LMFDB - Embedded newform 2009.2.a.u.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2009,2,Mod(1,2009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2009, 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("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2009 = 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2009.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:	$16.0419457661$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 27 x^{18} + 52 x^{17} + 302 x^{16} - 552 x^{15} - 1820 x^{14} + 3090 x^{13} + \cdots + 49 $ x^20 - 2x^19 - 27x^18 + 52x^17 + 302x^16 - 552x^15 - 1820x^14 + 3090x^13 + 6449x^12 - 9852x^11 - 13797x^10 + 18080x^9 + 17721x^8 - 18446x^7 - 13352x^6 + 9524x^5 + 5690x^4 - 1972x^3 - 1179x^2 + 42*x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-0.466765$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.466765 q^{2} +2.80691 q^{3} -1.78213 q^{4} +2.27147 q^{5} +1.31017 q^{6} -1.76537 q^{8} +4.87872 q^{9} +O(q^{10})$	\(q+0.466765 q^{2} +2.80691 q^{3} -1.78213 q^{4} +2.27147 q^{5} +1.31017 q^{6} -1.76537 q^{8} +4.87872 q^{9} +1.06024 q^{10} +0.320339 q^{11} -5.00227 q^{12} +0.931491 q^{13} +6.37579 q^{15} +2.74025 q^{16} +1.87955 q^{17} +2.27722 q^{18} -2.54918 q^{19} -4.04805 q^{20} +0.149523 q^{22} +6.69701 q^{23} -4.95522 q^{24} +0.159556 q^{25} +0.434787 q^{26} +5.27340 q^{27} +5.03242 q^{29} +2.97600 q^{30} -0.853263 q^{31} +4.80978 q^{32} +0.899163 q^{33} +0.877307 q^{34} -8.69452 q^{36} +1.35625 q^{37} -1.18987 q^{38} +2.61461 q^{39} -4.00997 q^{40} +1.00000 q^{41} -4.71866 q^{43} -0.570886 q^{44} +11.0819 q^{45} +3.12593 q^{46} +1.26882 q^{47} +7.69163 q^{48} +0.0744752 q^{50} +5.27571 q^{51} -1.66004 q^{52} -0.803888 q^{53} +2.46144 q^{54} +0.727640 q^{55} -7.15532 q^{57} +2.34896 q^{58} +14.5391 q^{59} -11.3625 q^{60} -9.36939 q^{61} -0.398273 q^{62} -3.23546 q^{64} +2.11585 q^{65} +0.419698 q^{66} +14.0552 q^{67} -3.34960 q^{68} +18.7979 q^{69} -8.32228 q^{71} -8.61273 q^{72} +5.02750 q^{73} +0.633048 q^{74} +0.447859 q^{75} +4.54298 q^{76} +1.22041 q^{78} -14.8847 q^{79} +6.22438 q^{80} +0.165777 q^{81} +0.466765 q^{82} -18.0099 q^{83} +4.26933 q^{85} -2.20250 q^{86} +14.1255 q^{87} -0.565516 q^{88} -0.612144 q^{89} +5.17262 q^{90} -11.9349 q^{92} -2.39503 q^{93} +0.592241 q^{94} -5.79038 q^{95} +13.5006 q^{96} -3.82089 q^{97} +1.56285 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 8 q^{3} + 18 q^{4} + 8 q^{5} + 12 q^{6} - 6 q^{8} + 16 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 8 * q^3 + 18 * q^4 + 8 * q^5 + 12 * q^6 - 6 * q^8 + 16 * q^9	$ 20 q - 2 q^{2} + 8 q^{3} + 18 q^{4} + 8 q^{5} + 12 q^{6} - 6 q^{8} + 16 q^{9} + 16 q^{10} + 6 q^{12} + 12 q^{13} + 14 q^{16} + 8 q^{17} - 18 q^{18} + 36 q^{19} + 24 q^{20} - 8 q^{22} - 12 q^{23} + 36 q^{24} + 20 q^{25} - 22 q^{26} + 32 q^{27} + 4 q^{29} + 28 q^{30} + 80 q^{31} + 6 q^{32} - 12 q^{33} + 48 q^{34} + 26 q^{36} + 4 q^{37} + 12 q^{38} - 28 q^{39} - 4 q^{40} + 20 q^{41} - 20 q^{44} + 40 q^{45} + 8 q^{46} + 32 q^{47} + 16 q^{48} + 6 q^{50} - 20 q^{51} + 36 q^{52} + 4 q^{53} - 50 q^{54} + 64 q^{55} - 4 q^{57} + 32 q^{59} + 20 q^{60} + 44 q^{61} - 8 q^{62} - 30 q^{64} - 8 q^{65} + 32 q^{66} - 4 q^{67} - 48 q^{68} - 24 q^{69} + 8 q^{71} - 8 q^{72} + 48 q^{73} - 38 q^{74} + 24 q^{75} + 84 q^{76} + 30 q^{78} - 4 q^{79} + 56 q^{80} - 2 q^{82} + 8 q^{83} - 12 q^{85} - 24 q^{86} + 40 q^{87} - 48 q^{88} + 20 q^{89} + 48 q^{90} - 50 q^{92} + 48 q^{93} + 26 q^{94} + 20 q^{95} + 70 q^{96} + 8 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 2 * q^2 + 8 * q^3 + 18 * q^4 + 8 * q^5 + 12 * q^6 - 6 * q^8 + 16 * q^9 + 16 * q^10 + 6 * q^12 + 12 * q^13 + 14 * q^16 + 8 * q^17 - 18 * q^18 + 36 * q^19 + 24 * q^20 - 8 * q^22 - 12 * q^23 + 36 * q^24 + 20 * q^25 - 22 * q^26 + 32 * q^27 + 4 * q^29 + 28 * q^30 + 80 * q^31 + 6 * q^32 - 12 * q^33 + 48 * q^34 + 26 * q^36 + 4 * q^37 + 12 * q^38 - 28 * q^39 - 4 * q^40 + 20 * q^41 - 20 * q^44 + 40 * q^45 + 8 * q^46 + 32 * q^47 + 16 * q^48 + 6 * q^50 - 20 * q^51 + 36 * q^52 + 4 * q^53 - 50 * q^54 + 64 * q^55 - 4 * q^57 + 32 * q^59 + 20 * q^60 + 44 * q^61 - 8 * q^62 - 30 * q^64 - 8 * q^65 + 32 * q^66 - 4 * q^67 - 48 * q^68 - 24 * q^69 + 8 * q^71 - 8 * q^72 + 48 * q^73 - 38 * q^74 + 24 * q^75 + 84 * q^76 + 30 * q^78 - 4 * q^79 + 56 * q^80 - 2 * q^82 + 8 * q^83 - 12 * q^85 - 24 * q^86 + 40 * q^87 - 48 * q^88 + 20 * q^89 + 48 * q^90 - 50 * q^92 + 48 * q^93 + 26 * q^94 + 20 * q^95 + 70 * q^96 + 8 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.466765	0.330053	0.165026	−	0.986289i	$-0.447229\pi$
$2$	0.466765	0.330053	0.165026	+	0.986289i	$0.447229\pi$
$3$	2.80691	1.62057	0.810284	−	0.586037i	$-0.199313\pi$
$3$	2.80691	1.62057	0.810284	+	0.586037i	$0.199313\pi$
$4$	−1.78213	−0.891065
$5$	2.27147	1.01583	0.507915	−	0.861407i	$-0.330416\pi$
$5$	2.27147	1.01583	0.507915	+	0.861407i	$0.330416\pi$
$6$	1.31017	0.534873
$7$	0	0
$7$	0	0
$8$	−1.76537	−0.624151
$9$	4.87872	1.62624
$10$	1.06024	0.335278
$11$	0.320339	0.0965859	0.0482930	−	0.998833i	$-0.484622\pi$
$11$	0.320339	0.0965859	0.0482930	+	0.998833i	$0.484622\pi$
$12$	−5.00227	−1.44403
$13$	0.931491	0.258349	0.129175	−	0.991622i	$-0.458767\pi$
$13$	0.931491	0.258349	0.129175	+	0.991622i	$0.458767\pi$
$14$	0	0
$15$	6.37579	1.64622
$16$	2.74025	0.685062
$17$	1.87955	0.455857	0.227929	−	0.973678i	$-0.426805\pi$
$17$	1.87955	0.455857	0.227929	+	0.973678i	$0.426805\pi$
$18$	2.27722	0.536745
$19$	−2.54918	−0.584823	−0.292411	−	0.956293i	$-0.594458\pi$
$19$	−2.54918	−0.584823	−0.292411	+	0.956293i	$0.594458\pi$
$20$	−4.04805	−0.905171
$21$	0	0
$22$	0.149523	0.0318784
$23$	6.69701	1.39642	0.698211	−	0.715892i	$-0.253980\pi$
$23$	6.69701	1.39642	0.698211	+	0.715892i	$0.253980\pi$
$24$	−4.95522	−1.01148
$25$	0.159556	0.0319112
$26$	0.434787	0.0852688
$27$	5.27340	1.01487
$28$	0	0
