LMFDB - Embedded newform 2009.2.a.m.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$16.0419457661$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.233489.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + x^{2} + 5x - 1 $ x^5 - x^4 - 6x^3 + x^2 + 5x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.16000$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.35647 q^{2} +2.22790 q^{3} -0.160001 q^{4} -2.22790 q^{5} +3.02207 q^{6} -2.92997 q^{8} +1.96354 q^{9} +O(q^{10})$	\(q+1.35647 q^{2} +2.22790 q^{3} -0.160001 q^{4} -2.22790 q^{5} +3.02207 q^{6} -2.92997 q^{8} +1.96354 q^{9} -3.02207 q^{10} -1.12857 q^{11} -0.356466 q^{12} -2.22790 q^{13} -4.96354 q^{15} -3.65440 q^{16} -4.05350 q^{17} +2.66347 q^{18} +3.61580 q^{19} +0.356466 q^{20} -1.53086 q^{22} -2.68583 q^{23} -6.52767 q^{24} -0.0364641 q^{25} -3.02207 q^{26} -2.30914 q^{27} -3.72230 q^{29} -6.73287 q^{30} -0.345260 q^{31} +0.902868 q^{32} -2.51433 q^{33} -5.49844 q^{34} -0.314167 q^{36} +3.34930 q^{37} +4.90471 q^{38} -4.96354 q^{39} +6.52767 q^{40} +1.00000 q^{41} -12.6805 q^{43} +0.180572 q^{44} -4.37456 q^{45} -3.64324 q^{46} +7.31284 q^{47} -8.14163 q^{48} -0.0494623 q^{50} -9.03080 q^{51} +0.356466 q^{52} -8.35617 q^{53} -3.13227 q^{54} +2.51433 q^{55} +8.05564 q^{57} -5.04917 q^{58} +5.22500 q^{59} +0.794170 q^{60} -5.60864 q^{61} -0.468334 q^{62} +8.53351 q^{64} +4.96354 q^{65} -3.41061 q^{66} -8.83249 q^{67} +0.648564 q^{68} -5.98377 q^{69} +9.92933 q^{71} -5.75310 q^{72} -0.815796 q^{73} +4.54321 q^{74} -0.0812383 q^{75} -0.578531 q^{76} -6.73287 q^{78} -8.84184 q^{79} +8.14163 q^{80} -11.0351 q^{81} +1.35647 q^{82} +7.48907 q^{83} +9.03080 q^{85} -17.2007 q^{86} -8.29290 q^{87} +3.30666 q^{88} +15.7637 q^{89} -5.93394 q^{90} +0.429735 q^{92} -0.769205 q^{93} +9.91961 q^{94} -8.05564 q^{95} +2.01150 q^{96} +2.10829 q^{97} -2.21598 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} - q^{6} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 - q^6 - 3 * q^8 + 5 * q^9	$ 5 q - 2 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} - q^{6} - 3 q^{8} + 5 q^{9} + q^{10} - 6 q^{11} + 7 q^{12} - 2 q^{13} - 20 q^{15} - 12 q^{16} + 3 q^{17} - 8 q^{18} - 7 q^{19} - 7 q^{20} - 13 q^{22} - 16 q^{24} - 5 q^{25} + q^{26} - 13 q^{27} - 10 q^{29} + 14 q^{30} + 6 q^{31} - 3 q^{32} + 17 q^{33} - q^{34} - 15 q^{36} - 18 q^{37} + 7 q^{38} - 20 q^{39} + 16 q^{40} + 5 q^{41} - 14 q^{43} + 2 q^{44} + 7 q^{45} - 3 q^{46} - 3 q^{47} - 9 q^{48} - 4 q^{50} - 7 q^{52} - 9 q^{53} + 25 q^{54} - 17 q^{55} + 31 q^{57} - 5 q^{58} + 19 q^{59} - 3 q^{60} + 23 q^{61} - 36 q^{62} - q^{64} + 20 q^{65} - 23 q^{66} - 11 q^{67} + 24 q^{68} - 19 q^{69} + 25 q^{72} - 13 q^{73} + 2 q^{74} - 11 q^{75} - 12 q^{76} + 14 q^{78} - 41 q^{79} + 9 q^{80} - 7 q^{81} - 2 q^{82} + 2 q^{83} + 20 q^{86} - 32 q^{87} - 10 q^{88} - 14 q^{89} - 22 q^{90} + 17 q^{92} - 15 q^{93} - 10 q^{94} - 31 q^{95} + 33 q^{96} + 27 q^{97} - 9 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 - q^6 - 3 * q^8 + 5 * q^9 + q^10 - 6 * q^11 + 7 * q^12 - 2 * q^13 - 20 * q^15 - 12 * q^16 + 3 * q^17 - 8 * q^18 - 7 * q^19 - 7 * q^20 - 13 * q^22 - 16 * q^24 - 5 * q^25 + q^26 - 13 * q^27 - 10 * q^29 + 14 * q^30 + 6 * q^31 - 3 * q^32 + 17 * q^33 - q^34 - 15 * q^36 - 18 * q^37 + 7 * q^38 - 20 * q^39 + 16 * q^40 + 5 * q^41 - 14 * q^43 + 2 * q^44 + 7 * q^45 - 3 * q^46 - 3 * q^47 - 9 * q^48 - 4 * q^50 - 7 * q^52 - 9 * q^53 + 25 * q^54 - 17 * q^55 + 31 * q^57 - 5 * q^58 + 19 * q^59 - 3 * q^60 + 23 * q^61 - 36 * q^62 - q^64 + 20 * q^65 - 23 * q^66 - 11 * q^67 + 24 * q^68 - 19 * q^69 + 25 * q^72 - 13 * q^73 + 2 * q^74 - 11 * q^75 - 12 * q^76 + 14 * q^78 - 41 * q^79 + 9 * q^80 - 7 * q^81 - 2 * q^82 + 2 * q^83 + 20 * q^86 - 32 * q^87 - 10 * q^88 - 14 * q^89 - 22 * q^90 + 17 * q^92 - 15 * q^93 - 10 * q^94 - 31 * q^95 + 33 * q^96 + 27 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.35647	0.959166	0.479583	−	0.877496i	$-0.340788\pi$
$2$	1.35647	0.959166	0.479583	+	0.877496i	$0.340788\pi$
$3$	2.22790	1.28628	0.643139	−	0.765749i	$-0.277632\pi$
$3$	2.22790	1.28628	0.643139	+	0.765749i	$0.277632\pi$
$4$	−0.160001	−0.0800004
$5$	−2.22790	−0.996347	−0.498173	−	0.867077i	$-0.665996\pi$
$5$	−2.22790	−0.996347	−0.498173	+	0.867077i	$0.665996\pi$
$6$	3.02207	1.23375
$7$	0	0
$7$	0	0
$8$	−2.92997	−1.03590
$9$	1.96354	0.654512
$10$	−3.02207	−0.955662
$11$	−1.12857	−0.340276	−0.170138	−	0.985420i	$-0.554421\pi$
$11$	−1.12857	−0.340276	−0.170138	+	0.985420i	$0.554421\pi$
$12$	−0.356466	−0.102903
$13$	−2.22790	−0.617908	−0.308954	−	0.951077i	$-0.599979\pi$
$13$	−2.22790	−0.617908	−0.308954	+	0.951077i	$0.599979\pi$
$14$	0	0
$15$	−4.96354	−1.28158
$16$	−3.65440	−0.913600
$17$	−4.05350	−0.983119	−0.491560	−	0.870844i	$-0.663573\pi$
$17$	−4.05350	−0.983119	−0.491560	+	0.870844i	$0.663573\pi$
$18$	2.66347	0.627786
$19$	3.61580	0.829521	0.414761	−	0.909931i	$-0.363865\pi$
$19$	3.61580	0.829521	0.414761	+	0.909931i	$0.363865\pi$
$20$	0.356466	0.0797082
$21$	0	0
$22$	−1.53086	−0.326381
$23$	−2.68583	−0.560035	−0.280017	−	0.959995i	$-0.590340\pi$
$23$	−2.68583	−0.560035	−0.280017	+	0.959995i	$0.590340\pi$
$24$	−6.52767	−1.33246
$25$	−0.0364641	−0.00729282
$26$	−3.02207	−0.592677
$27$	−2.30914	−0.444394
$28$	0	0
$29$	−3.72230	−0.691213	−0.345607	−	0.938380i	$-0.612327\pi$
$29$	−3.72230	−0.691213	−0.345607	+	0.938380i	$0.612327\pi$
$30$	−6.73287	−1.22925
$31$	−0.345260	−0.0620106	−0.0310053	−	0.999519i	$-0.509871\pi$
$31$	−0.345260	−0.0620106	−0.0310053	+	0.999519i	$0.509871\pi$
$32$	0.902868	0.159606
$33$	−2.51433	−0.437689
$34$	−5.49844	−0.942974
$35$	0	0
$36$	−0.314167	−0.0523612
$37$	3.34930	0.550622	0.275311	−	0.961355i	$-0.411219\pi$
$37$	3.34930	0.550622	0.275311	+	0.961355i	$0.411219\pi$
$38$	4.90471	0.795649
