LMFDB - Embedded newform 2009.2.a.u.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.7
Root			$0.979921$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.979921 q^{2} +1.94904 q^{3} -1.03976 q^{4} +1.73965 q^{5} -1.90990 q^{6} +2.97872 q^{8} +0.798739 q^{9} +O(q^{10})$	\(q-0.979921 q^{2} +1.94904 q^{3} -1.03976 q^{4} +1.73965 q^{5} -1.90990 q^{6} +2.97872 q^{8} +0.798739 q^{9} -1.70472 q^{10} -0.677386 q^{11} -2.02652 q^{12} +1.88536 q^{13} +3.39064 q^{15} -0.839397 q^{16} +3.26016 q^{17} -0.782701 q^{18} +1.13591 q^{19} -1.80881 q^{20} +0.663784 q^{22} +5.51242 q^{23} +5.80563 q^{24} -1.97361 q^{25} -1.84751 q^{26} -4.29034 q^{27} +4.66436 q^{29} -3.32256 q^{30} -5.77725 q^{31} -5.13490 q^{32} -1.32025 q^{33} -3.19470 q^{34} -0.830493 q^{36} +1.70719 q^{37} -1.11310 q^{38} +3.67464 q^{39} +5.18193 q^{40} +1.00000 q^{41} +10.4114 q^{43} +0.704315 q^{44} +1.38953 q^{45} -5.40173 q^{46} +1.55033 q^{47} -1.63601 q^{48} +1.93398 q^{50} +6.35417 q^{51} -1.96032 q^{52} +3.87319 q^{53} +4.20419 q^{54} -1.17842 q^{55} +2.21393 q^{57} -4.57070 q^{58} -1.22452 q^{59} -3.52544 q^{60} +0.260432 q^{61} +5.66125 q^{62} +6.71058 q^{64} +3.27987 q^{65} +1.29374 q^{66} +0.416828 q^{67} -3.38977 q^{68} +10.7439 q^{69} +6.70200 q^{71} +2.37922 q^{72} -3.71849 q^{73} -1.67291 q^{74} -3.84664 q^{75} -1.18107 q^{76} -3.60085 q^{78} -3.44896 q^{79} -1.46026 q^{80} -10.7582 q^{81} -0.979921 q^{82} +17.2822 q^{83} +5.67155 q^{85} -10.2023 q^{86} +9.09101 q^{87} -2.01774 q^{88} -2.98187 q^{89} -1.36163 q^{90} -5.73157 q^{92} -11.2601 q^{93} -1.51920 q^{94} +1.97609 q^{95} -10.0081 q^{96} +11.2229 q^{97} -0.541054 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 8 q^{3} + 18 q^{4} + 8 q^{5} + 12 q^{6} - 6 q^{8} + 16 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 8 * q^3 + 18 * q^4 + 8 * q^5 + 12 * q^6 - 6 * q^8 + 16 * q^9	$ 20 q - 2 q^{2} + 8 q^{3} + 18 q^{4} + 8 q^{5} + 12 q^{6} - 6 q^{8} + 16 q^{9} + 16 q^{10} + 6 q^{12} + 12 q^{13} + 14 q^{16} + 8 q^{17} - 18 q^{18} + 36 q^{19} + 24 q^{20} - 8 q^{22} - 12 q^{23} + 36 q^{24} + 20 q^{25} - 22 q^{26} + 32 q^{27} + 4 q^{29} + 28 q^{30} + 80 q^{31} + 6 q^{32} - 12 q^{33} + 48 q^{34} + 26 q^{36} + 4 q^{37} + 12 q^{38} - 28 q^{39} - 4 q^{40} + 20 q^{41} - 20 q^{44} + 40 q^{45} + 8 q^{46} + 32 q^{47} + 16 q^{48} + 6 q^{50} - 20 q^{51} + 36 q^{52} + 4 q^{53} - 50 q^{54} + 64 q^{55} - 4 q^{57} + 32 q^{59} + 20 q^{60} + 44 q^{61} - 8 q^{62} - 30 q^{64} - 8 q^{65} + 32 q^{66} - 4 q^{67} - 48 q^{68} - 24 q^{69} + 8 q^{71} - 8 q^{72} + 48 q^{73} - 38 q^{74} + 24 q^{75} + 84 q^{76} + 30 q^{78} - 4 q^{79} + 56 q^{80} - 2 q^{82} + 8 q^{83} - 12 q^{85} - 24 q^{86} + 40 q^{87} - 48 q^{88} + 20 q^{89} + 48 q^{90} - 50 q^{92} + 48 q^{93} + 26 q^{94} + 20 q^{95} + 70 q^{96} + 8 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 2 * q^2 + 8 * q^3 + 18 * q^4 + 8 * q^5 + 12 * q^6 - 6 * q^8 + 16 * q^9 + 16 * q^10 + 6 * q^12 + 12 * q^13 + 14 * q^16 + 8 * q^17 - 18 * q^18 + 36 * q^19 + 24 * q^20 - 8 * q^22 - 12 * q^23 + 36 * q^24 + 20 * q^25 - 22 * q^26 + 32 * q^27 + 4 * q^29 + 28 * q^30 + 80 * q^31 + 6 * q^32 - 12 * q^33 + 48 * q^34 + 26 * q^36 + 4 * q^37 + 12 * q^38 - 28 * q^39 - 4 * q^40 + 20 * q^41 - 20 * q^44 + 40 * q^45 + 8 * q^46 + 32 * q^47 + 16 * q^48 + 6 * q^50 - 20 * q^51 + 36 * q^52 + 4 * q^53 - 50 * q^54 + 64 * q^55 - 4 * q^57 + 32 * q^59 + 20 * q^60 + 44 * q^61 - 8 * q^62 - 30 * q^64 - 8 * q^65 + 32 * q^66 - 4 * q^67 - 48 * q^68 - 24 * q^69 + 8 * q^71 - 8 * q^72 + 48 * q^73 - 38 * q^74 + 24 * q^75 + 84 * q^76 + 30 * q^78 - 4 * q^79 + 56 * q^80 - 2 * q^82 + 8 * q^83 - 12 * q^85 - 24 * q^86 + 40 * q^87 - 48 * q^88 + 20 * q^89 + 48 * q^90 - 50 * q^92 + 48 * q^93 + 26 * q^94 + 20 * q^95 + 70 * q^96 + 8 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.979921	−0.692909	−0.346454	−	0.938067i	$-0.612614\pi$
$2$	−0.979921	−0.692909	−0.346454	+	0.938067i	$0.612614\pi$
$3$	1.94904	1.12528	0.562638	−	0.826703i	$-0.309786\pi$
$3$	1.94904	1.12528	0.562638	+	0.826703i	$0.309786\pi$
$4$	−1.03976	−0.519878
$5$	1.73965	0.777996	0.388998	−	0.921239i	$-0.372821\pi$
$5$	1.73965	0.777996	0.388998	+	0.921239i	$0.372821\pi$
$6$	−1.90990	−0.779713
$7$	0	0
$7$	0	0
$8$	2.97872	1.05314
$9$	0.798739	0.266246
$10$	−1.70472	−0.539080
$11$	−0.677386	−0.204239	−0.102120	−	0.994772i	$-0.532562\pi$
$11$	−0.677386	−0.204239	−0.102120	+	0.994772i	$0.532562\pi$
$12$	−2.02652	−0.585006
$13$	1.88536	0.522905	0.261453	−	0.965216i	$-0.415798\pi$
$13$	1.88536	0.522905	0.261453	+	0.965216i	$0.415798\pi$
$14$	0	0
$15$	3.39064	0.875460
$16$	−0.839397	−0.209849
$17$	3.26016	0.790706	0.395353	−	0.918529i	$-0.370622\pi$
$17$	3.26016	0.790706	0.395353	+	0.918529i	$0.370622\pi$
$18$	−0.782701	−0.184484
$19$	1.13591	0.260595	0.130298	−	0.991475i	$-0.458407\pi$
$19$	1.13591	0.260595	0.130298	+	0.991475i	$0.458407\pi$
$20$	−1.80881	−0.404463
$21$	0	0
$22$	0.663784	0.141519
$23$	5.51242	1.14942	0.574709	−	0.818358i	$-0.305115\pi$
$23$	5.51242	1.14942	0.574709	+	0.818358i	$0.305115\pi$
$24$	5.80563	1.18507
$25$	−1.97361	−0.394722
$26$	−1.84751	−0.362326
$27$	−4.29034	−0.825675
$28$	0	0
$29$	4.66436	0.866150	0.433075	−	0.901358i	$-0.357428\pi$
$29$	4.66436	0.866150	0.433075	+	0.901358i	$0.357428\pi$
$30$	−3.32256	−0.606614
$31$	−5.77725	−1.03762	−0.518812	−	0.854888i	$-0.673626\pi$
$31$	−5.77725	−1.03762	−0.518812	+	0.854888i	$0.673626\pi$
$32$	−5.13490	−0.907730
$33$	−1.32025	−0.229826
$34$	−3.19470	−0.547887
$35$	0	0
$36$	−0.830493	−0.138416
$37$	1.70719	0.280660	0.140330	−	0.990105i	$-0.455184\pi$
$37$	1.70719	0.280660	0.140330	+	0.990105i	$0.455184\pi$
$38$	−1.11310	−0.180569
$39$	3.67464	0.588413
$40$	5.18193	0.819336
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	10.4114	1.58772	0.793860	−	0.608101i	$-0.208068\pi$
