LMFDB - Embedded newform 2009.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$16.0419457661$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 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			1.3
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.80194 q^{2} -0.198062 q^{3} +5.85086 q^{4} +2.49396 q^{5} -0.554958 q^{6} +10.7899 q^{8} -2.96077 q^{9} +O(q^{10})$	\(q+2.80194 q^{2} -0.198062 q^{3} +5.85086 q^{4} +2.49396 q^{5} -0.554958 q^{6} +10.7899 q^{8} -2.96077 q^{9} +6.98792 q^{10} -1.10992 q^{11} -1.15883 q^{12} -5.15883 q^{13} -0.493959 q^{15} +18.5308 q^{16} +6.45473 q^{17} -8.29590 q^{18} +1.86294 q^{19} +14.5918 q^{20} -3.10992 q^{22} -3.08815 q^{23} -2.13706 q^{24} +1.21983 q^{25} -14.4547 q^{26} +1.18060 q^{27} +0.219833 q^{29} -1.38404 q^{30} +0.670251 q^{31} +30.3424 q^{32} +0.219833 q^{33} +18.0858 q^{34} -17.3230 q^{36} +1.33513 q^{37} +5.21983 q^{38} +1.02177 q^{39} +26.9095 q^{40} -1.00000 q^{41} +11.3448 q^{43} -6.49396 q^{44} -7.38404 q^{45} -8.65279 q^{46} -4.44504 q^{47} -3.67025 q^{48} +3.41789 q^{50} -1.27844 q^{51} -30.1836 q^{52} -6.89008 q^{53} +3.30798 q^{54} -2.76809 q^{55} -0.368977 q^{57} +0.615957 q^{58} -13.3056 q^{59} -2.89008 q^{60} -6.27413 q^{61} +1.87800 q^{62} +47.9560 q^{64} -12.8659 q^{65} +0.615957 q^{66} -14.7138 q^{67} +37.7657 q^{68} +0.611645 q^{69} -6.98792 q^{71} -31.9463 q^{72} -5.20775 q^{73} +3.74094 q^{74} -0.241603 q^{75} +10.8998 q^{76} +2.86294 q^{78} +0.792249 q^{79} +46.2150 q^{80} +8.64848 q^{81} -2.80194 q^{82} +8.76809 q^{83} +16.0978 q^{85} +31.7875 q^{86} -0.0435405 q^{87} -11.9758 q^{88} -9.70709 q^{89} -20.6896 q^{90} -18.0683 q^{92} -0.132751 q^{93} -12.4547 q^{94} +4.64609 q^{95} -6.00969 q^{96} -8.29590 q^{97} +3.28621 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 4 q^{2} - 5 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 9 q^{8} + 4 q^{9}+O(q^{10}) $ 3 * q + 4 * q^2 - 5 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 9 * q^8 + 4 * q^9	$ 3 q + 4 q^{2} - 5 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 9 q^{8} + 4 q^{9} + 2 q^{10} - 4 q^{11} + 5 q^{12} - 7 q^{13} + 8 q^{15} + 18 q^{16} - 3 q^{17} - 11 q^{18} + 11 q^{19} + 16 q^{20} - 10 q^{22} - 13 q^{23} - q^{24} + 5 q^{25} - 21 q^{26} - 8 q^{27} + 2 q^{29} + 6 q^{30} + 27 q^{32} + 2 q^{33} + 17 q^{34} - 32 q^{36} + 3 q^{37} + 17 q^{38} + 36 q^{40} - 3 q^{41} + 11 q^{43} - 10 q^{44} - 12 q^{45} - 8 q^{46} - 13 q^{47} - 9 q^{48} + 16 q^{50} + 26 q^{51} - 35 q^{52} - 20 q^{53} + 15 q^{54} + 12 q^{55} - 16 q^{57} + 12 q^{58} - 4 q^{59} - 8 q^{60} - 8 q^{61} - 14 q^{62} + 49 q^{64} + 12 q^{66} - 36 q^{67} + 52 q^{68} + 31 q^{69} - 2 q^{71} - 23 q^{72} + 2 q^{73} - 3 q^{74} + q^{75} + 10 q^{76} + 14 q^{78} + 20 q^{79} + 58 q^{80} + 27 q^{81} - 4 q^{82} + 6 q^{83} + 30 q^{85} + 31 q^{86} + 6 q^{87} + 2 q^{88} + q^{89} - 16 q^{90} - q^{92} - 14 q^{93} - 15 q^{94} - 26 q^{95} + 4 q^{96} - 11 q^{97} + 18 q^{99}+O(q^{100}) $ 3 * q + 4 * q^2 - 5 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 9 * q^8 + 4 * q^9 + 2 * q^10 - 4 * q^11 + 5 * q^12 - 7 * q^13 + 8 * q^15 + 18 * q^16 - 3 * q^17 - 11 * q^18 + 11 * q^19 + 16 * q^20 - 10 * q^22 - 13 * q^23 - q^24 + 5 * q^25 - 21 * q^26 - 8 * q^27 + 2 * q^29 + 6 * q^30 + 27 * q^32 + 2 * q^33 + 17 * q^34 - 32 * q^36 + 3 * q^37 + 17 * q^38 + 36 * q^40 - 3 * q^41 + 11 * q^43 - 10 * q^44 - 12 * q^45 - 8 * q^46 - 13 * q^47 - 9 * q^48 + 16 * q^50 + 26 * q^51 - 35 * q^52 - 20 * q^53 + 15 * q^54 + 12 * q^55 - 16 * q^57 + 12 * q^58 - 4 * q^59 - 8 * q^60 - 8 * q^61 - 14 * q^62 + 49 * q^64 + 12 * q^66 - 36 * q^67 + 52 * q^68 + 31 * q^69 - 2 * q^71 - 23 * q^72 + 2 * q^73 - 3 * q^74 + q^75 + 10 * q^76 + 14 * q^78 + 20 * q^79 + 58 * q^80 + 27 * q^81 - 4 * q^82 + 6 * q^83 + 30 * q^85 + 31 * q^86 + 6 * q^87 + 2 * q^88 + q^89 - 16 * q^90 - q^92 - 14 * q^93 - 15 * q^94 - 26 * q^95 + 4 * q^96 - 11 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.80194	1.98127	0.990635	−	0.136540i	$-0.0435982\pi$
$2$	2.80194	1.98127	0.990635	+	0.136540i	$0.0435982\pi$
$3$	−0.198062	−0.114351	−0.0571757	−	0.998364i	$-0.518210\pi$
$3$	−0.198062	−0.114351	−0.0571757	+	0.998364i	$0.518210\pi$
$4$	5.85086	2.92543
$5$	2.49396	1.11533	0.557666	−	0.830065i	$-0.311697\pi$
$5$	2.49396	1.11533	0.557666	+	0.830065i	$0.311697\pi$
$6$	−0.554958	−0.226561
$7$	0	0
$7$	0	0
$8$	10.7899	3.81479
$9$	−2.96077	−0.986924
$10$	6.98792	2.20977
$11$	−1.10992	−0.334652	−0.167326	−	0.985902i	$-0.553513\pi$
$11$	−1.10992	−0.334652	−0.167326	+	0.985902i	$0.553513\pi$
$12$	−1.15883	−0.334526
$13$	−5.15883	−1.43080	−0.715402	−	0.698714i	$-0.753756\pi$
$13$	−5.15883	−1.43080	−0.715402	+	0.698714i	$0.753756\pi$
$14$	0	0
$15$	−0.493959	−0.127540
$16$	18.5308	4.63270
$17$	6.45473	1.56550	0.782751	−	0.622335i	$-0.213816\pi$
$17$	6.45473	1.56550	0.782751	+	0.622335i	$0.213816\pi$
$18$	−8.29590	−1.95536
$19$	1.86294	0.427387	0.213693	−	0.976901i	$-0.431451\pi$
$19$	1.86294	0.427387	0.213693	+	0.976901i	$0.431451\pi$
$20$	14.5918	3.26282
$21$	0	0
$22$	−3.10992	−0.663036
$23$	−3.08815	−0.643923	−0.321961	−	0.946753i	$-0.604342\pi$
$23$	−3.08815	−0.643923	−0.321961	+	0.946753i	$0.604342\pi$
$24$	−2.13706	−0.436226
$25$	1.21983	0.243967
$26$	−14.4547	−2.83481
$27$	1.18060	0.227207
$28$	0	0
$29$	0.219833	0.0408219	0.0204109	−	0.999792i	$-0.493503\pi$
