LMFDB - Embedded newform 5929.2.a.bb.1.2

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:	$1$
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			1.2
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	$-0.716304\pi$
$2$	−1.77748	−1.25687	−0.628436	+	0.777862i	$0.716304\pi$
$3$	−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	$-0.703006\pi$
$13$	−4.29348	−1.19080	−0.595398	+	0.803431i	$0.703006\pi$
$14$	0	0
$15$	−1.71658	−0.443219
$16$	−4.97458	−1.24364
$17$	−2.75556	−0.668321	−0.334160	−	0.942516i	$-0.608453\pi$
$17$	−2.75556	−0.668321	−0.334160	+	0.942516i	$0.608453\pi$
$18$	4.65351	1.09684
$19$	1.93910	0.444859	0.222429	−	0.974949i	$-0.428601\pi$
$19$	1.93910	0.444859	0.222429	+	0.974949i	$0.428601\pi$
$20$	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	$-0.795750\pi$
$29$	−8.62809	−1.60220	−0.801098	+	0.598533i	$0.795750\pi$
$30$	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	$-0.229998\pi$
$41$	9.60616	1.50023	0.750115	+	0.661307i	$0.229998\pi$
$42$	0	0
$43$	4.70820	0.717994	0.358997	−	0.933339i	$-0.383119\pi$
$43$	4.70820	0.717994	0.358997	+	0.933339i	$0.383119\pi$
$44$	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	$-0.520159\pi$
$61$	−0.988609	−0.126578	−0.0632892	+	0.997995i	$0.520159\pi$
$62$	−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	$-0.698322\pi$
$73$	−9.97108	−1.16703	−0.583513	+	0.812104i	$0.698322\pi$
$74$	−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	$-0.615191\pi$
$79$	−6.29348	−0.708071	−0.354036	+	0.935232i	$0.615191\pi$
$80$	−13.8168	−1.54477
$81$	5.70820	0.634245
$82$	−17.0748	−1.88560
$83$	−1.72146	−0.188955	−0.0944773	−	0.995527i	$-0.530118\pi$
$83$	−1.72146	−0.188955	−0.0944773	+	0.995527i	$0.530118\pi$
$84$	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	$-0.445706\pi$
$101$	3.41179	0.339486	0.169743	+	0.985488i	$0.445706\pi$
$102$	−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	$-0.550173\pi$
$107$	−3.24746	−0.313944	−0.156972	+	0.987603i	$0.550173\pi$
$108$	4.02577	0.387380
$109$	−12.6912	−1.21559	−0.607796	−	0.794093i	$-0.707946\pi$
$109$	−12.6912	−1.21559	−0.607796	+	0.794093i	$0.707946\pi$
$110$	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	$-0.833053\pi$
$127$	−19.5093	−1.73117	−0.865585	+	0.500762i	$0.833053\pi$
$128$	−10.8969	−0.963161
$129$	−2.90983	−0.256196
$130$	21.1966	1.85907
$131$	−6.89796	−0.602677	−0.301339	−	0.953517i	$-0.597433\pi$
$131$	−6.89796	−0.602677	−0.301339	+	0.953517i	$0.597433\pi$
$132$	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	$-0.513521\pi$
$139$	−1.00134	−0.0849322	−0.0424661	+	0.999098i	$0.513521\pi$
$140$	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	$-0.291124\pi$
$149$	14.8948	1.22023	0.610113	+	0.792314i	$0.291124\pi$
$150$	2.98191	0.243472
$151$	−15.8046	−1.28616	−0.643080	−	0.765799i	$-0.722344\pi$
$151$	−15.8046	−1.28616	−0.643080	+	0.765799i	$0.722344\pi$
$152$	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	$-0.673595\pi$
$167$	−13.4069	−1.03746	−0.518729	+	0.854939i	$0.673595\pi$
$168$	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	$-0.786011\pi$
$173$	−20.5821	−1.56483	−0.782413	+	0.622760i	$0.786011\pi$
$174$	−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	$-0.422030\pi$
$193$	6.73803	0.485014	0.242507	+	0.970150i	$0.422030\pi$
$194$	20.6476	1.48241
$195$	7.37009	0.527783
$196$	0	0
$197$	10.9216	0.778129	0.389065	−	0.921210i	$-0.372798\pi$
$197$	10.9216	0.778129	0.389065	+	0.921210i	$0.372798\pi$
