LMFDB - Embedded newform 2009.2.a.s.1.11

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:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 25 x^{15} + 77 x^{14} + 247 x^{13} - 790 x^{12} - 1231 x^{11} + 4173 x^{10} + \cdots - 464 $ x^17 - 3x^16 - 25x^15 + 77x^14 + 247x^13 - 790x^12 - 1231x^11 + 4173x^10 + 3251x^9 - 12183x^8 - 4259x^7 + 19567x^6 + 2029x^5 - 16136x^4 + 299x^3 + 5775x^2 - 312x - 464
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			1.11
Root			$1.17557$ 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)

$f(q)$	$=$	$q+1.17557 q^{2} +2.72860 q^{3} -0.618039 q^{4} -2.82853 q^{5} +3.20766 q^{6} -3.07768 q^{8} +4.44528 q^{9} +O(q^{10})$	\(q+1.17557 q^{2} +2.72860 q^{3} -0.618039 q^{4} -2.82853 q^{5} +3.20766 q^{6} -3.07768 q^{8} +4.44528 q^{9} -3.32513 q^{10} +4.71688 q^{11} -1.68638 q^{12} +2.95777 q^{13} -7.71794 q^{15} -2.38195 q^{16} +5.06492 q^{17} +5.22573 q^{18} -4.50858 q^{19} +1.74814 q^{20} +5.54501 q^{22} +1.60921 q^{23} -8.39778 q^{24} +3.00058 q^{25} +3.47706 q^{26} +3.94360 q^{27} +7.93993 q^{29} -9.07296 q^{30} +7.31455 q^{31} +3.35522 q^{32} +12.8705 q^{33} +5.95416 q^{34} -2.74736 q^{36} +1.35260 q^{37} -5.30014 q^{38} +8.07058 q^{39} +8.70532 q^{40} +1.00000 q^{41} -1.02962 q^{43} -2.91522 q^{44} -12.5736 q^{45} +1.89174 q^{46} +7.85022 q^{47} -6.49940 q^{48} +3.52738 q^{50} +13.8202 q^{51} -1.82802 q^{52} +1.72187 q^{53} +4.63597 q^{54} -13.3418 q^{55} -12.3021 q^{57} +9.33393 q^{58} -11.1850 q^{59} +4.76999 q^{60} -6.96462 q^{61} +8.59876 q^{62} +8.70819 q^{64} -8.36614 q^{65} +15.1301 q^{66} +0.648015 q^{67} -3.13032 q^{68} +4.39090 q^{69} +12.1249 q^{71} -13.6812 q^{72} -12.0878 q^{73} +1.59007 q^{74} +8.18739 q^{75} +2.78648 q^{76} +9.48752 q^{78} +5.45115 q^{79} +6.73741 q^{80} -2.57532 q^{81} +1.17557 q^{82} -12.1586 q^{83} -14.3263 q^{85} -1.21039 q^{86} +21.6649 q^{87} -14.5171 q^{88} +5.93969 q^{89} -14.7811 q^{90} -0.994555 q^{92} +19.9585 q^{93} +9.22847 q^{94} +12.7526 q^{95} +9.15508 q^{96} +6.86976 q^{97} +20.9679 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) $ 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9	$ 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9} - 2 q^{10} + 15 q^{11} + 4 q^{12} - 5 q^{13} + 24 q^{15} + 33 q^{16} + 4 q^{17} + 10 q^{18} + 5 q^{19} - 26 q^{20} + 16 q^{22} + 12 q^{23} + 16 q^{24} + 24 q^{25} + 31 q^{26} - 11 q^{27} + 14 q^{29} - 33 q^{30} - 3 q^{31} + 16 q^{32} + 4 q^{33} - 24 q^{34} + 57 q^{36} + 24 q^{37} + 45 q^{39} + 36 q^{40} + 17 q^{41} + 14 q^{43} - 9 q^{44} - 21 q^{45} + 44 q^{46} + 19 q^{47} - 60 q^{48} - 4 q^{50} + 2 q^{51} - 25 q^{52} + 4 q^{53} + 68 q^{54} + 9 q^{55} - 12 q^{57} - q^{58} - 27 q^{59} + 66 q^{60} - q^{61} - 23 q^{62} + 75 q^{64} + 22 q^{65} - 16 q^{66} + 49 q^{67} + 45 q^{68} + 12 q^{69} + 40 q^{71} - 23 q^{72} - 14 q^{73} + 33 q^{74} + 27 q^{75} - 9 q^{76} - 12 q^{78} + 61 q^{79} - 82 q^{80} + 53 q^{81} + 3 q^{82} - 18 q^{83} - 13 q^{85} - 4 q^{86} - 17 q^{87} + 74 q^{88} + 18 q^{89} - 20 q^{90} + 28 q^{92} - 36 q^{93} - 5 q^{94} + 20 q^{95} + 148 q^{96} + 26 q^{97} + 38 q^{99}+O(q^{100}) $ 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9 - 2 * q^10 + 15 * q^11 + 4 * q^12 - 5 * q^13 + 24 * q^15 + 33 * q^16 + 4 * q^17 + 10 * q^18 + 5 * q^19 - 26 * q^20 + 16 * q^22 + 12 * q^23 + 16 * q^24 + 24 * q^25 + 31 * q^26 - 11 * q^27 + 14 * q^29 - 33 * q^30 - 3 * q^31 + 16 * q^32 + 4 * q^33 - 24 * q^34 + 57 * q^36 + 24 * q^37 + 45 * q^39 + 36 * q^40 + 17 * q^41 + 14 * q^43 - 9 * q^44 - 21 * q^45 + 44 * q^46 + 19 * q^47 - 60 * q^48 - 4 * q^50 + 2 * q^51 - 25 * q^52 + 4 * q^53 + 68 * q^54 + 9 * q^55 - 12 * q^57 - q^58 - 27 * q^59 + 66 * q^60 - q^61 - 23 * q^62 + 75 * q^64 + 22 * q^65 - 16 * q^66 + 49 * q^67 + 45 * q^68 + 12 * q^69 + 40 * q^71 - 23 * q^72 - 14 * q^73 + 33 * q^74 + 27 * q^75 - 9 * q^76 - 12 * q^78 + 61 * q^79 - 82 * q^80 + 53 * q^81 + 3 * q^82 - 18 * q^83 - 13 * q^85 - 4 * q^86 - 17 * q^87 + 74 * q^88 + 18 * q^89 - 20 * q^90 + 28 * q^92 - 36 * q^93 - 5 * q^94 + 20 * q^95 + 148 * q^96 + 26 * q^97 + 38 * 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 $

$2$	1.17557	0.831252	0.415626	−	0.909536i	$-0.363562\pi$
$2$	1.17557	0.831252	0.415626	+	0.909536i	$0.363562\pi$
$3$	2.72860	1.57536	0.787680	−	0.616084i	$-0.211282\pi$
$3$	2.72860	1.57536	0.787680	+	0.616084i	$0.211282\pi$
$4$	−0.618039	−0.309020
$5$	−2.82853	−1.26496	−0.632478	−	0.774578i	$-0.717962\pi$
$5$	−2.82853	−1.26496	−0.632478	+	0.774578i	$0.717962\pi$
$6$	3.20766	1.30952
$7$	0	0
$7$	0	0
$8$	−3.07768	−1.08813
$9$	4.44528	1.48176
$10$	−3.32513	−1.05150
$11$	4.71688	1.42219	0.711096	−	0.703095i	$-0.248199\pi$
$11$	4.71688	1.42219	0.711096	+	0.703095i	$0.248199\pi$
$12$	−1.68638	−0.486817
$13$	2.95777	0.820338	0.410169	−	0.912010i	$-0.365470\pi$
$13$	2.95777	0.820338	0.410169	+	0.912010i	$0.365470\pi$
$14$	0	0
$15$	−7.71794	−1.99276
$16$	−2.38195	−0.595487
$17$	5.06492	1.22842	0.614211	−	0.789142i	$-0.289474\pi$
$17$	5.06492	1.22842	0.614211	+	0.789142i	$0.289474\pi$
$18$	5.22573	1.23172
$19$	−4.50858	−1.03434	−0.517170	−	0.855883i	$-0.673014\pi$
$19$	−4.50858	−1.03434	−0.517170	+	0.855883i	$0.673014\pi$
$20$	1.74814	0.390896
$21$	0	0
$22$	5.54501	1.18220
$23$	1.60921	0.335543	0.167772	−	0.985826i	$-0.446343\pi$
$23$	1.60921	0.335543	0.167772	+	0.985826i	$0.446343\pi$
$24$	−8.39778	−1.71419
$25$	3.00058	0.600116
$26$	3.47706	0.681908
$27$	3.94360	0.758946
$28$	0	0
$29$	7.93993	1.47441	0.737204	−	0.675670i	$-0.236146\pi$
$29$	7.93993	1.47441	0.737204	+	0.675670i	$0.236146\pi$
$30$	−9.07296	−1.65649
$31$	7.31455	1.31373	0.656866	−	0.754007i	$-0.271882\pi$
$31$	7.31455	1.31373	0.656866	+	0.754007i	$0.271882\pi$
$32$	3.35522	0.593125
$33$	12.8705	2.24047
