LMFDB - Embedded newform 2009.2.a.r.1.3

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			1.3
Root			$-1.98553$ 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)

$f(q)$	$=$	$q-1.98553 q^{2} -2.88783 q^{3} +1.94233 q^{4} -3.91440 q^{5} +5.73388 q^{6} +0.114499 q^{8} +5.33958 q^{9} +O(q^{10})$	\(q-1.98553 q^{2} -2.88783 q^{3} +1.94233 q^{4} -3.91440 q^{5} +5.73388 q^{6} +0.114499 q^{8} +5.33958 q^{9} +7.77216 q^{10} +3.19605 q^{11} -5.60914 q^{12} +4.29241 q^{13} +11.3041 q^{15} -4.11201 q^{16} -2.11427 q^{17} -10.6019 q^{18} +6.53696 q^{19} -7.60307 q^{20} -6.34585 q^{22} +0.914272 q^{23} -0.330653 q^{24} +10.3225 q^{25} -8.52272 q^{26} -6.75632 q^{27} +5.76197 q^{29} -22.4447 q^{30} +1.96648 q^{31} +7.93552 q^{32} -9.22965 q^{33} +4.19794 q^{34} +10.3712 q^{36} -0.535849 q^{37} -12.9793 q^{38} -12.3958 q^{39} -0.448193 q^{40} -1.00000 q^{41} -4.90872 q^{43} +6.20779 q^{44} -20.9013 q^{45} -1.81532 q^{46} -5.59786 q^{47} +11.8748 q^{48} -20.4957 q^{50} +6.10565 q^{51} +8.33730 q^{52} +2.37296 q^{53} +13.4149 q^{54} -12.5106 q^{55} -18.8777 q^{57} -11.4406 q^{58} -6.23062 q^{59} +21.9564 q^{60} +2.19304 q^{61} -3.90450 q^{62} -7.53221 q^{64} -16.8022 q^{65} +18.3258 q^{66} +11.2466 q^{67} -4.10661 q^{68} -2.64026 q^{69} +3.34949 q^{71} +0.611374 q^{72} +1.76606 q^{73} +1.06394 q^{74} -29.8097 q^{75} +12.6970 q^{76} +24.6122 q^{78} +11.4766 q^{79} +16.0960 q^{80} +3.49239 q^{81} +1.98553 q^{82} -16.3013 q^{83} +8.27609 q^{85} +9.74642 q^{86} -16.6396 q^{87} +0.365943 q^{88} +11.1139 q^{89} +41.5001 q^{90} +1.77582 q^{92} -5.67886 q^{93} +11.1147 q^{94} -25.5883 q^{95} -22.9165 q^{96} +14.5110 q^{97} +17.0655 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.98553	−1.40398	−0.701991	−	0.712186i	$-0.747705\pi$
$2$	−1.98553	−1.40398	−0.701991	+	0.712186i	$0.747705\pi$
$3$	−2.88783	−1.66729	−0.833646	−	0.552300i	$-0.813750\pi$
$3$	−2.88783	−1.66729	−0.833646	+	0.552300i	$0.813750\pi$
$4$	1.94233	0.971167
$5$	−3.91440	−1.75057	−0.875286	−	0.483605i	$-0.839327\pi$
$5$	−3.91440	−1.75057	−0.875286	+	0.483605i	$0.839327\pi$
$6$	5.73388	2.34085
$7$	0	0
$7$	0	0
$8$	0.114499	0.0404813
$9$	5.33958	1.77986
$10$	7.77216	2.45777
$11$	3.19605	0.963644	0.481822	−	0.876269i	$-0.339975\pi$
$11$	3.19605	0.963644	0.481822	+	0.876269i	$0.339975\pi$
$12$	−5.60914	−1.61922
$13$	4.29241	1.19050	0.595251	−	0.803540i	$-0.297053\pi$
$13$	4.29241	1.19050	0.595251	+	0.803540i	$0.297053\pi$
$14$	0	0
$15$	11.3041	2.91872
$16$	−4.11201	−1.02800
$17$	−2.11427	−0.512785	−0.256392	−	0.966573i	$-0.582534\pi$
$17$	−2.11427	−0.512785	−0.256392	+	0.966573i	$0.582534\pi$
$18$	−10.6019	−2.49889
$19$	6.53696	1.49968	0.749841	−	0.661618i	$-0.230130\pi$
$19$	6.53696	1.49968	0.749841	+	0.661618i	$0.230130\pi$
$20$	−7.60307	−1.70010
$21$	0	0
$22$	−6.34585	−1.35294
$23$	0.914272	0.190639	0.0953194	−	0.995447i	$-0.469613\pi$
$23$	0.914272	0.190639	0.0953194	+	0.995447i	$0.469613\pi$
$24$	−0.330653	−0.0674942
$25$	10.3225	2.06451
$26$	−8.52272	−1.67144
$27$	−6.75632	−1.30025
$28$	0	0
$29$	5.76197	1.06997	0.534986	−	0.844861i	$-0.320317\pi$
$29$	5.76197	1.06997	0.534986	+	0.844861i	$0.320317\pi$
$30$	−22.4447	−4.09782
$31$	1.96648	0.353190	0.176595	−	0.984284i	$-0.443492\pi$
$31$	1.96648	0.353190	0.176595	+	0.984284i	$0.443492\pi$
$32$	7.93552	1.40282
$33$	−9.22965	−1.60668
$34$	4.19794	0.719941
$35$	0	0
$36$	10.3712	1.72854
$37$	−0.535849	−0.0880930	−0.0440465	−	0.999029i	$-0.514025\pi$
$37$	−0.535849	−0.0880930	−0.0440465	+	0.999029i	$0.514025\pi$
$38$	−12.9793	−2.10553
$39$	−12.3958	−1.98491
$40$	−0.448193	−0.0708655
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−4.90872	−0.748573	−0.374286	−	0.927313i	$-0.622112\pi$
$43$	−4.90872	−0.748573	−0.374286	+	0.927313i	$0.622112\pi$
$44$	6.20779	0.935859
$45$	−20.9013	−3.11578
$46$	−1.81532	−0.267654
$47$	−5.59786	−0.816532	−0.408266	−	0.912863i	$-0.633866\pi$
$47$	−5.59786	−0.816532	−0.408266	+	0.912863i	$0.633866\pi$
$48$	11.8748	1.71398
$49$	0	0
$50$	−20.4957	−2.89853
$51$	6.10565	0.854962
$52$	8.33730	1.15618
$53$	2.37296	0.325951	0.162975	−	0.986630i	$-0.447891\pi$
$53$	2.37296	0.325951	0.162975	+	0.986630i	$0.447891\pi$
$54$	13.4149	1.82554
$55$	−12.5106	−1.68693
$56$	0	0
$57$	−18.8777	−2.50041
$58$	−11.4406	−1.50222
$59$	−6.23062	−0.811158	−0.405579	−	0.914060i	$-0.632930\pi$
$59$	−6.23062	−0.811158	−0.405579	+	0.914060i	$0.632930\pi$
$60$	21.9564	2.83456
$61$	2.19304	0.280790	0.140395	−	0.990096i	$-0.455163\pi$
$61$	2.19304	0.280790	0.140395	+	0.990096i	$0.455163\pi$
$62$	−3.90450	−0.495872
$63$	0	0
$64$	−7.53221	−0.941526
$65$	−16.8022	−2.08406
$66$	18.3258	2.25574
$67$	11.2466	1.37399	0.686997	−	0.726660i	$-0.258928\pi$
$67$	11.2466	1.37399	0.686997	+	0.726660i	$0.258928\pi$
$68$	−4.10661	−0.498000
$69$	−2.64026	−0.317851
$70$	0	0
$71$	3.34949	0.397512	0.198756	−	0.980049i	$-0.436310\pi$
$71$	3.34949	0.397512	0.198756	+	0.980049i	$0.436310\pi$
$72$	0.611374	0.0720511
$73$	1.76606	0.206702	0.103351	−	0.994645i	$-0.467043\pi$
$73$	1.76606	0.206702	0.103351	+	0.994645i	$0.467043\pi$
$74$	1.06394	0.123681
$75$	−29.8097	−3.44213
$76$	12.6970	1.45644
$77$	0	0
$78$	24.6122	2.78678
$79$	11.4766	1.29122	0.645609	−	0.763668i	$-0.276604\pi$
