LMFDB - Embedded newform 2009.2.a.a.1.2

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:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 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			1.2
Root			$-0.618034$ 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)

$f(q)$	$=$	$q+0.618034 q^{2} +1.61803 q^{3} -1.61803 q^{4} -1.61803 q^{5} +1.00000 q^{6} -2.23607 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q+0.618034 q^{2} +1.61803 q^{3} -1.61803 q^{4} -1.61803 q^{5} +1.00000 q^{6} -2.23607 q^{8} -0.381966 q^{9} -1.00000 q^{10} -1.00000 q^{11} -2.61803 q^{12} +6.23607 q^{13} -2.61803 q^{15} +1.85410 q^{16} +4.23607 q^{17} -0.236068 q^{18} -2.85410 q^{19} +2.61803 q^{20} -0.618034 q^{22} -3.61803 q^{23} -3.61803 q^{24} -2.38197 q^{25} +3.85410 q^{26} -5.47214 q^{27} -5.85410 q^{29} -1.61803 q^{30} -8.09017 q^{31} +5.61803 q^{32} -1.61803 q^{33} +2.61803 q^{34} +0.618034 q^{36} -2.76393 q^{37} -1.76393 q^{38} +10.0902 q^{39} +3.61803 q^{40} +1.00000 q^{41} -1.00000 q^{43} +1.61803 q^{44} +0.618034 q^{45} -2.23607 q^{46} -9.70820 q^{47} +3.00000 q^{48} -1.47214 q^{50} +6.85410 q^{51} -10.0902 q^{52} +2.38197 q^{53} -3.38197 q^{54} +1.61803 q^{55} -4.61803 q^{57} -3.61803 q^{58} -8.38197 q^{59} +4.23607 q^{60} -9.47214 q^{61} -5.00000 q^{62} -0.236068 q^{64} -10.0902 q^{65} -1.00000 q^{66} -12.0902 q^{67} -6.85410 q^{68} -5.85410 q^{69} -5.94427 q^{71} +0.854102 q^{72} +9.94427 q^{73} -1.70820 q^{74} -3.85410 q^{75} +4.61803 q^{76} +6.23607 q^{78} -11.7082 q^{79} -3.00000 q^{80} -7.70820 q^{81} +0.618034 q^{82} +5.47214 q^{83} -6.85410 q^{85} -0.618034 q^{86} -9.47214 q^{87} +2.23607 q^{88} +9.32624 q^{89} +0.381966 q^{90} +5.85410 q^{92} -13.0902 q^{93} -6.00000 q^{94} +4.61803 q^{95} +9.09017 q^{96} -2.56231 q^{97} +0.381966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 3 q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 3 * q^9	$ 2 q - q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 3 q^{9} - 2 q^{10} - 2 q^{11} - 3 q^{12} + 8 q^{13} - 3 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + q^{19} + 3 q^{20} + q^{22} - 5 q^{23} - 5 q^{24} - 7 q^{25} + q^{26} - 2 q^{27} - 5 q^{29} - q^{30} - 5 q^{31} + 9 q^{32} - q^{33} + 3 q^{34} - q^{36} - 10 q^{37} - 8 q^{38} + 9 q^{39} + 5 q^{40} + 2 q^{41} - 2 q^{43} + q^{44} - q^{45} - 6 q^{47} + 6 q^{48} + 6 q^{50} + 7 q^{51} - 9 q^{52} + 7 q^{53} - 9 q^{54} + q^{55} - 7 q^{57} - 5 q^{58} - 19 q^{59} + 4 q^{60} - 10 q^{61} - 10 q^{62} + 4 q^{64} - 9 q^{65} - 2 q^{66} - 13 q^{67} - 7 q^{68} - 5 q^{69} + 6 q^{71} - 5 q^{72} + 2 q^{73} + 10 q^{74} - q^{75} + 7 q^{76} + 8 q^{78} - 10 q^{79} - 6 q^{80} - 2 q^{81} - q^{82} + 2 q^{83} - 7 q^{85} + q^{86} - 10 q^{87} + 3 q^{89} + 3 q^{90} + 5 q^{92} - 15 q^{93} - 12 q^{94} + 7 q^{95} + 7 q^{96} + 15 q^{97} + 3 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 3 * q^9 - 2 * q^10 - 2 * q^11 - 3 * q^12 + 8 * q^13 - 3 * q^15 - 3 * q^16 + 4 * q^17 + 4 * q^18 + q^19 + 3 * q^20 + q^22 - 5 * q^23 - 5 * q^24 - 7 * q^25 + q^26 - 2 * q^27 - 5 * q^29 - q^30 - 5 * q^31 + 9 * q^32 - q^33 + 3 * q^34 - q^36 - 10 * q^37 - 8 * q^38 + 9 * q^39 + 5 * q^40 + 2 * q^41 - 2 * q^43 + q^44 - q^45 - 6 * q^47 + 6 * q^48 + 6 * q^50 + 7 * q^51 - 9 * q^52 + 7 * q^53 - 9 * q^54 + q^55 - 7 * q^57 - 5 * q^58 - 19 * q^59 + 4 * q^60 - 10 * q^61 - 10 * q^62 + 4 * q^64 - 9 * q^65 - 2 * q^66 - 13 * q^67 - 7 * q^68 - 5 * q^69 + 6 * q^71 - 5 * q^72 + 2 * q^73 + 10 * q^74 - q^75 + 7 * q^76 + 8 * q^78 - 10 * q^79 - 6 * q^80 - 2 * q^81 - q^82 + 2 * q^83 - 7 * q^85 + q^86 - 10 * q^87 + 3 * q^89 + 3 * q^90 + 5 * q^92 - 15 * q^93 - 12 * q^94 + 7 * q^95 + 7 * q^96 + 15 * q^97 + 3 * 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 $

$2$	0.618034	0.437016	0.218508	−	0.975835i	$-0.429881\pi$
$2$	0.618034	0.437016	0.218508	+	0.975835i	$0.429881\pi$
$3$	1.61803	0.934172	0.467086	−	0.884212i	$-0.345304\pi$
$3$	1.61803	0.934172	0.467086	+	0.884212i	$0.345304\pi$
$4$	−1.61803	−0.809017
$5$	−1.61803	−0.723607	−0.361803	−	0.932254i	$-0.617839\pi$
$5$	−1.61803	−0.723607	−0.361803	+	0.932254i	$0.617839\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−2.23607	−0.790569
$9$	−0.381966	−0.127322
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	−2.61803	−0.755761
$13$	6.23607	1.72957	0.864787	−	0.502139i	$-0.167453\pi$
$13$	6.23607	1.72957	0.864787	+	0.502139i	$0.167453\pi$
$14$	0	0
$15$	−2.61803	−0.675973
$16$	1.85410	0.463525
$17$	4.23607	1.02740	0.513699	−	0.857971i	$-0.328275\pi$
$17$	4.23607	1.02740	0.513699	+	0.857971i	$0.328275\pi$
$18$	−0.236068	−0.0556418
$19$	−2.85410	−0.654776	−0.327388	−	0.944890i	$-0.606168\pi$
$19$	−2.85410	−0.654776	−0.327388	+	0.944890i	$0.606168\pi$
$20$	2.61803	0.585410
$21$	0	0
$22$	−0.618034	−0.131765
$23$	−3.61803	−0.754412	−0.377206	−	0.926129i	$-0.623115\pi$
$23$	−3.61803	−0.754412	−0.377206	+	0.926129i	$0.623115\pi$
$24$	−3.61803	−0.738528
$25$	−2.38197	−0.476393
$26$	3.85410	0.755852
$27$	−5.47214	−1.05311
$28$	0	0
$29$	−5.85410	−1.08708	−0.543540	−	0.839383i	$-0.682916\pi$
$29$	−5.85410	−1.08708	−0.543540	+	0.839383i	$0.682916\pi$
$30$	−1.61803	−0.295411
$31$	−8.09017	−1.45304	−0.726519	−	0.687147i	$-0.758863\pi$
$31$	−8.09017	−1.45304	−0.726519	+	0.687147i	$0.758863\pi$
$32$	5.61803	0.993137
$33$	−1.61803	−0.281664
$34$	2.61803	0.448989
$35$	0	0
$36$	0.618034	0.103006
$37$	−2.76393	−0.454388	−0.227194	−	0.973850i	$-0.572955\pi$
$37$	−2.76393	−0.454388	−0.227194	+	0.973850i	$0.572955\pi$
$38$	−1.76393	−0.286148
$39$	10.0902	1.61572
$40$	3.61803	0.572061
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	1.61803	0.243928
$45$	0.618034	0.0921311
$46$	−2.23607	−0.329690