$43$	10.4114	1.58772	0.793860	+	0.608101i	$0.208068\pi$
$44$	0.704315	0.106180
$45$	1.38953	0.207139
$46$	−5.40173	−0.796442
$47$	1.55033	0.226139	0.113069	−	0.993587i	$-0.463932\pi$
$47$	1.55033	0.226139	0.113069	+	0.993587i	$0.463932\pi$
$48$	−1.63601	−0.236138
$49$	0	0
$50$	1.93398	0.273506
$51$	6.35417	0.889762
$52$	−1.96032	−0.271847
$53$	3.87319	0.532024	0.266012	−	0.963970i	$-0.414294\pi$
$53$	3.87319	0.532024	0.266012	+	0.963970i	$0.414294\pi$
$54$	4.20419	0.572118
$55$	−1.17842	−0.158897
$56$	0	0
$57$	2.21393	0.293242
$58$	−4.57070	−0.600163
$59$	−1.22452	−0.159418	−0.0797092	−	0.996818i	$-0.525399\pi$
$59$	−1.22452	−0.159418	−0.0797092	+	0.996818i	$0.525399\pi$
$60$	−3.52544	−0.455132
$61$	0.260432	0.0333449	0.0166725	−	0.999861i	$-0.494693\pi$
$61$	0.260432	0.0333449	0.0166725	+	0.999861i	$0.494693\pi$
$62$	5.66125	0.718979
$63$	0	0
$64$	6.71058	0.838823
$65$	3.27987	0.406818
$66$	1.29374	0.159248
$67$	0.416828	0.0509237	0.0254618	−	0.999676i	$-0.491894\pi$
$67$	0.416828	0.0509237	0.0254618	+	0.999676i	$0.491894\pi$
$68$	−3.38977	−0.411070
$69$	10.7439	1.29341
$70$	0	0
$71$	6.70200	0.795381	0.397690	−	0.917520i	$-0.369812\pi$
$71$	6.70200	0.795381	0.397690	+	0.917520i	$0.369812\pi$
$72$	2.37922	0.280394
$73$	−3.71849	−0.435216	−0.217608	−	0.976036i	$-0.569825\pi$
$73$	−3.71849	−0.435216	−0.217608	+	0.976036i	$0.569825\pi$
$74$	−1.67291	−0.194472
$75$	−3.84664	−0.444171
$76$	−1.18107	−0.135478
$77$	0	0
$78$	−3.60085	−0.407716
$79$	−3.44896	−0.388038	−0.194019	−	0.980998i	$-0.562152\pi$
$79$	−3.44896	−0.388038	−0.194019	+	0.980998i	$0.562152\pi$
$80$	−1.46026	−0.163262
$81$	−10.7582	−1.19536
$82$	−0.979921	−0.108214
$83$	17.2822	1.89697	0.948485	−	0.316824i	$-0.102616\pi$
$83$	17.2822	1.89697	0.948485	+	0.316824i	$0.102616\pi$
$84$	0	0
$85$	5.67155	0.615166
$86$	−10.2023	−1.10014
$87$	9.09101	0.974658
$88$	−2.01774	−0.215092
$89$	−2.98187	−0.316078	−0.158039	−	0.987433i	$-0.550517\pi$
$89$	−2.98187	−0.316078	−0.158039	+	0.987433i	$0.550517\pi$
$90$	−1.36163	−0.143528
$91$	0	0
$92$	−5.73157	−0.597557
$93$	−11.2601	−1.16761
$94$	−1.51920	−0.156694
$95$	1.97609	0.202742
$96$	−10.0081	−1.02145
$97$	11.2229	1.13951	0.569756	−	0.821814i	$-0.307038\pi$
$97$	11.2229	1.13951	0.569756	+	0.821814i	$0.307038\pi$
$98$	0	0
$99$	−0.541054	−0.0543780
$100$	2.05207	0.205207
$101$	−3.19285	−0.317701	−0.158850	−	0.987303i	$-0.550779\pi$
$101$	−3.19285	−0.317701	−0.158850	+	0.987303i	$0.550779\pi$
$102$	−6.22658	−0.616524
$103$	2.77735	0.273660	0.136830	−	0.990595i	$-0.456309\pi$
$103$	2.77735	0.273660	0.136830	+	0.990595i	$0.456309\pi$
$104$	5.61596	0.550691
$105$	0	0
$106$	−3.79542	−0.368644
$107$	−4.01877	−0.388509	−0.194254	−	0.980951i	$-0.562229\pi$
$107$	−4.01877	−0.388509	−0.194254	+	0.980951i	$0.562229\pi$
$108$	4.46090	0.429250
$109$	−7.10831	−0.680852	−0.340426	−	0.940271i	$-0.610571\pi$
$109$	−7.10831	−0.680852	−0.340426	+	0.940271i	$0.610571\pi$
$110$	1.15475	0.110101
$111$	3.32737	0.315820
$112$	0	0
$113$	−4.12863	−0.388388	−0.194194	−	0.980963i	$-0.562209\pi$
$113$	−4.12863	−0.388388	−0.194194	+	0.980963i	$0.562209\pi$
$114$	−2.16947	−0.203190
$115$	9.58969	0.894243
$116$	−4.84980	−0.450292
$117$	1.50591	0.139222
$118$	1.19993	0.110462
$119$	0	0
$120$	10.0998	0.921979
$121$	−10.5411	−0.958286
$122$	−0.255203	−0.0231050
$123$	1.94904	0.175739
$124$	6.00693	0.539438
$125$	−12.1317	−1.08509
$126$	0	0
$127$	−7.19477	−0.638433	−0.319216	−	0.947682i	$-0.603420\pi$
$127$	−7.19477	−0.638433	−0.319216	+	0.947682i	$0.603420\pi$
$128$	3.69395	0.326502
$129$	20.2921	1.78662
$130$	−3.21402	−0.281888
$131$	10.2846	0.898571	0.449285	−	0.893388i	$-0.351679\pi$
$131$	10.2846	0.898571	0.449285	+	0.893388i	$0.351679\pi$
$132$	1.37274	0.119481
$133$	0	0
$134$	−0.408459	−0.0352855
$135$	−7.46369	−0.642372
$136$	9.71111	0.832721
$137$	19.1960	1.64003	0.820013	−	0.572344i	$-0.193966\pi$
$137$	19.1960	1.64003	0.820013	+	0.572344i	$0.193966\pi$
$138$	−10.5282	−0.896217
$139$	14.1800	1.20273	0.601365	−	0.798975i	$-0.294624\pi$
$139$	14.1800	1.20273	0.601365	+	0.798975i	$0.294624\pi$
$140$	0	0
$141$	3.02165	0.254469
$142$	−6.56742	−0.551126
$143$	−1.27712	−0.106798
$144$	−0.670459	−0.0558716
$145$	8.11437	0.673862
$146$	3.64382	0.301565
$147$	0	0
$148$	−1.77506	−0.145909
$149$	15.2571	1.24991	0.624955	−	0.780661i	$-0.285117\pi$
$149$	15.2571	1.24991	0.624955	+	0.780661i	$0.285117\pi$
$150$	3.76940	0.307770
$151$	−10.6087	−0.863323	−0.431661	−	0.902036i	$-0.642072\pi$
$151$	−10.6087	−0.863323	−0.431661	+	0.902036i	$0.642072\pi$
$152$	3.38355	0.274442
$153$	2.60402	0.210522
$154$	0	0
$155$	−10.0504	−0.807268
$156$	−3.82073	−0.305903
$157$	16.2090	1.29362	0.646809	−	0.762652i	$-0.276103\pi$
$157$	16.2090	1.29362	0.646809	+	0.762652i	$0.276103\pi$
$158$	3.37970	0.268875
$159$	7.54899	0.598674
$160$	−8.93293	−0.706210
$161$	0	0
$162$	10.5422	0.828275
$163$	11.8477	0.927980	0.463990	−	0.885840i	$-0.346417\pi$
$163$	11.8477	0.927980	0.463990	+	0.885840i	$0.346417\pi$
$164$	−1.03976	−0.0811913
$165$	−2.29677	−0.178804
$166$	−16.9352	−1.31443
$167$	3.40860	0.263765	0.131883	−	0.991265i	$-0.457898\pi$
$167$	3.40860	0.263765	0.131883	+	0.991265i	$0.457898\pi$
$168$	0	0
$169$	−9.44541	−0.726570
$170$	−5.55767	−0.426254
$171$	0.907295	0.0693826
$172$	−10.8253	−0.825420
$173$	−4.91871	−0.373963	−0.186981	−	0.982363i	$-0.559870\pi$
$173$	−4.91871	−0.373963	−0.186981	+	0.982363i	$0.559870\pi$
$174$	−8.90847	−0.675349
$175$	0	0
$176$	0.568596	0.0428595
$177$	−2.38662	−0.179390
$178$	2.92200	0.219013
$179$	1.72011	0.128567	0.0642834	−	0.997932i	$-0.479524\pi$
$179$	1.72011	0.128567	0.0642834	+	0.997932i	$0.479524\pi$
$180$	−1.44477	−0.107687
$181$	−12.4001	−0.921690	−0.460845	−	0.887481i	$-0.652454\pi$
