LMFDB - Embedded newform 2009.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2009, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.0419457661$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.633117.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 4x^{2} + 6x - 3 $ x^5 - x^4 - 6x^3 + 4x^2 + 6*x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.45719$ 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)

$f(q)$	$=$	$q-2.45719 q^{2} +1.45719 q^{3} +4.03778 q^{4} +2.26685 q^{5} -3.58059 q^{6} -5.00722 q^{8} -0.876597 q^{9} +O(q^{10})$	\(q-2.45719 q^{2} +1.45719 q^{3} +4.03778 q^{4} +2.26685 q^{5} -3.58059 q^{6} -5.00722 q^{8} -0.876597 q^{9} -5.57007 q^{10} -5.41988 q^{11} +5.88382 q^{12} -3.23628 q^{13} +3.30322 q^{15} +4.22813 q^{16} -2.83206 q^{17} +2.15397 q^{18} +4.32097 q^{19} +9.15303 q^{20} +13.3177 q^{22} +6.99907 q^{23} -7.29647 q^{24} +0.138589 q^{25} +7.95216 q^{26} -5.64894 q^{27} +8.06741 q^{29} -8.11665 q^{30} -9.18123 q^{31} -0.374872 q^{32} -7.89779 q^{33} +6.95892 q^{34} -3.53951 q^{36} -0.0469023 q^{37} -10.6174 q^{38} -4.71588 q^{39} -11.3506 q^{40} +1.00000 q^{41} -6.31281 q^{43} -21.8843 q^{44} -1.98711 q^{45} -17.1980 q^{46} -5.26448 q^{47} +6.16119 q^{48} -0.340538 q^{50} -4.12685 q^{51} -13.0674 q^{52} +6.43622 q^{53} +13.8805 q^{54} -12.2860 q^{55} +6.29647 q^{57} -19.8232 q^{58} -2.45253 q^{59} +13.3377 q^{60} -5.28319 q^{61} +22.5600 q^{62} -7.53512 q^{64} -7.33615 q^{65} +19.4064 q^{66} -8.78423 q^{67} -11.4353 q^{68} +10.1990 q^{69} -12.1364 q^{71} +4.38931 q^{72} -2.42993 q^{73} +0.115248 q^{74} +0.201950 q^{75} +17.4471 q^{76} +11.5878 q^{78} +4.92882 q^{79} +9.58451 q^{80} -5.60179 q^{81} -2.45719 q^{82} +1.63593 q^{83} -6.41985 q^{85} +15.5118 q^{86} +11.7558 q^{87} +27.1385 q^{88} -1.68625 q^{89} +4.88271 q^{90} +28.2607 q^{92} -13.3788 q^{93} +12.9358 q^{94} +9.79497 q^{95} -0.546260 q^{96} -18.8278 q^{97} +4.75105 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9}+O(q^{10}) $ 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9	$ 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9} + 2 q^{11} + 2 q^{12} - 5 q^{13} - 5 q^{15} - q^{16} - 13 q^{17} + 21 q^{18} + 23 q^{20} + q^{22} + 2 q^{23} - 2 q^{24} + 22 q^{25} - 10 q^{27} - 5 q^{29} - 33 q^{30} - 17 q^{31} - 12 q^{32} - 3 q^{33} + 8 q^{34} + 15 q^{36} - 7 q^{37} + 3 q^{38} + 5 q^{39} - 7 q^{40} + 5 q^{41} + q^{43} - 47 q^{44} + 23 q^{45} - 24 q^{46} - 9 q^{47} + 19 q^{48} + 2 q^{50} + 5 q^{51} - 20 q^{52} + 5 q^{53} - 2 q^{54} - 33 q^{55} - 3 q^{57} - 27 q^{58} - 7 q^{59} - 16 q^{60} - 22 q^{61} + 28 q^{62} - 3 q^{64} - 31 q^{65} + 42 q^{66} - 3 q^{67} - 17 q^{68} + 22 q^{69} - 24 q^{71} - 12 q^{72} - 40 q^{73} - 5 q^{74} - 24 q^{75} + 19 q^{76} + 30 q^{78} - 42 q^{79} - 24 q^{80} + 9 q^{81} - q^{82} + 12 q^{83} - 23 q^{85} + 16 q^{86} + 32 q^{87} + 26 q^{88} - 8 q^{89} + 59 q^{90} + 12 q^{92} - 11 q^{93} + 23 q^{94} - 17 q^{95} + 17 q^{96} - 16 q^{97} - 45 q^{99}+O(q^{100}) $ 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9 + 2 * q^11 + 2 * q^12 - 5 * q^13 - 5 * q^15 - q^16 - 13 * q^17 + 21 * q^18 + 23 * q^20 + q^22 + 2 * q^23 - 2 * q^24 + 22 * q^25 - 10 * q^27 - 5 * q^29 - 33 * q^30 - 17 * q^31 - 12 * q^32 - 3 * q^33 + 8 * q^34 + 15 * q^36 - 7 * q^37 + 3 * q^38 + 5 * q^39 - 7 * q^40 + 5 * q^41 + q^43 - 47 * q^44 + 23 * q^45 - 24 * q^46 - 9 * q^47 + 19 * q^48 + 2 * q^50 + 5 * q^51 - 20 * q^52 + 5 * q^53 - 2 * q^54 - 33 * q^55 - 3 * q^57 - 27 * q^58 - 7 * q^59 - 16 * q^60 - 22 * q^61 + 28 * q^62 - 3 * q^64 - 31 * q^65 + 42 * q^66 - 3 * q^67 - 17 * q^68 + 22 * q^69 - 24 * q^71 - 12 * q^72 - 40 * q^73 - 5 * q^74 - 24 * q^75 + 19 * q^76 + 30 * q^78 - 42 * q^79 - 24 * q^80 + 9 * q^81 - q^82 + 12 * q^83 - 23 * q^85 + 16 * q^86 + 32 * q^87 + 26 * q^88 - 8 * q^89 + 59 * q^90 + 12 * q^92 - 11 * q^93 + 23 * q^94 - 17 * q^95 + 17 * q^96 - 16 * q^97 - 45 * 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 $

$2$	−2.45719	−1.73750	−0.868748	−	0.495255i	$-0.835075\pi$
$2$	−2.45719	−1.73750	−0.868748	+	0.495255i	$0.835075\pi$
$3$	1.45719	0.841309	0.420655	−	0.907221i	$-0.361800\pi$
$3$	1.45719	0.841309	0.420655	+	0.907221i	$0.361800\pi$
$4$	4.03778	2.01889
$5$	2.26685	1.01376	0.506882	−	0.862015i	$-0.330798\pi$
$5$	2.26685	1.01376	0.506882	+	0.862015i	$0.330798\pi$
$6$	−3.58059	−1.46177
$7$	0	0
$7$	0	0
$8$	−5.00722	−1.77032
$9$	−0.876597	−0.292199
$10$	−5.57007	−1.76141
$11$	−5.41988	−1.63415	−0.817077	−	0.576528i	$-0.804407\pi$
$11$	−5.41988	−1.63415	−0.817077	+	0.576528i	$0.804407\pi$
$12$	5.88382	1.69851
$13$	−3.23628	−0.897584	−0.448792	−	0.893636i	$-0.648146\pi$
$13$	−3.23628	−0.897584	−0.448792	+	0.893636i	$0.648146\pi$
$14$	0	0
$15$	3.30322	0.852889
$16$	4.22813	1.05703
$17$	−2.83206	−0.686876	−0.343438	−	0.939175i	$-0.611592\pi$
$17$	−2.83206	−0.686876	−0.343438	+	0.939175i	$0.611592\pi$
$18$	2.15397	0.507694
$19$	4.32097	0.991298	0.495649	−	0.868523i	$-0.334930\pi$
$19$	4.32097	0.991298	0.495649	+	0.868523i	$0.334930\pi$
$20$	9.15303	2.04668
$21$	0	0
$22$	13.3177	2.83934
$23$	6.99907	1.45941	0.729703	−	0.683764i	$-0.239658\pi$
$23$	6.99907	1.45941	0.729703	+	0.683764i	$0.239658\pi$
$24$	−7.29647	−1.48939
$25$	0.138589	0.0277177
$26$	7.95216	1.55955
$27$	−5.64894	−1.08714
$28$	0	0
$29$	8.06741	1.49808	0.749040	−	0.662524i	$-0.230515\pi$
$29$	8.06741	1.49808	0.749040	+	0.662524i	$0.230515\pi$
$30$	−8.11665	−1.48189
$31$	−9.18123	−1.64900	−0.824498	−	0.565864i	$-0.808543\pi$
$31$	−9.18123	−1.64900	−0.824498	+	0.565864i	$0.808543\pi$
$32$	−0.374872	−0.0662686
$33$	−7.89779	−1.37483
$34$	6.95892	1.19344
$35$	0	0
$36$	−3.53951	−0.589918
$37$	−0.0469023	−0.00771068	−0.00385534	−	0.999993i	$-0.501227\pi$
$37$	−0.0469023	−0.00771068	−0.00385534	+	0.999993i	$0.501227\pi$