$29$	0.219833	0.0408219	0.0204109	+	0.999792i	$0.493503\pi$
$30$	−1.38404	−0.252691
$31$	0.670251	0.120381	0.0601903	−	0.998187i	$-0.480829\pi$
$31$	0.670251	0.120381	0.0601903	+	0.998187i	$0.480829\pi$
$32$	30.3424	5.36383
$33$	0.219833	0.0382679
$34$	18.0858	3.10168
$35$	0	0
$36$	−17.3230	−2.88717
$37$	1.33513	0.219493	0.109747	−	0.993960i	$-0.464996\pi$
$37$	1.33513	0.219493	0.109747	+	0.993960i	$0.464996\pi$
$38$	5.21983	0.846769
$39$	1.02177	0.163614
$40$	26.9095	4.25476
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	11.3448	1.73007	0.865034	−	0.501713i	$-0.167297\pi$
$43$	11.3448	1.73007	0.865034	+	0.501713i	$0.167297\pi$
$44$	−6.49396	−0.979001
$45$	−7.38404	−1.10075
$46$	−8.65279	−1.27578
$47$	−4.44504	−0.648376	−0.324188	−	0.945993i	$-0.605091\pi$
$47$	−4.44504	−0.648376	−0.324188	+	0.945993i	$0.605091\pi$
$48$	−3.67025	−0.529755
$49$	0	0
$50$	3.41789	0.483363
$51$	−1.27844	−0.179017
$52$	−30.1836	−4.18571
$53$	−6.89008	−0.946426	−0.473213	−	0.880948i	$-0.656906\pi$
$53$	−6.89008	−0.946426	−0.473213	+	0.880948i	$0.656906\pi$
$54$	3.30798	0.450159
$55$	−2.76809	−0.373249
$56$	0	0
$57$	−0.368977	−0.0488723
$58$	0.615957	0.0808791
$59$	−13.3056	−1.73224	−0.866120	−	0.499836i	$-0.833393\pi$
$59$	−13.3056	−1.73224	−0.866120	+	0.499836i	$0.833393\pi$
$60$	−2.89008	−0.373108
$61$	−6.27413	−0.803320	−0.401660	−	0.915789i	$-0.631567\pi$
$61$	−6.27413	−0.803320	−0.401660	+	0.915789i	$0.631567\pi$
$62$	1.87800	0.238507
$63$	0	0
$64$	47.9560	5.99450
$65$	−12.8659	−1.59582
$66$	0.615957	0.0758191
$67$	−14.7138	−1.79758	−0.898788	−	0.438384i	$-0.855551\pi$
$67$	−14.7138	−1.79758	−0.898788	+	0.438384i	$0.855551\pi$
$68$	37.7657	4.57976
$69$	0.611645	0.0736334
$70$	0	0
$71$	−6.98792	−0.829313	−0.414657	−	0.909978i	$-0.636098\pi$
$71$	−6.98792	−0.829313	−0.414657	+	0.909978i	$0.636098\pi$
$72$	−31.9463	−3.76491
$73$	−5.20775	−0.609521	−0.304761	−	0.952429i	$-0.598576\pi$
$73$	−5.20775	−0.609521	−0.304761	+	0.952429i	$0.598576\pi$
$74$	3.74094	0.434875
$75$	−0.241603	−0.0278979
$76$	10.8998	1.25029
$77$	0	0
$78$	2.86294	0.324164
$79$	0.792249	0.0891350	0.0445675	−	0.999006i	$-0.485809\pi$
$79$	0.792249	0.0891350	0.0445675	+	0.999006i	$0.485809\pi$
$80$	46.2150	5.16700
$81$	8.64848	0.960942
$82$	−2.80194	−0.309422
$83$	8.76809	0.962422	0.481211	−	0.876605i	$-0.340197\pi$
$83$	8.76809	0.962422	0.481211	+	0.876605i	$0.340197\pi$
$84$	0	0
$85$	16.0978	1.74606
$86$	31.7875	3.42773
$87$	−0.0435405	−0.00466803
$88$	−11.9758	−1.27663
$89$	−9.70709	−1.02895	−0.514475	−	0.857506i	$-0.672013\pi$
$89$	−9.70709	−1.02895	−0.514475	+	0.857506i	$0.672013\pi$
$90$	−20.6896	−2.18088
$91$	0	0
$92$	−18.0683	−1.88375
$93$	−0.132751	−0.0137657
$94$	−12.4547	−1.28461
$95$	4.64609	0.476679
$96$	−6.00969	−0.613361
$97$	−8.29590	−0.842321	−0.421160	−	0.906986i	$-0.638377\pi$
$97$	−8.29590	−0.842321	−0.421160	+	0.906986i	$0.638377\pi$
$98$	0	0
$99$	3.28621	0.330276
$100$	7.13706	0.713706
$101$	7.46011	0.742308	0.371154	−	0.928571i	$-0.378962\pi$
$101$	7.46011	0.742308	0.371154	+	0.928571i	$0.378962\pi$
$102$	−3.58211	−0.354681
$103$	4.59179	0.452443	0.226221	−	0.974076i	$-0.427363\pi$
$103$	4.59179	0.452443	0.226221	+	0.974076i	$0.427363\pi$
$104$	−55.6631	−5.45821
$105$	0	0
$106$	−19.3056	−1.87512
$107$	0.137063	0.0132504	0.00662521	−	0.999978i	$-0.497891\pi$
$107$	0.137063	0.0132504	0.00662521	+	0.999978i	$0.497891\pi$
$108$	6.90754	0.664679
$109$	−7.48188	−0.716634	−0.358317	−	0.933600i	$-0.616649\pi$
$109$	−7.48188	−0.716634	−0.358317	+	0.933600i	$0.616649\pi$
$110$	−7.75600	−0.739506
$111$	−0.264438	−0.0250993
$112$	0	0
$113$	10.7899	1.01502	0.507512	−	0.861645i	$-0.330565\pi$
$113$	10.7899	1.01502	0.507512	+	0.861645i	$0.330565\pi$
$114$	−1.03385	−0.0968291
$115$	−7.70171	−0.718188
$116$	1.28621	0.119421
$117$	15.2741	1.41209
$118$	−37.2814	−3.43203
$119$	0	0
$120$	−5.32975	−0.486537
$121$	−9.76809	−0.888008
$122$	−17.5797	−1.59159
$123$	0.198062	0.0178587
$124$	3.92154	0.352165
$125$	−9.42758	−0.843229
$126$	0	0
$127$	0.963164	0.0854670	0.0427335	−	0.999087i	$-0.486393\pi$
$127$	0.963164	0.0854670	0.0427335	+	0.999087i	$0.486393\pi$
$128$	73.6848	6.51288
$129$	−2.24698	−0.197836
$130$	−36.0495	−3.16175
$131$	10.5918	0.925409	0.462705	−	0.886512i	$-0.346879\pi$
$131$	10.5918	0.925409	0.462705	+	0.886512i	$0.346879\pi$
$132$	1.28621	0.111950
$133$	0	0
$134$	−41.2271	−3.56148
$135$	2.94438	0.253412
$136$	69.6456	5.97206
$137$	−6.89008	−0.588660	−0.294330	−	0.955704i	$-0.595096\pi$
$137$	−6.89008	−0.588660	−0.294330	+	0.955704i	$0.595096\pi$
$138$	1.71379	0.145888
$139$	7.57971	0.642903	0.321451	−	0.946926i	$-0.395829\pi$
$139$	7.57971	0.642903	0.321451	+	0.946926i	$0.395829\pi$
$140$	0	0
$141$	0.880395	0.0741426
$142$	−19.5797	−1.64309
$143$	5.72587	0.478822
$144$	−54.8654	−4.57212
$145$	0.548253	0.0455300
$146$	−14.5918	−1.20763
$147$	0	0
$148$	7.81163	0.642112
$149$	11.2620	0.922623	0.461311	−	0.887238i	$-0.347379\pi$
$149$	11.2620	0.922623	0.461311	+	0.887238i	$0.347379\pi$
$150$	−0.676956	−0.0552732
$151$	−4.19567	−0.341439	−0.170719	−	0.985320i	$-0.554609\pi$
$151$	−4.19567	−0.341439	−0.170719	+	0.985320i	$0.554609\pi$
$152$	20.1008	1.63039
$153$	−19.1110	−1.54503
$154$	0	0
$155$	1.67158	0.134264
$156$	5.97823	0.478641
$157$	−11.0814	−0.884395	−0.442198	−	0.896918i	$-0.645801\pi$