$34$	5.95416	1.02113
$35$	0	0
$36$	−2.74736	−0.457893
$37$	1.35260	0.222366	0.111183	−	0.993800i	$-0.464536\pi$
$37$	1.35260	0.222366	0.111183	+	0.993800i	$0.464536\pi$
$38$	−5.30014	−0.859797
$39$	8.07058	1.29233
$40$	8.70532	1.37643
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−1.02962	−0.157016	−0.0785080	−	0.996913i	$-0.525016\pi$
$43$	−1.02962	−0.157016	−0.0785080	+	0.996913i	$0.525016\pi$
$44$	−2.91522	−0.439485
$45$	−12.5736	−1.87436
$46$	1.89174	0.278921
$47$	7.85022	1.14507	0.572536	−	0.819880i	$-0.305960\pi$
$47$	7.85022	1.14507	0.572536	+	0.819880i	$0.305960\pi$
$48$	−6.49940	−0.938107
$49$	0	0
$50$	3.52738	0.498847
$51$	13.8202	1.93521
$52$	−1.82802	−0.253500
$53$	1.72187	0.236517	0.118258	−	0.992983i	$-0.462269\pi$
$53$	1.72187	0.236517	0.118258	+	0.992983i	$0.462269\pi$
$54$	4.63597	0.630876
$55$	−13.3418	−1.79901
$56$	0	0
$57$	−12.3021	−1.62946
$58$	9.33393	1.22561
$59$	−11.1850	−1.45616	−0.728079	−	0.685493i	$-0.759587\pi$
$59$	−11.1850	−1.45616	−0.728079	+	0.685493i	$0.759587\pi$
$60$	4.76999	0.615803
$61$	−6.96462	−0.891728	−0.445864	−	0.895101i	$-0.647103\pi$
$61$	−6.96462	−0.891728	−0.445864	+	0.895101i	$0.647103\pi$
$62$	8.59876	1.09204
$63$	0	0
$64$	8.70819	1.08852
$65$	−8.36614	−1.03769
$66$	15.1301	1.86239
$67$	0.648015	0.0791677	0.0395838	−	0.999216i	$-0.487397\pi$
$67$	0.648015	0.0791677	0.0395838	+	0.999216i	$0.487397\pi$
$68$	−3.13032	−0.379607
$69$	4.39090	0.528602
$70$	0	0
$71$	12.1249	1.43896	0.719479	−	0.694514i	$-0.244381\pi$
$71$	12.1249	1.43896	0.719479	+	0.694514i	$0.244381\pi$
$72$	−13.6812	−1.61234
$73$	−12.0878	−1.41477	−0.707385	−	0.706829i	$-0.750125\pi$
$73$	−12.0878	−1.41477	−0.707385	+	0.706829i	$0.750125\pi$
$74$	1.59007	0.184842
$75$	8.18739	0.945398
$76$	2.78648	0.319631
$77$	0	0
$78$	9.48752	1.07425
$79$	5.45115	0.613303	0.306651	−	0.951822i	$-0.400791\pi$
$79$	5.45115	0.613303	0.306651	+	0.951822i	$0.400791\pi$
$80$	6.73741	0.753266
$81$	−2.57532	−0.286147
$82$	1.17557	0.129820
$83$	−12.1586	−1.33458	−0.667288	−	0.744800i	$-0.732545\pi$
$83$	−12.1586	−1.33458	−0.667288	+	0.744800i	$0.732545\pi$
$84$	0	0
$85$	−14.3263	−1.55390
$86$	−1.21039	−0.130520
$87$	21.6649	2.32272
$88$	−14.5171	−1.54752
$89$	5.93969	0.629606	0.314803	−	0.949157i	$-0.398062\pi$
$89$	5.93969	0.629606	0.314803	+	0.949157i	$0.398062\pi$
$90$	−14.7811	−1.55807
$91$	0	0
$92$	−0.994555	−0.103690
$93$	19.9585	2.06960
$94$	9.22847	0.951844
$95$	12.7526	1.30839
$96$	9.15508	0.934386
$97$	6.86976	0.697518	0.348759	−	0.937212i	$-0.386603\pi$
$97$	6.86976	0.697518	0.348759	+	0.937212i	$0.386603\pi$
$98$	0	0
$99$	20.9679	2.10735
$100$	−1.85448	−0.185448
$101$	−18.9155	−1.88216	−0.941080	−	0.338184i	$-0.890187\pi$
$101$	−18.9155	−1.88216	−0.941080	+	0.338184i	$0.890187\pi$
$102$	16.2465	1.60865
$103$	−7.85352	−0.773831	−0.386915	−	0.922115i	$-0.626459\pi$
$103$	−7.85352	−0.773831	−0.386915	+	0.922115i	$0.626459\pi$
$104$	−9.10308	−0.892630
$105$	0	0
$106$	2.02417	0.196605
$107$	11.6249	1.12382	0.561910	−	0.827199i	$-0.310067\pi$
$107$	11.6249	1.12382	0.561910	+	0.827199i	$0.310067\pi$
$108$	−2.43730	−0.234529
$109$	−7.62432	−0.730278	−0.365139	−	0.930953i	$-0.618978\pi$
$109$	−7.62432	−0.730278	−0.365139	+	0.930953i	$0.618978\pi$
$110$	−15.6842	−1.49543
$111$	3.69071	0.350307
$112$	0	0
$113$	−1.64402	−0.154657	−0.0773283	−	0.997006i	$-0.524639\pi$
$113$	−1.64402	−0.154657	−0.0773283	+	0.997006i	$0.524639\pi$
$114$	−14.4620	−1.35449
$115$	−4.55170	−0.424448
$116$	−4.90719	−0.455621
$117$	13.1481	1.21554
$118$	−13.1487	−1.21043
$119$	0	0
$120$	23.7534	2.16838
$121$	11.2489	1.02263
$122$	−8.18738	−0.741251
$123$	2.72860	0.246030
$124$	−4.52068	−0.405969
$125$	5.65542	0.505836
$126$	0	0
$127$	4.19475	0.372224	0.186112	−	0.982529i	$-0.440411\pi$
$127$	4.19475	0.372224	0.186112	+	0.982529i	$0.440411\pi$
$128$	3.52663	0.311713
$129$	−2.80943	−0.247357
$130$	−9.83497	−0.862584
$131$	−20.7949	−1.81686	−0.908430	−	0.418037i	$-0.862718\pi$
$131$	−20.7949	−1.81686	−0.908430	+	0.418037i	$0.862718\pi$
$132$	−7.95447	−0.692348
$133$	0	0
$134$	0.761786	0.0658083
$135$	−11.1546	−0.960034
$136$	−15.5882	−1.33668
$137$	2.66542	0.227723	0.113861	−	0.993497i	$-0.463678\pi$
$137$	2.66542	0.227723	0.113861	+	0.993497i	$0.463678\pi$
$138$	5.16180	0.439401
$139$	−7.95421	−0.674668	−0.337334	−	0.941385i	$-0.609525\pi$
$139$	−7.95421	−0.674668	−0.337334	+	0.941385i	$0.609525\pi$
$140$	0	0
$141$	21.4201	1.80390
$142$	14.2536	1.19614
$143$	13.9514	1.16668
$144$	−10.5884	−0.882369
$145$	−22.4583	−1.86506
$146$	−14.2100	−1.17603
$147$	0	0
$148$	−0.835960	−0.0687155
$149$	−0.0794937	−0.00651238	−0.00325619	−	0.999995i	$-0.501036\pi$
$149$	−0.0794937	−0.00651238	−0.00325619	+	0.999995i	$0.501036\pi$
$150$	9.62484	0.785865
$151$	14.6821	1.19481	0.597406	−	0.801939i	$-0.296198\pi$
$151$	14.6821	1.19481	0.597406	+	0.801939i	$0.296198\pi$
$152$	13.8760	1.12549
$153$	22.5150	1.82023
$154$	0	0
$155$	−20.6894	−1.66181
$156$	−4.98794	−0.399355
$157$	10.8291	0.864256	0.432128	−	0.901812i	$-0.357763\pi$
$157$	10.8291	0.864256	0.432128	+	0.901812i	$0.357763\pi$
$158$	6.40820	0.509809
$159$	4.69829	0.372599
$160$	−9.49035	−0.750278
$161$	0	0
$162$	−3.02747	−0.237860
$163$	16.6528	1.30435	0.652174	−	0.758069i	$-0.273857\pi$
$163$	16.6528	1.30435	0.652174	+	0.758069i	$0.273857\pi$
$164$	−0.618039	−0.0482608
$165$	−36.4046	−2.83409
$166$	−14.2932	−1.10937
$167$	7.39264	0.572060	0.286030	−	0.958221i	$-0.407664\pi$
$167$	7.39264	0.572060	0.286030	+	0.958221i	$0.407664\pi$
$168$	0	0
$169$	−4.25160	−0.327046
$170$	−16.8415	−1.29168
$171$	−20.0419	−1.53264
$172$	0.636348	0.0485211
$173$	−14.3518	−1.09115	−0.545573	−	0.838063i	$-0.683688\pi$
$173$	−14.3518	−1.09115	−0.545573	+	0.838063i	$0.683688\pi$
$174$	25.4686	1.93077
