LMFDB - Embedded newform 2009.2.a.l.1.5

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:	$1$
Dimension:	$5$
Coefficient field:	5.5.233489.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + x^{2} + 5x - 1 $ x^5 - x^4 - 6x^3 + x^2 + 5x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.881963$ 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)

$f(q)$	$=$	$q+1.97027 q^{2} +0.515563 q^{3} +1.88196 q^{4} -0.515563 q^{5} +1.01580 q^{6} -0.232565 q^{8} -2.73420 q^{9} +O(q^{10})$	\(q+1.97027 q^{2} +0.515563 q^{3} +1.88196 q^{4} -0.515563 q^{5} +1.01580 q^{6} -0.232565 q^{8} -2.73420 q^{9} -1.01580 q^{10} -4.48583 q^{11} +0.970270 q^{12} -0.515563 q^{13} -0.265805 q^{15} -4.22214 q^{16} -5.38359 q^{17} -5.38710 q^{18} +3.91309 q^{19} -0.970270 q^{20} -8.83830 q^{22} +2.14565 q^{23} -0.119902 q^{24} -4.73420 q^{25} -1.01580 q^{26} -2.95634 q^{27} -3.58854 q^{29} -0.523707 q^{30} +6.17848 q^{31} -7.85363 q^{32} -2.31273 q^{33} -10.6071 q^{34} -5.14565 q^{36} -9.53276 q^{37} +7.70984 q^{38} -0.265805 q^{39} +0.119902 q^{40} -1.00000 q^{41} +9.50489 q^{43} -8.44217 q^{44} +1.40965 q^{45} +4.22752 q^{46} +10.2670 q^{47} -2.17678 q^{48} -9.32764 q^{50} -2.77558 q^{51} -0.970270 q^{52} -1.71302 q^{53} -5.82478 q^{54} +2.31273 q^{55} +2.01744 q^{57} -7.07040 q^{58} +4.21652 q^{59} -0.500235 q^{60} -15.4161 q^{61} +12.1733 q^{62} -7.02948 q^{64} +0.265805 q^{65} -4.55670 q^{66} -3.77956 q^{67} -10.1317 q^{68} +1.10622 q^{69} +6.37594 q^{71} +0.635879 q^{72} +3.49673 q^{73} -18.7821 q^{74} -2.44077 q^{75} +7.36429 q^{76} -0.523707 q^{78} -7.02575 q^{79} +2.17678 q^{80} +6.67841 q^{81} -1.97027 q^{82} +7.25513 q^{83} +2.77558 q^{85} +18.7272 q^{86} -1.85012 q^{87} +1.04325 q^{88} -3.29929 q^{89} +2.77739 q^{90} +4.03804 q^{92} +3.18539 q^{93} +20.2287 q^{94} -2.01744 q^{95} -4.04904 q^{96} -19.3033 q^{97} +12.2651 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 2 q^{3} + 6 q^{4} + 2 q^{5} + q^{6} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 + 2 * q^5 + q^6 - 3 * q^8 + 5 * q^9	$ 5 q - 2 q^{2} - 2 q^{3} + 6 q^{4} + 2 q^{5} + q^{6} - 3 q^{8} + 5 q^{9} - q^{10} - 6 q^{11} - 7 q^{12} + 2 q^{13} - 20 q^{15} - 12 q^{16} - 3 q^{17} - 8 q^{18} + 7 q^{19} + 7 q^{20} - 13 q^{22} + 16 q^{24} - 5 q^{25} - q^{26} + 13 q^{27} - 10 q^{29} + 14 q^{30} - 6 q^{31} - 3 q^{32} - 17 q^{33} + q^{34} - 15 q^{36} - 18 q^{37} - 7 q^{38} - 20 q^{39} - 16 q^{40} - 5 q^{41} - 14 q^{43} + 2 q^{44} - 7 q^{45} - 3 q^{46} + 3 q^{47} + 9 q^{48} - 4 q^{50} + 7 q^{52} - 9 q^{53} - 25 q^{54} + 17 q^{55} + 31 q^{57} - 5 q^{58} - 19 q^{59} - 3 q^{60} - 23 q^{61} + 36 q^{62} - q^{64} + 20 q^{65} + 23 q^{66} - 11 q^{67} - 24 q^{68} + 19 q^{69} + 25 q^{72} + 13 q^{73} + 2 q^{74} + 11 q^{75} + 12 q^{76} + 14 q^{78} - 41 q^{79} - 9 q^{80} - 7 q^{81} + 2 q^{82} - 2 q^{83} + 20 q^{86} + 32 q^{87} - 10 q^{88} + 14 q^{89} + 22 q^{90} + 17 q^{92} - 15 q^{93} + 10 q^{94} - 31 q^{95} - 33 q^{96} - 27 q^{97} - 9 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 + 2 * q^5 + q^6 - 3 * q^8 + 5 * q^9 - q^10 - 6 * q^11 - 7 * q^12 + 2 * q^13 - 20 * q^15 - 12 * q^16 - 3 * q^17 - 8 * q^18 + 7 * q^19 + 7 * q^20 - 13 * q^22 + 16 * q^24 - 5 * q^25 - q^26 + 13 * q^27 - 10 * q^29 + 14 * q^30 - 6 * q^31 - 3 * q^32 - 17 * q^33 + q^34 - 15 * q^36 - 18 * q^37 - 7 * q^38 - 20 * q^39 - 16 * q^40 - 5 * q^41 - 14 * q^43 + 2 * q^44 - 7 * q^45 - 3 * q^46 + 3 * q^47 + 9 * q^48 - 4 * q^50 + 7 * q^52 - 9 * q^53 - 25 * q^54 + 17 * q^55 + 31 * q^57 - 5 * q^58 - 19 * q^59 - 3 * q^60 - 23 * q^61 + 36 * q^62 - q^64 + 20 * q^65 + 23 * q^66 - 11 * q^67 - 24 * q^68 + 19 * q^69 + 25 * q^72 + 13 * q^73 + 2 * q^74 + 11 * q^75 + 12 * q^76 + 14 * q^78 - 41 * q^79 - 9 * q^80 - 7 * q^81 + 2 * q^82 - 2 * q^83 + 20 * q^86 + 32 * q^87 - 10 * q^88 + 14 * q^89 + 22 * q^90 + 17 * q^92 - 15 * q^93 + 10 * q^94 - 31 * q^95 - 33 * q^96 - 27 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.97027	1.39319	0.696596	−	0.717464i	$-0.254697\pi$
$2$	1.97027	1.39319	0.696596	+	0.717464i	$0.254697\pi$
$3$	0.515563	0.297660	0.148830	−	0.988863i	$-0.452449\pi$
$3$	0.515563	0.297660	0.148830	+	0.988863i	$0.452449\pi$
$4$	1.88196	0.940981
$5$	−0.515563	−0.230567	−0.115283	−	0.993333i	$-0.536778\pi$
$5$	−0.515563	−0.230567	−0.115283	+	0.993333i	$0.536778\pi$
$6$	1.01580	0.414698
$7$	0	0
$7$	0	0
$8$	−0.232565	−0.0822242
$9$	−2.73420	−0.911398
$10$	−1.01580	−0.321223
$11$	−4.48583	−1.35253	−0.676265	−	0.736659i	$-0.736402\pi$
$11$	−4.48583	−1.35253	−0.676265	+	0.736659i	$0.736402\pi$
$12$	0.970270	0.280093
$13$	−0.515563	−0.142991	−0.0714957	−	0.997441i	$-0.522777\pi$
$13$	−0.515563	−0.142991	−0.0714957	+	0.997441i	$0.522777\pi$
$14$	0	0
$15$	−0.265805	−0.0686305
$16$	−4.22214	−1.05554
$17$	−5.38359	−1.30571	−0.652856	−	0.757482i	$-0.726430\pi$
$17$	−5.38359	−1.30571	−0.652856	+	0.757482i	$0.726430\pi$
$18$	−5.38710	−1.26975
$19$	3.91309	0.897724	0.448862	−	0.893601i	$-0.351829\pi$
$19$	3.91309	0.897724	0.448862	+	0.893601i	$0.351829\pi$
$20$	−0.970270	−0.216959
$21$	0	0
$22$	−8.83830	−1.88433
$23$	2.14565	0.447400	0.223700	−	0.974658i	$-0.428186\pi$
$23$	2.14565	0.447400	0.223700	+	0.974658i	$0.428186\pi$
$24$	−0.119902	−0.0244749
$25$	−4.73420	−0.946839
$26$	−1.01580	−0.199214
$27$	−2.95634	−0.568947
$28$	0	0
$29$	−3.58854	−0.666375	−0.333188	−	0.942861i	$-0.608124\pi$
$29$	−3.58854	−0.666375	−0.333188	+	0.942861i	$0.608124\pi$
$30$	−0.523707	−0.0956154
$31$	6.17848	1.10969	0.554844	−	0.831955i	$-0.312778\pi$
$31$	6.17848	1.10969	0.554844	+	0.831955i	$0.312778\pi$
$32$	−7.85363	−1.38834
$33$	−2.31273	−0.402594
$34$	−10.6071	−1.81911
$35$	0	0
$36$	−5.14565	−0.857609
$37$	−9.53276	−1.56718	−0.783588	−	0.621281i	$-0.786612\pi$
$37$	−9.53276	−1.56718	−0.783588	+	0.621281i	$0.786612\pi$
$38$	7.70984	1.25070