$47$	−9.70820	−1.41609	−0.708044	−	0.706169i	$-0.750422\pi$
$47$	−9.70820	−1.41609	−0.708044	+	0.706169i	$0.750422\pi$
$48$	3.00000	0.433013
$49$	0	0
$50$	−1.47214	−0.208191
$51$	6.85410	0.959766
$52$	−10.0902	−1.39925
$53$	2.38197	0.327188	0.163594	−	0.986528i	$-0.447691\pi$
$53$	2.38197	0.327188	0.163594	+	0.986528i	$0.447691\pi$
$54$	−3.38197	−0.460227
$55$	1.61803	0.218176
$56$	0	0
$57$	−4.61803	−0.611674
$58$	−3.61803	−0.475071
$59$	−8.38197	−1.09124	−0.545620	−	0.838033i	$-0.683706\pi$
$59$	−8.38197	−1.09124	−0.545620	+	0.838033i	$0.683706\pi$
$60$	4.23607	0.546874
$61$	−9.47214	−1.21278	−0.606391	−	0.795166i	$-0.707384\pi$
$61$	−9.47214	−1.21278	−0.606391	+	0.795166i	$0.707384\pi$
$62$	−5.00000	−0.635001
$63$	0	0
$64$	−0.236068	−0.0295085
$65$	−10.0902	−1.25153
$66$	−1.00000	−0.123091
$67$	−12.0902	−1.47705	−0.738525	−	0.674226i	$-0.764477\pi$
$67$	−12.0902	−1.47705	−0.738525	+	0.674226i	$0.764477\pi$
$68$	−6.85410	−0.831182
$69$	−5.85410	−0.704751
$70$	0	0
$71$	−5.94427	−0.705455	−0.352728	−	0.935726i	$-0.614746\pi$
$71$	−5.94427	−0.705455	−0.352728	+	0.935726i	$0.614746\pi$
$72$	0.854102	0.100657
$73$	9.94427	1.16389	0.581944	−	0.813229i	$-0.302292\pi$
$73$	9.94427	1.16389	0.581944	+	0.813229i	$0.302292\pi$
$74$	−1.70820	−0.198575
$75$	−3.85410	−0.445033
$76$	4.61803	0.529725
$77$	0	0
$78$	6.23607	0.706096
$79$	−11.7082	−1.31728	−0.658638	−	0.752460i	$-0.728867\pi$
$79$	−11.7082	−1.31728	−0.658638	+	0.752460i	$0.728867\pi$
$80$	−3.00000	−0.335410
$81$	−7.70820	−0.856467
$82$	0.618034	0.0682504
$83$	5.47214	0.600645	0.300322	−	0.953838i	$-0.402906\pi$
$83$	5.47214	0.600645	0.300322	+	0.953838i	$0.402906\pi$
$84$	0	0
$85$	−6.85410	−0.743432
$86$	−0.618034	−0.0666443
$87$	−9.47214	−1.01552
$88$	2.23607	0.238366
$89$	9.32624	0.988579	0.494290	−	0.869297i	$-0.335428\pi$
$89$	9.32624	0.988579	0.494290	+	0.869297i	$0.335428\pi$
$90$	0.381966	0.0402628
$91$	0	0
$92$	5.85410	0.610332
$93$	−13.0902	−1.35739
$94$	−6.00000	−0.618853
$95$	4.61803	0.473800
$96$	9.09017	0.927762
$97$	−2.56231	−0.260163	−0.130081	−	0.991503i	$-0.541524\pi$
$97$	−2.56231	−0.260163	−0.130081	+	0.991503i	$0.541524\pi$
$98$	0	0
$99$	0.381966	0.0383890
$100$	3.85410	0.385410
$101$	17.4721	1.73854	0.869271	−	0.494335i	$-0.164589\pi$
$101$	17.4721	1.73854	0.869271	+	0.494335i	$0.164589\pi$
$102$	4.23607	0.419433
$103$	1.09017	0.107418	0.0537088	−	0.998557i	$-0.482896\pi$
$103$	1.09017	0.107418	0.0537088	+	0.998557i	$0.482896\pi$
$104$	−13.9443	−1.36735
$105$	0	0
$106$	1.47214	0.142986
$107$	−0.763932	−0.0738521	−0.0369260	−	0.999318i	$-0.511757\pi$
$107$	−0.763932	−0.0738521	−0.0369260	+	0.999318i	$0.511757\pi$
$108$	8.85410	0.851986
$109$	8.47214	0.811483	0.405742	−	0.913988i	$-0.367013\pi$
$109$	8.47214	0.811483	0.405742	+	0.913988i	$0.367013\pi$
$110$	1.00000	0.0953463
$111$	−4.47214	−0.424476
$112$	0	0
$113$	14.4164	1.35618	0.678091	−	0.734978i	$-0.262808\pi$
$113$	14.4164	1.35618	0.678091	+	0.734978i	$0.262808\pi$
$114$	−2.85410	−0.267311
$115$	5.85410	0.545898
$116$	9.47214	0.879466
$117$	−2.38197	−0.220213
$118$	−5.18034	−0.476889
$119$	0	0
$120$	5.85410	0.534404
$121$	−10.0000	−0.909091
$122$	−5.85410	−0.530005
$123$	1.61803	0.145893
$124$	13.0902	1.17553
$125$	11.9443	1.06833
$126$	0	0
$127$	−3.29180	−0.292100	−0.146050	−	0.989277i	$-0.546656\pi$
$127$	−3.29180	−0.292100	−0.146050	+	0.989277i	$0.546656\pi$
$128$	−11.3820	−1.00603
$129$	−1.61803	−0.142460
$130$	−6.23607	−0.546939
$131$	−10.8541	−0.948327	−0.474164	−	0.880437i	$-0.657249\pi$
$131$	−10.8541	−0.948327	−0.474164	+	0.880437i	$0.657249\pi$
$132$	2.61803	0.227871
$133$	0	0
$134$	−7.47214	−0.645494
$135$	8.85410	0.762040
$136$	−9.47214	−0.812229
$137$	15.7984	1.34975	0.674873	−	0.737934i	$-0.264198\pi$
$137$	15.7984	1.34975	0.674873	+	0.737934i	$0.264198\pi$
$138$	−3.61803	−0.307988
$139$	5.94427	0.504187	0.252093	−	0.967703i	$-0.418881\pi$
$139$	5.94427	0.504187	0.252093	+	0.967703i	$0.418881\pi$
$140$	0	0
$141$	−15.7082	−1.32287
$142$	−3.67376	−0.308295
$143$	−6.23607	−0.521486
$144$	−0.708204	−0.0590170
$145$	9.47214	0.786618
$146$	6.14590	0.508638
$147$	0	0
$148$	4.47214	0.367607
$149$	18.9443	1.55198	0.775988	−	0.630748i	$-0.217252\pi$
$149$	18.9443	1.55198	0.775988	+	0.630748i	$0.217252\pi$
$150$	−2.38197	−0.194487
$151$	−19.9443	−1.62304	−0.811521	−	0.584323i	$-0.801360\pi$
$151$	−19.9443	−1.62304	−0.811521	+	0.584323i	$0.801360\pi$
$152$	6.38197	0.517646
$153$	−1.61803	−0.130810
$154$	0	0
$155$	13.0902	1.05143
$156$	−16.3262	−1.30715
$157$	8.00000	0.638470	0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000	0.638470	0.319235	+	0.947676i	$0.396574\pi$
$158$	−7.23607	−0.575671
$159$	3.85410	0.305650
$160$	−9.09017	−0.718641
$161$	0	0
$162$	−4.76393	−0.374290
$163$	−16.9443	−1.32718	−0.663589	−	0.748097i	$-0.730968\pi$
$163$	−16.9443	−1.32718	−0.663589	+	0.748097i	$0.730968\pi$
$164$	−1.61803	−0.126347
$165$	2.61803	0.203814
$166$	3.38197	0.262491
$167$	10.4164	0.806046	0.403023	−	0.915190i	$-0.367959\pi$
$167$	10.4164	0.806046	0.403023	+	0.915190i	$0.367959\pi$
$168$	0	0
$169$	25.8885	1.99143
$170$	−4.23607	−0.324892
$171$	1.09017	0.0833674
$172$	1.61803	0.123374
$173$	−4.70820	−0.357958	−0.178979	−	0.983853i	$-0.557279\pi$
$173$	−4.70820	−0.357958	−0.178979	+	0.983853i	$0.557279\pi$
$174$	−5.85410	−0.443798
$175$	0	0
$176$	−1.85410	−0.139758
$177$	−13.5623	−1.01941
$178$	5.76393	0.432025
$179$	3.03444	0.226805	0.113402	−	0.993549i	$-0.463825\pi$
$179$	3.03444	0.226805	0.113402	+	0.993549i	$0.463825\pi$
$180$	−1.00000	−0.0745356
$181$	2.94427	0.218846	0.109423	−	0.993995i	$-0.465100\pi$
$181$	2.94427	0.218846	0.109423	+	0.993995i	$0.465100\pi$
$182$	0	0
$183$	−15.3262	−1.13295