$175$	0	0
$176$	−11.2354	−0.846898
$177$	−30.5193	−2.29397
$178$	6.98251	0.523361
$179$	2.36978	0.177125	0.0885627	−	0.996071i	$-0.471773\pi$
$179$	2.36978	0.177125	0.0885627	+	0.996071i	$0.471773\pi$
$180$	7.77098	0.579215
$181$	20.2014	1.50156	0.750780	−	0.660552i	$-0.229678\pi$
$181$	20.2014	1.50156	0.750780	+	0.660552i	$0.229678\pi$
$182$	0	0
$183$	−19.0037	−1.40479
$184$	−4.95264	−0.365113
$185$	−3.82587	−0.281284
$186$	23.4626	1.72036
$187$	23.8906	1.74705
$188$	−4.85174	−0.353850
$189$	0	0
$190$	14.9916	1.08761
$191$	−16.2663	−1.17699	−0.588494	−	0.808501i	$-0.700279\pi$
$191$	−16.2663	−1.17699	−0.588494	+	0.808501i	$0.700279\pi$
$192$	23.7612	1.71482
$193$	−24.7700	−1.78298	−0.891490	−	0.453040i	$-0.850339\pi$
$193$	−24.7700	−1.78298	−0.891490	+	0.453040i	$0.850339\pi$
$194$	8.07587	0.579814
$195$	−22.8279	−1.63474
$196$	0	0
$197$	−18.8114	−1.34025	−0.670127	−	0.742246i	$-0.733761\pi$
$197$	−18.8114	−1.34025	−0.670127	+	0.742246i	$0.733761\pi$
$198$	24.6491	1.75174
$199$	4.66599	0.330763	0.165382	−	0.986230i	$-0.447114\pi$
$199$	4.66599	0.330763	0.165382	+	0.986230i	$0.447114\pi$
$200$	−9.23483	−0.653001
$201$	1.76818	0.124718
$202$	−22.2364	−1.56455
$203$	0	0
$204$	−8.54140	−0.598017
$205$	−2.82853	−0.197553
$206$	−9.23235	−0.643249
$207$	7.15339	0.497195
$208$	−7.04526	−0.488501
$209$	−21.2664	−1.47103
$210$	0	0
$211$	−18.7594	−1.29145	−0.645725	−	0.763570i	$-0.723445\pi$
$211$	−18.7594	−1.29145	−0.645725	+	0.763570i	$0.723445\pi$
$212$	−1.06418	−0.0730883
$213$	33.0840	2.26688
$214$	13.6658	0.934177
$215$	2.91232	0.198619
$216$	−12.1372	−0.825828
$217$	0	0
$218$	−8.96291	−0.607045
$219$	−32.9828	−2.22877
$220$	8.24578	0.555930
$221$	14.9809	1.00772
$222$	4.33868	0.291193
$223$	−4.94608	−0.331214	−0.165607	−	0.986192i	$-0.552958\pi$
$223$	−4.94608	−0.331214	−0.165607	+	0.986192i	$0.552958\pi$
$224$	0	0
$225$	13.3384	0.889227
$226$	−1.93266	−0.128559
$227$	−16.4193	−1.08978	−0.544892	−	0.838506i	$-0.683429\pi$
$227$	−16.4193	−1.08978	−0.544892	+	0.838506i	$0.683429\pi$
$228$	7.60320	0.503534
$229$	2.22991	0.147356	0.0736782	−	0.997282i	$-0.476526\pi$
$229$	2.22991	0.147356	0.0736782	+	0.997282i	$0.476526\pi$
$230$	−5.35083	−0.352823
$231$	0	0
$232$	−24.4366	−1.60434
$233$	12.6535	0.828957	0.414479	−	0.910059i	$-0.363964\pi$
$233$	12.6535	0.828957	0.414479	+	0.910059i	$0.363964\pi$
$234$	15.4565	1.01042
$235$	−22.2046	−1.44847
$236$	6.91275	0.449981
$237$	14.8740	0.966173
$238$	0	0
$239$	−5.62327	−0.363739	−0.181870	−	0.983323i	$-0.558215\pi$
$239$	−5.62327	−0.363739	−0.181870	+	0.983323i	$0.558215\pi$
$240$	18.3837	1.18666
$241$	23.2442	1.49729	0.748645	−	0.662971i	$-0.230705\pi$
$241$	23.2442	1.49729	0.748645	+	0.662971i	$0.230705\pi$
$242$	13.2239	0.850065
$243$	−18.8578	−1.20973
$244$	4.30441	0.275561
$245$	0	0
$246$	3.20766	0.204513
$247$	−13.3353	−0.848507
$248$	−22.5119	−1.42951
$249$	−33.1759	−2.10244
$250$	6.64834	0.420478
$251$	−22.6110	−1.42720	−0.713598	−	0.700556i	$-0.752935\pi$
$251$	−22.6110	−1.42720	−0.713598	+	0.700556i	$0.752935\pi$
$252$	0	0
$253$	7.59045	0.477207
$254$	4.93121	0.309412
$255$	−39.0907	−2.44796
$256$	−13.2706	−0.829412
$257$	5.47074	0.341256	0.170628	−	0.985336i	$-0.445420\pi$
$257$	5.47074	0.341256	0.170628	+	0.985336i	$0.445420\pi$
$258$	−3.30268	−0.205616
$259$	0	0
$260$	5.17060	0.320667
$261$	35.2952	2.18472
$262$	−24.4458	−1.51027
$263$	−10.7545	−0.663148	−0.331574	−	0.943429i	$-0.607580\pi$
$263$	−10.7545	−0.663148	−0.331574	+	0.943429i	$0.607580\pi$
$264$	−39.6113	−2.43791
$265$	−4.87035	−0.299183
$266$	0	0
$267$	16.2071	0.991856
$268$	−0.400499	−0.0244644
$269$	−20.4906	−1.24933	−0.624667	−	0.780891i	$-0.714765\pi$
$269$	−20.4906	−1.24933	−0.624667	+	0.780891i	$0.714765\pi$
$270$	−13.1130	−0.798030
$271$	14.8238	0.900481	0.450240	−	0.892907i	$-0.351338\pi$
$271$	14.8238	0.900481	0.450240	+	0.892907i	$0.351338\pi$
$272$	−12.0644	−0.731510
$273$	0	0
$274$	3.13339	0.189295
$275$	14.1534	0.853480
$276$	−2.71375	−0.163348
$277$	19.4149	1.16653	0.583265	−	0.812282i	$-0.301775\pi$
$277$	19.4149	1.16653	0.583265	+	0.812282i	$0.301775\pi$
$278$	−9.35072	−0.560819
$279$	32.5152	1.94664
$280$	0	0
$281$	9.51673	0.567720	0.283860	−	0.958866i	$-0.408385\pi$
$281$	9.51673	0.567720	0.283860	+	0.958866i	$0.408385\pi$
$282$	25.1808	1.49950
$283$	14.3030	0.850225	0.425112	−	0.905141i	$-0.360235\pi$
$283$	14.3030	0.850225	0.425112	+	0.905141i	$0.360235\pi$
$284$	−7.49365	−0.444666
$285$	34.7969	2.06119
$286$	16.4009	0.969804
$287$	0	0
$288$	14.9149	0.878870
$289$	8.65339	0.509023
$290$	−26.4013	−1.55034
$291$	18.7448	1.09884
$292$	7.47073	0.437191
$293$	−9.08991	−0.531038	−0.265519	−	0.964106i	$-0.585543\pi$
$293$	−9.08991	−0.531038	−0.265519	+	0.964106i	$0.585543\pi$
$294$	0	0
$295$	31.6370	1.84198
$296$	−4.16288	−0.241962
$297$	18.6015	1.07937
$298$	−0.0934503	−0.00541343
$299$	4.75967	0.275259
$300$	−5.06013	−0.292147
$301$	0	0
$302$	17.2598	0.993191
$303$	−51.6128	−2.96508
$304$	10.7392	0.615936
$305$	19.6996	1.12800
$306$	26.4679	1.51307
$307$	25.2170	1.43921	0.719606	−	0.694383i	$-0.244323\pi$
$307$	25.2170	1.43921	0.719606	+	0.694383i	$0.244323\pi$
$308$	0	0
$309$	−21.4292	−1.21906
$310$	−24.3218	−1.38139
$311$	−16.9161	−0.959225	−0.479613	−	0.877480i	$-0.659223\pi$
$311$	−16.9161	−0.959225	−0.479613	+	0.877480i	$0.659223\pi$
$312$	−24.8387	−1.40621
$313$	−0.875735	−0.0494995	−0.0247497	−	0.999694i	$-0.507879\pi$
$313$	−0.875735	−0.0494995	−0.0247497	+	0.999694i	$0.507879\pi$
$314$	12.7303	0.718415
$315$	0	0
$316$	−3.36903	−0.189523
$317$	−12.9270	−0.726051	−0.363026	−	0.931779i	$-0.618256\pi$
$317$	−12.9270	−0.726051	−0.363026	+	0.931779i	$0.618256\pi$
$318$	5.52317	0.309724
$319$	37.4517	2.09689
$320$	−24.6314	−1.37694