$39$	−0.265805	−0.0425628
$40$	0.119902	0.0189582
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	9.50489	1.44948	0.724741	−	0.689021i	$-0.241959\pi$
$43$	9.50489	1.44948	0.724741	+	0.689021i	$0.241959\pi$
$44$	−8.44217	−1.27270
$45$	1.40965	0.210138
$46$	4.22752	0.623313
$47$	10.2670	1.49759	0.748794	−	0.662802i	$-0.230633\pi$
$47$	10.2670	1.49759	0.748794	+	0.662802i	$0.230633\pi$
$48$	−2.17678	−0.314191
$49$	0	0
$50$	−9.32764	−1.31913
$51$	−2.77558	−0.388659
$52$	−0.970270	−0.134552
$53$	−1.71302	−0.235302	−0.117651	−	0.993055i	$-0.537536\pi$
$53$	−1.71302	−0.235302	−0.117651	+	0.993055i	$0.537536\pi$
$54$	−5.82478	−0.792652
$55$	2.31273	0.311848
$56$	0	0
$57$	2.01744	0.267217
$58$	−7.07040	−0.928388
$59$	4.21652	0.548944	0.274472	−	0.961595i	$-0.411497\pi$
$59$	4.21652	0.548944	0.274472	+	0.961595i	$0.411497\pi$
$60$	−0.500235	−0.0645800
$61$	−15.4161	−1.97383	−0.986916	−	0.161238i	$-0.948451\pi$
$61$	−15.4161	−1.97383	−0.986916	+	0.161238i	$0.948451\pi$
$62$	12.1733	1.54601
$63$	0	0
$64$	−7.02948	−0.878685
$65$	0.265805	0.0329690
$66$	−4.55670	−0.560891
$67$	−3.77956	−0.461747	−0.230873	−	0.972984i	$-0.574158\pi$
$67$	−3.77956	−0.461747	−0.230873	+	0.972984i	$0.574158\pi$
$68$	−10.1317	−1.22865
$69$	1.10622	0.133173
$70$	0	0
$71$	6.37594	0.756685	0.378342	−	0.925666i	$-0.376494\pi$
$71$	6.37594	0.756685	0.378342	+	0.925666i	$0.376494\pi$
$72$	0.635879	0.0749390
$73$	3.49673	0.409261	0.204630	−	0.978839i	$-0.434401\pi$
$73$	3.49673	0.409261	0.204630	+	0.978839i	$0.434401\pi$
$74$	−18.7821	−2.18337
$75$	−2.44077	−0.281836
$76$	7.36429	0.844742
$77$	0	0
$78$	−0.523707	−0.0592982
$79$	−7.02575	−0.790459	−0.395229	−	0.918582i	$-0.629335\pi$
$79$	−7.02575	−0.790459	−0.395229	+	0.918582i	$0.629335\pi$
$80$	2.17678	0.243371
$81$	6.67841	0.742045
$82$	−1.97027	−0.217580
$83$	7.25513	0.796354	0.398177	−	0.917309i	$-0.369643\pi$
$83$	7.25513	0.796354	0.398177	+	0.917309i	$0.369643\pi$
$84$	0	0
$85$	2.77558	0.301054
$86$	18.7272	2.01941
$87$	−1.85012	−0.198353
$88$	1.04325	0.111211
$89$	−3.29929	−0.349724	−0.174862	−	0.984593i	$-0.555948\pi$
$89$	−3.29929	−0.349724	−0.174862	+	0.984593i	$0.555948\pi$
$90$	2.77739	0.292762
$91$	0	0
$92$	4.03804	0.420995
$93$	3.18539	0.330310
$94$	20.2287	2.08643
$95$	−2.01744	−0.206985
$96$	−4.04904	−0.413253
$97$	−19.3033	−1.95995	−0.979976	−	0.199117i	$-0.936193\pi$
$97$	−19.3033	−1.95995	−0.979976	+	0.199117i	$0.936193\pi$
$98$	0	0
$99$	12.2651	1.23269
$100$	−8.90958	−0.890958
$101$	19.6836	1.95859	0.979297	−	0.202431i	$-0.0648841\pi$
$101$	19.6836	1.95859	0.979297	+	0.202431i	$0.0648841\pi$
$102$	−5.46864	−0.541476
$103$	−3.53553	−0.348366	−0.174183	−	0.984713i	$-0.555728\pi$
$103$	−3.53553	−0.348366	−0.174183	+	0.984713i	$0.555728\pi$
$104$	0.119902	0.0117574
$105$	0	0
$106$	−3.37512	−0.327821
$107$	−1.95357	−0.188858	−0.0944292	−	0.995532i	$-0.530103\pi$
$107$	−1.95357	−0.188858	−0.0944292	+	0.995532i	$0.530103\pi$
$108$	−5.56372	−0.535369
$109$	5.12897	0.491266	0.245633	−	0.969363i	$-0.421004\pi$
$109$	5.12897	0.491266	0.245633	+	0.969363i	$0.421004\pi$
$110$	4.55670	0.434464
$111$	−4.91473	−0.466486
$112$	0	0
$113$	−15.0460	−1.41541	−0.707706	−	0.706507i	$-0.750270\pi$
$113$	−15.0460	−1.41541	−0.707706	+	0.706507i	$0.750270\pi$
$114$	3.97491	0.372284
$115$	−1.10622	−0.103155
$116$	−6.75350	−0.627047
$117$	1.40965	0.130322
$118$	8.30768	0.764784
$119$	0	0
$120$	0.0618170	0.00564309
$121$	9.12269	0.829336
$122$	−30.3739	−2.74992
$123$	−0.515563	−0.0464867
$124$	11.6277	1.04420
$125$	5.01859	0.448876
$126$	0	0
$127$	1.40476	0.124653	0.0623263	−	0.998056i	$-0.480148\pi$
$127$	1.40476	0.124653	0.0623263	+	0.998056i	$0.480148\pi$
$128$	1.85728	0.164162
$129$	4.90037	0.431453
$130$	0.523707	0.0459322
$131$	−8.70153	−0.760256	−0.380128	−	0.924934i	$-0.624120\pi$
$131$	−8.70153	−0.760256	−0.380128	+	0.924934i	$0.624120\pi$
$132$	−4.35247	−0.378834
$133$	0	0
$134$	−7.44675	−0.643301
$135$	1.52418	0.131180
$136$	1.25204	0.107361
$137$	14.3634	1.22715	0.613573	−	0.789638i	$-0.289732\pi$
$137$	14.3634	1.22715	0.613573	+	0.789638i	$0.289732\pi$
$138$	2.17955	0.185536
$139$	−17.7700	−1.50723	−0.753614	−	0.657317i	$-0.771691\pi$
$139$	−17.7700	−1.50723	−0.753614	+	0.657317i	$0.771691\pi$
$140$	0	0
$141$	5.29326	0.445773
$142$	12.5623	1.05421
$143$	2.31273	0.193400
$144$	11.5442	0.962013
$145$	1.85012	0.153644
$146$	6.88949	0.570178
$147$	0	0
$148$	−17.9403	−1.47468
$149$	15.7091	1.28694	0.643471	−	0.765471i	$-0.277494\pi$
$149$	15.7091	1.28694	0.643471	+	0.765471i	$0.277494\pi$
$150$	−4.80898	−0.392652
$151$	−17.0951	−1.39118	−0.695589	−	0.718440i	$-0.744856\pi$
$151$	−17.0951	−1.39118	−0.695589	+	0.718440i	$0.744856\pi$
$152$	−0.910048	−0.0738147
$153$	14.7198	1.19002
$154$	0	0
$155$	−3.18539	−0.255857
$156$	−0.500235	−0.0400508
$157$	1.44102	0.115006	0.0575031	−	0.998345i	$-0.481686\pi$
$157$	1.44102	0.115006	0.0575031	+	0.998345i	$0.481686\pi$
$158$	−13.8426	−1.10126
$159$	−0.883171	−0.0700400
$160$	4.04904	0.320104
$161$	0	0
$162$	13.1583	1.03381
$163$	−7.92585	−0.620800	−0.310400	−	0.950606i	$-0.600463\pi$
$163$	−7.92585	−0.620800	−0.310400	+	0.950606i	$0.600463\pi$
$164$	−1.88196	−0.146957
$165$	1.19236	0.0928248
$166$	14.2946	1.10947
$167$	7.86926	0.608942	0.304471	−	0.952522i	$-0.401520\pi$
$167$	7.86926	0.608942	0.304471	+	0.952522i	$0.401520\pi$
$168$	0	0
$169$	−12.7342	−0.979553
$170$	5.46864	0.419426
$171$	−10.6991	−0.818184
$172$	17.8878	1.36394
$173$	−7.75750	−0.589792	−0.294896	−	0.955529i	$-0.595285\pi$
$173$	−7.75750	−0.589792	−0.294896	+	0.955529i	$0.595285\pi$
$174$	−3.64523	−0.276344
$175$	0	0
$176$	18.9398	1.42764
$177$	2.17388	0.163399
$178$	−6.50048	−0.487232
$179$	12.3695	0.924539	0.462270	−	0.886739i	$-0.347035\pi$
$179$	12.3695	0.924539	0.462270	+	0.886739i	$0.347035\pi$