$198$	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	$-0.433519\pi$
$211$	6.02361	0.414682	0.207341	+	0.978269i	$0.433519\pi$
$212$	−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	$-0.305340\pi$
$227$	17.3003	1.14826	0.574132	+	0.818763i	$0.305340\pi$
$228$	−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	$-0.387872\pi$
$233$	10.5330	0.690042	0.345021	+	0.938595i	$0.387872\pi$
$234$	−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	$-0.397812\pi$
$239$	9.75646	0.631093	0.315546	+	0.948910i	$0.397812\pi$
$240$	8.53926	0.551207
$241$	12.5501	0.808422	0.404211	−	0.914666i	$-0.367546\pi$
$241$	12.5501	0.808422	0.404211	+	0.914666i	$0.367546\pi$
$242$	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	$-0.418842\pi$
$263$	8.18034	0.504421	0.252211	+	0.967672i	$0.418842\pi$
$264$	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	$-0.733550\pi$
$271$	−22.0472	−1.33927	−0.669636	+	0.742689i	$0.733550\pi$
$272$	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	$-0.757386\pi$
$277$	−24.0770	−1.44664	−0.723322	+	0.690511i	$0.757386\pi$
$278$	1.77986	0.106749
$279$	−0.525146	−0.0314396
$280$	0	0
$281$	−15.4418	−0.921182	−0.460591	−	0.887612i	$-0.652363\pi$
$281$	−15.4418	−0.921182	−0.460591	+	0.887612i	$0.652363\pi$
$282$	14.3311	0.853406
$283$	−3.35732	−0.199572	−0.0997860	−	0.995009i	$-0.531816\pi$
$283$	−3.35732	−0.199572	−0.0997860	+	0.995009i	$0.531816\pi$
$284$	−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	$-0.435999\pi$
$293$	6.83705	0.399425	0.199712	+	0.979855i	$0.435999\pi$
$294$	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	$-0.609293\pi$
$307$	−11.7970	−0.673293	−0.336646	+	0.941631i	$0.609293\pi$
$308$	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	$-0.494052\pi$
$337$	0.685979	0.0373676	0.0186838	+	0.999825i	$0.494052\pi$
$338$	−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	$-0.695869\pi$
$347$	−21.5055	−1.15447	−0.577237	+	0.816577i	$0.695869\pi$
$348$	6.18271	0.331428
$349$	19.4429	1.04075	0.520377	−	0.853937i	$-0.325792\pi$
$349$	19.4429	1.04075	0.520377	+	0.853937i	$0.325792\pi$
$350$	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	$-0.583015\pi$
$359$	−9.77127	−0.515708	−0.257854	+	0.966184i	$0.583015\pi$
$360$	−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	$-0.464701\pi$
$373$	4.27475	0.221338	0.110669	+	0.993857i	$0.464701\pi$
$374$	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	$-0.553598\pi$
$409$	−6.77852	−0.335176	−0.167588	+	0.985857i	$0.553598\pi$
$410$	−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	$-0.528336\pi$
$431$	−3.69129	−0.177803	−0.0889016	+	0.996040i	$0.528336\pi$
$432$	−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	$-0.610057\pi$
$439$	−14.2017	−0.677811	−0.338905	+	0.940820i	$0.610057\pi$
$440$	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	$-0.650730\pi$
$457$	−19.4977	−0.912063	−0.456032	+	0.889964i	$0.650730\pi$
$458$	−7.86736	−0.367617
$459$	−9.56767	−0.446580
$460$	14.0733	0.656169
$461$	12.2251	0.569380	0.284690	−	0.958620i	$-0.408109\pi$
$461$	12.2251	0.569380	0.284690	+	0.958620i	$0.408109\pi$
$462$	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	$-0.691654\pi$
$479$	−24.7914	−1.13275	−0.566374	+	0.824149i	$0.691654\pi$
$480$	−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	$-0.334486\pi$
$491$	22.0193	0.993719	0.496859	+	0.867831i	$0.334486\pi$