$79$	11.4766	1.29122	0.645609	+	0.763668i	$0.276604\pi$
$80$	16.0960	1.79959
$81$	3.49239	0.388043
$82$	1.98553	0.219265
$83$	−16.3013	−1.78930	−0.894652	−	0.446764i	$-0.852576\pi$
$83$	−16.3013	−1.78930	−0.894652	+	0.446764i	$0.852576\pi$
$84$	0	0
$85$	8.27609	0.897668
$86$	9.74642	1.05098
$87$	−16.6396	−1.78395
$88$	0.365943	0.0390096
$89$	11.1139	1.17807	0.589037	−	0.808106i	$-0.299507\pi$
$89$	11.1139	1.17807	0.589037	+	0.808106i	$0.299507\pi$
$90$	41.5001	4.37449
$91$	0	0
$92$	1.77582	0.185142
$93$	−5.67886	−0.588870
$94$	11.1147	1.14640
$95$	−25.5883	−2.62530
$96$	−22.9165	−2.33890
$97$	14.5110	1.47337	0.736686	−	0.676235i	$-0.236390\pi$
$97$	14.5110	1.47337	0.736686	+	0.676235i	$0.236390\pi$
$98$	0	0
$99$	17.0655	1.71515
$100$	20.0498	2.00498
$101$	0.825332	0.0821236	0.0410618	−	0.999157i	$-0.486926\pi$
$101$	0.825332	0.0821236	0.0410618	+	0.999157i	$0.486926\pi$
$102$	−12.1230	−1.20035
$103$	13.2270	1.30330	0.651648	−	0.758521i	$-0.274078\pi$
$103$	13.2270	1.30330	0.651648	+	0.758521i	$0.274078\pi$
$104$	0.491475	0.0481931
$105$	0	0
$106$	−4.71158	−0.457629
$107$	−10.2713	−0.992961	−0.496480	−	0.868048i	$-0.665375\pi$
$107$	−10.2713	−0.992961	−0.496480	+	0.868048i	$0.665375\pi$
$108$	−13.1230	−1.26276
$109$	−13.5088	−1.29390	−0.646952	−	0.762531i	$-0.723957\pi$
$109$	−13.5088	−1.29390	−0.646952	+	0.762531i	$0.723957\pi$
$110$	24.8402	2.36842
$111$	1.54744	0.146877
$112$	0	0
$113$	11.5710	1.08851	0.544256	−	0.838919i	$-0.316812\pi$
$113$	11.5710	1.08851	0.544256	+	0.838919i	$0.316812\pi$
$114$	37.4822	3.51053
$115$	−3.57883	−0.333727
$116$	11.1917	1.03912
$117$	22.9197	2.11893
$118$	12.3711	1.13885
$119$	0	0
$120$	1.29431	0.118154
$121$	−0.785290	−0.0713900
$122$	−4.35435	−0.394224
$123$	2.88783	0.260387
$124$	3.81956	0.343006
$125$	−20.8345	−1.86349
$126$	0	0
$127$	−18.6045	−1.65089	−0.825443	−	0.564486i	$-0.809074\pi$
$127$	−18.6045	−1.65089	−0.825443	+	0.564486i	$0.809074\pi$
$128$	−0.915607	−0.0809290
$129$	14.1756	1.24809
$130$	33.3613	2.92598
$131$	5.92612	0.517767	0.258884	−	0.965909i	$-0.416645\pi$
$131$	5.92612	0.517767	0.258884	+	0.965909i	$0.416645\pi$
$132$	−17.9271	−1.56035
$133$	0	0
$134$	−22.3305	−1.92906
$135$	26.4470	2.27619
$136$	−0.242080	−0.0207582
$137$	−18.0162	−1.53922	−0.769612	−	0.638512i	$-0.779550\pi$
$137$	−18.0162	−1.53922	−0.769612	+	0.638512i	$0.779550\pi$
$138$	5.24233	0.446257
$139$	8.66263	0.734754	0.367377	−	0.930072i	$-0.380256\pi$
$139$	8.66263	0.734754	0.367377	+	0.930072i	$0.380256\pi$
$140$	0	0
$141$	16.1657	1.36140
$142$	−6.65052	−0.558099
$143$	13.7188	1.14722
$144$	−21.9564	−1.82970
$145$	−22.5547	−1.87306
$146$	−3.50657	−0.290206
$147$	0	0
$148$	−1.04080	−0.0855530
$149$	−2.25750	−0.184942	−0.0924709	−	0.995715i	$-0.529476\pi$
$149$	−2.25750	−0.184942	−0.0924709	+	0.995715i	$0.529476\pi$
$150$	59.1882	4.83269
$151$	20.9049	1.70121	0.850607	−	0.525802i	$-0.176235\pi$
$151$	20.9049	1.70121	0.850607	+	0.525802i	$0.176235\pi$
$152$	0.748473	0.0607092
$153$	−11.2893	−0.912686
$154$	0	0
$155$	−7.69758	−0.618285
$156$	−24.0767	−1.92768
$157$	−15.1052	−1.20553	−0.602763	−	0.797920i	$-0.705934\pi$
$157$	−15.1052	−1.20553	−0.602763	+	0.797920i	$0.705934\pi$
$158$	−22.7871	−1.81285
$159$	−6.85270	−0.543455
$160$	−31.0628	−2.45573
$161$	0	0
$162$	−6.93425	−0.544806
$163$	2.43485	0.190712	0.0953560	−	0.995443i	$-0.469601\pi$
$163$	2.43485	0.190712	0.0953560	+	0.995443i	$0.469601\pi$
$164$	−1.94233	−0.151671
$165$	36.1285	2.81260
$166$	32.3668	2.51215
$167$	15.2584	1.18073	0.590364	−	0.807137i	$-0.298984\pi$
$167$	15.2584	1.18073	0.590364	+	0.807137i	$0.298984\pi$
$168$	0	0
$169$	5.42482	0.417294
$170$	−16.4324	−1.26031
$171$	34.9047	2.66923
$172$	−9.53437	−0.726989
$173$	5.32837	0.405108	0.202554	−	0.979271i	$-0.435076\pi$
$173$	5.32837	0.405108	0.202554	+	0.979271i	$0.435076\pi$
$174$	33.0385	2.50464
$175$	0	0
$176$	−13.1422	−0.990628
$177$	17.9930	1.35244
$178$	−22.0670	−1.65399
$179$	3.05992	0.228710	0.114355	−	0.993440i	$-0.463520\pi$
$179$	3.05992	0.228710	0.114355	+	0.993440i	$0.463520\pi$
$180$	−40.5972	−3.02594
$181$	1.44066	0.107083	0.0535416	−	0.998566i	$-0.482949\pi$
$181$	1.44066	0.107083	0.0535416	+	0.998566i	$0.482949\pi$
$182$	0	0
$183$	−6.33313	−0.468159
$184$	0.104683	0.00771732
$185$	2.09753	0.154213
$186$	11.2756	0.826764
$187$	−6.75729	−0.494142
$188$	−10.8729	−0.792988
$189$	0	0
$190$	50.8063	3.68588
$191$	11.9688	0.866029	0.433015	−	0.901387i	$-0.357450\pi$
$191$	11.9688	0.866029	0.433015	+	0.901387i	$0.357450\pi$
$192$	21.7518	1.56980
$193$	−1.40182	−0.100905	−0.0504525	−	0.998726i	$-0.516066\pi$
$193$	−1.40182	−0.100905	−0.0504525	+	0.998726i	$0.516066\pi$
$194$	−28.8121	−2.06859
$195$	48.5220	3.47474
$196$	0	0
$197$	−17.5560	−1.25081	−0.625406	−	0.780300i	$-0.715067\pi$
$197$	−17.5560	−1.25081	−0.625406	+	0.780300i	$0.715067\pi$
$198$	−33.8842	−2.40804
$199$	13.0263	0.923411	0.461706	−	0.887033i	$-0.347238\pi$
$199$	13.0263	0.923411	0.461706	+	0.887033i	$0.347238\pi$
$200$	1.18191	0.0835740
$201$	−32.4784	−2.29085
$202$	−1.63872	−0.115300
$203$	0	0
$204$	11.8592	0.830311
$205$	3.91440	0.273394
$206$	−26.2627	−1.82981
$207$	4.88183	0.339311
$208$	−17.6504	−1.22384
$209$	20.8924	1.44516
$210$	0	0