$180$	2.65291	0.197736
$181$	−6.45029	−0.479446	−0.239723	−	0.970841i	$-0.577057\pi$
$181$	−6.45029	−0.479446	−0.239723	+	0.970841i	$0.577057\pi$
$182$	0	0
$183$	−7.94797	−0.587531
$184$	−0.499004	−0.0367871
$185$	4.91473	0.361338
$186$	6.27608	0.460185
$187$	24.1499	1.76602
$188$	19.3220	1.40920
$189$	0	0
$190$	−3.97491	−0.288370
$191$	−12.7555	−0.922958	−0.461479	−	0.887151i	$-0.652681\pi$
$191$	−12.7555	−0.922958	−0.461479	+	0.887151i	$0.652681\pi$
$192$	−3.62414	−0.261550
$193$	−20.1431	−1.44993	−0.724966	−	0.688785i	$-0.758145\pi$
$193$	−20.1431	−1.44993	−0.724966	+	0.688785i	$0.758145\pi$
$194$	−38.0327	−2.73059
$195$	0.137039	0.00981357
$196$	0	0
$197$	20.2152	1.44027	0.720135	−	0.693834i	$-0.244080\pi$
$197$	20.2152	1.44027	0.720135	+	0.693834i	$0.244080\pi$
$198$	24.1656	1.71738
$199$	−6.58552	−0.466835	−0.233418	−	0.972377i	$-0.574991\pi$
$199$	−6.58552	−0.466835	−0.233418	+	0.972377i	$0.574991\pi$
$200$	1.10101	0.0778531
$201$	−1.94860	−0.137444
$202$	38.7820	2.72869
$203$	0	0
$204$	−5.22354	−0.365721
$205$	0.515563	0.0360085
$206$	−6.96594	−0.485340
$207$	−5.86663	−0.407759
$208$	2.17678	0.150932
$209$	−17.5535	−1.21420
$210$	0	0
$211$	−19.7713	−1.36111	−0.680557	−	0.732695i	$-0.738262\pi$
$211$	−19.7713	−1.36111	−0.680557	+	0.732695i	$0.738262\pi$
$212$	−3.22385	−0.221415
$213$	3.28720	0.225235
$214$	−3.84905	−0.263116
$215$	−4.90037	−0.334202
$216$	0.687541	0.0467813
$217$	0	0
$218$	10.1055	0.684428
$219$	1.80278	0.121821
$220$	4.35247	0.293443
$221$	2.77558	0.186706
$222$	−9.68335	−0.649904
$223$	22.9084	1.53406	0.767031	−	0.641609i	$-0.221733\pi$
$223$	22.9084	1.53406	0.767031	+	0.641609i	$0.221733\pi$
$224$	0	0
$225$	12.9442	0.862948
$226$	−29.6448	−1.97194
$227$	0.352978	0.0234280	0.0117140	−	0.999931i	$-0.496271\pi$
$227$	0.352978	0.0234280	0.0117140	+	0.999931i	$0.496271\pi$
$228$	3.79675	0.251446
$229$	−13.5439	−0.895009	−0.447504	−	0.894282i	$-0.647687\pi$
$229$	−13.5439	−0.895009	−0.447504	+	0.894282i	$0.647687\pi$
$230$	−2.17955	−0.143715
$231$	0	0
$232$	0.834570	0.0547922
$233$	−14.4939	−0.949526	−0.474763	−	0.880114i	$-0.657466\pi$
$233$	−14.4939	−0.949526	−0.474763	+	0.880114i	$0.657466\pi$
$234$	2.77739	0.181564
$235$	−5.29326	−0.345294
$236$	7.93533	0.516546
$237$	−3.62222	−0.235288
$238$	0	0
$239$	−5.66844	−0.366661	−0.183330	−	0.983051i	$-0.558688\pi$
$239$	−5.66844	−0.366661	−0.183330	+	0.983051i	$0.558688\pi$
$240$	1.12227	0.0724419
$241$	−14.9194	−0.961046	−0.480523	−	0.876982i	$-0.659553\pi$
$241$	−14.9194	−0.961046	−0.480523	+	0.876982i	$0.659553\pi$
$242$	17.9742	1.15542
$243$	12.3121	0.789825
$244$	−29.0125	−1.85734
$245$	0	0
$246$	−1.01580	−0.0647649
$247$	−2.01744	−0.128367
$248$	−1.43690	−0.0912432
$249$	3.74048	0.237043
$250$	9.88797	0.625370
$251$	−0.263911	−0.0166579	−0.00832895	−	0.999965i	$-0.502651\pi$
$251$	−0.263911	−0.0166579	−0.00832895	+	0.999965i	$0.502651\pi$
$252$	0	0
$253$	−9.62504	−0.605121
$254$	2.76776	0.173665
$255$	1.43099	0.0896118
$256$	17.7183	1.10739
$257$	6.36991	0.397344	0.198672	−	0.980066i	$-0.436337\pi$
$257$	6.36991	0.397344	0.198672	+	0.980066i	$0.436337\pi$
$258$	9.65504	0.601097
$259$	0	0
$260$	0.500235	0.0310232
$261$	9.81177	0.607334
$262$	−17.1444	−1.05918
$263$	−14.4440	−0.890654	−0.445327	−	0.895368i	$-0.646913\pi$
$263$	−14.4440	−0.890654	−0.445327	+	0.895368i	$0.646913\pi$
$264$	0.537860	0.0331030
$265$	0.883171	0.0542528
$266$	0	0
$267$	−1.70099	−0.104099
$268$	−7.11299	−0.434495
$269$	14.8840	0.907491	0.453745	−	0.891131i	$-0.350088\pi$
$269$	14.8840	0.907491	0.453745	+	0.891131i	$0.350088\pi$
$270$	3.00304	0.182759
$271$	−1.12037	−0.0680577	−0.0340289	−	0.999421i	$-0.510834\pi$
$271$	−1.12037	−0.0680577	−0.0340289	+	0.999421i	$0.510834\pi$
$272$	22.7303	1.37823
$273$	0	0
$274$	28.2997	1.70965
$275$	21.2368	1.28063
$276$	2.08186	0.125313
$277$	4.10457	0.246620	0.123310	−	0.992368i	$-0.460649\pi$
$277$	4.10457	0.246620	0.123310	+	0.992368i	$0.460649\pi$
$278$	−35.0116	−2.09986
$279$	−16.8932	−1.01137
$280$	0	0
$281$	18.7308	1.11739	0.558694	−	0.829374i	$-0.311303\pi$
$281$	18.7308	1.11739	0.558694	+	0.829374i	$0.311303\pi$
$282$	10.4291	0.621046
$283$	7.05737	0.419517	0.209758	−	0.977753i	$-0.432732\pi$
$283$	7.05737	0.419517	0.209758	+	0.977753i	$0.432732\pi$
$284$	11.9993	0.712026
$285$	−1.04012	−0.0616113
$286$	4.55670	0.269443
$287$	0	0
$288$	21.4734	1.26533
$289$	11.9831	0.704886
$290$	3.64523	0.214055
$291$	−9.95205	−0.583400
$292$	6.58071	0.385107
$293$	−8.05119	−0.470356	−0.235178	−	0.971952i	$-0.575567\pi$
$293$	−8.05119	−0.470356	−0.235178	+	0.971952i	$0.575567\pi$
$294$	0	0
$295$	−2.17388	−0.126568
$296$	2.21699	0.128860
$297$	13.2616	0.769518
$298$	30.9512	1.79296
$299$	−1.10622	−0.0639743
$300$	−4.59345	−0.265203
$301$	0	0
$302$	−33.6819	−1.93818
$303$	10.1481	0.582995
$304$	−16.5216	−0.947579
$305$	7.94797	0.455100
$306$	29.0020	1.65793
$307$	−16.1909	−0.924065	−0.462033	−	0.886863i	$-0.652880\pi$
$307$	−16.1909	−0.924065	−0.462033	+	0.886863i	$0.652880\pi$
$308$	0	0
$309$	−1.82279	−0.103695
$310$	−6.27608	−0.356458
$311$	1.74080	0.0987120	0.0493560	−	0.998781i	$-0.484283\pi$
$311$	1.74080	0.0987120	0.0493560	+	0.998781i	$0.484283\pi$
$312$	0.0618170	0.00349970
$313$	6.61975	0.374171	0.187085	−	0.982344i	$-0.440096\pi$
$313$	6.61975	0.374171	0.187085	+	0.982344i	$0.440096\pi$
$314$	2.83921	0.160226
$315$	0	0
$316$	−13.2222	−0.743807
$317$	−1.42465	−0.0800164	−0.0400082	−	0.999199i	$-0.512738\pi$
$317$	−1.42465	−0.0800164	−0.0400082	+	0.999199i	$0.512738\pi$
$318$	−1.74009	−0.0975791
$319$	16.0976	0.901292
$320$	3.62414	0.202595
$321$	−1.00719	−0.0562156
$322$	0	0
$323$	−21.0665	−1.17217
$324$	12.5685	0.698251
$325$	2.44077	0.135390
$326$	−15.6161	−0.864893
$327$	2.64431	0.146230