$38$	−10.6174	−1.72238
$39$	−4.71588	−0.755145
$40$	−11.3506	−1.79469
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−6.31281	−0.962695	−0.481348	−	0.876530i	$-0.659852\pi$
$43$	−6.31281	−0.962695	−0.481348	+	0.876530i	$0.659852\pi$
$44$	−21.8843	−3.29918
$45$	−1.98711	−0.296221
$46$	−17.1980	−2.53571
$47$	−5.26448	−0.767903	−0.383952	−	0.923353i	$-0.625437\pi$
$47$	−5.26448	−0.767903	−0.383952	+	0.923353i	$0.625437\pi$
$48$	6.16119	0.889291
$49$	0	0
$50$	−0.340538	−0.0481594
$51$	−4.12685	−0.577875
$52$	−13.0674	−1.81212
$53$	6.43622	0.884082	0.442041	−	0.896995i	$-0.354255\pi$
$53$	6.43622	0.884082	0.442041	+	0.896995i	$0.354255\pi$
$54$	13.8805	1.88890
$55$	−12.2860	−1.65665
$56$	0	0
$57$	6.29647	0.833988
$58$	−19.8232	−2.60291
$59$	−2.45253	−0.319292	−0.159646	−	0.987174i	$-0.551035\pi$
$59$	−2.45253	−0.319292	−0.159646	+	0.987174i	$0.551035\pi$
$60$	13.3377	1.72189
$61$	−5.28319	−0.676443	−0.338221	−	0.941067i	$-0.609825\pi$
$61$	−5.28319	−0.676443	−0.338221	+	0.941067i	$0.609825\pi$
$62$	22.5600	2.86513
$63$	0	0
$64$	−7.53512	−0.941891
$65$	−7.33615	−0.909938
$66$	19.4064	2.38876
$67$	−8.78423	−1.07316	−0.536582	−	0.843848i	$-0.680285\pi$
$67$	−8.78423	−1.07316	−0.536582	+	0.843848i	$0.680285\pi$
$68$	−11.4353	−1.38673
$69$	10.1990	1.22781
$70$	0	0
$71$	−12.1364	−1.44033	−0.720165	−	0.693802i	$-0.755934\pi$
$71$	−12.1364	−1.44033	−0.720165	+	0.693802i	$0.755934\pi$
$72$	4.38931	0.517286
$73$	−2.42993	−0.284402	−0.142201	−	0.989838i	$-0.545418\pi$
$73$	−2.42993	−0.284402	−0.142201	+	0.989838i	$0.545418\pi$
$74$	0.115248	0.0133973
$75$	0.201950	0.0233192
$76$	17.4471	2.00132
$77$	0	0
$78$	11.5878	1.31206
$79$	4.92882	0.554536	0.277268	−	0.960793i	$-0.410571\pi$
$79$	4.92882	0.554536	0.277268	+	0.960793i	$0.410571\pi$
$80$	9.58451	1.07158
$81$	−5.60179	−0.622421
$82$	−2.45719	−0.271351
$83$	1.63593	0.179567	0.0897833	−	0.995961i	$-0.471383\pi$
$83$	1.63593	0.179567	0.0897833	+	0.995961i	$0.471383\pi$
$84$	0	0
$85$	−6.41985	−0.696330
$86$	15.5118	1.67268
$87$	11.7558	1.26035
$88$	27.1385	2.89298
$89$	−1.68625	−0.178742	−0.0893712	−	0.995998i	$-0.528486\pi$
$89$	−1.68625	−0.178742	−0.0893712	+	0.995998i	$0.528486\pi$
$90$	4.88271	0.514682
$91$	0	0
$92$	28.2607	2.94638
$93$	−13.3788	−1.38732
$94$	12.9358	1.33423
$95$	9.79497	1.00494
$96$	−0.546260	−0.0557524
$97$	−18.8278	−1.91168	−0.955838	−	0.293894i	$-0.905049\pi$
$97$	−18.8278	−1.91168	−0.955838	+	0.293894i	$0.905049\pi$
$98$	0	0
$99$	4.75105	0.477498
$100$	0.559591	0.0559591
$101$	−7.44903	−0.741207	−0.370603	−	0.928791i	$-0.620849\pi$
$101$	−7.44903	−0.741207	−0.370603	+	0.928791i	$0.620849\pi$
$102$	10.1405	1.00406
$103$	−3.68672	−0.363264	−0.181632	−	0.983367i	$-0.558138\pi$
$103$	−3.68672	−0.363264	−0.181632	+	0.983367i	$0.558138\pi$
$104$	16.2048	1.58901
$105$	0	0
$106$	−15.8150	−1.53609
$107$	−8.58781	−0.830215	−0.415108	−	0.909772i	$-0.636256\pi$
$107$	−8.58781	−0.830215	−0.415108	+	0.909772i	$0.636256\pi$
$108$	−22.8092	−2.19482
$109$	−2.91912	−0.279601	−0.139800	−	0.990180i	$-0.544646\pi$
$109$	−2.91912	−0.279601	−0.139800	+	0.990180i	$0.544646\pi$
$110$	30.1891	2.87842
$111$	−0.0683455	−0.00648707
$112$	0	0
$113$	−7.03990	−0.662258	−0.331129	−	0.943585i	$-0.607430\pi$
$113$	−7.03990	−0.662258	−0.331129	+	0.943585i	$0.607430\pi$
$114$	−15.4716	−1.44905
$115$	15.8658	1.47949
$116$	32.5745	3.02446
$117$	2.83692	0.262273
$118$	6.02633	0.554768
$119$	0	0
$120$	−16.5400	−1.50989
$121$	18.3751	1.67046
$122$	12.9818	1.17532
$123$	1.45719	0.131390
$124$	−37.0718	−3.32915
$125$	−11.0201	−0.985665
$126$	0	0
$127$	19.1099	1.69573	0.847863	−	0.530216i	$-0.177889\pi$
$127$	19.1099	1.69573	0.847863	+	0.530216i	$0.177889\pi$
$128$	19.2650	1.70280
$129$	−9.19897	−0.809924
$130$	18.0263	1.58101
$131$	−9.99440	−0.873215	−0.436608	−	0.899652i	$-0.643820\pi$
$131$	−9.99440	−0.873215	−0.436608	+	0.899652i	$0.643820\pi$
$132$	−31.8896	−2.77563
$133$	0	0
$134$	21.5845	1.86462
$135$	−12.8053	−1.10210
$136$	14.1808	1.21599
$137$	4.66385	0.398459	0.199230	−	0.979953i	$-0.436156\pi$
$137$	4.66385	0.398459	0.199230	+	0.979953i	$0.436156\pi$
$138$	−25.0608	−2.13332
$139$	10.3954	0.881725	0.440862	−	0.897575i	$-0.354673\pi$
$139$	10.3954	0.881725	0.440862	+	0.897575i	$0.354673\pi$
$140$	0	0
$141$	−7.67135	−0.646044
$142$	29.8215	2.50257
$143$	17.5403	1.46679
$144$	−3.70636	−0.308864
$145$	18.2876	1.51870
$146$	5.97080	0.494147
$147$	0	0
$148$	−0.189381	−0.0155670
$149$	6.23050	0.510422	0.255211	−	0.966885i	$-0.417855\pi$
$149$	6.23050	0.510422	0.255211	+	0.966885i	$0.417855\pi$
$150$	−0.496229	−0.0405169
$151$	−21.1548	−1.72156	−0.860778	−	0.508981i	$-0.830022\pi$
$151$	−21.1548	−1.72156	−0.860778	+	0.508981i	$0.830022\pi$
$152$	−21.6360	−1.75492
$153$	2.48258	0.200704
$154$	0	0
$155$	−20.8124	−1.67169
$156$	−19.0417	−1.52456
$157$	−20.4912	−1.63538	−0.817688	−	0.575662i	$-0.804745\pi$
$157$	−20.4912	−1.63538	−0.817688	+	0.575662i	$0.804745\pi$
$158$	−12.1111	−0.963504
$159$	9.37879	0.743787
$160$	−0.849777	−0.0671808
$161$	0	0
$162$	13.7647	1.08145
$163$	−1.63497	−0.128060	−0.0640302	−	0.997948i	$-0.520395\pi$
$163$	−1.63497	−0.128060	−0.0640302	+	0.997948i	$0.520395\pi$
$164$	4.03778	0.315298
$165$	−17.9031	−1.39375
$166$	−4.01979	−0.311996
$167$	19.8243	1.53405	0.767026	−	0.641616i	$-0.221736\pi$
$167$	19.8243	1.53405	0.767026	+	0.641616i	$0.221736\pi$
$168$	0	0
$169$	−2.52647	−0.194344
$170$	15.7748	1.20987
$171$	−3.78775	−0.289656
$172$	−25.4898	−1.94358
$173$	9.31394	0.708126	0.354063	−	0.935222i	$-0.384800\pi$
$173$	9.31394	0.708126	0.354063	+	0.935222i	$0.384800\pi$
$174$	−28.8861	−2.18985
$175$	0	0
$176$	−22.9159	−1.72735
$177$	−3.57380	−0.268623
$178$	4.14344	0.310564