$211$	−14.2083	−0.978141	−0.489071	−	0.872244i	$-0.662664\pi$
$211$	−14.2083	−0.978141	−0.489071	+	0.872244i	$0.662664\pi$
$212$	4.60907	0.316552
$213$	−9.67278	−0.662768
$214$	20.3939	1.39410
$215$	19.2147	1.31043
$216$	−0.773589	−0.0526361
$217$	0	0
$218$	26.8220	1.81662
$219$	−5.10010	−0.344633
$220$	−24.2998	−1.63829
$221$	−9.07531	−0.610471
$222$	−3.07249	−0.206212
$223$	−18.5430	−1.24173	−0.620867	−	0.783916i	$-0.713219\pi$
$223$	−18.5430	−1.24173	−0.620867	+	0.783916i	$0.713219\pi$
$224$	0	0
$225$	55.1180	3.67453
$226$	−22.9747	−1.52825
$227$	7.59779	0.504283	0.252142	−	0.967690i	$-0.418865\pi$
$227$	7.59779	0.504283	0.252142	+	0.967690i	$0.418865\pi$
$228$	−36.6667	−2.42831
$229$	11.4759	0.758350	0.379175	−	0.925325i	$-0.376208\pi$
$229$	11.4759	0.758350	0.379175	+	0.925325i	$0.376208\pi$
$230$	7.10587	0.468547
$231$	0	0
$232$	0.659737	0.0433139
$233$	16.4472	1.07749	0.538745	−	0.842469i	$-0.318899\pi$
$233$	16.4472	1.07749	0.538745	+	0.842469i	$0.318899\pi$
$234$	−45.5078	−2.97494
$235$	21.9123	1.42940
$236$	−12.1019	−0.787769
$237$	−33.1425	−2.15284
$238$	0	0
$239$	25.9119	1.67610	0.838052	−	0.545590i	$-0.183695\pi$
$239$	25.9119	1.67610	0.838052	+	0.545590i	$0.183695\pi$
$240$	−46.4827	−3.00044
$241$	13.0371	0.839791	0.419896	−	0.907572i	$-0.362067\pi$
$241$	13.0371	0.839791	0.419896	+	0.907572i	$0.362067\pi$
$242$	1.55922	0.100230
$243$	10.1835	0.653274
$244$	4.25961	0.272694
$245$	0	0
$246$	−5.73388	−0.365579
$247$	28.0594	1.78537
$248$	0.225159	0.0142976
$249$	47.0755	2.98329
$250$	41.3676	2.61631
$251$	−22.4395	−1.41637	−0.708185	−	0.706027i	$-0.750486\pi$
$251$	−22.4395	−1.41637	−0.708185	+	0.706027i	$0.750486\pi$
$252$	0	0
$253$	2.92206	0.183708
$254$	36.9399	2.31781
$255$	−23.9000	−1.49667
$256$	16.8824	1.05515
$257$	14.2822	0.890896	0.445448	−	0.895308i	$-0.353044\pi$
$257$	14.2822	0.890896	0.445448	+	0.895308i	$0.353044\pi$
$258$	−28.1460	−1.75230
$259$	0	0
$260$	−32.6355	−2.02397
$261$	30.7665	1.90440
$262$	−11.7665	−0.726936
$263$	−10.9699	−0.676435	−0.338218	−	0.941068i	$-0.609824\pi$
$263$	−10.9699	−0.676435	−0.338218	+	0.941068i	$0.609824\pi$
$264$	−1.05678	−0.0650404
$265$	−9.28870	−0.570600
$266$	0	0
$267$	−32.0951	−1.96419
$268$	21.8447	1.33438
$269$	−26.1958	−1.59719	−0.798594	−	0.601871i	$-0.794422\pi$
$269$	−26.1958	−1.59719	−0.798594	+	0.601871i	$0.794422\pi$
$270$	−52.5112	−3.19573
$271$	−6.75994	−0.410637	−0.205319	−	0.978695i	$-0.565823\pi$
$271$	−6.75994	−0.410637	−0.205319	+	0.978695i	$0.565823\pi$
$272$	8.69388	0.527144
$273$	0	0
$274$	35.7716	2.16104
$275$	32.9913	1.98945
$276$	−5.12828	−0.308686
$277$	−5.90308	−0.354682	−0.177341	−	0.984149i	$-0.556749\pi$
$277$	−5.90308	−0.354682	−0.177341	+	0.984149i	$0.556749\pi$
$278$	−17.1999	−1.03158
$279$	10.5002	0.628629
$280$	0	0
$281$	−18.8607	−1.12514	−0.562568	−	0.826751i	$-0.690187\pi$
$281$	−18.8607	−1.12514	−0.562568	+	0.826751i	$0.690187\pi$
$282$	−32.0975	−1.91138
$283$	6.82909	0.405947	0.202974	−	0.979184i	$-0.434939\pi$
$283$	6.82909	0.405947	0.202974	+	0.979184i	$0.434939\pi$
$284$	6.50583	0.386050
$285$	73.8947	4.37715
$286$	−27.2390	−1.61068
$287$	0	0
$288$	42.3724	2.49682
$289$	−12.5299	−0.737052
$290$	44.7830	2.62975
$291$	−41.9054	−2.45654
$292$	3.43029	0.200742
$293$	−19.5724	−1.14343	−0.571716	−	0.820451i	$-0.693722\pi$
$293$	−19.5724	−1.14343	−0.571716	+	0.820451i	$0.693722\pi$
$294$	0	0
$295$	24.3891	1.41999
$296$	−0.0613539	−0.00356612
$297$	−21.5935	−1.25298
$298$	4.48234	0.259655
$299$	3.92443	0.226956
$300$	−57.9005	−3.34288
$301$	0	0
$302$	−41.5073	−2.38847
$303$	−2.38342	−0.136924
$304$	−26.8800	−1.54168
$305$	−8.58443	−0.491543
$306$	22.4153	1.28139
$307$	10.0292	0.572397	0.286198	−	0.958170i	$-0.407608\pi$
$307$	10.0292	0.572397	0.286198	+	0.958170i	$0.407608\pi$
$308$	0	0
$309$	−38.1974	−2.17298
$310$	15.2838	0.868061
$311$	10.5167	0.596345	0.298172	−	0.954512i	$-0.403623\pi$
$311$	10.5167	0.596345	0.298172	+	0.954512i	$0.403623\pi$
$312$	−1.41930	−0.0803519
$313$	−11.0397	−0.624003	−0.312001	−	0.950082i	$-0.600999\pi$
$313$	−11.0397	−0.624003	−0.312001	+	0.950082i	$0.600999\pi$
$314$	29.9918	1.69254
$315$	0	0
$316$	22.2914	1.25399
$317$	−1.69428	−0.0951604	−0.0475802	−	0.998867i	$-0.515151\pi$
$317$	−1.69428	−0.0951604	−0.0475802	+	0.998867i	$0.515151\pi$
$318$	13.6063	0.763001
$319$	18.4155	1.03107
$320$	29.4841	1.64821
$321$	29.6617	1.65556
$322$	0	0
$323$	−13.8209	−0.769015
$324$	6.78339	0.376855
$325$	44.3086	2.45780
$326$	−4.83447	−0.267756
$327$	39.0110	2.15731
$328$	−0.114499	−0.00632212
$329$	0	0
$330$	−71.7343	−3.94884
$331$	−15.6034	−0.857639	−0.428819	−	0.903390i	$-0.641070\pi$
$331$	−15.6034	−0.857639	−0.428819	+	0.903390i	$0.641070\pi$
$332$	−31.6626	−1.73771
$333$	−2.86121	−0.156793
$334$	−30.2960	−1.65772
$335$	−44.0238	−2.40528
$336$	0	0
$337$	3.78150	0.205991	0.102996	−	0.994682i	$-0.467157\pi$
$337$	3.78150	0.205991	0.102996	+	0.994682i	$0.467157\pi$
$338$	−10.7712	−0.585874
$339$	−33.4152	−1.81487
$340$	16.0749	0.871785
$341$	6.28495	0.340349
$342$	−69.3043	−3.74755
$343$	0	0
$344$	−0.562041	−0.0303032
$345$	10.3351	0.556421
$346$	−10.5796	−0.568765
$347$	5.99695	0.321933	0.160966	−	0.986960i	$-0.448539\pi$