$39$	−4.96354	−0.794802
$40$	6.52767	1.03212
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−12.6805	−1.93376	−0.966880	−	0.255232i	$-0.917848\pi$
$43$	−12.6805	−1.93376	−0.966880	+	0.255232i	$0.917848\pi$
$44$	0.180572	0.0272222
$45$	−4.37456	−0.652121
$46$	−3.64324	−0.537166
$47$	7.31284	1.06669	0.533344	−	0.845899i	$-0.320935\pi$
$47$	7.31284	1.06669	0.533344	+	0.845899i	$0.320935\pi$
$48$	−8.14163	−1.17514
$49$	0	0
$50$	−0.0494623	−0.00699502
$51$	−9.03080	−1.26456
$52$	0.356466	0.0494329
$53$	−8.35617	−1.14781	−0.573904	−	0.818922i	$-0.694572\pi$
$53$	−8.35617	−1.14781	−0.573904	+	0.818922i	$0.694572\pi$
$54$	−3.13227	−0.426247
$55$	2.51433	0.339032
$56$	0	0
$57$	8.05564	1.06700
$58$	−5.04917	−0.662988
$59$	5.22500	0.680238	0.340119	−	0.940382i	$-0.389533\pi$
$59$	5.22500	0.680238	0.340119	+	0.940382i	$0.389533\pi$
$60$	0.794170	0.102527
$61$	−5.60864	−0.718112	−0.359056	−	0.933316i	$-0.616901\pi$
$61$	−5.60864	−0.718112	−0.359056	+	0.933316i	$0.616901\pi$
$62$	−0.468334	−0.0594785
$63$	0	0
$64$	8.53351	1.06669
$65$	4.96354	0.615651
$66$	−3.41061	−0.419816
$67$	−8.83249	−1.07906	−0.539530	−	0.841966i	$-0.681398\pi$
$67$	−8.83249	−1.07906	−0.539530	+	0.841966i	$0.681398\pi$
$68$	0.648564	0.0786499
$69$	−5.98377	−0.720361
$70$	0	0
$71$	9.92933	1.17839	0.589197	−	0.807989i	$-0.299444\pi$
$71$	9.92933	1.17839	0.589197	+	0.807989i	$0.299444\pi$
$72$	−5.75310	−0.678009
$73$	−0.815796	−0.0954817	−0.0477408	−	0.998860i	$-0.515202\pi$
$73$	−0.815796	−0.0954817	−0.0477408	+	0.998860i	$0.515202\pi$
$74$	4.54321	0.528138
$75$	−0.0812383	−0.00938059
$76$	−0.578531	−0.0663620
$77$	0	0
$78$	−6.73287	−0.762347
$79$	−8.84184	−0.994785	−0.497392	−	0.867526i	$-0.665709\pi$
$79$	−8.84184	−0.994785	−0.497392	+	0.867526i	$0.665709\pi$
$80$	8.14163	0.910262
$81$	−11.0351	−1.22613
$82$	1.35647	0.149797
$83$	7.48907	0.822033	0.411016	−	0.911628i	$-0.365174\pi$
$83$	7.48907	0.822033	0.411016	+	0.911628i	$0.365174\pi$
$84$	0	0
$85$	9.03080	0.979528
$86$	−17.2007	−1.85480
$87$	−8.29290	−0.889093
$88$	3.30666	0.352491
$89$	15.7637	1.67095	0.835473	−	0.549532i	$-0.185194\pi$
$89$	15.7637	1.67095	0.835473	+	0.549532i	$0.185194\pi$
$90$	−5.93394	−0.625492
$91$	0	0
$92$	0.429735	0.0448030
$93$	−0.769205	−0.0797629
$94$	9.91961	1.02313
$95$	−8.05564	−0.826491
$96$	2.01150	0.205298
$97$	2.10829	0.214064	0.107032	−	0.994256i	$-0.465865\pi$
$97$	2.10829	0.214064	0.107032	+	0.994256i	$0.465865\pi$
$98$	0	0
$99$	−2.21598	−0.222714
$100$	0.00583428	0.000583428 0
$101$	−7.84179	−0.780287	−0.390144	−	0.920754i	$-0.627575\pi$
$101$	−7.84179	−0.780287	−0.390144	+	0.920754i	$0.627575\pi$
$102$	−12.2500	−1.21293
$103$	6.90910	0.680774	0.340387	−	0.940285i	$-0.389442\pi$
$103$	6.90910	0.680774	0.340387	+	0.940285i	$0.389442\pi$
$104$	6.52767	0.640091
$105$	0	0
$106$	−11.3349	−1.10094
$107$	19.5675	1.89167	0.945833	−	0.324654i	$-0.105248\pi$
$107$	19.5675	1.89167	0.945833	+	0.324654i	$0.105248\pi$
$108$	0.369464	0.0355517
$109$	3.92210	0.375669	0.187835	−	0.982201i	$-0.439853\pi$
$109$	3.92210	0.375669	0.187835	+	0.982201i	$0.439853\pi$
$110$	3.41061	0.325188
$111$	7.46191	0.708253
$112$	0	0
$113$	−5.10800	−0.480520	−0.240260	−	0.970709i	$-0.577233\pi$
$113$	−5.10800	−0.480520	−0.240260	+	0.970709i	$0.577233\pi$
$114$	10.9272	1.02343
$115$	5.98377	0.557989
$116$	0.595570	0.0552973
$117$	−4.37456	−0.404428
$118$	7.08754	0.652461
$119$	0	0
$120$	14.5430	1.32759
$121$	−9.72634	−0.884213
$122$	−7.60792	−0.688789
$123$	2.22790	0.200883
$124$	0.0552419	0.00496087
$125$	11.2207	1.00361
$126$	0	0
$127$	−19.3732	−1.71909	−0.859547	−	0.511056i	$-0.829254\pi$
$127$	−19.3732	−1.71909	−0.859547	+	0.511056i	$0.829254\pi$
$128$	9.76967	0.863525
$129$	−28.2509	−2.48735
$130$	6.73287	0.590511
$131$	0.309091	0.0270054	0.0135027	−	0.999909i	$-0.495702\pi$
$131$	0.309091	0.0270054	0.0135027	+	0.999909i	$0.495702\pi$
$132$	0.402295	0.0350153
$133$	0	0
$134$	−11.9810	−1.03500
$135$	5.14453	0.442770
$136$	11.8766	1.01841
$137$	−17.3675	−1.48381	−0.741905	−	0.670505i	$-0.766077\pi$
$137$	−17.3675	−1.48381	−0.741905	+	0.670505i	$0.766077\pi$
$138$	−8.11677	−0.690946
$139$	15.1514	1.28512	0.642562	−	0.766233i	$-0.277871\pi$
$139$	15.1514	1.28512	0.642562	+	0.766233i	$0.277871\pi$
$140$	0	0
$141$	16.2923	1.37206
$142$	13.4688	1.13028
$143$	2.51433	0.210259
$144$	−7.17554	−0.597962
$145$	8.29290	0.688688
$146$	−1.10660	−0.0915828
$147$	0	0
$148$	−0.535891	−0.0440500
$149$	−10.4934	−0.859654	−0.429827	−	0.902911i	$-0.641425\pi$
$149$	−10.4934	−0.859654	−0.429827	+	0.902911i	$0.641425\pi$
$150$	−0.110197	−0.00899755
$151$	−5.11950	−0.416619	−0.208309	−	0.978063i	$-0.566796\pi$
$151$	−5.11950	−0.416619	−0.208309	+	0.978063i	$0.566796\pi$
$152$	−10.5942	−0.859301
$153$	−7.95920	−0.643463
$154$	0	0
$155$	0.769205	0.0617841
$156$	0.794170	0.0635845
$157$	−15.0958	−1.20478	−0.602388	−	0.798203i	$-0.705784\pi$
$157$	−15.0958	−1.20478	−0.602388	+	0.798203i	$0.705784\pi$
$158$	−11.9937	−0.954164
$159$	−18.6167	−1.47640
$160$	−2.01150	−0.159023
$161$	0	0
$162$	−14.9688	−1.17606
$163$	7.61624	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$163$	7.61624	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$164$	−0.160001	−0.0124940
$165$	5.60168	0.436090
$166$	10.1587	0.788466
$167$	−8.24963	−0.638375	−0.319188	−	0.947692i	$-0.603410\pi$
$167$	−8.24963	−0.638375	−0.319188	+	0.947692i	$0.603410\pi$
$168$	0	0
$169$	−8.03646	−0.618190
$170$	12.2500	0.939530
$171$	7.09975	0.542932
$172$	2.02889	0.154702
$173$	23.7381	1.80477	0.902386	−	0.430929i	$-0.141814\pi$
$173$	23.7381	1.80477	0.902386	+	0.430929i	$0.141814\pi$
$174$	−11.2490	−0.852787
$175$	0	0
$176$	4.12423	0.310876
$177$	11.6408	0.874975
$178$	21.3829	1.60271
$179$	11.4555	0.856221	0.428111	−	0.903726i	$-0.359179\pi$