$179$	−17.3459	−1.29649	−0.648245	−	0.761432i	$-0.724497\pi$
$179$	−17.3459	−1.29649	−0.648245	+	0.761432i	$0.724497\pi$
$180$	−8.02352	−0.598038
$181$	−10.1355	−0.753364	−0.376682	−	0.926343i	$-0.622935\pi$
$181$	−10.1355	−0.753364	−0.376682	+	0.926343i	$0.622935\pi$
$182$	0	0
$183$	−7.69861	−0.569097
$184$	−35.0459	−2.58362
$185$	−0.106320	−0.00781681
$186$	32.8742	2.41046
$187$	15.3494	1.12246
$188$	−21.2568	−1.55031
$189$	0	0
$190$	−24.0681	−1.74608
$191$	18.1959	1.31661	0.658306	−	0.752750i	$-0.271273\pi$
$191$	18.1959	1.31661	0.658306	+	0.752750i	$0.271273\pi$
$192$	−10.9801	−0.792421
$193$	1.29950	0.0935398	0.0467699	−	0.998906i	$-0.485107\pi$
$193$	1.29950	0.0935398	0.0467699	+	0.998906i	$0.485107\pi$
$194$	46.2635	3.32153
$195$	−10.6902	−0.765539
$196$	0	0
$197$	5.64679	0.402317	0.201159	−	0.979559i	$-0.435529\pi$
$197$	5.64679	0.402317	0.201159	+	0.979559i	$0.435529\pi$
$198$	−11.6742	−0.829651
$199$	11.5069	0.815699	0.407850	−	0.913049i	$-0.366279\pi$
$199$	11.5069	0.815699	0.407850	+	0.913049i	$0.366279\pi$
$200$	−0.693943	−0.0490692
$201$	−12.8003	−0.902863
$202$	18.3037	1.28784
$203$	0	0
$204$	−16.6633	−1.16667
$205$	2.26685	0.158323
$206$	9.05898	0.631169
$207$	−6.13536	−0.426437
$208$	−13.6834	−0.948775
$209$	−23.4191	−1.61993
$210$	0	0
$211$	−9.92599	−0.683333	−0.341667	−	0.939821i	$-0.610991\pi$
$211$	−9.92599	−0.683333	−0.341667	+	0.939821i	$0.610991\pi$
$212$	25.9880	1.78487
$213$	−17.6851	−1.21176
$214$	21.1019	1.44250
$215$	−14.3102	−0.975946
$216$	28.2855	1.92458
$217$	0	0
$218$	7.17282	0.485805
$219$	−3.54087	−0.239270
$220$	−49.6083	−3.34459
$221$	9.16536	0.616529
$222$	0.167938	0.0112713
$223$	11.8232	0.791738	0.395869	−	0.918307i	$-0.370443\pi$
$223$	11.8232	0.791738	0.395869	+	0.918307i	$0.370443\pi$
$224$	0	0
$225$	−0.121486	−0.00809909
$226$	17.2984	1.15067
$227$	−1.60275	−0.106378	−0.0531892	−	0.998584i	$-0.516939\pi$
$227$	−1.60275	−0.106378	−0.0531892	+	0.998584i	$0.516939\pi$
$228$	25.4238	1.68373
$229$	9.93349	0.656423	0.328212	−	0.944604i	$-0.393554\pi$
$229$	9.93349	0.656423	0.328212	+	0.944604i	$0.393554\pi$
$230$	−38.9853	−2.57061
$231$	0	0
$232$	−40.3953	−2.65208
$233$	−7.91248	−0.518364	−0.259182	−	0.965829i	$-0.583453\pi$
$233$	−7.91248	−0.518364	−0.259182	+	0.965829i	$0.583453\pi$
$234$	−6.97084	−0.455698
$235$	−11.9338	−0.778473
$236$	−9.90278	−0.644616
$237$	7.18223	0.466536
$238$	0	0
$239$	27.1893	1.75873	0.879365	−	0.476148i	$-0.157967\pi$
$239$	27.1893	1.75873	0.879365	+	0.476148i	$0.157967\pi$
$240$	13.9665	0.901531
$241$	−19.4014	−1.24975	−0.624877	−	0.780723i	$-0.714851\pi$
$241$	−19.4014	−1.24975	−0.624877	+	0.780723i	$0.714851\pi$
$242$	−45.1510	−2.90242
$243$	8.78395	0.563490
$244$	−21.3324	−1.36566
$245$	0	0
$246$	−3.58059	−0.228290
$247$	−13.9839	−0.889773
$248$	45.9724	2.91925
$249$	2.38386	0.151071
$250$	27.0784	1.71259
$251$	−27.4697	−1.73387	−0.866935	−	0.498421i	$-0.833913\pi$
$251$	−27.4697	−1.73387	−0.866935	+	0.498421i	$0.833913\pi$
$252$	0	0
$253$	−37.9341	−2.38489
$254$	−46.9566	−2.94632
$255$	−9.35494	−0.585829
$256$	−32.2675	−2.01672
$257$	−21.6328	−1.34942	−0.674710	−	0.738083i	$-0.735731\pi$
$257$	−21.6328	−1.34942	−0.674710	+	0.738083i	$0.735731\pi$
$258$	22.6036	1.40724
$259$	0	0
$260$	−29.6218	−1.83707
$261$	−7.07187	−0.437738
$262$	24.5581	1.51721
$263$	−9.84482	−0.607058	−0.303529	−	0.952822i	$-0.598165\pi$
$263$	−9.84482	−0.607058	−0.303529	+	0.952822i	$0.598165\pi$
$264$	39.5460	2.43389
$265$	14.5899	0.896251
$266$	0	0
$267$	−2.45719	−0.150378
$268$	−35.4688	−2.16660
$269$	26.0627	1.58907	0.794535	−	0.607219i	$-0.207715\pi$
$269$	26.0627	1.58907	0.794535	+	0.607219i	$0.207715\pi$
$270$	31.4650	1.91490
$271$	−25.4506	−1.54602	−0.773008	−	0.634396i	$-0.781249\pi$
$271$	−25.4506	−1.54602	−0.773008	+	0.634396i	$0.781249\pi$
$272$	−11.9743	−0.726050
$273$	0	0
$274$	−11.4600	−0.692321
$275$	−0.751133	−0.0452950
$276$	41.1812	2.47882
$277$	29.3678	1.76454	0.882270	−	0.470743i	$-0.156014\pi$
$277$	29.3678	1.76454	0.882270	+	0.470743i	$0.156014\pi$
$278$	−25.5434	−1.53199
$279$	8.04823	0.481835
$280$	0	0
$281$	24.2120	1.44437	0.722184	−	0.691701i	$-0.243139\pi$
$281$	24.2120	1.44437	0.722184	+	0.691701i	$0.243139\pi$
$282$	18.8500	1.12250
$283$	−8.91251	−0.529794	−0.264897	−	0.964277i	$-0.585338\pi$
$283$	−8.91251	−0.529794	−0.264897	+	0.964277i	$0.585338\pi$
$284$	−49.0043	−2.90787
$285$	14.2731	0.845467
$286$	−43.0997	−2.54854
$287$	0	0
$288$	0.328612	0.0193636
$289$	−8.97942	−0.528201
$290$	−44.9361	−2.63874
$291$	−27.4357	−1.60831
$292$	−9.81153	−0.574176
$293$	8.79238	0.513656	0.256828	−	0.966457i	$-0.417323\pi$
$293$	8.79238	0.513656	0.256828	+	0.966457i	$0.417323\pi$
$294$	0	0
$295$	−5.55950	−0.323687
$296$	0.234850	0.0136504
$297$	30.6166	1.77655
$298$	−15.3095	−0.886856
$299$	−22.6510	−1.30994
$300$	0.815430	0.0470789
$301$	0	0
$302$	51.9814	2.99120
$303$	−10.8547	−0.623584
$304$	18.2696	1.04783
$305$	−11.9762	−0.685753
$306$	−6.10016	−0.348723
$307$	−25.4509	−1.45256	−0.726281	−	0.687398i	$-0.758753\pi$
$307$	−25.4509	−1.45256	−0.726281	+	0.687398i	$0.758753\pi$
$308$	0	0
$309$	−5.37226	−0.305617
$310$	51.1401	2.90456
$311$	8.20774	0.465418	0.232709	−	0.972546i	$-0.425241\pi$
$311$	8.20774	0.465418	0.232709	+	0.972546i	$0.425241\pi$
$312$	23.6135	1.33685
$313$	−7.84025	−0.443157	−0.221578	−	0.975143i	$-0.571121\pi$
$313$	−7.84025	−0.443157	−0.221578	+	0.975143i	$0.571121\pi$
$314$	50.3508	2.84146
$315$	0	0
$316$	19.9015	1.11955
$317$	32.4359	1.82178	0.910891	−	0.412647i	$-0.135396\pi$
$317$	32.4359	1.82178	0.910891	+	0.412647i	$0.135396\pi$
$318$	−23.0455	−1.29233
$319$	−43.7244	−2.44810
$320$	−17.0810	−0.954855
$321$	−12.5141	−0.698468
$322$	0	0
$323$	−12.2373	−0.680899
$324$	−22.6188	−1.25660