$157$	−11.0814	−0.884395	−0.442198	+	0.896918i	$0.645801\pi$
$158$	2.21983	0.176600
$159$	1.36467	0.108225
$160$	75.6728	5.98246
$161$	0	0
$162$	24.2325	1.90389
$163$	−7.67994	−0.601539	−0.300770	−	0.953697i	$-0.597244\pi$
$163$	−7.67994	−0.601539	−0.300770	+	0.953697i	$0.597244\pi$
$164$	−5.85086	−0.456875
$165$	0.548253	0.0426815
$166$	24.5676	1.90682
$167$	21.3448	1.65171	0.825856	−	0.563882i	$-0.190693\pi$
$167$	21.3448	1.65171	0.825856	+	0.563882i	$0.190693\pi$
$168$	0	0
$169$	13.6136	1.04720
$170$	45.1051	3.45941
$171$	−5.51573	−0.421798
$172$	66.3769	5.06119
$173$	13.3056	1.01160	0.505802	−	0.862649i	$-0.331196\pi$
$173$	13.3056	1.01160	0.505802	+	0.862649i	$0.331196\pi$
$174$	−0.121998	−0.00924863
$175$	0	0
$176$	−20.5676	−1.55034
$177$	2.63533	0.198084
$178$	−27.1987	−2.03863
$179$	6.37196	0.476263	0.238131	−	0.971233i	$-0.423465\pi$
$179$	6.37196	0.476263	0.238131	+	0.971233i	$0.423465\pi$
$180$	−43.2030	−3.22016
$181$	−6.07606	−0.451630	−0.225815	−	0.974170i	$-0.572505\pi$
$181$	−6.07606	−0.451630	−0.225815	+	0.974170i	$0.572505\pi$
$182$	0	0
$183$	1.24267	0.0918606
$184$	−33.3207	−2.45643
$185$	3.32975	0.244808
$186$	−0.371961	−0.0272735
$187$	−7.16421	−0.523899
$188$	−26.0073	−1.89678
$189$	0	0
$190$	13.0180	0.944429
$191$	−5.87800	−0.425317	−0.212659	−	0.977127i	$-0.568212\pi$
$191$	−5.87800	−0.425317	−0.212659	+	0.977127i	$0.568212\pi$
$192$	−9.49827	−0.685479
$193$	13.2862	0.956362	0.478181	−	0.878261i	$-0.341296\pi$
$193$	13.2862	0.956362	0.478181	+	0.878261i	$0.341296\pi$
$194$	−23.2446	−1.66886
$195$	2.54825	0.182484
$196$	0	0
$197$	4.09352	0.291651	0.145826	−	0.989310i	$-0.453416\pi$
$197$	4.09352	0.291651	0.145826	+	0.989310i	$0.453416\pi$
$198$	9.20775	0.654366
$199$	1.67696	0.118876	0.0594381	−	0.998232i	$-0.481069\pi$
$199$	1.67696	0.118876	0.0594381	+	0.998232i	$0.481069\pi$
$200$	13.1618	0.930681
$201$	2.91425	0.205555
$202$	20.9028	1.47071
$203$	0	0
$204$	−7.47996	−0.523702
$205$	−2.49396	−0.174186
$206$	12.8659	0.896411
$207$	9.14329	0.635503
$208$	−95.5973	−6.62848
$209$	−2.06770	−0.143026
$210$	0	0
$211$	−21.6775	−1.49234	−0.746172	−	0.665753i	$-0.768110\pi$
$211$	−21.6775	−1.49234	−0.746172	+	0.665753i	$0.768110\pi$
$212$	−40.3129	−2.76870
$213$	1.38404	0.0948331
$214$	0.384043	0.0262526
$215$	28.2935	1.92960
$216$	12.7385	0.866748
$217$	0	0
$218$	−20.9638	−1.41984
$219$	1.03146	0.0696995
$220$	−16.1957	−1.09191
$221$	−33.2989	−2.23993
$222$	−0.740939	−0.0497286
$223$	12.1763	0.815385	0.407692	−	0.913119i	$-0.366334\pi$
$223$	12.1763	0.815385	0.407692	+	0.913119i	$0.366334\pi$
$224$	0	0
$225$	−3.61165	−0.240776
$226$	30.2325	2.01104
$227$	3.01208	0.199919	0.0999594	−	0.994992i	$-0.468129\pi$
$227$	3.01208	0.199919	0.0999594	+	0.994992i	$0.468129\pi$
$228$	−2.15883	−0.142972
$229$	17.0834	1.12890	0.564450	−	0.825467i	$-0.309088\pi$
$229$	17.0834	1.12890	0.564450	+	0.825467i	$0.309088\pi$
$230$	−21.5797	−1.42292
$231$	0	0
$232$	2.37196	0.155727
$233$	14.7681	0.967489	0.483745	−	0.875209i	$-0.339276\pi$
$233$	14.7681	0.967489	0.483745	+	0.875209i	$0.339276\pi$
$234$	42.7972	2.79774
$235$	−11.0858	−0.723155
$236$	−77.8491	−5.06754
$237$	−0.156915	−0.0101927
$238$	0	0
$239$	11.5797	0.749029	0.374515	−	0.927221i	$-0.377809\pi$
$239$	11.5797	0.749029	0.374515	+	0.927221i	$0.377809\pi$
$240$	−9.15346	−0.590853
$241$	−30.7090	−1.97814	−0.989070	−	0.147443i	$-0.952896\pi$
$241$	−30.7090	−1.97814	−0.989070	+	0.147443i	$0.952896\pi$
$242$	−27.3696	−1.75938
$243$	−5.25475	−0.337092
$244$	−36.7090	−2.35005
$245$	0	0
$246$	0.554958	0.0353828
$247$	−9.61058	−0.611507
$248$	7.23191	0.459227
$249$	−1.73663	−0.110054
$250$	−26.4155	−1.67066
$251$	13.3840	0.844793	0.422397	−	0.906411i	$-0.361189\pi$
$251$	13.3840	0.844793	0.422397	+	0.906411i	$0.361189\pi$
$252$	0	0
$253$	3.42758	0.215490
$254$	2.69873	0.169333
$255$	−3.18837	−0.199664
$256$	110.548	6.90927
$257$	−21.9191	−1.36728	−0.683639	−	0.729820i	$-0.739604\pi$
$257$	−21.9191	−1.36728	−0.683639	+	0.729820i	$0.739604\pi$
$258$	−6.29590	−0.391965
$259$	0	0
$260$	−75.2766	−4.66846
$261$	−0.650874	−0.0402881
$262$	29.6775	1.83348
$263$	14.3720	0.886213	0.443107	−	0.896469i	$-0.353876\pi$
$263$	14.3720	0.886213	0.443107	+	0.896469i	$0.353876\pi$
$264$	2.37196	0.145984
$265$	−17.1836	−1.05558
$266$	0	0
$267$	1.92261	0.117662
$268$	−86.0883	−5.25868
$269$	21.5013	1.31095	0.655477	−	0.755215i	$-0.272467\pi$
$269$	21.5013	1.31095	0.655477	+	0.755215i	$0.272467\pi$
$270$	8.24996	0.502077
$271$	26.2741	1.59604	0.798020	−	0.602631i	$-0.205881\pi$
$271$	26.2741	1.59604	0.798020	+	0.602631i	$0.205881\pi$
$272$	119.611	7.25250
$273$	0	0
$274$	−19.3056	−1.16629
$275$	−1.35391	−0.0816440
$276$	3.57865	0.215409
$277$	−3.18598	−0.191427	−0.0957135	−	0.995409i	$-0.530513\pi$
$277$	−3.18598	−0.191427	−0.0957135	+	0.995409i	$0.530513\pi$
$278$	21.2379	1.27376
$279$	−1.98446	−0.118807
$280$	0	0
$281$	−6.58104	−0.392592	−0.196296	−	0.980545i	$-0.562891\pi$
$281$	−6.58104	−0.392592	−0.196296	+	0.980545i	$0.562891\pi$
$282$	2.46681	0.146897
$283$	−22.4155	−1.33246	−0.666232	−	0.745745i	$-0.732094\pi$
$283$	−22.4155	−1.33246	−0.666232	+	0.745745i	$0.732094\pi$
$284$	−40.8853	−2.42610
$285$	−0.920215	−0.0545088
$286$	16.0435	0.948674
$287$	0	0
$288$	−89.8370	−5.29369
$289$	24.6635	1.45080
$290$	1.53617	0.0902071
$291$	1.64310	0.0963205