$179$	11.4555	0.856221	0.428111	+	0.903726i	$0.359179\pi$
$180$	0.699933	0.0521699
$181$	−17.7517	−1.31948	−0.659738	−	0.751495i	$-0.729333\pi$
$181$	−17.7517	−1.31948	−0.659738	+	0.751495i	$0.729333\pi$
$182$	0	0
$183$	−12.4955	−0.923692
$184$	7.86940	0.580140
$185$	−7.46191	−0.548610
$186$	−1.04340	−0.0765059
$187$	4.57465	0.334531
$188$	−1.17006	−0.0853354
$189$	0	0
$190$	−10.9272	−0.792742
$191$	16.4578	1.19085	0.595423	−	0.803413i	$-0.296985\pi$
$191$	16.4578	1.19085	0.595423	+	0.803413i	$0.296985\pi$
$192$	19.0118	1.37206
$193$	19.7096	1.41873	0.709365	−	0.704842i	$-0.248982\pi$
$193$	19.7096	1.41873	0.709365	+	0.704842i	$0.248982\pi$
$194$	2.85982	0.205323
$195$	11.0583	0.791898
$196$	0	0
$197$	12.9492	0.922592	0.461296	−	0.887246i	$-0.347385\pi$
$197$	12.9492	0.922592	0.461296	+	0.887246i	$0.347385\pi$
$198$	−3.00590	−0.213620
$199$	−25.7131	−1.82276	−0.911378	−	0.411570i	$-0.864981\pi$
$199$	−25.7131	−1.82276	−0.911378	+	0.411570i	$0.864981\pi$
$200$	0.106839	0.00755463
$201$	−19.6779	−1.38797
$202$	−10.6371	−0.748425
$203$	0	0
$204$	1.44494	0.101166
$205$	−2.22790	−0.155603
$206$	9.37196	0.652975
$207$	−5.27373	−0.366549
$208$	8.14163	0.564521
$209$	−4.08067	−0.282266
$210$	0	0
$211$	13.4799	0.927993	0.463996	−	0.885837i	$-0.346415\pi$
$211$	13.4799	0.927993	0.463996	+	0.885837i	$0.346415\pi$
$212$	1.33699	0.0918251
$213$	22.1216	1.51574
$214$	26.5427	1.81442
$215$	28.2509	1.92670
$216$	6.76570	0.460347
$217$	0	0
$218$	5.32019	0.360329
$219$	−1.81751	−0.122816
$220$	−0.402295	−0.0271227
$221$	9.03080	0.607477
$222$	10.1218	0.679332
$223$	2.59701	0.173909	0.0869544	−	0.996212i	$-0.472287\pi$
$223$	2.59701	0.173909	0.0869544	+	0.996212i	$0.472287\pi$
$224$	0	0
$225$	−0.0715986	−0.00477324
$226$	−6.92882	−0.460898
$227$	10.1112	0.671102	0.335551	−	0.942022i	$-0.391077\pi$
$227$	10.1112	0.671102	0.335551	+	0.942022i	$0.391077\pi$
$228$	−1.28891	−0.0853601
$229$	13.5898	0.898042	0.449021	−	0.893521i	$-0.351773\pi$
$229$	13.5898	0.898042	0.449021	+	0.893521i	$0.351773\pi$
$230$	8.11677	0.535204
$231$	0	0
$232$	10.9062	0.716028
$233$	9.26227	0.606792	0.303396	−	0.952865i	$-0.401880\pi$
$233$	9.26227	0.606792	0.303396	+	0.952865i	$0.401880\pi$
$234$	−5.93394	−0.387914
$235$	−16.2923	−1.06279
$236$	−0.836005	−0.0544193
$237$	−19.6987	−1.27957
$238$	0	0
$239$	−10.5580	−0.682942	−0.341471	−	0.939892i	$-0.610925\pi$
$239$	−10.5580	−0.682942	−0.341471	+	0.939892i	$0.610925\pi$
$240$	18.1387	1.17085
$241$	−9.01525	−0.580723	−0.290362	−	0.956917i	$-0.593776\pi$
$241$	−9.01525	−0.580723	−0.290362	+	0.956917i	$0.593776\pi$
$242$	−13.1934	−0.848107
$243$	−17.6578	−1.13275
$244$	0.897386	0.0574493
$245$	0	0
$246$	3.02207	0.192680
$247$	−8.05564	−0.512568
$248$	1.01160	0.0642368
$249$	16.6849	1.05736
$250$	15.2205	0.962632
$251$	−21.2912	−1.34389	−0.671945	−	0.740601i	$-0.734541\pi$
$251$	−21.2912	−1.34389	−0.671945	+	0.740601i	$0.734541\pi$
$252$	0	0
$253$	3.03114	0.190566
$254$	−26.2791	−1.64890
$255$	20.1197	1.25995
$256$	−3.81479	−0.238424
$257$	−8.45793	−0.527591	−0.263796	−	0.964579i	$-0.584974\pi$
$257$	−8.45793	−0.527591	−0.263796	+	0.964579i	$0.584974\pi$
$258$	−38.3214	−2.38578
$259$	0	0
$260$	−0.794170	−0.0492523
$261$	−7.30886	−0.452407
$262$	0.419271	0.0259026
$263$	−2.72257	−0.167881	−0.0839405	−	0.996471i	$-0.526751\pi$
$263$	−2.72257	−0.167881	−0.0839405	+	0.996471i	$0.526751\pi$
$264$	7.36691	0.453402
$265$	18.6167	1.14362
$266$	0	0
$267$	35.1199	2.14930
$268$	1.41321	0.0863253
$269$	−29.5788	−1.80345	−0.901726	−	0.432309i	$-0.857699\pi$
$269$	−29.5788	−1.80345	−0.901726	+	0.432309i	$0.857699\pi$
$270$	6.97837	0.424690
$271$	−8.11601	−0.493013	−0.246506	−	0.969141i	$-0.579283\pi$
$271$	−8.11601	−0.493013	−0.246506	+	0.969141i	$0.579283\pi$
$272$	14.8131	0.898177
$273$	0	0
$274$	−23.5585	−1.42322
$275$	0.0411521	0.00248157
$276$	0.957407	0.0576291
$277$	−1.09394	−0.0657286	−0.0328643	−	0.999460i	$-0.510463\pi$
$277$	−1.09394	−0.0657286	−0.0328643	+	0.999460i	$0.510463\pi$
$278$	20.5523	1.23265
$279$	−0.677931	−0.0405867
$280$	0	0
$281$	7.95015	0.474266	0.237133	−	0.971477i	$-0.423792\pi$
$281$	7.95015	0.474266	0.237133	+	0.971477i	$0.423792\pi$
$282$	22.0999	1.31603
$283$	27.6594	1.64418	0.822089	−	0.569358i	$-0.192808\pi$
$283$	27.6594	1.64418	0.822089	+	0.569358i	$0.192808\pi$
$284$	−1.58870	−0.0942721
$285$	−17.9472	−1.06310
$286$	3.41061	0.201673
$287$	0	0
$288$	1.77281	0.104464
$289$	−0.569108	−0.0334769
$290$	11.2490	0.660566
$291$	4.69706	0.275346
$292$	0.130528	0.00763857
$293$	9.57574	0.559421	0.279710	−	0.960084i	$-0.409762\pi$
$293$	9.57574	0.559421	0.279710	+	0.960084i	$0.409762\pi$
$294$	0	0
$295$	−11.6408	−0.677753
$296$	−9.81334	−0.570389
$297$	2.60601	0.151216
$298$	−14.2339	−0.824551
$299$	5.98377	0.346050
$300$	0.0129982	0.000750451 0
$301$	0	0
$302$	−6.94442	−0.399606
$303$	−17.4707	−1.00367
$304$	−13.2136	−0.757850
$305$	12.4955	0.715489
$306$	−10.7964	−0.617188
$307$	−8.24141	−0.470362	−0.235181	−	0.971952i	$-0.575568\pi$
$307$	−8.24141	−0.470362	−0.235181	+	0.971952i	$0.575568\pi$
$308$	0	0
$309$	15.3928	0.875665
$310$	1.04340	0.0592612
$311$	11.6642	0.661418	0.330709	−	0.943733i	$-0.392712\pi$
$311$	11.6642	0.661418	0.330709	+	0.943733i	$0.392712\pi$
$312$	14.5430	0.823335
$313$	−30.6181	−1.73064	−0.865319	−	0.501222i	$-0.832884\pi$
$313$	−30.6181	−1.73064	−0.865319	+	0.501222i	$0.832884\pi$
$314$	−20.4769	−1.15558
$315$	0	0
$316$	1.41470	0.0795832
$317$	−20.8117	−1.16890	−0.584450	−	0.811430i	$-0.698690\pi$
$317$	−20.8117	−1.16890	−0.584450	+	0.811430i	$0.698690\pi$
$318$	−25.2529	−1.41611
$319$	4.20086	0.235203
$320$	−19.0118	−1.06279
$321$	43.5945	2.43321
$322$	0	0
$323$	−14.6567	−0.815518
$324$	1.76563	0.0980906
$325$	0.0812383	0.00450629
$326$	10.3312	0.572191