$328$	0.232565	0.0128413
$329$	0	0
$330$	2.34926	0.129323
$331$	−0.170479	−0.00937039	−0.00468519	−	0.999989i	$-0.501491\pi$
$331$	−0.170479	−0.00937039	−0.00468519	+	0.999989i	$0.501491\pi$
$332$	13.6539	0.749354
$333$	26.0644	1.42832
$334$	15.5046	0.848372
$335$	1.94860	0.106463
$336$	0	0
$337$	0.121912	0.00664096	0.00332048	−	0.999994i	$-0.498943\pi$
$337$	0.121912	0.00664096	0.00332048	+	0.999994i	$0.498943\pi$
$338$	−25.0898	−1.36471
$339$	−7.75718	−0.421312
$340$	5.22354	0.283286
$341$	−27.7156	−1.50088
$342$	−21.0802	−1.13989
$343$	0	0
$344$	−2.21051	−0.119183
$345$	−0.570325	−0.0307053
$346$	−15.2844	−0.821693
$347$	−5.12595	−0.275176	−0.137588	−	0.990490i	$-0.543935\pi$
$347$	−5.12595	−0.275176	−0.137588	+	0.990490i	$0.543935\pi$
$348$	−3.48185	−0.186647
$349$	31.8658	1.70573	0.852867	−	0.522128i	$-0.174862\pi$
$349$	31.8658	1.70573	0.852867	+	0.522128i	$0.174862\pi$
$350$	0	0
$351$	1.52418	0.0813545
$352$	35.2301	1.87777
$353$	−13.7005	−0.729204	−0.364602	−	0.931163i	$-0.618795\pi$
$353$	−13.7005	−0.729204	−0.364602	+	0.931163i	$0.618795\pi$
$354$	4.28313	0.227646
$355$	−3.28720	−0.174466
$356$	−6.20913	−0.329083
$357$	0	0
$358$	24.3712	1.28806
$359$	18.6815	0.985972	0.492986	−	0.870037i	$-0.335905\pi$
$359$	18.6815	0.985972	0.492986	+	0.870037i	$0.335905\pi$
$360$	−0.327835	−0.0172784
$361$	−3.68774	−0.194092
$362$	−12.7088	−0.667960
$363$	4.70332	0.246860
$364$	0	0
$365$	−1.80278	−0.0943619
$366$	−15.6596	−0.818543
$367$	−18.1189	−0.945800	−0.472900	−	0.881116i	$-0.656793\pi$
$367$	−18.1189	−0.945800	−0.472900	+	0.881116i	$0.656793\pi$
$368$	−9.05925	−0.472246
$369$	2.73420	0.142337
$370$	9.68335	0.503413
$371$	0	0
$372$	5.99479	0.310815
$373$	−12.2889	−0.636294	−0.318147	−	0.948041i	$-0.603061\pi$
$373$	−12.2889	−0.636294	−0.318147	+	0.948041i	$0.603061\pi$
$374$	47.5818	2.46040
$375$	2.58740	0.133613
$376$	−2.38774	−0.123138
$377$	1.85012	0.0952859
$378$	0	0
$379$	24.5683	1.26199	0.630995	−	0.775787i	$-0.282647\pi$
$379$	24.5683	1.26199	0.630995	+	0.775787i	$0.282647\pi$
$380$	−3.79675	−0.194769
$381$	0.724244	0.0371041
$382$	−25.1318	−1.28586
$383$	20.5808	1.05163	0.525814	−	0.850599i	$-0.323761\pi$
$383$	20.5808	1.05163	0.525814	+	0.850599i	$0.323761\pi$
$384$	0.957545	0.0488645
$385$	0	0
$386$	−39.6873	−2.02003
$387$	−25.9882	−1.32106
$388$	−36.3281	−1.84428
$389$	1.57921	0.0800690	0.0400345	−	0.999198i	$-0.487253\pi$
$389$	1.57921	0.0800690	0.0400345	+	0.999198i	$0.487253\pi$
$390$	0.270004	0.0136722
$391$	−11.5513	−0.584176
$392$	0	0
$393$	−4.48618	−0.226298
$394$	39.8293	2.00657
$395$	3.62222	0.182253
$396$	23.0825	1.15994
$397$	30.7798	1.54480	0.772398	−	0.635139i	$-0.219057\pi$
$397$	30.7798	1.54480	0.772398	+	0.635139i	$0.219057\pi$
$398$	−12.9753	−0.650391
$399$	0	0
$400$	19.9884	0.999422
$401$	1.93612	0.0966854	0.0483427	−	0.998831i	$-0.484606\pi$
$401$	1.93612	0.0966854	0.0483427	+	0.998831i	$0.484606\pi$
$402$	−3.83927	−0.191485
$403$	−3.18539	−0.158676
$404$	37.0438	1.84300
$405$	−3.44314	−0.171091
$406$	0	0
$407$	42.7623	2.11965
$408$	0.645503	0.0319572
$409$	5.14647	0.254477	0.127238	−	0.991872i	$-0.459389\pi$
$409$	5.14647	0.254477	0.127238	+	0.991872i	$0.459389\pi$
$410$	1.01580	0.0501667
$411$	7.40522	0.365273
$412$	−6.65373	−0.327806
$413$	0	0
$414$	−11.5589	−0.568087
$415$	−3.74048	−0.183613
$416$	4.04904	0.198520
$417$	−9.16153	−0.448642
$418$	−34.5850	−1.69161
$419$	−1.25489	−0.0613055	−0.0306527	−	0.999530i	$-0.509759\pi$
$419$	−1.25489	−0.0613055	−0.0306527	+	0.999530i	$0.509759\pi$
$420$	0	0
$421$	1.44769	0.0705560	0.0352780	−	0.999378i	$-0.488768\pi$
$421$	1.44769	0.0705560	0.0352780	+	0.999378i	$0.488768\pi$
$422$	−38.9549	−1.89629
$423$	−28.0718	−1.36490
$424$	0.398390	0.0193475
$425$	25.4870	1.23630
$426$	6.47666	0.313795
$427$	0	0
$428$	−3.67654	−0.177712
$429$	1.19236	0.0575675
$430$	−9.65504	−0.465608
$431$	8.01734	0.386181	0.193091	−	0.981181i	$-0.438149\pi$
$431$	8.01734	0.386181	0.193091	+	0.981181i	$0.438149\pi$
$432$	12.4821	0.600544
$433$	−36.9842	−1.77735	−0.888673	−	0.458542i	$-0.848372\pi$
$433$	−36.9842	−1.77735	−0.888673	+	0.458542i	$0.848372\pi$
$434$	0	0
$435$	0.953852	0.0457337
$436$	9.65253	0.462273
$437$	8.39613	0.401641
$438$	3.55197	0.169719
$439$	6.61302	0.315622	0.157811	−	0.987469i	$-0.449556\pi$
$439$	6.61302	0.315622	0.157811	+	0.987469i	$0.449556\pi$
$440$	−0.537860	−0.0256415
$441$	0	0
$442$	5.46864	0.260117
$443$	−17.1102	−0.812931	−0.406465	−	0.913666i	$-0.633239\pi$
$443$	−17.1102	−0.812931	−0.406465	+	0.913666i	$0.633239\pi$
$444$	−9.24934	−0.438954
$445$	1.70099	0.0806346
$446$	45.1358	2.13724
$447$	8.09904	0.383071
$448$	0	0
$449$	29.0713	1.37196	0.685980	−	0.727621i	$-0.259374\pi$
$449$	29.0713	1.37196	0.685980	+	0.727621i	$0.259374\pi$
$450$	25.5036	1.20225
$451$	4.48583	0.211230
$452$	−28.3161	−1.33188
$453$	−8.81358	−0.414098
$454$	0.695463	0.0326397
$455$	0	0
$456$	−0.469187	−0.0219717
$457$	−28.8842	−1.35114	−0.675572	−	0.737294i	$-0.736103\pi$
$457$	−28.8842	−1.35114	−0.675572	+	0.737294i	$0.736103\pi$
$458$	−26.6852	−1.24692
$459$	15.9157	0.742882
$460$	−2.08186	−0.0970673
$461$	−40.2707	−1.87559	−0.937796	−	0.347188i	$-0.887137\pi$
$461$	−40.2707	−1.87559	−0.937796	+	0.347188i	$0.887137\pi$
$462$	0	0
$463$	−1.14609	−0.0532632	−0.0266316	−	0.999645i	$-0.508478\pi$
$463$	−1.14609	−0.0532632	−0.0266316	+	0.999645i	$0.508478\pi$
$464$	15.1513	0.703383
$465$	−1.64227	−0.0761584
$466$	−28.5569	−1.32287
$467$	−33.6181	−1.55566	−0.777830	−	0.628475i	$-0.783680\pi$
$467$	−33.6181	−1.55566	−0.777830	+	0.628475i	$0.783680\pi$
$468$	2.65291	0.122631
$469$	0	0
$470$	−10.4291	−0.481060
$471$	0.742938	0.0342328
$472$	−0.980616	−0.0451365
$473$	−42.6373	−1.96047
$474$	−7.13674	−0.327801
$475$	−18.5253	−0.850000
$476$	0	0
$477$	4.68374	0.214454
