1.60220	0.801098	+	0.598533i	$0.204250\pi$
$30$	−3.05119	−0.557069
$31$	0.200588	0.0360266	0.0180133	−	0.999838i	$-0.494266\pi$
$31$	0.200588	0.0360266	0.0180133	+	0.999838i	$0.494266\pi$
$32$	−5.85410	−1.03487
$33$	0	0
$34$	4.89796	0.839993
$35$	0	0
$36$	−3.03548	−0.505913
$37$	1.03548	0.170232	0.0851159	−	0.996371i	$-0.472874\pi$
$37$	1.03548	0.170232	0.0851159	+	0.996371i	$0.472874\pi$
$38$	−3.44671	−0.559130
$39$	−2.65351	−0.424902
$40$	−4.14974	−0.656131
$41$	−9.60616	−1.50023	−0.750115	−	0.661307i	$-0.770002\pi$
$41$	−9.60616	−1.50023	−0.750115	+	0.661307i	$0.770002\pi$
$42$	0	0
$43$	−4.70820	−0.717994	−0.358997	−	0.933339i	$-0.616881\pi$
$43$	−4.70820	−0.717994	−0.358997	+	0.933339i	$0.616881\pi$
$44$	0	0
$45$	−7.27155	−1.08398
$46$	7.76777	1.14530
$47$	13.0455	1.90289	0.951443	−	0.307823i	$-0.0996006\pi$
$47$	13.0455	1.90289	0.951443	+	0.307823i	$0.0996006\pi$
$48$	3.07446	0.443760
$49$	0	0
$50$	4.82484	0.682335
$51$	−1.70303	−0.238472
$52$	4.97807	0.690334
$53$	−3.90012	−0.535723	−0.267861	−	0.963457i	$-0.586317\pi$
$53$	−3.90012	−0.535723	−0.267861	+	0.963457i	$0.586317\pi$
$54$	6.17167	0.839857
$55$	0	0
$56$	0	0
$57$	1.19843	0.158736
$58$	15.3363	2.01375
$59$	8.55713	1.11404	0.557022	−	0.830498i	$-0.311944\pi$
$59$	8.55713	1.11404	0.557022	+	0.830498i	$0.311944\pi$
$60$	−1.99029	−0.256945
$61$	0.988609	0.126578	0.0632892	−	0.997995i	$-0.479841\pi$
$61$	0.988609	0.126578	0.0632892	+	0.997995i	$0.479841\pi$
$62$	0.356542	0.0452808
$63$	0	0
$64$	−0.456423	−0.0570529
$65$	11.9251	1.47912
$66$	0	0
$67$	−5.41745	−0.661846	−0.330923	−	0.943658i	$-0.607360\pi$
$67$	−5.41745	−0.661846	−0.330923	+	0.943658i	$0.607360\pi$
$68$	3.19493	0.387442
$69$	−2.70087	−0.325146
$70$	0	0
$71$	−2.01705	−0.239380	−0.119690	−	0.992811i	$-0.538190\pi$
$71$	−2.01705	−0.239380	−0.119690	+	0.992811i	$0.538190\pi$
$72$	3.91151	0.460976
$73$	9.97108	1.16703	0.583513	−	0.812104i	$-0.301678\pi$
$73$	9.97108	1.16703	0.583513	+	0.812104i	$0.301678\pi$
$74$	1.84055	0.213960
$75$	−1.67760	−0.193713
$76$	−2.24828	−0.257896
$77$	0	0
$78$	−4.71658	−0.534047
$79$	6.29348	0.708071	0.354036	−	0.935232i	$-0.384809\pi$
$79$	6.29348	0.708071	0.354036	+	0.935232i	$0.384809\pi$
$80$	−13.8168	−1.54477
$81$	5.70820	0.634245
$82$	−17.0748	−1.88560
$83$	1.72146	0.188955	0.0944773	−	0.995527i	$-0.469882\pi$
$83$	1.72146	0.188955	0.0944773	+	0.995527i	$0.469882\pi$
$84$	0	0
$85$	7.65351	0.830140
$86$	−8.36876	−0.902426
$87$	−5.33245	−0.571699
$88$	0	0
$89$	15.3035	1.62217	0.811086	−	0.584928i	$-0.198877\pi$
$89$	15.3035	1.62217	0.811086	+	0.584928i	$0.198877\pi$
$90$	−12.9251	−1.36242
$91$	0	0
$92$	5.06691	0.528262
$93$	−0.123970	−0.0128551
$94$	23.1882	2.39168
$95$	−5.38581	−0.552572
$96$	3.61803	0.369264
$97$	−11.6162	−1.17945	−0.589724	−	0.807605i	$-0.700764\pi$
$97$	−11.6162	−1.17945	−0.589724	+	0.807605i	$0.700764\pi$
$98$	0	0
$99$	0	0
$100$	3.14723	0.314723
$101$	−3.41179	−0.339486	−0.169743	−	0.985488i	$-0.554294\pi$
$101$	−3.41179	−0.339486	−0.169743	+	0.985488i	$0.554294\pi$
$102$	−3.02710	−0.299728
$103$	18.1826	1.79158	0.895791	−	0.444475i	$-0.146610\pi$
$103$	18.1826	1.79158	0.895791	+	0.444475i	$0.146610\pi$
$104$	−6.41473	−0.629016
$105$	0	0
$106$	−6.93240	−0.673334
$107$	3.24746	0.313944	0.156972	−	0.987603i	$-0.449827\pi$
$107$	3.24746	0.313944	0.156972	+	0.987603i	$0.449827\pi$
$108$	4.02577	0.387380
$109$	12.6912	1.21559	0.607796	−	0.794093i	$-0.292054\pi$
$109$	12.6912	1.21559	0.607796	+	0.794093i	$0.292054\pi$
$110$	0	0
$111$	−0.639962	−0.0607425
$112$	0	0
$113$	−18.4480	−1.73545	−0.867723	−	0.497048i	$-0.834417\pi$
$113$	−18.4480	−1.73545	−0.867723	+	0.497048i	$0.834417\pi$
$114$	2.13018	0.199510
$115$	12.1379	1.13186
$116$	10.0038	0.928833
$117$	−11.2405	−1.03918
$118$	15.2102	1.40021
$119$	0	0
$120$	2.56468	0.234122
$121$	0	0
$122$	1.75724	0.159093
$123$	5.93693	0.535315
$124$	0.232572	0.0208855
$125$	−6.34817	−0.567797
$126$	0	0
$127$	19.5093	1.73117	0.865585	−	0.500762i	$-0.166947\pi$
$127$	19.5093	1.73117	0.865585	+	0.500762i	$0.166947\pi$
$128$	10.8969	0.963161
$129$	2.90983	0.256196
$130$	21.1966	1.85907
$131$	6.89796	0.602677	0.301339	−	0.953517i	$-0.402567\pi$
$131$	6.89796	0.602677	0.301339	+	0.953517i	$0.402567\pi$
$132$	0	0
$133$	0	0
$134$	−9.62943	−0.831856
$135$	9.64380	0.830006
$136$	−4.11698	−0.353028
$137$	−2.61070	−0.223047	−0.111523	−	0.993762i	$-0.535573\pi$
$137$	−2.61070	−0.223047	−0.111523	+	0.993762i	$0.535573\pi$
$138$	−4.80075	−0.408667
$139$	1.00134	0.0849322	0.0424661	−	0.999098i	$-0.486479\pi$
$139$	1.00134	0.0849322	0.0424661	+	0.999098i	$0.486479\pi$
$140$	0	0
$141$	−8.06258	−0.678992
$142$	−3.58527	−0.300869
$143$	0	0
$144$	13.0236	1.08530
$145$	23.9644	1.99013
$146$	17.7234	1.46680
$147$	0	0
$148$	1.20059	0.0986877
$149$	−14.8948	−1.22023	−0.610113	−	0.792314i	$-0.708876\pi$
$149$	−14.8948	−1.22023	−0.610113	+	0.792314i	$0.708876\pi$
$150$	−2.98191	−0.243472
$151$	15.8046	1.28616	0.643080	−	0.765799i	$-0.277656\pi$
$151$	15.8046	1.28616	0.643080	+	0.765799i	$0.277656\pi$
$152$	2.89713	0.234988
$153$	−7.21414	−0.583229
$154$	0	0
$155$	0.557129	0.0447497