$184$	8.09017	0.596415
$185$	4.47214	0.328798
$186$	−8.09017	−0.593200
$187$	−4.23607	−0.309772
$188$	15.7082	1.14564
$189$	0	0
$190$	2.85410	0.207058
$191$	22.4721	1.62603	0.813013	−	0.582245i	$-0.197826\pi$
$191$	22.4721	1.62603	0.813013	+	0.582245i	$0.197826\pi$
$192$	−0.381966	−0.0275660
$193$	−22.7082	−1.63457	−0.817286	−	0.576232i	$-0.804522\pi$
$193$	−22.7082	−1.63457	−0.817286	+	0.576232i	$0.804522\pi$
$194$	−1.58359	−0.113695
$195$	−16.3262	−1.16915
$196$	0	0
$197$	−9.61803	−0.685257	−0.342628	−	0.939471i	$-0.611317\pi$
$197$	−9.61803	−0.685257	−0.342628	+	0.939471i	$0.611317\pi$
$198$	0.236068	0.0167766
$199$	21.3607	1.51422	0.757109	−	0.653288i	$-0.226611\pi$
$199$	21.3607	1.51422	0.757109	+	0.653288i	$0.226611\pi$
$200$	5.32624	0.376622
$201$	−19.5623	−1.37982
$202$	10.7984	0.759771
$203$	0	0
$204$	−11.0902	−0.776467
$205$	−1.61803	−0.113008
$206$	0.673762	0.0469432
$207$	1.38197	0.0960533
$208$	11.5623	0.801702
$209$	2.85410	0.197422
$210$	0	0
$211$	14.0344	0.966171	0.483085	−	0.875573i	$-0.339516\pi$
$211$	14.0344	0.966171	0.483085	+	0.875573i	$0.339516\pi$
$212$	−3.85410	−0.264701
$213$	−9.61803	−0.659017
$214$	−0.472136	−0.0322745
$215$	1.61803	0.110349
$216$	12.2361	0.832559
$217$	0	0
$218$	5.23607	0.354631
$219$	16.0902	1.08727
$220$	−2.61803	−0.176508
$221$	26.4164	1.77696
$222$	−2.76393	−0.185503
$223$	1.32624	0.0888115	0.0444057	−	0.999014i	$-0.485861\pi$
$223$	1.32624	0.0888115	0.0444057	+	0.999014i	$0.485861\pi$
$224$	0	0
$225$	0.909830	0.0606553
$226$	8.90983	0.592673
$227$	−5.65248	−0.375168	−0.187584	−	0.982249i	$-0.560066\pi$
$227$	−5.65248	−0.375168	−0.187584	+	0.982249i	$0.560066\pi$
$228$	7.47214	0.494854
$229$	−21.2361	−1.40332	−0.701659	−	0.712512i	$-0.747557\pi$
$229$	−21.2361	−1.40332	−0.701659	+	0.712512i	$0.747557\pi$
$230$	3.61803	0.238566
$231$	0	0
$232$	13.0902	0.859412
$233$	−6.32624	−0.414446	−0.207223	−	0.978294i	$-0.566443\pi$
$233$	−6.32624	−0.414446	−0.207223	+	0.978294i	$0.566443\pi$
$234$	−1.47214	−0.0962365
$235$	15.7082	1.02469
$236$	13.5623	0.882831
$237$	−18.9443	−1.23056
$238$	0	0
$239$	−6.14590	−0.397545	−0.198773	−	0.980046i	$-0.563696\pi$
$239$	−6.14590	−0.397545	−0.198773	+	0.980046i	$0.563696\pi$
$240$	−4.85410	−0.313331
$241$	4.76393	0.306872	0.153436	−	0.988159i	$-0.450966\pi$
$241$	4.76393	0.306872	0.153436	+	0.988159i	$0.450966\pi$
$242$	−6.18034	−0.397287
$243$	3.94427	0.253025
$244$	15.3262	0.981162
$245$	0	0
$246$	1.00000	0.0637577
$247$	−17.7984	−1.13248
$248$	18.0902	1.14873
$249$	8.85410	0.561106
$250$	7.38197	0.466877
$251$	−2.05573	−0.129756	−0.0648782	−	0.997893i	$-0.520666\pi$
$251$	−2.05573	−0.129756	−0.0648782	+	0.997893i	$0.520666\pi$
$252$	0	0
$253$	3.61803	0.227464
$254$	−2.03444	−0.127652
$255$	−11.0902	−0.694493
$256$	−6.56231	−0.410144
$257$	−24.1246	−1.50485	−0.752426	−	0.658677i	$-0.771116\pi$
$257$	−24.1246	−1.50485	−0.752426	+	0.658677i	$0.771116\pi$
$258$	−1.00000	−0.0622573
$259$	0	0
$260$	16.3262	1.01251
$261$	2.23607	0.138409
$262$	−6.70820	−0.414434
$263$	−12.7082	−0.783621	−0.391811	−	0.920046i	$-0.628151\pi$
$263$	−12.7082	−0.783621	−0.391811	+	0.920046i	$0.628151\pi$
$264$	3.61803	0.222675
$265$	−3.85410	−0.236756
$266$	0	0
$267$	15.0902	0.923503
$268$	19.5623	1.19496
$269$	−23.2705	−1.41883	−0.709414	−	0.704792i	$-0.751040\pi$
$269$	−23.2705	−1.41883	−0.709414	+	0.704792i	$0.751040\pi$
$270$	5.47214	0.333024
$271$	−4.23607	−0.257323	−0.128661	−	0.991689i	$-0.541068\pi$
$271$	−4.23607	−0.257323	−0.128661	+	0.991689i	$0.541068\pi$
$272$	7.85410	0.476225
$273$	0	0
$274$	9.76393	0.589861
$275$	2.38197	0.143638
$276$	9.47214	0.570156
$277$	−0.819660	−0.0492486	−0.0246243	−	0.999697i	$-0.507839\pi$
$277$	−0.819660	−0.0492486	−0.0246243	+	0.999697i	$0.507839\pi$
$278$	3.67376	0.220338
$279$	3.09017	0.185004
$280$	0	0
$281$	−24.7082	−1.47397	−0.736984	−	0.675910i	$-0.763751\pi$
$281$	−24.7082	−1.47397	−0.736984	+	0.675910i	$0.763751\pi$
$282$	−9.70820	−0.578115
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	9.61803	0.570725
$285$	7.47214	0.442611
$286$	−3.85410	−0.227898
$287$	0	0
$288$	−2.14590	−0.126448
$289$	0.944272	0.0555454
$290$	5.85410	0.343765
$291$	−4.14590	−0.243037
$292$	−16.0902	−0.941606
$293$	12.2361	0.714839	0.357419	−	0.933944i	$-0.383657\pi$
$293$	12.2361	0.714839	0.357419	+	0.933944i	$0.383657\pi$
$294$	0	0
$295$	13.5623	0.789628
$296$	6.18034	0.359225
$297$	5.47214	0.317526
$298$	11.7082	0.678238
$299$	−22.5623	−1.30481
$300$	6.23607	0.360040
$301$	0	0
$302$	−12.3262	−0.709295
$303$	28.2705	1.62410
$304$	−5.29180	−0.303505
$305$	15.3262	0.877578
$306$	−1.00000	−0.0571662
$307$	−23.5279	−1.34281	−0.671403	−	0.741092i	$-0.734308\pi$
$307$	−23.5279	−1.34281	−0.671403	+	0.741092i	$0.734308\pi$
$308$	0	0
$309$	1.76393	0.100347
$310$	8.09017	0.459491
$311$	−0.618034	−0.0350455	−0.0175227	−	0.999846i	$-0.505578\pi$
$311$	−0.618034	−0.0350455	−0.0175227	+	0.999846i	$0.505578\pi$
$312$	−22.5623	−1.27734
$313$	29.4721	1.66586	0.832932	−	0.553376i	$-0.186661\pi$
$313$	29.4721	1.66586	0.832932	+	0.553376i	$0.186661\pi$
$314$	4.94427	0.279021
$315$	0	0
$316$	18.9443	1.06570
$317$	−8.12461	−0.456324	−0.228162	−	0.973623i	$-0.573272\pi$
$317$	−8.12461	−0.456324	−0.228162	+	0.973623i	$0.573272\pi$
$318$	2.38197	0.133574
$319$	5.85410	0.327767
$320$	0.381966	0.0213525
$321$	−1.23607	−0.0689906
$322$	0	0
$323$	−12.0902	−0.672715
$324$	12.4721	0.692896
$325$	−14.8541	−0.823957
$326$	−10.4721	−0.579998
$327$	13.7082	0.758065
$328$	−2.23607	−0.123466
$329$	0	0
$330$	1.61803	0.0890698
$331$	33.8885	1.86268	0.931341	−	0.364147i	$-0.118639\pi$
$331$	33.8885	1.86268	0.931341	+	0.364147i	$0.118639\pi$
$332$	−8.85410	−0.485932