$181$	−12.4001	−0.921690	−0.460845	+	0.887481i	$0.652454\pi$
$182$	0	0
$183$	0.507591	0.0375222
$184$	16.4199	1.21049
$185$	2.96992	0.218353
$186$	11.0340	0.809050
$187$	−2.20839	−0.161493
$188$	−1.61196	−0.117565
$189$	0	0
$190$	−1.93641	−0.140482
$191$	−25.0181	−1.81025	−0.905123	−	0.425149i	$-0.860222\pi$
$191$	−25.0181	−1.81025	−0.905123	+	0.425149i	$0.860222\pi$
$192$	13.0792	0.943908
$193$	−1.38078	−0.0993906	−0.0496953	−	0.998764i	$-0.515825\pi$
$193$	−1.38078	−0.0993906	−0.0496953	+	0.998764i	$0.515825\pi$
$194$	−10.9975	−0.789578
$195$	6.39259	0.457783
$196$	0	0
$197$	−4.49668	−0.320375	−0.160188	−	0.987087i	$-0.551210\pi$
$197$	−4.49668	−0.320375	−0.160188	+	0.987087i	$0.551210\pi$
$198$	0.530190	0.0376790
$199$	−13.9802	−0.991033	−0.495516	−	0.868599i	$-0.665021\pi$
$199$	−13.9802	−0.991033	−0.495516	+	0.868599i	$0.665021\pi$
$200$	−5.87883	−0.415696
$201$	0.812413	0.0573032
$202$	3.12874	0.220137
$203$	0	0
$204$	−6.60679	−0.462568
$205$	1.73965	0.121503
$206$	−2.72158	−0.189622
$207$	4.40298	0.306028
$208$	−1.58257	−0.109731
$209$	−0.769448	−0.0532239
$210$	0	0
$211$	4.14054	0.285047	0.142523	−	0.989791i	$-0.454478\pi$
$211$	4.14054	0.285047	0.142523	+	0.989791i	$0.454478\pi$
$212$	−4.02718	−0.276588
$213$	13.0624	0.895023
$214$	3.93807	0.269201
$215$	18.1122	1.23524
$216$	−12.7797	−0.869549
$217$	0	0
$218$	6.96558	0.471768
$219$	−7.24746	−0.489738
$220$	1.22526	0.0826073
$221$	6.14659	0.413464
$222$	−3.26056	−0.218835
$223$	16.4500	1.10158	0.550788	−	0.834645i	$-0.314327\pi$
$223$	16.4500	1.10158	0.550788	+	0.834645i	$0.314327\pi$
$224$	0	0
$225$	−1.57640	−0.105093
$226$	4.04573	0.269118
$227$	−16.0069	−1.06241	−0.531206	−	0.847243i	$-0.678261\pi$
$227$	−16.0069	−1.06241	−0.531206	+	0.847243i	$0.678261\pi$
$228$	−2.30194	−0.152450
$229$	7.13320	0.471375	0.235688	−	0.971829i	$-0.424266\pi$
$229$	7.13320	0.471375	0.235688	+	0.971829i	$0.424266\pi$
$230$	−9.39713	−0.619628
$231$	0	0
$232$	13.8938	0.912174
$233$	7.55748	0.495107	0.247554	−	0.968874i	$-0.420373\pi$
$233$	7.55748	0.495107	0.247554	+	0.968874i	$0.420373\pi$
$234$	−1.47567	−0.0964679
$235$	2.69703	0.175935
$236$	1.27320	0.0828781
$237$	−6.72214	−0.436650
$238$	0	0
$239$	−2.75968	−0.178509	−0.0892544	−	0.996009i	$-0.528448\pi$
$239$	−2.75968	−0.178509	−0.0892544	+	0.996009i	$0.528448\pi$
$240$	−2.84610	−0.183715
$241$	2.58086	0.166248	0.0831238	−	0.996539i	$-0.473510\pi$
$241$	2.58086	0.166248	0.0831238	+	0.996539i	$0.473510\pi$
$242$	10.3295	0.664005
$243$	−8.09717	−0.519434
$244$	−0.270786	−0.0173353
$245$	0	0
$246$	−1.90990	−0.121771
$247$	2.14160	0.136267
$248$	−17.2088	−1.09276
$249$	33.6836	2.13461
$250$	11.8881	0.751867
$251$	9.39766	0.593175	0.296587	−	0.955006i	$-0.404151\pi$
$251$	9.39766	0.593175	0.296587	+	0.955006i	$0.404151\pi$
$252$	0	0
$253$	−3.73403	−0.234757
$254$	7.05030	0.442375
$255$	11.0540	0.692231
$256$	−17.0409	−1.06506
$257$	−0.0606071	−0.00378057	−0.00189028	−	0.999998i	$-0.500602\pi$
$257$	−0.0606071	−0.00378057	−0.00189028	+	0.999998i	$0.500602\pi$
$258$	−19.8847	−1.23797
$259$	0	0
$260$	−3.41027	−0.211496
$261$	3.72561	0.230609
$262$	−10.0781	−0.622627
$263$	23.1796	1.42932	0.714659	−	0.699473i	$-0.246582\pi$
$263$	23.1796	1.42932	0.714659	+	0.699473i	$0.246582\pi$
$264$	−3.93265	−0.242038
$265$	6.73801	0.413913
$266$	0	0
$267$	−5.81178	−0.355675
$268$	−0.433400	−0.0264741
$269$	−17.5546	−1.07033	−0.535163	−	0.844749i	$-0.679750\pi$
$269$	−17.5546	−1.07033	−0.535163	+	0.844749i	$0.679750\pi$
$270$	7.31382	0.445105
$271$	19.0008	1.15421	0.577107	−	0.816668i	$-0.304181\pi$
$271$	19.0008	1.15421	0.577107	+	0.816668i	$0.304181\pi$
$272$	−2.73657	−0.165929
$273$	0	0
$274$	−18.8106	−1.13639
$275$	1.33690	0.0806178
$276$	−11.1710	−0.672417
$277$	15.8464	0.952119	0.476060	−	0.879413i	$-0.342065\pi$
$277$	15.8464	0.952119	0.476060	+	0.879413i	$0.342065\pi$
$278$	−13.8952	−0.833382
$279$	−4.61452	−0.276264
$280$	0	0
$281$	−28.5894	−1.70550	−0.852749	−	0.522321i	$-0.825066\pi$
$281$	−28.5894	−1.70550	−0.852749	+	0.522321i	$0.825066\pi$
$282$	−2.96097	−0.176323
$283$	11.1864	0.664965	0.332482	−	0.943109i	$-0.392114\pi$
$283$	11.1864	0.664965	0.332482	+	0.943109i	$0.392114\pi$
$284$	−6.96844	−0.413501
$285$	3.85146	0.228141
$286$	1.25147	0.0740012
$287$	0	0
$288$	−4.10144	−0.241680
$289$	−6.37134	−0.374785
$290$	−7.95144	−0.466924
$291$	21.8738	1.28227
$292$	3.86632	0.226259
$293$	−26.8287	−1.56735	−0.783675	−	0.621171i	$-0.786657\pi$
$293$	−26.8287	−1.56735	−0.783675	+	0.621171i	$0.786657\pi$
$294$	0	0
$295$	−2.13023	−0.124027
$296$	5.08524	0.295573
$297$	2.90621	0.168635
$298$	−14.9507	−0.866074
$299$	10.3929	0.601037
$300$	3.99956	0.230915
$301$	0	0
$302$	10.3957	0.598204
$303$	−6.22298	−0.357501
$304$	−0.953479	−0.0546858
$305$	0.453061	0.0259422
$306$	−2.55173	−0.145873
$307$	25.2452	1.44082	0.720411	−	0.693548i	$-0.243953\pi$
$307$	25.2452	1.44082	0.720411	+	0.693548i	$0.243953\pi$
$308$	0	0
$309$	5.41315	0.307944
$310$	9.84860	0.559363
$311$	−12.2880	−0.696789	−0.348395	−	0.937348i	$-0.613273\pi$
$311$	−12.2880	−0.696789	−0.348395	+	0.937348i	$0.613273\pi$
$312$	10.9457	0.619679
$313$	−17.5621	−0.992671	−0.496335	−	0.868131i	$-0.665321\pi$
$313$	−17.5621	−0.992671	−0.496335	+	0.868131i	$0.665321\pi$
$314$	−15.8835	−0.896360
$315$	0	0
$316$	3.58607	0.201732
$317$	−17.3375	−0.973773	−0.486887	−	0.873465i	$-0.661868\pi$
$317$	−17.3375	−0.973773	−0.486887	+	0.873465i	$0.661868\pi$
$318$	−7.39741	−0.414826
$319$	−3.15957	−0.176902
$320$	11.6741	0.652601
$321$	−7.83272	−0.437180
$322$	0	0
$323$	3.70325	0.206054
$324$	11.1859	0.621441
$325$	−3.72097	−0.206402
$326$	−11.6098	−0.643006
$327$	−13.8543	−0.766147
$328$	2.97872	0.164472
$329$	0	0
$330$	2.25066	0.123894