$156$	−3.07662	−0.246327
$157$	−4.59123	−0.366420	−0.183210	−	0.983074i	$-0.558649\pi$
$157$	−4.59123	−0.366420	−0.183210	+	0.983074i	$0.558649\pi$
$158$	11.1866	0.889955
$159$	2.41041	0.191158
$160$	−16.2597	−1.28544
$161$	0	0
$162$	10.1462	0.797164
$163$	8.03764	0.629557	0.314778	−	0.949165i	$-0.398070\pi$
$163$	8.03764	0.629557	0.314778	+	0.949165i	$0.398070\pi$
$164$	−11.1379	−0.869721
$165$	0	0
$166$	3.05987	0.237492
$167$	13.4069	1.03746	0.518729	−	0.854939i	$-0.326405\pi$
$167$	13.4069	1.03746	0.518729	+	0.854939i	$0.326405\pi$
$168$	0	0
$169$	5.43394	0.417995
$170$	13.6040	1.04338
$171$	5.07662	0.388219
$172$	−5.45893	−0.416239
$173$	20.5821	1.56483	0.782413	−	0.622760i	$-0.213989\pi$
$173$	20.5821	1.56483	0.782413	+	0.622760i	$0.213989\pi$
$174$	−9.47835	−0.718552
$175$	0	0
$176$	0	0
$177$	−5.28860	−0.397515
$178$	27.2018	2.03886
$179$	−3.71520	−0.277687	−0.138843	−	0.990314i	$-0.544338\pi$
$179$	−3.71520	−0.277687	−0.138843	+	0.990314i	$0.544338\pi$
$180$	−8.43100	−0.628410
$181$	−4.77183	−0.354687	−0.177344	−	0.984149i	$-0.556750\pi$
$181$	−4.77183	−0.354687	−0.177344	+	0.984149i	$0.556750\pi$
$182$	0	0
$183$	−0.610994	−0.0451660
$184$	−6.52920	−0.481339
$185$	2.87603	0.211450
$186$	−0.220355	−0.0161572
$187$	0	0
$188$	15.1257	1.10315
$189$	0	0
$190$	−9.57319	−0.694512
$191$	−0.829158	−0.0599958	−0.0299979	−	0.999550i	$-0.509550\pi$
$191$	−0.829158	−0.0599958	−0.0299979	+	0.999550i	$0.509550\pi$
$192$	0.282085	0.0203577
$193$	−6.73803	−0.485014	−0.242507	−	0.970150i	$-0.577970\pi$
$193$	−6.73803	−0.485014	−0.242507	+	0.970150i	$0.577970\pi$
$194$	−20.6476	−1.48241
$195$	−7.37009	−0.527783
$196$	0	0
$197$	−10.9216	−0.778129	−0.389065	−	0.921210i	$-0.627202\pi$
$197$	−10.9216	−0.778129	−0.389065	+	0.921210i	$0.627202\pi$
$198$	0	0
$199$	−20.9746	−1.48685	−0.743424	−	0.668820i	$-0.766800\pi$
$199$	−20.9746	−1.48685	−0.743424	+	0.668820i	$0.766800\pi$
$200$	−4.05552	−0.286768
$201$	3.34817	0.236161
$202$	−6.06440	−0.426690
$203$	0	0
$204$	−1.97458	−0.138248
$205$	−26.6810	−1.86348
$206$	32.3192	2.25179
$207$	−11.4411	−0.795208
$208$	−21.3582	−1.48093
$209$	0	0
$210$	0	0
$211$	−6.02361	−0.414682	−0.207341	−	0.978269i	$-0.566481\pi$
$211$	−6.02361	−0.414682	−0.207341	+	0.978269i	$0.566481\pi$
$212$	−4.52199	−0.310572
$213$	1.24660	0.0854159
$214$	5.77231	0.394587
$215$	−13.0770	−0.891841
$216$	−5.18759	−0.352971
$217$	0	0
$218$	22.5583	1.52784
$219$	−6.16247	−0.416421
$220$	0	0
$221$	11.8309	0.795833
$222$	−1.13752	−0.0763455
$223$	4.62507	0.309718	0.154859	−	0.987937i	$-0.450508\pi$
$223$	4.62507	0.309718	0.154859	+	0.987937i	$0.450508\pi$
$224$	0	0
$225$	−7.10644	−0.473763
$226$	−32.7911	−2.18123
$227$	−17.3003	−1.14826	−0.574132	−	0.818763i	$-0.694660\pi$
$227$	−17.3003	−1.14826	−0.574132	+	0.818763i	$0.694660\pi$
$228$	1.38952	0.0920230
$229$	4.42612	0.292486	0.146243	−	0.989249i	$-0.453282\pi$
$229$	4.42612	0.292486	0.146243	+	0.989249i	$0.453282\pi$
$230$	21.5749	1.42260
$231$	0	0
$232$	−12.8909	−0.846330
$233$	−10.5330	−0.690042	−0.345021	−	0.938595i	$-0.612128\pi$
$233$	−10.5330	−0.690042	−0.345021	+	0.938595i	$0.612128\pi$
$234$	−19.9798	−1.30612
$235$	36.2338	2.36363
$236$	9.92157	0.645839
$237$	−3.88958	−0.252656
$238$	0	0
$239$	−9.75646	−0.631093	−0.315546	−	0.948910i	$-0.602188\pi$
$239$	−9.75646	−0.631093	−0.315546	+	0.948910i	$0.602188\pi$
$240$	8.53926	0.551207
$241$	−12.5501	−0.808422	−0.404211	−	0.914666i	$-0.632454\pi$
$241$	−12.5501	−0.808422	−0.404211	+	0.914666i	$0.632454\pi$
$242$	0	0
$243$	−13.9443	−0.894525
$244$	1.14624	0.0733807
$245$	0	0
$246$	10.5528	0.672822
$247$	−8.32546	−0.529736
$248$	−0.299691	−0.0190304
$249$	−1.06392	−0.0674232
$250$	−11.2838	−0.713648
$251$	10.9912	0.693758	0.346879	−	0.937910i	$-0.387241\pi$
$251$	10.9912	0.693758	0.346879	+	0.937910i	$0.387241\pi$
$252$	0	0
$253$	0	0
$254$	34.6775	2.17586
$255$	−4.73013	−0.296212
$256$	20.2819	1.26762
$257$	−5.33280	−0.332651	−0.166325	−	0.986071i	$-0.553190\pi$
$257$	−5.33280	−0.332651	−0.166325	+	0.986071i	$0.553190\pi$
$258$	5.17218	0.322006
$259$	0	0
$260$	13.8265	0.857484
$261$	−22.5886	−1.39820
$262$	12.2610	0.757488
$263$	−8.18034	−0.504421	−0.252211	−	0.967672i	$-0.581158\pi$
$263$	−8.18034	−0.504421	−0.252211	+	0.967672i	$0.581158\pi$
$264$	0	0
$265$	−10.8325	−0.665436
$266$	0	0
$267$	−9.45810	−0.578826
$268$	−6.28126	−0.383689
$269$	−12.8439	−0.783107	−0.391554	−	0.920155i	$-0.628062\pi$
$269$	−12.8439	−0.783107	−0.391554	+	0.920155i	$0.628062\pi$
$270$	17.1417	1.04321
$271$	22.0472	1.33927	0.669636	−	0.742689i	$-0.266450\pi$
$271$	22.0472	1.33927	0.669636	+	0.742689i	$0.266450\pi$
$272$	−13.7077	−0.831153
$273$	0	0
$274$	−4.64047	−0.280341
$275$	0	0
$276$	−3.13152	−0.188495
$277$	24.0770	1.44664	0.723322	−	0.690511i	$-0.242614\pi$
$277$	24.0770	1.44664	0.723322	+	0.690511i	$0.242614\pi$
$278$	1.77986	0.106749
$279$	−0.525146	−0.0314396
$280$	0	0
$281$	15.4418	0.921182	0.460591	−	0.887612i	$-0.347637\pi$
$281$	15.4418	0.921182	0.460591	+	0.887612i	$0.347637\pi$
$282$	−14.3311	−0.853406
$283$	3.35732	0.199572	0.0997860	−	0.995009i	$-0.468184\pi$