$325$	−0.448512	−0.0248790
$326$	4.01742	0.222504
$327$	−4.25371	−0.235230
$328$	−5.00722	−0.276478
$329$	0	0
$330$	43.9913	2.42164
$331$	13.8576	0.761685	0.380843	−	0.924640i	$-0.375634\pi$
$331$	13.8576	0.761685	0.380843	+	0.924640i	$0.375634\pi$
$332$	6.60553	0.362526
$333$	0.0411144	0.00225305
$334$	−48.7121	−2.66541
$335$	−19.9125	−1.08794
$336$	0	0
$337$	18.6080	1.01364	0.506822	−	0.862050i	$-0.330820\pi$
$337$	18.6080	1.01364	0.506822	+	0.862050i	$0.330820\pi$
$338$	6.20802	0.337672
$339$	−10.2585	−0.557164
$340$	−25.9220	−1.40582
$341$	49.7611	2.69472
$342$	9.30722	0.503277
$343$	0	0
$344$	31.6097	1.70428
$345$	23.1195	1.24471
$346$	−22.8861	−1.23037
$347$	23.3306	1.25245	0.626225	−	0.779642i	$-0.284599\pi$
$347$	23.3306	1.25245	0.626225	+	0.779642i	$0.284599\pi$
$348$	47.4672	2.54451
$349$	5.59571	0.299531	0.149766	−	0.988722i	$-0.452148\pi$
$349$	5.59571	0.299531	0.149766	+	0.988722i	$0.452148\pi$
$350$	0	0
$351$	18.2816	0.975798
$352$	2.03176	0.108293
$353$	19.4280	1.03405	0.517023	−	0.855971i	$-0.327040\pi$
$353$	19.4280	1.03405	0.517023	+	0.855971i	$0.327040\pi$
$354$	8.78150	0.466732
$355$	−27.5114	−1.46016
$356$	−6.80872	−0.360862
$357$	0	0
$358$	42.6221	2.25265
$359$	14.3127	0.755398	0.377699	−	0.925929i	$-0.376715\pi$
$359$	14.3127	0.755398	0.377699	+	0.925929i	$0.376715\pi$
$360$	9.94990	0.524406
$361$	−0.329226	−0.0173277
$362$	24.9048	1.30897
$363$	26.7760	1.40537
$364$	0	0
$365$	−5.50827	−0.288316
$366$	18.9169	0.988804
$367$	21.2458	1.10902	0.554512	−	0.832176i	$-0.312905\pi$
$367$	21.2458	1.10902	0.554512	+	0.832176i	$0.312905\pi$
$368$	29.5929	1.54264
$369$	−0.876597	−0.0456338
$370$	0.261249	0.0135817
$371$	0	0
$372$	−54.0207	−2.80084
$373$	28.2272	1.46155	0.730774	−	0.682620i	$-0.239160\pi$
$373$	28.2272	1.46155	0.730774	+	0.682620i	$0.239160\pi$
$374$	−37.7165	−1.95027
$375$	−16.0583	−0.829249
$376$	26.3604	1.35943
$377$	−26.1084	−1.34465
$378$	0	0
$379$	−8.57635	−0.440538	−0.220269	−	0.975439i	$-0.570693\pi$
$379$	−8.57635	−0.440538	−0.220269	+	0.975439i	$0.570693\pi$
$380$	39.5500	2.02887
$381$	27.8467	1.42663
$382$	−44.7109	−2.28761
$383$	−2.63393	−0.134588	−0.0672938	−	0.997733i	$-0.521436\pi$
$383$	−2.63393	−0.134588	−0.0672938	+	0.997733i	$0.521436\pi$
$384$	28.0727	1.43258
$385$	0	0
$386$	−3.19311	−0.162525
$387$	5.53379	0.281298
$388$	−76.0227	−3.85947
$389$	−13.2656	−0.672595	−0.336298	−	0.941756i	$-0.609175\pi$
$389$	−13.2656	−0.672595	−0.336298	+	0.941756i	$0.609175\pi$
$390$	26.2678	1.33012
$391$	−19.8218	−1.00243
$392$	0	0
$393$	−14.5637	−0.734644
$394$	−13.8752	−0.699025
$395$	11.1729	0.562169
$396$	19.1837	0.964017
$397$	−2.28602	−0.114732	−0.0573661	−	0.998353i	$-0.518270\pi$
$397$	−2.28602	−0.114732	−0.0573661	+	0.998353i	$0.518270\pi$
$398$	−28.2745	−1.41727
$399$	0	0
$400$	0.585970	0.0292985
$401$	2.79191	0.139421	0.0697107	−	0.997567i	$-0.477792\pi$
$401$	2.79191	0.139421	0.0697107	+	0.997567i	$0.477792\pi$
$402$	31.4527	1.56872
$403$	29.7130	1.48011
$404$	−30.0776	−1.49642
$405$	−12.6984	−0.630988
$406$	0	0
$407$	0.254204	0.0126004
$408$	20.6641	1.02302
$409$	10.8769	0.537826	0.268913	−	0.963164i	$-0.413336\pi$
$409$	10.8769	0.537826	0.268913	+	0.963164i	$0.413336\pi$
$410$	−5.57007	−0.275086
$411$	6.79611	0.335227
$412$	−14.8862	−0.733390
$413$	0	0
$414$	15.0757	0.740932
$415$	3.70840	0.182038
$416$	1.21319	0.0594816
$417$	15.1480	0.741803
$418$	57.5452	2.81463
$419$	24.9047	1.21668	0.608338	−	0.793678i	$-0.291836\pi$
$419$	24.9047	1.21668	0.608338	+	0.793678i	$0.291836\pi$
$420$	0	0
$421$	−7.16405	−0.349155	−0.174577	−	0.984643i	$-0.555856\pi$
$421$	−7.16405	−0.349155	−0.174577	+	0.984643i	$0.555856\pi$
$422$	24.3900	1.18729
$423$	4.61483	0.224380
$424$	−32.2276	−1.56511
$425$	−0.392491	−0.0190386
$426$	43.4557	2.10543
$427$	0	0
$428$	−34.6757	−1.67611
$429$	25.5595	1.23402
$430$	35.1628	1.69570
$431$	−14.6538	−0.705850	−0.352925	−	0.935652i	$-0.614813\pi$
$431$	−14.6538	−0.705850	−0.352925	+	0.935652i	$0.614813\pi$
$432$	−23.8844	−1.14914
$433$	29.4173	1.41370	0.706851	−	0.707362i	$-0.250115\pi$
$433$	29.4173	1.41370	0.706851	+	0.707362i	$0.250115\pi$
$434$	0	0
$435$	26.6485	1.27770
$436$	−11.7868	−0.564483
$437$	30.2427	1.44671
$438$	8.70059	0.415730
$439$	−26.5607	−1.26767	−0.633837	−	0.773466i	$-0.718521\pi$
$439$	−26.5607	−1.26767	−0.633837	+	0.773466i	$0.718521\pi$
$440$	61.5188	2.93280
$441$	0	0
$442$	−22.5210	−1.07122
$443$	−12.2373	−0.581409	−0.290705	−	0.956813i	$-0.593890\pi$
$443$	−12.2373	−0.581409	−0.290705	+	0.956813i	$0.593890\pi$
$444$	−0.275964	−0.0130967
$445$	−3.82247	−0.181203
$446$	−29.0518	−1.37564
$447$	9.07902	0.429423
$448$	0	0
$449$	−23.4334	−1.10589	−0.552944	−	0.833218i	$-0.686496\pi$
$449$	−23.4334	−1.10589	−0.552944	+	0.833218i	$0.686496\pi$
$450$	0.298515	0.0140721
$451$	−5.41988	−0.255212
$452$	−28.4256	−1.33703
$453$	−30.8266	−1.44836
$454$	3.93826	0.184832
$455$	0	0
$456$	−31.5278	−1.47643
$457$	−8.25626	−0.386212	−0.193106	−	0.981178i	$-0.561856\pi$
$457$	−8.25626	−0.386212	−0.193106	+	0.981178i	$0.561856\pi$
$458$	−24.4085	−1.14053
$459$	15.9981	0.746729
$460$	64.0627	2.98694
$461$	8.79238	0.409502	0.204751	−	0.978814i	$-0.434362\pi$
$461$	8.79238	0.409502	0.204751	+	0.978814i	$0.434362\pi$
$462$	0	0
$463$	36.8884	1.71435	0.857175	−	0.515025i	$-0.172217\pi$
$463$	36.8884	1.71435	0.857175	+	0.515025i	$0.172217\pi$
$464$	34.1100	1.58352
$465$	−30.3277	−1.40641
$466$	19.4425	0.900655
$467$	21.8803	1.01250	0.506250	−	0.862387i	$-0.331031\pi$
$467$	21.8803	1.01250	0.506250	+	0.862387i	$0.331031\pi$
$468$	11.4549	0.529501
$469$	0	0
$470$	29.3235	1.35259
$471$	−29.8596	−1.37586
$472$	12.2803	0.565249
$473$	34.2147	1.57319
$474$	−17.6481	−0.810605
$475$	0.598837	0.0274765