$331$	−18.7901	−1.03280	−0.516398	−	0.856349i	$-0.672728\pi$
$331$	−18.7901	−1.03280	−0.516398	+	0.856349i	$0.672728\pi$
$332$	−17.9693	−0.986192
$333$	1.36360	0.0747248
$334$	−3.34016	−0.182765
$335$	0.725136	0.0396184
$336$	0	0
$337$	18.8132	1.02482	0.512411	−	0.858740i	$-0.328752\pi$
$337$	18.8132	1.02482	0.512411	+	0.858740i	$0.328752\pi$
$338$	9.25575	0.503446
$339$	−8.04684	−0.437044
$340$	−5.89702	−0.319811
$341$	3.91343	0.211924
$342$	−0.889077	−0.0480758
$343$	0	0
$344$	31.0126	1.67208
$345$	18.6906	1.00627
$346$	4.81995	0.259122
$347$	11.3737	0.610572	0.305286	−	0.952261i	$-0.401248\pi$
$347$	11.3737	0.610572	0.305286	+	0.952261i	$0.401248\pi$
$348$	−9.45243	−0.506703
$349$	−6.20350	−0.332066	−0.166033	−	0.986120i	$-0.553096\pi$
$349$	−6.20350	−0.332066	−0.166033	+	0.986120i	$0.553096\pi$
$350$	0	0
$351$	−8.08884	−0.431750
$352$	3.47830	0.185394
$353$	18.1712	0.967157	0.483579	−	0.875301i	$-0.339337\pi$
$353$	18.1712	0.967157	0.483579	+	0.875301i	$0.339337\pi$
$354$	2.33870	0.124301
$355$	11.6591	0.618803
$356$	3.10042	0.164322
$357$	0	0
$358$	−1.68557	−0.0890850
$359$	−3.28681	−0.173471	−0.0867356	−	0.996231i	$-0.527644\pi$
$359$	−3.28681	−0.173471	−0.0867356	+	0.996231i	$0.527644\pi$
$360$	4.13901	0.218145
$361$	−17.7097	−0.932090
$362$	12.1511	0.638647
$363$	−20.5451	−1.07834
$364$	0	0
$365$	−6.46887	−0.338596
$366$	−0.497399	−0.0259995
$367$	−12.5808	−0.656714	−0.328357	−	0.944554i	$-0.606495\pi$
$367$	−12.5808	−0.656714	−0.328357	+	0.944554i	$0.606495\pi$
$368$	−4.62711	−0.241205
$369$	0.798739	0.0415807
$370$	−2.91028	−0.151298
$371$	0	0
$372$	11.7077	0.607017
$373$	27.9806	1.44878	0.724389	−	0.689391i	$-0.242122\pi$
$373$	27.9806	1.44878	0.724389	+	0.689391i	$0.242122\pi$
$374$	2.16404	0.111900
$375$	−23.6450	−1.22102
$376$	4.61800	0.238155
$377$	8.79401	0.452915
$378$	0	0
$379$	−33.3470	−1.71292	−0.856461	−	0.516212i	$-0.827342\pi$
$379$	−33.3470	−1.71292	−0.856461	+	0.516212i	$0.827342\pi$
$380$	−2.05465	−0.105401
$381$	−14.0229	−0.718413
$382$	24.5158	1.25434
$383$	10.1217	0.517196	0.258598	−	0.965985i	$-0.416740\pi$
$383$	10.1217	0.517196	0.258598	+	0.965985i	$0.416740\pi$
$384$	7.19964	0.367405
$385$	0	0
$386$	1.35305	0.0688686
$387$	8.31597	0.422725
$388$	−11.6691	−0.592407
$389$	−7.21978	−0.366058	−0.183029	−	0.983108i	$-0.558590\pi$
$389$	−7.21978	−0.366058	−0.183029	+	0.983108i	$0.558590\pi$
$390$	−6.26423	−0.317202
$391$	17.9714	0.908851
$392$	0	0
$393$	20.0451	1.01114
$394$	4.40639	0.221991
$395$	−5.99998	−0.301892
$396$	0.562564	0.0282699
$397$	27.2552	1.36790	0.683950	−	0.729529i	$-0.260261\pi$
$397$	27.2552	1.36790	0.683950	+	0.729529i	$0.260261\pi$
$398$	13.6995	0.686695
$399$	0	0
$400$	1.65664	0.0828322
$401$	−11.6741	−0.582978	−0.291489	−	0.956574i	$-0.594151\pi$
$401$	−11.6741	−0.582978	−0.291489	+	0.956574i	$0.594151\pi$
$402$	−0.796100	−0.0397059
$403$	−10.8922	−0.542580
$404$	3.31979	0.165165
$405$	−18.7156	−0.929985
$406$	0	0
$407$	−1.15643	−0.0573219
$408$	18.9273	0.937041
$409$	−13.0387	−0.644720	−0.322360	−	0.946617i	$-0.604476\pi$
$409$	−13.0387	−0.644720	−0.322360	+	0.946617i	$0.604476\pi$
$410$	−1.70472	−0.0841902
$411$	37.4137	1.84548
$412$	−2.88777	−0.142270
$413$	0	0
$414$	−4.31457	−0.212050
$415$	30.0650	1.47583
$416$	−9.68114	−0.474657
$417$	27.6373	1.35340
$418$	0.753998	0.0368793
$419$	−4.92473	−0.240589	−0.120294	−	0.992738i	$-0.538384\pi$
$419$	−4.92473	−0.240589	−0.120294	+	0.992738i	$0.538384\pi$
$420$	0	0
$421$	−11.8751	−0.578757	−0.289378	−	0.957215i	$-0.593449\pi$
$421$	−11.8751	−0.578757	−0.289378	+	0.957215i	$0.593449\pi$
$422$	−4.05740	−0.197511
$423$	1.23831	0.0602086
$424$	11.5372	0.560294
$425$	−6.43429	−0.312109
$426$	−12.8001	−0.620169
$427$	0	0
$428$	4.17854	0.201977
$429$	−2.48915	−0.120177
$430$	−17.7485	−0.855908
$431$	2.46381	0.118678	0.0593388	−	0.998238i	$-0.481101\pi$
$431$	2.46381	0.118678	0.0593388	+	0.998238i	$0.481101\pi$
$432$	3.60130	0.173267
$433$	−26.6785	−1.28209	−0.641045	−	0.767504i	$-0.721499\pi$
$433$	−26.6785	−1.28209	−0.641045	+	0.767504i	$0.721499\pi$
$434$	0	0
$435$	15.8152	0.758280
$436$	7.39090	0.353960
$437$	6.26160	0.299533
$438$	7.10194	0.339344
$439$	9.36107	0.446779	0.223390	−	0.974729i	$-0.428288\pi$
$439$	9.36107	0.446779	0.223390	+	0.974729i	$0.428288\pi$
$440$	−3.51017	−0.167341
$441$	0	0
$442$	−6.02317	−0.286493
$443$	−28.2942	−1.34430	−0.672148	−	0.740417i	$-0.734628\pi$
$443$	−28.2942	−1.34430	−0.672148	+	0.740417i	$0.734628\pi$
$444$	−3.45965	−0.164188
$445$	−5.18742	−0.245907
$446$	−16.1197	−0.763291
$447$	29.7366	1.40649
$448$	0	0
$449$	−37.8785	−1.78760	−0.893799	−	0.448468i	$-0.851970\pi$
$449$	−37.8785	−1.78760	−0.893799	+	0.448468i	$0.851970\pi$
$450$	1.54475	0.0728201
$451$	−0.677386	−0.0318968
$452$	4.29276	0.201915
$453$	−20.6767	−0.971477
$454$	15.6854	0.736155
$455$	0	0
$456$	6.59467	0.308824
$457$	−38.5590	−1.80371	−0.901857	−	0.432035i	$-0.857796\pi$
$457$	−38.5590	−1.80371	−0.901857	+	0.432035i	$0.857796\pi$
$458$	−6.98997	−0.326620
$459$	−13.9872	−0.652866
$460$	−9.97093	−0.464897
$461$	−31.6904	−1.47597	−0.737985	−	0.674817i	$-0.764222\pi$
$461$	−31.6904	−1.47597	−0.737985	+	0.674817i	$0.764222\pi$
$462$	0	0
$463$	−12.2820	−0.570791	−0.285395	−	0.958410i	$-0.592125\pi$
$463$	−12.2820	−0.570791	−0.285395	+	0.958410i	$0.592125\pi$
$464$	−3.91525	−0.181761
$465$	−19.5886	−0.908399
$466$	−7.40573	−0.343064
$467$	−40.2120	−1.86079	−0.930396	−	0.366557i	$-0.880537\pi$
$467$	−40.2120	−1.86079	−0.930396	+	0.366557i	$0.880537\pi$
$468$	−1.56578	−0.0723783
$469$	0	0
$470$	−2.64288	−0.121907
$471$	31.5919	1.45568
$472$	−3.64749	−0.167889
$473$	−7.05251	−0.324275
$474$	6.58716	0.302558
$475$	−2.24184	−0.102863
$476$	0	0
$477$	3.09367	0.141650
$478$	2.70427	0.123690