$478$	−11.1683	−0.510828
$479$	30.7074	1.40305	0.701527	−	0.712643i	$-0.252502\pi$
$479$	30.7074	1.40305	0.701527	+	0.712643i	$0.252502\pi$
$480$	2.08753	0.0952824
$481$	4.91473	0.224093
$482$	−29.3953	−1.33892
$483$	0	0
$484$	17.1686	0.780389
$485$	9.95205	0.451899
$486$	24.2583	1.10038
$487$	32.5352	1.47431	0.737154	−	0.675725i	$-0.236169\pi$
$487$	32.5352	1.47431	0.737154	+	0.675725i	$0.236169\pi$
$488$	3.58525	0.162297
$489$	−4.08627	−0.184788
$490$	0	0
$491$	−12.9510	−0.584470	−0.292235	−	0.956347i	$-0.594399\pi$
$491$	−12.9510	−0.584470	−0.292235	+	0.956347i	$0.594399\pi$
$492$	−0.970270	−0.0437431
$493$	19.3192	0.870095
$494$	−3.97491	−0.178839
$495$	−6.32345	−0.284218
$496$	−26.0864	−1.17131
$497$	0	0
$498$	7.36974	0.330246
$499$	−3.95552	−0.177073	−0.0885367	−	0.996073i	$-0.528219\pi$
$499$	−3.95552	−0.177073	−0.0885367	+	0.996073i	$0.528219\pi$
$500$	9.44479	0.422384
$501$	4.05710	0.181258
$502$	−0.519975	−0.0232076
$503$	10.4604	0.466408	0.233204	−	0.972428i	$-0.425079\pi$
$503$	10.4604	0.466408	0.233204	+	0.972428i	$0.425079\pi$
$504$	0	0
$505$	−10.1481	−0.451586
$506$	−18.9639	−0.843049
$507$	−6.56528	−0.291574
$508$	2.64371	0.117296
$509$	−23.3062	−1.03303	−0.516516	−	0.856278i	$-0.672771\pi$
$509$	−23.3062	−1.03303	−0.516516	+	0.856278i	$0.672771\pi$
$510$	2.81943	0.124846
$511$	0	0
$512$	31.1953	1.37865
$513$	−11.5684	−0.510758
$514$	12.5504	0.553576
$515$	1.82279	0.0803215
$516$	9.22231	0.405989
$517$	−46.0558	−2.02553
$518$	0	0
$519$	−3.99948	−0.175558
$520$	−0.0618170	−0.00271085
$521$	0.0654355	0.00286678	0.00143339	−	0.999999i	$-0.499544\pi$
$521$	0.0654355	0.00286678	0.00143339	+	0.999999i	$0.499544\pi$
$522$	19.3318	0.846132
$523$	25.0586	1.09574	0.547868	−	0.836565i	$-0.315440\pi$
$523$	25.0586	1.09574	0.547868	+	0.836565i	$0.315440\pi$
$524$	−16.3760	−0.715387
$525$	0	0
$526$	−28.4585	−1.24085
$527$	−33.2624	−1.44893
$528$	9.76466	0.424952
$529$	−18.3962	−0.799834
$530$	1.74009	0.0755845
$531$	−11.5288	−0.500307
$532$	0	0
$533$	0.515563	0.0223315
$534$	−3.35141	−0.145030
$535$	1.00719	0.0435444
$536$	0.878994	0.0379668
$537$	6.37725	0.275199
$538$	29.3254	1.26431
$539$	0	0
$540$	2.86844	0.123438
$541$	−28.9067	−1.24280	−0.621399	−	0.783495i	$-0.713435\pi$
$541$	−28.9067	−1.24280	−0.621399	+	0.783495i	$0.713435\pi$
$542$	−2.20743	−0.0948174
$543$	−3.32553	−0.142712
$544$	42.2807	1.81277
$545$	−2.64431	−0.113270
$546$	0	0
$547$	−6.28935	−0.268913	−0.134457	−	0.990919i	$-0.542929\pi$
$547$	−6.28935	−0.268913	−0.134457	+	0.990919i	$0.542929\pi$
$548$	27.0313	1.15472
$549$	42.1507	1.79895
$550$	41.8422	1.78416
$551$	−14.0423	−0.598221
$552$	−0.257268	−0.0109501
$553$	0	0
$554$	8.08712	0.343589
$555$	2.53385	0.107556
$556$	−33.4424	−1.41827
$557$	18.3912	0.779262	0.389631	−	0.920971i	$-0.372603\pi$
$557$	18.3912	0.779262	0.389631	+	0.920971i	$0.372603\pi$
$558$	−33.2841	−1.40903
$559$	−4.90037	−0.207263
$560$	0	0
$561$	12.4508	0.525672
$562$	36.9048	1.55674
$563$	7.43320	0.313272	0.156636	−	0.987656i	$-0.449935\pi$
$563$	7.43320	0.313272	0.156636	+	0.987656i	$0.449935\pi$
$564$	9.96171	0.419464
$565$	7.75718	0.326347
$566$	13.9049	0.584467
$567$	0	0
$568$	−1.48282	−0.0622178
$569$	−9.23020	−0.386950	−0.193475	−	0.981105i	$-0.561976\pi$
$569$	−9.23020	−0.386950	−0.193475	+	0.981105i	$0.561976\pi$
$570$	−2.04931	−0.0858363
$571$	−16.1376	−0.675338	−0.337669	−	0.941265i	$-0.609638\pi$
$571$	−16.1376	−0.675338	−0.337669	+	0.941265i	$0.609638\pi$
$572$	4.35247	0.181986
$573$	−6.57628	−0.274728
$574$	0	0
$575$	−10.1579	−0.423615
$576$	19.2200	0.800832
$577$	18.5031	0.770294	0.385147	−	0.922855i	$-0.374151\pi$
$577$	18.5031	0.770294	0.385147	+	0.922855i	$0.374151\pi$
$578$	23.6099	0.982041
$579$	−10.3850	−0.431587
$580$	3.48185	0.144576
$581$	0	0
$582$	−19.6082	−0.812787
$583$	7.68434	0.318253
$584$	−0.813217	−0.0336512
$585$	−0.726762	−0.0300479
$586$	−15.8630	−0.655295
$587$	−28.8110	−1.18916	−0.594579	−	0.804037i	$-0.702681\pi$
$587$	−28.8110	−1.18916	−0.594579	+	0.804037i	$0.702681\pi$
$588$	0	0
$589$	24.1769	0.996193
$590$	−4.28313	−0.176334
$591$	10.4222	0.428711
$592$	40.2486	1.65421
$593$	43.6151	1.79106	0.895529	−	0.445003i	$-0.146797\pi$
$593$	43.6151	1.79106	0.895529	+	0.445003i	$0.146797\pi$
$594$	26.1290	1.07209
$595$	0	0
$596$	29.5640	1.21099
$597$	−3.39525	−0.138958
$598$	−2.17955	−0.0891284
$599$	−31.4670	−1.28571	−0.642853	−	0.765990i	$-0.722249\pi$
$599$	−31.4670	−1.28571	−0.642853	+	0.765990i	$0.722249\pi$
$600$	0.567639	0.0231738
$601$	43.0423	1.75573	0.877866	−	0.478906i	$-0.158966\pi$
$601$	43.0423	1.75573	0.877866	+	0.478906i	$0.158966\pi$
$602$	0	0
$603$	10.3340	0.420835
$604$	−32.1723	−1.30907
$605$	−4.70332	−0.191217
$606$	19.9946	0.812224
$607$	31.0535	1.26042	0.630212	−	0.776423i	$-0.282968\pi$
$607$	31.0535	1.26042	0.630212	+	0.776423i	$0.282968\pi$
$608$	−30.7319	−1.24634
$609$	0	0
$610$	15.6596	0.634041
$611$	−5.29326	−0.214142
$612$	27.7021	1.11979
$613$	−31.5085	−1.27262	−0.636309	−	0.771434i	$-0.719540\pi$
$613$	−31.5085	−1.27262	−0.636309	+	0.771434i	$0.719540\pi$
$614$	−31.9005	−1.28740
$615$	0.265805	0.0107183
$616$	0	0
$617$	−47.8573	−1.92666	−0.963331	−	0.268315i	$-0.913533\pi$
$617$	−47.8573	−1.92666	−0.963331	+	0.268315i	$0.913533\pi$
$618$	−3.59138	−0.144466
$619$	−18.1352	−0.728915	−0.364458	−	0.931220i	$-0.618746\pi$
$619$	−18.1352	−0.728915	−0.364458	+	0.931220i	$0.618746\pi$
$620$	−5.99479	−0.240757
$621$	−6.34327	−0.254547
$622$	3.42985	0.137525
$623$	0	0
$624$	1.12227	0.0449266
$625$	21.0836	0.843343
$626$	13.0427	0.521291
$627$	−9.04991	−0.361418
$628$	2.71195	0.108219
$629$	51.3205	2.04628
$630$	0	0
$631$	−33.0495	−1.31568	−0.657839	−	0.753158i	$-0.728529\pi$
$631$	−33.0495	−1.31568	−0.657839	+	0.753158i	$0.728529\pi$
$632$	1.63395	0.0649949