$476$	0	0
$477$	−5.64197	−0.258328
$478$	−66.8093	−3.05579
$479$	−34.3678	−1.57030	−0.785152	−	0.619303i	$-0.787415\pi$
$479$	−34.3678	−1.57030	−0.785152	+	0.619303i	$0.787415\pi$
$480$	−1.23829	−0.0565198
$481$	0.151789	0.00692098
$482$	47.6729	2.17144
$483$	0	0
$484$	74.1945	3.37248
$485$	−42.6798	−1.93799
$486$	−21.5838	−0.979062
$487$	15.9585	0.723146	0.361573	−	0.932344i	$-0.382240\pi$
$487$	15.9585	0.723146	0.361573	+	0.932344i	$0.382240\pi$
$488$	26.4541	1.19752
$489$	−2.38246	−0.107738
$490$	0	0
$491$	−1.69863	−0.0766581	−0.0383290	−	0.999265i	$-0.512204\pi$
$491$	−1.69863	−0.0766581	−0.0383290	+	0.999265i	$0.512204\pi$
$492$	5.88382	0.265263
$493$	−22.8474	−1.02900
$494$	34.3611	1.54598
$495$	10.7699	0.484071
$496$	−38.8194	−1.74304
$497$	0	0
$498$	−5.85760	−0.262485
$499$	−23.0520	−1.03195	−0.515975	−	0.856604i	$-0.672570\pi$
$499$	−23.0520	−1.03195	−0.515975	+	0.856604i	$0.672570\pi$
$500$	−44.4967	−1.98995
$501$	28.8878	1.29061
$502$	67.4982	3.01259
$503$	−34.6937	−1.54692	−0.773458	−	0.633848i	$-0.781474\pi$
$503$	−34.6937	−1.54692	−0.773458	+	0.633848i	$0.781474\pi$
$504$	0	0
$505$	−16.8858	−0.751409
$506$	93.2112	4.14374
$507$	−3.68155	−0.163503
$508$	77.1615	3.42349
$509$	7.41125	0.328498	0.164249	−	0.986419i	$-0.447480\pi$
$509$	7.41125	0.328498	0.164249	+	0.986419i	$0.447480\pi$
$510$	22.9869	1.01788
$511$	0	0
$512$	40.7573	1.80124
$513$	−24.4089	−1.07768
$514$	53.1560	2.34461
$515$	−8.35723	−0.368264
$516$	−37.1434	−1.63515
$517$	28.5328	1.25487
$518$	0	0
$519$	13.5722	0.595753
$520$	36.7337	1.61088
$521$	24.2278	1.06144	0.530719	−	0.847548i	$-0.321922\pi$
$521$	24.2278	1.06144	0.530719	+	0.847548i	$0.321922\pi$
$522$	17.3769	0.760567
$523$	43.3265	1.89454	0.947268	−	0.320442i	$-0.103831\pi$
$523$	43.3265	1.89454	0.947268	+	0.320442i	$0.103831\pi$
$524$	−40.3552	−1.76293
$525$	0	0
$526$	24.1906	1.05476
$527$	26.0018	1.13266
$528$	−33.3929	−1.45324
$529$	25.9869	1.12987
$530$	−35.8502	−1.55723
$531$	2.14988	0.0932968
$532$	0	0
$533$	−3.23628	−0.140179
$534$	6.03778	0.261280
$535$	−19.4672	−0.841643
$536$	43.9846	1.89984
$537$	−25.2762	−1.09075
$538$	−64.0410	−2.76100
$539$	0	0
$540$	−51.7049	−2.22503
$541$	−12.7180	−0.546788	−0.273394	−	0.961902i	$-0.588146\pi$
$541$	−12.7180	−0.546788	−0.273394	+	0.961902i	$0.588146\pi$
$542$	62.5370	2.68620
$543$	−14.7693	−0.633812
$544$	1.06166	0.0455183
$545$	−6.61718	−0.283449
$546$	0	0
$547$	−4.71489	−0.201594	−0.100797	−	0.994907i	$-0.532139\pi$
$547$	−4.71489	−0.201594	−0.100797	+	0.994907i	$0.532139\pi$
$548$	18.8316	0.804446
$549$	4.63122	0.197656
$550$	1.84568	0.0786999
$551$	34.8590	1.48504
$552$	−51.0685	−2.17362
$553$	0	0
$554$	−72.1623	−3.06588
$555$	−0.154929	−0.00657636
$556$	41.9743	1.78011
$557$	−11.0756	−0.469288	−0.234644	−	0.972081i	$-0.575392\pi$
$557$	−11.0756	−0.469288	−0.234644	+	0.972081i	$0.575392\pi$
$558$	−19.7760	−0.837187
$559$	20.4301	0.864099
$560$	0	0
$561$	22.3670	0.944337
$562$	−59.4935	−2.50958
$563$	−24.9735	−1.05251	−0.526255	−	0.850327i	$-0.676404\pi$
$563$	−24.9735	−1.05251	−0.526255	+	0.850327i	$0.676404\pi$
$564$	−30.9752	−1.30429
$565$	−15.9584	−0.671374
$566$	21.8997	0.920515
$567$	0	0
$568$	60.7698	2.54985
$569$	3.14116	0.131684	0.0658422	−	0.997830i	$-0.479027\pi$
$569$	3.14116	0.131684	0.0658422	+	0.997830i	$0.479027\pi$
$570$	−35.0718	−1.46900
$571$	7.13418	0.298556	0.149278	−	0.988795i	$-0.452305\pi$
$571$	7.13418	0.298556	0.149278	+	0.988795i	$0.452305\pi$
$572$	70.8238	2.96129
$573$	26.5150	1.10768
$574$	0	0
$575$	0.969990	0.0404514
$576$	6.60527	0.275219
$577$	−4.41995	−0.184005	−0.0920024	−	0.995759i	$-0.529327\pi$
$577$	−4.41995	−0.184005	−0.0920024	+	0.995759i	$0.529327\pi$
$578$	22.0642	0.917748
$579$	1.89361	0.0786959
$580$	73.8413	3.06609
$581$	0	0
$582$	67.4148	2.79443
$583$	−34.8835	−1.44473
$584$	12.1672	0.503482
$585$	6.43085	0.265883
$586$	−21.6046	−0.892476
$587$	−29.7123	−1.22636	−0.613178	−	0.789944i	$-0.710109\pi$
$587$	−29.7123	−1.22636	−0.613178	+	0.789944i	$0.710109\pi$
$588$	0	0
$589$	−39.6718	−1.63465
$590$	13.6608	0.562404
$591$	8.22845	0.338473
$592$	−0.198309	−0.00815044
$593$	14.3020	0.587315	0.293657	−	0.955911i	$-0.405128\pi$
$593$	14.3020	0.587315	0.293657	+	0.955911i	$0.405128\pi$
$594$	−75.2307	−3.08675
$595$	0	0
$596$	25.1574	1.03049
$597$	16.7677	0.686255
$598$	55.6577	2.27601
$599$	38.6159	1.57780	0.788902	−	0.614518i	$-0.210650\pi$
$599$	38.6159	1.57780	0.788902	+	0.614518i	$0.210650\pi$
$600$	−1.01121	−0.0412824
$601$	−2.04839	−0.0835557	−0.0417779	−	0.999127i	$-0.513302\pi$
$601$	−2.04839	−0.0835557	−0.0417779	+	0.999127i	$0.513302\pi$
$602$	0	0
$603$	7.70022	0.313577
$604$	−85.4186	−3.47563
$605$	41.6534	1.69345
$606$	26.6720	1.08347
$607$	−5.79770	−0.235321	−0.117661	−	0.993054i	$-0.537540\pi$
$607$	−5.79770	−0.235321	−0.117661	+	0.993054i	$0.537540\pi$
$608$	−1.61981	−0.0656920
$609$	0	0
$610$	29.4277	1.19149
$611$	17.0373	0.689257
$612$	10.0241	0.405201
$613$	45.3061	1.82989	0.914947	−	0.403573i	$-0.132232\pi$
$613$	45.3061	1.82989	0.914947	+	0.403573i	$0.132232\pi$
$614$	62.5378	2.52382
$615$	3.30322	0.133199
$616$	0	0
$617$	−22.8349	−0.919300	−0.459650	−	0.888100i	$-0.652025\pi$
$617$	−22.8349	−0.919300	−0.459650	+	0.888100i	$0.652025\pi$
$618$	13.2007	0.531008
$619$	−15.2514	−0.613007	−0.306503	−	0.951870i	$-0.599159\pi$
$619$	−15.2514	−0.613007	−0.306503	+	0.951870i	$0.599159\pi$
$620$	−84.0360	−3.37497
$621$	−39.5373	−1.58658
$622$	−20.1680	−0.808662
$623$	0	0
$624$	−19.9393	−0.798213
$625$	−25.6737	−1.02695
$626$	19.2650	0.769983
$627$	−34.1261	−1.36287
$628$	−82.7390	−3.30165
$629$	0.132830	0.00529628
$630$	0	0
$631$	−40.2426	−1.60203	−0.801016	−	0.598643i	$-0.795707\pi$
$631$	−40.2426	−1.60203	−0.801016	+	0.598643i	$0.795707\pi$