$347$	5.99695	0.321933	0.160966	+	0.986960i	$0.448539\pi$
$348$	−32.3197	−1.73252
$349$	−4.19992	−0.224817	−0.112408	−	0.993662i	$-0.535856\pi$
$349$	−4.19992	−0.224817	−0.112408	+	0.993662i	$0.535856\pi$
$350$	0	0
$351$	−29.0009	−1.54796
$352$	25.3623	1.35181
$353$	−25.1178	−1.33688	−0.668442	−	0.743764i	$-0.733039\pi$
$353$	−25.1178	−1.33688	−0.668442	+	0.743764i	$0.733039\pi$
$354$	−35.7256	−1.89880
$355$	−13.1113	−0.695873
$356$	21.5869	1.14411
$357$	0	0
$358$	−6.07558	−0.321104
$359$	14.0928	0.743791	0.371896	−	0.928275i	$-0.378708\pi$
$359$	14.0928	0.743791	0.371896	+	0.928275i	$0.378708\pi$
$360$	−2.39316	−0.126131
$361$	23.7319	1.24905
$362$	−2.86047	−0.150343
$363$	2.26779	0.119028
$364$	0	0
$365$	−6.91308	−0.361847
$366$	12.5746	0.657287
$367$	6.36673	0.332340	0.166170	−	0.986097i	$-0.446860\pi$
$367$	6.36673	0.332340	0.166170	+	0.986097i	$0.446860\pi$
$368$	−3.75949	−0.195977
$369$	−5.33958	−0.277968
$370$	−4.16470	−0.216513
$371$	0	0
$372$	−11.0302	−0.571891
$373$	−16.9752	−0.878943	−0.439472	−	0.898257i	$-0.644834\pi$
$373$	−16.9752	−0.878943	−0.439472	+	0.898257i	$0.644834\pi$
$374$	13.4168	0.693767
$375$	60.1666	3.10699
$376$	−0.640946	−0.0330543
$377$	24.7328	1.27380
$378$	0	0
$379$	7.32773	0.376400	0.188200	−	0.982131i	$-0.439735\pi$
$379$	7.32773	0.376400	0.188200	+	0.982131i	$0.439735\pi$
$380$	−49.7010	−2.54961
$381$	53.7268	2.75251
$382$	−23.7644	−1.21589
$383$	27.6154	1.41108	0.705541	−	0.708669i	$-0.250704\pi$
$383$	27.6154	1.41108	0.705541	+	0.708669i	$0.250704\pi$
$384$	2.64412	0.134932
$385$	0	0
$386$	2.78335	0.141669
$387$	−26.2105	−1.33236
$388$	28.1853	1.43089
$389$	−0.260739	−0.0132200	−0.00661000	−	0.999978i	$-0.502104\pi$
$389$	−0.260739	−0.0132200	−0.00661000	+	0.999978i	$0.502104\pi$
$390$	−96.3420	−4.87847
$391$	−1.93301	−0.0977568
$392$	0	0
$393$	−17.1136	−0.863269
$394$	34.8579	1.75612
$395$	−44.9240	−2.26037
$396$	33.1470	1.66570
$397$	11.6456	0.584474	0.292237	−	0.956346i	$-0.405600\pi$
$397$	11.6456	0.584474	0.292237	+	0.956346i	$0.405600\pi$
$398$	−25.8642	−1.29645
$399$	0	0
$400$	−42.4463	−2.12232
$401$	−4.55769	−0.227600	−0.113800	−	0.993504i	$-0.536302\pi$
$401$	−4.55769	−0.227600	−0.113800	+	0.993504i	$0.536302\pi$
$402$	64.4869	3.21631
$403$	8.44094	0.420473
$404$	1.60307	0.0797558
$405$	−13.6706	−0.679298
$406$	0	0
$407$	−1.71260	−0.0848903
$408$	0.699088	0.0346100
$409$	3.19474	0.157970	0.0789850	−	0.996876i	$-0.474832\pi$
$409$	3.19474	0.157970	0.0789850	+	0.996876i	$0.474832\pi$
$410$	−7.77216	−0.383840
$411$	52.0276	2.56633
$412$	25.6913	1.26572
$413$	0	0
$414$	−9.69302	−0.476386
$415$	63.8099	3.13231
$416$	34.0625	1.67005
$417$	−25.0162	−1.22505
$418$	−41.4826	−2.02898
$419$	14.8953	0.727682	0.363841	−	0.931461i	$-0.381465\pi$
$419$	14.8953	0.727682	0.363841	+	0.931461i	$0.381465\pi$
$420$	0	0
$421$	3.93379	0.191721	0.0958606	−	0.995395i	$-0.469440\pi$
$421$	3.93379	0.191721	0.0958606	+	0.995395i	$0.469440\pi$
$422$	28.2111	1.37329
$423$	−29.8902	−1.45331
$424$	0.271700	0.0131949
$425$	−21.8246	−1.05865
$426$	19.2056	0.930514
$427$	0	0
$428$	−19.9502	−0.964331
$429$	−39.6175	−1.91275
$430$	−38.1514	−1.83982
$431$	−23.4231	−1.12825	−0.564125	−	0.825689i	$-0.690786\pi$
$431$	−23.4231	−1.12825	−0.564125	+	0.825689i	$0.690786\pi$
$432$	27.7821	1.33666
$433$	−13.1672	−0.632775	−0.316388	−	0.948630i	$-0.602470\pi$
$433$	−13.1672	−0.632775	−0.316388	+	0.948630i	$0.602470\pi$
$434$	0	0
$435$	65.1341	3.12294
$436$	−26.2385	−1.25660
$437$	5.97656	0.285898
$438$	10.1264	0.483858
$439$	−12.6509	−0.603795	−0.301898	−	0.953340i	$-0.597620\pi$
$439$	−12.6509	−0.603795	−0.301898	+	0.953340i	$0.597620\pi$
$440$	−1.43245	−0.0682892
$441$	0	0
$442$	18.0193	0.857091
$443$	8.75101	0.415773	0.207887	−	0.978153i	$-0.433341\pi$
$443$	8.75101	0.415773	0.207887	+	0.978153i	$0.433341\pi$
$444$	3.00565	0.142642
$445$	−43.5043	−2.06230
$446$	36.8178	1.74337
$447$	6.51929	0.308352
$448$	0	0
$449$	4.81821	0.227385	0.113693	−	0.993516i	$-0.463732\pi$
$449$	4.81821	0.227385	0.113693	+	0.993516i	$0.463732\pi$
$450$	−109.438	−5.15898
$451$	−3.19605	−0.150496
$452$	22.4748	1.05713
$453$	−60.3698	−2.83642
$454$	−15.0856	−0.708005
$455$	0	0
$456$	−2.16146	−0.101220
$457$	−12.9238	−0.604552	−0.302276	−	0.953220i	$-0.597746\pi$
$457$	−12.9238	−0.604552	−0.302276	+	0.953220i	$0.597746\pi$
$458$	−22.7858	−1.06471
$459$	14.2847	0.666751
$460$	−6.95127	−0.324105
$461$	26.0036	1.21111	0.605554	−	0.795804i	$-0.292951\pi$
$461$	26.0036	1.21111	0.605554	+	0.795804i	$0.292951\pi$
$462$	0	0
$463$	12.2251	0.568150	0.284075	−	0.958802i	$-0.408313\pi$
$463$	12.2251	0.568150	0.284075	+	0.958802i	$0.408313\pi$
$464$	−23.6933	−1.09993
$465$	22.2293	1.03086
$466$	−32.6564	−1.51278
$467$	−8.56519	−0.396350	−0.198175	−	0.980167i	$-0.563501\pi$
$467$	−8.56519	−0.396350	−0.198175	+	0.980167i	$0.563501\pi$
$468$	44.5177	2.05783
$469$	0	0
$470$	−43.5075	−2.00685
$471$	43.6213	2.00996
$472$	−0.713397	−0.0328368
$473$	−15.6885	−0.721358
$474$	65.8054	3.02254
$475$	67.4780	3.09610
$476$	0	0
$477$	12.6706	0.580147
$478$	−51.4490	−2.35322
$479$	1.48588	0.0678918	0.0339459	−	0.999424i	$-0.489193\pi$
$479$	1.48588	0.0678918	0.0339459	+	0.999424i	$0.489193\pi$
$480$	89.7042	4.09442