$29$	5.03242	0.934497	0.467249	−	0.884126i	$-0.345245\pi$
$29$	5.03242	0.934497	0.467249	+	0.884126i	$0.345245\pi$
$30$	2.97600	0.543340
$31$	−0.853263	−0.153251	−0.0766253	−	0.997060i	$-0.524415\pi$
$31$	−0.853263	−0.153251	−0.0766253	+	0.997060i	$0.524415\pi$
$32$	4.80978	0.850258
$33$	0.899163	0.156524
$34$	0.877307	0.150457
$35$	0	0
$36$	−8.69452	−1.44909
$37$	1.35625	0.222966	0.111483	−	0.993766i	$-0.464440\pi$
$37$	1.35625	0.222966	0.111483	+	0.993766i	$0.464440\pi$
$38$	−1.18987	−0.193022
$39$	2.61461	0.418672
$40$	−4.00997	−0.634032
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−4.71866	−0.719589	−0.359794	−	0.933032i	$-0.617153\pi$
$43$	−4.71866	−0.719589	−0.359794	+	0.933032i	$0.617153\pi$
$44$	−0.570886	−0.0860644
$45$	11.0819	1.65199
$46$	3.12593	0.460893
$47$	1.26882	0.185076	0.0925382	−	0.995709i	$-0.470502\pi$
$47$	1.26882	0.185076	0.0925382	+	0.995709i	$0.470502\pi$
$48$	7.69163	1.11019
$49$	0	0
$50$	0.0744752	0.0105324
$51$	5.27571	0.738748
$52$	−1.66004	−0.230206
$53$	−0.803888	−0.110422	−0.0552112	−	0.998475i	$-0.517583\pi$
$53$	−0.803888	−0.110422	−0.0552112	+	0.998475i	$0.517583\pi$
$54$	2.46144	0.334960
$55$	0.727640	0.0981149
$56$	0	0
$57$	−7.15532	−0.947745
$58$	2.34896	0.308433
$59$	14.5391	1.89283	0.946414	−	0.322956i	$-0.104677\pi$
$59$	14.5391	1.89283	0.946414	+	0.322956i	$0.104677\pi$
$60$	−11.3625	−1.46689
$61$	−9.36939	−1.19963	−0.599814	−	0.800139i	$-0.704759\pi$
$61$	−9.36939	−1.19963	−0.599814	+	0.800139i	$0.704759\pi$
$62$	−0.398273	−0.0505808
$63$	0	0
$64$	−3.23546	−0.404433
$65$	2.11585	0.262439
$66$	0.419698	0.0516612
$67$	14.0552	1.71711	0.858557	−	0.512718i	$-0.171362\pi$
$67$	14.0552	1.71711	0.858557	+	0.512718i	$0.171362\pi$
$68$	−3.34960	−0.406198
$69$	18.7979	2.26300
$70$	0	0
$71$	−8.32228	−0.987673	−0.493837	−	0.869555i	$-0.664406\pi$
$71$	−8.32228	−0.987673	−0.493837	+	0.869555i	$0.664406\pi$
$72$	−8.61273	−1.01502
$73$	5.02750	0.588425	0.294212	−	0.955740i	$-0.404943\pi$
$73$	5.02750	0.588425	0.294212	+	0.955740i	$0.404943\pi$
$74$	0.633048	0.0735904
$75$	0.447859	0.0517143
$76$	4.54298	0.521115
$77$	0	0
$78$	1.22041	0.138184
$79$	−14.8847	−1.67466	−0.837331	−	0.546696i	$-0.815886\pi$
$79$	−14.8847	−1.67466	−0.837331	+	0.546696i	$0.815886\pi$
$80$	6.22438	0.695907
$81$	0.165777	0.0184196
$82$	0.466765	0.0515456
$83$	−18.0099	−1.97685	−0.988423	−	0.151723i	$-0.951518\pi$
$83$	−18.0099	−1.97685	−0.988423	+	0.151723i	$0.951518\pi$
$84$	0	0
$85$	4.26933	0.463073
$86$	−2.20250	−0.237502
$87$	14.1255	1.51442
$88$	−0.565516	−0.0602842
$89$	−0.612144	−0.0648871	−0.0324436	−	0.999474i	$-0.510329\pi$
$89$	−0.612144	−0.0648871	−0.0324436	+	0.999474i	$0.510329\pi$
$90$	5.17262	0.545242
$91$	0	0
$92$	−11.9349	−1.24430
$93$	−2.39503	−0.248353
$94$	0.592241	0.0610850
$95$	−5.79038	−0.594081
$96$	13.5006	1.37790
$97$	−3.82089	−0.387953	−0.193976	−	0.981006i	$-0.562138\pi$
$97$	−3.82089	−0.387953	−0.193976	+	0.981006i	$0.562138\pi$
$98$	0	0
$99$	1.56285	0.157072
$100$	−0.284350	−0.0284350
$101$	3.63329	0.361526	0.180763	−	0.983527i	$-0.442143\pi$
$101$	3.63329	0.361526	0.180763	+	0.983527i	$0.442143\pi$
$102$	2.46252	0.243826
$103$	15.9823	1.57478	0.787390	−	0.616455i	$-0.211432\pi$
$103$	15.9823	1.57478	0.787390	+	0.616455i	$0.211432\pi$
$104$	−1.64442	−0.161249
$105$	0	0
$106$	−0.375227	−0.0364452
$107$	13.4601	1.30124	0.650618	−	0.759405i	$-0.274510\pi$
$107$	13.4601	1.30124	0.650618	+	0.759405i	$0.274510\pi$
$108$	−9.39789	−0.904313
$109$	−4.62844	−0.443324	−0.221662	−	0.975124i	$-0.571148\pi$
$109$	−4.62844	−0.443324	−0.221662	+	0.975124i	$0.571148\pi$
$110$	0.339637	0.0323831
$111$	3.80686	0.361331
$112$	0	0
$113$	−4.41749	−0.415563	−0.207781	−	0.978175i	$-0.566624\pi$
$113$	−4.41749	−0.415563	−0.207781	+	0.978175i	$0.566624\pi$
$114$	−3.33985	−0.312806
$115$	15.2120	1.41853
$116$	−8.96843	−0.832698
$117$	4.54449	0.420138
$118$	6.78634	0.624733
$119$	0	0
$120$	−11.2556	−1.02749
$121$	−10.8974	−0.990671
$122$	−4.37331	−0.395940
$123$	2.80691	0.253090
$124$	1.52063	0.136556
$125$	−10.9949	−0.983414
$126$	0	0
$127$	0.0653425	0.00579821	0.00289910	−	0.999996i	$-0.499077\pi$
$127$	0.0653425	0.00579821	0.00289910	+	0.999996i	$0.499077\pi$
$128$	−11.1298	−0.983742
$129$	−13.2448	−1.16614
$130$	0.987605	0.0866187
$131$	8.90915	0.778396	0.389198	−	0.921154i	$-0.372752\pi$
$131$	8.90915	0.778396	0.389198	+	0.921154i	$0.372752\pi$
$132$	−1.60242	−0.139473
$133$	0	0
$134$	6.56047	0.566738
$135$	11.9784	1.03093
$136$	−3.31809	−0.284524
$137$	6.44539	0.550667	0.275334	−	0.961349i	$-0.411212\pi$
$137$	6.44539	0.550667	0.275334	+	0.961349i	$0.411212\pi$
$138$	8.77419	0.746909
$139$	−8.52778	−0.723317	−0.361658	−	0.932311i	$-0.617789\pi$
$139$	−8.52778	−0.723317	−0.361658	+	0.932311i	$0.617789\pi$
$140$	0	0
$141$	3.56146	0.299929
$142$	−3.88455	−0.325984
$143$	0.298393	0.0249529
$144$	13.3689	1.11408
$145$	11.4310	0.949291
$146$	2.34666	0.194211
$147$	0	0
$148$	−2.41701	−0.198677
$149$	−1.72931	−0.141671	−0.0708353	−	0.997488i	$-0.522566\pi$
$149$	−1.72931	−0.141671	−0.0708353	+	0.997488i	$0.522566\pi$
$150$	0.209045	0.0170684
$151$	−22.5130	−1.83208	−0.916039	−	0.401089i	$-0.868632\pi$
$151$	−22.5130	−1.83208	−0.916039	+	0.401089i	$0.868632\pi$
$152$	4.50024	0.365018
$153$	9.16979	0.741334
$154$	0	0
$155$	−1.93816	−0.155677
$156$	−4.65957	−0.373064
$157$	−16.6002	−1.32484	−0.662421	−	0.749132i	$-0.730471\pi$
$157$	−16.6002	−1.32484	−0.662421	+	0.749132i	$0.730471\pi$
$158$	−6.94767	−0.552727
$159$	−2.25644	−0.178947
$160$	10.9253	0.863718
$161$	0	0
$162$	0.0773787	0.00607944
$163$	−20.5202	−1.60727	−0.803635	−	0.595123i	$-0.797103\pi$
$163$	−20.5202	−1.60727	−0.803635	+	0.595123i	$0.797103\pi$
$164$	−1.78213	−0.139161
$165$	2.04242	0.159002
$166$	−8.40640	−0.652463
$167$	−16.4001	−1.26908	−0.634540	−	0.772890i	$-0.718810\pi$
$167$	−16.4001	−1.26908	−0.634540	+	0.772890i	$0.718810\pi$