$327$	8.73804	0.483215
$328$	−2.92997	−0.161780
$329$	0	0
$330$	7.59849	0.418283
$331$	−0.667000	−0.0366616	−0.0183308	−	0.999832i	$-0.505835\pi$
$331$	−0.667000	−0.0366616	−0.0183308	+	0.999832i	$0.505835\pi$
$332$	−1.19826	−0.0657629
$333$	6.57647	0.360389
$334$	−11.1903	−0.612308
$335$	19.6779	1.07512
$336$	0	0
$337$	0.0671610	0.00365849	0.00182925	−	0.999998i	$-0.499418\pi$
$337$	0.0671610	0.00365849	0.00182925	+	0.999998i	$0.499418\pi$
$338$	−10.9012	−0.592946
$339$	−11.3801	−0.618082
$340$	−1.44494	−0.0783626
$341$	0.389649	0.0211007
$342$	9.63057	0.520762
$343$	0	0
$344$	37.1535	2.00318
$345$	13.3312	0.717729
$346$	32.1999	1.73108
$347$	28.5133	1.53068	0.765338	−	0.643628i	$-0.222572\pi$
$347$	28.5133	1.53068	0.765338	+	0.643628i	$0.222572\pi$
$348$	1.32687	0.0711278
$349$	−30.8596	−1.65188	−0.825938	−	0.563761i	$-0.809354\pi$
$349$	−30.8596	−1.65188	−0.825938	+	0.563761i	$0.809354\pi$
$350$	0	0
$351$	5.14453	0.274595
$352$	−1.01895	−0.0543100
$353$	−18.8658	−1.00413	−0.502064	−	0.864831i	$-0.667426\pi$
$353$	−18.8658	−1.00413	−0.502064	+	0.864831i	$0.667426\pi$
$354$	15.7903	0.839246
$355$	−22.1216	−1.17409
$356$	−2.52220	−0.133676
$357$	0	0
$358$	15.5389	0.821258
$359$	−0.647576	−0.0341777	−0.0170889	−	0.999854i	$-0.505440\pi$
$359$	−0.647576	−0.0341777	−0.0170889	+	0.999854i	$0.505440\pi$
$360$	12.8173	0.675532
$361$	−5.92599	−0.311894
$362$	−24.0796	−1.26560
$363$	−21.6693	−1.13734
$364$	0	0
$365$	1.81751	0.0951329
$366$	−16.9497	−0.885974
$367$	10.1637	0.530539	0.265269	−	0.964174i	$-0.414539\pi$
$367$	10.1637	0.530539	0.265269	+	0.964174i	$0.414539\pi$
$368$	9.81510	0.511648
$369$	1.96354	0.102218
$370$	−10.1218	−0.526208
$371$	0	0
$372$	0.123073	0.00638106
$373$	6.96897	0.360840	0.180420	−	0.983590i	$-0.442254\pi$
$373$	6.96897	0.360840	0.180420	+	0.983590i	$0.442254\pi$
$374$	6.20535	0.320871
$375$	24.9987	1.29093
$376$	−21.4264	−1.10498
$377$	8.29290	0.427106
$378$	0	0
$379$	−36.4593	−1.87279	−0.936394	−	0.350950i	$-0.885859\pi$
$379$	−36.4593	−1.87279	−0.936394	+	0.350950i	$0.885859\pi$
$380$	1.28891	0.0661196
$381$	−43.1616	−2.21123
$382$	22.3245	1.14222
$383$	20.1784	1.03107	0.515534	−	0.856869i	$-0.327593\pi$
$383$	20.1784	1.03107	0.515534	+	0.856869i	$0.327593\pi$
$384$	21.7658	1.11073
$385$	0	0
$386$	26.7354	1.36080
$387$	−24.8986	−1.26567
$388$	−0.337328	−0.0171252
$389$	−18.2388	−0.924745	−0.462373	−	0.886686i	$-0.653002\pi$
$389$	−18.2388	−0.924745	−0.462373	+	0.886686i	$0.653002\pi$
$390$	15.0001	0.759562
$391$	10.8870	0.550581
$392$	0	0
$393$	0.688623	0.0347364
$394$	17.5651	0.884919
$395$	19.6987	0.991151
$396$	0.354559	0.0178172
$397$	−37.6739	−1.89080	−0.945400	−	0.325912i	$-0.894329\pi$
$397$	−37.6739	−1.89080	−0.945400	+	0.325912i	$0.894329\pi$
$398$	−34.8790	−1.74833
$399$	0	0
$400$	0.133254	0.00666272
$401$	−25.6232	−1.27956	−0.639780	−	0.768558i	$-0.720975\pi$
$401$	−25.6232	−1.27956	−0.639780	+	0.768558i	$0.720975\pi$
$402$	−26.6924	−1.33130
$403$	0.769205	0.0383168
$404$	1.25469	0.0624233
$405$	24.5852	1.22165
$406$	0	0
$407$	−3.77991	−0.187363
$408$	26.4599	1.30996
$409$	4.09136	0.202305	0.101152	−	0.994871i	$-0.467747\pi$
$409$	4.09136	0.202305	0.101152	+	0.994871i	$0.467747\pi$
$410$	−3.02207	−0.149249
$411$	−38.6931	−1.90859
$412$	−1.10546	−0.0544622
$413$	0	0
$414$	−7.15363	−0.351582
$415$	−16.6849	−0.819030
$416$	−2.01150	−0.0986219
$417$	33.7558	1.65303
$418$	−5.53529	−0.270740
$419$	33.7334	1.64798	0.823992	−	0.566602i	$-0.191742\pi$
$419$	33.7334	1.64798	0.823992	+	0.566602i	$0.191742\pi$
$420$	0	0
$421$	0.804296	0.0391990	0.0195995	−	0.999808i	$-0.493761\pi$
$421$	0.804296	0.0391990	0.0195995	+	0.999808i	$0.493761\pi$
$422$	18.2850	0.890099
$423$	14.3590	0.698159
$424$	24.4833	1.18901
$425$	0.147807	0.00716971
$426$	30.0071	1.45385
$427$	0	0
$428$	−3.13082	−0.151334
$429$	5.60168	0.270452
$430$	38.3214	1.84802
$431$	−39.8279	−1.91844	−0.959221	−	0.282656i	$-0.908785\pi$
$431$	−39.8279	−1.91844	−0.959221	+	0.282656i	$0.908785\pi$
$432$	8.43851	0.405998
$433$	6.07965	0.292169	0.146085	−	0.989272i	$-0.453333\pi$
$433$	6.07965	0.292169	0.146085	+	0.989272i	$0.453333\pi$
$434$	0	0
$435$	18.4758	0.885845
$436$	−0.627539	−0.0300537
$437$	−9.71143	−0.464561
$438$	−2.46539	−0.117801
$439$	−40.0899	−1.91339	−0.956694	−	0.291094i	$-0.905981\pi$
$439$	−40.0899	−1.91339	−0.956694	+	0.291094i	$0.905981\pi$
$440$	−7.36691	−0.351204
$441$	0	0
$442$	12.2500	0.582672
$443$	18.0821	0.859106	0.429553	−	0.903042i	$-0.358671\pi$
$443$	18.0821	0.859106	0.429553	+	0.903042i	$0.358671\pi$
$444$	−1.19391	−0.0566605
$445$	−35.1199	−1.66484
$446$	3.52276	0.166807
$447$	−23.3783	−1.10575
$448$	0	0
$449$	−11.4042	−0.538200	−0.269100	−	0.963112i	$-0.586726\pi$
$449$	−11.4042	−0.538200	−0.269100	+	0.963112i	$0.586726\pi$
$450$	−0.0971210	−0.00457833
$451$	−1.12857	−0.0531421
$452$	0.817283	0.0384418
$453$	−11.4057	−0.535888
$454$	13.7155	0.643698
$455$	0	0
$456$	−23.6028	−1.10530
$457$	28.1756	1.31800	0.658999	−	0.752144i	$-0.270980\pi$
$457$	28.1756	1.31800	0.658999	+	0.752144i	$0.270980\pi$
$458$	18.4341	0.861371
$459$	9.36010	0.436892
$460$	−0.957407	−0.0446393
$461$	−29.6306	−1.38003	−0.690017	−	0.723793i	$-0.742397\pi$
$461$	−29.6306	−1.38003	−0.690017	+	0.723793i	$0.742397\pi$
$462$	0	0
$463$	29.1404	1.35427	0.677135	−	0.735859i	$-0.263221\pi$
$463$	29.1404	1.35427	0.677135	+	0.735859i	$0.263221\pi$
$464$	13.6028	0.631492
$465$	1.71371	0.0794715
$466$	12.5640	0.582014
$467$	−15.8591	−0.733871	−0.366936	−	0.930246i	$-0.619593\pi$
$467$	−15.8591	−0.733871	−0.366936	+	0.930246i	$0.619593\pi$
$468$	0.699933	0.0323544
$469$	0	0
$470$	−22.0999	−1.01939
$471$	−33.6319	−1.54968
$472$	−15.3091	−0.704658
$473$	14.3108	0.658011
$474$	−26.7206	−1.22732
$475$	−0.131847	−0.00604955
$476$	0	0