$481$	−2.30009	−0.104875
$482$	−25.8855	−1.17905
$483$	0	0
$484$	−1.52530	−0.0693316
$485$	−56.8020	−2.57925
$486$	−20.2197	−0.917185
$487$	24.5056	1.11045	0.555227	−	0.831699i	$-0.312631\pi$
$487$	24.5056	1.11045	0.555227	+	0.831699i	$0.312631\pi$
$488$	0.251100	0.0113668
$489$	−7.03144	−0.317973
$490$	0	0
$491$	−17.3862	−0.784627	−0.392314	−	0.919831i	$-0.628325\pi$
$491$	−17.3862	−0.784627	−0.392314	+	0.919831i	$0.628325\pi$
$492$	5.60914	0.252879
$493$	−12.1823	−0.548665
$494$	−55.7127	−2.50663
$495$	−66.8014	−3.00250
$496$	−8.08617	−0.363080
$497$	0	0
$498$	−93.4699	−4.18849
$499$	−9.14252	−0.409276	−0.204638	−	0.978838i	$-0.565602\pi$
$499$	−9.14252	−0.409276	−0.204638	+	0.978838i	$0.565602\pi$
$500$	−40.4676	−1.80976
$501$	−44.0636	−1.96862
$502$	44.5544	1.98856
$503$	−28.4679	−1.26932	−0.634661	−	0.772791i	$-0.718860\pi$
$503$	−28.4679	−1.26932	−0.634661	+	0.772791i	$0.718860\pi$
$504$	0	0
$505$	−3.23068	−0.143763
$506$	−5.80183	−0.257923
$507$	−15.6660	−0.695751
$508$	−36.1362	−1.60328
$509$	−2.46925	−0.109448	−0.0547238	−	0.998502i	$-0.517428\pi$
$509$	−2.46925	−0.109448	−0.0547238	+	0.998502i	$0.517428\pi$
$510$	47.4541	2.10130
$511$	0	0
$512$	−31.6893	−1.40048
$513$	−44.1658	−1.94997
$514$	−28.3577	−1.25080
$515$	−51.7758	−2.28152
$516$	27.5337	1.21210
$517$	−17.8910	−0.786846
$518$	0	0
$519$	−15.3874	−0.675433
$520$	−1.92383	−0.0843655
$521$	29.4123	1.28858	0.644288	−	0.764783i	$-0.277154\pi$
$521$	29.4123	1.28858	0.644288	+	0.764783i	$0.277154\pi$
$522$	−61.0879	−2.67374
$523$	22.1947	0.970508	0.485254	−	0.874373i	$-0.338727\pi$
$523$	22.1947	0.970508	0.485254	+	0.874373i	$0.338727\pi$
$524$	11.5105	0.502838
$525$	0	0
$526$	21.7812	0.949704
$527$	−4.15766	−0.181110
$528$	37.9524	1.65167
$529$	−22.1641	−0.963657
$530$	18.4430	0.801113
$531$	−33.2689	−1.44375
$532$	0	0
$533$	−4.29241	−0.185925
$534$	63.7259	2.75769
$535$	40.2059	1.73825
$536$	1.28772	0.0556212
$537$	−8.83655	−0.381325
$538$	52.0126	2.24242
$539$	0	0
$540$	51.3688	2.21056
$541$	−18.5727	−0.798501	−0.399251	−	0.916842i	$-0.630730\pi$
$541$	−18.5727	−0.798501	−0.399251	+	0.916842i	$0.630730\pi$
$542$	13.4221	0.576528
$543$	−4.16038	−0.178539
$544$	−16.7778	−0.719343
$545$	52.8787	2.26507
$546$	0	0
$547$	−9.15859	−0.391593	−0.195796	−	0.980645i	$-0.562729\pi$
$547$	−9.15859	−0.391593	−0.195796	+	0.980645i	$0.562729\pi$
$548$	−34.9934	−1.49484
$549$	11.7099	0.499767
$550$	−65.5052	−2.79315
$551$	37.6658	1.60462
$552$	−0.302306	−0.0128670
$553$	0	0
$554$	11.7207	0.497967
$555$	−6.05731	−0.257118
$556$	16.8257	0.713569
$557$	33.9540	1.43868	0.719339	−	0.694659i	$-0.244445\pi$
$557$	33.9540	1.43868	0.719339	+	0.694659i	$0.244445\pi$
$558$	−20.8484	−0.882584
$559$	−21.0703	−0.891177
$560$	0	0
$561$	19.5139	0.823879
$562$	37.4486	1.57967
$563$	27.3213	1.15146	0.575728	−	0.817641i	$-0.304719\pi$
$563$	27.3213	1.15146	0.575728	+	0.817641i	$0.304719\pi$
$564$	31.3991	1.32214
$565$	−45.2937	−1.90552
$566$	−13.5594	−0.569943
$567$	0	0
$568$	0.383512	0.0160918
$569$	6.99276	0.293152	0.146576	−	0.989199i	$-0.453175\pi$
$569$	6.99276	0.293152	0.146576	+	0.989199i	$0.453175\pi$
$570$	−146.720	−6.14544
$571$	17.2519	0.721968	0.360984	−	0.932572i	$-0.382441\pi$
$571$	17.2519	0.721968	0.360984	+	0.932572i	$0.382441\pi$
$572$	26.6464	1.11414
$573$	−34.5638	−1.44392
$574$	0	0
$575$	9.43760	0.393575
$576$	−40.2188	−1.67579
$577$	41.9763	1.74750	0.873748	−	0.486378i	$-0.161682\pi$
$577$	41.9763	1.74750	0.873748	+	0.486378i	$0.161682\pi$
$578$	24.8785	1.03481
$579$	4.04821	0.168238
$580$	−43.8087	−1.81906
$581$	0	0
$582$	83.2046	3.44894
$583$	7.58408	0.314100
$584$	0.202212	0.00836758
$585$	−89.7169	−3.70934
$586$	38.8616	1.60536
$587$	1.32225	0.0545753	0.0272876	−	0.999628i	$-0.491313\pi$
$587$	1.32225	0.0545753	0.0272876	+	0.999628i	$0.491313\pi$
$588$	0	0
$589$	12.8548	0.529673
$590$	−48.4254	−1.99364
$591$	50.6987	2.08547
$592$	2.20341	0.0905598
$593$	−31.5305	−1.29480	−0.647400	−	0.762150i	$-0.724144\pi$
$593$	−31.5305	−1.29480	−0.647400	+	0.762150i	$0.724144\pi$
$594$	42.8746	1.75917
$595$	0	0
$596$	−4.38482	−0.179609
$597$	−37.6178	−1.53960
$598$	−7.79209	−0.318642
$599$	33.0779	1.35153	0.675763	−	0.737119i	$-0.263814\pi$
$599$	33.0779	1.35153	0.675763	+	0.737119i	$0.263814\pi$
$600$	−3.41317	−0.139342
$601$	22.4760	0.916816	0.458408	−	0.888742i	$-0.348420\pi$
$601$	22.4760	0.916816	0.458408	+	0.888742i	$0.348420\pi$
$602$	0	0
$603$	60.0523	2.44552
$604$	40.6042	1.65216
$605$	3.07394	0.124973
$606$	4.73236	0.192239
$607$	27.3071	1.10836	0.554181	−	0.832396i	$-0.313031\pi$
$607$	27.3071	1.10836	0.554181	+	0.832396i	$0.313031\pi$
$608$	51.8742	2.10378
$609$	0	0
$610$	17.0447	0.690118
$611$	−24.0283	−0.972082
$612$	−21.9276	−0.886370
$613$	−31.3906	−1.26785	−0.633926	−	0.773393i	$-0.718558\pi$
$613$	−31.3906	−1.26785	−0.633926	+	0.773393i	$0.718558\pi$
$614$	−19.9133	−0.803635
$615$	−11.3041	−0.455827
$616$	0	0
$617$	21.8950	0.881461	0.440731	−	0.897639i	$-0.354719\pi$
$617$	21.8950	0.881461	0.440731	+	0.897639i	$0.354719\pi$
$618$	75.8422	3.05082
$619$	−29.9295	−1.20297	−0.601485	−	0.798884i	$-0.705424\pi$
$619$	−29.9295	−1.20297	−0.601485	+	0.798884i	$0.705424\pi$
$620$	−14.9513	−0.600458
$621$	−6.17712	−0.247879