$283$	3.35732	0.199572	0.0997860	+	0.995009i	$0.468184\pi$
$284$	−2.33867	−0.138774
$285$	3.32861	0.197170
$286$	0	0
$287$	0	0
$288$	15.3262	0.903107
$289$	−9.40691	−0.553348
$290$	42.5963	2.50134
$291$	7.17922	0.420853
$292$	11.5610	0.676555
$293$	−6.83705	−0.399425	−0.199712	−	0.979855i	$-0.564001\pi$
$293$	−6.83705	−0.399425	−0.199712	+	0.979855i	$0.564001\pi$
$294$	0	0
$295$	23.7673	1.38379
$296$	−1.54707	−0.0899218
$297$	0	0
$298$	−26.4752	−1.53367
$299$	18.7629	1.08509
$300$	−1.94510	−0.112300
$301$	0	0
$302$	28.0924	1.61654
$303$	2.10860	0.121136
$304$	9.64618	0.553246
$305$	2.74585	0.157227
$306$	−12.8230	−0.733043
$307$	11.7970	0.673293	0.336646	−	0.941631i	$-0.390707\pi$
$307$	11.7970	0.673293	0.336646	+	0.941631i	$0.390707\pi$
$308$	0	0
$309$	−11.2375	−0.639276
$310$	0.990289	0.0562446
$311$	−25.3139	−1.43542	−0.717709	−	0.696343i	$-0.754809\pi$
$311$	−25.3139	−1.43542	−0.717709	+	0.696343i	$0.754809\pi$
$312$	3.96452	0.224447
$313$	19.6543	1.11093	0.555464	−	0.831540i	$-0.312540\pi$
$313$	19.6543	1.11093	0.555464	+	0.831540i	$0.312540\pi$
$314$	−8.16083	−0.460542
$315$	0	0
$316$	7.29697	0.410487
$317$	3.61056	0.202789	0.101395	−	0.994846i	$-0.467670\pi$
$317$	3.61056	0.202789	0.101395	+	0.994846i	$0.467670\pi$
$318$	4.28446	0.240261
$319$	0	0
$320$	−1.26771	−0.0708670
$321$	−2.00704	−0.112022
$322$	0	0
$323$	−5.34329	−0.297308
$324$	6.61838	0.367688
$325$	11.6543	0.646464
$326$	14.2868	0.791272
$327$	−7.84357	−0.433750
$328$	14.3522	0.792469
$329$	0	0
$330$	0	0
$331$	−26.5335	−1.45841	−0.729205	−	0.684295i	$-0.760110\pi$
$331$	−26.5335	−1.45841	−0.729205	+	0.684295i	$0.760110\pi$
$332$	1.99595	0.109542
$333$	−2.71092	−0.148558
$334$	23.8306	1.30395
$335$	−15.0469	−0.822098
$336$	0	0
$337$	−0.685979	−0.0373676	−0.0186838	−	0.999825i	$-0.505948\pi$
$337$	−0.685979	−0.0373676	−0.0186838	+	0.999825i	$0.505948\pi$
$338$	9.65874	0.525366
$339$	11.4015	0.619246
$340$	8.87387	0.481253
$341$	0	0
$342$	9.02361	0.487941
$343$	0	0
$344$	7.03436	0.379267
$345$	−7.50161	−0.403873
$346$	36.5843	1.96678
$347$	21.5055	1.15447	0.577237	−	0.816577i	$-0.304131\pi$
$347$	21.5055	1.15447	0.577237	+	0.816577i	$0.304131\pi$
$348$	−6.18271	−0.331428
$349$	−19.4429	−1.04075	−0.520377	−	0.853937i	$-0.674208\pi$
$349$	−19.4429	−1.04075	−0.520377	+	0.853937i	$0.674208\pi$
$350$	0	0
$351$	14.9075	0.795705
$352$	0	0
$353$	20.9307	1.11403	0.557015	−	0.830502i	$-0.311947\pi$
$353$	20.9307	1.11403	0.557015	+	0.830502i	$0.311947\pi$
$354$	−9.40040	−0.499625
$355$	−5.60232	−0.297340
$356$	17.7437	0.940413
$357$	0	0
$358$	−6.60370	−0.349017
$359$	9.77127	0.515708	0.257854	−	0.966184i	$-0.416985\pi$
$359$	9.77127	0.515708	0.257854	+	0.966184i	$0.416985\pi$
$360$	10.8642	0.572591
$361$	−15.2399	−0.802100
$362$	−8.48185	−0.445796
$363$	0	0
$364$	0	0
$365$	27.6945	1.44960
$366$	−1.08603	−0.0567678
$367$	−9.89969	−0.516759	−0.258380	−	0.966043i	$-0.583189\pi$
$367$	−9.89969	−0.516759	−0.258380	+	0.966043i	$0.583189\pi$
$368$	−21.7394	−1.13324
$369$	25.1493	1.30922
$370$	5.11210	0.265765
$371$	0	0
$372$	−0.143737	−0.00745242
$373$	−4.27475	−0.221338	−0.110669	−	0.993857i	$-0.535299\pi$
$373$	−4.27475	−0.221338	−0.110669	+	0.993857i	$0.535299\pi$
$374$	0	0
$375$	3.92338	0.202603
$376$	−19.4909	−1.00516
$377$	37.0445	1.90789
$378$	0	0
$379$	4.32594	0.222209	0.111104	−	0.993809i	$-0.464561\pi$
$379$	4.32594	0.222209	0.111104	+	0.993809i	$0.464561\pi$
$380$	−6.24458	−0.320340
$381$	−12.0574	−0.617720
$382$	−1.47382	−0.0754070
$383$	1.32210	0.0675561	0.0337781	−	0.999429i	$-0.489246\pi$
$383$	1.32210	0.0675561	0.0337781	+	0.999429i	$0.489246\pi$
$384$	−6.73467	−0.343677
$385$	0	0
$386$	−11.9767	−0.609600
$387$	12.3262	0.626578
$388$	−13.4684	−0.683756
$389$	−38.5092	−1.95249	−0.976246	−	0.216665i	$-0.930482\pi$
$389$	−38.5092	−1.95249	−0.976246	+	0.216665i	$0.930482\pi$
$390$	−13.1002	−0.663356
$391$	12.0420	0.608992
$392$	0	0
$393$	−4.26317	−0.215049
$394$	−19.4129	−0.978008
$395$	17.4800	0.879516
$396$	0	0
$397$	0.410109	0.0205828	0.0102914	−	0.999947i	$-0.496724\pi$
$397$	0.410109	0.0205828	0.0102914	+	0.999947i	$0.496724\pi$
$398$	−37.2820	−1.86878
$399$	0	0
$400$	−13.5031	−0.675154
$401$	−1.56684	−0.0782443	−0.0391221	−	0.999234i	$-0.512456\pi$
$401$	−1.56684	−0.0782443	−0.0391221	+	0.999234i	$0.512456\pi$
$402$	5.95131	0.296824
$403$	0.861219	0.0429004
$404$	−3.95580	−0.196808
$405$	15.8544	0.787814
$406$	0	0
$407$	0	0
$408$	2.54443	0.125968
$409$	6.77852	0.335176	0.167588	−	0.985857i	$-0.446402\pi$
$409$	6.77852	0.335176	0.167588	+	0.985857i	$0.446402\pi$
$410$	−47.4250	−2.34215
$411$	1.61350	0.0795880
$412$	21.0818	1.03863
$413$	0	0
$414$	−20.3363	−0.999474
$415$	4.78133	0.234706
$416$	−25.1344	−1.23232
$417$	−0.618859	−0.0303057
$418$	0	0
$419$	−28.7218	−1.40315	−0.701577	−	0.712594i	$-0.747520\pi$
$419$	−28.7218	−1.40315	−0.701577	+	0.712594i	$0.747520\pi$
$420$	0	0
$421$	12.2256	0.595838	0.297919	−	0.954591i	$-0.403707\pi$
$421$	12.2256	0.595838	0.297919	+	0.954591i	$0.403707\pi$
$422$	−10.7069	−0.521202
$423$	−34.1537	−1.66061
$424$	5.82703	0.282985
$425$	7.47973	0.362820
$426$	2.21582	0.107357
$427$	0	0
$428$	3.76527	0.182001