$321$	31.7197	1.77042
$322$	0	0
$323$	−22.8356	−1.27061
$324$	1.59165	0.0884250
$325$	8.87502	0.492297
$326$	19.5765	1.08424
$327$	−20.8038	−1.15045
$328$	−3.07768	−0.169937
$329$	0	0
$330$	−42.7961	−2.35585
$331$	−22.3039	−1.22594	−0.612968	−	0.790108i	$-0.710025\pi$
$331$	−22.3039	−1.22594	−0.612968	+	0.790108i	$0.710025\pi$
$332$	7.51447	0.412410
$333$	6.01269	0.329493
$334$	8.69055	0.475526
$335$	−1.83293	−0.100144
$336$	0	0
$337$	−14.3364	−0.780953	−0.390477	−	0.920613i	$-0.627690\pi$
$337$	−14.3364	−0.780953	−0.390477	+	0.920613i	$0.627690\pi$
$338$	−4.99805	−0.271858
$339$	−4.48589	−0.243640
$340$	8.85420	0.480186
$341$	34.5019	1.86838
$342$	−23.5606	−1.27401
$343$	0	0
$344$	3.16886	0.170853
$345$	−12.4198	−0.668658
$346$	−16.8715	−0.907017
$347$	−33.4640	−1.79644	−0.898221	−	0.439545i	$-0.855140\pi$
$347$	−33.4640	−1.79644	−0.898221	+	0.439545i	$0.855140\pi$
$348$	−13.3898	−0.717767
$349$	7.30788	0.391182	0.195591	−	0.980686i	$-0.437338\pi$
$349$	7.30788	0.391182	0.195591	+	0.980686i	$0.437338\pi$
$350$	0	0
$351$	11.6643	0.622592
$352$	15.8262	0.843539
$353$	20.2309	1.07678	0.538392	−	0.842694i	$-0.319032\pi$
$353$	20.2309	1.07678	0.538392	+	0.842694i	$0.319032\pi$
$354$	−35.8776	−1.90687
$355$	−34.2956	−1.82022
$356$	−3.67096	−0.194560
$357$	0	0
$358$	2.78583	0.147236
$359$	35.3862	1.86761	0.933805	−	0.357782i	$-0.116467\pi$
$359$	35.3862	1.86761	0.933805	+	0.357782i	$0.116467\pi$
$360$	38.6976	2.03954
$361$	1.32729	0.0698573
$362$	23.7482	1.24818
$363$	30.6939	1.61101
$364$	0	0
$365$	34.1907	1.78962
$366$	−22.3401	−1.16774
$367$	−15.8701	−0.828413	−0.414207	−	0.910183i	$-0.635941\pi$
$367$	−15.8701	−0.828413	−0.414207	+	0.910183i	$0.635941\pi$
$368$	−3.83306	−0.199812
$369$	4.44528	0.231412
$370$	−4.49757	−0.233818
$371$	0	0
$372$	−12.3351	−0.639548
$373$	−4.94499	−0.256042	−0.128021	−	0.991771i	$-0.540862\pi$
$373$	−4.94499	−0.256042	−0.128021	+	0.991771i	$0.540862\pi$
$374$	28.0850	1.45224
$375$	15.4314	0.796875
$376$	−24.1605	−1.24598
$377$	23.4845	1.20951
$378$	0	0
$379$	25.4026	1.30484	0.652422	−	0.757856i	$-0.273753\pi$
$379$	25.4026	1.30484	0.652422	+	0.757856i	$0.273753\pi$
$380$	−7.88164	−0.404320
$381$	11.4458	0.586386
$382$	−19.1221	−0.978374
$383$	−8.79723	−0.449517	−0.224759	−	0.974414i	$-0.572159\pi$
$383$	−8.79723	−0.449517	−0.224759	+	0.974414i	$0.572159\pi$
$384$	9.62277	0.491060
$385$	0	0
$386$	−29.1188	−1.48211
$387$	−4.57696	−0.232660
$388$	−4.24578	−0.215547
$389$	14.9916	0.760107	0.380053	−	0.924965i	$-0.375906\pi$
$389$	14.9916	0.760107	0.380053	+	0.924965i	$0.375906\pi$
$390$	−26.8357	−1.35888
$391$	8.15051	0.412189
$392$	0	0
$393$	−56.7411	−2.86221
$394$	−22.1141	−1.11409
$395$	−15.4187	−0.775801
$396$	−12.9590	−0.651212
$397$	1.30202	0.0653464	0.0326732	−	0.999466i	$-0.489598\pi$
$397$	1.30202	0.0653464	0.0326732	+	0.999466i	$0.489598\pi$
$398$	5.48519	0.274948
$399$	0	0
$400$	−7.14722	−0.357361
$401$	−22.9368	−1.14541	−0.572705	−	0.819761i	$-0.694106\pi$
$401$	−22.9368	−1.14541	−0.572705	+	0.819761i	$0.694106\pi$
$402$	2.07861	0.103672
$403$	21.6348	1.07770
$404$	11.6905	0.581624
$405$	7.28437	0.361963
$406$	0	0
$407$	6.38005	0.316247
$408$	−42.5341	−2.10575
$409$	9.78196	0.483687	0.241843	−	0.970315i	$-0.422248\pi$
$409$	9.78196	0.483687	0.241843	+	0.970315i	$0.422248\pi$
$410$	−3.32513	−0.164216
$411$	7.27289	0.358745
$412$	4.85379	0.239129
$413$	0	0
$414$	8.40930	0.413294
$415$	34.3909	1.68818
$416$	9.92398	0.486563
$417$	−21.7039	−1.06284
$418$	−25.0001	−1.22280
$419$	17.0753	0.834182	0.417091	−	0.908865i	$-0.363050\pi$
$419$	17.0753	0.834182	0.417091	+	0.908865i	$0.363050\pi$
$420$	0	0
$421$	2.50171	0.121926	0.0609628	−	0.998140i	$-0.480583\pi$
$421$	2.50171	0.121926	0.0609628	+	0.998140i	$0.480583\pi$
$422$	−22.0529	−1.07352
$423$	34.8964	1.69672
$424$	−5.29936	−0.257360
$425$	15.1977	0.737196
$426$	38.8925	1.88435
$427$	0	0
$428$	−7.18463	−0.347282
$429$	38.0680	1.83794
$430$	3.42363	0.165102
$431$	6.17111	0.297252	0.148626	−	0.988893i	$-0.452515\pi$
$431$	6.17111	0.297252	0.148626	+	0.988893i	$0.452515\pi$
$432$	−9.39345	−0.451943
$433$	−8.89038	−0.427244	−0.213622	−	0.976916i	$-0.568526\pi$
$433$	−8.89038	−0.427244	−0.213622	+	0.976916i	$0.568526\pi$
$434$	0	0
$435$	−61.2799	−2.93815
$436$	4.71213	0.225670
$437$	−7.25525	−0.347066
$438$	−38.7735	−1.85267
$439$	−8.59031	−0.409993	−0.204997	−	0.978763i	$-0.565718\pi$
$439$	−8.59031	−0.409993	−0.204997	+	0.978763i	$0.565718\pi$
$440$	41.0619	1.95755
$441$	0	0
$442$	17.6110	0.837671
$443$	4.32990	0.205720	0.102860	−	0.994696i	$-0.467201\pi$
$443$	4.32990	0.205720	0.102860	+	0.994696i	$0.467201\pi$
$444$	−2.28100	−0.108252
$445$	−16.8006	−0.796424
$446$	−5.81445	−0.275322
$447$	−0.216907	−0.0102593
$448$	0	0
$449$	18.4438	0.870416	0.435208	−	0.900330i	$-0.356675\pi$
$449$	18.4438	0.870416	0.435208	+	0.900330i	$0.356675\pi$
$450$	15.6802	0.739172
$451$	4.71688	0.222109
$452$	1.01607	0.0477920
$453$	40.0616	1.88226
$454$	−19.3020	−0.905886
$455$	0	0
$456$	37.8621	1.77305
$457$	29.0862	1.36059	0.680297	−	0.732937i	$-0.261851\pi$
$457$	29.0862	1.36059	0.680297	+	0.732937i	$0.261851\pi$
$458$	2.62141	0.122490
$459$	19.9740	0.932307
$460$	2.81313	0.131163
$461$	−37.9708	−1.76848	−0.884238	−	0.467037i	$-0.845321\pi$
$461$	−37.9708	−1.76848	−0.884238	+	0.467037i	$0.845321\pi$
$462$	0	0
$463$	9.55999	0.444290	0.222145	−	0.975014i	$-0.428694\pi$
$463$	9.55999	0.444290	0.222145	+	0.975014i	$0.428694\pi$
$464$	−18.9125	−0.877991
$465$	−56.4533	−2.61796
$466$	14.8750	0.689073
$467$	−14.9165	−0.690253	−0.345127	−	0.938556i	$-0.612164\pi$
$467$	−14.9165	−0.690253	−0.345127	+	0.938556i	$0.612164\pi$
$468$	−8.12605	−0.375627
$469$	0	0
$470$	−26.1030	−1.20404
$471$	29.5483	1.36152
$472$	34.4238	1.58448