$633$	−10.1934	−0.405150
$634$	−2.80695	−0.111478
$635$	−0.724244	−0.0287407
$636$	−1.66209	−0.0659064
$637$	0	0
$638$	31.7166	1.25567
$639$	−17.4331	−0.689641
$640$	−0.957545	−0.0378503
$641$	13.2045	0.521544	0.260772	−	0.965400i	$-0.416023\pi$
$641$	13.2045	0.521544	0.260772	+	0.965400i	$0.416023\pi$
$642$	−1.98443	−0.0783191
$643$	24.0434	0.948177	0.474089	−	0.880477i	$-0.342778\pi$
$643$	24.0434	0.948177	0.474089	+	0.880477i	$0.342778\pi$
$644$	0	0
$645$	−2.52645	−0.0994787
$646$	−41.5066	−1.63306
$647$	21.4468	0.843161	0.421580	−	0.906791i	$-0.361476\pi$
$647$	21.4468	0.843161	0.421580	+	0.906791i	$0.361476\pi$
$648$	−1.55317	−0.0610141
$649$	−18.9146	−0.742463
$650$	4.80898	0.188624
$651$	0	0
$652$	−14.9161	−0.584161
$653$	−12.4924	−0.488866	−0.244433	−	0.969666i	$-0.578602\pi$
$653$	−12.4924	−0.488866	−0.244433	+	0.969666i	$0.578602\pi$
$654$	5.21000	0.203727
$655$	4.48618	0.175290
$656$	4.22214	0.164847
$657$	−9.56073	−0.373000
$658$	0	0
$659$	−12.4259	−0.484046	−0.242023	−	0.970271i	$-0.577811\pi$
$659$	−12.4259	−0.484046	−0.242023	+	0.970271i	$0.577811\pi$
$660$	2.24397	0.0873464
$661$	−21.1939	−0.824347	−0.412173	−	0.911105i	$-0.635230\pi$
$661$	−21.1939	−0.824347	−0.412173	+	0.911105i	$0.635230\pi$
$662$	−0.335890	−0.0130547
$663$	1.43099	0.0555749
$664$	−1.68729	−0.0654796
$665$	0	0
$666$	51.3539	1.98992
$667$	−7.69977	−0.298136
$668$	14.8097	0.573003
$669$	11.8107	0.456630
$670$	3.83927	0.148324
$671$	69.1541	2.66966
$672$	0	0
$673$	−7.84607	−0.302444	−0.151222	−	0.988500i	$-0.548321\pi$
$673$	−7.84607	−0.302444	−0.151222	+	0.988500i	$0.548321\pi$
$674$	0.240199	0.00925213
$675$	13.9959	0.538702
$676$	−23.9653	−0.921742
$677$	−24.4760	−0.940689	−0.470344	−	0.882483i	$-0.655870\pi$
$677$	−24.4760	−0.940689	−0.470344	+	0.882483i	$0.655870\pi$
$678$	−15.2837	−0.586968
$679$	0	0
$680$	−0.645503	−0.0247539
$681$	0.181982	0.00697358
$682$	−54.6072	−2.09102
$683$	−45.2927	−1.73308	−0.866539	−	0.499109i	$-0.833661\pi$
$683$	−45.2927	−1.73308	−0.866539	+	0.499109i	$0.833661\pi$
$684$	−20.1354	−0.769896
$685$	−7.40522	−0.282939
$686$	0	0
$687$	−6.98275	−0.266409
$688$	−40.1310	−1.52998
$689$	0.883171	0.0336461
$690$	−1.12369	−0.0427783
$691$	50.8550	1.93462	0.967308	−	0.253605i	$-0.0816162\pi$
$691$	50.8550	1.93462	0.967308	+	0.253605i	$0.0816162\pi$
$692$	−14.5993	−0.554983
$693$	0	0
$694$	−10.0995	−0.383372
$695$	9.16153	0.347516
$696$	0.430273	0.0163095
$697$	5.38359	0.203918
$698$	62.7841	2.37641
$699$	−7.47251	−0.282636
$700$	0	0
$701$	22.8323	0.862366	0.431183	−	0.902265i	$-0.358096\pi$
$701$	22.8323	0.862366	0.431183	+	0.902265i	$0.358096\pi$
$702$	3.00304	0.113342
$703$	−37.3025	−1.40689
$704$	31.5331	1.18845
$705$	−2.72901	−0.102780
$706$	−26.9937	−1.01592
$707$	0	0
$708$	4.09116	0.153755
$709$	−10.4301	−0.391709	−0.195855	−	0.980633i	$-0.562748\pi$
$709$	−10.4301	−0.391709	−0.195855	+	0.980633i	$0.562748\pi$
$710$	−6.47666	−0.243065
$711$	19.2098	0.720423
$712$	0.767300	0.0287558
$713$	13.2569	0.496474
$714$	0	0
$715$	−1.19236	−0.0445916
$716$	23.2789	0.869974
$717$	−2.92243	−0.109140
$718$	36.8076	1.37365
$719$	−38.4021	−1.43216	−0.716078	−	0.698020i	$-0.754065\pi$
$719$	−38.4021	−1.43216	−0.716078	+	0.698020i	$0.754065\pi$
$720$	−5.95174	−0.221808
$721$	0	0
$722$	−7.26585	−0.270407
$723$	−7.69191	−0.286065
$724$	−12.1392	−0.451150
$725$	16.9889	0.630950
$726$	9.26681	0.343923
$727$	3.22664	0.119669	0.0598347	−	0.998208i	$-0.480943\pi$
$727$	3.22664	0.119669	0.0598347	+	0.998208i	$0.480943\pi$
$728$	0	0
$729$	−13.6875	−0.506946
$730$	−3.55197	−0.131464
$731$	−51.1705	−1.89261
$732$	−14.9578	−0.552856
$733$	−20.6124	−0.761336	−0.380668	−	0.924712i	$-0.624306\pi$
$733$	−20.6124	−0.761336	−0.380668	+	0.924712i	$0.624306\pi$
$734$	−35.6991	−1.31768
$735$	0	0
$736$	−16.8512	−0.621142
$737$	16.9545	0.624526
$738$	5.38710	0.198302
$739$	−31.7682	−1.16861	−0.584307	−	0.811533i	$-0.698634\pi$
$739$	−31.7682	−1.16861	−0.584307	+	0.811533i	$0.698634\pi$
$740$	9.24934	0.340013
$741$	−1.04012	−0.0382097
$742$	0	0
$743$	−38.9143	−1.42763	−0.713813	−	0.700337i	$-0.753033\pi$
$743$	−38.9143	−1.42763	−0.713813	+	0.700337i	$0.753033\pi$
$744$	−0.740812	−0.0271595
$745$	−8.09904	−0.296726
$746$	−24.2124	−0.886479
$747$	−19.8369	−0.725796
$748$	45.4492	1.66179
$749$	0	0
$750$	5.09787	0.186148
$751$	−18.7285	−0.683413	−0.341707	−	0.939807i	$-0.611005\pi$
$751$	−18.7285	−0.683413	−0.341707	+	0.939807i	$0.611005\pi$
$752$	−43.3485	−1.58076
$753$	−0.136063	−0.00495839
$754$	3.64523	0.132752
$755$	8.81358	0.320759
$756$	0	0
$757$	−7.02375	−0.255282	−0.127641	−	0.991820i	$-0.540741\pi$
$757$	−7.02375	−0.255282	−0.127641	+	0.991820i	$0.540741\pi$
$758$	48.4063	1.75819
$759$	−4.96231	−0.180121
$760$	0.469187	0.0170192
$761$	−12.9753	−0.470353	−0.235176	−	0.971953i	$-0.575567\pi$
$761$	−12.9753	−0.470353	−0.235176	+	0.971953i	$0.575567\pi$
$762$	1.42696	0.0516932
$763$	0	0
$764$	−24.0054	−0.868486
$765$	−7.58898	−0.274380
$766$	40.5497	1.46512
$767$	−2.17388	−0.0784942
$768$	9.13490	0.329627
$769$	39.1892	1.41320	0.706599	−	0.707615i	$-0.250229\pi$
$769$	39.1892	1.41320	0.706599	+	0.707615i	$0.250229\pi$
$770$	0	0
$771$	3.28409	0.118274
$772$	−37.9086	−1.36436
$773$	16.4767	0.592625	0.296312	−	0.955091i	$-0.404243\pi$
$773$	16.4767	0.592625	0.296312	+	0.955091i	$0.404243\pi$
$774$	−51.2038	−1.84048
$775$	−29.2501	−1.05070
$776$	4.48927	0.161156
$777$	0	0
$778$	3.11147	0.111551
$779$	−3.91309	−0.140201
$780$	0.257902	0.00923439
$781$	−28.6014	−1.02344
$782$	−22.7592	−0.813868
$783$	10.6089	0.379133
$784$	0	0
$785$	−0.742938	−0.0265166
$786$	−8.83899	−0.315276
$787$	6.95620	0.247962	0.123981	−	0.992285i	$-0.460434\pi$
$787$	6.95620	0.247962	0.123981	+	0.992285i	$0.460434\pi$
$788$	38.0442	1.35527