$292$	−30.4698	−1.78311
$293$	12.7681	0.745920	0.372960	−	0.927848i	$-0.378343\pi$
$293$	12.7681	0.745920	0.372960	+	0.927848i	$0.378343\pi$
$294$	0	0
$295$	−33.1836	−1.93202
$296$	14.4058	0.837321
$297$	−1.31037	−0.0760355
$298$	31.5555	1.82796
$299$	15.9312	0.921327
$300$	−1.41358	−0.0816132
$301$	0	0
$302$	−11.7560	−0.676482
$303$	−1.47757	−0.0848839
$304$	34.5217	1.97996
$305$	−15.6474	−0.895968
$306$	−53.5478	−3.06112
$307$	12.6703	0.723129	0.361565	−	0.932347i	$-0.382243\pi$
$307$	12.6703	0.723129	0.361565	+	0.932347i	$0.382243\pi$
$308$	0	0
$309$	−0.909461	−0.0517374
$310$	4.68366	0.266014
$311$	22.0586	1.25083	0.625414	−	0.780293i	$-0.284930\pi$
$311$	22.0586	1.25083	0.625414	+	0.780293i	$0.284930\pi$
$312$	11.0248	0.624154
$313$	5.30127	0.299646	0.149823	−	0.988713i	$-0.452130\pi$
$313$	5.30127	0.299646	0.149823	+	0.988713i	$0.452130\pi$
$314$	−31.0495	−1.75223
$315$	0	0
$316$	4.63533	0.260758
$317$	−32.6896	−1.83603	−0.918016	−	0.396543i	$-0.870210\pi$
$317$	−32.6896	−1.83603	−0.918016	+	0.396543i	$0.870210\pi$
$318$	3.82371	0.214423
$319$	−0.243996	−0.0136611
$320$	119.600	6.68586
$321$	−0.0271471	−0.00151520
$322$	0	0
$323$	12.0248	0.669075
$324$	50.6010	2.81117
$325$	−6.29291	−0.349068
$326$	−21.5187	−1.19181
$327$	1.48188	0.0819480
$328$	−10.7899	−0.595770
$329$	0	0
$330$	1.53617	0.0845635
$331$	−0.879330	−0.0483324	−0.0241662	−	0.999708i	$-0.507693\pi$
$331$	−0.879330	−0.0483324	−0.0241662	+	0.999708i	$0.507693\pi$
$332$	51.3008	2.81550
$333$	−3.95300	−0.216623
$334$	59.8068	3.27248
$335$	−36.6956	−2.00489
$336$	0	0
$337$	31.5821	1.72039	0.860193	−	0.509968i	$-0.170343\pi$
$337$	31.5821	1.72039	0.860193	+	0.509968i	$0.170343\pi$
$338$	38.1444	2.07478
$339$	−2.13706	−0.116069
$340$	94.1861	5.10796
$341$	−0.743923	−0.0402857
$342$	−15.4547	−0.835696
$343$	0	0
$344$	122.409	6.59985
$345$	1.52542	0.0821258
$346$	37.2814	2.00426
$347$	−15.2862	−0.820607	−0.410303	−	0.911949i	$-0.634577\pi$
$347$	−15.2862	−0.820607	−0.410303	+	0.911949i	$0.634577\pi$
$348$	−0.254749	−0.0136560
$349$	18.2634	0.977616	0.488808	−	0.872391i	$-0.337432\pi$
$349$	18.2634	0.977616	0.488808	+	0.872391i	$0.337432\pi$
$350$	0	0
$351$	−6.09054	−0.325089
$352$	−33.6775	−1.79502
$353$	2.23921	0.119181	0.0595906	−	0.998223i	$-0.481020\pi$
$353$	2.23921	0.119181	0.0595906	+	0.998223i	$0.481020\pi$
$354$	7.38404	0.392457
$355$	−17.4276	−0.924960
$356$	−56.7948	−3.01012
$357$	0	0
$358$	17.8538	0.943605
$359$	−5.70709	−0.301209	−0.150604	−	0.988594i	$-0.548122\pi$
$359$	−5.70709	−0.301209	−0.150604	+	0.988594i	$0.548122\pi$
$360$	−79.6728	−4.19912
$361$	−15.5295	−0.817340
$362$	−17.0248	−0.894801
$363$	1.93469	0.101545
$364$	0	0
$365$	−12.9879	−0.679819
$366$	3.48188	0.182001
$367$	−24.1715	−1.26174	−0.630871	−	0.775888i	$-0.717302\pi$
$367$	−24.1715	−1.26174	−0.630871	+	0.775888i	$0.717302\pi$
$368$	−57.2258	−2.98310
$369$	2.96077	0.154132
$370$	9.32975	0.485031
$371$	0	0
$372$	−0.776710	−0.0402705
$373$	−19.9366	−1.03228	−0.516139	−	0.856505i	$-0.672631\pi$
$373$	−19.9366	−1.03228	−0.516139	+	0.856505i	$0.672631\pi$
$374$	−20.0737	−1.03798
$375$	1.86725	0.0964243
$376$	−47.9614	−2.47342
$377$	−1.13408	−0.0584081
$378$	0	0
$379$	3.76702	0.193499	0.0967494	−	0.995309i	$-0.469155\pi$
$379$	3.76702	0.193499	0.0967494	+	0.995309i	$0.469155\pi$
$380$	27.1836	1.39449
$381$	−0.190766	−0.00977326
$382$	−16.4698	−0.842668
$383$	3.36227	0.171804	0.0859021	−	0.996304i	$-0.472623\pi$
$383$	3.36227	0.171804	0.0859021	+	0.996304i	$0.472623\pi$
$384$	−14.5942	−0.744756
$385$	0	0
$386$	37.2271	1.89481
$387$	−33.5894	−1.70745
$388$	−48.5381	−2.46415
$389$	3.11529	0.157952	0.0789758	−	0.996877i	$-0.474835\pi$
$389$	3.11529	0.157952	0.0789758	+	0.996877i	$0.474835\pi$
$390$	7.14005	0.361550
$391$	−19.9332	−1.00806
$392$	0	0
$393$	−2.09783	−0.105822
$394$	11.4698	0.577840
$395$	1.97584	0.0994151
$396$	19.2271	0.966200
$397$	−30.7439	−1.54299	−0.771497	−	0.636233i	$-0.780492\pi$
$397$	−30.7439	−1.54299	−0.771497	+	0.636233i	$0.780492\pi$
$398$	4.69873	0.235526
$399$	0	0
$400$	22.6045	1.13022
$401$	−3.55496	−0.177526	−0.0887631	−	0.996053i	$-0.528291\pi$
$401$	−3.55496	−0.177526	−0.0887631	+	0.996053i	$0.528291\pi$
$402$	8.16554	0.407260
$403$	−3.45771	−0.172241
$404$	43.6480	2.17157
$405$	21.5690	1.07177
$406$	0	0
$407$	−1.48188	−0.0734539
$408$	−13.7942	−0.682913
$409$	−13.4577	−0.665441	−0.332721	−	0.943025i	$-0.607967\pi$
$409$	−13.4577	−0.665441	−0.332721	+	0.943025i	$0.607967\pi$
$410$	−6.98792	−0.345109
$411$	1.36467	0.0673140
$412$	26.8659	1.32359
$413$	0	0
$414$	25.6189	1.25910
$415$	21.8672	1.07342
$416$	−156.532	−7.67459
$417$	−1.50125	−0.0735168
$418$	−5.79358	−0.283373
$419$	−14.8116	−0.723595	−0.361798	−	0.932257i	$-0.617837\pi$
$419$	−14.8116	−0.723595	−0.361798	+	0.932257i	$0.617837\pi$
$420$	0	0
$421$	21.8866	1.06669	0.533344	−	0.845898i	$-0.320935\pi$
$421$	21.8866	1.06669	0.533344	+	0.845898i	$0.320935\pi$
$422$	−60.7391	−2.95673
$423$	13.1608	0.639898
$424$	−74.3430	−3.61042
$425$	7.87369	0.381930
$426$	3.87800	0.187890
$427$	0	0
$428$	0.801938	0.0387631
$429$	−1.13408	−0.0547539
$430$	79.2766	3.82306
$431$	10.0242	0.482847	0.241423	−	0.970420i	$-0.422386\pi$
$431$	10.0242	0.482847	0.241423	+	0.970420i	$0.422386\pi$
$432$	21.8775	1.05258
$433$	6.17151	0.296584	0.148292	−	0.988944i	$-0.452623\pi$