$473$	−4.85661	−0.223307
$474$	17.4854	0.803133
$475$	−13.5283	−0.620723
$476$	0	0
$477$	7.65418	0.350461
$478$	−6.61054	−0.302359
$479$	22.3841	1.02276	0.511378	−	0.859356i	$-0.329135\pi$
$479$	22.3841	1.02276	0.511378	+	0.859356i	$0.329135\pi$
$480$	−25.8954	−1.18196
$481$	4.00068	0.182415
$482$	27.3251	1.24463
$483$	0	0
$484$	−6.95229	−0.316013
$485$	−19.4313	−0.882330
$486$	−22.1687	−1.00559
$487$	−16.6500	−0.754485	−0.377242	−	0.926115i	$-0.623128\pi$
$487$	−16.6500	−0.754485	−0.377242	+	0.926115i	$0.623128\pi$
$488$	21.4349	0.970312
$489$	45.4389	2.05482
$490$	0	0
$491$	28.5654	1.28914	0.644570	−	0.764546i	$-0.277037\pi$
$491$	28.5654	1.28914	0.644570	+	0.764546i	$0.277037\pi$
$492$	−1.68638	−0.0760281
$493$	40.2151	1.81120
$494$	−15.6766	−0.705324
$495$	−59.3082	−2.66570
$496$	−17.4229	−0.782311
$497$	0	0
$498$	−39.0005	−1.74766
$499$	−16.2914	−0.729304	−0.364652	−	0.931144i	$-0.618812\pi$
$499$	−16.2914	−0.729304	−0.364652	+	0.931144i	$0.618812\pi$
$500$	−3.49527	−0.156313
$501$	20.1716	0.901200
$502$	−26.5808	−1.18636
$503$	1.49014	0.0664419	0.0332210	−	0.999448i	$-0.489423\pi$
$503$	1.49014	0.0664419	0.0332210	+	0.999448i	$0.489423\pi$
$504$	0	0
$505$	53.5030	2.38085
$506$	8.92309	0.396680
$507$	−11.6009	−0.515216
$508$	−2.59252	−0.115024
$509$	11.5080	0.510085	0.255042	−	0.966930i	$-0.417911\pi$
$509$	11.5080	0.510085	0.255042	+	0.966930i	$0.417911\pi$
$510$	−45.9538	−2.03487
$511$	0	0
$512$	−22.6537	−1.00116
$513$	−17.7800	−0.785007
$514$	6.43123	0.283670
$515$	22.2139	0.978862
$516$	1.73634	0.0764381
$517$	37.0285	1.62851
$518$	0	0
$519$	−39.1603	−1.71895
$520$	25.7483	1.12914
$521$	25.5384	1.11886	0.559428	−	0.828879i	$-0.311021\pi$
$521$	25.5384	1.11886	0.559428	+	0.828879i	$0.311021\pi$
$522$	41.4919	1.81605
$523$	−22.5171	−0.984604	−0.492302	−	0.870424i	$-0.663844\pi$
$523$	−22.5171	−0.984604	−0.492302	+	0.870424i	$0.663844\pi$
$524$	12.8521	0.561445
$525$	0	0
$526$	−12.6426	−0.551244
$527$	37.0476	1.61382
$528$	−30.6569	−1.33417
$529$	−20.4104	−0.887411
$530$	−5.72543	−0.248697
$531$	−49.7203	−2.15768
$532$	0	0
$533$	2.95777	0.128115
$534$	19.0525	0.824482
$535$	−32.8813	−1.42158
$536$	−1.99439	−0.0861444
$537$	6.46618	0.279036
$538$	−24.0881	−1.03851
$539$	0	0
$540$	6.89397	0.296669
$541$	29.4571	1.26646	0.633230	−	0.773964i	$-0.281729\pi$
$541$	29.4571	1.26646	0.633230	+	0.773964i	$0.281729\pi$
$542$	17.4264	0.748527
$543$	55.1217	2.36550
$544$	16.9939	0.728609
$545$	21.5656	0.923770
$546$	0	0
$547$	12.6629	0.541425	0.270713	−	0.962660i	$-0.412741\pi$
$547$	12.6629	0.541425	0.270713	+	0.962660i	$0.412741\pi$
$548$	−1.64734	−0.0703708
$549$	−30.9597	−1.32133
$550$	16.6382	0.709457
$551$	−35.7978	−1.52504
$552$	−13.5138	−0.575185
$553$	0	0
$554$	22.8236	0.969681
$555$	−10.4393	−0.443123
$556$	4.91602	0.208486
$557$	17.1721	0.727605	0.363802	−	0.931476i	$-0.381478\pi$
$557$	17.1721	0.727605	0.363802	+	0.931476i	$0.381478\pi$
$558$	38.2239	1.61815
$559$	−3.04539	−0.128806
$560$	0	0
$561$	65.1880	2.75224
$562$	11.1876	0.471919
$563$	9.82712	0.414164	0.207082	−	0.978324i	$-0.433603\pi$
$563$	9.82712	0.414164	0.207082	+	0.978324i	$0.433603\pi$
$564$	−13.2385	−0.557441
$565$	4.65017	0.195634
$566$	16.8141	0.706751
$567$	0	0
$568$	−37.3165	−1.56577
$569$	6.30004	0.264111	0.132056	−	0.991242i	$-0.457842\pi$
$569$	6.30004	0.264111	0.132056	+	0.991242i	$0.457842\pi$
$570$	40.9062	1.71337
$571$	−18.6795	−0.781714	−0.390857	−	0.920451i	$-0.627821\pi$
$571$	−18.6795	−0.781714	−0.390857	+	0.920451i	$0.627821\pi$
$572$	−8.62254	−0.360526
$573$	−44.3843	−1.85418
$574$	0	0
$575$	4.82856	0.201365
$576$	38.7104	1.61293
$577$	6.54037	0.272279	0.136140	−	0.990690i	$-0.456530\pi$
$577$	6.54037	0.272279	0.136140	+	0.990690i	$0.456530\pi$
$578$	10.1726	0.423126
$579$	−67.5874	−2.80884
$580$	13.8801	0.576341
$581$	0	0
$582$	22.0358	0.913415
$583$	8.12184	0.336372
$584$	37.2024	1.53945
$585$	−37.1898	−1.53761
$586$	−10.6858	−0.441427
$587$	−6.12081	−0.252633	−0.126316	−	0.991990i	$-0.540315\pi$
$587$	−6.12081	−0.252633	−0.126316	+	0.991990i	$0.540315\pi$
$588$	0	0
$589$	−32.9782	−1.35884
$590$	37.1914	1.53115
$591$	−51.3288	−2.11138
$592$	−3.22182	−0.132416
$593$	−43.9787	−1.80599	−0.902995	−	0.429651i	$-0.858637\pi$
$593$	−43.9787	−1.80599	−0.902995	+	0.429651i	$0.858637\pi$
$594$	21.8673	0.897227
$595$	0	0
$596$	0.0491303	0.00201245
$597$	12.7316	0.521071
$598$	5.59532	0.228810
$599$	−45.0087	−1.83901	−0.919503	−	0.393082i	$-0.871409\pi$
$599$	−45.0087	−1.83901	−0.919503	+	0.393082i	$0.871409\pi$
$600$	−25.1982	−1.02871
$601$	−16.6713	−0.680038	−0.340019	−	0.940419i	$-0.610433\pi$
$601$	−16.6713	−0.680038	−0.340019	+	0.940419i	$0.610433\pi$
$602$	0	0
$603$	2.88061	0.117308
$604$	−9.07411	−0.369220
$605$	−31.8180	−1.29359
$606$	−60.6744	−2.46473
$607$	−20.0189	−0.812543	−0.406272	−	0.913752i	$-0.633171\pi$
$607$	−20.0189	−0.812543	−0.406272	+	0.913752i	$0.633171\pi$
$608$	−15.1273	−0.613493
$609$	0	0
$610$	23.1582	0.937650
$611$	23.2191	0.939346
$612$	−13.9151	−0.562486
$613$	24.0654	0.971992	0.485996	−	0.873961i	$-0.338457\pi$
$613$	24.0654	0.971992	0.485996	+	0.873961i	$0.338457\pi$
$614$	29.6443	1.19635
$615$	−7.71794	−0.311217
$616$	0	0
$617$	−34.0652	−1.37141	−0.685707	−	0.727878i	$-0.740507\pi$
$617$	−34.0652	−1.37141	−0.685707	+	0.727878i	$0.740507\pi$
$618$	−25.1914	−1.01335
$619$	−6.76477	−0.271899	−0.135950	−	0.990716i	$-0.543409\pi$
$619$	−6.76477	−0.271899	−0.135950	+	0.990716i	$0.543409\pi$
$620$	12.7869	0.513533
$621$	6.34608	0.254659
$622$	−19.8861	−0.797358
$623$	0	0
$624$	−19.2237	−0.769564
$625$	−30.9994	−1.23998
$626$	−1.02949	−0.0411465
$627$	−58.0277	−2.31740
$628$	−6.69281	−0.267072
$629$	6.85081	0.273160
$630$	0	0