$632$	−24.6797	−0.981706
$633$	−14.4640	−0.574894
$634$	−79.7012	−3.16534
$635$	43.3191	1.71907
$636$	37.8695	1.50162
$637$	0	0
$638$	107.439	4.25355
$639$	10.6388	0.420863
$640$	43.6707	1.72624
$641$	8.41075	0.332205	0.166102	−	0.986109i	$-0.446882\pi$
$641$	8.41075	0.332205	0.166102	+	0.986109i	$0.446882\pi$
$642$	30.7495	1.21358
$643$	23.9146	0.943101	0.471550	−	0.881839i	$-0.343695\pi$
$643$	23.9146	0.943101	0.471550	+	0.881839i	$0.343695\pi$
$644$	0	0
$645$	−20.8526	−0.821072
$646$	30.0693	1.18306
$647$	−10.9669	−0.431152	−0.215576	−	0.976487i	$-0.569163\pi$
$647$	−10.9669	−0.431152	−0.215576	+	0.976487i	$0.569163\pi$
$648$	28.0494	1.10188
$649$	13.2924	0.521772
$650$	1.10208	0.0432271
$651$	0	0
$652$	−6.60164	−0.258540
$653$	29.3523	1.14865	0.574323	−	0.818629i	$-0.305265\pi$
$653$	29.3523	1.14865	0.574323	+	0.818629i	$0.305265\pi$
$654$	10.4522	0.408712
$655$	−22.6558	−0.885234
$656$	4.22813	0.165081
$657$	2.13007	0.0831019
$658$	0	0
$659$	−12.7905	−0.498245	−0.249123	−	0.968472i	$-0.580142\pi$
$659$	−12.7905	−0.498245	−0.249123	+	0.968472i	$0.580142\pi$
$660$	−72.2887	−2.81383
$661$	−15.1159	−0.587942	−0.293971	−	0.955814i	$-0.594977\pi$
$661$	−15.1159	−0.587942	−0.293971	+	0.955814i	$0.594977\pi$
$662$	−34.0509	−1.32342
$663$	13.3557	0.518691
$664$	−8.19146	−0.317890
$665$	0	0
$666$	−0.101026	−0.00391467
$667$	56.4643	2.18631
$668$	80.0463	3.09708
$669$	17.2286	0.666096
$670$	48.9288	1.89028
$671$	28.6342	1.10541
$672$	0	0
$673$	10.3101	0.397425	0.198713	−	0.980058i	$-0.436324\pi$
$673$	10.3101	0.397425	0.198713	+	0.980058i	$0.436324\pi$
$674$	−45.7235	−1.76120
$675$	−0.782878	−0.0301330
$676$	−10.2013	−0.392359
$677$	1.97105	0.0757535	0.0378768	−	0.999282i	$-0.487941\pi$
$677$	1.97105	0.0757535	0.0378768	+	0.999282i	$0.487941\pi$
$678$	25.2070	0.968070
$679$	0	0
$680$	32.1456	1.23273
$681$	−2.33551	−0.0894970
$682$	−122.273	−4.68206
$683$	−9.53970	−0.365026	−0.182513	−	0.983203i	$-0.558423\pi$
$683$	−9.53970	−0.365026	−0.182513	+	0.983203i	$0.558423\pi$
$684$	−15.2941	−0.584785
$685$	10.5722	0.403944
$686$	0	0
$687$	14.4750	0.552255
$688$	−26.6914	−1.01760
$689$	−20.8294	−0.793538
$690$	−56.8090	−2.16268
$691$	−16.3915	−0.623562	−0.311781	−	0.950154i	$-0.600925\pi$
$691$	−16.3915	−0.623562	−0.311781	+	0.950154i	$0.600925\pi$
$692$	37.6077	1.42963
$693$	0	0
$694$	−57.3276	−2.17613
$695$	23.5647	0.893861
$696$	−58.8637	−2.23122
$697$	−2.83206	−0.107272
$698$	−13.7497	−0.520434
$699$	−11.5300	−0.436104
$700$	0	0
$701$	12.1383	0.458457	0.229229	−	0.973373i	$-0.426380\pi$
$701$	12.1383	0.458457	0.229229	+	0.973373i	$0.426380\pi$
$702$	−44.9213	−1.69544
$703$	−0.202663	−0.00764359
$704$	40.8394	1.53919
$705$	−17.3898	−0.654936
$706$	−47.7382	−1.79665
$707$	0	0
$708$	−14.4302	−0.542321
$709$	−29.6150	−1.11222	−0.556108	−	0.831110i	$-0.687706\pi$
$709$	−29.6150	−1.11222	−0.556108	+	0.831110i	$0.687706\pi$
$710$	67.6008	2.53701
$711$	−4.32059	−0.162035
$712$	8.44344	0.316431
$713$	−64.2600	−2.40656
$714$	0	0
$715$	39.7611	1.48698
$716$	−70.0388	−2.61747
$717$	39.6200	1.47964
$718$	−35.1691	−1.31250
$719$	−42.0273	−1.56735	−0.783676	−	0.621169i	$-0.786658\pi$
$719$	−42.0273	−1.56735	−0.783676	+	0.621169i	$0.786658\pi$
$720$	−8.40175	−0.313115
$721$	0	0
$722$	0.808971	0.0301068
$723$	−28.2715	−1.05143
$724$	−40.9249	−1.52096
$725$	1.11805	0.0415234
$726$	−65.7936	−2.44183
$727$	41.0718	1.52327	0.761635	−	0.648007i	$-0.224397\pi$
$727$	41.0718	1.52327	0.761635	+	0.648007i	$0.224397\pi$
$728$	0	0
$729$	29.6052	1.09649
$730$	13.5349	0.500948
$731$	17.8783	0.661252
$732$	−31.0853	−1.14895
$733$	−9.51418	−0.351414	−0.175707	−	0.984442i	$-0.556221\pi$
$733$	−9.51418	−0.351414	−0.175707	+	0.984442i	$0.556221\pi$
$734$	−52.2051	−1.92693
$735$	0	0
$736$	−2.62375	−0.0967128
$737$	47.6094	1.75372
$738$	2.15397	0.0792886
$739$	−45.4606	−1.67230	−0.836148	−	0.548504i	$-0.815197\pi$
$739$	−45.4606	−1.67230	−0.836148	+	0.548504i	$0.815197\pi$
$740$	−0.429298	−0.0157813
$741$	−20.3772	−0.748574
$742$	0	0
$743$	−51.1920	−1.87805	−0.939027	−	0.343845i	$-0.888271\pi$
$743$	−51.1920	−1.87805	−0.939027	+	0.343845i	$0.888271\pi$
$744$	66.9906	2.45599
$745$	14.1236	0.517448
$746$	−69.3595	−2.53943
$747$	−1.43405	−0.0524692
$748$	61.9777	2.26613
$749$	0	0
$750$	39.4584	1.44082
$751$	−32.2359	−1.17631	−0.588153	−	0.808750i	$-0.700145\pi$
$751$	−32.2359	−1.17631	−0.588153	+	0.808750i	$0.700145\pi$
$752$	−22.2589	−0.811698
$753$	−40.0285	−1.45872
$754$	64.1534	2.33633
$755$	−47.9547	−1.74525
$756$	0	0
$757$	−26.3465	−0.957581	−0.478790	−	0.877929i	$-0.658925\pi$
$757$	−26.3465	−0.957581	−0.478790	+	0.877929i	$0.658925\pi$
$758$	21.0737	0.765432
$759$	−55.2772	−2.00643
$760$	−49.0456	−1.77907
$761$	30.0811	1.09044	0.545219	−	0.838293i	$-0.316446\pi$
$761$	30.0811	1.09044	0.545219	+	0.838293i	$0.316446\pi$
$762$	−68.4246	−2.47876
$763$	0	0
$764$	73.4713	2.65810
$765$	5.62762	0.203467
$766$	6.47207	0.233845
$767$	7.93707	0.286591
$768$	−47.0198	−1.69668
$769$	0.608700	0.0219503	0.0109751	−	0.999940i	$-0.496506\pi$
$769$	0.608700	0.0219503	0.0109751	+	0.999940i	$0.496506\pi$
$770$	0	0
$771$	−31.5232	−1.13528
$772$	5.24708	0.188847
$773$	8.67944	0.312178	0.156089	−	0.987743i	$-0.450111\pi$
$773$	8.67944	0.312178	0.156089	+	0.987743i	$0.450111\pi$
$774$	−13.5976	−0.488755
$775$	−1.27241	−0.0457064
$776$	94.2751	3.38428
$777$	0	0
$778$	32.5962	1.16863
$779$	4.32097	0.154815
$780$	−43.1646	−1.54554
$781$	65.7780	2.35372
$782$	48.7059	1.74172
$783$	−45.5723	−1.62862
$784$	0	0
$785$	−46.4504	−1.65789
$786$	35.7859	1.27644
$787$	−34.2640	−1.22138	−0.610689	−	0.791870i	$-0.709108\pi$
$787$	−34.2640	−1.22138	−0.610689	+	0.791870i	$0.709108\pi$
$788$	22.8005	0.812235
$789$	−14.3458	−0.510723