$429$	0	0
$430$	−23.2441	−1.12093
$431$	3.69129	0.177803	0.0889016	−	0.996040i	$-0.471664\pi$
$431$	3.69129	0.177803	0.0889016	+	0.996040i	$0.471664\pi$
$432$	−17.2724	−0.831019
$433$	−29.0749	−1.39725	−0.698625	−	0.715488i	$-0.746204\pi$
$433$	−29.0749	−1.39725	−0.698625	+	0.715488i	$0.746204\pi$
$434$	0	0
$435$	−14.8108	−0.710124
$436$	14.7148	0.704709
$437$	−8.47403	−0.405368
$438$	−10.9537	−0.523387
$439$	14.2017	0.677811	0.338905	−	0.940820i	$-0.389943\pi$
$439$	14.2017	0.677811	0.338905	+	0.940820i	$0.389943\pi$
$440$	0	0
$441$	0	0
$442$	21.0293	1.00026
$443$	27.2356	1.29400	0.647001	−	0.762489i	$-0.276023\pi$
$443$	27.2356	1.29400	0.647001	+	0.762489i	$0.276023\pi$
$444$	−0.742004	−0.0352140
$445$	42.5053	2.01495
$446$	8.22100	0.389275
$447$	9.20547	0.435404
$448$	0	0
$449$	−41.9159	−1.97813	−0.989067	−	0.147467i	$-0.952888\pi$
$449$	−41.9159	−1.97813	−0.989067	+	0.147467i	$0.952888\pi$
$450$	−12.6316	−0.595459
$451$	0	0
$452$	−21.3896	−1.00608
$453$	−9.76777	−0.458930
$454$	−30.7511	−1.44322
$455$	0	0
$456$	−1.79053	−0.0838491
$457$	19.4977	0.912063	0.456032	−	0.889964i	$-0.349270\pi$
$457$	19.4977	0.912063	0.456032	+	0.889964i	$0.349270\pi$
$458$	7.86736	0.367617
$459$	9.56767	0.446580
$460$	14.0733	0.656169
$461$	−12.2251	−0.569380	−0.284690	−	0.958620i	$-0.591891\pi$
$461$	−12.2251	−0.569380	−0.284690	+	0.958620i	$0.591891\pi$
$462$	0	0
$463$	13.8550	0.643894	0.321947	−	0.946758i	$-0.395663\pi$
$463$	13.8550	0.643894	0.321947	+	0.946758i	$0.395663\pi$
$464$	−42.9211	−1.99256
$465$	−0.344325	−0.0159677
$466$	−18.7223	−0.867294
$467$	16.4207	0.759861	0.379930	−	0.925015i	$-0.375948\pi$
$467$	16.4207	0.759861	0.379930	+	0.925015i	$0.375948\pi$
$468$	−13.0328	−0.602440
$469$	0	0
$470$	64.4050	2.97078
$471$	2.83753	0.130747
$472$	−12.7849	−0.588473
$473$	0	0
$474$	−6.91367	−0.317555
$475$	−5.26352	−0.241507
$476$	0	0
$477$	10.2106	0.467513
$478$	−17.3420	−0.793202
$479$	24.7914	1.13275	0.566374	−	0.824149i	$-0.308346\pi$
$479$	24.7914	1.13275	0.566374	+	0.824149i	$0.308346\pi$
$480$	10.0490	0.458673
$481$	4.44581	0.202711
$482$	−22.3076	−1.01608
$483$	0	0
$484$	0	0
$485$	−32.2639	−1.46503
$486$	−24.7857	−1.12430
$487$	−14.3342	−0.649544	−0.324772	−	0.945792i	$-0.605288\pi$
$487$	−14.3342	−0.649544	−0.324772	+	0.945792i	$0.605288\pi$
$488$	−1.47704	−0.0668627
$489$	−4.96754	−0.224640
$490$	0	0
$491$	−22.0193	−0.993719	−0.496859	−	0.867831i	$-0.665514\pi$
$491$	−22.0193	−0.993719	−0.496859	+	0.867831i	$0.665514\pi$
$492$	6.88358	0.310336
$493$	23.7752	1.07078
$494$	−14.7984	−0.665810
$495$	0	0
$496$	−0.997839	−0.0448043
$497$	0	0
$498$	−1.89110	−0.0847423
$499$	−25.3117	−1.13311	−0.566554	−	0.824024i	$-0.691724\pi$
$499$	−25.3117	−1.13311	−0.566554	+	0.824024i	$0.691724\pi$
$500$	−7.36038	−0.329166
$501$	−8.28593	−0.370188
$502$	19.5367	0.871964
$503$	26.0214	1.16024	0.580119	−	0.814531i	$-0.303006\pi$
$503$	26.0214	1.16024	0.580119	+	0.814531i	$0.303006\pi$
$504$	0	0
$505$	−9.47619	−0.421685
$506$	0	0
$507$	−3.35836	−0.149150
$508$	22.6201	1.00360
$509$	−38.1269	−1.68994	−0.844972	−	0.534810i	$-0.820383\pi$
$509$	−38.1269	−1.68994	−0.844972	+	0.534810i	$0.820383\pi$
$510$	−8.40773	−0.372301
$511$	0	0
$512$	14.2570	0.630077
$513$	−6.73280	−0.297261
$514$	−9.47896	−0.418099
$515$	50.5018	2.22538
$516$	3.37380	0.148523
$517$	0	0
$518$	0	0
$519$	−12.7204	−0.558364
$520$	−17.8168	−0.781319
$521$	26.0420	1.14092	0.570460	−	0.821325i	$-0.306765\pi$
$521$	26.0420	1.14092	0.570460	+	0.821325i	$0.306765\pi$
$522$	−40.1509	−1.75736
$523$	−19.1230	−0.836189	−0.418095	−	0.908403i	$-0.637302\pi$
$523$	−19.1230	−0.836189	−0.418095	+	0.908403i	$0.637302\pi$
$524$	7.99784	0.349387
$525$	0	0
$526$	−14.5404	−0.633993
$527$	0.552731	0.0240773
$528$	0	0
$529$	−3.90228	−0.169664
$530$	−19.2546	−0.836368
$531$	−22.4029	−0.972201
$532$	0	0
$533$	−41.2438	−1.78647
$534$	−16.8116	−0.727510
$535$	9.01977	0.389959
$536$	8.09401	0.349608
$537$	2.29612	0.0990848
$538$	−22.8298	−0.984265
$539$	0	0
$540$	11.1815	0.481176
$541$	10.8860	0.468027	0.234014	−	0.972233i	$-0.424814\pi$
$541$	10.8860	0.468027	0.234014	+	0.972233i	$0.424814\pi$
$542$	39.1886	1.68329
$543$	2.94915	0.126560
$544$	−16.1313	−0.691624
$545$	35.2495	1.50992
$546$	0	0
$547$	−12.9091	−0.551951	−0.275976	−	0.961165i	$-0.589001\pi$
$547$	−12.9091	−0.551951	−0.275976	+	0.961165i	$0.589001\pi$
$548$	−3.02697	−0.129306
$549$	−2.58821	−0.110462
$550$	0	0
$551$	−16.7307	−0.712751
$552$	4.03527	0.171752
$553$	0	0
$554$	42.7964	1.81825
$555$	−1.77748	−0.0754500
$556$	1.16100	0.0492373
$557$	−0.762626	−0.0323135	−0.0161567	−	0.999869i	$-0.505143\pi$
$557$	−0.762626	−0.0323135	−0.0161567	+	0.999869i	$0.505143\pi$
$558$	−0.933438	−0.0395156
$559$	−20.2146	−0.854985
$560$	0	0
$561$	0	0
$562$	27.4476	1.15781
$563$	22.2281	0.936803	0.468402	−	0.883516i	$-0.344830\pi$
$563$	22.2281	0.936803	0.468402	+	0.883516i	$0.344830\pi$
$564$	−9.34817	−0.393629
$565$	−51.2392	−2.15565
$566$	5.96758	0.250836
$567$	0	0
$568$	3.01360	0.126448
$569$	−20.5131	−0.859955	−0.429978	−	0.902839i	$-0.641479\pi$
$569$	−20.5131	−0.859955	−0.429978	+	0.902839i	$0.641479\pi$