$622$	−20.8811	−0.837258
$623$	0	0
$624$	50.9715	2.04049
$625$	29.9419	1.19768
$626$	21.9197	0.876089
$627$	−60.3339	−2.40950
$628$	−29.3393	−1.17077
$629$	1.13293	0.0451728
$630$	0	0
$631$	23.9830	0.954749	0.477374	−	0.878700i	$-0.341589\pi$
$631$	23.9830	0.954749	0.477374	+	0.878700i	$0.341589\pi$
$632$	1.31405	0.0522702
$633$	41.0313	1.63085
$634$	3.36405	0.133604
$635$	72.8256	2.88999
$636$	−13.3102	−0.527785
$637$	0	0
$638$	−36.5646	−1.44761
$639$	17.8849	0.707515
$640$	3.58405	0.141672
$641$	25.2377	0.996830	0.498415	−	0.866939i	$-0.333916\pi$
$641$	25.2377	0.996830	0.498415	+	0.866939i	$0.333916\pi$
$642$	−58.8942	−2.32437
$643$	44.5203	1.75571	0.877855	−	0.478926i	$-0.158974\pi$
$643$	44.5203	1.75571	0.877855	+	0.478926i	$0.158974\pi$
$644$	0	0
$645$	−55.4888	−2.18487
$646$	27.4418	1.07968
$647$	10.7010	0.420699	0.210349	−	0.977626i	$-0.432540\pi$
$647$	10.7010	0.420699	0.210349	+	0.977626i	$0.432540\pi$
$648$	0.399873	0.0157085
$649$	−19.9133	−0.781667
$650$	−87.9760	−3.45070
$651$	0	0
$652$	4.72929	0.185213
$653$	−12.4430	−0.486934	−0.243467	−	0.969909i	$-0.578285\pi$
$653$	−12.4430	−0.486934	−0.243467	+	0.969909i	$0.578285\pi$
$654$	−77.4576	−3.02883
$655$	−23.1972	−0.906389
$656$	4.11201	0.160547
$657$	9.43004	0.367901
$658$	0	0
$659$	28.6780	1.11714	0.558568	−	0.829459i	$-0.311351\pi$
$659$	28.6780	1.11714	0.558568	+	0.829459i	$0.311351\pi$
$660$	70.1737	2.73151
$661$	−47.6672	−1.85404	−0.927020	−	0.375012i	$-0.877639\pi$
$661$	−47.6672	−1.85404	−0.927020	+	0.375012i	$0.877639\pi$
$662$	30.9810	1.20411
$663$	26.2080	1.01783
$664$	−1.86648	−0.0724334
$665$	0	0
$666$	5.68102	0.220135
$667$	5.26801	0.203978
$668$	29.6368	1.14668
$669$	53.5492	2.07033
$670$	87.4107	3.37697
$671$	7.00906	0.270582
$672$	0	0
$673$	−19.5176	−0.752346	−0.376173	−	0.926549i	$-0.622760\pi$
$673$	−19.5176	−0.752346	−0.376173	+	0.926549i	$0.622760\pi$
$674$	−7.50828	−0.289208
$675$	−69.7423	−2.68438
$676$	10.5368	0.405262
$677$	−21.6744	−0.833014	−0.416507	−	0.909132i	$-0.636746\pi$
$677$	−21.6744	−0.833014	−0.416507	+	0.909132i	$0.636746\pi$
$678$	66.3470	2.54804
$679$	0	0
$680$	0.947600	0.0363388
$681$	−21.9412	−0.840787
$682$	−12.4790	−0.477845
$683$	−21.9036	−0.838120	−0.419060	−	0.907959i	$-0.637640\pi$
$683$	−21.9036	−0.838120	−0.419060	+	0.907959i	$0.637640\pi$
$684$	67.7965	2.59226
$685$	70.5224	2.69452
$686$	0	0
$687$	−33.1405	−1.26439
$688$	20.1847	0.769534
$689$	10.1857	0.388045
$690$	−20.5206	−0.781205
$691$	46.3046	1.76151	0.880755	−	0.473572i	$-0.157035\pi$
$691$	46.3046	1.76151	0.880755	+	0.473572i	$0.157035\pi$
$692$	10.3495	0.393428
$693$	0	0
$694$	−11.9071	−0.451988
$695$	−33.9090	−1.28624
$696$	−1.90521	−0.0722168
$697$	2.11427	0.0800836
$698$	8.33907	0.315639
$699$	−47.4967	−1.79649
$700$	0	0
$701$	27.8454	1.05171	0.525854	−	0.850575i	$-0.323746\pi$
$701$	27.8454	1.05171	0.525854	+	0.850575i	$0.323746\pi$
$702$	57.5823	2.17330
$703$	−3.50282	−0.132112
$704$	−24.0733	−0.907296
$705$	−63.2789	−2.38322
$706$	49.8721	1.87696
$707$	0	0
$708$	34.9484	1.31344
$709$	−32.2734	−1.21205	−0.606027	−	0.795444i	$-0.707238\pi$
$709$	−32.2734	−1.21205	−0.606027	+	0.795444i	$0.707238\pi$
$710$	26.0328	0.976994
$711$	61.2802	2.29819
$712$	1.27253	0.0476900
$713$	1.79790	0.0673317
$714$	0	0
$715$	−53.7007	−2.00829
$716$	5.94339	0.222115
$717$	−74.8294	−2.79455
$718$	−27.9817	−1.04427
$719$	−0.180252	−0.00672228	−0.00336114	−	0.999994i	$-0.501070\pi$
$719$	−0.180252	−0.00672228	−0.00336114	+	0.999994i	$0.501070\pi$
$720$	85.9461	3.20302
$721$	0	0
$722$	−47.1204	−1.75364
$723$	−37.6489	−1.40018
$724$	2.79824	0.103996
$725$	59.4781	2.20896
$726$	−4.50276	−0.167113
$727$	37.9209	1.40641	0.703205	−	0.710987i	$-0.251752\pi$
$727$	37.9209	1.40641	0.703205	+	0.710987i	$0.251752\pi$
$728$	0	0
$729$	−39.8855	−1.47724
$730$	13.7261	0.508027
$731$	10.3783	0.383857
$732$	−12.3011	−0.454660
$733$	−19.9157	−0.735604	−0.367802	−	0.929904i	$-0.619890\pi$
$733$	−19.9157	−0.735604	−0.367802	+	0.929904i	$0.619890\pi$
$734$	−12.6413	−0.466600
$735$	0	0
$736$	7.25522	0.267431
$737$	35.9448	1.32404
$738$	10.6019	0.390262
$739$	10.2749	0.377970	0.188985	−	0.981980i	$-0.439480\pi$
$739$	10.2749	0.377970	0.188985	+	0.981980i	$0.439480\pi$
$740$	4.07410	0.149767
$741$	−81.0308	−2.97674
$742$	0	0
$743$	25.5723	0.938158	0.469079	−	0.883156i	$-0.344586\pi$
$743$	25.5723	0.938158	0.469079	+	0.883156i	$0.344586\pi$
$744$	−0.650221	−0.0238383
$745$	8.83676	0.323754
$746$	33.7048	1.23402
$747$	−87.0423	−3.18471
$748$	−13.1249	−0.479895
$749$	0	0
$750$	−119.463	−4.36216
$751$	−12.2647	−0.447545	−0.223773	−	0.974641i	$-0.571837\pi$
$751$	−12.2647	−0.447545	−0.223773	+	0.974641i	$0.571837\pi$
$752$	23.0184	0.839396
$753$	64.8016	2.36150
$754$	−49.1077	−1.78840
$755$	−81.8300	−2.97810
$756$	0	0
$757$	25.0755	0.911384	0.455692	−	0.890138i	$-0.349392\pi$
$757$	25.0755	0.911384	0.455692	+	0.890138i	$0.349392\pi$
$758$	−14.5494	−0.528460
$759$	−8.43841	−0.306295
$760$	−2.92982	−0.106276
$761$	4.67814	0.169583	0.0847913	−	0.996399i	$-0.472978\pi$
$761$	4.67814	0.169583	0.0847913	+	0.996399i	$0.472978\pi$
$762$	−106.676	−3.86447
$763$	0	0
$764$	23.2473	0.841059
$765$	44.1908	1.59772
$766$	−54.8313	−1.98114