$790$	−27.4539	−0.976766
$791$	0	0
$792$	−23.7895	−0.845325
$793$	17.0979	0.607164
$794$	5.61719	0.199347
$795$	21.2603	0.754024
$796$	46.4622	1.64681
$797$	−13.1568	−0.466036	−0.233018	−	0.972472i	$-0.574860\pi$
$797$	−13.1568	−0.466036	−0.233018	+	0.972472i	$0.574860\pi$
$798$	0	0
$799$	14.9093	0.527454
$800$	−0.0519530	−0.00183681
$801$	1.47816	0.0522283
$802$	−6.86026	−0.242244
$803$	13.1699	0.464756
$804$	−51.6848	−1.82278
$805$	0	0
$806$	−73.0106	−2.57169
$807$	37.9783	1.33690
$808$	37.2990	1.31217
$809$	−2.04798	−0.0720033	−0.0360017	−	0.999352i	$-0.511462\pi$
$809$	−2.04798	−0.0720033	−0.0360017	+	0.999352i	$0.511462\pi$
$810$	31.2023	1.09634
$811$	−5.48050	−0.192446	−0.0962232	−	0.995360i	$-0.530676\pi$
$811$	−5.48050	−0.192446	−0.0962232	+	0.995360i	$0.530676\pi$
$812$	0	0
$813$	−37.0864	−1.30068
$814$	−0.624629	−0.0218932
$815$	−3.70622	−0.129823
$816$	−17.4489	−0.610832
$817$	−27.2775	−0.954318
$818$	−26.7265	−0.934471
$819$	0	0
$820$	9.15303	0.319638
$821$	−1.55848	−0.0543913	−0.0271957	−	0.999630i	$-0.508658\pi$
$821$	−1.55848	−0.0543913	−0.0271957	+	0.999630i	$0.508658\pi$
$822$	−16.6993	−0.582456
$823$	39.3703	1.37236	0.686182	−	0.727430i	$-0.259286\pi$
$823$	39.3703	1.37236	0.686182	+	0.727430i	$0.259286\pi$
$824$	18.4602	0.643093
$825$	−1.09454	−0.0381071
$826$	0	0
$827$	−26.3888	−0.917628	−0.458814	−	0.888532i	$-0.651726\pi$
$827$	−26.3888	−0.917628	−0.458814	+	0.888532i	$0.651726\pi$
$828$	−24.7733	−0.860930
$829$	−45.0610	−1.56503	−0.782517	−	0.622629i	$-0.786065\pi$
$829$	−45.0610	−1.56503	−0.782517	+	0.622629i	$0.786065\pi$
$830$	−9.11224	−0.316291
$831$	42.7945	1.48452
$832$	24.3858	0.845425
$833$	0	0
$834$	−37.2216	−1.28888
$835$	44.9387	1.55517
$836$	−94.5613	−3.27047
$837$	51.8642	1.79269
$838$	−61.1957	−2.11397
$839$	42.0761	1.45263	0.726314	−	0.687363i	$-0.241232\pi$
$839$	42.0761	1.45263	0.726314	+	0.687363i	$0.241232\pi$
$840$	0	0
$841$	36.0831	1.24425
$842$	17.6034	0.606655
$843$	35.2815	1.21516
$844$	−40.0790	−1.37958
$845$	−5.72712	−0.197019
$846$	−11.3395	−0.389860
$847$	0	0
$848$	27.2131	0.934503
$849$	−12.9872	−0.445720
$850$	0.964426	0.0330795
$851$	−0.328272	−0.0112530
$852$	−71.4086	−2.44642
$853$	20.2803	0.694384	0.347192	−	0.937794i	$-0.387135\pi$
$853$	20.2803	0.694384	0.347192	+	0.937794i	$0.387135\pi$
$854$	0	0
$855$	−8.58624	−0.293643
$856$	43.0011	1.46975
$857$	49.2604	1.68270	0.841351	−	0.540490i	$-0.181761\pi$
$857$	49.2604	1.68270	0.841351	+	0.540490i	$0.181761\pi$
$858$	−62.8045	−2.14411
$859$	12.7326	0.434430	0.217215	−	0.976124i	$-0.430303\pi$
$859$	12.7326	0.434430	0.217215	+	0.976124i	$0.430303\pi$
$860$	−57.7814	−1.97033
$861$	0	0
$862$	36.0072	1.22641
$863$	−14.7535	−0.502216	−0.251108	−	0.967959i	$-0.580795\pi$
$863$	−14.7535	−0.502216	−0.251108	+	0.967959i	$0.580795\pi$
$864$	2.11763	0.0720432
$865$	21.1133	0.717872
$866$	−72.2838	−2.45630
$867$	−13.0847	−0.444381
$868$	0	0
$869$	−26.7136	−0.906197
$870$	−65.4804	−2.21999
$871$	28.4282	0.963254
$872$	14.6167	0.494982
$873$	16.5044	0.558590
$874$	−74.3122	−2.51365
$875$	0	0
$876$	−14.2973	−0.483060
$877$	−20.7432	−0.700450	−0.350225	−	0.936666i	$-0.613895\pi$
$877$	−20.7432	−0.700450	−0.350225	+	0.936666i	$0.613895\pi$
$878$	65.2648	2.20258
$879$	12.8122	0.432144
$880$	−51.9469	−1.75113
$881$	19.5041	0.657110	0.328555	−	0.944485i	$-0.393438\pi$
$881$	19.5041	0.657110	0.328555	+	0.944485i	$0.393438\pi$
$882$	0	0
$883$	27.7626	0.934286	0.467143	−	0.884182i	$-0.345283\pi$
$883$	27.7626	0.934286	0.467143	+	0.884182i	$0.345283\pi$
$884$	37.0077	1.24470
$885$	−8.10125	−0.272321
$886$	30.0693	1.01020
$887$	−35.3228	−1.18602	−0.593012	−	0.805194i	$-0.702061\pi$
$887$	−35.3228	−1.18602	−0.593012	+	0.805194i	$0.702061\pi$
$888$	0.342221	0.0114842
$889$	0	0
$890$	9.39254	0.314839
$891$	30.3610	1.01713
$892$	47.7394	1.59843
$893$	−22.7476	−0.761221
$894$	−22.3089	−0.746120
$895$	−39.3204	−1.31434
$896$	0	0
$897$	−33.0068	−1.10206
$898$	57.5802	1.92148
$899$	−74.0687	−2.47033
$900$	−0.490535	−0.0163512
$901$	−18.2278	−0.607255
$902$	13.3177	0.443430
$903$	0	0
$904$	35.2503	1.17241
$905$	−22.9756	−0.763734
$906$	75.7469	2.51652
$907$	10.5803	0.351312	0.175656	−	0.984452i	$-0.443795\pi$
$907$	10.5803	0.351312	0.175656	+	0.984452i	$0.443795\pi$
$908$	−6.47156	−0.214766
$909$	6.52980	0.216580
$910$	0	0
$911$	−18.0853	−0.599192	−0.299596	−	0.954066i	$-0.596852\pi$
$911$	−18.0853	−0.599192	−0.299596	+	0.954066i	$0.596852\pi$
$912$	26.6223	0.881552
$913$	−8.86654	−0.293440
$914$	20.2872	0.671041
$915$	−17.4516	−0.576930
$916$	40.1093	1.32525
$917$	0	0
$918$	−39.3105	−1.29744
$919$	9.90775	0.326826	0.163413	−	0.986558i	$-0.447750\pi$
$919$	9.90775	0.326826	0.163413	+	0.986558i	$0.447750\pi$
$920$	−79.4436	−2.61918
$921$	−37.0869	−1.22205
$922$	−21.6046	−0.711508
$923$	39.2770	1.29282
$924$	0	0
$925$	−0.00650012	−0.000213722 0
$926$	−90.6419	−2.97868
$927$	3.23177	0.106145
$928$	−3.02425	−0.0992757
$929$	15.2665	0.500878	0.250439	−	0.968132i	$-0.419425\pi$
$929$	15.2665	0.500878	0.250439	+	0.968132i	$0.419425\pi$
$930$	74.5208	2.44363
$931$	0	0
$932$	−31.9489	−1.04652
$933$	11.9602	0.391561
$934$	−53.7641	−1.75921
$935$	34.7948	1.13791
$936$	−14.2051	−0.464307
$937$	−21.2126	−0.692985	−0.346492	−	0.938053i	$-0.612627\pi$
$937$	−21.2126	−0.692985	−0.346492	+	0.938053i	$0.612627\pi$
$938$	0	0
$939$	−11.4247	−0.372832
$940$	−48.1859	−1.57165
$941$	34.1282	1.11255	0.556274	−	0.830999i	$-0.312230\pi$
$941$	34.1282	1.11255	0.556274	+	0.830999i	$0.312230\pi$
$942$	73.3707	2.39055
$943$	6.99907	0.227921
$944$	−10.3696	−0.337502
$945$	0	0
$946$	−84.0720	−2.73342
$947$	−18.3584	−0.596567	−0.298284	−	0.954477i	$-0.596414\pi$
$947$	−18.3584	−0.596567	−0.298284	+	0.954477i	$0.596414\pi$