$570$	5.91656	0.247817
$571$	−19.5654	−0.818785	−0.409393	−	0.912358i	$-0.634259\pi$
$571$	−19.5654	−0.818785	−0.409393	+	0.912358i	$0.634259\pi$
$572$	0	0
$573$	0.512448	0.0214078
$574$	0	0
$575$	11.8623	0.494691
$576$	1.19493	0.0497888
$577$	19.5716	0.814776	0.407388	−	0.913255i	$-0.366440\pi$
$577$	19.5716	0.814776	0.407388	+	0.913255i	$0.366440\pi$
$578$	−16.7206	−0.695487
$579$	4.16433	0.173064
$580$	27.7855	1.15373
$581$	0	0
$582$	12.7609	0.528958
$583$	0	0
$584$	−14.8974	−0.616460
$585$	−31.2202	−1.29080
$586$	−12.1528	−0.502026
$587$	−1.57068	−0.0648290	−0.0324145	−	0.999475i	$-0.510320\pi$
$587$	−1.57068	−0.0648290	−0.0324145	+	0.999475i	$0.510320\pi$
$588$	0	0
$589$	−0.388959	−0.0160268
$590$	42.2460	1.73924
$591$	6.74990	0.277654
$592$	−5.15107	−0.211708
$593$	30.1230	1.23700	0.618502	−	0.785783i	$-0.287740\pi$
$593$	30.1230	1.23700	0.618502	+	0.785783i	$0.287740\pi$
$594$	0	0
$595$	0	0
$596$	−17.2697	−0.707396
$597$	12.9630	0.530540
$598$	33.3507	1.36381
$599$	5.77792	0.236079	0.118040	−	0.993009i	$-0.462339\pi$
$599$	5.77792	0.236079	0.118040	+	0.993009i	$0.462339\pi$
$600$	2.50645	0.102325
$601$	−45.5645	−1.85862	−0.929308	−	0.369305i	$-0.879596\pi$
$601$	−45.5645	−1.85862	−0.929308	+	0.369305i	$0.879596\pi$
$602$	0	0
$603$	14.1831	0.577579
$604$	18.3246	0.745619
$605$	0	0
$606$	3.74801	0.152252
$607$	−34.7211	−1.40928	−0.704642	−	0.709563i	$-0.748892\pi$
$607$	−34.7211	−1.40928	−0.704642	+	0.709563i	$0.748892\pi$
$608$	11.3517	0.460371
$609$	0	0
$610$	4.88070	0.197614
$611$	56.0107	2.26595
$612$	−8.36444	−0.338112
$613$	−24.1423	−0.975097	−0.487548	−	0.873096i	$-0.662109\pi$
$613$	−24.1423	−0.975097	−0.487548	+	0.873096i	$0.662109\pi$
$614$	20.9690	0.846242
$615$	16.4897	0.664931
$616$	0	0
$617$	−13.4967	−0.543358	−0.271679	−	0.962388i	$-0.587579\pi$
$617$	−13.4967	−0.543358	−0.271679	+	0.962388i	$0.587579\pi$
$618$	−19.9744	−0.803488
$619$	43.4856	1.74783	0.873917	−	0.486074i	$-0.161572\pi$
$619$	43.4856	1.74783	0.873917	+	0.486074i	$0.161572\pi$
$620$	0.645964	0.0259425
$621$	15.1736	0.608894
$622$	−44.9950	−1.80414
$623$	0	0
$624$	13.2001	0.528427
$625$	−31.2040	−1.24816
$626$	34.9353	1.39629
$627$	0	0
$628$	−5.32330	−0.212423
$629$	2.85332	0.113769
$630$	0	0
$631$	6.42012	0.255581	0.127790	−	0.991801i	$-0.459212\pi$
$631$	6.42012	0.255581	0.127790	+	0.991801i	$0.459212\pi$
$632$	−9.40286	−0.374026
$633$	3.72279	0.147968
$634$	6.41771	0.254880
$635$	54.1868	2.15034
$636$	2.79475	0.110819
$637$	0	0
$638$	0	0
$639$	5.28070	0.208901
$640$	30.2660	1.19637
$641$	−6.39600	−0.252627	−0.126313	−	0.991990i	$-0.540314\pi$
$641$	−6.39600	−0.252627	−0.126313	+	0.991990i	$0.540314\pi$
$642$	−3.56748	−0.140797
$643$	−0.652660	−0.0257384	−0.0128692	−	0.999917i	$-0.504097\pi$
$643$	−0.652660	−0.0257384	−0.0128692	+	0.999917i	$0.504097\pi$
$644$	0	0
$645$	8.08201	0.318229
$646$	−9.49761	−0.373678
$647$	−17.9621	−0.706165	−0.353082	−	0.935592i	$-0.614866\pi$
$647$	−17.9621	−0.706165	−0.353082	+	0.935592i	$0.614866\pi$
$648$	−8.52842	−0.335028
$649$	0	0
$650$	20.7153	0.812522
$651$	0	0
$652$	9.31925	0.364970
$653$	−16.9181	−0.662055	−0.331028	−	0.943621i	$-0.607395\pi$
$653$	−16.9181	−0.662055	−0.331028	+	0.943621i	$0.607395\pi$
$654$	−13.9418	−0.545168
$655$	19.1590	0.748603
$656$	47.7866	1.86575
$657$	−26.1046	−1.01844
$658$	0	0
$659$	23.6249	0.920297	0.460148	−	0.887842i	$-0.347796\pi$
$659$	23.6249	0.920297	0.460148	+	0.887842i	$0.347796\pi$
$660$	0	0
$661$	20.9819	0.816103	0.408051	−	0.912959i	$-0.366208\pi$
$661$	20.9819	0.816103	0.408051	+	0.912959i	$0.366208\pi$
$662$	−47.1628	−1.83303
$663$	−7.31191	−0.283971
$664$	−2.57197	−0.0998118
$665$	0	0
$666$	−4.81862	−0.186718
$667$	37.7056	1.45997
$668$	15.5446	0.601440
$669$	−2.85845	−0.110514
$670$	−26.7456	−1.03327
$671$	0	0
$672$	0	0
$673$	12.0986	0.466368	0.233184	−	0.972433i	$-0.425086\pi$
$673$	12.0986	0.466368	0.233184	+	0.972433i	$0.425086\pi$
$674$	−1.21932	−0.0469663
$675$	9.42483	0.362762
$676$	6.30038	0.242322
$677$	9.42988	0.362420	0.181210	−	0.983444i	$-0.441999\pi$
$677$	9.42988	0.362420	0.181210	+	0.983444i	$0.441999\pi$
$678$	20.2660	0.778312
$679$	0	0
$680$	−11.4348	−0.438506
$681$	10.6922	0.409726
$682$	0	0
$683$	−15.2986	−0.585385	−0.292692	−	0.956207i	$-0.594551\pi$
$683$	−15.2986	−0.585385	−0.292692	+	0.956207i	$0.594551\pi$
$684$	5.88609	0.225060
$685$	−7.25117	−0.277053
$686$	0	0
$687$	−2.73549	−0.104366
$688$	23.4213	0.892929
$689$	−16.7451	−0.637936
$690$	−13.3340	−0.507617
$691$	−22.8193	−0.868086	−0.434043	−	0.900892i	$-0.642913\pi$
$691$	−22.8193	−0.868086	−0.434043	+	0.900892i	$0.642913\pi$
$692$	23.8639	0.907169
$693$	0	0
$694$	38.2256	1.45102
$695$	2.78119	0.105497
$696$	7.96703	0.301989
$697$	−26.4703	−1.00263
$698$	−34.5594	−1.30809
$699$	6.50978	0.246222
$700$	0	0
$701$	−32.3242	−1.22087	−0.610433	−	0.792068i	$-0.709005\pi$
$701$	−32.3242	−1.22087	−0.610433	+	0.792068i	$0.709005\pi$
$702$	26.4979	1.00010
$703$	−2.00789	−0.0757292
$704$	0	0
$705$	−22.3937	−0.843396
$706$	37.2040	1.40019
$707$	0	0
$708$	−6.13186	−0.230450
$709$	14.5598	0.546804	0.273402	−	0.961900i	$-0.411851\pi$