$631$	−5.90673	−0.235143	−0.117572	−	0.993064i	$-0.537511\pi$
$631$	−5.90673	−0.235143	−0.117572	+	0.993064i	$0.537511\pi$
$632$	−16.7769	−0.667350
$633$	−51.1869	−2.03450
$634$	−15.1965	−0.603532
$635$	−11.8650	−0.470847
$636$	−2.90373	−0.115140
$637$	0	0
$638$	44.0270	1.74305
$639$	53.8985	2.13219
$640$	−9.97517	−0.394303
$641$	−6.29419	−0.248605	−0.124303	−	0.992244i	$-0.539669\pi$
$641$	−6.29419	−0.248605	−0.124303	+	0.992244i	$0.539669\pi$
$642$	37.2887	1.47167
$643$	−6.27693	−0.247538	−0.123769	−	0.992311i	$-0.539498\pi$
$643$	−6.27693	−0.247538	−0.123769	+	0.992311i	$0.539498\pi$
$644$	0	0
$645$	7.94657	0.312896
$646$	−26.8448	−1.05619
$647$	−8.45932	−0.332570	−0.166285	−	0.986078i	$-0.553177\pi$
$647$	−8.45932	−0.332570	−0.166285	+	0.986078i	$0.553177\pi$
$648$	7.92603	0.311364
$649$	−52.7581	−2.07094
$650$	10.4332	0.409223
$651$	0	0
$652$	−10.2921	−0.403069
$653$	−20.7360	−0.811462	−0.405731	−	0.913993i	$-0.632983\pi$
$653$	−20.7360	−0.811462	−0.405731	+	0.913993i	$0.632983\pi$
$654$	−24.4562	−0.956314
$655$	58.8190	2.29825
$656$	−2.38195	−0.0929995
$657$	−53.7336	−2.09635
$658$	0	0
$659$	−29.2206	−1.13827	−0.569137	−	0.822243i	$-0.692723\pi$
$659$	−29.2206	−1.13827	−0.569137	+	0.822243i	$0.692723\pi$
$660$	22.4995	0.875790
$661$	16.2903	0.633621	0.316810	−	0.948489i	$-0.397388\pi$
$661$	16.2903	0.633621	0.316810	+	0.948489i	$0.397388\pi$
$662$	−26.2198	−1.01906
$663$	40.8768	1.58752
$664$	37.4202	1.45219
$665$	0	0
$666$	7.06833	0.273892
$667$	12.7770	0.494728
$668$	−4.56894	−0.176778
$669$	−13.4959	−0.521781
$670$	−2.15473	−0.0832447
$671$	−32.8512	−1.26821
$672$	0	0
$673$	−33.1283	−1.27700	−0.638502	−	0.769621i	$-0.720445\pi$
$673$	−33.1283	−1.27700	−0.638502	+	0.769621i	$0.720445\pi$
$674$	−16.8534	−0.649169
$675$	11.8331	0.455455
$676$	2.62766	0.101064
$677$	43.2111	1.66074	0.830369	−	0.557215i	$-0.188130\pi$
$677$	43.2111	1.66074	0.830369	+	0.557215i	$0.188130\pi$
$678$	−5.27347	−0.202526
$679$	0	0
$680$	44.0917	1.69084
$681$	−44.8016	−1.71680
$682$	40.5593	1.55310
$683$	−37.8993	−1.45018	−0.725088	−	0.688656i	$-0.758201\pi$
$683$	−37.8993	−1.45018	−0.725088	+	0.688656i	$0.758201\pi$
$684$	12.3867	0.473617
$685$	−7.53923	−0.288059
$686$	0	0
$687$	6.08453	0.232139
$688$	2.45251	0.0935011
$689$	5.09289	0.194024
$690$	−14.6003	−0.555824
$691$	30.9744	1.17832	0.589160	−	0.808016i	$-0.299459\pi$
$691$	30.9744	1.17832	0.589160	+	0.808016i	$0.299459\pi$
$692$	8.86996	0.337185
$693$	0	0
$694$	−39.3392	−1.49330
$695$	22.4987	0.853425
$696$	−66.6778	−2.52742
$697$	5.06492	0.191847
$698$	8.59091	0.325171
$699$	34.5263	1.30591
$700$	0	0
$701$	−18.2468	−0.689173	−0.344586	−	0.938755i	$-0.611981\pi$
$701$	−18.2468	−0.689173	−0.344586	+	0.938755i	$0.611981\pi$
$702$	13.7121	0.517531
$703$	−6.09831	−0.230002
$704$	41.0755	1.54809
$705$	−60.5875	−2.28186
$706$	23.7829	0.895080
$707$	0	0
$708$	18.8621	0.708883
$709$	−44.8300	−1.68363	−0.841814	−	0.539768i	$-0.818512\pi$
$709$	−44.8300	−1.68363	−0.841814	+	0.539768i	$0.818512\pi$
$710$	−40.3168	−1.51306
$711$	24.2319	0.908767
$712$	−18.2805	−0.685090
$713$	11.7706	0.440814
$714$	0	0
$715$	−39.4621	−1.47580
$716$	−1.46462	−0.0547352
$717$	−15.3437	−0.573020
$718$	41.5988	1.55246
$719$	22.4791	0.838329	0.419165	−	0.907910i	$-0.362323\pi$
$719$	22.4791	0.838329	0.419165	+	0.907910i	$0.362323\pi$
$720$	29.9497	1.11616
$721$	0	0
$722$	1.56032	0.0580691
$723$	63.4242	2.35877
$724$	−12.4853	−0.464012
$725$	23.8244	0.884815
$726$	36.0828	1.33916
$727$	−14.9987	−0.556271	−0.278135	−	0.960542i	$-0.589716\pi$
$727$	−14.9987	−0.556271	−0.278135	+	0.960542i	$0.589716\pi$
$728$	0	0
$729$	−43.7296	−1.61961
$730$	40.1935	1.48763
$731$	−5.21496	−0.192882
$732$	11.7450	0.434108
$733$	7.35860	0.271796	0.135898	−	0.990723i	$-0.456608\pi$
$733$	7.35860	0.271796	0.135898	+	0.990723i	$0.456608\pi$
$734$	−18.6564	−0.688620
$735$	0	0
$736$	5.39926	0.199019
$737$	3.05661	0.112592
$738$	5.22573	0.192362
$739$	−1.92445	−0.0707921	−0.0353960	−	0.999373i	$-0.511269\pi$
$739$	−1.92445	−0.0707921	−0.0353960	+	0.999373i	$0.511269\pi$
$740$	2.36454	0.0869221
$741$	−36.3869	−1.33670
$742$	0	0
$743$	−7.15152	−0.262364	−0.131182	−	0.991358i	$-0.541877\pi$
$743$	−7.15152	−0.262364	−0.131182	+	0.991358i	$0.541877\pi$
$744$	−61.4260	−2.25199
$745$	0.224850	0.00823788
$746$	−5.81317	−0.212835
$747$	−54.0482	−1.97752
$748$	−14.7653	−0.539874
$749$	0	0
$750$	18.1407	0.662404
$751$	31.3196	1.14287	0.571434	−	0.820648i	$-0.306387\pi$
$751$	31.3196	1.14287	0.571434	+	0.820648i	$0.306387\pi$
$752$	−18.6988	−0.681876
$753$	−61.6965	−2.24835
$754$	27.6076	1.00541
$755$	−41.5288	−1.51139
$756$	0	0
$757$	28.0634	1.01998	0.509990	−	0.860180i	$-0.329649\pi$
$757$	28.0634	1.01998	0.509990	+	0.860180i	$0.329649\pi$
$758$	29.8625	1.08465
$759$	20.7113	0.751774
$760$	−39.2486	−1.42370
$761$	14.4551	0.523996	0.261998	−	0.965068i	$-0.415619\pi$
$761$	14.4551	0.523996	0.261998	+	0.965068i	$0.415619\pi$
$762$	13.4553	0.487435
$763$	0	0
$764$	10.0532	0.363713
$765$	−63.6843	−2.30251
$766$	−10.3417	−0.373662
$767$	−33.0825	−1.19454
$768$	−36.2102	−1.30662
$769$	−10.4927	−0.378377	−0.189189	−	0.981941i	$-0.560586\pi$
$769$	−10.4927	−0.378377	−0.189189	+	0.981941i	$0.560586\pi$
$770$	0	0
$771$	14.9275	0.537601
$772$	15.3088	0.550976
$773$	8.37676	0.301291	0.150646	−	0.988588i	$-0.451865\pi$
$773$	8.37676	0.301291	0.150646	+	0.988588i	$0.451865\pi$
$774$	−5.38053	−0.193399
$775$	21.9479	0.788391
$776$	−21.1429	−0.758987
$777$	0	0
$778$	17.6237	0.631840
$779$	−4.50858	−0.161537
$780$	14.1085	0.505166
$781$	57.1916	2.04648
$782$	9.58149	0.342633
$783$	31.3119	1.11900
$784$	0	0
$785$	−30.6304	−1.09325
$786$	−66.7030	−2.37922
$787$	32.1245	1.14512	0.572558	−	0.819864i	$-0.305951\pi$
$787$	32.1245	1.14512	0.572558	+	0.819864i	$0.305951\pi$