$948$	29.0003	0.941886
$949$	7.86394	0.255274
$950$	−1.47146	−0.0477403
$951$	47.2653	1.53268
$952$	0	0
$953$	−16.0790	−0.520849	−0.260424	−	0.965494i	$-0.583862\pi$
$953$	−16.0790	−0.520849	−0.260424	+	0.965494i	$0.583862\pi$
$954$	13.8634	0.448844
$955$	41.2474	1.33473
$956$	109.785	3.55069
$957$	−63.7147	−2.05960
$958$	84.4482	2.72840
$959$	0	0
$960$	−24.8902	−0.803328
$961$	53.2949	1.71919
$962$	−0.372974	−0.0120252
$963$	7.52805	0.242588
$964$	−78.3386	−2.52312
$965$	2.94576	0.0948273
$966$	0	0
$967$	38.0340	1.22309	0.611546	−	0.791209i	$-0.290548\pi$
$967$	38.0340	1.22309	0.611546	+	0.791209i	$0.290548\pi$
$968$	−92.0080	−2.95725
$969$	−17.8320	−0.572847
$970$	104.872	3.36725
$971$	−60.7488	−1.94952	−0.974761	−	0.223250i	$-0.928333\pi$
$971$	−60.7488	−1.94952	−0.974761	+	0.223250i	$0.928333\pi$
$972$	35.4677	1.13763
$973$	0	0
$974$	−39.2129	−1.25646
$975$	−0.653567	−0.0209309
$976$	−22.3380	−0.715021
$977$	−4.23580	−0.135515	−0.0677576	−	0.997702i	$-0.521584\pi$
$977$	−4.23580	−0.135515	−0.0677576	+	0.997702i	$0.521584\pi$
$978$	5.85415	0.187195
$979$	9.13928	0.292093
$980$	0	0
$981$	2.55889	0.0816990
$982$	4.17386	0.133193
$983$	7.21490	0.230120	0.115060	−	0.993359i	$-0.463294\pi$
$983$	7.21490	0.230120	0.115060	+	0.993359i	$0.463294\pi$
$984$	−7.29647	−0.232603
$985$	12.8004	0.407855
$986$	56.1404	1.78788
$987$	0	0
$988$	−56.4639	−1.79636
$989$	−44.1838	−1.40496
$990$	−26.4637	−0.841071
$991$	−20.9196	−0.664533	−0.332267	−	0.943186i	$-0.607813\pi$
$991$	−20.9196	−0.664533	−0.332267	+	0.943186i	$0.607813\pi$
$992$	3.44178	0.109277
$993$	20.1932	0.640813
$994$	0	0
$995$	26.0843	0.826927
$996$	9.62551	0.304996
$997$	18.4455	0.584175	0.292088	−	0.956392i	$-0.405650\pi$
$997$	18.4455	0.584175	0.292088	+	0.956392i	$0.405650\pi$
$998$	56.6432	1.79301
$999$	0.264948	0.00838258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.n.1.1		5
7.6	odd	2		287.2.a.e.1.1	✓	5
21.20	even	2		2583.2.a.r.1.5		5
28.27	even	2		4592.2.a.bb.1.5		5
35.34	odd	2		7175.2.a.n.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.e.1.1	✓	5	7.6	odd	2
2009.2.a.n.1.1		5	1.1	even	1	trivial
2583.2.a.r.1.5		5	21.20	even	2
4592.2.a.bb.1.5		5	28.27	even	2
7175.2.a.n.1.5		5	35.34	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)

\(f(q)\)	\(=\)	\(q-2.45719 q^{2} +1.45719 q^{3} +4.03778 q^{4} +2.26685 q^{5} -3.58059 q^{6} -5.00722 q^{8} -0.876597 q^{9} +O(q^{10})\)	\(q-2.45719 q^{2} +1.45719 q^{3} +4.03778 q^{4} +2.26685 q^{5} -3.58059 q^{6} -5.00722 q^{8} -0.876597 q^{9} -5.57007 q^{10} -5.41988 q^{11} +5.88382 q^{12} -3.23628 q^{13} +3.30322 q^{15} +4.22813 q^{16} -2.83206 q^{17} +2.15397 q^{18} +4.32097 q^{19} +9.15303 q^{20} +13.3177 q^{22} +6.99907 q^{23} -7.29647 q^{24} +0.138589 q^{25} +7.95216 q^{26} -5.64894 q^{27} +8.06741 q^{29} -8.11665 q^{30} -9.18123 q^{31} -0.374872 q^{32} -7.89779 q^{33} +6.95892 q^{34} -3.53951 q^{36} -0.0469023 q^{37} -10.6174 q^{38} -4.71588 q^{39} -11.3506 q^{40} +1.00000 q^{41} -6.31281 q^{43} -21.8843 q^{44} -1.98711 q^{45} -17.1980 q^{46} -5.26448 q^{47} +6.16119 q^{48} -0.340538 q^{50} -4.12685 q^{51} -13.0674 q^{52} +6.43622 q^{53} +13.8805 q^{54} -12.2860 q^{55} +6.29647 q^{57} -19.8232 q^{58} -2.45253 q^{59} +13.3377 q^{60} -5.28319 q^{61} +22.5600 q^{62} -7.53512 q^{64} -7.33615 q^{65} +19.4064 q^{66} -8.78423 q^{67} -11.4353 q^{68} +10.1990 q^{69} -12.1364 q^{71} +4.38931 q^{72} -2.42993 q^{73} +0.115248 q^{74} +0.201950 q^{75} +17.4471 q^{76} +11.5878 q^{78} +4.92882 q^{79} +9.58451 q^{80} -5.60179 q^{81} -2.45719 q^{82} +1.63593 q^{83} -6.41985 q^{85} +15.5118 q^{86} +11.7558 q^{87} +27.1385 q^{88} -1.68625 q^{89} +4.88271 q^{90} +28.2607 q^{92} -13.3788 q^{93} +12.9358 q^{94} +9.79497 q^{95} -0.546260 q^{96} -18.8278 q^{97} +4.75105 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9}+O(q^{10}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9} + 2 q^{11} + 2 q^{12} - 5 q^{13} - 5 q^{15} - q^{16} - 13 q^{17} + 21 q^{18} + 23 q^{20} + q^{22} + 2 q^{23} - 2 q^{24} + 22 q^{25} - 10 q^{27} - 5 q^{29} - 33 q^{30} - 17 q^{31} - 12 q^{32} - 3 q^{33} + 8 q^{34} + 15 q^{36} - 7 q^{37} + 3 q^{38} + 5 q^{39} - 7 q^{40} + 5 q^{41} + q^{43} - 47 q^{44} + 23 q^{45} - 24 q^{46} - 9 q^{47} + 19 q^{48} + 2 q^{50} + 5 q^{51} - 20 q^{52} + 5 q^{53} - 2 q^{54} - 33 q^{55} - 3 q^{57} - 27 q^{58} - 7 q^{59} - 16 q^{60} - 22 q^{61} + 28 q^{62} - 3 q^{64} - 31 q^{65} + 42 q^{66} - 3 q^{67} - 17 q^{68} + 22 q^{69} - 24 q^{71} - 12 q^{72} - 40 q^{73} - 5 q^{74} - 24 q^{75} + 19 q^{76} + 30 q^{78} - 42 q^{79} - 24 q^{80} + 9 q^{81} - q^{82} + 12 q^{83} - 23 q^{85} + 16 q^{86} + 32 q^{87} + 26 q^{88} - 8 q^{89} + 59 q^{90} + 12 q^{92} - 11 q^{93} + 23 q^{94} - 17 q^{95} + 17 q^{96} - 16 q^{97} - 45 q^{99}+O(q^{100}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9 + 2 * q^11 + 2 * q^12 - 5 * q^13 - 5 * q^15 - q^16 - 13 * q^17 + 21 * q^18 + 23 * q^20 + q^22 + 2 * q^23 - 2 * q^24 + 22 * q^25 - 10 * q^27 - 5 * q^29 - 33 * q^30 - 17 * q^31 - 12 * q^32 - 3 * q^33 + 8 * q^34 + 15 * q^36 - 7 * q^37 + 3 * q^38 + 5 * q^39 - 7 * q^40 + 5 * q^41 + q^43 - 47 * q^44 + 23 * q^45 - 24 * q^46 - 9 * q^47 + 19 * q^48 + 2 * q^50 + 5 * q^51 - 20 * q^52 + 5 * q^53 - 2 * q^54 - 33 * q^55 - 3 * q^57 - 27 * q^58 - 7 * q^59 - 16 * q^60 - 22 * q^61 + 28 * q^62 - 3 * q^64 - 31 * q^65 + 42 * q^66 - 3 * q^67 - 17 * q^68 + 22 * q^69 - 24 * q^71 - 12 * q^72 - 40 * q^73 - 5 * q^74 - 24 * q^75 + 19 * q^76 + 30 * q^78 - 42 * q^79 - 24 * q^80 + 9 * q^81 - q^82 + 12 * q^83 - 23 * q^85 + 16 * q^86 + 32 * q^87 + 26 * q^88 - 8 * q^89 + 59 * q^90 + 12 * q^92 - 11 * q^93 + 23 * q^94 - 17 * q^95 + 17 * q^96 - 16 * q^97 - 45 * q^99

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