$433$	6.17151	0.296584	0.148292	+	0.988944i	$0.452623\pi$
$434$	0	0
$435$	−0.108588	−0.00520641
$436$	−43.7754	−2.09646
$437$	−5.75302	−0.275204
$438$	2.89008	0.138094
$439$	25.4252	1.21348	0.606739	−	0.794901i	$-0.292477\pi$
$439$	25.4252	1.21348	0.606739	+	0.794901i	$0.292477\pi$
$440$	−29.8672	−1.42387
$441$	0	0
$442$	−93.3014	−4.43789
$443$	19.1454	0.909627	0.454813	−	0.890587i	$-0.349706\pi$
$443$	19.1454	0.909627	0.454813	+	0.890587i	$0.349706\pi$
$444$	−1.54719	−0.0734263
$445$	−24.2091	−1.14762
$446$	34.1172	1.61550
$447$	−2.23059	−0.105503
$448$	0	0
$449$	15.8649	0.748709	0.374354	−	0.927286i	$-0.377864\pi$
$449$	15.8649	0.748709	0.374354	+	0.927286i	$0.377864\pi$
$450$	−10.1196	−0.477043
$451$	1.10992	0.0522639
$452$	63.1299	2.96938
$453$	0.831004	0.0390440
$454$	8.43967	0.396093
$455$	0	0
$456$	−3.98121	−0.186437
$457$	18.7004	0.874767	0.437383	−	0.899275i	$-0.355905\pi$
$457$	18.7004	0.874767	0.437383	+	0.899275i	$0.355905\pi$
$458$	47.8665	2.23666
$459$	7.62048	0.355694
$460$	−45.0616	−2.10101
$461$	−7.86725	−0.366414	−0.183207	−	0.983074i	$-0.558648\pi$
$461$	−7.86725	−0.366414	−0.183207	+	0.983074i	$0.558648\pi$
$462$	0	0
$463$	27.7995	1.29195	0.645977	−	0.763357i	$-0.276450\pi$
$463$	27.7995	1.29195	0.645977	+	0.763357i	$0.276450\pi$
$464$	4.07367	0.189115
$465$	−0.331077	−0.0153533
$466$	41.3793	1.91686
$467$	−16.4504	−0.761235	−0.380617	−	0.924733i	$-0.624288\pi$
$467$	−16.4504	−0.761235	−0.380617	+	0.924733i	$0.624288\pi$
$468$	89.3667	4.13098
$469$	0	0
$470$	−31.0616	−1.43276
$471$	2.19482	0.101132
$472$	−143.565	−6.60813
$473$	−12.5918	−0.578971
$474$	−0.439665	−0.0201945
$475$	2.27247	0.104268
$476$	0	0
$477$	20.4000	0.934050
$478$	32.4456	1.48403
$479$	29.7778	1.36058	0.680291	−	0.732942i	$-0.261854\pi$
$479$	29.7778	1.36058	0.680291	+	0.732942i	$0.261854\pi$
$480$	−14.9879	−0.684102
$481$	−6.88769	−0.314052
$482$	−86.0447	−3.91923
$483$	0	0
$484$	−57.1517	−2.59780
$485$	−20.6896	−0.939468
$486$	−14.7235	−0.667871
$487$	9.80864	0.444472	0.222236	−	0.974993i	$-0.428664\pi$
$487$	9.80864	0.444472	0.222236	+	0.974993i	$0.428664\pi$
$488$	−67.6969	−3.06450
$489$	1.52111	0.0687868
$490$	0	0
$491$	−21.5907	−0.974376	−0.487188	−	0.873297i	$-0.661977\pi$
$491$	−21.5907	−0.974376	−0.487188	+	0.873297i	$0.661977\pi$
$492$	1.15883	0.0522443
$493$	1.41896	0.0639067
$494$	−26.9282	−1.21156
$495$	8.19567	0.368368
$496$	12.4203	0.557687
$497$	0	0
$498$	−4.86592	−0.218047
$499$	9.19700	0.411714	0.205857	−	0.978582i	$-0.434002\pi$
$499$	9.19700	0.411714	0.205857	+	0.978582i	$0.434002\pi$
$500$	−55.1594	−2.46680
$501$	−4.22760	−0.188875
$502$	37.5013	1.67376
$503$	4.63773	0.206786	0.103393	−	0.994641i	$-0.467030\pi$
$503$	4.63773	0.206786	0.103393	+	0.994641i	$0.467030\pi$
$504$	0	0
$505$	18.6052	0.827921
$506$	9.60388	0.426944
$507$	−2.69633	−0.119748
$508$	5.63533	0.250028
$509$	−31.4282	−1.39303	−0.696515	−	0.717543i	$-0.745267\pi$
$509$	−31.4282	−1.39303	−0.696515	+	0.717543i	$0.745267\pi$
$510$	−8.93362	−0.395588
$511$	0	0
$512$	162.380	7.17625
$513$	2.19939	0.0971055
$514$	−61.4161	−2.70895
$515$	11.4517	0.504624
$516$	−13.1468	−0.578753
$517$	4.93362	0.216981
$518$	0	0
$519$	−2.63533	−0.115678
$520$	−138.821	−6.08772
$521$	−40.4053	−1.77019	−0.885095	−	0.465410i	$-0.845907\pi$
$521$	−40.4053	−1.77019	−0.885095	+	0.465410i	$0.845907\pi$
$522$	−1.82371	−0.0798215
$523$	−27.5013	−1.20255	−0.601273	−	0.799044i	$-0.705340\pi$
$523$	−27.5013	−1.20255	−0.601273	+	0.799044i	$0.705340\pi$
$524$	61.9711	2.70722
$525$	0	0
$526$	40.2693	1.75583
$527$	4.32629	0.188456
$528$	4.07367	0.177284
$529$	−13.4634	−0.585363
$530$	−48.1473	−2.09139
$531$	39.3948	1.70959
$532$	0	0
$533$	5.15883	0.223454
$534$	5.38703	0.233119
$535$	0.341830	0.0147786
$536$	−158.760	−6.85737
$537$	−1.26205	−0.0544613
$538$	60.2452	2.59735
$539$	0	0
$540$	17.2271	0.741338
$541$	24.6504	1.05980	0.529902	−	0.848059i	$-0.322229\pi$
$541$	24.6504	1.05980	0.529902	+	0.848059i	$0.322229\pi$
$542$	73.6185	3.16218
$543$	1.20344	0.0516445
$544$	195.852	8.39709
$545$	−18.6595	−0.799285
$546$	0	0
$547$	37.3056	1.59507	0.797536	−	0.603272i	$-0.206136\pi$
$547$	37.3056	1.59507	0.797536	+	0.603272i	$0.206136\pi$
$548$	−40.3129	−1.72208
$549$	18.5763	0.792815
$550$	−3.79358	−0.161759
$551$	0.409534	0.0174467
$552$	6.59956	0.280896
$553$	0	0
$554$	−8.92692	−0.379268
$555$	−0.659498	−0.0279941
$556$	44.3478	1.88077
$557$	1.15346	0.0488735	0.0244368	−	0.999701i	$-0.492221\pi$
$557$	1.15346	0.0488735	0.0244368	+	0.999701i	$0.492221\pi$
$558$	−5.56033	−0.235388
$559$	−58.5260	−2.47539
$560$	0	0
$561$	1.41896	0.0599085
$562$	−18.4397	−0.777830
$563$	−4.73855	−0.199706	−0.0998529	−	0.995002i	$-0.531837\pi$
$563$	−4.73855	−0.199706	−0.0998529	+	0.995002i	$0.531837\pi$
$564$	5.15106	0.216899
$565$	26.9095	1.13209
$566$	−62.8068	−2.63997
$567$	0	0
$568$	−75.3986	−3.16366
$569$	−12.6116	−0.528708	−0.264354	−	0.964426i	$-0.585159\pi$
$569$	−12.6116	−0.528708	−0.264354	+	0.964426i	$0.585159\pi$
$570$	−2.57838	−0.107997
$571$	29.5013	1.23459	0.617295	−	0.786732i	$-0.288229\pi$
$571$	29.5013	1.23459	0.617295	+	0.786732i	$0.288229\pi$
$572$	33.5013	1.40076
$573$	1.16421	0.0486356
$574$	0	0
$575$	−3.76702	−0.157096
$576$	−141.987	−5.91611
$577$	−9.52781	−0.396648	−0.198324	−	0.980137i	$-0.563550\pi$
$577$	−9.52781	−0.396648	−0.198324	+	0.980137i	$0.563550\pi$