$479$	−29.7514	−1.35938	−0.679689	−	0.733500i	$-0.737885\pi$
$479$	−29.7514	−1.35938	−0.679689	+	0.733500i	$0.737885\pi$
$480$	−17.4106	−0.794682
$481$	3.21867	0.146759
$482$	−2.52903	−0.115194
$483$	0	0
$484$	10.9602	0.498192
$485$	19.5239	0.886536
$486$	7.93459	0.359920
$487$	−32.7577	−1.48439	−0.742197	−	0.670182i	$-0.766216\pi$
$487$	−32.7577	−1.48439	−0.742197	+	0.670182i	$0.766216\pi$
$488$	0.775754	0.0351167
$489$	23.0915	1.04423
$490$	0	0
$491$	−29.3914	−1.32642	−0.663208	−	0.748436i	$-0.730805\pi$
$491$	−29.3914	−1.32642	−0.663208	+	0.748436i	$0.730805\pi$
$492$	−2.02652	−0.0913626
$493$	15.2066	0.684870
$494$	−2.09860	−0.0944204
$495$	−0.941246	−0.0423059
$496$	4.84941	0.217745
$497$	0	0
$498$	−33.0073	−1.47909
$499$	35.4165	1.58546	0.792729	−	0.609574i	$-0.208660\pi$
$499$	35.4165	1.58546	0.792729	+	0.609574i	$0.208660\pi$
$500$	12.6140	0.564113
$501$	6.64348	0.296809
$502$	−9.20896	−0.411016
$503$	−33.3813	−1.48840	−0.744200	−	0.667957i	$-0.767169\pi$
$503$	−33.3813	−1.48840	−0.744200	+	0.667957i	$0.767169\pi$
$504$	0	0
$505$	−5.55445	−0.247170
$506$	3.65905	0.162665
$507$	−18.4094	−0.817592
$508$	7.48080	0.331907
$509$	−3.13863	−0.139117	−0.0695587	−	0.997578i	$-0.522159\pi$
$509$	−3.13863	−0.139117	−0.0695587	+	0.997578i	$0.522159\pi$
$510$	−10.8321	−0.479653
$511$	0	0
$512$	9.31087	0.411486
$513$	−4.87343	−0.215167
$514$	0.0593901	0.00261959
$515$	4.83162	0.212907
$516$	−21.0989	−0.928825
$517$	−1.05017	−0.0461865
$518$	0	0
$519$	−9.58675	−0.420811
$520$	9.76982	0.428435
$521$	25.9690	1.13772	0.568862	−	0.822433i	$-0.307384\pi$
$521$	25.9690	1.13772	0.568862	+	0.822433i	$0.307384\pi$
$522$	−3.65080	−0.159791
$523$	−25.7256	−1.12490	−0.562451	−	0.826831i	$-0.690141\pi$
$523$	−25.7256	−1.12490	−0.562451	+	0.826831i	$0.690141\pi$
$524$	−10.6935	−0.467147
$525$	0	0
$526$	−22.7142	−0.990386
$527$	−18.8348	−0.820456
$528$	1.10821	0.0482288
$529$	7.38673	0.321162
$530$	−6.60272	−0.286804
$531$	−0.978068	−0.0424446
$532$	0	0
$533$	1.88536	0.0816641
$534$	5.69508	0.246450
$535$	−6.99126	−0.302258
$536$	1.24161	0.0536296
$537$	3.35255	0.144673
$538$	17.2022	0.741638
$539$	0	0
$540$	7.76041	0.333955
$541$	41.5983	1.78845	0.894225	−	0.447618i	$-0.147728\pi$
$541$	41.5983	1.78845	0.894225	+	0.447618i	$0.147728\pi$
$542$	−18.6192	−0.799765
$543$	−24.1682	−1.03716
$544$	−16.7406	−0.717747
$545$	−12.3660	−0.529700
$546$	0	0
$547$	−41.9978	−1.79570	−0.897848	−	0.440306i	$-0.854870\pi$
$547$	−41.9978	−1.79570	−0.897848	+	0.440306i	$0.854870\pi$
$548$	−19.9592	−0.852614
$549$	0.208017	0.00887796
$550$	−1.31005	−0.0558608
$551$	5.29829	0.225715
$552$	32.0030	1.36214
$553$	0	0
$554$	−15.5282	−0.659732
$555$	5.78847	0.245707
$556$	−14.7437	−0.625272
$557$	36.6619	1.55341	0.776707	−	0.629862i	$-0.216889\pi$
$557$	36.6619	1.55341	0.776707	+	0.629862i	$0.216889\pi$
$558$	4.52186	0.191426
$559$	19.6292	0.830227
$560$	0	0
$561$	−4.30422	−0.181725
$562$	28.0153	1.18175
$563$	−7.07723	−0.298270	−0.149135	−	0.988817i	$-0.547649\pi$
$563$	−7.07723	−0.298270	−0.149135	+	0.988817i	$0.547649\pi$
$564$	−3.14178	−0.132293
$565$	−7.18237	−0.302165
$566$	−10.9618	−0.460760
$567$	0	0
$568$	19.9634	0.837644
$569$	−14.8716	−0.623451	−0.311726	−	0.950172i	$-0.600907\pi$
$569$	−14.8716	−0.623451	−0.311726	+	0.950172i	$0.600907\pi$
$570$	−3.77413	−0.158081
$571$	−23.6590	−0.990097	−0.495049	−	0.868865i	$-0.664850\pi$
$571$	−23.6590	−0.990097	−0.495049	+	0.868865i	$0.664850\pi$
$572$	1.32789	0.0555219
$573$	−48.7612	−2.03703
$574$	0	0
$575$	−10.8794	−0.453701
$576$	5.36001	0.223334
$577$	31.5757	1.31451	0.657257	−	0.753666i	$-0.271716\pi$
$577$	31.5757	1.31451	0.657257	+	0.753666i	$0.271716\pi$
$578$	6.24341	0.259692
$579$	−2.69119	−0.111842
$580$	−8.43696	−0.350326
$581$	0	0
$582$	−21.4346	−0.888493
$583$	−2.62365	−0.108660
$584$	−11.0763	−0.458342
$585$	2.61976	0.108314
$586$	26.2900	1.08603
$587$	−25.1629	−1.03858	−0.519292	−	0.854597i	$-0.673804\pi$
$587$	−25.1629	−1.03858	−0.519292	+	0.854597i	$0.673804\pi$
$588$	0	0
$589$	−6.56243	−0.270400
$590$	2.08746	0.0859392
$591$	−8.76419	−0.360511
$592$	−1.43301	−0.0588963
$593$	−35.2189	−1.44627	−0.723134	−	0.690708i	$-0.757299\pi$
$593$	−35.2189	−1.44627	−0.723134	+	0.690708i	$0.757299\pi$
$594$	−2.84786	−0.116849
$595$	0	0
$596$	−15.8637	−0.649801
$597$	−27.2480	−1.11519
$598$	−10.1842	−0.416464
$599$	15.4584	0.631614	0.315807	−	0.948823i	$-0.397725\pi$
$599$	15.4584	0.631614	0.315807	+	0.948823i	$0.397725\pi$
$600$	−11.4581	−0.467773
$601$	−34.5234	−1.40824	−0.704119	−	0.710082i	$-0.748658\pi$
$601$	−34.5234	−1.40824	−0.704119	+	0.710082i	$0.748658\pi$
$602$	0	0
$603$	0.332937	0.0135582
$604$	11.0304	0.448822
$605$	−18.3379	−0.745543
$606$	6.09803	0.247715
$607$	37.7324	1.53151	0.765756	−	0.643131i	$-0.222365\pi$
$607$	37.7324	1.53151	0.765756	+	0.643131i	$0.222365\pi$
$608$	−5.83277	−0.236550
$609$	0	0
$610$	−0.443964	−0.0179756
$611$	2.92293	0.118249
$612$	−2.70754	−0.109446
$613$	−5.94007	−0.239917	−0.119959	−	0.992779i	$-0.538276\pi$
$613$	−5.94007	−0.239917	−0.119959	+	0.992779i	$0.538276\pi$
$614$	−24.7383	−0.998358
$615$	3.39064	0.136724
$616$	0	0
$617$	19.1976	0.772867	0.386433	−	0.922317i	$-0.373707\pi$
$617$	19.1976	0.772867	0.386433	+	0.922317i	$0.373707\pi$
$618$	−5.30446	−0.213377
$619$	15.7695	0.633831	0.316916	−	0.948454i	$-0.397353\pi$
$619$	15.7695	0.633831	0.316916	+	0.948454i	$0.397353\pi$
$620$	10.4500	0.419681
$621$	−23.6501	−0.949046
$622$	12.0413	0.482811
$623$	0	0
$624$	−3.08448	−0.123478
$625$	−11.2368	−0.449472
$626$	17.2095	0.687830
$627$	−1.49968	−0.0598915
$628$	−16.8534	−0.672524
$629$	5.56572	0.221920
$630$	0	0
$631$	25.5635	1.01767	0.508833	−	0.860865i	$-0.330077\pi$
$631$	25.5635	1.01767	0.508833	+	0.860865i	$0.330077\pi$
$632$	−10.2735	−0.408657