$168$	0	0
$169$	−12.1323	−0.933256
$170$	1.99277	0.152839
$171$	−12.4368	−0.951063
$172$	8.40927	0.641201
$173$	7.56985	0.575525	0.287763	−	0.957702i	$-0.407089\pi$
$173$	7.56985	0.575525	0.287763	+	0.957702i	$0.407089\pi$
$174$	6.59331	0.499837
$175$	0	0
$176$	0.877810	0.0661674
$177$	40.8099	3.06746
$178$	−0.285727	−0.0214162
$179$	17.1235	1.27987	0.639935	−	0.768429i	$-0.278961\pi$
$179$	17.1235	1.27987	0.639935	+	0.768429i	$0.278961\pi$
$180$	−19.7493	−1.47203
$181$	0.190820	0.0141835	0.00709176	−	0.999975i	$-0.497743\pi$
$181$	0.190820	0.0141835	0.00709176	+	0.999975i	$0.497743\pi$
$182$	0	0
$183$	−26.2990	−1.94408
$184$	−11.8227	−0.871579
$185$	3.08067	0.226495
$186$	−1.11792	−0.0819696
$187$	0.602093	0.0440294
$188$	−2.26120	−0.164915
$189$	0	0
$190$	−2.70275	−0.196078
$191$	2.95437	0.213771	0.106886	−	0.994271i	$-0.465912\pi$
$191$	2.95437	0.213771	0.106886	+	0.994271i	$0.465912\pi$
$192$	−9.08164	−0.655411
$193$	23.4286	1.68643	0.843213	−	0.537580i	$-0.180661\pi$
$193$	23.4286	1.68643	0.843213	+	0.537580i	$0.180661\pi$
$194$	−1.78346	−0.128045
$195$	5.93899	0.425300
$196$	0	0
$197$	8.36683	0.596112	0.298056	−	0.954548i	$-0.403662\pi$
$197$	8.36683	0.596112	0.298056	+	0.954548i	$0.403662\pi$
$198$	0.729482	0.0518421
$199$	18.2077	1.29071	0.645355	−	0.763883i	$-0.276710\pi$
$199$	18.2077	1.29071	0.645355	+	0.763883i	$0.276710\pi$
$200$	−0.281675	−0.0199174
$201$	39.4516	2.78270
$202$	1.69589	0.119323
$203$	0	0
$204$	−9.40201	−0.658272
$205$	2.27147	0.158646
$206$	7.45996	0.519760
$207$	32.6729	2.27092
$208$	2.55252	0.176985
$209$	−0.816604	−0.0564857
$210$	0	0
$211$	−7.56043	−0.520481	−0.260241	−	0.965544i	$-0.583802\pi$
$211$	−7.56043	−0.520481	−0.260241	+	0.965544i	$0.583802\pi$
$212$	1.43263	0.0983936
$213$	−23.3599	−1.60059
$214$	6.28270	0.429476
$215$	−10.7183	−0.730980
$216$	−9.30949	−0.633430
$217$	0	0
$218$	−2.16039	−0.146320
$219$	14.1117	0.953582
$220$	−1.29675	−0.0874268
$221$	1.75078	0.117770
$222$	1.77691	0.119258
$223$	−16.2995	−1.09150	−0.545749	−	0.837949i	$-0.683755\pi$
$223$	−16.2995	−1.09150	−0.545749	+	0.837949i	$0.683755\pi$
$224$	0	0
$225$	0.778430	0.0518953
$226$	−2.06193	−0.137158
$227$	28.9743	1.92309	0.961546	−	0.274644i	$-0.0885601\pi$
$227$	28.9743	1.92309	0.961546	+	0.274644i	$0.0885601\pi$
$228$	12.7517	0.844503
$229$	−12.2509	−0.809563	−0.404781	−	0.914414i	$-0.632652\pi$
$229$	−12.2509	−0.809563	−0.404781	+	0.914414i	$0.632652\pi$
$230$	7.10044	0.468189
$231$	0	0
$232$	−8.88407	−0.583268
$233$	−20.1260	−1.31850	−0.659249	−	0.751925i	$-0.729126\pi$
$233$	−20.1260	−1.31850	−0.659249	+	0.751925i	$0.729126\pi$
$234$	2.12121	0.138668
$235$	2.88208	0.188006
$236$	−25.9106	−1.68663
$237$	−41.7800	−2.71391
$238$	0	0
$239$	14.4092	0.932054	0.466027	−	0.884770i	$-0.345685\pi$
$239$	14.4092	0.932054	0.466027	+	0.884770i	$0.345685\pi$
$240$	17.4713	1.12777
$241$	−23.9520	−1.54288	−0.771442	−	0.636300i	$-0.780464\pi$
$241$	−23.9520	−1.54288	−0.771442	+	0.636300i	$0.780464\pi$
$242$	−5.08652	−0.326974
$243$	−15.3549	−0.985017
$244$	16.6975	1.06895
$245$	0	0
$246$	1.31017	0.0835331
$247$	−2.37454	−0.151088
$248$	1.50632	0.0956515
$249$	−50.5522	−3.20361
$250$	−5.13204	−0.324578
$251$	12.9890	0.819858	0.409929	−	0.912117i	$-0.365553\pi$
$251$	12.9890	0.819858	0.409929	+	0.912117i	$0.365553\pi$
$252$	0	0
$253$	2.14532	0.134875
$254$	0.0304996	0.00191371
$255$	11.9836	0.750442
$256$	1.27594	0.0797460
$257$	2.36642	0.147613	0.0738067	−	0.997273i	$-0.476485\pi$
$257$	2.36642	0.147613	0.0738067	+	0.997273i	$0.476485\pi$
$258$	−6.18222	−0.384889
$259$	0	0
$260$	−3.77072	−0.233850
$261$	24.5518	1.51972
$262$	4.15848	0.256912
$263$	−20.6902	−1.27581	−0.637907	−	0.770114i	$-0.720200\pi$
$263$	−20.6902	−1.27581	−0.637907	+	0.770114i	$0.720200\pi$
$264$	−1.58735	−0.0976947
$265$	−1.82600	−0.112171
$266$	0	0
$267$	−1.71823	−0.105154
$268$	−25.0482	−1.53006
$269$	−23.8476	−1.45402	−0.727008	−	0.686629i	$-0.759090\pi$
$269$	−23.8476	−1.45402	−0.727008	+	0.686629i	$0.759090\pi$
$270$	5.59108	0.340262
$271$	0.887845	0.0539328	0.0269664	−	0.999636i	$-0.491415\pi$
$271$	0.887845	0.0539328	0.0269664	+	0.999636i	$0.491415\pi$
$272$	5.15043	0.312291
$273$	0	0
$274$	3.00848	0.181749
$275$	0.0511121	0.00308217
$276$	−33.5003	−2.01648
$277$	−12.7327	−0.765035	−0.382517	−	0.923948i	$-0.624943\pi$
$277$	−12.7327	−0.765035	−0.382517	+	0.923948i	$0.624943\pi$
$278$	−3.98047	−0.238733
$279$	−4.16284	−0.249222
$280$	0	0
$281$	−9.05386	−0.540108	−0.270054	−	0.962845i	$-0.587042\pi$
$281$	−9.05386	−0.540108	−0.270054	+	0.962845i	$0.587042\pi$
$282$	1.66236	0.0989924
$283$	−1.36511	−0.0811476	−0.0405738	−	0.999177i	$-0.512919\pi$
$283$	−1.36511	−0.0811476	−0.0405738	+	0.999177i	$0.512919\pi$
$284$	14.8314	0.880081
$285$	−16.2531	−0.962748
$286$	0.139280	0.00823577
$287$	0	0
$288$	23.4656	1.38272
$289$	−13.4673	−0.792194
$290$	5.33558	0.313316
$291$	−10.7249	−0.628704
$292$	−8.95967	−0.524325
$293$	−18.9433	−1.10668	−0.553341	−	0.832955i	$-0.686647\pi$
$293$	−18.9433	−1.10668	−0.553341	+	0.832955i	$0.686647\pi$
$294$	0	0
$295$	33.0250	1.92279
$296$	−2.39427	−0.139164
$297$	1.68928	0.0980219
$298$	−0.807181	−0.0467588
$299$	6.23820	0.360765
$300$	−0.798143	−0.0460808
$301$	0	0
$302$	−10.5083	−0.604682
$303$	10.1983	0.585877
$304$	−6.98540	−0.400640
$305$	−21.2823	−1.21862
$306$	4.28014	0.244679
$307$	15.9514	0.910396	0.455198	−	0.890390i	$-0.349568\pi$
$307$	15.9514	0.910396	0.455198	+	0.890390i	$0.349568\pi$
$308$	0	0
$309$	44.8607	2.55204
$310$	−0.904664	−0.0513815
$311$	22.9682	1.30241	0.651204	−	0.758903i	$-0.274264\pi$
$311$	22.9682	1.30241	0.651204	+	0.758903i	$0.274264\pi$
$312$	−4.61574	−0.261315
$313$	−11.7387	−0.663512	−0.331756	−	0.943365i	$-0.607641\pi$
$313$	−11.7387	−0.663512	−0.331756	+	0.943365i	$0.607641\pi$
$314$	−7.74840	−0.437268
$315$	0	0