$578$	69.1057	2.87442
$579$	−2.63150	−0.109361
$580$	3.20775	0.133195
$581$	0	0
$582$	4.60388	0.190837
$583$	7.64742	0.316724
$584$	−56.1909	−2.32520
$585$	38.0930	1.57495
$586$	35.7754	1.47787
$587$	39.8474	1.64468	0.822339	−	0.568998i	$-0.192669\pi$
$587$	39.8474	1.64468	0.822339	+	0.568998i	$0.192669\pi$
$588$	0	0
$589$	1.24864	0.0514491
$590$	−92.9783	−3.82786
$591$	−0.810772	−0.0333507
$592$	24.7409	1.01685
$593$	−22.3532	−0.917935	−0.458967	−	0.888453i	$-0.651781\pi$
$593$	−22.3532	−0.917935	−0.458967	+	0.888453i	$0.651781\pi$
$594$	−3.67158	−0.150647
$595$	0	0
$596$	65.8926	2.69907
$597$	−0.332142	−0.0135937
$598$	44.6383	1.82540
$599$	13.3545	0.545650	0.272825	−	0.962064i	$-0.412042\pi$
$599$	13.3545	0.545650	0.272825	+	0.962064i	$0.412042\pi$
$600$	−2.60686	−0.106425
$601$	−0.831478	−0.0339167	−0.0169583	−	0.999856i	$-0.505398\pi$
$601$	−0.831478	−0.0339167	−0.0169583	+	0.999856i	$0.505398\pi$
$602$	0	0
$603$	43.5642	1.77407
$604$	−24.5483	−0.998854
$605$	−24.3612	−0.990424
$606$	−4.14005	−0.168178
$607$	7.75600	0.314807	0.157403	−	0.987534i	$-0.449688\pi$
$607$	7.75600	0.314807	0.157403	+	0.987534i	$0.449688\pi$
$608$	56.5260	2.29243
$609$	0	0
$610$	−43.8431	−1.77515
$611$	22.9312	0.927698
$612$	−111.816	−4.51988
$613$	24.3744	0.984471	0.492235	−	0.870462i	$-0.336180\pi$
$613$	24.3744	0.984471	0.492235	+	0.870462i	$0.336180\pi$
$614$	35.5013	1.43271
$615$	0.493959	0.0199184
$616$	0	0
$617$	−14.5090	−0.584111	−0.292056	−	0.956401i	$-0.594339\pi$
$617$	−14.5090	−0.584111	−0.292056	+	0.956401i	$0.594339\pi$
$618$	−2.54825	−0.102506
$619$	19.5603	0.786196	0.393098	−	0.919497i	$-0.371403\pi$
$619$	19.5603	0.786196	0.393098	+	0.919497i	$0.371403\pi$
$620$	9.78017	0.392781
$621$	−3.64588	−0.146304
$622$	61.8068	2.47823
$623$	0	0
$624$	18.9342	0.757975
$625$	−29.6112	−1.18445
$626$	14.8538	0.593679
$627$	0.409534	0.0163552
$628$	−64.8359	−2.58723
$629$	8.61788	0.343617
$630$	0	0
$631$	−5.79417	−0.230662	−0.115331	−	0.993327i	$-0.536793\pi$
$631$	−5.79417	−0.230662	−0.115331	+	0.993327i	$0.536793\pi$
$632$	8.54825	0.340031
$633$	4.29350	0.170651
$634$	−91.5943	−3.63767
$635$	2.40209	0.0953241
$636$	7.98446	0.316604
$637$	0	0
$638$	−0.683661	−0.0270664
$639$	20.6896	0.818469
$640$	183.767	7.26403
$641$	−31.5448	−1.24594	−0.622972	−	0.782244i	$-0.714075\pi$
$641$	−31.5448	−1.24594	−0.622972	+	0.782244i	$0.714075\pi$
$642$	−0.0760644	−0.00300202
$643$	7.45712	0.294080	0.147040	−	0.989131i	$-0.453025\pi$
$643$	7.45712	0.294080	0.147040	+	0.989131i	$0.453025\pi$
$644$	0	0
$645$	−5.60388	−0.220652
$646$	33.6926	1.32562
$647$	−25.5797	−1.00564	−0.502821	−	0.864390i	$-0.667705\pi$
$647$	−25.5797	−1.00564	−0.502821	+	0.864390i	$0.667705\pi$
$648$	93.3159	3.66579
$649$	14.7681	0.579698
$650$	−17.6324	−0.691598
$651$	0	0
$652$	−44.9342	−1.75976
$653$	38.0737	1.48994	0.744969	−	0.667099i	$-0.232464\pi$
$653$	38.0737	1.48994	0.744969	+	0.667099i	$0.232464\pi$
$654$	4.15213	0.162361
$655$	26.4155	1.03214
$656$	−18.5308	−0.723506
$657$	15.4190	0.601551
$658$	0	0
$659$	−15.3357	−0.597395	−0.298697	−	0.954348i	$-0.596552\pi$
$659$	−15.3357	−0.597395	−0.298697	+	0.954348i	$0.596552\pi$
$660$	3.20775	0.124862
$661$	−23.4819	−0.913339	−0.456670	−	0.889636i	$-0.650958\pi$
$661$	−23.4819	−0.913339	−0.456670	+	0.889636i	$0.650958\pi$
$662$	−2.46383	−0.0957594
$663$	6.59525	0.256138
$664$	94.6064	3.67144
$665$	0	0
$666$	−11.0761	−0.429189
$667$	−0.678875	−0.0262861
$668$	124.885	4.83196
$669$	−2.41166	−0.0932403
$670$	−102.819	−3.97224
$671$	6.96376	0.268833
$672$	0	0
$673$	4.42029	0.170390	0.0851948	−	0.996364i	$-0.472849\pi$
$673$	4.42029	0.170390	0.0851948	+	0.996364i	$0.472849\pi$
$674$	88.4911	3.40855
$675$	1.44014	0.0554310
$676$	79.6510	3.06350
$677$	39.0965	1.50260	0.751300	−	0.659960i	$-0.229427\pi$
$677$	39.0965	1.50260	0.751300	+	0.659960i	$0.229427\pi$
$678$	−5.98792	−0.229965
$679$	0	0
$680$	173.693	6.66083
$681$	−0.596580	−0.0228610
$682$	−2.08443	−0.0798168
$683$	33.8974	1.29705	0.648524	−	0.761195i	$-0.275387\pi$
$683$	33.8974	1.29705	0.648524	+	0.761195i	$0.275387\pi$
$684$	−32.2717	−1.23394
$685$	−17.1836	−0.656551
$686$	0	0
$687$	−3.38357	−0.129091
$688$	210.228	8.01488
$689$	35.5448	1.35415
$690$	4.27413	0.162713
$691$	23.0562	0.877100	0.438550	−	0.898707i	$-0.355492\pi$
$691$	23.0562	0.877100	0.438550	+	0.898707i	$0.355492\pi$
$692$	77.8491	2.95938
$693$	0	0
$694$	−42.8310	−1.62584
$695$	18.9035	0.717050
$696$	−0.469796	−0.0178076
$697$	−6.45473	−0.244490
$698$	51.1728	1.93692
$699$	−2.92500	−0.110634
$700$	0	0
$701$	−17.9812	−0.679141	−0.339571	−	0.940581i	$-0.610282\pi$
$701$	−17.9812	−0.679141	−0.339571	+	0.940581i	$0.610282\pi$
$702$	−17.0653	−0.644089
$703$	2.48725	0.0938086
$704$	−53.2271	−2.00607
$705$	2.19567	0.0826937
$706$	6.27413	0.236130
$707$	0	0
$708$	15.4190	0.579480
$709$	24.5676	0.922657	0.461328	−	0.887229i	$-0.347373\pi$
$709$	24.5676	0.922657	0.461328	+	0.887229i	$0.347373\pi$
$710$	−48.8310	−1.83259
$711$	−2.34567	−0.0879694
$712$	−104.738	−3.92523
$713$	−2.06983	−0.0775159
$714$	0	0
$715$	14.2801	0.534045
$716$	37.2814	1.39327
$717$	−2.29350	−0.0856525
$718$	−15.9909	−0.596775
$719$	−37.1353	−1.38491	−0.692456	−	0.721460i	$-0.743471\pi$
$719$	−37.1353	−1.38491	−0.692456	+	0.721460i	$0.743471\pi$
$720$	−136.832	−5.09943
$721$	0	0