$477$	−16.4076	−0.751254
$478$	−14.3216	−0.655055
$479$	−3.67832	−0.168067	−0.0840333	−	0.996463i	$-0.526780\pi$
$479$	−3.67832	−0.168067	−0.0840333	+	0.996463i	$0.526780\pi$
$480$	−4.48142	−0.204548
$481$	−7.46191	−0.340234
$482$	−12.2289	−0.557010
$483$	0	0
$484$	1.55622	0.0707374
$485$	−4.69706	−0.213282
$486$	−23.9521	−1.08649
$487$	28.9815	1.31328	0.656638	−	0.754205i	$-0.271978\pi$
$487$	28.9815	1.31328	0.656638	+	0.754205i	$0.271978\pi$
$488$	16.4331	0.743892
$489$	16.9682	0.767330
$490$	0	0
$491$	−39.5204	−1.78353	−0.891766	−	0.452496i	$-0.850534\pi$
$491$	−39.5204	−1.78353	−0.891766	+	0.452496i	$0.850534\pi$
$492$	−0.356466	−0.0160707
$493$	15.0883	0.679545
$494$	−10.9272	−0.491638
$495$	4.93698	0.221901
$496$	1.26172	0.0566528
$497$	0	0
$498$	22.6325	1.01419
$499$	5.38189	0.240927	0.120463	−	0.992718i	$-0.461562\pi$
$499$	5.38189	0.240927	0.120463	+	0.992718i	$0.461562\pi$
$500$	−1.79533	−0.0802895
$501$	−18.3793	−0.821128
$502$	−28.8808	−1.28901
$503$	−3.46954	−0.154699	−0.0773495	−	0.997004i	$-0.524646\pi$
$503$	−3.46954	−0.154699	−0.0773495	+	0.997004i	$0.524646\pi$
$504$	0	0
$505$	17.4707	0.777437
$506$	4.11164	0.182785
$507$	−17.9044	−0.795164
$508$	3.09973	0.137528
$509$	33.7241	1.49479	0.747397	−	0.664378i	$-0.231304\pi$
$509$	33.7241	1.49479	0.747397	+	0.664378i	$0.231304\pi$
$510$	27.2917	1.20850
$511$	0	0
$512$	−24.7140	−1.09221
$513$	−8.34938	−0.368634
$514$	−11.4729	−0.506048
$515$	−15.3928	−0.678287
$516$	4.52017	0.198989
$517$	−8.25302	−0.362967
$518$	0	0
$519$	52.8860	2.32144
$520$	−14.5430	−0.637753
$521$	−8.34928	−0.365789	−0.182894	−	0.983133i	$-0.558547\pi$
$521$	−8.34928	−0.365789	−0.182894	+	0.983133i	$0.558547\pi$
$522$	−9.91422	−0.433934
$523$	12.9946	0.568215	0.284107	−	0.958792i	$-0.408303\pi$
$523$	12.9946	0.568215	0.284107	+	0.958792i	$0.408303\pi$
$524$	−0.0494548	−0.00216044
$525$	0	0
$526$	−3.69307	−0.161026
$527$	1.39951	0.0609638
$528$	9.18837	0.399873
$529$	−15.7863	−0.686361
$530$	25.2529	1.09692
$531$	10.2595	0.445224
$532$	0	0
$533$	−2.22790	−0.0965010
$534$	47.6389	2.06154
$535$	−43.5945	−1.88476
$536$	25.8789	1.11780
$537$	25.5216	1.10134
$538$	−40.1226	−1.72981
$539$	0	0
$540$	−0.823128	−0.0354218
$541$	−35.8515	−1.54137	−0.770687	−	0.637214i	$-0.780087\pi$
$541$	−35.8515	−1.54137	−0.770687	+	0.637214i	$0.780087\pi$
$542$	−11.0091	−0.472881
$543$	−39.5491	−1.69721
$544$	−3.65978	−0.156912
$545$	−8.73804	−0.374297
$546$	0	0
$547$	−37.4317	−1.60046	−0.800232	−	0.599691i	$-0.795290\pi$
$547$	−37.4317	−1.60046	−0.800232	+	0.599691i	$0.795290\pi$
$548$	2.77882	0.118705
$549$	−11.0128	−0.470013
$550$	0.0558215	0.00238024
$551$	−13.4591	−0.573376
$552$	17.5322	0.746221
$553$	0	0
$554$	−1.48389	−0.0630447
$555$	−16.6244	−0.705666
$556$	−2.42424	−0.102810
$557$	−14.4468	−0.612131	−0.306066	−	0.952010i	$-0.599013\pi$
$557$	−14.4468	−0.612131	−0.306066	+	0.952010i	$0.599013\pi$
$558$	−0.919590	−0.0389294
$559$	28.2509	1.19489
$560$	0	0
$561$	10.1919	0.430300
$562$	10.7841	0.454900
$563$	5.73581	0.241736	0.120868	−	0.992669i	$-0.461432\pi$
$563$	5.73581	0.241736	0.120868	+	0.992669i	$0.461432\pi$
$564$	−2.60678	−0.109765
$565$	11.3801	0.478764
$566$	37.5190	1.57704
$567$	0	0
$568$	−29.0926	−1.22070
$569$	11.7364	0.492017	0.246009	−	0.969268i	$-0.420881\pi$
$569$	11.7364	0.492017	0.246009	+	0.969268i	$0.420881\pi$
$570$	−24.3447	−1.01969
$571$	7.16254	0.299743	0.149872	−	0.988705i	$-0.452114\pi$
$571$	7.16254	0.299743	0.149872	+	0.988705i	$0.452114\pi$
$572$	−0.402295	−0.0168208
$573$	36.6663	1.53176
$574$	0	0
$575$	0.0979365	0.00408423
$576$	16.7558	0.698160
$577$	29.0407	1.20898	0.604491	−	0.796612i	$-0.293377\pi$
$577$	29.0407	1.20898	0.604491	+	0.796612i	$0.293377\pi$
$578$	−0.771975	−0.0321099
$579$	43.9110	1.82488
$580$	−1.32687	−0.0550953
$581$	0	0
$582$	6.37140	0.264103
$583$	9.43049	0.390571
$584$	2.39025	0.0989094
$585$	9.74608	0.402951
$586$	12.9892	0.536577
$587$	−8.38291	−0.346000	−0.173000	−	0.984922i	$-0.555346\pi$
$587$	−8.38291	−0.346000	−0.173000	+	0.984922i	$0.555346\pi$
$588$	0	0
$589$	−1.24839	−0.0514391
$590$	−15.7903	−0.650077
$591$	28.8495	1.18671
$592$	−12.2397	−0.503048
$593$	−2.29106	−0.0940824	−0.0470412	−	0.998893i	$-0.514979\pi$
$593$	−2.29106	−0.0940824	−0.0470412	+	0.998893i	$0.514979\pi$
$594$	3.53497	0.145042
$595$	0	0
$596$	1.67895	0.0687726
$597$	−57.2863	−2.34457
$598$	8.11677	0.331919
$599$	6.77016	0.276621	0.138311	−	0.990389i	$-0.455833\pi$
$599$	6.77016	0.276621	0.138311	+	0.990389i	$0.455833\pi$
$600$	0.238026	0.00971736
$601$	41.3732	1.68765	0.843824	−	0.536619i	$-0.180299\pi$
$601$	41.3732	1.68765	0.843824	+	0.536619i	$0.180299\pi$
$602$	0	0
$603$	−17.3429	−0.706258
$604$	0.819123	0.0333297
$605$	21.6693	0.880982
$606$	−23.6984	−0.962683
$607$	17.5678	0.713056	0.356528	−	0.934285i	$-0.383960\pi$
$607$	17.5678	0.713056	0.356528	+	0.934285i	$0.383960\pi$
$608$	3.26459	0.132397
$609$	0	0
$610$	16.9497	0.686273
$611$	−16.2923	−0.659115
$612$	1.27348	0.0514773
$613$	−15.5816	−0.629333	−0.314666	−	0.949202i	$-0.601893\pi$
$613$	−15.5816	−0.629333	−0.314666	+	0.949202i	$0.601893\pi$
$614$	−11.1792	−0.451155
$615$	−4.96354	−0.200149
$616$	0	0
$617$	3.07666	0.123862	0.0619309	−	0.998080i	$-0.480274\pi$
$617$	3.07666	0.123862	0.0619309	+	0.998080i	$0.480274\pi$
$618$	20.8798	0.839908
$619$	46.9740	1.88804	0.944021	−	0.329885i	$-0.107010\pi$
$619$	46.9740	1.88804	0.944021	+	0.329885i	$0.107010\pi$
$620$	−0.123073	−0.00494275
$621$	6.20196	0.248876
$622$	15.8221	0.634409
$623$	0	0
$624$	18.1387	0.726131
$625$	−24.8163	−0.992654
$626$	−41.5324	−1.65997
$627$	−9.09132	−0.363072
$628$	2.41534	0.0963826
$629$	−13.5764	−0.541327
$630$	0	0
$631$	4.85357	0.193218	0.0966089	−	0.995322i	$-0.469200\pi$
$631$	4.85357	0.193218	0.0966089	+	0.995322i	$0.469200\pi$