$492$	−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	$-0.696994\pi$
$503$	−26.0214	−1.16024	−0.580119	+	0.814531i	$0.696994\pi$
$504$	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	$-0.362698\pi$
$523$	19.1230	0.836189	0.418095	+	0.908403i	$0.362698\pi$
$524$	−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	$-0.575186\pi$
$541$	−10.8860	−0.468027	−0.234014	+	0.972233i	$0.575186\pi$
$542$	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	$-0.410999\pi$
$547$	12.9091	0.551951	0.275976	+	0.961165i	$0.410999\pi$
$548$	−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	$-0.494857\pi$
$557$	0.762626	0.0323135	0.0161567	+	0.999869i	$0.494857\pi$
$558$	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	$-0.655170\pi$
$563$	−22.2281	−0.936803	−0.468402	+	0.883516i	$0.655170\pi$
$564$	−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	$-0.358521\pi$
$569$	20.5131	0.859955	0.429978	+	0.902839i	$0.358521\pi$
$570$	5.91656	0.247817
$571$	19.5654	0.818785	0.409393	−	0.912358i	$-0.365741\pi$
$571$	19.5654	0.818785	0.409393	+	0.912358i	$0.365741\pi$
$572$	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	$-0.712260\pi$
$593$	−30.1230	−1.23700	−0.618502	+	0.785783i	$0.712260\pi$
$594$	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	$-0.120404\pi$
$601$	45.5645	1.85862	0.929308	+	0.369305i	$0.120404\pi$
$602$	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	$-0.251108\pi$
$607$	34.7211	1.40928	0.704642	+	0.709563i	$0.251108\pi$
$608$	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	$-0.337891\pi$
$613$	24.1423	0.975097	0.487548	+	0.873096i	$0.337891\pi$
$614$	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	$-0.652204\pi$
$659$	−23.6249	−0.920297	−0.460148	+	0.887842i	$0.652204\pi$
$660$	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	$-0.574914\pi$
$673$	−12.0986	−0.466368	−0.233184	+	0.972433i	$0.574914\pi$
$674$	−1.21932	−0.0469663
$675$	9.42483	0.362762
$676$	6.30038	0.242322
$677$	−9.42988	−0.362420	−0.181210	−	0.983444i	$-0.558001\pi$
$677$	−9.42988	−0.362420	−0.181210	+	0.983444i	$0.558001\pi$
$678$	−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	$-0.290995\pi$
$701$	32.3242	1.22087	0.610433	+	0.792068i	$0.290995\pi$
$702$	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	$-0.463136\pi$
$733$	6.25696	0.231106	0.115553	+	0.993301i	$0.463136\pi$
$734$	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	$-0.555026\pi$
$739$	−9.35201	−0.344019	−0.172010	+	0.985095i	$0.555026\pi$
$740$	3.33461	0.122583
$741$	5.14542	0.189022
$742$	0	0
$743$	−25.2066	−0.924740	−0.462370	−	0.886687i	$-0.653001\pi$
$743$	−25.2066	−0.924740	−0.462370	+	0.886687i	$0.653001\pi$
$744$	−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	$-0.571123\pi$
$761$	−12.2255	−0.443172	−0.221586	+	0.975141i	$0.571123\pi$
$762$	−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	$-0.515039\pi$
$769$	−2.61946	−0.0944603	−0.0472301	+	0.998884i	$0.515039\pi$
$770$	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	$-0.326185\pi$
$787$	29.1375	1.03864	0.519320	+	0.854580i	$0.326185\pi$
$788$	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	$-0.327466\pi$
$809$	29.3461	1.03175	0.515877	+	0.856663i	$0.327466\pi$
$810$	−28.1810	−0.990180
$811$	1.03940	0.0364982	0.0182491	−	0.999833i	$-0.494191\pi$
$811$	1.03940	0.0364982	0.0182491	+	0.999833i	$0.494191\pi$
$812$	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	$-0.665893\pi$
$821$	−28.5323	−0.995786	−0.497893	+	0.867239i	$0.665893\pi$