$316$	26.5265	1.49223
$317$	11.9881	0.673318	0.336659	−	0.941627i	$-0.390703\pi$
$317$	11.9881	0.673318	0.336659	+	0.941627i	$0.390703\pi$
$318$	−1.05323	−0.0590620
$319$	1.61208	0.0902593
$320$	−7.34924	−0.410835
$321$	37.7812	2.10874
$322$	0	0
$323$	−4.79131	−0.266596
$324$	−0.295435	−0.0164131
$325$	0.148625	0.00824423
$326$	−9.57813	−0.530484
$327$	−12.9916	−0.718437
$328$	−1.76537	−0.0974760
$329$	0	0
$330$	0.953329	0.0524790
$331$	−14.5008	−0.797038	−0.398519	−	0.917160i	$-0.630476\pi$
$331$	−14.5008	−0.797038	−0.398519	+	0.917160i	$0.630476\pi$
$332$	32.0960	1.76150
$333$	6.61675	0.362596
$334$	−7.65500	−0.418863
$335$	31.9259	1.74430
$336$	0	0
$337$	−8.58460	−0.467633	−0.233817	−	0.972281i	$-0.575122\pi$
$337$	−8.58460	−0.467633	−0.233817	+	0.972281i	$0.575122\pi$
$338$	−5.66294	−0.308024
$339$	−12.3995	−0.673448
$340$	−7.60850	−0.412629
$341$	−0.273334	−0.0148019
$342$	−5.80505	−0.313901
$343$	0	0
$344$	8.33016	0.449132
$345$	42.6987	2.29882
$346$	3.53334	0.189954
$347$	−24.9483	−1.33930	−0.669648	−	0.742679i	$-0.733555\pi$
$347$	−24.9483	−1.33930	−0.669648	+	0.742679i	$0.733555\pi$
$348$	−25.1736	−1.34944
$349$	6.93479	0.371211	0.185605	−	0.982624i	$-0.440575\pi$
$349$	6.93479	0.371211	0.185605	+	0.982624i	$0.440575\pi$
$350$	0	0
$351$	4.91213	0.262190
$352$	1.54076	0.0821230
$353$	−0.707619	−0.0376627	−0.0188314	−	0.999823i	$-0.505995\pi$
$353$	−0.707619	−0.0376627	−0.0188314	+	0.999823i	$0.505995\pi$
$354$	19.0486	1.01242
$355$	−18.9038	−1.00331
$356$	1.09092	0.0578187
$357$	0	0
$358$	7.99265	0.422425
$359$	6.76868	0.357237	0.178619	−	0.983918i	$-0.442837\pi$
$359$	6.76868	0.357237	0.178619	+	0.983918i	$0.442837\pi$
$360$	−19.5635	−1.03109
$361$	−12.5017	−0.657982
$362$	0.0890680	0.00468131
$363$	−30.5879	−1.60545
$364$	0	0
$365$	11.4198	0.597740
$366$	−12.2755	−0.641648
$367$	9.62173	0.502250	0.251125	−	0.967955i	$-0.419199\pi$
$367$	9.62173	0.502250	0.251125	+	0.967955i	$0.419199\pi$
$368$	18.3515	0.956637
$369$	4.87872	0.253976
$370$	1.43795	0.0747553
$371$	0	0
$372$	4.26826	0.221299
$373$	2.74305	0.142029	0.0710147	−	0.997475i	$-0.477376\pi$
$373$	2.74305	0.142029	0.0710147	+	0.997475i	$0.477376\pi$
$374$	0.281036	0.0145320
$375$	−30.8617	−1.59369
$376$	−2.23993	−0.115516
$377$	4.68766	0.241427
$378$	0	0
$379$	15.8925	0.816344	0.408172	−	0.912905i	$-0.366166\pi$
$379$	15.8925	0.816344	0.408172	+	0.912905i	$0.366166\pi$
$380$	10.3192	0.529365
$381$	0.183410	0.00939639
$382$	1.37900	0.0705557
$383$	24.0653	1.22968	0.614839	−	0.788652i	$-0.289221\pi$
$383$	24.0653	1.22968	0.614839	+	0.788652i	$0.289221\pi$
$384$	−31.2402	−1.59422
$385$	0	0
$386$	10.9356	0.556609
$387$	−23.0210	−1.17022
$388$	6.80933	0.345691
$389$	27.8481	1.41196	0.705978	−	0.708233i	$-0.250508\pi$
$389$	27.8481	1.41196	0.705978	+	0.708233i	$0.250508\pi$
$390$	2.77211	0.140371
$391$	12.5873	0.636569
$392$	0	0
$393$	25.0071	1.26144
$394$	3.90534	0.196748
$395$	−33.8102	−1.70117
$396$	−2.78520	−0.139961
$397$	18.2798	0.917438	0.458719	−	0.888581i	$-0.348309\pi$
$397$	18.2798	0.917438	0.458719	+	0.888581i	$0.348309\pi$
$398$	8.49872	0.426002
$399$	0	0
$400$	0.437223	0.0218612
$401$	22.1227	1.10475	0.552376	−	0.833595i	$-0.313721\pi$
$401$	22.1227	1.10475	0.552376	+	0.833595i	$0.313721\pi$
$402$	18.4146	0.918438
$403$	−0.794807	−0.0395922
$404$	−6.47499	−0.322143
$405$	0.376556	0.0187112
$406$	0	0
$407$	0.434459	0.0215353
$408$	−9.31356	−0.461090
$409$	7.22800	0.357401	0.178701	−	0.983903i	$-0.442811\pi$
$409$	7.22800	0.357401	0.178701	+	0.983903i	$0.442811\pi$
$410$	1.06024	0.0523616
$411$	18.0916	0.892393
$412$	−28.4825	−1.40323
$413$	0	0
$414$	15.2505	0.749523
$415$	−40.9089	−2.00814
$416$	4.48027	0.219663
$417$	−23.9367	−1.17218
$418$	−0.381162	−0.0186432
$419$	−14.7285	−0.719536	−0.359768	−	0.933042i	$-0.617144\pi$
$419$	−14.7285	−0.719536	−0.359768	+	0.933042i	$0.617144\pi$
$420$	0	0
$421$	−19.6784	−0.959067	−0.479533	−	0.877524i	$-0.659194\pi$
$421$	−19.6784	−0.959067	−0.479533	+	0.877524i	$0.659194\pi$
$422$	−3.52894	−0.171786
$423$	6.19022	0.300979
$424$	1.41916	0.0689203
$425$	0.299893	0.0145469
$426$	−10.9036	−0.528280
$427$	0	0
$428$	−23.9876	−1.15949
$429$	0.837562	0.0404379
$430$	−5.00291	−0.241262
$431$	−16.5151	−0.795504	−0.397752	−	0.917493i	$-0.630210\pi$
$431$	−16.5151	−0.795504	−0.397752	+	0.917493i	$0.630210\pi$
$432$	14.4504	0.695247
$433$	34.1999	1.64354	0.821771	−	0.569818i	$-0.192986\pi$
$433$	34.1999	1.64354	0.821771	+	0.569818i	$0.192986\pi$
$434$	0	0
$435$	32.0857	1.53839
$436$	8.24849	0.395031
$437$	−17.0719	−0.816660
$438$	6.58686	0.314732
$439$	41.3982	1.97583	0.987914	−	0.155003i	$-0.0495388\pi$
$439$	41.3982	1.97583	0.987914	+	0.155003i	$0.0495388\pi$
$440$	−1.28455	−0.0612385
$441$	0	0
$442$	0.817203	0.0388704
$443$	−34.9038	−1.65833	−0.829165	−	0.559004i	$-0.811184\pi$
$443$	−34.9038	−1.65833	−0.829165	+	0.559004i	$0.811184\pi$
$444$	−6.78432	−0.321969
$445$	−1.39046	−0.0659143
$446$	−7.60805	−0.360252
$447$	−4.85401	−0.229587
$448$	0	0
$449$	−16.0721	−0.758490	−0.379245	−	0.925296i	$-0.623816\pi$
$449$	−16.0721	−0.758490	−0.379245	+	0.925296i	$0.623816\pi$
$450$	0.363344	0.0171282
$451$	0.320339	0.0150842
$452$	7.87255	0.370294
$453$	−63.1918	−2.96901
$454$	13.5242	0.634722
$455$	0	0
$456$	12.6318	0.591536
$457$	15.5751	0.728572	0.364286	−	0.931287i	$-0.381313\pi$
$457$	15.5751	0.728572	0.364286	+	0.931287i	$0.381313\pi$
$458$	−5.71829	−0.267198
$459$	9.91161	0.462634
$460$	−27.1098	−1.26400
$461$	21.6127	1.00661	0.503303	−	0.864110i	$-0.332118\pi$
$461$	21.6127	1.00661	0.503303	+	0.864110i	$0.332118\pi$
$462$	0	0
$463$	26.2084	1.21801	0.609004	−	0.793167i	$-0.291569\pi$
$463$	26.2084	1.21801	0.609004	+	0.793167i	$0.291569\pi$
$464$	13.7901	0.640189
$465$	−5.44023	−0.252285
$466$	−9.39411	−0.435174
$467$	−12.6773	−0.586635	−0.293318	−	0.956015i	$-0.594759\pi$