$709$	14.5598	0.546804	0.273402	+	0.961900i	$0.411851\pi$
$710$	−9.95804	−0.373718
$711$	−16.4765	−0.617918
$712$	−22.8645	−0.856882
$713$	0.876587	0.0328285
$714$	0	0
$715$	0	0
$716$	−4.30759	−0.160982
$717$	6.02982	0.225188
$718$	17.3683	0.648178
$719$	−44.8602	−1.67300	−0.836501	−	0.547965i	$-0.815403\pi$
$719$	−44.8602	−1.67300	−0.836501	+	0.547965i	$0.815403\pi$
$720$	36.1729	1.34808
$721$	0	0
$722$	−27.0887	−1.00814
$723$	7.75638	0.288463
$724$	−5.53270	−0.205621
$725$	23.4202	0.869806
$726$	0	0
$727$	−28.3582	−1.05175	−0.525874	−	0.850562i	$-0.676262\pi$
$727$	−28.3582	−1.05175	−0.525874	+	0.850562i	$0.676262\pi$
$728$	0	0
$729$	−8.50658	−0.315058
$730$	49.2266	1.82196
$731$	−12.9737	−0.479850
$732$	−0.708417	−0.0261838
$733$	−6.25696	−0.231106	−0.115553	−	0.993301i	$-0.536864\pi$
$733$	−6.25696	−0.231106	−0.115553	+	0.993301i	$0.536864\pi$
$734$	−17.5965	−0.649500
$735$	0	0
$736$	−25.5830	−0.943001
$737$	0	0
$738$	44.7024	1.64552
$739$	9.35201	0.344019	0.172010	−	0.985095i	$-0.444974\pi$
$739$	9.35201	0.344019	0.172010	+	0.985095i	$0.444974\pi$
$740$	3.33461	0.122583
$741$	5.14542	0.189022
$742$	0	0
$743$	25.2066	0.924740	0.462370	−	0.886687i	$-0.346999\pi$
$743$	25.2066	0.924740	0.462370	+	0.886687i	$0.346999\pi$
$744$	0.185219	0.00679047
$745$	−41.3700	−1.51568
$746$	−7.59830	−0.278193
$747$	−4.50684	−0.164897
$748$	0	0
$749$	0	0
$750$	6.97375	0.254645
$751$	−34.7493	−1.26802	−0.634010	−	0.773325i	$-0.718592\pi$
$751$	−34.7493	−1.26802	−0.634010	+	0.773325i	$0.718592\pi$
$752$	−64.8960	−2.36651
$753$	−6.79293	−0.247548
$754$	65.8460	2.39797
$755$	43.8970	1.59758
$756$	0	0
$757$	34.7960	1.26468	0.632341	−	0.774690i	$-0.282094\pi$
$757$	34.7960	1.26468	0.632341	+	0.774690i	$0.282094\pi$
$758$	7.68929	0.279288
$759$	0	0
$760$	8.04674	0.291886
$761$	12.2255	0.443172	0.221586	−	0.975141i	$-0.428877\pi$
$761$	12.2255	0.443172	0.221586	+	0.975141i	$0.428877\pi$
$762$	−21.4319	−0.776394
$763$	0	0
$764$	−0.961368	−0.0347811
$765$	−20.0372	−0.724445
$766$	2.35001	0.0849094
$767$	36.7398	1.32660
$768$	−12.5349	−0.452315
$769$	2.61946	0.0944603	0.0472301	−	0.998884i	$-0.484961\pi$
$769$	2.61946	0.0944603	0.0472301	+	0.998884i	$0.484961\pi$
$770$	0	0
$771$	3.29585	0.118697
$772$	−7.81241	−0.281175
$773$	0.212804	0.00765405	0.00382702	−	0.999993i	$-0.498782\pi$
$773$	0.212804	0.00765405	0.00382702	+	0.999993i	$0.498782\pi$
$774$	21.9097	0.787528
$775$	0.544479	0.0195583
$776$	17.3554	0.623022
$777$	0	0
$778$	−68.4494	−2.45403
$779$	18.6273	0.667391
$780$	−8.54526	−0.305969
$781$	0	0
$782$	21.4045	0.765425
$783$	29.9579	1.07061
$784$	0	0
$785$	−12.7521	−0.455141
$786$	−7.57772	−0.270288
$787$	−29.1375	−1.03864	−0.519320	−	0.854580i	$-0.673815\pi$
$787$	−29.1375	−1.03864	−0.519320	+	0.854580i	$0.673815\pi$
$788$	−12.6630	−0.451101
$789$	5.05573	0.179989
$790$	31.0705	1.10544
$791$	0	0
$792$	0	0
$793$	4.24457	0.150729
$794$	0.728962	0.0258699
$795$	6.69486	0.237442
$796$	−24.3190	−0.861963
$797$	−32.2284	−1.14159	−0.570794	−	0.821093i	$-0.693365\pi$
$797$	−32.2284	−1.14159	−0.570794	+	0.821093i	$0.693365\pi$
$798$	0	0
$799$	35.9477	1.27174
$800$	−15.8905	−0.561813
$801$	−40.0652	−1.41563
$802$	−2.78503	−0.0983430
$803$	0	0
$804$	3.88203	0.136909
$805$	0	0
$806$	1.53080	0.0539202
$807$	7.93797	0.279430
$808$	5.09743	0.179327
$809$	−29.3461	−1.03175	−0.515877	−	0.856663i	$-0.672534\pi$
$809$	−29.3461	−1.03175	−0.515877	+	0.856663i	$0.672534\pi$
$810$	28.1810	0.990180
$811$	−1.03940	−0.0364982	−0.0182491	−	0.999833i	$-0.505809\pi$
$811$	−1.03940	−0.0364982	−0.0182491	+	0.999833i	$0.505809\pi$
$812$	0	0
$813$	−13.6259	−0.477882
$814$	0	0
$815$	22.3244	0.781990
$816$	8.47184	0.296574
$817$	9.12966	0.319406
$818$	12.0487	0.421274
$819$	0	0
$820$	−30.9352	−1.08031
$821$	28.5323	0.995786	0.497893	−	0.867239i	$-0.334107\pi$
$821$	28.5323	0.995786	0.497893	+	0.867239i	$0.334107\pi$
$822$	2.86797	0.100032
$823$	26.6577	0.929227	0.464614	−	0.885513i	$-0.346193\pi$
$823$	26.6577	0.929227	0.464614	+	0.885513i	$0.346193\pi$
$824$	−27.1659	−0.946370
$825$	0	0
$826$	0	0
$827$	1.71964	0.0597978	0.0298989	−	0.999553i	$-0.490481\pi$
$827$	1.71964	0.0597978	0.0298989	+	0.999553i	$0.490481\pi$
$828$	−13.2653	−0.461002
$829$	−27.9605	−0.971107	−0.485554	−	0.874207i	$-0.661382\pi$
$829$	−27.9605	−0.971107	−0.485554	+	0.874207i	$0.661382\pi$
$830$	8.49873	0.294995
$831$	−14.8804	−0.516195
$832$	−1.95964	−0.0679383
$833$	0	0
$834$	−1.10001	−0.0380903
$835$	37.2375	1.28866
$836$	0	0
$837$	0.696468	0.0240735
$838$	−51.0526	−1.76358
$839$	−35.8624	−1.23811	−0.619054	−	0.785348i	$-0.712484\pi$
$839$	−35.8624	−1.23811	−0.619054	+	0.785348i	$0.712484\pi$
$840$	0	0
$841$	45.4439	1.56703
$842$	21.7308	0.748892
$843$	−9.54358	−0.328698
$844$	−6.98407	−0.240402
$845$	15.0927	0.519204
$846$	−60.7076	−2.08717
$847$	0	0
$848$	19.4014	0.666248
$849$	−2.07494	−0.0712117
$850$	13.2951	0.456018
$851$	4.52515	0.155120
$852$	1.44538	0.0495178
$853$	15.1427	0.518478	0.259239	−	0.965813i	$-0.416528\pi$
$853$	15.1427	0.518478	0.259239	+	0.965813i	$0.416528\pi$
$854$	0	0
$855$	14.1002	0.482218
$856$	−4.85191	−0.165835