$788$	11.6262	0.414165
$789$	−29.3447	−1.04470
$790$	−18.1258	−0.644887
$791$	0	0
$792$	−64.5324	−2.29306
$793$	−20.5997	−0.731518
$794$	1.53061	0.0543194
$795$	−13.2893	−0.471322
$796$	−2.88377	−0.102212
$797$	36.4800	1.29219	0.646094	−	0.763258i	$-0.276401\pi$
$797$	36.4800	1.29219	0.646094	+	0.763258i	$0.276401\pi$
$798$	0	0
$799$	39.7607	1.40663
$800$	10.0676	0.355944
$801$	26.4036	0.932924
$802$	−26.9638	−0.952125
$803$	−57.0167	−2.01207
$804$	−1.09280	−0.0385402
$805$	0	0
$806$	25.4331	0.895844
$807$	−55.9107	−1.96815
$808$	58.2159	2.04803
$809$	41.9241	1.47397	0.736987	−	0.675907i	$-0.236248\pi$
$809$	41.9241	1.47397	0.736987	+	0.675907i	$0.236248\pi$
$810$	8.56328	0.300883
$811$	4.59446	0.161333	0.0806666	−	0.996741i	$-0.474295\pi$
$811$	4.59446	0.161333	0.0806666	+	0.996741i	$0.474295\pi$
$812$	0	0
$813$	40.4482	1.41858
$814$	7.50019	0.262881
$815$	−47.1029	−1.64994
$816$	−32.9189	−1.15239
$817$	4.64214	0.162408
$818$	11.4994	0.402066
$819$	0	0
$820$	1.74814	0.0610478
$821$	19.6723	0.686567	0.343284	−	0.939232i	$-0.388461\pi$
$821$	19.6723	0.686567	0.343284	+	0.939232i	$0.388461\pi$
$822$	8.54978	0.298208
$823$	10.9571	0.381939	0.190970	−	0.981596i	$-0.438837\pi$
$823$	10.9571	0.381939	0.190970	+	0.981596i	$0.438837\pi$
$824$	24.1707	0.842025
$825$	38.6189	1.34454
$826$	0	0
$827$	−16.3400	−0.568197	−0.284099	−	0.958795i	$-0.591694\pi$
$827$	−16.3400	−0.568197	−0.284099	+	0.958795i	$0.591694\pi$
$828$	−4.42108	−0.153643
$829$	−23.6076	−0.819927	−0.409964	−	0.912102i	$-0.634459\pi$
$829$	−23.6076	−0.819927	−0.409964	+	0.912102i	$0.634459\pi$
$830$	40.4288	1.40330
$831$	52.9757	1.83771
$832$	25.7568	0.892957
$833$	0	0
$834$	−25.5144	−0.883492
$835$	−20.9103	−0.723631
$836$	13.1435	0.454577
$837$	28.8457	0.997052
$838$	20.0731	0.693415
$839$	−12.4470	−0.429719	−0.214860	−	0.976645i	$-0.568929\pi$
$839$	−12.4470	−0.429719	−0.214860	+	0.976645i	$0.568929\pi$
$840$	0	0
$841$	34.0425	1.17388
$842$	2.94093	0.101351
$843$	25.9674	0.894364
$844$	11.5940	0.399083
$845$	12.0258	0.413699
$846$	41.0231	1.41040
$847$	0	0
$848$	−4.10140	−0.140843
$849$	39.0272	1.33941
$850$	17.8659	0.612796
$851$	2.17662	0.0746135
$852$	−20.4472	−0.700510
$853$	−51.3305	−1.75752	−0.878761	−	0.477262i	$-0.841629\pi$
$853$	−51.3305	−1.75752	−0.878761	+	0.477262i	$0.841629\pi$
$854$	0	0
$855$	56.6891	1.93873
$856$	−35.7777	−1.22286
$857$	11.8437	0.404572	0.202286	−	0.979326i	$-0.435163\pi$
$857$	11.8437	0.404572	0.202286	+	0.979326i	$0.435163\pi$
$858$	44.7515	1.52779
$859$	30.3860	1.03676	0.518379	−	0.855151i	$-0.326536\pi$
$859$	30.3860	1.03676	0.518379	+	0.855151i	$0.326536\pi$
$860$	−1.79993	−0.0613770
$861$	0	0
$862$	7.25456	0.247091
$863$	3.30286	0.112431	0.0562154	−	0.998419i	$-0.482097\pi$
$863$	3.30286	0.112431	0.0562154	+	0.998419i	$0.482097\pi$
$864$	13.2317	0.450150
$865$	40.5944	1.38025
$866$	−10.4512	−0.355148
$867$	23.6117	0.801894
$868$	0	0
$869$	25.7124	0.872234
$870$	−72.0387	−2.44234
$871$	1.91668	0.0649442
$872$	23.4653	0.794634
$873$	30.5380	1.03355
$874$	−8.52904	−0.288499
$875$	0	0
$876$	20.3847	0.688734
$877$	−6.28757	−0.212316	−0.106158	−	0.994349i	$-0.533855\pi$
$877$	−6.28757	−0.212316	−0.106158	+	0.994349i	$0.533855\pi$
$878$	−10.0985	−0.340808
$879$	−24.8028	−0.836577
$880$	31.7796	1.07129
$881$	−26.0595	−0.877967	−0.438983	−	0.898495i	$-0.644661\pi$
$881$	−26.0595	−0.877967	−0.438983	+	0.898495i	$0.644661\pi$
$882$	0	0
$883$	52.5138	1.76723	0.883615	−	0.468214i	$-0.155102\pi$
$883$	52.5138	1.76723	0.883615	+	0.468214i	$0.155102\pi$
$884$	−9.25876	−0.311406
$885$	86.3248	2.90178
$886$	5.09009	0.171005
$887$	18.6179	0.625128	0.312564	−	0.949897i	$-0.398812\pi$
$887$	18.6179	0.625128	0.312564	+	0.949897i	$0.398812\pi$
$888$	−11.3588	−0.381178
$889$	0	0
$890$	−19.7502	−0.662029
$891$	−12.1475	−0.406956
$892$	3.05687	0.102352
$893$	−35.3933	−1.18439
$894$	−0.254989	−0.00852810
$895$	−6.70298	−0.224056
$896$	0	0
$897$	12.9873	0.433632
$898$	21.6819	0.723535
$899$	58.0770	1.93698
$900$	−8.24366	−0.274789
$901$	8.72112	0.290542
$902$	5.54501	0.184629
$903$	0	0
$904$	5.05978	0.168286
$905$	−57.1403	−1.89941
$906$	47.0952	1.56463
$907$	−15.8713	−0.526998	−0.263499	−	0.964660i	$-0.584877\pi$
$907$	−15.8713	−0.526998	−0.263499	+	0.964660i	$0.584877\pi$
$908$	10.1477	0.336765
$909$	−84.0846	−2.78891
$910$	0	0
$911$	−28.5926	−0.947315	−0.473657	−	0.880709i	$-0.657067\pi$
$911$	−28.5926	−0.947315	−0.473657	+	0.880709i	$0.657067\pi$
$912$	29.3030	0.970321
$913$	−57.3505	−1.89802
$914$	34.1928	1.13100
$915$	53.7525	1.77700
$916$	−1.37817	−0.0455360
$917$	0	0
$918$	23.4808	0.774982
$919$	−55.8471	−1.84222	−0.921112	−	0.389297i	$-0.872718\pi$
$919$	−55.8471	−1.84222	−0.921112	+	0.389297i	$0.872718\pi$
$920$	14.0087	0.461853
$921$	68.8073	2.26728
$922$	−44.6372	−1.47005
$923$	35.8626	1.18043
$924$	0	0
$925$	4.05858	0.133445
$926$	11.2384	0.369317
$927$	−34.9111	−1.14663
$928$	26.6402	0.874509
$929$	2.24329	0.0735999	0.0368000	−	0.999323i	$-0.488284\pi$
$929$	2.24329	0.0735999	0.0368000	+	0.999323i	$0.488284\pi$
$930$	−66.3646	−2.17618
$931$	0	0
$932$	−7.82035	−0.256164
$933$	−46.1574	−1.51113
$934$	−17.5354	−0.573775
$935$	−67.5753	−2.20995
$936$	−40.4657	−1.32266
$937$	−15.8394	−0.517450	−0.258725	−	0.965951i	$-0.583302\pi$
$937$	−15.8394	−0.517450	−0.258725	+	0.965951i	$0.583302\pi$
$938$	0	0
$939$	−2.38953	−0.0779795
$940$	13.7233	0.447605
$941$	−21.0187	−0.685189	−0.342594	−	0.939483i	$-0.611306\pi$
$941$	−21.0187	−0.685189	−0.342594	+	0.939483i	$0.611306\pi$
$942$	34.7361	1.13176
$943$	1.60921	0.0524031
$944$	26.6420	0.867124
$945$	0	0
$946$	−5.70928	−0.185625
$947$	29.0720	0.944714	0.472357	−	0.881407i	$-0.343403\pi$
$947$	29.0720	0.944714	0.472357	+	0.881407i	$0.343403\pi$