$467$	−12.6773	−0.586635	−0.293318	+	0.956015i	$0.594759\pi$
$468$	−8.09887	−0.374370
$469$	0	0
$470$	1.34525	0.0620520
$471$	−46.5953	−2.14700
$472$	−25.6668	−1.18141
$473$	−1.51157	−0.0695022
$474$	−19.5015	−0.895732
$475$	−0.406738	−0.0186624
$476$	0	0
$477$	−3.92195	−0.179574
$478$	6.72571	0.307627
$479$	25.9651	1.18638	0.593189	−	0.805063i	$-0.297869\pi$
$479$	25.9651	1.18638	0.593189	+	0.805063i	$0.297869\pi$
$480$	30.6662	1.39971
$481$	1.26333	0.0576030
$482$	−11.1800	−0.509233
$483$	0	0
$484$	19.4206	0.882753
$485$	−8.67902	−0.394094
$486$	−7.16712	−0.325107
$487$	−3.06725	−0.138990	−0.0694952	−	0.997582i	$-0.522139\pi$
$487$	−3.06725	−0.138990	−0.0694952	+	0.997582i	$0.522139\pi$
$488$	16.5404	0.748749
$489$	−57.5984	−2.60469
$490$	0	0
$491$	−19.4798	−0.879111	−0.439556	−	0.898215i	$-0.644864\pi$
$491$	−19.4798	−0.879111	−0.439556	+	0.898215i	$0.644864\pi$
$492$	−5.00227	−0.225520
$493$	9.45867	0.425997
$494$	−1.10835	−0.0498672
$495$	3.54995	0.159559
$496$	−2.33815	−0.104986
$497$	0	0
$498$	−23.5960	−1.05736
$499$	−38.0744	−1.70445	−0.852223	−	0.523179i	$-0.824746\pi$
$499$	−38.0744	−1.70445	−0.852223	+	0.523179i	$0.824746\pi$
$500$	19.5943	0.876286
$501$	−46.0336	−2.05663
$502$	6.06281	0.270596
$503$	2.94322	0.131232	0.0656158	−	0.997845i	$-0.479099\pi$
$503$	2.94322	0.131232	0.0656158	+	0.997845i	$0.479099\pi$
$504$	0	0
$505$	8.25289	0.367249
$506$	1.00136	0.0445158
$507$	−34.0543	−1.51240
$508$	−0.116449	−0.00516658
$509$	−10.1307	−0.449037	−0.224518	−	0.974470i	$-0.572081\pi$
$509$	−10.1307	−0.449037	−0.224518	+	0.974470i	$0.572081\pi$
$510$	5.59352	0.247685
$511$	0	0
$512$	22.8551	1.01006
$513$	−13.4429	−0.593517
$514$	1.10456	0.0487202
$515$	36.3032	1.59971
$516$	23.6040	1.03911
$517$	0.406453	0.0178758
$518$	0	0
$519$	21.2479	0.932678
$520$	−3.73525	−0.163802
$521$	−22.3941	−0.981101	−0.490551	−	0.871413i	$-0.663204\pi$
$521$	−22.3941	−0.981101	−0.490551	+	0.871413i	$0.663204\pi$
$522$	11.4599	0.501587
$523$	−2.18787	−0.0956689	−0.0478344	−	0.998855i	$-0.515232\pi$
$523$	−2.18787	−0.0956689	−0.0478344	+	0.998855i	$0.515232\pi$
$524$	−15.8773	−0.693602
$525$	0	0
$526$	−9.65747	−0.421086
$527$	−1.60375	−0.0698604
$528$	2.46393	0.107229
$529$	21.8499	0.949996
$530$	−0.852315	−0.0370222
$531$	70.9322	3.07820
$532$	0	0
$533$	0.931491	0.0403474
$534$	−0.802010	−0.0347064
$535$	30.5741	1.32183
$536$	−24.8125	−1.07174
$537$	48.0640	2.07412
$538$	−11.1312	−0.479902
$539$	0	0
$540$	−21.3470	−0.918628
$541$	−29.5763	−1.27159	−0.635793	−	0.771860i	$-0.719327\pi$
$541$	−29.5763	−1.27159	−0.635793	+	0.771860i	$0.719327\pi$
$542$	0.414415	0.0178007
$543$	0.535613	0.0229854
$544$	9.04022	0.387596
$545$	−10.5133	−0.450342
$546$	0	0
$547$	−21.8661	−0.934925	−0.467462	−	0.884013i	$-0.654832\pi$
$547$	−21.8661	−0.934925	−0.467462	+	0.884013i	$0.654832\pi$
$548$	−11.4865	−0.490680
$549$	−45.7107	−1.95088
$550$	0.0238573	0.00101728
$551$	−12.8286	−0.546515
$552$	−33.1851	−1.41245
$553$	0	0
$554$	−5.94319	−0.252502
$555$	8.64714	0.367051
$556$	15.1976	0.644522
$557$	13.1900	0.558880	0.279440	−	0.960163i	$-0.409851\pi$
$557$	13.1900	0.558880	0.279440	+	0.960163i	$0.409851\pi$
$558$	−1.94307	−0.0822565
$559$	−4.39539	−0.185905
$560$	0	0
$561$	1.69002	0.0713526
$562$	−4.22602	−0.178264
$563$	−34.3884	−1.44930	−0.724649	−	0.689119i	$-0.757998\pi$
$563$	−34.3884	−1.44930	−0.724649	+	0.689119i	$0.757998\pi$
$564$	−6.34699	−0.267256
$565$	−10.0342	−0.422141
$566$	−0.637187	−0.0267830
$567$	0	0
$568$	14.6919	0.616457
$569$	15.9614	0.669138	0.334569	−	0.942371i	$-0.391409\pi$
$569$	15.9614	0.669138	0.334569	+	0.942371i	$0.391409\pi$
$570$	−7.58636	−0.317758
$571$	−4.62863	−0.193702	−0.0968510	−	0.995299i	$-0.530877\pi$
$571$	−4.62863	−0.193702	−0.0968510	+	0.995299i	$0.530877\pi$
$572$	−0.531776	−0.0222347
$573$	8.29265	0.346431
$574$	0	0
$575$	1.06855	0.0445615
$576$	−15.7849	−0.657705
$577$	6.80651	0.283359	0.141679	−	0.989913i	$-0.454750\pi$
$577$	6.80651	0.283359	0.141679	+	0.989913i	$0.454750\pi$
$578$	−6.28607	−0.261466
$579$	65.7618	2.73297
$580$	−20.3715	−0.845880
$581$	0	0
$582$	−5.00600	−0.207505
$583$	−0.257517	−0.0106653
$584$	−8.87538	−0.367266
$585$	10.3226	0.426789
$586$	−8.84208	−0.365263
$587$	−6.97160	−0.287749	−0.143874	−	0.989596i	$-0.545956\pi$
$587$	−6.97160	−0.287749	−0.143874	+	0.989596i	$0.545956\pi$
$588$	0	0
$589$	2.17512	0.0896245
$590$	15.4149	0.634623
$591$	23.4849	0.966040
$592$	3.71645	0.152745
$593$	−7.60609	−0.312345	−0.156172	−	0.987730i	$-0.549916\pi$
$593$	−7.60609	−0.312345	−0.156172	+	0.987730i	$0.549916\pi$
$594$	0.788496	0.0323524
$595$	0	0
$596$	3.08186	0.126238
$597$	51.1073	2.09168
$598$	2.91177	0.119071
$599$	−30.7633	−1.25695	−0.628476	−	0.777829i	$-0.716321\pi$
$599$	−30.7633	−1.25695	−0.628476	+	0.777829i	$0.716321\pi$
$600$	−0.790635	−0.0322775
$601$	−15.2390	−0.621614	−0.310807	−	0.950473i	$-0.600599\pi$
$601$	−15.2390	−0.621614	−0.310807	+	0.950473i	$0.600599\pi$
$602$	0	0
$603$	68.5714	2.79244
$604$	40.1210	1.63250
$605$	−24.7530	−1.00635
$606$	4.76021	0.193370
$607$	9.81497	0.398377	0.199189	−	0.979961i	$-0.436169\pi$
$607$	9.81497	0.398377	0.199189	+	0.979961i	$0.436169\pi$
$608$	−12.2610	−0.497250
$609$	0	0
$610$	−9.93381	−0.402208
$611$	1.18189	0.0478143
$612$	−16.3418	−0.660577
$613$	−13.5042	−0.545431	−0.272716	−	0.962095i	$-0.587922\pi$
$613$	−13.5042	−0.545431	−0.272716	+	0.962095i	$0.587922\pi$
$614$	7.44557	0.300479
$615$	6.37579	0.257097
$616$	0	0
$617$	−35.4412	−1.42681	−0.713405	−	0.700752i	$-0.752848\pi$
$617$	−35.4412	−1.42681	−0.713405	+	0.700752i	$0.752848\pi$
$618$	20.9394	0.842307
$619$	10.9607	0.440548	0.220274	−	0.975438i	$-0.429305\pi$
$619$	10.9607	0.440548	0.220274	+	0.975438i	$0.429305\pi$
$620$	3.45405	0.138718
$621$	35.3160	1.41718
$622$	10.7208	0.429863
$623$	0	0
$624$	7.16468	0.286817
$625$	−25.7723	−1.03089