$333$	1.05573	0.0578535
$334$	6.43769	0.352255
$335$	19.5623	1.06880
$336$	0	0
$337$	−20.4721	−1.11519	−0.557594	−	0.830114i	$-0.688275\pi$
$337$	−20.4721	−1.11519	−0.557594	+	0.830114i	$0.688275\pi$
$338$	16.0000	0.870285
$339$	23.3262	1.26691
$340$	11.0902	0.601449
$341$	8.09017	0.438107
$342$	0.673762	0.0364329
$343$	0	0
$344$	2.23607	0.120561
$345$	9.47214	0.509963
$346$	−2.90983	−0.156433
$347$	−4.29180	−0.230396	−0.115198	−	0.993343i	$-0.536750\pi$
$347$	−4.29180	−0.230396	−0.115198	+	0.993343i	$0.536750\pi$
$348$	15.3262	0.821573
$349$	−16.7082	−0.894370	−0.447185	−	0.894442i	$-0.647573\pi$
$349$	−16.7082	−0.894370	−0.447185	+	0.894442i	$0.647573\pi$
$350$	0	0
$351$	−34.1246	−1.82144
$352$	−5.61803	−0.299442
$353$	−10.3607	−0.551443	−0.275722	−	0.961238i	$-0.588917\pi$
$353$	−10.3607	−0.551443	−0.275722	+	0.961238i	$0.588917\pi$
$354$	−8.38197	−0.445496
$355$	9.61803	0.510472
$356$	−15.0902	−0.799777
$357$	0	0
$358$	1.87539	0.0991173
$359$	22.1803	1.17063	0.585317	−	0.810805i	$-0.300970\pi$
$359$	22.1803	1.17063	0.585317	+	0.810805i	$0.300970\pi$
$360$	−1.38197	−0.0728360
$361$	−10.8541	−0.571269
$362$	1.81966	0.0956392
$363$	−16.1803	−0.849248
$364$	0	0
$365$	−16.0902	−0.842198
$366$	−9.47214	−0.495116
$367$	−27.2705	−1.42351	−0.711755	−	0.702428i	$-0.752099\pi$
$367$	−27.2705	−1.42351	−0.711755	+	0.702428i	$0.752099\pi$
$368$	−6.70820	−0.349689
$369$	−0.381966	−0.0198844
$370$	2.76393	0.143690
$371$	0	0
$372$	21.1803	1.09815
$373$	12.7426	0.659789	0.329895	−	0.944018i	$-0.392987\pi$
$373$	12.7426	0.659789	0.329895	+	0.944018i	$0.392987\pi$
$374$	−2.61803	−0.135375
$375$	19.3262	0.998003
$376$	21.7082	1.11952
$377$	−36.5066	−1.88018
$378$	0	0
$379$	−10.6525	−0.547181	−0.273590	−	0.961846i	$-0.588211\pi$
$379$	−10.6525	−0.547181	−0.273590	+	0.961846i	$0.588211\pi$
$380$	−7.47214	−0.383312
$381$	−5.32624	−0.272871
$382$	13.8885	0.710600
$383$	23.1803	1.18446	0.592230	−	0.805769i	$-0.298248\pi$
$383$	23.1803	1.18446	0.592230	+	0.805769i	$0.298248\pi$
$384$	−18.4164	−0.939808
$385$	0	0
$386$	−14.0344	−0.714334
$387$	0.381966	0.0194164
$388$	4.14590	0.210476
$389$	−30.6869	−1.55589	−0.777944	−	0.628333i	$-0.783737\pi$
$389$	−30.6869	−1.55589	−0.777944	+	0.628333i	$0.783737\pi$
$390$	−10.0902	−0.510936
$391$	−15.3262	−0.775081
$392$	0	0
$393$	−17.5623	−0.885901
$394$	−5.94427	−0.299468
$395$	18.9443	0.953190
$396$	−0.618034	−0.0310574
$397$	34.4508	1.72904	0.864519	−	0.502600i	$-0.167623\pi$
$397$	34.4508	1.72904	0.864519	+	0.502600i	$0.167623\pi$
$398$	13.2016	0.661738
$399$	0	0
$400$	−4.41641	−0.220820
$401$	21.2361	1.06048	0.530239	−	0.847848i	$-0.322102\pi$
$401$	21.2361	1.06048	0.530239	+	0.847848i	$0.322102\pi$
$402$	−12.0902	−0.603003
$403$	−50.4508	−2.51314
$404$	−28.2705	−1.40651
$405$	12.4721	0.619745
$406$	0	0
$407$	2.76393	0.137003
$408$	−15.3262	−0.758762
$409$	25.6525	1.26843	0.634217	−	0.773155i	$-0.281323\pi$
$409$	25.6525	1.26843	0.634217	+	0.773155i	$0.281323\pi$
$410$	−1.00000	−0.0493865
$411$	25.5623	1.26090
$412$	−1.76393	−0.0869027
$413$	0	0
$414$	0.854102	0.0419768
$415$	−8.85410	−0.434631
$416$	35.0344	1.71770
$417$	9.61803	0.470997
$418$	1.76393	0.0862767
$419$	9.27051	0.452894	0.226447	−	0.974023i	$-0.427289\pi$
$419$	9.27051	0.452894	0.226447	+	0.974023i	$0.427289\pi$
$420$	0	0
$421$	−20.4721	−0.997751	−0.498875	−	0.866674i	$-0.666253\pi$
$421$	−20.4721	−0.997751	−0.498875	+	0.866674i	$0.666253\pi$
$422$	8.67376	0.422232
$423$	3.70820	0.180299
$424$	−5.32624	−0.258665
$425$	−10.0902	−0.489445
$426$	−5.94427	−0.288001
$427$	0	0
$428$	1.23607	0.0597476
$429$	−10.0902	−0.487158
$430$	1.00000	0.0482243
$431$	−9.47214	−0.456257	−0.228128	−	0.973631i	$-0.573261\pi$
$431$	−9.47214	−0.456257	−0.228128	+	0.973631i	$0.573261\pi$
$432$	−10.1459	−0.488145
$433$	0.965558	0.0464018	0.0232009	−	0.999731i	$-0.492614\pi$
$433$	0.965558	0.0464018	0.0232009	+	0.999731i	$0.492614\pi$
$434$	0	0
$435$	15.3262	0.734837
$436$	−13.7082	−0.656504
$437$	10.3262	0.493971
$438$	9.94427	0.475156
$439$	13.9443	0.665524	0.332762	−	0.943011i	$-0.392019\pi$
$439$	13.9443	0.665524	0.332762	+	0.943011i	$0.392019\pi$
$440$	−3.61803	−0.172483
$441$	0	0
$442$	16.3262	0.776560
$443$	16.8541	0.800763	0.400381	−	0.916349i	$-0.368878\pi$
$443$	16.8541	0.800763	0.400381	+	0.916349i	$0.368878\pi$
$444$	7.23607	0.343409
$445$	−15.0902	−0.715343
$446$	0.819660	0.0388120
$447$	30.6525	1.44981
$448$	0	0
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	0.562306	0.0265074
$451$	−1.00000	−0.0470882
$452$	−23.3262	−1.09717
$453$	−32.2705	−1.51620
$454$	−3.49342	−0.163954
$455$	0	0
$456$	10.3262	0.483570
$457$	−16.4164	−0.767927	−0.383964	−	0.923348i	$-0.625441\pi$
$457$	−16.4164	−0.767927	−0.383964	+	0.923348i	$0.625441\pi$
$458$	−13.1246	−0.613273
$459$	−23.1803	−1.08197
$460$	−9.47214	−0.441641
$461$	−23.6525	−1.10161	−0.550803	−	0.834635i	$-0.685678\pi$
$461$	−23.6525	−1.10161	−0.550803	+	0.834635i	$0.685678\pi$
$462$	0	0
$463$	31.3820	1.45844	0.729222	−	0.684277i	$-0.239882\pi$
$463$	31.3820	1.45844	0.729222	+	0.684277i	$0.239882\pi$
$464$	−10.8541	−0.503889
$465$	21.1803	0.982215
$466$	−3.90983	−0.181119
$467$	4.23607	0.196022	0.0980109	−	0.995185i	$-0.468752\pi$
$467$	4.23607	0.196022	0.0980109	+	0.995185i	$0.468752\pi$
$468$	3.85410	0.178156
$469$	0	0
$470$	9.70820	0.447806
$471$	12.9443	0.596441
$472$	18.7426	0.862700
$473$	1.00000	0.0459800
$474$	−11.7082	−0.537776
$475$	6.79837	0.311931
$476$	0	0
$477$	−0.909830	−0.0416583
$478$	−3.79837	−0.173734
$479$	−0.562306	−0.0256924	−0.0128462	−	0.999917i	$-0.504089\pi$
$479$	−0.562306	−0.0256924	−0.0128462	+	0.999917i	$0.504089\pi$
$480$	−14.7082	−0.671335