$633$	8.07006	0.320756
$634$	16.9894	0.674736
$635$	−12.5164	−0.496698
$636$	−7.84911	−0.311237
$637$	0	0
$638$	3.09613	0.122577
$639$	5.35315	0.211767
$640$	6.42619	0.254017
$641$	−30.3147	−1.19736	−0.598679	−	0.800989i	$-0.704308\pi$
$641$	−30.3147	−1.19736	−0.598679	+	0.800989i	$0.704308\pi$
$642$	7.67544	0.302926
$643$	49.8612	1.96633	0.983167	−	0.182708i	$-0.0584865\pi$
$643$	49.8612	1.96633	0.983167	+	0.182708i	$0.0584865\pi$
$644$	0	0
$645$	35.3012	1.38999
$646$	−3.62889	−0.142777
$647$	29.0743	1.14303	0.571514	−	0.820592i	$-0.306356\pi$
$647$	29.0743	1.14303	0.571514	+	0.820592i	$0.306356\pi$
$648$	−32.0458	−1.25888
$649$	0.829469	0.0325595
$650$	3.64626	0.143018
$651$	0	0
$652$	−12.3187	−0.482436
$653$	−12.6476	−0.494937	−0.247468	−	0.968896i	$-0.579599\pi$
$653$	−12.6476	−0.494937	−0.247468	+	0.968896i	$0.579599\pi$
$654$	13.5762	0.530870
$655$	17.8916	0.699084
$656$	−0.839397	−0.0327730
$657$	−2.97010	−0.115875
$658$	0	0
$659$	0.414490	0.0161462	0.00807311	−	0.999967i	$-0.497430\pi$
$659$	0.414490	0.0161462	0.00807311	+	0.999967i	$0.497430\pi$
$660$	2.38808	0.0929560
$661$	12.2570	0.476744	0.238372	−	0.971174i	$-0.423386\pi$
$661$	12.2570	0.476744	0.238372	+	0.971174i	$0.423386\pi$
$662$	18.4128	0.715633
$663$	11.9799	0.465261
$664$	51.4789	1.99777
$665$	0	0
$666$	−1.33622	−0.0517774
$667$	25.7119	0.995569
$668$	−3.54411	−0.137126
$669$	32.0617	1.23958
$670$	−0.710576	−0.0274519
$671$	−0.176413	−0.00681034
$672$	0	0
$673$	3.73093	0.143817	0.0719083	−	0.997411i	$-0.477091\pi$
$673$	3.73093	0.143817	0.0719083	+	0.997411i	$0.477091\pi$
$674$	−18.4355	−0.710108
$675$	8.46745	0.325912
$676$	9.82092	0.377728
$677$	−41.1372	−1.58103	−0.790516	−	0.612442i	$-0.790187\pi$
$677$	−41.1372	−1.58103	−0.790516	+	0.612442i	$0.790187\pi$
$678$	7.88526	0.302832
$679$	0	0
$680$	16.8939	0.647853
$681$	−31.1979	−1.19551
$682$	−3.83485	−0.146844
$683$	13.8301	0.529192	0.264596	−	0.964359i	$-0.414761\pi$
$683$	13.8301	0.529192	0.264596	+	0.964359i	$0.414761\pi$
$684$	−0.943365	−0.0360705
$685$	33.3944	1.27593
$686$	0	0
$687$	13.9029	0.530427
$688$	−8.73928	−0.333182
$689$	7.30238	0.278198
$690$	−18.3153	−0.697253
$691$	−24.3580	−0.926621	−0.463310	−	0.886196i	$-0.653338\pi$
$691$	−24.3580	−0.926621	−0.463310	+	0.886196i	$0.653338\pi$
$692$	5.11426	0.194415
$693$	0	0
$694$	−11.1453	−0.423070
$695$	24.6682	0.935719
$696$	27.0796	1.02645
$697$	3.26016	0.123487
$698$	6.07893	0.230091
$699$	14.7298	0.557132
$700$	0	0
$701$	−36.3988	−1.37476	−0.687382	−	0.726296i	$-0.741240\pi$
$701$	−36.3988	−1.37476	−0.687382	+	0.726296i	$0.741240\pi$
$702$	7.92642	0.299163
$703$	1.93921	0.0731388
$704$	−4.54565	−0.171321
$705$	5.25662	0.197976
$706$	−17.8064	−0.670151
$707$	0	0
$708$	2.48151	0.0932607
$709$	−16.7296	−0.628294	−0.314147	−	0.949374i	$-0.601719\pi$
$709$	−16.7296	−0.628294	−0.314147	+	0.949374i	$0.601719\pi$
$710$	−11.4250	−0.428774
$711$	−2.75482	−0.103314
$712$	−8.88216	−0.332873
$713$	−31.8466	−1.19266
$714$	0	0
$715$	−2.22174	−0.0830884
$716$	−1.78849	−0.0668390
$717$	−5.37871	−0.200872
$718$	3.22081	0.120200
$719$	−10.9547	−0.408542	−0.204271	−	0.978914i	$-0.565482\pi$
$719$	−10.9547	−0.408542	−0.204271	+	0.978914i	$0.565482\pi$
$720$	−1.16637	−0.0434679
$721$	0	0
$722$	17.3541	0.645853
$723$	5.03018	0.187074
$724$	12.8930	0.479166
$725$	−9.20564	−0.341889
$726$	20.1325	0.747189
$727$	34.9204	1.29513	0.647563	−	0.762012i	$-0.275788\pi$
$727$	34.9204	1.29513	0.647563	+	0.762012i	$0.275788\pi$
$728$	0	0
$729$	16.4930	0.610853
$730$	6.33898	0.234616
$731$	33.9428	1.25542
$732$	−0.527771	−0.0195070
$733$	3.95157	0.145955	0.0729773	−	0.997334i	$-0.476750\pi$
$733$	3.95157	0.145955	0.0729773	+	0.997334i	$0.476750\pi$
$734$	12.3282	0.455043
$735$	0	0
$736$	−28.3057	−1.04336
$737$	−0.282354	−0.0104006
$738$	−0.782701	−0.0288116
$739$	−24.7462	−0.910304	−0.455152	−	0.890414i	$-0.650415\pi$
$739$	−24.7462	−0.910304	−0.455152	+	0.890414i	$0.650415\pi$
$740$	−3.08799	−0.113517
$741$	4.17405	0.153338
$742$	0	0
$743$	−39.1126	−1.43490	−0.717451	−	0.696609i	$-0.754691\pi$
$743$	−39.1126	−1.43490	−0.717451	+	0.696609i	$0.754691\pi$
$744$	−33.5406	−1.22966
$745$	26.5420	0.972425
$746$	−27.4187	−1.00387
$747$	13.8040	0.505061
$748$	2.29618	0.0839568
$749$	0	0
$750$	23.1703	0.846058
$751$	−44.9993	−1.64205	−0.821025	−	0.570893i	$-0.806597\pi$
$751$	−44.9993	−1.64205	−0.821025	+	0.570893i	$0.806597\pi$
$752$	−1.30134	−0.0474551
$753$	18.3164	0.667485
$754$	−8.61743	−0.313828
$755$	−18.4554	−0.671662
$756$	0	0
$757$	33.4050	1.21412	0.607062	−	0.794655i	$-0.292348\pi$
$757$	33.4050	1.21412	0.607062	+	0.794655i	$0.292348\pi$
$758$	32.6774	1.18690
$759$	−7.27776	−0.264166
$760$	5.88621	0.213515
$761$	−0.228451	−0.00828133	−0.00414067	−	0.999991i	$-0.501318\pi$
$761$	−0.228451	−0.00828133	−0.00414067	+	0.999991i	$0.501318\pi$
$762$	13.7413	0.497794
$763$	0	0
$764$	26.0127	0.941107
$765$	4.53009	0.163786
$766$	−9.91849	−0.358370
$767$	−2.30866	−0.0833607
$768$	−33.2134	−1.19849
$769$	16.6555	0.600613	0.300307	−	0.953843i	$-0.402911\pi$
$769$	16.6555	0.600613	0.300307	+	0.953843i	$0.402911\pi$
$770$	0	0
$771$	−0.118125	−0.00425418
$772$	1.43567	0.0516710
$773$	−43.5903	−1.56783	−0.783916	−	0.620866i	$-0.786781\pi$
$773$	−43.5903	−1.56783	−0.783916	+	0.620866i	$0.786781\pi$
$774$	−8.14899	−0.292909
$775$	11.4020	0.409573
$776$	33.4299	1.20006
$777$	0	0
$778$	7.07482	0.253644
$779$	1.13591	0.0406982
$780$	−6.64673	−0.237991
$781$	−4.53984	−0.162448
$782$	−17.6105	−0.629751
$783$	−20.0117	−0.715159
$784$	0	0
$785$	28.1980	1.00643
$786$	−19.6426	−0.700627
$787$	10.7834	0.384388	0.192194	−	0.981357i	$-0.438440\pi$
$787$	10.7834	0.384388	0.192194	+	0.981357i	$0.438440\pi$
$788$	4.67545	0.166556
$789$	45.1779	1.60838
$790$	5.87951	0.209184