$857$	−25.3267	−0.865142	−0.432571	−	0.901600i	$-0.642394\pi$
$857$	−25.3267	−0.865142	−0.432571	+	0.901600i	$0.642394\pi$
$858$	0	0
$859$	−41.5291	−1.41696	−0.708478	−	0.705733i	$-0.750618\pi$
$859$	−41.5291	−1.41696	−0.708478	+	0.705733i	$0.750618\pi$
$860$	−15.1621	−0.517023
$861$	0	0
$862$	6.56121	0.223476
$863$	−24.0504	−0.818684	−0.409342	−	0.912381i	$-0.634242\pi$
$863$	−24.0504	−0.818684	−0.409342	+	0.912381i	$0.634242\pi$
$864$	−20.3262	−0.691513
$865$	57.1664	1.94372
$866$	−51.6801	−1.75616
$867$	5.81379	0.197447
$868$	0	0
$869$	0	0
$870$	−26.3260	−0.892534
$871$	−23.2597	−0.788124
$872$	−18.9614	−0.642114
$873$	30.4117	1.02928
$874$	−15.0625	−0.509495
$875$	0	0
$876$	−7.14507	−0.241410
$877$	33.8052	1.14152	0.570760	−	0.821117i	$-0.306649\pi$
$877$	33.8052	1.14152	0.570760	+	0.821117i	$0.306649\pi$
$878$	25.2433	0.851921
$879$	4.22553	0.142524
$880$	0	0
$881$	36.8296	1.24082	0.620410	−	0.784278i	$-0.286966\pi$
$881$	36.8296	1.24082	0.620410	+	0.784278i	$0.286966\pi$
$882$	0	0
$883$	53.4103	1.79740	0.898701	−	0.438563i	$-0.144512\pi$
$883$	53.4103	1.79740	0.898701	+	0.438563i	$0.144512\pi$
$884$	13.7174	0.461365
$885$	−14.6890	−0.493765
$886$	48.4108	1.62639
$887$	−11.4616	−0.384843	−0.192421	−	0.981312i	$-0.561634\pi$
$887$	−11.4616	−0.384843	−0.192421	+	0.981312i	$0.561634\pi$
$888$	0.956144	0.0320861
$889$	0	0
$890$	75.5525	2.53253
$891$	0	0
$892$	5.36254	0.179551
$893$	−25.2965	−0.846516
$894$	16.3626	0.547246
$895$	−10.3189	−0.344923
$896$	0	0
$897$	−11.5961	−0.387183
$898$	−74.5049	−2.48626
$899$	1.73069	0.0577217
$900$	−8.23956	−0.274652
$901$	−10.7470	−0.358034
$902$	0	0
$903$	0	0
$904$	27.5626	0.916717
$905$	−13.2537	−0.440567
$906$	−17.3621	−0.576816
$907$	57.0582	1.89459	0.947293	−	0.320369i	$-0.103807\pi$
$907$	57.0582	1.89459	0.947293	+	0.320369i	$0.103807\pi$
$908$	−20.0589	−0.665677
$909$	8.93218	0.296262
$910$	0	0
$911$	6.67566	0.221175	0.110587	−	0.993866i	$-0.464727\pi$
$911$	6.67566	0.221175	0.110587	+	0.993866i	$0.464727\pi$
$912$	−5.96167	−0.197410
$913$	0	0
$914$	34.6568	1.14635
$915$	−1.69703	−0.0561019
$916$	5.13186	0.169562
$917$	0	0
$918$	17.0064	0.561294
$919$	−29.1339	−0.961038	−0.480519	−	0.876984i	$-0.659552\pi$
$919$	−29.1339	−0.961038	−0.480519	+	0.876984i	$0.659552\pi$
$920$	−18.1347	−0.597885
$921$	−7.29097	−0.240246
$922$	−21.7299	−0.715637
$923$	−8.66015	−0.285052
$924$	0	0
$925$	2.81073	0.0924161
$926$	24.6270	0.809292
$927$	−47.6026	−1.56347
$928$	−50.5097	−1.65806
$929$	−2.34472	−0.0769277	−0.0384638	−	0.999260i	$-0.512246\pi$
$929$	−2.34472	−0.0769277	−0.0384638	+	0.999260i	$0.512246\pi$
$930$	−0.612032	−0.0200693
$931$	0	0
$932$	−12.2125	−0.400035
$933$	15.6448	0.512189
$934$	29.1876	0.955047
$935$	0	0
$936$	16.7940	0.548928
$937$	−8.78780	−0.287085	−0.143542	−	0.989644i	$-0.545849\pi$
$937$	−8.78780	−0.287085	−0.143542	+	0.989644i	$0.545849\pi$
$938$	0	0
$939$	−12.1470	−0.396404
$940$	42.0113	1.37026
$941$	−8.88871	−0.289764	−0.144882	−	0.989449i	$-0.546280\pi$
$941$	−8.88871	−0.289764	−0.144882	+	0.989449i	$0.546280\pi$
$942$	5.04367	0.164332
$943$	−41.9798	−1.36705
$944$	−42.5681	−1.38547
$945$	0	0
$946$	0	0
$947$	−7.86275	−0.255505	−0.127752	−	0.991806i	$-0.540776\pi$
$947$	−7.86275	−0.255505	−0.127752	+	0.991806i	$0.540776\pi$
$948$	−4.50978	−0.146471
$949$	42.8106	1.38969
$950$	−9.35582	−0.303543
$951$	−2.23145	−0.0723597
$952$	0	0
$953$	−17.4644	−0.565727	−0.282864	−	0.959160i	$-0.591284\pi$
$953$	−17.4644	−0.565727	−0.282864	+	0.959160i	$0.591284\pi$
$954$	18.1493	0.587604
$955$	−2.30297	−0.0745225
$956$	−11.3121	−0.365860
$957$	0	0
$958$	44.0663	1.42372
$959$	0	0
$960$	0.783486	0.0252869
$961$	−30.9598	−0.998702
$962$	7.90236	0.254782
$963$	−8.50196	−0.273972
$964$	−14.5512	−0.468663
$965$	−18.7148	−0.602450
$966$	0	0
$967$	−45.6122	−1.46679	−0.733395	−	0.679802i	$-0.762066\pi$
$967$	−45.6122	−1.46679	−0.733395	+	0.679802i	$0.762066\pi$
$968$	0	0
$969$	3.30233	0.106086
$970$	−57.3485	−1.84135
$971$	−2.38378	−0.0764992	−0.0382496	−	0.999268i	$-0.512178\pi$
$971$	−2.38378	−0.0764992	−0.0382496	+	0.999268i	$0.512178\pi$
$972$	−16.1677	−0.518579
$973$	0	0
$974$	−25.4788	−0.816393
$975$	−7.20275	−0.230673
$976$	−4.91791	−0.157418
$977$	−19.2662	−0.616380	−0.308190	−	0.951325i	$-0.599723\pi$
$977$	−19.2662	−0.616380	−0.308190	+	0.951325i	$0.599723\pi$
$978$	−8.82972	−0.282343
$979$	0	0
$980$	0	0
$981$	−33.2259	−1.06082
$982$	−39.1390	−1.24898
$983$	16.2256	0.517517	0.258759	−	0.965942i	$-0.416687\pi$
$983$	16.2256	0.517517	0.258759	+	0.965942i	$0.416687\pi$
$984$	−8.87016	−0.282770
$985$	−30.3345	−0.966537
$986$	42.2600	1.34583
$987$	0	0
$988$	−9.65296	−0.307101
$989$	−20.5753	−0.654256
$990$	0	0
$991$	−50.5214	−1.60487	−0.802433	−	0.596743i	$-0.796461\pi$
$991$	−50.5214	−1.60487	−0.802433	+	0.596743i	$0.796461\pi$
$992$	−1.17426	−0.0372828
$993$	16.3986	0.520393
$994$	0	0
$995$	−58.2566	−1.84686
$996$	−1.23356	−0.0390869
$997$	45.0206	1.42582	0.712909	−	0.701257i	$-0.247377\pi$
$997$	45.0206	1.42582	0.712909	+	0.701257i	$0.247377\pi$
$998$	−44.9912	−1.42417
$999$	3.59533	0.113751

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bi.1.3		4