$822$	−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	$-0.509519\pi$
$827$	−1.71964	−0.0597978	−0.0298989	+	0.999553i	$0.509519\pi$
$828$	−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	$-0.583472\pi$
$853$	−15.1427	−0.518478	−0.259239	+	0.965813i	$0.583472\pi$
$854$	0	0
$855$	−14.1002	−0.482218
$856$	−4.85191	−0.165835
$857$	25.3267	0.865142	0.432571	−	0.901600i	$-0.357606\pi$
$857$	25.3267	0.865142	0.432571	+	0.901600i	$0.357606\pi$
$858$	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	$-0.693351\pi$
$877$	−33.8052	−1.14152	−0.570760	+	0.821117i	$0.693351\pi$
$878$	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	$-0.438366\pi$
$887$	11.4616	0.384843	0.192421	+	0.981312i	$0.438366\pi$
$888$	−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	$-0.340448\pi$
$919$	29.1339	0.961038	0.480519	+	0.876984i	$0.340448\pi$
$920$	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	$-0.454151\pi$
$937$	8.78780	0.287085	0.143542	+	0.989644i	$0.454151\pi$
$938$	0	0
$939$	−12.1470	−0.396404
$940$	42.0113	1.37026
$941$	8.88871	0.289764	0.144882	−	0.989449i	$-0.453720\pi$
$941$	8.88871	0.289764	0.144882	+	0.989449i	$0.453720\pi$
$942$	−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	$-0.408716\pi$
$953$	17.4644	0.565727	0.282864	+	0.959160i	$0.408716\pi$
$954$	−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	$-0.237934\pi$
$967$	45.6122	1.46679	0.733395	+	0.679802i	$0.237934\pi$
$968$	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	$-0.752623\pi$
$997$	−45.0206	−1.42582	−0.712909	+	0.701257i	$0.752623\pi$
$998$	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.bb.1.2		4
7.6	odd	2		847.2.a.k.1.2		4
11.7	odd	10		539.2.f.d.148.2		8
11.8	odd	10		539.2.f.d.295.2		8
11.10	odd	2		5929.2.a.bi.1.3		4
21.20	even	2		7623.2.a.co.1.3		4
77.6	even	10		847.2.f.p.729.1		8
77.13	even	10		847.2.f.p.323.1		8
77.18	odd	30		539.2.q.b.324.1		16
77.19	even	30		539.2.q.c.361.1		16
77.20	odd	10		847.2.f.s.323.2		8
77.27	odd	10		847.2.f.s.729.2		8
77.30	odd	30		539.2.q.b.361.1		16
77.40	even	30		539.2.q.c.214.2		16
77.41	even	10		77.2.f.a.64.2	✓	8
77.48	odd	10		847.2.f.q.148.1		8
77.51	odd	30		539.2.q.b.214.2		16
77.52	even	30		539.2.q.c.471.2		16
77.62	even	10		77.2.f.a.71.2	yes	8
77.69	odd	10		847.2.f.q.372.1		8
77.73	even	30		539.2.q.c.324.1		16
77.74	odd	30		539.2.q.b.471.2		16
77.76	even	2		847.2.a.l.1.3		4
231.41	odd	10		693.2.m.g.64.1		8
231.62	odd	10		693.2.m.g.379.1		8
231.230	odd	2		7623.2.a.ch.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.2	✓	8	77.41	even	10
77.2.f.a.71.2	yes	8	77.62	even	10
539.2.f.d.148.2		8	11.7	odd	10
539.2.f.d.295.2		8	11.8	odd	10
539.2.q.b.214.2		16	77.51	odd	30
539.2.q.b.324.1		16	77.18	odd	30
539.2.q.b.361.1		16	77.30	odd	30
539.2.q.b.471.2		16	77.74	odd	30
539.2.q.c.214.2		16	77.40	even	30
539.2.q.c.324.1		16	77.73	even	30
539.2.q.c.361.1		16	77.19	even	30
539.2.q.c.471.2		16	77.52	even	30
693.2.m.g.64.1		8	231.41	odd	10
693.2.m.g.379.1		8	231.62	odd	10
847.2.a.k.1.2		4	7.6	odd	2
847.2.a.l.1.3		4	77.76	even	2
847.2.f.p.323.1		8	77.13	even	10
847.2.f.p.729.1		8	77.6	even	10
847.2.f.q.148.1		8	77.48	odd	10
847.2.f.q.372.1		8	77.69	odd	10
847.2.f.s.323.2		8	77.20	odd	10
847.2.f.s.729.2		8	77.27	odd	10
5929.2.a.bb.1.2		4	1.1	even	1	trivial
5929.2.a.bi.1.3		4	11.10	odd	2
7623.2.a.ch.1.2		4	231.230	odd	2
7623.2.a.co.1.3		4	21.20	even	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more