$789$	−7.44678	−0.265112
$790$	7.13674	0.253914
$791$	0	0
$792$	−2.85245	−0.101357
$793$	7.94797	0.282241
$794$	60.6446	2.15220
$795$	0.455330	0.0161489
$796$	−12.3937	−0.439283
$797$	−39.3286	−1.39309	−0.696545	−	0.717513i	$-0.745280\pi$
$797$	−39.3286	−1.39309	−0.696545	+	0.717513i	$0.745280\pi$
$798$	0	0
$799$	−55.2731	−1.95542
$800$	37.1806	1.31453
$801$	9.02089	0.318738
$802$	3.81469	0.134701
$803$	−15.6857	−0.553537
$804$	−3.66719	−0.129332
$805$	0	0
$806$	−6.27608	−0.221066
$807$	7.67361	0.270124
$808$	−4.57773	−0.161044
$809$	−18.1188	−0.637022	−0.318511	−	0.947919i	$-0.603183\pi$
$809$	−18.1188	−0.637022	−0.318511	+	0.947919i	$0.603183\pi$
$810$	−6.78391	−0.238362
$811$	33.5622	1.17853	0.589264	−	0.807940i	$-0.299418\pi$
$811$	33.5622	1.17853	0.589264	+	0.807940i	$0.299418\pi$
$812$	0	0
$813$	−0.577622	−0.0202581
$814$	84.2533	2.95308
$815$	4.08627	0.143136
$816$	11.7189	0.410243
$817$	37.1935	1.30123
$818$	10.1399	0.354535
$819$	0	0
$820$	0.970270	0.0338833
$821$	11.6779	0.407563	0.203781	−	0.979016i	$-0.434677\pi$
$821$	11.6779	0.407563	0.203781	+	0.979016i	$0.434677\pi$
$822$	14.5903	0.508895
$823$	10.9047	0.380114	0.190057	−	0.981773i	$-0.439133\pi$
$823$	10.9047	0.380114	0.190057	+	0.981773i	$0.439133\pi$
$824$	0.822241	0.0286441
$825$	10.9489	0.381192
$826$	0	0
$827$	−28.0860	−0.976647	−0.488324	−	0.872663i	$-0.662391\pi$
$827$	−28.0860	−0.976647	−0.488324	+	0.872663i	$0.662391\pi$
$828$	−11.0408	−0.383694
$829$	−48.0994	−1.67056	−0.835281	−	0.549823i	$-0.814695\pi$
$829$	−48.0994	−1.67056	−0.835281	+	0.549823i	$0.814695\pi$
$830$	−7.36974	−0.255808
$831$	2.11617	0.0734090
$832$	3.62414	0.125644
$833$	0	0
$834$	−18.0507	−0.625044
$835$	−4.05710	−0.140402
$836$	−33.0350	−1.14254
$837$	−18.2657	−0.631354
$838$	−2.47248	−0.0854103
$839$	48.3307	1.66856	0.834281	−	0.551340i	$-0.185883\pi$
$839$	48.3307	1.66856	0.834281	+	0.551340i	$0.185883\pi$
$840$	0	0
$841$	−16.1224	−0.555944
$842$	2.85234	0.0982980
$843$	9.65692	0.332602
$844$	−37.2089	−1.28078
$845$	6.56528	0.225852
$846$	−55.3091	−1.90157
$847$	0	0
$848$	7.23263	0.248369
$849$	3.63851	0.124873
$850$	50.2162	1.72240
$851$	−20.4540	−0.701154
$852$	6.18638	0.211942
$853$	−0.00307791	−0.000105386 0	−5.26929e−5	−	1.00000i	$-0.500017\pi$
$853$	−0.00307791	−0.000105386 0	−5.26929e−5		1.00000i	$0.500017\pi$
$854$	0	0
$855$	5.51608	0.188646
$856$	0.454332	0.0155287
$857$	−31.2650	−1.06799	−0.533997	−	0.845487i	$-0.679311\pi$
$857$	−31.2650	−1.06799	−0.533997	+	0.845487i	$0.679311\pi$
$858$	2.34926	0.0802025
$859$	39.1039	1.33421	0.667105	−	0.744964i	$-0.267533\pi$
$859$	39.1039	1.33421	0.667105	+	0.744964i	$0.267533\pi$
$860$	−9.22231	−0.314478
$861$	0	0
$862$	15.7963	0.538025
$863$	37.9955	1.29338	0.646692	−	0.762751i	$-0.276152\pi$
$863$	37.9955	1.29338	0.646692	+	0.762751i	$0.276152\pi$
$864$	23.2180	0.789891
$865$	3.99948	0.135986
$866$	−72.8688	−2.47618
$867$	6.17802	0.209817
$868$	0	0
$869$	31.5163	1.06912
$870$	1.87935	0.0637158
$871$	1.94860	0.0660258
$872$	−1.19282	−0.0403940
$873$	52.7789	1.78630
$874$	16.5426	0.559563
$875$	0	0
$876$	3.39277	0.114631
$877$	−10.3150	−0.348313	−0.174156	−	0.984718i	$-0.555720\pi$
$877$	−10.3150	−0.348313	−0.174156	+	0.984718i	$0.555720\pi$
$878$	13.0294	0.439722
$879$	−4.15089	−0.140006
$880$	−9.76466	−0.329167
$881$	−37.4138	−1.26050	−0.630252	−	0.776391i	$-0.717048\pi$
$881$	−37.4138	−1.26050	−0.630252	+	0.776391i	$0.717048\pi$
$882$	0	0
$883$	32.8240	1.10462	0.552308	−	0.833640i	$-0.313747\pi$
$883$	32.8240	1.10462	0.552308	+	0.833640i	$0.313747\pi$
$884$	5.22354	0.175687
$885$	−1.12077	−0.0376743
$886$	−33.7117	−1.13257
$887$	0.833865	0.0279984	0.0139992	−	0.999902i	$-0.495544\pi$
$887$	0.833865	0.0279984	0.0139992	+	0.999902i	$0.495544\pi$
$888$	1.14300	0.0383564
$889$	0	0
$890$	3.35141	0.112339
$891$	−29.9582	−1.00364
$892$	43.1128	1.44352
$893$	40.1755	1.34442
$894$	15.9573	0.533691
$895$	−6.37725	−0.213168
$896$	0	0
$897$	−0.570325	−0.0190426
$898$	57.2783	1.91140
$899$	−22.1717	−0.739469
$900$	24.3605	0.812018
$901$	9.22222	0.307237
$902$	8.83830	0.294283
$903$	0	0
$904$	3.49919	0.116381
$905$	3.32553	0.110544
$906$	−17.3651	−0.576918
$907$	50.1221	1.66428	0.832139	−	0.554567i	$-0.187116\pi$
$907$	50.1221	1.66428	0.832139	+	0.554567i	$0.187116\pi$
$908$	0.664292	0.0220453
$909$	−53.8189	−1.78506
$910$	0	0
$911$	15.0089	0.497266	0.248633	−	0.968598i	$-0.420019\pi$
$911$	15.0089	0.497266	0.248633	+	0.968598i	$0.420019\pi$
$912$	−8.51793	−0.282057
$913$	−32.5453	−1.07709
$914$	−56.9096	−1.88240
$915$	4.09768	0.135465
$916$	−25.4892	−0.842187
$917$	0	0
$918$	31.3582	1.03498
$919$	41.6557	1.37410	0.687048	−	0.726612i	$-0.258906\pi$
$919$	41.6557	1.37410	0.687048	+	0.726612i	$0.258906\pi$
$920$	0.257268	0.00848188
$921$	−8.34744	−0.275057
$922$	−79.3440	−2.61306
$923$	−3.28720	−0.108199
$924$	0	0
$925$	45.1299	1.48386
$926$	−2.25810	−0.0742058
$927$	9.66682	0.317500
$928$	28.1831	0.925155
$929$	18.7449	0.615000	0.307500	−	0.951548i	$-0.400508\pi$
$929$	18.7449	0.615000	0.307500	+	0.951548i	$0.400508\pi$
$930$	−3.23571	−0.106103
$931$	0	0
$932$	−27.2770	−0.893487
$933$	0.897494	0.0293826
$934$	−66.2367	−2.16733
$935$	−12.4508	−0.407184
$936$	−0.327835	−0.0107156
$937$	31.6122	1.03272	0.516362	−	0.856370i	$-0.327286\pi$
$937$	31.6122	1.03272	0.516362	+	0.856370i	$0.327286\pi$
$938$	0	0
$939$	3.41290	0.111376
$940$	−9.96171	−0.324915
$941$	−13.2860	−0.433111	−0.216555	−	0.976270i	$-0.569482\pi$
$941$	−13.2860	−0.433111	−0.216555	+	0.976270i	$0.569482\pi$
$942$	1.46379	0.0476928
$943$	−2.14565	−0.0698721
$944$	−17.8027	−0.579430
$945$	0	0
$946$	−84.0071	−2.73131
$947$	11.7274	0.381091	0.190545	−	0.981678i	$-0.438974\pi$
$947$	11.7274	0.381091	0.190545	+	0.981678i	$0.438974\pi$
$948$	−6.81687	−0.221402