$948$	−9.19274	−0.298566
$949$	−35.7529	−1.16059
$950$	−15.9035	−0.515977
$951$	−35.2726	−1.14379
$952$	0	0
$953$	56.7231	1.83744	0.918720	−	0.394909i	$-0.129224\pi$
$953$	56.7231	1.83744	0.918720	+	0.394909i	$0.129224\pi$
$954$	8.99802	0.291322
$955$	46.0097	1.48884
$956$	3.47540	0.112403
$957$	102.191	3.30336
$958$	26.3140	0.850168
$959$	0	0
$960$	−67.2093	−2.16917
$961$	22.5027	0.725893
$962$	4.70307	0.151633
$963$	51.6758	1.66523
$964$	−14.3658	−0.462692
$965$	70.0625	2.25539
$966$	0	0
$967$	46.1274	1.48336	0.741678	−	0.670756i	$-0.234030\pi$
$967$	46.1274	1.48336	0.741678	+	0.670756i	$0.234030\pi$
$968$	−34.6207	−1.11275
$969$	−62.3093	−2.00166
$970$	−22.8428	−0.733439
$971$	−15.3334	−0.492073	−0.246036	−	0.969261i	$-0.579128\pi$
$971$	−15.3334	−0.492073	−0.246036	+	0.969261i	$0.579128\pi$
$972$	11.6549	0.373830
$973$	0	0
$974$	−19.5732	−0.627167
$975$	24.2164	0.775546
$976$	16.5894	0.531012
$977$	9.77789	0.312822	0.156411	−	0.987692i	$-0.450008\pi$
$977$	9.77789	0.312822	0.156411	+	0.987692i	$0.450008\pi$
$978$	53.4165	1.70807
$979$	28.0168	0.895420
$980$	0	0
$981$	−33.8922	−1.08210
$982$	33.5806	1.07160
$983$	7.31956	0.233458	0.116729	−	0.993164i	$-0.462759\pi$
$983$	7.31956	0.233458	0.116729	+	0.993164i	$0.462759\pi$
$984$	−8.39778	−0.267711
$985$	53.2085	1.69536
$986$	47.2756	1.50556
$987$	0	0
$988$	8.24176	0.262205
$989$	−1.65688	−0.0526857
$990$	−69.7208	−2.21587
$991$	−26.1469	−0.830585	−0.415292	−	0.909688i	$-0.636321\pi$
$991$	−26.1469	−0.830585	−0.415292	+	0.909688i	$0.636321\pi$
$992$	24.5420	0.779208
$993$	−60.8586	−1.93129
$994$	0	0
$995$	−13.1979	−0.418401
$996$	20.5040	0.649695
$997$	−6.05871	−0.191881	−0.0959407	−	0.995387i	$-0.530586\pi$
$997$	−6.05871	−0.191881	−0.0959407	+	0.995387i	$0.530586\pi$
$998$	−19.1517	−0.606236
$999$	5.33411	0.168764

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.s.1.11		17
7.2	even	3		287.2.e.d.165.7	✓	34
7.4	even	3		287.2.e.d.247.7	yes	34
7.6	odd	2		2009.2.a.r.1.11		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.7	✓	34	7.2	even	3
287.2.e.d.247.7	yes	34	7.4	even	3
2009.2.a.r.1.11		17	7.6	odd	2
2009.2.a.s.1.11		17	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)

\(f(q)\)	\(=\)	\(q+1.17557 q^{2} +2.72860 q^{3} -0.618039 q^{4} -2.82853 q^{5} +3.20766 q^{6} -3.07768 q^{8} +4.44528 q^{9} +O(q^{10})\)	\(q+1.17557 q^{2} +2.72860 q^{3} -0.618039 q^{4} -2.82853 q^{5} +3.20766 q^{6} -3.07768 q^{8} +4.44528 q^{9} -3.32513 q^{10} +4.71688 q^{11} -1.68638 q^{12} +2.95777 q^{13} -7.71794 q^{15} -2.38195 q^{16} +5.06492 q^{17} +5.22573 q^{18} -4.50858 q^{19} +1.74814 q^{20} +5.54501 q^{22} +1.60921 q^{23} -8.39778 q^{24} +3.00058 q^{25} +3.47706 q^{26} +3.94360 q^{27} +7.93993 q^{29} -9.07296 q^{30} +7.31455 q^{31} +3.35522 q^{32} +12.8705 q^{33} +5.95416 q^{34} -2.74736 q^{36} +1.35260 q^{37} -5.30014 q^{38} +8.07058 q^{39} +8.70532 q^{40} +1.00000 q^{41} -1.02962 q^{43} -2.91522 q^{44} -12.5736 q^{45} +1.89174 q^{46} +7.85022 q^{47} -6.49940 q^{48} +3.52738 q^{50} +13.8202 q^{51} -1.82802 q^{52} +1.72187 q^{53} +4.63597 q^{54} -13.3418 q^{55} -12.3021 q^{57} +9.33393 q^{58} -11.1850 q^{59} +4.76999 q^{60} -6.96462 q^{61} +8.59876 q^{62} +8.70819 q^{64} -8.36614 q^{65} +15.1301 q^{66} +0.648015 q^{67} -3.13032 q^{68} +4.39090 q^{69} +12.1249 q^{71} -13.6812 q^{72} -12.0878 q^{73} +1.59007 q^{74} +8.18739 q^{75} +2.78648 q^{76} +9.48752 q^{78} +5.45115 q^{79} +6.73741 q^{80} -2.57532 q^{81} +1.17557 q^{82} -12.1586 q^{83} -14.3263 q^{85} -1.21039 q^{86} +21.6649 q^{87} -14.5171 q^{88} +5.93969 q^{89} -14.7811 q^{90} -0.994555 q^{92} +19.9585 q^{93} +9.22847 q^{94} +12.7526 q^{95} +9.15508 q^{96} +6.86976 q^{97} +20.9679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9	\( 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9} - 2 q^{10} + 15 q^{11} + 4 q^{12} - 5 q^{13} + 24 q^{15} + 33 q^{16} + 4 q^{17} + 10 q^{18} + 5 q^{19} - 26 q^{20} + 16 q^{22} + 12 q^{23} + 16 q^{24} + 24 q^{25} + 31 q^{26} - 11 q^{27} + 14 q^{29} - 33 q^{30} - 3 q^{31} + 16 q^{32} + 4 q^{33} - 24 q^{34} + 57 q^{36} + 24 q^{37} + 45 q^{39} + 36 q^{40} + 17 q^{41} + 14 q^{43} - 9 q^{44} - 21 q^{45} + 44 q^{46} + 19 q^{47} - 60 q^{48} - 4 q^{50} + 2 q^{51} - 25 q^{52} + 4 q^{53} + 68 q^{54} + 9 q^{55} - 12 q^{57} - q^{58} - 27 q^{59} + 66 q^{60} - q^{61} - 23 q^{62} + 75 q^{64} + 22 q^{65} - 16 q^{66} + 49 q^{67} + 45 q^{68} + 12 q^{69} + 40 q^{71} - 23 q^{72} - 14 q^{73} + 33 q^{74} + 27 q^{75} - 9 q^{76} - 12 q^{78} + 61 q^{79} - 82 q^{80} + 53 q^{81} + 3 q^{82} - 18 q^{83} - 13 q^{85} - 4 q^{86} - 17 q^{87} + 74 q^{88} + 18 q^{89} - 20 q^{90} + 28 q^{92} - 36 q^{93} - 5 q^{94} + 20 q^{95} + 148 q^{96} + 26 q^{97} + 38 q^{99}+O(q^{100}) \) 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9 - 2 * q^10 + 15 * q^11 + 4 * q^12 - 5 * q^13 + 24 * q^15 + 33 * q^16 + 4 * q^17 + 10 * q^18 + 5 * q^19 - 26 * q^20 + 16 * q^22 + 12 * q^23 + 16 * q^24 + 24 * q^25 + 31 * q^26 - 11 * q^27 + 14 * q^29 - 33 * q^30 - 3 * q^31 + 16 * q^32 + 4 * q^33 - 24 * q^34 + 57 * q^36 + 24 * q^37 + 45 * q^39 + 36 * q^40 + 17 * q^41 + 14 * q^43 - 9 * q^44 - 21 * q^45 + 44 * q^46 + 19 * q^47 - 60 * q^48 - 4 * q^50 + 2 * q^51 - 25 * q^52 + 4 * q^53 + 68 * q^54 + 9 * q^55 - 12 * q^57 - q^58 - 27 * q^59 + 66 * q^60 - q^61 - 23 * q^62 + 75 * q^64 + 22 * q^65 - 16 * q^66 + 49 * q^67 + 45 * q^68 + 12 * q^69 + 40 * q^71 - 23 * q^72 - 14 * q^73 + 33 * q^74 + 27 * q^75 - 9 * q^76 - 12 * q^78 + 61 * q^79 - 82 * q^80 + 53 * q^81 + 3 * q^82 - 18 * q^83 - 13 * q^85 - 4 * q^86 - 17 * q^87 + 74 * q^88 + 18 * q^89 - 20 * q^90 + 28 * q^92 - 36 * q^93 - 5 * q^94 + 20 * q^95 + 148 * q^96 + 26 * q^97 + 38 * q^99

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