$632$	25.9063	1.03050
$633$	30.0318	1.19366
$634$	−28.2303	−1.12117
$635$	43.1616	1.71281
$636$	2.97869	0.118113
$637$	0	0
$638$	5.69832	0.225599
$639$	19.4966	0.771274
$640$	−21.7658	−0.860371
$641$	−9.57828	−0.378319	−0.189160	−	0.981946i	$-0.560576\pi$
$641$	−9.57828	−0.378319	−0.189160	+	0.981946i	$0.560576\pi$
$642$	59.1345	2.33385
$643$	−8.31243	−0.327810	−0.163905	−	0.986476i	$-0.552409\pi$
$643$	−8.31243	−0.327810	−0.163905	+	0.986476i	$0.552409\pi$
$644$	0	0
$645$	62.9402	2.47827
$646$	−19.8813	−0.782217
$647$	−20.3902	−0.801620	−0.400810	−	0.916161i	$-0.631271\pi$
$647$	−20.3902	−0.801620	−0.400810	+	0.916161i	$0.631271\pi$
$648$	32.3326	1.27014
$649$	−5.89676	−0.231468
$650$	0.110197	0.00432228
$651$	0	0
$652$	−1.21860	−0.0477243
$653$	15.6258	0.611484	0.305742	−	0.952114i	$-0.401095\pi$
$653$	15.6258	0.611484	0.305742	+	0.952114i	$0.401095\pi$
$654$	11.8529	0.463483
$655$	−0.688623	−0.0269067
$656$	−3.65440	−0.142680
$657$	−1.60184	−0.0624939
$658$	0	0
$659$	19.6929	0.767127	0.383564	−	0.923514i	$-0.374697\pi$
$659$	19.6929	0.767127	0.383564	+	0.923514i	$0.374697\pi$
$660$	−0.896273	−0.0348874
$661$	32.8527	1.27782	0.638910	−	0.769281i	$-0.279386\pi$
$661$	32.8527	1.27782	0.638910	+	0.769281i	$0.279386\pi$
$662$	−0.904763	−0.0351646
$663$	20.1197	0.781385
$664$	−21.9427	−0.851543
$665$	0	0
$666$	8.92076	0.345673
$667$	9.99747	0.387103
$668$	1.31995	0.0510703
$669$	5.78588	0.223695
$670$	26.6924	1.03122
$671$	6.32972	0.244356
$672$	0	0
$673$	−2.56402	−0.0988358	−0.0494179	−	0.998778i	$-0.515737\pi$
$673$	−2.56402	−0.0988358	−0.0494179	+	0.998778i	$0.515737\pi$
$674$	0.0911016	0.00350910
$675$	0.0842006	0.00324088
$676$	1.28584	0.0494554
$677$	−22.7084	−0.872753	−0.436377	−	0.899764i	$-0.643738\pi$
$677$	−22.7084	−0.872753	−0.436377	+	0.899764i	$0.643738\pi$
$678$	−15.4367	−0.592844
$679$	0	0
$680$	−26.4599	−1.01469
$681$	22.5267	0.863224
$682$	0.528546	0.0202391
$683$	39.4613	1.50994	0.754972	−	0.655757i	$-0.227650\pi$
$683$	39.4613	1.50994	0.754972	+	0.655757i	$0.227650\pi$
$684$	−1.13597	−0.0434347
$685$	38.6931	1.47839
$686$	0	0
$687$	30.2768	1.15513
$688$	46.3396	1.76668
$689$	18.6167	0.709240
$690$	18.0834	0.688421
$691$	−25.5873	−0.973387	−0.486694	−	0.873573i	$-0.661797\pi$
$691$	−25.5873	−0.973387	−0.486694	+	0.873573i	$0.661797\pi$
$692$	−3.79811	−0.144382
$693$	0	0
$694$	38.6774	1.46817
$695$	−33.7558	−1.28043
$696$	24.2979	0.921011
$697$	−4.05350	−0.153537
$698$	−41.8600	−1.58442
$699$	20.6354	0.780503
$700$	0	0
$701$	−28.4667	−1.07517	−0.537586	−	0.843209i	$-0.680664\pi$
$701$	−28.4667	−1.07517	−0.537586	+	0.843209i	$0.680664\pi$
$702$	6.97837	0.263382
$703$	12.1104	0.456753
$704$	−9.63063	−0.362968
$705$	−36.2975	−1.36704
$706$	−25.5909	−0.963125
$707$	0	0
$708$	−1.86253	−0.0699983
$709$	−18.5889	−0.698121	−0.349061	−	0.937100i	$-0.613499\pi$
$709$	−18.5889	−0.698121	−0.349061	+	0.937100i	$0.613499\pi$
$710$	−30.0071	−1.12615
$711$	−17.3613	−0.651098
$712$	−46.1870	−1.73093
$713$	0.927312	0.0347281
$714$	0	0
$715$	−5.60168	−0.209491
$716$	−1.83288	−0.0684980
$717$	−23.5222	−0.878454
$718$	−0.878414	−0.0327821
$719$	−16.6258	−0.620039	−0.310020	−	0.950730i	$-0.600336\pi$
$719$	−16.6258	−0.620039	−0.310020	+	0.950730i	$0.600336\pi$
$720$	15.9864	0.595777
$721$	0	0
$722$	−8.03841	−0.299158
$723$	−20.0851	−0.746972
$724$	2.84029	0.105559
$725$	0.135730	0.00504089
$726$	−29.3937	−1.09090
$727$	13.5357	0.502010	0.251005	−	0.967986i	$-0.419239\pi$
$727$	13.5357	0.502010	0.251005	+	0.967986i	$0.419239\pi$
$728$	0	0
$729$	−6.23430	−0.230900
$730$	2.46539	0.0912482
$731$	51.4005	1.90112
$732$	1.99929	0.0738957
$733$	−3.69061	−0.136316	−0.0681579	−	0.997675i	$-0.521712\pi$
$733$	−3.69061	−0.136316	−0.0681579	+	0.997675i	$0.521712\pi$
$734$	13.7867	0.508875
$735$	0	0
$736$	−2.42495	−0.0893850
$737$	9.96805	0.367178
$738$	2.66347	0.0980437
$739$	30.2567	1.11301	0.556505	−	0.830844i	$-0.312142\pi$
$739$	30.2567	1.11301	0.556505	+	0.830844i	$0.312142\pi$
$740$	1.19391	0.0438890
$741$	−17.9472	−0.659305
$742$	0	0
$743$	−42.1181	−1.54516	−0.772581	−	0.634917i	$-0.781034\pi$
$743$	−42.1181	−1.54516	−0.772581	+	0.634917i	$0.781034\pi$
$744$	2.25375	0.0826264
$745$	23.3783	0.856513
$746$	9.45317	0.346105
$747$	14.7051	0.538030
$748$	−0.731947	−0.0267626
$749$	0	0
$750$	33.9098	1.23821
$751$	−19.2262	−0.701573	−0.350786	−	0.936456i	$-0.614086\pi$
$751$	−19.2262	−0.701573	−0.350786	+	0.936456i	$0.614086\pi$
$752$	−26.7240	−0.974525
$753$	−47.4347	−1.72862
$754$	11.2490	0.409666
$755$	11.4057	0.415097
$756$	0	0
$757$	6.23128	0.226480	0.113240	−	0.993568i	$-0.463877\pi$
$757$	6.23128	0.226480	0.113240	+	0.993568i	$0.463877\pi$
$758$	−49.4558	−1.79631
$759$	6.75308	0.245121
$760$	23.6028	0.856162
$761$	28.5205	1.03387	0.516933	−	0.856026i	$-0.327073\pi$
$761$	28.5205	1.03387	0.516933	+	0.856026i	$0.327073\pi$
$762$	−58.5472	−2.12094
$763$	0	0
$764$	−2.63326	−0.0952681
$765$	17.7323	0.641113
$766$	27.3713	0.988966
$767$	−11.6408	−0.420324
$768$	−8.49896	−0.306680
$769$	−13.9303	−0.502340	−0.251170	−	0.967943i	$-0.580815\pi$
$769$	−13.9303	−0.502340	−0.251170	+	0.967943i	$0.580815\pi$
$770$	0	0
$771$	−18.8434	−0.678629
$772$	−3.15355	−0.113499
$773$	−39.7945	−1.43131	−0.715654	−	0.698455i	$-0.753871\pi$
$773$	−39.7945	−1.43131	−0.715654	+	0.698455i	$0.753871\pi$
$774$	−33.7741	−1.21399
$775$	0.0125896	0.000452232 0
$776$	−6.17722	−0.221749
$777$	0	0
$778$	−24.7403	−0.886984
$779$	3.61580	0.129549
$780$	−1.76933	−0.0633522
$781$	−11.2059	−0.400979
$782$	14.7679	0.528099
$783$	8.59530	0.307171
$784$	0	0
$785$	33.6319	1.20038
$786$	0.934093	0.0333180
$787$	22.0699	0.786708	0.393354	−	0.919387i	$-0.371315\pi$
$787$	22.0699	0.786708	0.393354	+	0.919387i	$0.371315\pi$
$788$	−2.07188	−0.0738077