$949$	−1.80278	−0.0585208
$950$	−36.4999	−1.18421
$951$	−0.734498	−0.0238177
$952$	0	0
$953$	−26.4827	−0.857858	−0.428929	−	0.903338i	$-0.641109\pi$
$953$	−26.4827	−0.857858	−0.428929	+	0.903338i	$0.641109\pi$
$954$	9.22823	0.298775
$955$	6.57628	0.212803
$956$	−10.6678	−0.345021
$957$	8.29932	0.268279
$958$	60.5018	1.95472
$959$	0	0
$960$	1.86847	0.0603046
$961$	7.17360	0.231406
$962$	9.68335	0.312204
$963$	5.34143	0.172125
$964$	−28.0778	−0.904326
$965$	10.3850	0.334306
$966$	0	0
$967$	−56.8542	−1.82831	−0.914154	−	0.405367i	$-0.867144\pi$
$967$	−56.8542	−1.82831	−0.914154	+	0.405367i	$0.867144\pi$
$968$	−2.12162	−0.0681915
$969$	−10.8611	−0.348908
$970$	19.6082	0.629582
$971$	28.8935	0.927237	0.463619	−	0.886035i	$-0.346551\pi$
$971$	28.8935	0.927237	0.463619	+	0.886035i	$0.346551\pi$
$972$	23.1710	0.743210
$973$	0	0
$974$	64.1030	2.05399
$975$	1.25837	0.0403002
$976$	65.0890	2.08345
$977$	34.4961	1.10363	0.551813	−	0.833968i	$-0.313936\pi$
$977$	34.4961	1.10363	0.551813	+	0.833968i	$0.313936\pi$
$978$	−8.05105	−0.257444
$979$	14.8000	0.473012
$980$	0	0
$981$	−14.0236	−0.447739
$982$	−25.5169	−0.814278
$983$	−41.0897	−1.31056	−0.655279	−	0.755387i	$-0.727449\pi$
$983$	−41.0897	−1.31056	−0.655279	+	0.755387i	$0.727449\pi$
$984$	0.119902	0.00382234
$985$	−10.4222	−0.332078
$986$	38.0641	1.21221
$987$	0	0
$988$	−3.79675	−0.120791
$989$	20.3942	0.648498
$990$	−12.4589	−0.395970
$991$	31.7193	1.00760	0.503799	−	0.863821i	$-0.331935\pi$
$991$	31.7193	1.00760	0.503799	+	0.863821i	$0.331935\pi$
$992$	−48.5235	−1.54062
$993$	−0.0878928	−0.00278919
$994$	0	0
$995$	3.39525	0.107637
$996$	7.03943	0.223053
$997$	−2.93215	−0.0928620	−0.0464310	−	0.998922i	$-0.514785\pi$
$997$	−2.93215	−0.0928620	−0.0464310	+	0.998922i	$0.514785\pi$
$998$	−7.79344	−0.246697
$999$	28.1820	0.891640

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.l.1.5		5
7.2	even	3		287.2.e.c.165.1	✓	10
7.4	even	3		287.2.e.c.247.1	yes	10
7.6	odd	2		2009.2.a.m.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.c.165.1	✓	10	7.2	even	3
287.2.e.c.247.1	yes	10	7.4	even	3
2009.2.a.l.1.5		5	1.1	even	1	trivial
2009.2.a.m.1.5		5	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.97027 q^{2} +0.515563 q^{3} +1.88196 q^{4} -0.515563 q^{5} +1.01580 q^{6} -0.232565 q^{8} -2.73420 q^{9} +O(q^{10})\)	\(q+1.97027 q^{2} +0.515563 q^{3} +1.88196 q^{4} -0.515563 q^{5} +1.01580 q^{6} -0.232565 q^{8} -2.73420 q^{9} -1.01580 q^{10} -4.48583 q^{11} +0.970270 q^{12} -0.515563 q^{13} -0.265805 q^{15} -4.22214 q^{16} -5.38359 q^{17} -5.38710 q^{18} +3.91309 q^{19} -0.970270 q^{20} -8.83830 q^{22} +2.14565 q^{23} -0.119902 q^{24} -4.73420 q^{25} -1.01580 q^{26} -2.95634 q^{27} -3.58854 q^{29} -0.523707 q^{30} +6.17848 q^{31} -7.85363 q^{32} -2.31273 q^{33} -10.6071 q^{34} -5.14565 q^{36} -9.53276 q^{37} +7.70984 q^{38} -0.265805 q^{39} +0.119902 q^{40} -1.00000 q^{41} +9.50489 q^{43} -8.44217 q^{44} +1.40965 q^{45} +4.22752 q^{46} +10.2670 q^{47} -2.17678 q^{48} -9.32764 q^{50} -2.77558 q^{51} -0.970270 q^{52} -1.71302 q^{53} -5.82478 q^{54} +2.31273 q^{55} +2.01744 q^{57} -7.07040 q^{58} +4.21652 q^{59} -0.500235 q^{60} -15.4161 q^{61} +12.1733 q^{62} -7.02948 q^{64} +0.265805 q^{65} -4.55670 q^{66} -3.77956 q^{67} -10.1317 q^{68} +1.10622 q^{69} +6.37594 q^{71} +0.635879 q^{72} +3.49673 q^{73} -18.7821 q^{74} -2.44077 q^{75} +7.36429 q^{76} -0.523707 q^{78} -7.02575 q^{79} +2.17678 q^{80} +6.67841 q^{81} -1.97027 q^{82} +7.25513 q^{83} +2.77558 q^{85} +18.7272 q^{86} -1.85012 q^{87} +1.04325 q^{88} -3.29929 q^{89} +2.77739 q^{90} +4.03804 q^{92} +3.18539 q^{93} +20.2287 q^{94} -2.01744 q^{95} -4.04904 q^{96} -19.3033 q^{97} +12.2651 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 2 q^{3} + 6 q^{4} + 2 q^{5} + q^{6} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 + 2 * q^5 + q^6 - 3 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} - 2 q^{3} + 6 q^{4} + 2 q^{5} + q^{6} - 3 q^{8} + 5 q^{9} - q^{10} - 6 q^{11} - 7 q^{12} + 2 q^{13} - 20 q^{15} - 12 q^{16} - 3 q^{17} - 8 q^{18} + 7 q^{19} + 7 q^{20} - 13 q^{22} + 16 q^{24} - 5 q^{25} - q^{26} + 13 q^{27} - 10 q^{29} + 14 q^{30} - 6 q^{31} - 3 q^{32} - 17 q^{33} + q^{34} - 15 q^{36} - 18 q^{37} - 7 q^{38} - 20 q^{39} - 16 q^{40} - 5 q^{41} - 14 q^{43} + 2 q^{44} - 7 q^{45} - 3 q^{46} + 3 q^{47} + 9 q^{48} - 4 q^{50} + 7 q^{52} - 9 q^{53} - 25 q^{54} + 17 q^{55} + 31 q^{57} - 5 q^{58} - 19 q^{59} - 3 q^{60} - 23 q^{61} + 36 q^{62} - q^{64} + 20 q^{65} + 23 q^{66} - 11 q^{67} - 24 q^{68} + 19 q^{69} + 25 q^{72} + 13 q^{73} + 2 q^{74} + 11 q^{75} + 12 q^{76} + 14 q^{78} - 41 q^{79} - 9 q^{80} - 7 q^{81} + 2 q^{82} - 2 q^{83} + 20 q^{86} + 32 q^{87} - 10 q^{88} + 14 q^{89} + 22 q^{90} + 17 q^{92} - 15 q^{93} + 10 q^{94} - 31 q^{95} - 33 q^{96} - 27 q^{97} - 9 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 + 2 * q^5 + q^6 - 3 * q^8 + 5 * q^9 - q^10 - 6 * q^11 - 7 * q^12 + 2 * q^13 - 20 * q^15 - 12 * q^16 - 3 * q^17 - 8 * q^18 + 7 * q^19 + 7 * q^20 - 13 * q^22 + 16 * q^24 - 5 * q^25 - q^26 + 13 * q^27 - 10 * q^29 + 14 * q^30 - 6 * q^31 - 3 * q^32 - 17 * q^33 + q^34 - 15 * q^36 - 18 * q^37 - 7 * q^38 - 20 * q^39 - 16 * q^40 - 5 * q^41 - 14 * q^43 + 2 * q^44 - 7 * q^45 - 3 * q^46 + 3 * q^47 + 9 * q^48 - 4 * q^50 + 7 * q^52 - 9 * q^53 - 25 * q^54 + 17 * q^55 + 31 * q^57 - 5 * q^58 - 19 * q^59 - 3 * q^60 - 23 * q^61 + 36 * q^62 - q^64 + 20 * q^65 + 23 * q^66 - 11 * q^67 - 24 * q^68 + 19 * q^69 + 25 * q^72 + 13 * q^73 + 2 * q^74 + 11 * q^75 + 12 * q^76 + 14 * q^78 - 41 * q^79 - 9 * q^80 - 7 * q^81 + 2 * q^82 - 2 * q^83 + 20 * q^86 + 32 * q^87 - 10 * q^88 + 14 * q^89 + 22 * q^90 + 17 * q^92 - 15 * q^93 + 10 * q^94 - 31 * q^95 - 33 * q^96 - 27 * q^97 - 9 * q^99

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