$481$	−17.2361	−0.785897
$482$	2.94427	0.134108
$483$	0	0
$484$	16.1803	0.735470
$485$	4.14590	0.188256
$486$	2.43769	0.110576
$487$	−10.7639	−0.487760	−0.243880	−	0.969805i	$-0.578420\pi$
$487$	−10.7639	−0.487760	−0.243880	+	0.969805i	$0.578420\pi$
$488$	21.1803	0.958789
$489$	−27.4164	−1.23981
$490$	0	0
$491$	21.2705	0.959925	0.479962	−	0.877289i	$-0.340650\pi$
$491$	21.2705	0.959925	0.479962	+	0.877289i	$0.340650\pi$
$492$	−2.61803	−0.118030
$493$	−24.7984	−1.11686
$494$	−11.0000	−0.494913
$495$	−0.618034	−0.0277786
$496$	−15.0000	−0.673520
$497$	0	0
$498$	5.47214	0.245212
$499$	24.6525	1.10360	0.551798	−	0.833978i	$-0.313942\pi$
$499$	24.6525	1.10360	0.551798	+	0.833978i	$0.313942\pi$
$500$	−19.3262	−0.864296
$501$	16.8541	0.752986
$502$	−1.27051	−0.0567056
$503$	−24.6869	−1.10074	−0.550368	−	0.834922i	$-0.685512\pi$
$503$	−24.6869	−1.10074	−0.550368	+	0.834922i	$0.685512\pi$
$504$	0	0
$505$	−28.2705	−1.25802
$506$	2.23607	0.0994053
$507$	41.8885	1.86034
$508$	5.32624	0.236314
$509$	−16.0344	−0.710714	−0.355357	−	0.934731i	$-0.615641\pi$
$509$	−16.0344	−0.710714	−0.355357	+	0.934731i	$0.615641\pi$
$510$	−6.85410	−0.303505
$511$	0	0
$512$	18.7082	0.826794
$513$	15.6180	0.689553
$514$	−14.9098	−0.657644
$515$	−1.76393	−0.0777281
$516$	2.61803	0.115253
$517$	9.70820	0.426966
$518$	0	0
$519$	−7.61803	−0.334395
$520$	22.5623	0.989423
$521$	23.9098	1.04751	0.523754	−	0.851869i	$-0.324531\pi$
$521$	23.9098	1.04751	0.523754	+	0.851869i	$0.324531\pi$
$522$	1.38197	0.0604870
$523$	−17.4721	−0.764003	−0.382002	−	0.924162i	$-0.624765\pi$
$523$	−17.4721	−0.764003	−0.382002	+	0.924162i	$0.624765\pi$
$524$	17.5623	0.767213
$525$	0	0
$526$	−7.85410	−0.342455
$527$	−34.2705	−1.49285
$528$	−3.00000	−0.130558
$529$	−9.90983	−0.430862
$530$	−2.38197	−0.103466
$531$	3.20163	0.138939
$532$	0	0
$533$	6.23607	0.270114
$534$	9.32624	0.403586
$535$	1.23607	0.0534399
$536$	27.0344	1.16771
$537$	4.90983	0.211875
$538$	−14.3820	−0.620051
$539$	0	0
$540$	−14.3262	−0.616503
$541$	40.7426	1.75166	0.875832	−	0.482617i	$-0.160314\pi$
$541$	40.7426	1.75166	0.875832	+	0.482617i	$0.160314\pi$
$542$	−2.61803	−0.112454
$543$	4.76393	0.204440
$544$	23.7984	1.02035
$545$	−13.7082	−0.587195
$546$	0	0
$547$	−15.0000	−0.641354	−0.320677	−	0.947189i	$-0.603910\pi$
$547$	−15.0000	−0.641354	−0.320677	+	0.947189i	$0.603910\pi$
$548$	−25.5623	−1.09197
$549$	3.61803	0.154414
$550$	1.47214	0.0627721
$551$	16.7082	0.711793
$552$	13.0902	0.557155
$553$	0	0
$554$	−0.506578	−0.0215224
$555$	7.23607	0.307154
$556$	−9.61803	−0.407895
$557$	−28.2148	−1.19550	−0.597749	−	0.801683i	$-0.703938\pi$
$557$	−28.2148	−1.19550	−0.597749	+	0.801683i	$0.703938\pi$
$558$	1.90983	0.0808496
$559$	−6.23607	−0.263758
$560$	0	0
$561$	−6.85410	−0.289380
$562$	−15.2705	−0.644148
$563$	−9.47214	−0.399203	−0.199601	−	0.979877i	$-0.563965\pi$
$563$	−9.47214	−0.399203	−0.199601	+	0.979877i	$0.563965\pi$
$564$	25.4164	1.07022
$565$	−23.3262	−0.981342
$566$	0	0
$567$	0	0
$568$	13.2918	0.557711
$569$	0.381966	0.0160128	0.00800642	−	0.999968i	$-0.497451\pi$
$569$	0.381966	0.0160128	0.00800642	+	0.999968i	$0.497451\pi$
$570$	4.61803	0.193428
$571$	19.8885	0.832310	0.416155	−	0.909294i	$-0.363377\pi$
$571$	19.8885	0.832310	0.416155	+	0.909294i	$0.363377\pi$
$572$	10.0902	0.421891
$573$	36.3607	1.51899
$574$	0	0
$575$	8.61803	0.359397
$576$	0.0901699	0.00375708
$577$	21.1803	0.881749	0.440875	−	0.897569i	$-0.354668\pi$
$577$	21.1803	0.881749	0.440875	+	0.897569i	$0.354668\pi$
$578$	0.583592	0.0242742
$579$	−36.7426	−1.52697
$580$	−15.3262	−0.636387
$581$	0	0
$582$	−2.56231	−0.106211
$583$	−2.38197	−0.0986510
$584$	−22.2361	−0.920135
$585$	3.85410	0.159348
$586$	7.56231	0.312396
$587$	37.0689	1.53000	0.764998	−	0.644032i	$-0.222740\pi$
$587$	37.0689	1.53000	0.764998	+	0.644032i	$0.222740\pi$
$588$	0	0
$589$	23.0902	0.951414
$590$	8.38197	0.345080
$591$	−15.5623	−0.640148
$592$	−5.12461	−0.210620
$593$	34.8328	1.43041	0.715206	−	0.698914i	$-0.246333\pi$
$593$	34.8328	1.43041	0.715206	+	0.698914i	$0.246333\pi$
$594$	3.38197	0.138764
$595$	0	0
$596$	−30.6525	−1.25557
$597$	34.5623	1.41454
$598$	−13.9443	−0.570224
$599$	26.6525	1.08899	0.544495	−	0.838764i	$-0.316721\pi$
$599$	26.6525	1.08899	0.544495	+	0.838764i	$0.316721\pi$
$600$	8.61803	0.351830
$601$	13.5623	0.553218	0.276609	−	0.960983i	$-0.410789\pi$
$601$	13.5623	0.553218	0.276609	+	0.960983i	$0.410789\pi$
$602$	0	0
$603$	4.61803	0.188061
$604$	32.2705	1.31307
$605$	16.1803	0.657824
$606$	17.4721	0.709757
$607$	−11.8328	−0.480279	−0.240140	−	0.970738i	$-0.577193\pi$
$607$	−11.8328	−0.480279	−0.240140	+	0.970738i	$0.577193\pi$
$608$	−16.0344	−0.650282
$609$	0	0
$610$	9.47214	0.383516
$611$	−60.5410	−2.44923
$612$	2.61803	0.105828
$613$	−6.27051	−0.253264	−0.126632	−	0.991950i	$-0.540417\pi$
$613$	−6.27051	−0.253264	−0.126632	+	0.991950i	$0.540417\pi$
$614$	−14.5410	−0.586828
$615$	−2.61803	−0.105569
$616$	0	0
$617$	−32.5967	−1.31230	−0.656148	−	0.754632i	$-0.727815\pi$
$617$	−32.5967	−1.31230	−0.656148	+	0.754632i	$0.727815\pi$
$618$	1.09017	0.0438531
$619$	5.67376	0.228048	0.114024	−	0.993478i	$-0.463626\pi$
$619$	5.67376	0.228048	0.114024	+	0.993478i	$0.463626\pi$
$620$	−21.1803	−0.850623
$621$	19.7984	0.794481
$622$	−0.381966	−0.0153154
$623$	0	0
$624$	18.7082	0.748928
$625$	−7.41641	−0.296656
$626$	18.2148	0.728009
$627$	4.61803	0.184427
$628$	−12.9443	−0.516533
$629$	−11.7082	−0.466837
$630$	0	0
$631$	−40.4853	−1.61169	−0.805847	−	0.592124i	$-0.798290\pi$
$631$	−40.4853	−1.61169	−0.805847	+	0.592124i	$0.798290\pi$
$632$	26.1803	1.04140
$633$	22.7082	0.902570
$634$	−5.02129	−0.199421
$635$	5.32624	0.211365
$636$	−6.23607	−0.247276
$637$	0	0