$789$	−6.06561	−0.215942
$790$	26.7206	0.950678
$791$	0	0
$792$	6.49275	0.230710
$793$	12.4955	0.443727
$794$	−51.1034	−1.81359
$795$	41.4762	1.47101
$796$	4.11412	0.145821
$797$	−13.9948	−0.495720	−0.247860	−	0.968796i	$-0.579727\pi$
$797$	−13.9948	−0.495720	−0.247860	+	0.968796i	$0.579727\pi$
$798$	0	0
$799$	−29.6426	−1.04868
$800$	−0.0329223	−0.00116398
$801$	30.9525	1.09365
$802$	−34.7570	−1.22731
$803$	0.920679	0.0324901
$804$	3.14848	0.111038
$805$	0	0
$806$	1.04340	0.0367522
$807$	−65.8986	−2.31974
$808$	22.9762	0.808300
$809$	−5.29163	−0.186044	−0.0930219	−	0.995664i	$-0.529653\pi$
$809$	−5.29163	−0.186044	−0.0930219	+	0.995664i	$0.529653\pi$
$810$	33.3489	1.17176
$811$	19.4147	0.681744	0.340872	−	0.940110i	$-0.389278\pi$
$811$	19.4147	0.681744	0.340872	+	0.940110i	$0.389278\pi$
$812$	0	0
$813$	−18.0817	−0.634151
$814$	−5.12732	−0.179712
$815$	−16.9682	−0.594371
$816$	33.0021	1.15531
$817$	−45.8502	−1.60409
$818$	5.54979	0.194044
$819$	0	0
$820$	0.356466	0.0124483
$821$	−3.44679	−0.120294	−0.0601470	−	0.998190i	$-0.519157\pi$
$821$	−3.44679	−0.120294	−0.0601470	+	0.998190i	$0.519157\pi$
$822$	−52.4859	−1.83066
$823$	39.7137	1.38433	0.692166	−	0.721738i	$-0.256657\pi$
$823$	39.7137	1.38433	0.692166	+	0.721738i	$0.256657\pi$
$824$	−20.2434	−0.705214
$825$	0.0916828	0.00319199
$826$	0	0
$827$	3.66589	0.127475	0.0637377	−	0.997967i	$-0.479698\pi$
$827$	3.66589	0.127475	0.0637377	+	0.997967i	$0.479698\pi$
$828$	0.843801	0.0293241
$829$	−5.76355	−0.200176	−0.100088	−	0.994979i	$-0.531912\pi$
$829$	−5.76355	−0.200176	−0.100088	+	0.994979i	$0.531912\pi$
$830$	−22.6325	−0.785585
$831$	−2.43719	−0.0845453
$832$	−19.0118	−0.659115
$833$	0	0
$834$	45.7886	1.58553
$835$	18.3793	0.636043
$836$	0.652910	0.0225814
$837$	0.797254	0.0275571
$838$	45.7582	1.58069
$839$	−2.49460	−0.0861232	−0.0430616	−	0.999072i	$-0.513711\pi$
$839$	−2.49460	−0.0861232	−0.0430616	+	0.999072i	$0.513711\pi$
$840$	0	0
$841$	−15.1445	−0.522224
$842$	1.09100	0.0375983
$843$	17.7121	0.610038
$844$	−2.15679	−0.0742398
$845$	17.9044	0.615931
$846$	19.4775	0.669651
$847$	0	0
$848$	30.5368	1.04864
$849$	61.6223	2.11487
$850$	0.200496	0.00687694
$851$	−8.99566	−0.308367
$852$	−3.53947	−0.121260
$853$	−34.6227	−1.18546	−0.592729	−	0.805402i	$-0.701949\pi$
$853$	−34.6227	−1.18546	−0.592729	+	0.805402i	$0.701949\pi$
$854$	0	0
$855$	−15.8175	−0.540948
$856$	−57.3323	−1.95958
$857$	−2.42362	−0.0827891	−0.0413946	−	0.999143i	$-0.513180\pi$
$857$	−2.42362	−0.0827891	−0.0413946	+	0.999143i	$0.513180\pi$
$858$	7.59849	0.259408
$859$	42.1876	1.43942	0.719711	−	0.694274i	$-0.244274\pi$
$859$	42.1876	1.43942	0.719711	+	0.694274i	$0.244274\pi$
$860$	−4.52017	−0.154136
$861$	0	0
$862$	−54.0252	−1.84011
$863$	50.2649	1.71104	0.855519	−	0.517771i	$-0.173238\pi$
$863$	50.2649	1.71104	0.855519	+	0.517771i	$0.173238\pi$
$864$	−2.08485	−0.0709279
$865$	−52.8860	−1.79818
$866$	8.24684	0.280239
$867$	−1.26791	−0.0430606
$868$	0	0
$869$	9.97860	0.338501
$870$	25.0617	0.849672
$871$	19.6779	0.666760
$872$	−11.4916	−0.389155
$873$	4.13970	0.140108
$874$	−13.1732	−0.445591
$875$	0	0
$876$	0.290803	0.00982533
$877$	10.6100	0.358275	0.179137	−	0.983824i	$-0.442669\pi$
$877$	10.6100	0.358275	0.179137	+	0.983824i	$0.442669\pi$
$878$	−54.3806	−1.83526
$879$	21.3338	0.719571
$880$	−9.18837	−0.309740
$881$	−2.45538	−0.0827238	−0.0413619	−	0.999144i	$-0.513170\pi$
$881$	−2.45538	−0.0827238	−0.0413619	+	0.999144i	$0.513170\pi$
$882$	0	0
$883$	−47.5296	−1.59950	−0.799750	−	0.600333i	$-0.795035\pi$
$883$	−47.5296	−1.59950	−0.799750	+	0.600333i	$0.795035\pi$
$884$	−1.44494	−0.0485984
$885$	−25.9345	−0.871779
$886$	24.5277	0.824025
$887$	4.34818	0.145998	0.0729988	−	0.997332i	$-0.476743\pi$
$887$	4.34818	0.145998	0.0729988	+	0.997332i	$0.476743\pi$
$888$	−21.8631	−0.733679
$889$	0	0
$890$	−47.6389	−1.59686
$891$	12.4539	0.417221
$892$	−0.415524	−0.0139128
$893$	26.4418	0.884840
$894$	−31.7118	−1.06060
$895$	−25.5216	−0.853093
$896$	0	0
$897$	13.3312	0.445117
$898$	−15.4695	−0.516223
$899$	1.28516	0.0428625
$900$	0.0114558	0.000381861 0
$901$	33.8718	1.12843
$902$	−1.53086	−0.0509721
$903$	0	0
$904$	14.9663	0.497770
$905$	39.5491	1.31466
$906$	−15.4715	−0.514005
$907$	12.9887	0.431282	0.215641	−	0.976473i	$-0.430816\pi$
$907$	12.9887	0.431282	0.215641	+	0.976473i	$0.430816\pi$
$908$	−1.61780	−0.0536884
$909$	−15.3976	−0.510707
$910$	0	0
$911$	−15.4395	−0.511535	−0.255767	−	0.966738i	$-0.582328\pi$
$911$	−15.4395	−0.511535	−0.255767	+	0.966738i	$0.582328\pi$
$912$	−29.4385	−0.974806
$913$	−8.45192	−0.279718
$914$	38.2192	1.26418
$915$	27.8387	0.920318
$916$	−2.17438	−0.0718437
$917$	0	0
$918$	12.6967	0.419052
$919$	40.2229	1.32683	0.663415	−	0.748252i	$-0.269106\pi$
$919$	40.2229	1.32683	0.663415	+	0.748252i	$0.269106\pi$
$920$	−17.5322	−0.578021
$921$	−18.3610	−0.605016
$922$	−40.1929	−1.32368
$923$	−22.1216	−0.728140
$924$	0	0
$925$	−0.122129	−0.00401559
$926$	39.5280	1.29897
$927$	13.5663	0.445575
$928$	−3.36074	−0.110322
$929$	−13.5103	−0.443258	−0.221629	−	0.975131i	$-0.571137\pi$
$929$	−13.5103	−0.443258	−0.221629	+	0.975131i	$0.571137\pi$
$930$	2.32459	0.0762264
$931$	0	0
$932$	−1.48197	−0.0485436
$933$	25.9867	0.850767
$934$	−21.5123	−0.703905
$935$	−10.1919	−0.333309
$936$	12.8173	0.418947
$937$	35.6590	1.16493	0.582465	−	0.812856i	$-0.302088\pi$
$937$	35.6590	1.16493	0.582465	+	0.812856i	$0.302088\pi$
$938$	0	0
$939$	−68.2141	−2.22608
$940$	2.60678	0.0850237
$941$	13.8134	0.450305	0.225153	−	0.974323i	$-0.427712\pi$
$941$	13.8134	0.450305	0.225153	+	0.974323i	$0.427712\pi$
$942$	−45.6206	−1.48640
$943$	−2.68583	−0.0874627
$944$	−19.0942	−0.621465
$945$	0	0
$946$	19.4121	0.631142
$947$	53.4437	1.73669	0.868343	−	0.495965i	$-0.165185\pi$
$947$	53.4437	1.73669	0.868343	+	0.495965i	$0.165185\pi$