7.6	odd	2		847.2.a.l.1.3		4
11.3	even	5		539.2.f.d.295.2		8
11.4	even	5		539.2.f.d.148.2		8
11.10	odd	2		5929.2.a.bb.1.2		4
21.20	even	2		7623.2.a.ch.1.2		4
77.3	odd	30		539.2.q.c.471.2		16
77.4	even	15		539.2.q.b.324.1		16
77.6	even	10		847.2.f.s.729.2		8
77.13	even	10		847.2.f.s.323.2		8
77.20	odd	10		847.2.f.p.323.1		8
77.25	even	15		539.2.q.b.471.2		16
77.26	odd	30		539.2.q.c.214.2		16
77.27	odd	10		847.2.f.p.729.1		8
77.37	even	15		539.2.q.b.214.2		16
77.41	even	10		847.2.f.q.372.1		8
77.47	odd	30		539.2.q.c.361.1		16
77.48	odd	10		77.2.f.a.71.2	yes	8
77.58	even	15		539.2.q.b.361.1		16
77.59	odd	30		539.2.q.c.324.1		16
77.62	even	10		847.2.f.q.148.1		8
77.69	odd	10		77.2.f.a.64.2	✓	8
77.76	even	2		847.2.a.k.1.2		4
231.125	even	10		693.2.m.g.379.1		8
231.146	even	10		693.2.m.g.64.1		8
231.230	odd	2		7623.2.a.co.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.2	✓	8	77.69	odd	10
77.2.f.a.71.2	yes	8	77.48	odd	10
539.2.f.d.148.2		8	11.4	even	5
539.2.f.d.295.2		8	11.3	even	5
539.2.q.b.214.2		16	77.37	even	15
539.2.q.b.324.1		16	77.4	even	15
539.2.q.b.361.1		16	77.58	even	15
539.2.q.b.471.2		16	77.25	even	15
539.2.q.c.214.2		16	77.26	odd	30
539.2.q.c.324.1		16	77.59	odd	30
539.2.q.c.361.1		16	77.47	odd	30
539.2.q.c.471.2		16	77.3	odd	30
693.2.m.g.64.1		8	231.146	even	10
693.2.m.g.379.1		8	231.125	even	10
847.2.a.k.1.2		4	77.76	even	2
847.2.a.l.1.3		4	7.6	odd	2
847.2.f.p.323.1		8	77.20	odd	10
847.2.f.p.729.1		8	77.27	odd	10
847.2.f.q.148.1		8	77.62	even	10
847.2.f.q.372.1		8	77.41	even	10
847.2.f.s.323.2		8	77.13	even	10
847.2.f.s.729.2		8	77.6	even	10
5929.2.a.bb.1.2		4	11.10	odd	2
5929.2.a.bi.1.3		4	1.1	even	1	trivial
7623.2.a.ch.1.2		4	21.20	even	2
7623.2.a.co.1.3		4	231.230	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:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q+1.77748 q^{2} -0.618034 q^{3} +1.15945 q^{4} +2.77748 q^{5} -1.09855 q^{6} -1.49406 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q+1.77748 q^{2} -0.618034 q^{3} +1.15945 q^{4} +2.77748 q^{5} -1.09855 q^{6} -1.49406 q^{8} -2.61803 q^{9} +4.93693 q^{10} -0.716580 q^{12} +4.29348 q^{13} -1.71658 q^{15} -4.97458 q^{16} +2.75556 q^{17} -4.65351 q^{18} -1.93910 q^{19} +3.22035 q^{20} +4.37009 q^{23} +0.923382 q^{24} +2.71442 q^{25} +7.63159 q^{26} +3.47214 q^{27} +8.62809 q^{29} -3.05119 q^{30} +0.200588 q^{31} -5.85410 q^{32} +4.89796 q^{34} -3.03548 q^{36} +1.03548 q^{37} -3.44671 q^{38} -2.65351 q^{39} -4.14974 q^{40} -9.60616 q^{41} -4.70820 q^{43} -7.27155 q^{45} +7.76777 q^{46} +13.0455 q^{47} +3.07446 q^{48} +4.82484 q^{50} -1.70303 q^{51} +4.97807 q^{52} -3.90012 q^{53} +6.17167 q^{54} +1.19843 q^{57} +15.3363 q^{58} +8.55713 q^{59} -1.99029 q^{60} +0.988609 q^{61} +0.356542 q^{62} -0.456423 q^{64} +11.9251 q^{65} -5.41745 q^{67} +3.19493 q^{68} -2.70087 q^{69} -2.01705 q^{71} +3.91151 q^{72} +9.97108 q^{73} +1.84055 q^{74} -1.67760 q^{75} -2.24828 q^{76} -4.71658 q^{78} +6.29348 q^{79} -13.8168 q^{80} +5.70820 q^{81} -17.0748 q^{82} +1.72146 q^{83} +7.65351 q^{85} -8.36876 q^{86} -5.33245 q^{87} +15.3035 q^{89} -12.9251 q^{90} +5.06691 q^{92} -0.123970 q^{93} +23.1882 q^{94} -5.38581 q^{95} +3.61803 q^{96} -11.6162 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} + q^{6} + 9 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 + q^6 + 9 * q^8 - 6 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} + q^{6} + 9 q^{8} - 6 q^{9} + 14 q^{10} + 7 q^{12} + 3 q^{15} - 4 q^{16} + 3 q^{17} - 3 q^{18} - 3 q^{19} + 17 q^{20} - 8 q^{23} + 12 q^{24} + 12 q^{26} - 4 q^{27} + 3 q^{29} + 12 q^{30} + 3 q^{31} - 10 q^{32} + 12 q^{34} - q^{36} - 7 q^{37} + 20 q^{38} + 5 q^{39} + 13 q^{40} - 4 q^{41} + 8 q^{43} - 9 q^{45} - 3 q^{46} + 14 q^{47} + 3 q^{48} + 33 q^{50} - 11 q^{51} + 17 q^{52} - 9 q^{53} - 2 q^{54} + 6 q^{57} + 3 q^{58} + 25 q^{59} + 21 q^{60} + 19 q^{61} - 10 q^{62} + 3 q^{64} + 12 q^{65} - 15 q^{67} + q^{68} - 14 q^{69} - 7 q^{71} - 6 q^{72} + 11 q^{73} + 8 q^{74} + 5 q^{75} + 26 q^{76} - 9 q^{78} + 8 q^{79} + 4 q^{80} - 4 q^{81} - 3 q^{82} + q^{83} + 15 q^{85} + 4 q^{86} - 6 q^{87} + 17 q^{89} - 16 q^{90} - 17 q^{92} - 11 q^{93} + 20 q^{94} + 17 q^{95} + 10 q^{96} + 15 q^{97}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 + q^6 + 9 * q^8 - 6 * q^9 + 14 * q^10 + 7 * q^12 + 3 * q^15 - 4 * q^16 + 3 * q^17 - 3 * q^18 - 3 * q^19 + 17 * q^20 - 8 * q^23 + 12 * q^24 + 12 * q^26 - 4 * q^27 + 3 * q^29 + 12 * q^30 + 3 * q^31 - 10 * q^32 + 12 * q^34 - q^36 - 7 * q^37 + 20 * q^38 + 5 * q^39 + 13 * q^40 - 4 * q^41 + 8 * q^43 - 9 * q^45 - 3 * q^46 + 14 * q^47 + 3 * q^48 + 33 * q^50 - 11 * q^51 + 17 * q^52 - 9 * q^53 - 2 * q^54 + 6 * q^57 + 3 * q^58 + 25 * q^59 + 21 * q^60 + 19 * q^61 - 10 * q^62 + 3 * q^64 + 12 * q^65 - 15 * q^67 + q^68 - 14 * q^69 - 7 * q^71 - 6 * q^72 + 11 * q^73 + 8 * q^74 + 5 * q^75 + 26 * q^76 - 9 * q^78 + 8 * q^79 + 4 * q^80 - 4 * q^81 - 3 * q^82 + q^83 + 15 * q^85 + 4 * q^86 - 6 * q^87 + 17 * q^89 - 16 * q^90 - 17 * q^92 - 11 * q^93 + 20 * q^94 + 17 * q^95 + 10 * q^96 + 15 * q^97

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