$638$	3.61803	0.143239
$639$	2.27051	0.0898200
$640$	18.4164	0.727972
$641$	17.1803	0.678583	0.339291	−	0.940681i	$-0.389813\pi$
$641$	17.1803	0.678583	0.339291	+	0.940681i	$0.389813\pi$
$642$	−0.763932	−0.0301500
$643$	−27.9230	−1.10118	−0.550588	−	0.834777i	$-0.685596\pi$
$643$	−27.9230	−1.10118	−0.550588	+	0.834777i	$0.685596\pi$
$644$	0	0
$645$	2.61803	0.103085
$646$	−7.47214	−0.293987
$647$	21.3607	0.839775	0.419887	−	0.907576i	$-0.362070\pi$
$647$	21.3607	0.839775	0.419887	+	0.907576i	$0.362070\pi$
$648$	17.2361	0.677097
$649$	8.38197	0.329021
$650$	−9.18034	−0.360083
$651$	0	0
$652$	27.4164	1.07371
$653$	27.6180	1.08078	0.540389	−	0.841416i	$-0.318277\pi$
$653$	27.6180	1.08078	0.540389	+	0.841416i	$0.318277\pi$
$654$	8.47214	0.331287
$655$	17.5623	0.686216
$656$	1.85410	0.0723905
$657$	−3.79837	−0.148189
$658$	0	0
$659$	39.0689	1.52191	0.760954	−	0.648806i	$-0.224731\pi$
$659$	39.0689	1.52191	0.760954	+	0.648806i	$0.224731\pi$
$660$	−4.23607	−0.164889
$661$	−30.7639	−1.19658	−0.598289	−	0.801280i	$-0.704153\pi$
$661$	−30.7639	−1.19658	−0.598289	+	0.801280i	$0.704153\pi$
$662$	20.9443	0.814022
$663$	42.7426	1.65999
$664$	−12.2361	−0.474852
$665$	0	0
$666$	0.652476	0.0252829
$667$	21.1803	0.820106
$668$	−16.8541	−0.652105
$669$	2.14590	0.0829652
$670$	12.0902	0.467084
$671$	9.47214	0.365668
$672$	0	0
$673$	19.8328	0.764499	0.382249	−	0.924059i	$-0.375150\pi$
$673$	19.8328	0.764499	0.382249	+	0.924059i	$0.375150\pi$
$674$	−12.6525	−0.487355
$675$	13.0344	0.501696
$676$	−41.8885	−1.61110
$677$	−31.9098	−1.22639	−0.613197	−	0.789930i	$-0.710117\pi$
$677$	−31.9098	−1.22639	−0.613197	+	0.789930i	$0.710117\pi$
$678$	14.4164	0.553659
$679$	0	0
$680$	15.3262	0.587734
$681$	−9.14590	−0.350472
$682$	5.00000	0.191460
$683$	18.0557	0.690883	0.345442	−	0.938440i	$-0.387729\pi$
$683$	18.0557	0.690883	0.345442	+	0.938440i	$0.387729\pi$
$684$	−1.76393	−0.0674456
$685$	−25.5623	−0.976686
$686$	0	0
$687$	−34.3607	−1.31094
$688$	−1.85410	−0.0706870
$689$	14.8541	0.565896
$690$	5.85410	0.222862
$691$	−5.67376	−0.215840	−0.107920	−	0.994160i	$-0.534419\pi$
$691$	−5.67376	−0.215840	−0.107920	+	0.994160i	$0.534419\pi$
$692$	7.61803	0.289594
$693$	0	0
$694$	−2.65248	−0.100687
$695$	−9.61803	−0.364833
$696$	21.1803	0.802839
$697$	4.23607	0.160453
$698$	−10.3262	−0.390854
$699$	−10.2361	−0.387164
$700$	0	0
$701$	7.61803	0.287729	0.143865	−	0.989597i	$-0.454047\pi$
$701$	7.61803	0.287729	0.143865	+	0.989597i	$0.454047\pi$
$702$	−21.0902	−0.795997
$703$	7.88854	0.297522
$704$	0.236068	0.00889715
$705$	25.4164	0.957237
$706$	−6.40325	−0.240990
$707$	0	0
$708$	21.9443	0.824716
$709$	−31.1246	−1.16891	−0.584455	−	0.811426i	$-0.698692\pi$
$709$	−31.1246	−1.16891	−0.584455	+	0.811426i	$0.698692\pi$
$710$	5.94427	0.223085
$711$	4.47214	0.167718
$712$	−20.8541	−0.781541
$713$	29.2705	1.09619
$714$	0	0
$715$	10.0902	0.377351
$716$	−4.90983	−0.183489
$717$	−9.94427	−0.371376
$718$	13.7082	0.511586
$719$	0.819660	0.0305682	0.0152841	−	0.999883i	$-0.495135\pi$
$719$	0.819660	0.0305682	0.0152841	+	0.999883i	$0.495135\pi$
$720$	1.14590	0.0427051
$721$	0	0
$722$	−6.70820	−0.249653
$723$	7.70820	0.286671
$724$	−4.76393	−0.177050
$725$	13.9443	0.517877
$726$	−10.0000	−0.371135
$727$	−41.1591	−1.52650	−0.763252	−	0.646100i	$-0.776399\pi$
$727$	−41.1591	−1.52650	−0.763252	+	0.646100i	$0.776399\pi$
$728$	0	0
$729$	29.5066	1.09284
$730$	−9.94427	−0.368054
$731$	−4.23607	−0.156677
$732$	24.7984	0.916574
$733$	2.05573	0.0759300	0.0379650	−	0.999279i	$-0.487912\pi$
$733$	2.05573	0.0759300	0.0379650	+	0.999279i	$0.487912\pi$
$734$	−16.8541	−0.622096
$735$	0	0
$736$	−20.3262	−0.749235
$737$	12.0902	0.445347
$738$	−0.236068	−0.00868978
$739$	−48.3262	−1.77771	−0.888855	−	0.458189i	$-0.848498\pi$
$739$	−48.3262	−1.77771	−0.888855	+	0.458189i	$0.848498\pi$
$740$	−7.23607	−0.266003
$741$	−28.7984	−1.05793
$742$	0	0
$743$	50.6869	1.85952	0.929761	−	0.368163i	$-0.120013\pi$
$743$	50.6869	1.85952	0.929761	+	0.368163i	$0.120013\pi$
$744$	29.2705	1.07311
$745$	−30.6525	−1.12302
$746$	7.87539	0.288338
$747$	−2.09017	−0.0764753
$748$	6.85410	0.250611
$749$	0	0
$750$	11.9443	0.436143
$751$	35.5410	1.29691	0.648455	−	0.761253i	$-0.275415\pi$
$751$	35.5410	1.29691	0.648455	+	0.761253i	$0.275415\pi$
$752$	−18.0000	−0.656392
$753$	−3.32624	−0.121215
$754$	−22.5623	−0.821671
$755$	32.2705	1.17444
$756$	0	0
$757$	4.65248	0.169097	0.0845486	−	0.996419i	$-0.473055\pi$
$757$	4.65248	0.169097	0.0845486	+	0.996419i	$0.473055\pi$
$758$	−6.58359	−0.239127
$759$	5.85410	0.212490
$760$	−10.3262	−0.374572
$761$	31.7771	1.15192	0.575959	−	0.817478i	$-0.304629\pi$
$761$	31.7771	1.15192	0.575959	+	0.817478i	$0.304629\pi$
$762$	−3.29180	−0.119249
$763$	0	0
$764$	−36.3607	−1.31548
$765$	2.61803	0.0946552
$766$	14.3262	0.517628
$767$	−52.2705	−1.88738
$768$	−10.6180	−0.383145
$769$	46.1803	1.66531	0.832653	−	0.553795i	$-0.186821\pi$
$769$	46.1803	1.66531	0.832653	+	0.553795i	$0.186821\pi$
$770$	0	0
$771$	−39.0344	−1.40579
$772$	36.7426	1.32240
$773$	10.8197	0.389156	0.194578	−	0.980887i	$-0.437666\pi$
$773$	10.8197	0.389156	0.194578	+	0.980887i	$0.437666\pi$
$774$	0.236068	0.00848529
$775$	19.2705	0.692217
$776$	5.72949	0.205677
$777$	0	0
$778$	−18.9656	−0.679948
$779$	−2.85410	−0.102259
$780$	26.4164	0.945859
$781$	5.94427	0.212703
$782$	−9.47214	−0.338723
$783$	32.0344	1.14482
$784$	0	0
$785$	−12.9443	−0.462001
$786$	−10.8541	−0.387153
$787$	−18.1803	−0.648059	−0.324030	−	0.946047i	$-0.605038\pi$
$787$	−18.1803	−0.648059	−0.324030	+	0.946047i	$0.605038\pi$
$788$	15.5623	0.554384
$789$	−20.5623	−0.732037
$790$	11.7082	0.416559
$791$	0	0
$792$	−0.854102	−0.0303492
$793$	−59.0689	−2.09760