$948$	3.15181	0.102366
$949$	1.81751	0.0589989
$950$	−0.178846	−0.00580252
$951$	−46.3663	−1.50353
$952$	0	0
$953$	43.4781	1.40840	0.704198	−	0.710004i	$-0.251307\pi$
$953$	43.4781	1.40840	0.704198	+	0.710004i	$0.251307\pi$
$954$	−22.2564	−0.720578
$955$	−36.6663	−1.18649
$956$	1.68929	0.0546356
$957$	9.35909	0.302536
$958$	−4.98951	−0.161204
$959$	0	0
$960$	−42.3564	−1.36705
$961$	−30.8808	−0.996155
$962$	−10.1218	−0.326341
$963$	38.4216	1.23812
$964$	1.44245	0.0464581
$965$	−43.9110	−1.41355
$966$	0	0
$967$	−60.5248	−1.94635	−0.973173	−	0.230075i	$-0.926103\pi$
$967$	−60.5248	−1.94635	−0.973173	+	0.230075i	$0.926103\pi$
$968$	28.4978	0.915956
$969$	−32.6536	−1.04898
$970$	−6.37140	−0.204573
$971$	−16.3175	−0.523653	−0.261826	−	0.965115i	$-0.584325\pi$
$971$	−16.3175	−0.523653	−0.261826	+	0.965115i	$0.584325\pi$
$972$	2.82526	0.0906201
$973$	0	0
$974$	39.3124	1.25965
$975$	0.180991	0.00579635
$976$	20.4962	0.656067
$977$	−14.1551	−0.452862	−0.226431	−	0.974027i	$-0.572706\pi$
$977$	−14.1551	−0.452862	−0.226431	+	0.974027i	$0.572706\pi$
$978$	23.0168	0.735997
$979$	−17.7903	−0.568582
$980$	0	0
$981$	7.70118	0.245880
$982$	−53.6081	−1.71070
$983$	−25.3167	−0.807476	−0.403738	−	0.914875i	$-0.632289\pi$
$983$	−25.3167	−0.807476	−0.403738	+	0.914875i	$0.632289\pi$
$984$	−6.52767	−0.208095
$985$	−28.8495	−0.919222
$986$	20.4668	0.651796
$987$	0	0
$988$	1.28891	0.0410056
$989$	34.0577	1.08297
$990$	6.69685	0.212840
$991$	−35.8520	−1.13887	−0.569437	−	0.822035i	$-0.692839\pi$
$991$	−35.8520	−1.13887	−0.569437	+	0.822035i	$0.692839\pi$
$992$	−0.311725	−0.00989727
$993$	−1.48601	−0.0471571
$994$	0	0
$995$	57.2863	1.81610
$996$	−2.66960	−0.0845894
$997$	−23.4249	−0.741873	−0.370937	−	0.928658i	$-0.620963\pi$
$997$	−23.4249	−0.741873	−0.370937	+	0.928658i	$0.620963\pi$
$998$	7.30035	0.231089
$999$	−7.73400	−0.244693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.m.1.4		5
7.3	odd	6		287.2.e.c.247.2	yes	10
7.5	odd	6		287.2.e.c.165.2	✓	10
7.6	odd	2		2009.2.a.l.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.c.165.2	✓	10	7.5	odd	6
287.2.e.c.247.2	yes	10	7.3	odd	6
2009.2.a.l.1.4		5	7.6	odd	2
2009.2.a.m.1.4		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.35647 q^{2} +2.22790 q^{3} -0.160001 q^{4} -2.22790 q^{5} +3.02207 q^{6} -2.92997 q^{8} +1.96354 q^{9} +O(q^{10})\)	\(q+1.35647 q^{2} +2.22790 q^{3} -0.160001 q^{4} -2.22790 q^{5} +3.02207 q^{6} -2.92997 q^{8} +1.96354 q^{9} -3.02207 q^{10} -1.12857 q^{11} -0.356466 q^{12} -2.22790 q^{13} -4.96354 q^{15} -3.65440 q^{16} -4.05350 q^{17} +2.66347 q^{18} +3.61580 q^{19} +0.356466 q^{20} -1.53086 q^{22} -2.68583 q^{23} -6.52767 q^{24} -0.0364641 q^{25} -3.02207 q^{26} -2.30914 q^{27} -3.72230 q^{29} -6.73287 q^{30} -0.345260 q^{31} +0.902868 q^{32} -2.51433 q^{33} -5.49844 q^{34} -0.314167 q^{36} +3.34930 q^{37} +4.90471 q^{38} -4.96354 q^{39} +6.52767 q^{40} +1.00000 q^{41} -12.6805 q^{43} +0.180572 q^{44} -4.37456 q^{45} -3.64324 q^{46} +7.31284 q^{47} -8.14163 q^{48} -0.0494623 q^{50} -9.03080 q^{51} +0.356466 q^{52} -8.35617 q^{53} -3.13227 q^{54} +2.51433 q^{55} +8.05564 q^{57} -5.04917 q^{58} +5.22500 q^{59} +0.794170 q^{60} -5.60864 q^{61} -0.468334 q^{62} +8.53351 q^{64} +4.96354 q^{65} -3.41061 q^{66} -8.83249 q^{67} +0.648564 q^{68} -5.98377 q^{69} +9.92933 q^{71} -5.75310 q^{72} -0.815796 q^{73} +4.54321 q^{74} -0.0812383 q^{75} -0.578531 q^{76} -6.73287 q^{78} -8.84184 q^{79} +8.14163 q^{80} -11.0351 q^{81} +1.35647 q^{82} +7.48907 q^{83} +9.03080 q^{85} -17.2007 q^{86} -8.29290 q^{87} +3.30666 q^{88} +15.7637 q^{89} -5.93394 q^{90} +0.429735 q^{92} -0.769205 q^{93} +9.91961 q^{94} -8.05564 q^{95} +2.01150 q^{96} +2.10829 q^{97} -2.21598 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} - q^{6} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 - q^6 - 3 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} - q^{6} - 3 q^{8} + 5 q^{9} + q^{10} - 6 q^{11} + 7 q^{12} - 2 q^{13} - 20 q^{15} - 12 q^{16} + 3 q^{17} - 8 q^{18} - 7 q^{19} - 7 q^{20} - 13 q^{22} - 16 q^{24} - 5 q^{25} + q^{26} - 13 q^{27} - 10 q^{29} + 14 q^{30} + 6 q^{31} - 3 q^{32} + 17 q^{33} - q^{34} - 15 q^{36} - 18 q^{37} + 7 q^{38} - 20 q^{39} + 16 q^{40} + 5 q^{41} - 14 q^{43} + 2 q^{44} + 7 q^{45} - 3 q^{46} - 3 q^{47} - 9 q^{48} - 4 q^{50} - 7 q^{52} - 9 q^{53} + 25 q^{54} - 17 q^{55} + 31 q^{57} - 5 q^{58} + 19 q^{59} - 3 q^{60} + 23 q^{61} - 36 q^{62} - q^{64} + 20 q^{65} - 23 q^{66} - 11 q^{67} + 24 q^{68} - 19 q^{69} + 25 q^{72} - 13 q^{73} + 2 q^{74} - 11 q^{75} - 12 q^{76} + 14 q^{78} - 41 q^{79} + 9 q^{80} - 7 q^{81} - 2 q^{82} + 2 q^{83} + 20 q^{86} - 32 q^{87} - 10 q^{88} - 14 q^{89} - 22 q^{90} + 17 q^{92} - 15 q^{93} - 10 q^{94} - 31 q^{95} + 33 q^{96} + 27 q^{97} - 9 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 - q^6 - 3 * q^8 + 5 * q^9 + q^10 - 6 * q^11 + 7 * q^12 - 2 * q^13 - 20 * q^15 - 12 * q^16 + 3 * q^17 - 8 * q^18 - 7 * q^19 - 7 * q^20 - 13 * q^22 - 16 * q^24 - 5 * q^25 + q^26 - 13 * q^27 - 10 * q^29 + 14 * q^30 + 6 * q^31 - 3 * q^32 + 17 * q^33 - q^34 - 15 * q^36 - 18 * q^37 + 7 * q^38 - 20 * q^39 + 16 * q^40 + 5 * q^41 - 14 * q^43 + 2 * q^44 + 7 * q^45 - 3 * q^46 - 3 * q^47 - 9 * q^48 - 4 * q^50 - 7 * q^52 - 9 * q^53 + 25 * q^54 - 17 * q^55 + 31 * q^57 - 5 * q^58 + 19 * q^59 - 3 * q^60 + 23 * q^61 - 36 * q^62 - q^64 + 20 * q^65 - 23 * q^66 - 11 * q^67 + 24 * q^68 - 19 * q^69 + 25 * q^72 - 13 * q^73 + 2 * q^74 - 11 * q^75 - 12 * q^76 + 14 * q^78 - 41 * q^79 + 9 * q^80 - 7 * q^81 - 2 * q^82 + 2 * q^83 + 20 * q^86 - 32 * q^87 - 10 * q^88 - 14 * q^89 - 22 * q^90 + 17 * q^92 - 15 * q^93 - 10 * q^94 - 31 * q^95 + 33 * q^96 + 27 * q^97 - 9 * q^99

Introduction

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