$722$	−43.5126	−1.61937
$723$	6.08230	0.226203
$724$	−35.5502	−1.32121
$725$	0.268159	0.00995917
$726$	5.42088	0.201188
$727$	27.5948	1.02343	0.511717	−	0.859154i	$-0.329010\pi$
$727$	27.5948	1.02343	0.511717	+	0.859154i	$0.329010\pi$
$728$	0	0
$729$	−24.9047	−0.922395
$730$	−36.3913	−1.34690
$731$	73.2277	2.70843
$732$	7.27067	0.268732
$733$	24.2586	0.896011	0.448006	−	0.894031i	$-0.352134\pi$
$733$	24.2586	0.896011	0.448006	+	0.894031i	$0.352134\pi$
$734$	−67.7271	−2.49985
$735$	0	0
$736$	−93.7018	−3.45390
$737$	16.3311	0.601563
$738$	8.29590	0.305376
$739$	21.0019	0.772568	0.386284	−	0.922380i	$-0.373758\pi$
$739$	21.0019	0.772568	0.386284	+	0.922380i	$0.373758\pi$
$740$	19.4819	0.716168
$741$	1.90349	0.0699266
$742$	0	0
$743$	−36.2059	−1.32827	−0.664134	−	0.747614i	$-0.731199\pi$
$743$	−36.2059	−1.32827	−0.664134	+	0.747614i	$0.731199\pi$
$744$	−1.43237	−0.0525132
$745$	28.0871	1.02903
$746$	−55.8611	−2.04522
$747$	−25.9603	−0.949838
$748$	−41.9168	−1.53263
$749$	0	0
$750$	5.23191	0.191042
$751$	−2.07367	−0.0756693	−0.0378347	−	0.999284i	$-0.512046\pi$
$751$	−2.07367	−0.0756693	−0.0378347	+	0.999284i	$0.512046\pi$
$752$	−82.3702	−3.00373
$753$	−2.65087	−0.0966032
$754$	−3.17762	−0.115722
$755$	−10.4638	−0.380818
$756$	0	0
$757$	−40.3177	−1.46537	−0.732685	−	0.680568i	$-0.761733\pi$
$757$	−40.3177	−1.46537	−0.732685	+	0.680568i	$0.761733\pi$
$758$	10.5550	0.383373
$759$	−0.678875	−0.0246416
$760$	50.1306	1.81843
$761$	15.6823	0.568484	0.284242	−	0.958753i	$-0.408258\pi$
$761$	15.6823	0.568484	0.284242	+	0.958753i	$0.408258\pi$
$762$	−0.534516	−0.0193635
$763$	0	0
$764$	−34.3913	−1.24423
$765$	−47.6620	−1.72322
$766$	9.42088	0.340390
$767$	68.6413	2.47849
$768$	−21.8955	−0.790084
$769$	28.6655	1.03370	0.516852	−	0.856075i	$-0.327104\pi$
$769$	28.6655	1.03370	0.516852	+	0.856075i	$0.327104\pi$
$770$	0	0
$771$	4.34136	0.156350
$772$	77.7357	2.79777
$773$	−39.8254	−1.43242	−0.716209	−	0.697885i	$-0.754124\pi$
$773$	−39.8254	−1.43242	−0.716209	+	0.697885i	$0.754124\pi$
$774$	−94.1154	−3.38291
$775$	0.817594	0.0293689
$776$	−89.5115	−3.21328
$777$	0	0
$778$	8.72886	0.312945
$779$	−1.86294	−0.0667466
$780$	14.9095	0.533844
$781$	7.75600	0.277532
$782$	−55.8514	−1.99724
$783$	0.259535	0.00927503
$784$	0	0
$785$	−27.6367	−0.986395
$786$	−5.87800	−0.209661
$787$	35.4249	1.26276	0.631381	−	0.775473i	$-0.282488\pi$
$787$	35.4249	1.26276	0.631381	+	0.775473i	$0.282488\pi$
$788$	23.9506	0.853205
$789$	−2.84654	−0.101340
$790$	5.53617	0.196968
$791$	0	0
$792$	35.4577	1.25994
$793$	32.3672	1.14939
$794$	−86.1426	−3.05708
$795$	3.40342	0.120707
$796$	9.81163	0.347764
$797$	−22.2150	−0.786897	−0.393449	−	0.919347i	$-0.628718\pi$
$797$	−22.2150	−0.786897	−0.393449	+	0.919347i	$0.628718\pi$
$798$	0	0
$799$	−28.6915	−1.01503
$800$	37.0127	1.30860
$801$	28.7405	1.01549
$802$	−9.96077	−0.351727
$803$	5.78017	0.203978
$804$	17.0508	0.601337
$805$	0	0
$806$	−9.68830	−0.341256
$807$	−4.25859	−0.149909
$808$	80.4935	2.83175
$809$	32.9288	1.15772	0.578858	−	0.815428i	$-0.303498\pi$
$809$	32.9288	1.15772	0.578858	+	0.815428i	$0.303498\pi$
$810$	60.4349	2.12347
$811$	34.6112	1.21536	0.607681	−	0.794181i	$-0.292100\pi$
$811$	34.6112	1.21536	0.607681	+	0.794181i	$0.292100\pi$
$812$	0	0
$813$	−5.20391	−0.182509
$814$	−4.15213	−0.145532
$815$	−19.1535	−0.670916
$816$	−23.6905	−0.829333
$817$	21.1347	0.739409
$818$	−37.7077	−1.31842
$819$	0	0
$820$	−14.5918	−0.509568
$821$	−49.9211	−1.74226	−0.871129	−	0.491055i	$-0.836611\pi$
$821$	−49.9211	−1.74226	−0.871129	+	0.491055i	$0.836611\pi$
$822$	3.82371	0.133367
$823$	37.6098	1.31100	0.655498	−	0.755197i	$-0.272459\pi$
$823$	37.6098	1.31100	0.655498	+	0.755197i	$0.272459\pi$
$824$	49.5448	1.72597
$825$	0.268159	0.00933609
$826$	0	0
$827$	47.1245	1.63868	0.819340	−	0.573308i	$-0.194340\pi$
$827$	47.1245	1.63868	0.819340	+	0.573308i	$0.194340\pi$
$828$	53.4961	1.85912
$829$	16.4504	0.571347	0.285673	−	0.958327i	$-0.407783\pi$
$829$	16.4504	0.571347	0.285673	+	0.958327i	$0.407783\pi$
$830$	61.2707	2.12674
$831$	0.631023	0.0218899
$832$	−247.397	−8.57695
$833$	0	0
$834$	−4.20642	−0.145657
$835$	53.2331	1.84221
$836$	−12.0978	−0.418412
$837$	0.791301	0.0273514
$838$	−41.5013	−1.43364
$839$	33.4467	1.15471	0.577354	−	0.816494i	$-0.304085\pi$
$839$	33.4467	1.15471	0.577354	+	0.816494i	$0.304085\pi$
$840$	0	0
$841$	−28.9517	−0.998334
$842$	61.3250	2.11340
$843$	1.30346	0.0448934
$844$	−126.832	−4.36574
$845$	33.9517	1.16797
$846$	36.8756	1.26781
$847$	0	0
$848$	−127.679	−4.38451
$849$	4.43967	0.152369
$850$	22.0616	0.756706
$851$	−4.12306	−0.141337
$852$	8.09783	0.277427
$853$	−2.00000	−0.0684787	−0.0342393	−	0.999414i	$-0.510901\pi$
$853$	−2.00000	−0.0684787	−0.0342393	+	0.999414i	$0.510901\pi$
$854$	0	0
$855$	−13.7560	−0.470445
$856$	1.47889	0.0505475
$857$	−26.4349	−0.902998	−0.451499	−	0.892272i	$-0.649111\pi$
$857$	−26.4349	−0.902998	−0.451499	+	0.892272i	$0.649111\pi$
$858$	−3.17762	−0.108482
$859$	−44.6762	−1.52433	−0.762166	−	0.647381i	$-0.775864\pi$
$859$	−44.6762	−1.52433	−0.762166	+	0.647381i	$0.775864\pi$
$860$	165.541	5.64491
$861$	0	0
$862$	28.0871	0.956650
$863$	39.8431	1.35627	0.678137	−	0.734935i	$-0.262788\pi$
$863$	39.8431	1.35627	0.678137	+	0.734935i	$0.262788\pi$
$864$	35.8224	1.21870
$865$	33.1836	1.12828
$866$	17.2922	0.587612
$867$	−4.88492	−0.165901