$794$	21.2918	0.755618
$795$	−6.23607	−0.221171
$796$	−34.5623	−1.22503
$797$	23.8328	0.844202	0.422101	−	0.906549i	$-0.361293\pi$
$797$	23.8328	0.844202	0.422101	+	0.906549i	$0.361293\pi$
$798$	0	0
$799$	−41.1246	−1.45488
$800$	−13.3820	−0.473124
$801$	−3.56231	−0.125868
$802$	13.1246	0.463446
$803$	−9.94427	−0.350926
$804$	31.6525	1.11630
$805$	0	0
$806$	−31.1803	−1.09828
$807$	−37.6525	−1.32543
$808$	−39.0689	−1.37444
$809$	52.8115	1.85675	0.928377	−	0.371639i	$-0.121204\pi$
$809$	52.8115	1.85675	0.928377	+	0.371639i	$0.121204\pi$
$810$	7.70820	0.270839
$811$	9.06888	0.318452	0.159226	−	0.987242i	$-0.449100\pi$
$811$	9.06888	0.318452	0.159226	+	0.987242i	$0.449100\pi$
$812$	0	0
$813$	−6.85410	−0.240384
$814$	1.70820	0.0598725
$815$	27.4164	0.960355
$816$	12.7082	0.444876
$817$	2.85410	0.0998524
$818$	15.8541	0.554326
$819$	0	0
$820$	2.61803	0.0914257
$821$	−20.7771	−0.725125	−0.362563	−	0.931959i	$-0.618098\pi$
$821$	−20.7771	−0.725125	−0.362563	+	0.931959i	$0.618098\pi$
$822$	15.7984	0.551032
$823$	−36.0344	−1.25608	−0.628041	−	0.778180i	$-0.716143\pi$
$823$	−36.0344	−1.25608	−0.628041	+	0.778180i	$0.716143\pi$
$824$	−2.43769	−0.0849211
$825$	3.85410	0.134183
$826$	0	0
$827$	35.2492	1.22574	0.612868	−	0.790185i	$-0.290016\pi$
$827$	35.2492	1.22574	0.612868	+	0.790185i	$0.290016\pi$
$828$	−2.23607	−0.0777087
$829$	7.36068	0.255647	0.127823	−	0.991797i	$-0.459201\pi$
$829$	7.36068	0.255647	0.127823	+	0.991797i	$0.459201\pi$
$830$	−5.47214	−0.189941
$831$	−1.32624	−0.0460067
$832$	−1.47214	−0.0510371
$833$	0	0
$834$	5.94427	0.205833
$835$	−16.8541	−0.583260
$836$	−4.61803	−0.159718
$837$	44.2705	1.53021
$838$	5.72949	0.197922
$839$	3.23607	0.111721	0.0558607	−	0.998439i	$-0.482210\pi$
$839$	3.23607	0.111721	0.0558607	+	0.998439i	$0.482210\pi$
$840$	0	0
$841$	5.27051	0.181742
$842$	−12.6525	−0.436033
$843$	−39.9787	−1.37694
$844$	−22.7082	−0.781649
$845$	−41.8885	−1.44101
$846$	2.29180	0.0787936
$847$	0	0
$848$	4.41641	0.151660
$849$	0	0
$850$	−6.23607	−0.213895
$851$	10.0000	0.342796
$852$	15.5623	0.533156
$853$	−28.2492	−0.967235	−0.483617	−	0.875279i	$-0.660677\pi$
$853$	−28.2492	−0.967235	−0.483617	+	0.875279i	$0.660677\pi$
$854$	0	0
$855$	−1.76393	−0.0603252
$856$	1.70820	0.0583852
$857$	−4.61803	−0.157749	−0.0788745	−	0.996885i	$-0.525133\pi$
$857$	−4.61803	−0.157749	−0.0788745	+	0.996885i	$0.525133\pi$
$858$	−6.23607	−0.212896
$859$	49.0344	1.67303	0.836517	−	0.547941i	$-0.184588\pi$
$859$	49.0344	1.67303	0.836517	+	0.547941i	$0.184588\pi$
$860$	−2.61803	−0.0892742
$861$	0	0
$862$	−5.85410	−0.199392
$863$	−34.2361	−1.16541	−0.582705	−	0.812684i	$-0.698006\pi$
$863$	−34.2361	−1.16541	−0.582705	+	0.812684i	$0.698006\pi$
$864$	−30.7426	−1.04589
$865$	7.61803	0.259021
$866$	0.596748	0.0202783
$867$	1.52786	0.0518890
$868$	0	0
$869$	11.7082	0.397174
$870$	9.47214	0.321135
$871$	−75.3951	−2.55467
$872$	−18.9443	−0.641534
$873$	0.978714	0.0331244
$874$	6.38197	0.215873
$875$	0	0
$876$	−26.0344	−0.879622
$877$	2.14590	0.0724618	0.0362309	−	0.999343i	$-0.488465\pi$
$877$	2.14590	0.0724618	0.0362309	+	0.999343i	$0.488465\pi$
$878$	8.61803	0.290845
$879$	19.7984	0.667783
$880$	3.00000	0.101130
$881$	−2.58359	−0.0870434	−0.0435217	−	0.999052i	$-0.513858\pi$
$881$	−2.58359	−0.0870434	−0.0435217	+	0.999052i	$0.513858\pi$
$882$	0	0
$883$	5.61803	0.189062	0.0945309	−	0.995522i	$-0.469865\pi$
$883$	5.61803	0.189062	0.0945309	+	0.995522i	$0.469865\pi$
$884$	−42.7426	−1.43759
$885$	21.9443	0.737649
$886$	10.4164	0.349946
$887$	−45.8885	−1.54079	−0.770393	−	0.637569i	$-0.779940\pi$
$887$	−45.8885	−1.54079	−0.770393	+	0.637569i	$0.779940\pi$
$888$	10.0000	0.335578
$889$	0	0
$890$	−9.32624	−0.312616
$891$	7.70820	0.258235
$892$	−2.14590	−0.0718500
$893$	27.7082	0.927220
$894$	18.9443	0.633591
$895$	−4.90983	−0.164118
$896$	0	0
$897$	−36.5066	−1.21892
$898$	−3.70820	−0.123744
$899$	47.3607	1.57957
$900$	−1.47214	−0.0490712
$901$	10.0902	0.336152
$902$	−0.618034	−0.0205783
$903$	0	0
$904$	−32.2361	−1.07216
$905$	−4.76393	−0.158358
$906$	−19.9443	−0.662604
$907$	−57.1591	−1.89794	−0.948968	−	0.315374i	$-0.897870\pi$
$907$	−57.1591	−1.89794	−0.948968	+	0.315374i	$0.897870\pi$
$908$	9.14590	0.303517
$909$	−6.67376	−0.221355
$910$	0	0
$911$	−11.6393	−0.385628	−0.192814	−	0.981235i	$-0.561761\pi$
$911$	−11.6393	−0.385628	−0.192814	+	0.981235i	$0.561761\pi$
$912$	−8.56231	−0.283526
$913$	−5.47214	−0.181101
$914$	−10.1459	−0.335596
$915$	24.7984	0.819809
$916$	34.3607	1.13531
$917$	0	0
$918$	−14.3262	−0.472836
$919$	−0.549150	−0.0181148	−0.00905740	−	0.999959i	$-0.502883\pi$
$919$	−0.549150	−0.0181148	−0.00905740	+	0.999959i	$0.502883\pi$
$920$	−13.0902	−0.431570
$921$	−38.0689	−1.25441
$922$	−14.6180	−0.481419
$923$	−37.0689	−1.22014
$924$	0	0
$925$	6.58359	0.216467
$926$	19.3951	0.637363
$927$	−0.416408	−0.0136766
$928$	−32.8885	−1.07962
$929$	4.43769	0.145596	0.0727980	−	0.997347i	$-0.476807\pi$
$929$	4.43769	0.145596	0.0727980	+	0.997347i	$0.476807\pi$
$930$	13.0902	0.429244
$931$	0	0
$932$	10.2361	0.335294
$933$	−1.00000	−0.0327385
$934$	2.61803	0.0856647
$935$	6.85410	0.224153
$936$	5.32624	0.174094
$937$	23.5836	0.770442	0.385221	−	0.922824i	$-0.374125\pi$
$937$	23.5836	0.770442	0.385221	+	0.922824i	$0.374125\pi$
$938$	0	0
$939$	47.6869	1.55620
$940$	−25.4164	−0.828992
$941$	−45.8673	−1.49523	−0.747615	−	0.664132i	$-0.768801\pi$
$941$	−45.8673	−1.49523	−0.747615	+	0.664132i	$0.768801\pi$
$942$	8.00000	0.260654
$943$	−3.61803	−0.117819
$944$	−15.5410	−0.505817
$945$	0	0
$946$	0.618034	0.0200940
$947$	−21.2705	−0.691199	−0.345599	−	0.938382i	$-0.612324\pi$
$947$	−21.2705	−0.691199	−0.345599	+	0.938382i	$0.612324\pi$
$948$	30.6525	0.995546