$767$	−26.7444	−0.965685
$768$	−48.7535	−1.75924
$769$	−27.9839	−1.00912	−0.504562	−	0.863375i	$-0.668346\pi$
$769$	−27.9839	−1.00912	−0.504562	+	0.863375i	$0.668346\pi$
$770$	0	0
$771$	−41.2445	−1.48538
$772$	−2.72280	−0.0979956
$773$	−11.2954	−0.406266	−0.203133	−	0.979151i	$-0.565112\pi$
$773$	−11.2954	−0.406266	−0.203133	+	0.979151i	$0.565112\pi$
$774$	52.0418	1.87060
$775$	20.2990	0.729163
$776$	1.66149	0.0596441
$777$	0	0
$778$	0.517705	0.0185606
$779$	−6.53696	−0.234211
$780$	94.2460	3.37455
$781$	10.7051	0.383060
$782$	3.83806	0.137249
$783$	−38.9297	−1.39124
$784$	0	0
$785$	59.1278	2.11036
$786$	33.9797	1.21201
$787$	−14.8798	−0.530406	−0.265203	−	0.964193i	$-0.585439\pi$
$787$	−14.8798	−0.530406	−0.265203	+	0.964193i	$0.585439\pi$
$788$	−34.0996	−1.21475
$789$	31.6794	1.12782
$790$	89.1980	3.17352
$791$	0	0
$792$	1.95398	0.0694317
$793$	9.41343	0.334281
$794$	−23.1226	−0.820592
$795$	26.8242	0.951357
$796$	25.3015	0.896787
$797$	44.4754	1.57540	0.787699	−	0.616060i	$-0.211272\pi$
$797$	44.4754	1.57540	0.787699	+	0.616060i	$0.211272\pi$
$798$	0	0
$799$	11.8354	0.418705
$800$	81.9146	2.89612
$801$	59.3437	2.09681
$802$	9.04943	0.319547
$803$	5.64442	0.199187
$804$	−63.0839	−2.22480
$805$	0	0
$806$	−16.7597	−0.590337
$807$	75.6492	2.66298
$808$	0.0944993	0.00332448
$809$	14.4973	0.509697	0.254849	−	0.966981i	$-0.417974\pi$
$809$	14.4973	0.509697	0.254849	+	0.966981i	$0.417974\pi$
$810$	27.1434	0.953723
$811$	−32.6855	−1.14774	−0.573871	−	0.818946i	$-0.694559\pi$
$811$	−32.6855	−1.14774	−0.573871	+	0.818946i	$0.694559\pi$
$812$	0	0
$813$	19.5216	0.684652
$814$	3.40042	0.119185
$815$	−9.53097	−0.333855
$816$	−25.1065	−0.878903
$817$	−32.0881	−1.12262
$818$	−6.34326	−0.221787
$819$	0	0
$820$	7.60307	0.265511
$821$	22.8968	0.799104	0.399552	−	0.916710i	$-0.369166\pi$
$821$	22.8968	0.799104	0.399552	+	0.916710i	$0.369166\pi$
$822$	−103.303	−3.60309
$823$	24.4053	0.850717	0.425358	−	0.905025i	$-0.360148\pi$
$823$	24.4053	0.850717	0.425358	+	0.905025i	$0.360148\pi$
$824$	1.51447	0.0527592
$825$	−95.2733	−3.31699
$826$	0	0
$827$	56.3653	1.96001	0.980007	−	0.198964i	$-0.0637577\pi$
$827$	56.3653	1.96001	0.980007	+	0.198964i	$0.0637577\pi$
$828$	9.48214	0.329527
$829$	36.3269	1.26169	0.630843	−	0.775910i	$-0.282709\pi$
$829$	36.3269	1.26169	0.630843	+	0.775910i	$0.282709\pi$
$830$	−126.697	−4.39770
$831$	17.0471	0.591358
$832$	−32.3314	−1.12089
$833$	0	0
$834$	49.6705	1.71995
$835$	−59.7273	−2.06695
$836$	40.5801	1.40349
$837$	−13.2862	−0.459237
$838$	−29.5751	−1.02165
$839$	15.6144	0.539069	0.269535	−	0.962991i	$-0.413130\pi$
$839$	15.6144	0.539069	0.269535	+	0.962991i	$0.413130\pi$
$840$	0	0
$841$	4.20031	0.144838
$842$	−7.81066	−0.269173
$843$	54.4666	1.87593
$844$	−27.5973	−0.949938
$845$	−21.2349	−0.730504
$846$	59.3480	2.04042
$847$	0	0
$848$	−9.75761	−0.335078
$849$	−19.7213	−0.676832
$850$	43.3334	1.48632
$851$	−0.489912	−0.0167940
$852$	−18.7878	−0.643658
$853$	−8.83035	−0.302346	−0.151173	−	0.988507i	$-0.548305\pi$
$853$	−8.83035	−0.302346	−0.151173	+	0.988507i	$0.548305\pi$
$854$	0	0
$855$	−136.631	−4.67267
$856$	−1.17604	−0.0401964
$857$	33.5652	1.14656	0.573282	−	0.819358i	$-0.305670\pi$
$857$	33.5652	1.14656	0.573282	+	0.819358i	$0.305670\pi$
$858$	78.6617	2.68547
$859$	−53.2333	−1.81630	−0.908148	−	0.418649i	$-0.862504\pi$
$859$	−53.2333	−1.81630	−0.908148	+	0.418649i	$0.862504\pi$
$860$	37.3214	1.27265
$861$	0	0
$862$	46.5073	1.58404
$863$	−6.14017	−0.209014	−0.104507	−	0.994524i	$-0.533326\pi$
$863$	−6.14017	−0.209014	−0.104507	+	0.994524i	$0.533326\pi$
$864$	−53.6149	−1.82402
$865$	−20.8574	−0.709171
$866$	26.1439	0.888405
$867$	36.1842	1.22888
$868$	0	0
$869$	36.6797	1.24427
$870$	−129.326	−4.38455
$871$	48.2752	1.63574
$872$	−1.54673	−0.0523790
$873$	77.4828	2.62240
$874$	−11.8667	−0.401395
$875$	0	0
$876$	−9.90609	−0.334696
$877$	24.6183	0.831300	0.415650	−	0.909525i	$-0.363554\pi$
$877$	24.6183	0.831300	0.415650	+	0.909525i	$0.363554\pi$
$878$	25.1188	0.847718
$879$	56.5219	1.90644
$880$	51.4437	1.73417
$881$	20.7994	0.700749	0.350375	−	0.936610i	$-0.386054\pi$
$881$	20.7994	0.700749	0.350375	+	0.936610i	$0.386054\pi$
$882$	0	0
$883$	−10.5005	−0.353371	−0.176686	−	0.984267i	$-0.556538\pi$
$883$	−10.5005	−0.353371	−0.176686	+	0.984267i	$0.556538\pi$
$884$	−17.6273	−0.592869
$885$	−70.4318	−2.36754
$886$	−17.3754	−0.583738
$887$	9.03388	0.303328	0.151664	−	0.988432i	$-0.451537\pi$
$887$	9.03388	0.303328	0.151664	+	0.988432i	$0.451537\pi$
$888$	0.177180	0.00594577
$889$	0	0
$890$	86.3792	2.89544
$891$	11.1618	0.373936
$892$	−36.0168	−1.20593
$893$	−36.5930	−1.22454
$894$	−12.9442	−0.432920
$895$	−11.9778	−0.400373
$896$	0	0
$897$	−11.3331	−0.378402
$898$	−9.56671	−0.319245
$899$	11.3308	0.377903
$900$	107.058	3.56858
$901$	−5.01706	−0.167143
$902$	6.34585	0.211294
$903$	0	0
$904$	1.32487	0.0440644
$905$	−5.63931	−0.187457
$906$	119.866	3.98228
$907$	−33.0621	−1.09781	−0.548905	−	0.835885i	$-0.684955\pi$
$907$	−33.0621	−1.09781	−0.548905	+	0.835885i	$0.684955\pi$
$908$	14.7574	0.489743
$909$	4.40693	0.146169
$910$	0	0
$911$	2.53984	0.0841488	0.0420744	−	0.999114i	$-0.486603\pi$
$911$	2.53984	0.0841488	0.0420744	+	0.999114i	$0.486603\pi$