$626$	−5.47922	−0.218994
$627$	−2.29213	−0.0915389
$628$	29.5838	1.18052
$629$	2.54913	0.101640
$630$	0	0
$631$	−19.9398	−0.793791	−0.396895	−	0.917864i	$-0.629912\pi$
$631$	−19.9398	−0.793791	−0.396895	+	0.917864i	$0.629912\pi$
$632$	26.2770	1.04524
$633$	−21.2214	−0.843476
$634$	5.59562	0.222230
$635$	0.148423	0.00589000
$636$	4.02127	0.159454
$637$	0	0
$638$	0.752464	0.0297903
$639$	−40.6021	−1.60620
$640$	−25.2809	−0.999315
$641$	−23.9109	−0.944422	−0.472211	−	0.881486i	$-0.656544\pi$
$641$	−23.9109	−0.944422	−0.472211	+	0.881486i	$0.656544\pi$
$642$	17.6349	0.695996
$643$	24.5332	0.967496	0.483748	−	0.875207i	$-0.339275\pi$
$643$	24.5332	0.967496	0.483748	+	0.875207i	$0.339275\pi$
$644$	0	0
$645$	−30.0852	−1.18460
$646$	−2.23642	−0.0879906
$647$	6.67512	0.262426	0.131213	−	0.991354i	$-0.458113\pi$
$647$	6.67512	0.262426	0.131213	+	0.991354i	$0.458113\pi$
$648$	−0.292656	−0.0114966
$649$	4.65744	0.182821
$650$	0.0693730	0.00272103
$651$	0	0
$652$	36.5697	1.43218
$653$	16.0137	0.626663	0.313331	−	0.949644i	$-0.398555\pi$
$653$	16.0137	0.626663	0.313331	+	0.949644i	$0.398555\pi$
$654$	−6.06403	−0.237122
$655$	20.2368	0.790718
$656$	2.74025	0.106989
$657$	24.5278	0.956921
$658$	0	0
$659$	−11.4362	−0.445492	−0.222746	−	0.974877i	$-0.571502\pi$
$659$	−11.4362	−0.445492	−0.222746	+	0.974877i	$0.571502\pi$
$660$	−3.63985	−0.141681
$661$	3.78575	0.147248	0.0736242	−	0.997286i	$-0.476543\pi$
$661$	3.78575	0.147248	0.0736242	+	0.997286i	$0.476543\pi$
$662$	−6.76848	−0.263064
$663$	4.91428	0.190855
$664$	31.7941	1.23385
$665$	0	0
$666$	3.08847	0.119676
$667$	33.7022	1.30495
$668$	29.2272	1.13083
$669$	−45.7513	−1.76885
$670$	14.9019	0.575710
$671$	−3.00139	−0.115867
$672$	0	0
$673$	−30.5832	−1.17890	−0.589448	−	0.807806i	$-0.700655\pi$
$673$	−30.5832	−1.17890	−0.589448	+	0.807806i	$0.700655\pi$
$674$	−4.00699	−0.154344
$675$	0.841403	0.0323856
$676$	21.6214	0.831592
$677$	27.6916	1.06427	0.532136	−	0.846659i	$-0.321389\pi$
$677$	27.6916	1.06427	0.532136	+	0.846659i	$0.321389\pi$
$678$	−5.78765	−0.222273
$679$	0	0
$680$	−7.53692	−0.289028
$681$	81.3282	3.11650
$682$	−0.127583	−0.00488539
$683$	−24.9576	−0.954977	−0.477488	−	0.878638i	$-0.658453\pi$
$683$	−24.9576	−0.954977	−0.477488	+	0.878638i	$0.658453\pi$
$684$	22.1639	0.847459
$685$	14.6405	0.559384
$686$	0	0
$687$	−34.3871	−1.31195
$688$	−12.9303	−0.492963
$689$	−0.748814	−0.0285276
$690$	19.9303	0.758732
$691$	39.8440	1.51574	0.757869	−	0.652406i	$-0.226240\pi$
$691$	39.8440	1.51574	0.757869	+	0.652406i	$0.226240\pi$
$692$	−13.4905	−0.512831
$693$	0	0
$694$	−11.6450	−0.442038
$695$	−19.3705	−0.734767
$696$	−24.9367	−0.945225
$697$	1.87955	0.0711929
$698$	3.23692	0.122519
$699$	−56.4918	−2.13672
$700$	0	0
$701$	−10.5909	−0.400014	−0.200007	−	0.979794i	$-0.564096\pi$
$701$	−10.5909	−0.400014	−0.200007	+	0.979794i	$0.564096\pi$
$702$	2.29281	0.0865365
$703$	−3.45732	−0.130395
$704$	−1.03645	−0.0390625
$705$	8.08973	0.304677
$706$	−0.330292	−0.0124307
$707$	0	0
$708$	−72.7285	−2.73330
$709$	27.3811	1.02832	0.514160	−	0.857694i	$-0.328104\pi$
$709$	27.3811	1.02832	0.514160	+	0.857694i	$0.328104\pi$
$710$	−8.82362	−0.331145
$711$	−72.6185	−2.72341
$712$	1.08066	0.0404994
$713$	−5.71431	−0.214003
$714$	0	0
$715$	0.677790	0.0253479
$716$	−30.5163	−1.14045
$717$	40.4453	1.51046
$718$	3.15938	0.117907
$719$	−44.5474	−1.66134	−0.830668	−	0.556768i	$-0.812041\pi$
$719$	−44.5474	−1.66134	−0.830668	+	0.556768i	$0.812041\pi$
$720$	30.3670	1.13171
$721$	0	0
$722$	−5.83534	−0.217169
$723$	−67.2310	−2.50035
$724$	−0.340066	−0.0126384
$725$	0.802953	0.0298209
$726$	−14.2774	−0.529883
$727$	−16.7899	−0.622702	−0.311351	−	0.950295i	$-0.600782\pi$
$727$	−16.7899	−0.622702	−0.311351	+	0.950295i	$0.600782\pi$
$728$	0	0
$729$	−43.5971	−1.61471
$730$	5.33036	0.197286
$731$	−8.86894	−0.328030
$732$	46.8683	1.73230
$733$	14.0597	0.519306	0.259653	−	0.965702i	$-0.416392\pi$
$733$	14.0597	0.519306	0.259653	+	0.965702i	$0.416392\pi$
$734$	4.49109	0.165769
$735$	0	0
$736$	32.2112	1.18732
$737$	4.50243	0.165849
$738$	2.27722	0.0838255
$739$	−45.9588	−1.69062	−0.845311	−	0.534275i	$-0.820585\pi$
$739$	−45.9588	−1.69062	−0.845311	+	0.534275i	$0.820585\pi$
$740$	−5.49015	−0.201822
$741$	−6.66512	−0.244849
$742$	0	0
$743$	37.3545	1.37041	0.685203	−	0.728352i	$-0.259714\pi$
$743$	37.3545	1.37041	0.685203	+	0.728352i	$0.259714\pi$
$744$	4.22810	0.155010
$745$	−3.92807	−0.143913
$746$	1.28036	0.0468772
$747$	−87.8655	−3.21483
$748$	−1.07301	−0.0392331
$749$	0	0
$750$	−14.4051	−0.526001
$751$	41.7770	1.52446	0.762232	−	0.647304i	$-0.224104\pi$
$751$	41.7770	1.52446	0.762232	+	0.647304i	$0.224104\pi$
$752$	3.47688	0.126789
$753$	36.4589	1.32864
$754$	2.18803	0.0796835
$755$	−51.1374	−1.86108
$756$	0	0
$757$	44.6881	1.62422	0.812109	−	0.583506i	$-0.198319\pi$
$757$	44.6881	1.62422	0.812109	+	0.583506i	$0.198319\pi$
$758$	7.41807	0.269437
$759$	6.02170	0.218574
$760$	10.2221	0.370796
$761$	−18.8264	−0.682456	−0.341228	−	0.939981i	$-0.610843\pi$
$761$	−18.8264	−0.682456	−0.341228	+	0.939981i	$0.610843\pi$
$762$	0.0856095	0.00310130
$763$	0	0
$764$	−5.26508	−0.190484
$765$	20.8289	0.753069
$766$	11.2328	0.405859
$767$	13.5430	0.489011
$768$	3.58143	0.129234
$769$	−26.6752	−0.961933	−0.480966	−	0.876739i	$-0.659714\pi$
$769$	−26.6752	−0.961933	−0.480966	+	0.876739i	$0.659714\pi$
$770$	0	0
$771$	6.64233	0.239218
$772$	−41.7528	−1.50272
$773$	−3.09354	−0.111267	−0.0556334	−	0.998451i	$-0.517718\pi$
$773$	−3.09354	−0.111267	−0.0556334	+	0.998451i	$0.517718\pi$
$774$	−10.7454	−0.386236
$775$	−0.136143	−0.00489041
$776$	6.74527	0.242141
$777$	0	0
$778$	12.9985	0.466020
$779$	−2.54918	−0.0913340
$780$	−10.5841	−0.378970
$781$	−2.66595	−0.0953953
$782$	5.87533	0.210101
$783$	26.5380	0.948390
$784$	0	0
$785$	−37.7068	−1.34581
$786$	11.6725	0.416343
$787$	7.65384	0.272830	0.136415	−	0.990652i	$-0.456442\pi$