$949$	62.0132	2.01303
$950$	4.20163	0.136319
$951$	−13.1459	−0.426285
$952$	0	0
$953$	−1.09017	−0.0353141	−0.0176570	−	0.999844i	$-0.505621\pi$
$953$	−1.09017	−0.0353141	−0.0176570	+	0.999844i	$0.505621\pi$
$954$	−0.562306	−0.0182053
$955$	−36.3607	−1.17660
$956$	9.94427	0.321621
$957$	9.47214	0.306191
$958$	−0.347524	−0.0112280
$959$	0	0
$960$	0.618034	0.0199470
$961$	34.4508	1.11132
$962$	−10.6525	−0.343450
$963$	0.291796	0.00940300
$964$	−7.70820	−0.248265
$965$	36.7426	1.18279
$966$	0	0
$967$	29.8885	0.961151	0.480575	−	0.876953i	$-0.340428\pi$
$967$	29.8885	0.961151	0.480575	+	0.876953i	$0.340428\pi$
$968$	22.3607	0.718699
$969$	−19.5623	−0.628432
$970$	2.56231	0.0822707
$971$	44.5967	1.43118	0.715589	−	0.698522i	$-0.246158\pi$
$971$	44.5967	1.43118	0.715589	+	0.698522i	$0.246158\pi$
$972$	−6.38197	−0.204702
$973$	0	0
$974$	−6.65248	−0.213159
$975$	−24.0344	−0.769718
$976$	−17.5623	−0.562156
$977$	27.2016	0.870257	0.435129	−	0.900368i	$-0.356703\pi$
$977$	27.2016	0.870257	0.435129	+	0.900368i	$0.356703\pi$
$978$	−16.9443	−0.541818
$979$	−9.32624	−0.298068
$980$	0	0
$981$	−3.23607	−0.103320
$982$	13.1459	0.419502
$983$	−43.4721	−1.38655	−0.693273	−	0.720675i	$-0.743832\pi$
$983$	−43.4721	−1.38655	−0.693273	+	0.720675i	$0.743832\pi$
$984$	−3.61803	−0.115339
$985$	15.5623	0.495856
$986$	−15.3262	−0.488087
$987$	0	0
$988$	28.7984	0.916198
$989$	3.61803	0.115047
$990$	−0.381966	−0.0121397
$991$	39.1803	1.24460	0.622302	−	0.782777i	$-0.286197\pi$
$991$	39.1803	1.24460	0.622302	+	0.782777i	$0.286197\pi$
$992$	−45.4508	−1.44307
$993$	54.8328	1.74007
$994$	0	0
$995$	−34.5623	−1.09570
$996$	−14.3262	−0.453944
$997$	−18.3951	−0.582579	−0.291290	−	0.956635i	$-0.594084\pi$
$997$	−18.3951	−0.582579	−0.291290	+	0.956635i	$0.594084\pi$
$998$	15.2361	0.482289
$999$	15.1246	0.478522

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.a.1.2		2
7.6	odd	2		287.2.a.b.1.2	✓	2
21.20	even	2		2583.2.a.g.1.1		2
28.27	even	2		4592.2.a.n.1.2		2
35.34	odd	2		7175.2.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.b.1.2	✓	2	7.6	odd	2
2009.2.a.a.1.2		2	1.1	even	1	trivial
2583.2.a.g.1.1		2	21.20	even	2
4592.2.a.n.1.2		2	28.27	even	2
7175.2.a.g.1.1		2	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.618034 q^{2} +1.61803 q^{3} -1.61803 q^{4} -1.61803 q^{5} +1.00000 q^{6} -2.23607 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q+0.618034 q^{2} +1.61803 q^{3} -1.61803 q^{4} -1.61803 q^{5} +1.00000 q^{6} -2.23607 q^{8} -0.381966 q^{9} -1.00000 q^{10} -1.00000 q^{11} -2.61803 q^{12} +6.23607 q^{13} -2.61803 q^{15} +1.85410 q^{16} +4.23607 q^{17} -0.236068 q^{18} -2.85410 q^{19} +2.61803 q^{20} -0.618034 q^{22} -3.61803 q^{23} -3.61803 q^{24} -2.38197 q^{25} +3.85410 q^{26} -5.47214 q^{27} -5.85410 q^{29} -1.61803 q^{30} -8.09017 q^{31} +5.61803 q^{32} -1.61803 q^{33} +2.61803 q^{34} +0.618034 q^{36} -2.76393 q^{37} -1.76393 q^{38} +10.0902 q^{39} +3.61803 q^{40} +1.00000 q^{41} -1.00000 q^{43} +1.61803 q^{44} +0.618034 q^{45} -2.23607 q^{46} -9.70820 q^{47} +3.00000 q^{48} -1.47214 q^{50} +6.85410 q^{51} -10.0902 q^{52} +2.38197 q^{53} -3.38197 q^{54} +1.61803 q^{55} -4.61803 q^{57} -3.61803 q^{58} -8.38197 q^{59} +4.23607 q^{60} -9.47214 q^{61} -5.00000 q^{62} -0.236068 q^{64} -10.0902 q^{65} -1.00000 q^{66} -12.0902 q^{67} -6.85410 q^{68} -5.85410 q^{69} -5.94427 q^{71} +0.854102 q^{72} +9.94427 q^{73} -1.70820 q^{74} -3.85410 q^{75} +4.61803 q^{76} +6.23607 q^{78} -11.7082 q^{79} -3.00000 q^{80} -7.70820 q^{81} +0.618034 q^{82} +5.47214 q^{83} -6.85410 q^{85} -0.618034 q^{86} -9.47214 q^{87} +2.23607 q^{88} +9.32624 q^{89} +0.381966 q^{90} +5.85410 q^{92} -13.0902 q^{93} -6.00000 q^{94} +4.61803 q^{95} +9.09017 q^{96} -2.56231 q^{97} +0.381966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 3 q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 3 * q^9	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 3 q^{9} - 2 q^{10} - 2 q^{11} - 3 q^{12} + 8 q^{13} - 3 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + q^{19} + 3 q^{20} + q^{22} - 5 q^{23} - 5 q^{24} - 7 q^{25} + q^{26} - 2 q^{27} - 5 q^{29} - q^{30} - 5 q^{31} + 9 q^{32} - q^{33} + 3 q^{34} - q^{36} - 10 q^{37} - 8 q^{38} + 9 q^{39} + 5 q^{40} + 2 q^{41} - 2 q^{43} + q^{44} - q^{45} - 6 q^{47} + 6 q^{48} + 6 q^{50} + 7 q^{51} - 9 q^{52} + 7 q^{53} - 9 q^{54} + q^{55} - 7 q^{57} - 5 q^{58} - 19 q^{59} + 4 q^{60} - 10 q^{61} - 10 q^{62} + 4 q^{64} - 9 q^{65} - 2 q^{66} - 13 q^{67} - 7 q^{68} - 5 q^{69} + 6 q^{71} - 5 q^{72} + 2 q^{73} + 10 q^{74} - q^{75} + 7 q^{76} + 8 q^{78} - 10 q^{79} - 6 q^{80} - 2 q^{81} - q^{82} + 2 q^{83} - 7 q^{85} + q^{86} - 10 q^{87} + 3 q^{89} + 3 q^{90} + 5 q^{92} - 15 q^{93} - 12 q^{94} + 7 q^{95} + 7 q^{96} + 15 q^{97} + 3 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 3 * q^9 - 2 * q^10 - 2 * q^11 - 3 * q^12 + 8 * q^13 - 3 * q^15 - 3 * q^16 + 4 * q^17 + 4 * q^18 + q^19 + 3 * q^20 + q^22 - 5 * q^23 - 5 * q^24 - 7 * q^25 + q^26 - 2 * q^27 - 5 * q^29 - q^30 - 5 * q^31 + 9 * q^32 - q^33 + 3 * q^34 - q^36 - 10 * q^37 - 8 * q^38 + 9 * q^39 + 5 * q^40 + 2 * q^41 - 2 * q^43 + q^44 - q^45 - 6 * q^47 + 6 * q^48 + 6 * q^50 + 7 * q^51 - 9 * q^52 + 7 * q^53 - 9 * q^54 + q^55 - 7 * q^57 - 5 * q^58 - 19 * q^59 + 4 * q^60 - 10 * q^61 - 10 * q^62 + 4 * q^64 - 9 * q^65 - 2 * q^66 - 13 * q^67 - 7 * q^68 - 5 * q^69 + 6 * q^71 - 5 * q^72 + 2 * q^73 + 10 * q^74 - q^75 + 7 * q^76 + 8 * q^78 - 10 * q^79 - 6 * q^80 - 2 * q^81 - q^82 + 2 * q^83 - 7 * q^85 + q^86 - 10 * q^87 + 3 * q^89 + 3 * q^90 + 5 * q^92 - 15 * q^93 - 12 * q^94 + 7 * q^95 + 7 * q^96 + 15 * q^97 + 3 * q^99

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