$912$	77.6251	2.57042
$913$	−52.0998	−1.72425
$914$	25.6607	0.848780
$915$	24.7904	0.819546
$916$	22.2901	0.736484
$917$	0	0
$918$	−28.3627	−0.936107
$919$	51.9454	1.71352	0.856760	−	0.515715i	$-0.172474\pi$
$919$	51.9454	1.71352	0.856760	+	0.515715i	$0.172474\pi$
$920$	−0.409770	−0.0135097
$921$	−28.9627	−0.954352
$922$	−51.6310	−1.70038
$923$	14.3774	0.473238
$924$	0	0
$925$	−5.53132	−0.181869
$926$	−24.2734	−0.797673
$927$	70.6267	2.31969
$928$	45.7242	1.50097
$929$	−10.1487	−0.332967	−0.166483	−	0.986044i	$-0.553241\pi$
$929$	−10.1487	−0.332967	−0.166483	+	0.986044i	$0.553241\pi$
$930$	−44.1370	−1.44731
$931$	0	0
$932$	31.9459	1.04642
$933$	−30.3703	−0.994280
$934$	17.0065	0.556468
$935$	26.4507	0.865032
$936$	2.62427	0.0857770
$937$	−16.7857	−0.548366	−0.274183	−	0.961678i	$-0.588407\pi$
$937$	−16.7857	−0.548366	−0.274183	+	0.961678i	$0.588407\pi$
$938$	0	0
$939$	31.8809	1.04039
$940$	42.5609	1.38818
$941$	26.0430	0.848977	0.424489	−	0.905433i	$-0.360454\pi$
$941$	26.0430	0.848977	0.424489	+	0.905433i	$0.360454\pi$
$942$	−86.6114	−2.82195
$943$	−0.914272	−0.0297728
$944$	25.6204	0.833872
$945$	0	0
$946$	31.1500	1.01277
$947$	−26.5111	−0.861495	−0.430748	−	0.902472i	$-0.641750\pi$
$947$	−26.5111	−0.861495	−0.430748	+	0.902472i	$0.641750\pi$
$948$	−64.3738	−2.09076
$949$	7.58068	0.246079
$950$	−133.980	−4.34687
$951$	4.89281	0.158660
$952$	0	0
$953$	−37.8685	−1.22668	−0.613341	−	0.789818i	$-0.710175\pi$
$953$	−37.8685	−1.22668	−0.613341	+	0.789818i	$0.710175\pi$
$954$	−25.1579	−0.814516
$955$	−46.8505	−1.51605
$956$	50.3296	1.62778
$957$	−53.1810	−1.71910
$958$	−2.95027	−0.0953189
$959$	0	0
$960$	−85.1451	−2.74805
$961$	−27.1330	−0.875257
$962$	4.56689	0.147242
$963$	−54.8443	−1.76733
$964$	25.3223	0.815578
$965$	5.48727	0.176642
$966$	0	0
$967$	7.54473	0.242622	0.121311	−	0.992615i	$-0.461290\pi$
$967$	7.54473	0.242622	0.121311	+	0.992615i	$0.461290\pi$
$968$	−0.0899146	−0.00288996
$969$	39.9124	1.28217
$970$	112.782	3.62121
$971$	−59.4703	−1.90849	−0.954247	−	0.299020i	$-0.903340\pi$
$971$	−59.4703	−1.90849	−0.954247	+	0.299020i	$0.903340\pi$
$972$	19.7798	0.634438
$973$	0	0
$974$	−48.6566	−1.55906
$975$	−127.956	−4.09786
$976$	−9.01780	−0.288653
$977$	12.4307	0.397692	0.198846	−	0.980031i	$-0.436281\pi$
$977$	12.4307	0.397692	0.198846	+	0.980031i	$0.436281\pi$
$978$	13.9611	0.446428
$979$	35.5206	1.13524
$980$	0	0
$981$	−72.1311	−2.30297
$982$	34.5208	1.10160
$983$	−23.1767	−0.739223	−0.369612	−	0.929186i	$-0.620509\pi$
$983$	−23.1767	−0.739223	−0.369612	+	0.929186i	$0.620509\pi$
$984$	0.330653	0.0105408
$985$	68.7211	2.18964
$986$	24.1884	0.770316
$987$	0	0
$988$	54.5006	1.73390
$989$	−4.48791	−0.142707
$990$	132.636	4.21546
$991$	45.5005	1.44537	0.722686	−	0.691177i	$-0.242907\pi$
$991$	45.5005	1.44537	0.722686	+	0.691177i	$0.242907\pi$
$992$	15.6050	0.495460
$993$	45.0599	1.42993
$994$	0	0
$995$	−50.9902	−1.61650
$996$	91.4364	2.89727
$997$	49.8846	1.57986	0.789931	−	0.613196i	$-0.210117\pi$
$997$	49.8846	1.57986	0.789931	+	0.613196i	$0.210117\pi$
$998$	18.1528	0.574616
$999$	3.62037	0.114543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.r.1.3		17
7.3	odd	6		287.2.e.d.247.15	yes	34
7.5	odd	6		287.2.e.d.165.15	✓	34
7.6	odd	2		2009.2.a.s.1.3		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.15	✓	34	7.5	odd	6
287.2.e.d.247.15	yes	34	7.3	odd	6
2009.2.a.r.1.3		17	1.1	even	1	trivial
2009.2.a.s.1.3		17	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)

\(f(q)\)	\(=\)	\(q-1.98553 q^{2} -2.88783 q^{3} +1.94233 q^{4} -3.91440 q^{5} +5.73388 q^{6} +0.114499 q^{8} +5.33958 q^{9} +O(q^{10})\)	\(q-1.98553 q^{2} -2.88783 q^{3} +1.94233 q^{4} -3.91440 q^{5} +5.73388 q^{6} +0.114499 q^{8} +5.33958 q^{9} +7.77216 q^{10} +3.19605 q^{11} -5.60914 q^{12} +4.29241 q^{13} +11.3041 q^{15} -4.11201 q^{16} -2.11427 q^{17} -10.6019 q^{18} +6.53696 q^{19} -7.60307 q^{20} -6.34585 q^{22} +0.914272 q^{23} -0.330653 q^{24} +10.3225 q^{25} -8.52272 q^{26} -6.75632 q^{27} +5.76197 q^{29} -22.4447 q^{30} +1.96648 q^{31} +7.93552 q^{32} -9.22965 q^{33} +4.19794 q^{34} +10.3712 q^{36} -0.535849 q^{37} -12.9793 q^{38} -12.3958 q^{39} -0.448193 q^{40} -1.00000 q^{41} -4.90872 q^{43} +6.20779 q^{44} -20.9013 q^{45} -1.81532 q^{46} -5.59786 q^{47} +11.8748 q^{48} -20.4957 q^{50} +6.10565 q^{51} +8.33730 q^{52} +2.37296 q^{53} +13.4149 q^{54} -12.5106 q^{55} -18.8777 q^{57} -11.4406 q^{58} -6.23062 q^{59} +21.9564 q^{60} +2.19304 q^{61} -3.90450 q^{62} -7.53221 q^{64} -16.8022 q^{65} +18.3258 q^{66} +11.2466 q^{67} -4.10661 q^{68} -2.64026 q^{69} +3.34949 q^{71} +0.611374 q^{72} +1.76606 q^{73} +1.06394 q^{74} -29.8097 q^{75} +12.6970 q^{76} +24.6122 q^{78} +11.4766 q^{79} +16.0960 q^{80} +3.49239 q^{81} +1.98553 q^{82} -16.3013 q^{83} +8.27609 q^{85} +9.74642 q^{86} -16.6396 q^{87} +0.365943 q^{88} +11.1139 q^{89} +41.5001 q^{90} +1.77582 q^{92} -5.67886 q^{93} +11.1147 q^{94} -25.5883 q^{95} -22.9165 q^{96} +14.5110 q^{97} +17.0655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} - q^{3} + 25 q^{4} + q^{5} - 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 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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