$791$	0	0
$792$	−1.61165	−0.0572675
$793$	0.491009	0.0174362
$794$	−26.7079	−0.947829
$795$	13.1326	0.465766
$796$	14.5360	0.515216
$797$	−32.2102	−1.14094	−0.570472	−	0.821317i	$-0.693240\pi$
$797$	−32.2102	−1.14094	−0.570472	+	0.821317i	$0.693240\pi$
$798$	0	0
$799$	5.05433	0.178809
$800$	10.1343	0.358301
$801$	−2.38174	−0.0841546
$802$	11.4397	0.403950
$803$	2.51885	0.0888883
$804$	−0.844711	−0.0297907
$805$	0	0
$806$	10.6735	0.375958
$807$	−34.2146	−1.20441
$808$	−9.51061	−0.334582
$809$	−4.28765	−0.150746	−0.0753728	−	0.997155i	$-0.524015\pi$
$809$	−4.28765	−0.150746	−0.0753728	+	0.997155i	$0.524015\pi$
$810$	18.3398	0.644394
$811$	−39.4989	−1.38699	−0.693497	−	0.720459i	$-0.743931\pi$
$811$	−39.4989	−1.38699	−0.693497	+	0.720459i	$0.743931\pi$
$812$	0	0
$813$	37.0332	1.29881
$814$	1.13321	0.0397188
$815$	20.6108	0.721965
$816$	−5.33367	−0.186716
$817$	11.8264	0.413752
$818$	12.7768	0.446732
$819$	0	0
$820$	−1.80881	−0.0631665
$821$	−50.1535	−1.75037	−0.875185	−	0.483788i	$-0.839261\pi$
$821$	−50.1535	−1.75037	−0.875185	+	0.483788i	$0.839261\pi$
$822$	−36.6625	−1.27875
$823$	27.5697	0.961019	0.480509	−	0.876990i	$-0.340452\pi$
$823$	27.5697	0.961019	0.480509	+	0.876990i	$0.340452\pi$
$824$	8.27295	0.288202
$825$	2.60566	0.0907173
$826$	0	0
$827$	11.8754	0.412948	0.206474	−	0.978452i	$-0.433801\pi$
$827$	11.8754	0.412948	0.206474	+	0.978452i	$0.433801\pi$
$828$	−4.57803	−0.159097
$829$	33.0097	1.14648	0.573238	−	0.819389i	$-0.305687\pi$
$829$	33.0097	1.14648	0.573238	+	0.819389i	$0.305687\pi$
$830$	−29.4613	−1.02262
$831$	30.8852	1.07140
$832$	12.6519	0.438625
$833$	0	0
$834$	−27.0823	−0.937785
$835$	5.92978	0.205208
$836$	0.800038	0.0276699
$837$	24.7863	0.856741
$838$	4.82584	0.166706
$839$	4.86694	0.168025	0.0840127	−	0.996465i	$-0.473226\pi$
$839$	4.86694	0.168025	0.0840127	+	0.996465i	$0.473226\pi$
$840$	0	0
$841$	−7.24372	−0.249784
$842$	11.6366	0.401025
$843$	−55.7217	−1.91916
$844$	−4.30515	−0.148189
$845$	−16.4317	−0.565269
$846$	−1.21344	−0.0417191
$847$	0	0
$848$	−3.25115	−0.111645
$849$	21.8028	0.748269
$850$	6.30510	0.216263
$851$	9.41074	0.322596
$852$	−13.5817	−0.465302
$853$	11.5153	0.394275	0.197137	−	0.980376i	$-0.436835\pi$
$853$	11.5153	0.394275	0.197137	+	0.980376i	$0.436835\pi$
$854$	0	0
$855$	1.57838	0.0539794
$856$	−11.9708	−0.409153
$857$	45.5891	1.55729	0.778647	−	0.627462i	$-0.215906\pi$
$857$	45.5891	1.55729	0.778647	+	0.627462i	$0.215906\pi$
$858$	2.43917	0.0832718
$859$	46.8185	1.59743	0.798714	−	0.601711i	$-0.205514\pi$
$859$	46.8185	1.59743	0.798714	+	0.601711i	$0.205514\pi$
$860$	−18.8322	−0.642173
$861$	0	0
$862$	−2.41434	−0.0822328
$863$	11.5316	0.392539	0.196269	−	0.980550i	$-0.437117\pi$
$863$	11.5316	0.392539	0.196269	+	0.980550i	$0.437117\pi$
$864$	22.0304	0.749490
$865$	−8.55685	−0.290942
$866$	26.1429	0.888371
$867$	−12.4180	−0.421736
$868$	0	0
$869$	2.33627	0.0792527
$870$	−15.4976	−0.525419
$871$	0.785872	0.0266283
$872$	−21.1737	−0.717030
$873$	8.96417	0.303391
$874$	−6.13587	−0.207549
$875$	0	0
$876$	7.53559	0.254604
$877$	−21.3142	−0.719728	−0.359864	−	0.933005i	$-0.617177\pi$
$877$	−21.3142	−0.719728	−0.359864	+	0.933005i	$0.617177\pi$
$878$	−9.17310	−0.309577
$879$	−52.2901	−1.76370
$880$	0.989158	0.0333445
$881$	1.93709	0.0652623	0.0326311	−	0.999467i	$-0.489611\pi$
$881$	1.93709	0.0652623	0.0326311	+	0.999467i	$0.489611\pi$
$882$	0	0
$883$	45.0457	1.51591	0.757955	−	0.652307i	$-0.226199\pi$
$883$	45.0457	1.51591	0.757955	+	0.652307i	$0.226199\pi$
$884$	−6.39095	−0.214951
$885$	−4.15190	−0.139564
$886$	27.7260	0.931474
$887$	29.4772	0.989747	0.494874	−	0.868965i	$-0.335214\pi$
$887$	29.4772	0.989747	0.494874	+	0.868965i	$0.335214\pi$
$888$	9.91131	0.332602
$889$	0	0
$890$	5.08326	0.170391
$891$	7.28747	0.244140
$892$	−17.1040	−0.572685
$893$	1.76103	0.0589307
$894$	−29.1395	−0.974572
$895$	2.99239	0.100024
$896$	0	0
$897$	20.2561	0.676333
$898$	37.1179	1.23864
$899$	−26.9472	−0.898739
$900$	1.63907	0.0546357
$901$	12.6272	0.420675
$902$	0.663784	0.0221016
$903$	0	0
$904$	−12.2980	−0.409026
$905$	−21.5718	−0.717071
$906$	20.2615	0.673144
$907$	27.9158	0.926929	0.463464	−	0.886116i	$-0.346606\pi$
$907$	27.9158	0.926929	0.463464	+	0.886116i	$0.346606\pi$
$908$	16.6432	0.552325
$909$	−2.55026	−0.0845866
$910$	0	0
$911$	13.3496	0.442292	0.221146	−	0.975241i	$-0.429020\pi$
$911$	13.3496	0.442292	0.221146	+	0.975241i	$0.429020\pi$
$912$	−1.85836	−0.0615366
$913$	−11.7067	−0.387436
$914$	37.7847	1.24981
$915$	0.883032	0.0291921
$916$	−7.41678	−0.245057
$917$	0	0
$918$	13.7063	0.452377
$919$	−39.3246	−1.29720	−0.648600	−	0.761129i	$-0.724645\pi$
$919$	−39.3246	−1.29720	−0.648600	+	0.761129i	$0.724645\pi$
$920$	28.5650	0.941759
$921$	49.2039	1.62132
$922$	31.0541	1.02271
$923$	12.6357	0.415909
$924$	0	0
$925$	−3.36933	−0.110783
$926$	12.0353	0.395506
$927$	2.21838	0.0728611
$928$	−23.9510	−0.786231
$929$	−14.1450	−0.464082	−0.232041	−	0.972706i	$-0.574540\pi$
$929$	−14.1450	−0.464082	−0.232041	+	0.972706i	$0.574540\pi$
$930$	19.1953	0.629438
$931$	0	0
$932$	−7.85793	−0.257395
$933$	−23.9498	−0.784080
$934$	39.4046	1.28936
$935$	−3.84183	−0.125641
$936$	4.48569	0.146619
$937$	19.1488	0.625563	0.312782	−	0.949825i	$-0.398739\pi$
$937$	19.1488	0.625563	0.312782	+	0.949825i	$0.398739\pi$
$938$	0	0
$939$	−34.2292	−1.11703
$940$	−2.80426	−0.0914648
$941$	18.9161	0.616647	0.308323	−	0.951282i	$-0.400232\pi$
$941$	18.9161	0.616647	0.308323	+	0.951282i	$0.400232\pi$
$942$	−30.9576	−1.00865
$943$	5.51242	0.179509
$944$	1.02785	0.0334538
$945$	0	0
$946$	6.91090	0.224693
$947$	47.4341	1.54140	0.770701	−	0.637197i	$-0.219906\pi$
$947$	47.4341	1.54140	0.770701	+	0.637197i	$0.219906\pi$
$948$	6.98938	0.227005
$949$	−7.01069	−0.227577
$950$	2.19683	0.0712745