$787$	7.65384	0.272830	0.136415	+	0.990652i	$0.456442\pi$
$788$	−14.9108	−0.531174
$789$	−58.0755	−2.06754
$790$	−15.7814	−0.561477
$791$	0	0
$792$	−2.75900	−0.0980367
$793$	−8.72751	−0.309923
$794$	8.53238	0.302803
$795$	−5.12542	−0.181780
$796$	−32.4485	−1.15011
$797$	33.7216	1.19448	0.597240	−	0.802062i	$-0.296264\pi$
$797$	33.7216	1.19448	0.597240	+	0.802062i	$0.296264\pi$
$798$	0	0
$799$	2.38481	0.0843684
$800$	0.767430	0.0271328
$801$	−2.98648	−0.105522
$802$	10.3261	0.364627
$803$	1.61051	0.0568336
$804$	−70.3079	−2.47957
$805$	0	0
$806$	−0.370988	−0.0130675
$807$	−66.9381	−2.35633
$808$	−6.41408	−0.225647
$809$	21.2975	0.748779	0.374390	−	0.927271i	$-0.377852\pi$
$809$	21.2975	0.748779	0.374390	+	0.927271i	$0.377852\pi$
$810$	0.175763	0.00617568
$811$	25.2190	0.885560	0.442780	−	0.896630i	$-0.353992\pi$
$811$	25.2190	0.885560	0.442780	+	0.896630i	$0.353992\pi$
$812$	0	0
$813$	2.49210	0.0874017
$814$	0.202790	0.00710780
$815$	−46.6110	−1.63271
$816$	14.4568	0.506088
$817$	12.0287	0.420832
$818$	3.37377	0.117961
$819$	0	0
$820$	−4.04805	−0.141364
$821$	11.6200	0.405541	0.202771	−	0.979226i	$-0.435005\pi$
$821$	11.6200	0.405541	0.202771	+	0.979226i	$0.435005\pi$
$822$	8.44453	0.294537
$823$	25.7465	0.897467	0.448733	−	0.893666i	$-0.351875\pi$
$823$	25.7465	0.897467	0.448733	+	0.893666i	$0.351875\pi$
$824$	−28.2146	−0.982900
$825$	0.143467	0.00499487
$826$	0	0
$827$	37.6105	1.30784	0.653922	−	0.756562i	$-0.273123\pi$
$827$	37.6105	1.30784	0.653922	+	0.756562i	$0.273123\pi$
$828$	−58.2273	−2.02354
$829$	22.5950	0.784758	0.392379	−	0.919804i	$-0.371652\pi$
$829$	22.5950	0.784758	0.392379	+	0.919804i	$0.371652\pi$
$830$	−19.0949	−0.662792
$831$	−35.7396	−1.23979
$832$	−3.01380	−0.104485
$833$	0	0
$834$	−11.1728	−0.386882
$835$	−37.2523	−1.28917
$836$	1.45529	0.0503324
$837$	−4.49960	−0.155529
$838$	−6.87476	−0.237485
$839$	−12.8657	−0.444173	−0.222087	−	0.975027i	$-0.571287\pi$
$839$	−12.8657	−0.444173	−0.222087	+	0.975027i	$0.571287\pi$
$840$	0	0
$841$	−3.67473	−0.126715
$842$	−9.18519	−0.316543
$843$	−25.4133	−0.875282
$844$	13.4737	0.463783
$845$	−27.5582	−0.948029
$846$	2.88938	0.0993389
$847$	0	0
$848$	−2.20285	−0.0756463
$849$	−3.83175	−0.131505
$850$	0.139980	0.00480126
$851$	9.08279	0.311354
$852$	41.6303	1.42623
$853$	8.25103	0.282510	0.141255	−	0.989973i	$-0.454886\pi$
$853$	8.25103	0.282510	0.141255	+	0.989973i	$0.454886\pi$
$854$	0	0
$855$	−28.2497	−0.966119
$856$	−23.7620	−0.812168
$857$	25.6038	0.874610	0.437305	−	0.899313i	$-0.355933\pi$
$857$	25.6038	0.874610	0.437305	+	0.899313i	$0.355933\pi$
$858$	0.390945	0.0133466
$859$	31.2201	1.06522	0.532609	−	0.846362i	$-0.321212\pi$
$859$	31.2201	1.06522	0.532609	+	0.846362i	$0.321212\pi$
$860$	19.1014	0.651351
$861$	0	0
$862$	−7.70866	−0.262558
$863$	53.2452	1.81249	0.906244	−	0.422755i	$-0.138937\pi$
$863$	53.2452	1.81249	0.906244	+	0.422755i	$0.138937\pi$
$864$	25.3639	0.862899
$865$	17.1947	0.584636
$866$	15.9633	0.542456
$867$	−37.8015	−1.28380
$868$	0	0
$869$	−4.76816	−0.161749
$870$	14.9765	0.507750
$871$	13.0923	0.443615
$872$	8.17090	0.276701
$873$	−18.6411	−0.630905
$874$	−7.96857	−0.269541
$875$	0	0
$876$	−25.1489	−0.849704
$877$	16.7100	0.564258	0.282129	−	0.959377i	$-0.408959\pi$
$877$	16.7100	0.564258	0.282129	+	0.959377i	$0.408959\pi$
$878$	19.3232	0.652127
$879$	−53.1722	−1.79345
$880$	1.99391	0.0672149
$881$	29.0551	0.978891	0.489446	−	0.872034i	$-0.337199\pi$
$881$	29.0551	0.978891	0.489446	+	0.872034i	$0.337199\pi$
$882$	0	0
$883$	−11.6912	−0.393440	−0.196720	−	0.980460i	$-0.563029\pi$
$883$	−11.6912	−0.393440	−0.196720	+	0.980460i	$0.563029\pi$
$884$	−3.12012	−0.104941
$885$	92.6982	3.11602
$886$	−16.2919	−0.547336
$887$	9.18476	0.308394	0.154197	−	0.988040i	$-0.450721\pi$
$887$	9.18476	0.308394	0.154197	+	0.988040i	$0.450721\pi$
$888$	−6.72050	−0.225525
$889$	0	0
$890$	−0.649020	−0.0217552
$891$	0.0531047	0.00177908
$892$	29.0479	0.972596
$893$	−3.23446	−0.108237
$894$	−2.26568	−0.0757758
$895$	38.8954	1.30013
$896$	0	0
$897$	17.5101	0.584644
$898$	−7.50190	−0.250342
$899$	−4.29398	−0.143212
$900$	−1.38726	−0.0462421
$901$	−1.51094	−0.0503369
$902$	0.149523	0.00497858
$903$	0	0
$904$	7.79849	0.259374
$905$	0.433440	0.0144080
$906$	−29.4957	−0.979929
$907$	46.6046	1.54748	0.773740	−	0.633504i	$-0.218384\pi$
$907$	46.6046	1.54748	0.773740	+	0.633504i	$0.218384\pi$
$908$	−51.6360	−1.71360
$909$	17.7258	0.587928
$910$	0	0
$911$	−38.3235	−1.26971	−0.634857	−	0.772630i	$-0.718941\pi$
$911$	−38.3235	−1.26971	−0.634857	+	0.772630i	$0.718941\pi$
$912$	−19.6074	−0.649265
$913$	−5.76929	−0.190936
$914$	7.26990	0.240467
$915$	−59.7373	−1.97485
$916$	21.8327	0.721373
$917$	0	0
$918$	4.62639	0.152694
$919$	50.3369	1.66046	0.830230	−	0.557421i	$-0.188209\pi$
$919$	50.3369	1.66046	0.830230	+	0.557421i	$0.188209\pi$
$920$	−26.8548	−0.885376
$921$	44.7742	1.47536
$922$	10.0881	0.332233
$923$	−7.75213	−0.255165
$924$	0	0
$925$	0.216397	0.00711510
$926$	12.2332	0.402007
$927$	77.9731	2.56097
$928$	24.2049	0.794564
$929$	−15.7291	−0.516056	−0.258028	−	0.966137i	$-0.583073\pi$
$929$	−15.7291	−0.516056	−0.258028	+	0.966137i	$0.583073\pi$
$930$	−2.53931	−0.0832672
$931$	0	0
$932$	35.8672	1.17487
$933$	64.4696	2.11064
$934$	−5.91732	−0.193621
$935$	1.36763	0.0447264
$936$	−8.02268	−0.262230
$937$	−36.3405	−1.18719	−0.593597	−	0.804763i	$-0.702293\pi$
$937$	−36.3405	−1.18719	−0.593597	+	0.804763i	$0.702293\pi$
$938$	0	0
$939$	−32.9495	−1.07527
$940$	−5.13625	−0.167526
$941$	10.2099	0.332832	0.166416	−	0.986056i	$-0.446780\pi$
$941$	10.2099	0.332832	0.166416	+	0.986056i	$0.446780\pi$
$942$	−21.7490	−0.708622
$943$	6.69701	0.218085
$944$	39.8407	1.29671
$945$	0	0
$946$	−0.705549	−0.0229394
$947$	22.1609	0.720134	0.360067	−	0.932926i	$-0.382754\pi$
$947$	22.1609	0.720134	0.360067	+	0.932926i	$0.382754\pi$