$951$	−33.7915	−1.09576
$952$	0	0
$953$	8.52637	0.276196	0.138098	−	0.990419i	$-0.455901\pi$
$953$	8.52637	0.276196	0.138098	+	0.990419i	$0.455901\pi$
$954$	−3.03155	−0.0981502
$955$	−43.5228	−1.40836
$956$	2.86939	0.0928027
$957$	−6.15812	−0.199064
$958$	29.1541	0.941925
$959$	0	0
$960$	22.7532	0.734356
$961$	2.37662	0.0766651
$962$	−3.15404	−0.101690
$963$	−3.20995	−0.103439
$964$	−2.68346	−0.0864284
$965$	−2.40207	−0.0773255
$966$	0	0
$967$	−16.3350	−0.525297	−0.262649	−	0.964892i	$-0.584596\pi$
$967$	−16.3350	−0.525297	−0.262649	+	0.964892i	$0.584596\pi$
$968$	−31.3991	−1.00921
$969$	7.21776	0.231868
$970$	−19.1319	−0.614288
$971$	28.9746	0.929839	0.464919	−	0.885353i	$-0.346083\pi$
$971$	28.9746	0.929839	0.464919	+	0.885353i	$0.346083\pi$
$972$	8.41908	0.270042
$973$	0	0
$974$	32.1000	1.02855
$975$	−7.25231	−0.232260
$976$	−0.218606	−0.00699740
$977$	−50.4697	−1.61467	−0.807334	−	0.590095i	$-0.799090\pi$
$977$	−50.4697	−1.61467	−0.807334	+	0.590095i	$0.799090\pi$
$978$	−22.6278	−0.723559
$979$	2.01988	0.0645556
$980$	0	0
$981$	−5.67768	−0.181274
$982$	28.8012	0.919084
$983$	33.1156	1.05622	0.528112	−	0.849175i	$-0.322900\pi$
$983$	33.1156	1.05622	0.528112	+	0.849175i	$0.322900\pi$
$984$	5.80563	0.185077
$985$	−7.82266	−0.249251
$986$	−14.9012	−0.474552
$987$	0	0
$988$	−2.22674	−0.0708421
$989$	57.3918	1.82495
$990$	0.922347	0.0293141
$991$	−13.2685	−0.421487	−0.210743	−	0.977541i	$-0.567588\pi$
$991$	−13.2685	−0.421487	−0.210743	+	0.977541i	$0.567588\pi$
$992$	29.6656	0.941883
$993$	−36.6225	−1.16218
$994$	0	0
$995$	−24.3208	−0.771020
$996$	−35.0228	−1.10974
$997$	1.78710	0.0565979	0.0282990	−	0.999600i	$-0.490991\pi$
$997$	1.78710	0.0565979	0.0282990	+	0.999600i	$0.490991\pi$
$998$	−34.7053	−1.09858
$999$	−7.32442	−0.231734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.u.1.7	yes	20
7.6	odd	2		2009.2.a.t.1.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2009.2.a.t.1.7	✓	20	7.6	odd	2
2009.2.a.u.1.7	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.979921 q^{2} +1.94904 q^{3} -1.03976 q^{4} +1.73965 q^{5} -1.90990 q^{6} +2.97872 q^{8} +0.798739 q^{9} +O(q^{10})\)	\(q-0.979921 q^{2} +1.94904 q^{3} -1.03976 q^{4} +1.73965 q^{5} -1.90990 q^{6} +2.97872 q^{8} +0.798739 q^{9} -1.70472 q^{10} -0.677386 q^{11} -2.02652 q^{12} +1.88536 q^{13} +3.39064 q^{15} -0.839397 q^{16} +3.26016 q^{17} -0.782701 q^{18} +1.13591 q^{19} -1.80881 q^{20} +0.663784 q^{22} +5.51242 q^{23} +5.80563 q^{24} -1.97361 q^{25} -1.84751 q^{26} -4.29034 q^{27} +4.66436 q^{29} -3.32256 q^{30} -5.77725 q^{31} -5.13490 q^{32} -1.32025 q^{33} -3.19470 q^{34} -0.830493 q^{36} +1.70719 q^{37} -1.11310 q^{38} +3.67464 q^{39} +5.18193 q^{40} +1.00000 q^{41} +10.4114 q^{43} +0.704315 q^{44} +1.38953 q^{45} -5.40173 q^{46} +1.55033 q^{47} -1.63601 q^{48} +1.93398 q^{50} +6.35417 q^{51} -1.96032 q^{52} +3.87319 q^{53} +4.20419 q^{54} -1.17842 q^{55} +2.21393 q^{57} -4.57070 q^{58} -1.22452 q^{59} -3.52544 q^{60} +0.260432 q^{61} +5.66125 q^{62} +6.71058 q^{64} +3.27987 q^{65} +1.29374 q^{66} +0.416828 q^{67} -3.38977 q^{68} +10.7439 q^{69} +6.70200 q^{71} +2.37922 q^{72} -3.71849 q^{73} -1.67291 q^{74} -3.84664 q^{75} -1.18107 q^{76} -3.60085 q^{78} -3.44896 q^{79} -1.46026 q^{80} -10.7582 q^{81} -0.979921 q^{82} +17.2822 q^{83} +5.67155 q^{85} -10.2023 q^{86} +9.09101 q^{87} -2.01774 q^{88} -2.98187 q^{89} -1.36163 q^{90} -5.73157 q^{92} -11.2601 q^{93} -1.51920 q^{94} +1.97609 q^{95} -10.0081 q^{96} +11.2229 q^{97} -0.541054 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 8 q^{3} + 18 q^{4} + 8 q^{5} + 12 q^{6} - 6 q^{8} + 16 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 8 * q^3 + 18 * q^4 + 8 * q^5 + 12 * q^6 - 6 * q^8 + 16 * q^9	\( 20 q - 2 q^{2} + 8 q^{3} + 18 q^{4} + 8 q^{5} + 12 q^{6} - 6 q^{8} + 16 q^{9} + 16 q^{10} + 6 q^{12} + 12 q^{13} + 14 q^{16} + 8 q^{17} - 18 q^{18} + 36 q^{19} + 24 q^{20} - 8 q^{22} - 12 q^{23} + 36 q^{24} + 20 q^{25} - 22 q^{26} + 32 q^{27} + 4 q^{29} + 28 q^{30} + 80 q^{31} + 6 q^{32} - 12 q^{33} + 48 q^{34} + 26 q^{36} + 4 q^{37} + 12 q^{38} - 28 q^{39} - 4 q^{40} + 20 q^{41} - 20 q^{44} + 40 q^{45} + 8 q^{46} + 32 q^{47} + 16 q^{48} + 6 q^{50} - 20 q^{51} + 36 q^{52} + 4 q^{53} - 50 q^{54} + 64 q^{55} - 4 q^{57} + 32 q^{59} + 20 q^{60} + 44 q^{61} - 8 q^{62} - 30 q^{64} - 8 q^{65} + 32 q^{66} - 4 q^{67} - 48 q^{68} - 24 q^{69} + 8 q^{71} - 8 q^{72} + 48 q^{73} - 38 q^{74} + 24 q^{75} + 84 q^{76} + 30 q^{78} - 4 q^{79} + 56 q^{80} - 2 q^{82} + 8 q^{83} - 12 q^{85} - 24 q^{86} + 40 q^{87} - 48 q^{88} + 20 q^{89} + 48 q^{90} - 50 q^{92} + 48 q^{93} + 26 q^{94} + 20 q^{95} + 70 q^{96} + 8 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 8 * q^3 + 18 * q^4 + 8 * q^5 + 12 * q^6 - 6 * q^8 + 16 * q^9 + 16 * q^10 + 6 * q^12 + 12 * q^13 + 14 * q^16 + 8 * q^17 - 18 * q^18 + 36 * q^19 + 24 * q^20 - 8 * q^22 - 12 * q^23 + 36 * q^24 + 20 * q^25 - 22 * q^26 + 32 * q^27 + 4 * q^29 + 28 * q^30 + 80 * q^31 + 6 * q^32 - 12 * q^33 + 48 * q^34 + 26 * q^36 + 4 * q^37 + 12 * q^38 - 28 * q^39 - 4 * q^40 + 20 * q^41 - 20 * q^44 + 40 * q^45 + 8 * q^46 + 32 * q^47 + 16 * q^48 + 6 * q^50 - 20 * q^51 + 36 * q^52 + 4 * q^53 - 50 * q^54 + 64 * q^55 - 4 * q^57 + 32 * q^59 + 20 * q^60 + 44 * q^61 - 8 * q^62 - 30 * q^64 - 8 * q^65 + 32 * q^66 - 4 * q^67 - 48 * q^68 - 24 * q^69 + 8 * q^71 - 8 * q^72 + 48 * q^73 - 38 * q^74 + 24 * q^75 + 84 * q^76 + 30 * q^78 - 4 * q^79 + 56 * q^80 - 2 * q^82 + 8 * q^83 - 12 * q^85 - 24 * q^86 + 40 * q^87 - 48 * q^88 + 20 * q^89 + 48 * q^90 - 50 * q^92 + 48 * q^93 + 26 * q^94 + 20 * q^95 + 70 * q^96 + 8 * q^97 - 8 * q^99

Introduction

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Database

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