$948$	74.4575	2.41827
$949$	4.68307	0.152019
$950$	−0.189851	−0.00615958
$951$	33.6494	1.09116
$952$	0	0
$953$	4.61414	0.149467	0.0747334	−	0.997204i	$-0.476189\pi$
$953$	4.61414	0.149467	0.0747334	+	0.997204i	$0.476189\pi$
$954$	−1.83063	−0.0592688
$955$	6.71076	0.217155
$956$	−25.6791	−0.830521
$957$	4.52497	0.146271
$958$	12.1196	0.391567
$959$	0	0
$960$	−20.6286	−0.665786
$961$	−30.2719	−0.976514
$962$	0.589679	0.0190120
$963$	65.6680	2.11612
$964$	42.6856	1.37481
$965$	53.2172	1.71312
$966$	0	0
$967$	23.8066	0.765568	0.382784	−	0.923838i	$-0.374965\pi$
$967$	23.8066	0.765568	0.382784	+	0.923838i	$0.374965\pi$
$968$	19.2379	0.618329
$969$	−13.4488	−0.432036
$970$	−4.05106	−0.130072
$971$	10.7890	0.346234	0.173117	−	0.984901i	$-0.444616\pi$
$971$	10.7890	0.346234	0.173117	+	0.984901i	$0.444616\pi$
$972$	27.3644	0.877714
$973$	0	0
$974$	−1.43169	−0.0458741
$975$	0.417177	0.0133603
$976$	−25.6745	−0.821820
$977$	49.9602	1.59837	0.799184	−	0.601087i	$-0.205265\pi$
$977$	49.9602	1.59837	0.799184	+	0.601087i	$0.205265\pi$
$978$	−26.8849	−0.859685
$979$	−0.196094	−0.00626718
$980$	0	0
$981$	−22.5809	−0.720952
$982$	−9.09249	−0.290153
$983$	29.2373	0.932525	0.466262	−	0.884646i	$-0.345600\pi$
$983$	29.2373	0.932525	0.466262	+	0.884646i	$0.345600\pi$
$984$	−4.95522	−0.157967
$985$	19.0050	0.605548
$986$	4.41498	0.140602
$987$	0	0
$988$	4.23174	0.134630
$989$	−31.6009	−1.00485
$990$	1.65699	0.0526627
$991$	−25.9738	−0.825083	−0.412542	−	0.910939i	$-0.635359\pi$
$991$	−25.9738	−0.825083	−0.412542	+	0.910939i	$0.635359\pi$
$992$	−4.10401	−0.130303
$993$	−40.7025	−1.29165
$994$	0	0
$995$	41.3582	1.31114
$996$	90.0906	2.85463
$997$	49.3201	1.56198	0.780991	−	0.624542i	$-0.214714\pi$
$997$	49.3201	1.56198	0.780991	+	0.624542i	$0.214714\pi$
$998$	−17.7718	−0.562557
$999$	7.15203	0.226280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.u.1.13	yes	20
7.6	odd	2		2009.2.a.t.1.13	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2009.2.a.t.1.13	✓	20	7.6	odd	2
2009.2.a.u.1.13	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2009 = 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2009.a (trivial)

\(f(q)\)	\(=\)	\(q+0.466765 q^{2} +2.80691 q^{3} -1.78213 q^{4} +2.27147 q^{5} +1.31017 q^{6} -1.76537 q^{8} +4.87872 q^{9} +O(q^{10})\)	\(q+0.466765 q^{2} +2.80691 q^{3} -1.78213 q^{4} +2.27147 q^{5} +1.31017 q^{6} -1.76537 q^{8} +4.87872 q^{9} +1.06024 q^{10} +0.320339 q^{11} -5.00227 q^{12} +0.931491 q^{13} +6.37579 q^{15} +2.74025 q^{16} +1.87955 q^{17} +2.27722 q^{18} -2.54918 q^{19} -4.04805 q^{20} +0.149523 q^{22} +6.69701 q^{23} -4.95522 q^{24} +0.159556 q^{25} +0.434787 q^{26} +5.27340 q^{27} +5.03242 q^{29} +2.97600 q^{30} -0.853263 q^{31} +4.80978 q^{32} +0.899163 q^{33} +0.877307 q^{34} -8.69452 q^{36} +1.35625 q^{37} -1.18987 q^{38} +2.61461 q^{39} -4.00997 q^{40} +1.00000 q^{41} -4.71866 q^{43} -0.570886 q^{44} +11.0819 q^{45} +3.12593 q^{46} +1.26882 q^{47} +7.69163 q^{48} +0.0744752 q^{50} +5.27571 q^{51} -1.66004 q^{52} -0.803888 q^{53} +2.46144 q^{54} +0.727640 q^{55} -7.15532 q^{57} +2.34896 q^{58} +14.5391 q^{59} -11.3625 q^{60} -9.36939 q^{61} -0.398273 q^{62} -3.23546 q^{64} +2.11585 q^{65} +0.419698 q^{66} +14.0552 q^{67} -3.34960 q^{68} +18.7979 q^{69} -8.32228 q^{71} -8.61273 q^{72} +5.02750 q^{73} +0.633048 q^{74} +0.447859 q^{75} +4.54298 q^{76} +1.22041 q^{78} -14.8847 q^{79} +6.22438 q^{80} +0.165777 q^{81} +0.466765 q^{82} -18.0099 q^{83} +4.26933 q^{85} -2.20250 q^{86} +14.1255 q^{87} -0.565516 q^{88} -0.612144 q^{89} +5.17262 q^{90} -11.9349 q^{92} -2.39503 q^{93} +0.592241 q^{94} -5.79038 q^{95} +13.5006 q^{96} -3.82089 q^{97} +1.56285 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 8 q^{3} + 18 q^{4} + 8 q^{5} + 12 q^{6} - 6 q^{8} + 16 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 8 * q^3 + 18 * q^4 + 8 * q^5 + 12 * q^6 - 6 * q^8 + 16 * q^9	\( 20 q - 2 q^{2} + 8 q^{3} + 18 q^{4} + 8 q^{5} + 12 q^{6} - 6 q^{8} + 16 q^{9} + 16 q^{10} + 6 q^{12} + 12 q^{13} + 14 q^{16} + 8 q^{17} - 18 q^{18} + 36 q^{19} + 24 q^{20} - 8 q^{22} - 12 q^{23} + 36 q^{24} + 20 q^{25} - 22 q^{26} + 32 q^{27} + 4 q^{29} + 28 q^{30} + 80 q^{31} + 6 q^{32} - 12 q^{33} + 48 q^{34} + 26 q^{36} + 4 q^{37} + 12 q^{38} - 28 q^{39} - 4 q^{40} + 20 q^{41} - 20 q^{44} + 40 q^{45} + 8 q^{46} + 32 q^{47} + 16 q^{48} + 6 q^{50} - 20 q^{51} + 36 q^{52} + 4 q^{53} - 50 q^{54} + 64 q^{55} - 4 q^{57} + 32 q^{59} + 20 q^{60} + 44 q^{61} - 8 q^{62} - 30 q^{64} - 8 q^{65} + 32 q^{66} - 4 q^{67} - 48 q^{68} - 24 q^{69} + 8 q^{71} - 8 q^{72} + 48 q^{73} - 38 q^{74} + 24 q^{75} + 84 q^{76} + 30 q^{78} - 4 q^{79} + 56 q^{80} - 2 q^{82} + 8 q^{83} - 12 q^{85} - 24 q^{86} + 40 q^{87} - 48 q^{88} + 20 q^{89} + 48 q^{90} - 50 q^{92} + 48 q^{93} + 26 q^{94} + 20 q^{95} + 70 q^{96} + 8 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 8 * q^3 + 18 * q^4 + 8 * q^5 + 12 * q^6 - 6 * q^8 + 16 * q^9 + 16 * q^10 + 6 * q^12 + 12 * q^13 + 14 * q^16 + 8 * q^17 - 18 * q^18 + 36 * q^19 + 24 * q^20 - 8 * q^22 - 12 * q^23 + 36 * q^24 + 20 * q^25 - 22 * q^26 + 32 * q^27 + 4 * q^29 + 28 * q^30 + 80 * q^31 + 6 * q^32 - 12 * q^33 + 48 * q^34 + 26 * q^36 + 4 * q^37 + 12 * q^38 - 28 * q^39 - 4 * q^40 + 20 * q^41 - 20 * q^44 + 40 * q^45 + 8 * q^46 + 32 * q^47 + 16 * q^48 + 6 * q^50 - 20 * q^51 + 36 * q^52 + 4 * q^53 - 50 * q^54 + 64 * q^55 - 4 * q^57 + 32 * q^59 + 20 * q^60 + 44 * q^61 - 8 * q^62 - 30 * q^64 - 8 * q^65 + 32 * q^66 - 4 * q^67 - 48 * q^68 - 24 * q^69 + 8 * q^71 - 8 * q^72 + 48 * q^73 - 38 * q^74 + 24 * q^75 + 84 * q^76 + 30 * q^78 - 4 * q^79 + 56 * q^80 - 2 * q^82 + 8 * q^83 - 12 * q^85 - 24 * q^86 + 40 * q^87 - 48 * q^88 + 20 * q^89 + 48 * q^90 - 50 * q^92 + 48 * q^93 + 26 * q^94 + 20 * q^95 + 70 * q^96 + 8 * q^97 - 8 * q^99

Introduction

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