$868$	0	0
$869$	−0.879330	−0.0298292
$870$	−0.304258	−0.0103153
$871$	75.9060	2.57198
$872$	−80.7284	−2.73381
$873$	24.5623	0.831306
$874$	−16.1196	−0.545254
$875$	0	0
$876$	6.03492	0.203901
$877$	−43.2247	−1.45960	−0.729798	−	0.683663i	$-0.760386\pi$
$877$	−43.2247	−1.45960	−0.729798	+	0.683663i	$0.760386\pi$
$878$	71.2398	2.40423
$879$	−2.52888	−0.0852969
$880$	−51.2948	−1.72915
$881$	10.0871	0.339842	0.169921	−	0.985458i	$-0.445649\pi$
$881$	10.0871	0.339842	0.169921	+	0.985458i	$0.445649\pi$
$882$	0	0
$883$	−7.96987	−0.268207	−0.134104	−	0.990967i	$-0.542816\pi$
$883$	−7.96987	−0.268207	−0.134104	+	0.990967i	$0.542816\pi$
$884$	−194.827	−6.55274
$885$	6.57242	0.220929
$886$	53.6443	1.80222
$887$	−46.0683	−1.54682	−0.773411	−	0.633905i	$-0.781451\pi$
$887$	−46.0683	−1.54682	−0.773411	+	0.633905i	$0.781451\pi$
$888$	−2.85325	−0.0957487
$889$	0	0
$890$	−67.8323	−2.27374
$891$	−9.59909	−0.321582
$892$	71.2417	2.38535
$893$	−8.28083	−0.277107
$894$	−6.24996	−0.209030
$895$	15.8914	0.531191
$896$	0	0
$897$	−3.15538	−0.105355
$898$	44.4523	1.48339
$899$	0.147343	0.00491416
$900$	−21.1312	−0.704374
$901$	−44.4736	−1.48163
$902$	3.10992	0.103549
$903$	0	0
$904$	116.421	3.87210
$905$	−15.1535	−0.503718
$906$	2.32842	0.0773566
$907$	−41.9415	−1.39265	−0.696323	−	0.717729i	$-0.745182\pi$
$907$	−41.9415	−1.39265	−0.696323	+	0.717729i	$0.745182\pi$
$908$	17.6233	0.584848
$909$	−22.0877	−0.732602
$910$	0	0
$911$	26.5042	0.878125	0.439062	−	0.898457i	$-0.355311\pi$
$911$	26.5042	0.878125	0.439062	+	0.898457i	$0.355311\pi$
$912$	−6.83745	−0.226410
$913$	−9.73184	−0.322077
$914$	52.3973	1.73315
$915$	3.09916	0.102455
$916$	99.9523	3.30252
$917$	0	0
$918$	21.3521	0.704725
$919$	−23.6582	−0.780411	−0.390206	−	0.920728i	$-0.627596\pi$
$919$	−23.6582	−0.780411	−0.390206	+	0.920728i	$0.627596\pi$
$920$	−83.1003	−2.73974
$921$	−2.50950	−0.0826908
$922$	−22.0435	−0.725965
$923$	36.0495	1.18658
$924$	0	0
$925$	1.62863	0.0535490
$926$	77.8926	2.55971
$927$	−13.5953	−0.446527
$928$	6.67025	0.218962
$929$	−25.3709	−0.832392	−0.416196	−	0.909275i	$-0.636637\pi$
$929$	−25.3709	−0.832392	−0.416196	+	0.909275i	$0.636637\pi$
$930$	−0.927656	−0.0304191
$931$	0	0
$932$	86.4059	2.83032
$933$	−4.36898	−0.143034
$934$	−46.0930	−1.50821
$935$	−17.8672	−0.584322
$936$	164.806	5.38684
$937$	16.6601	0.544261	0.272131	−	0.962260i	$-0.412272\pi$
$937$	16.6601	0.544261	0.272131	+	0.962260i	$0.412272\pi$
$938$	0	0
$939$	−1.04998	−0.0342649
$940$	−64.8611	−2.11554
$941$	0.102620	0.00334533	0.00167267	−	0.999999i	$-0.499468\pi$
$941$	0.102620	0.00334533	0.00167267	+	0.999999i	$0.499468\pi$
$942$	6.14974	0.200369
$943$	3.08815	0.100564
$944$	−246.563	−8.02494
$945$	0	0
$946$	−35.2814	−1.14710
$947$	−10.2911	−0.334416	−0.167208	−	0.985922i	$-0.553475\pi$
$947$	−10.2911	−0.334416	−0.167208	+	0.985922i	$0.553475\pi$
$948$	−0.918085	−0.0298180
$949$	26.8659	0.872105
$950$	6.36732	0.206583
$951$	6.47458	0.209953
$952$	0	0
$953$	42.8122	1.38682	0.693412	−	0.720541i	$-0.256107\pi$
$953$	42.8122	1.38682	0.693412	+	0.720541i	$0.256107\pi$
$954$	57.1594	1.85060
$955$	−14.6595	−0.474370
$956$	67.7512	2.19123
$957$	0.0483263	0.00156217
$958$	83.4355	2.69568
$959$	0	0
$960$	−23.6883	−0.764537
$961$	−30.5508	−0.985508
$962$	−19.2989	−0.622221
$963$	−0.405813	−0.0130771
$964$	−179.674	−5.78691
$965$	33.1353	1.06666
$966$	0	0
$967$	−29.4249	−0.946242	−0.473121	−	0.880997i	$-0.656873\pi$
$967$	−29.4249	−0.946242	−0.473121	+	0.880997i	$0.656873\pi$
$968$	−105.396	−3.38756
$969$	−2.38165	−0.0765096
$970$	−57.9711	−1.86134
$971$	19.5163	0.626309	0.313154	−	0.949702i	$-0.398614\pi$
$971$	19.5163	0.626309	0.313154	+	0.949702i	$0.398614\pi$
$972$	−30.7448	−0.986139
$973$	0	0
$974$	27.4832	0.880619
$975$	1.24639	0.0399164
$976$	−116.265	−3.72154
$977$	4.67025	0.149415	0.0747073	−	0.997206i	$-0.476198\pi$
$977$	4.67025	0.149415	0.0747073	+	0.997206i	$0.476198\pi$
$978$	4.26205	0.136285
$979$	10.7741	0.344340
$980$	0	0
$981$	22.1521	0.707263
$982$	−60.4959	−1.93050
$983$	54.4892	1.73793	0.868967	−	0.494869i	$-0.164784\pi$
$983$	54.4892	1.73793	0.868967	+	0.494869i	$0.164784\pi$
$984$	2.13706	0.0681271
$985$	10.2091	0.325288
$986$	3.97584	0.126616
$987$	0	0
$988$	−56.2301	−1.78892
$989$	−35.0344	−1.11403
$990$	22.9638	0.729836
$991$	−19.0073	−0.603787	−0.301893	−	0.953342i	$-0.597619\pi$
$991$	−19.0073	−0.603787	−0.301893	+	0.953342i	$0.597619\pi$
$992$	20.3370	0.645702
$993$	0.174162	0.00552687
$994$	0	0
$995$	4.18226	0.132587
$996$	−10.1608	−0.321956
$997$	38.4626	1.21812	0.609062	−	0.793123i	$-0.291546\pi$
$997$	38.4626	1.21812	0.609062	+	0.793123i	$0.291546\pi$
$998$	25.7694	0.815717
$999$	1.57625	0.0498705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.k.1.3		3
7.6	odd	2		287.2.a.d.1.3	✓	3
21.20	even	2		2583.2.a.l.1.1		3
28.27	even	2		4592.2.a.r.1.3		3
35.34	odd	2		7175.2.a.i.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.d.1.3	✓	3	7.6	odd	2
2009.2.a.k.1.3		3	1.1	even	1	trivial
2583.2.a.l.1.1		3	21.20	even	2
4592.2.a.r.1.3		3	28.27	even	2
7175.2.a.i.1.1		3	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.80194 q^{2} -0.198062 q^{3} +5.85086 q^{4} +2.49396 q^{5} -0.554958 q^{6} +10.7899 q^{8} -2.96077 q^{9} +O(q^{10})\)	\(q+2.80194 q^{2} -0.198062 q^{3} +5.85086 q^{4} +2.49396 q^{5} -0.554958 q^{6} +10.7899 q^{8} -2.96077 q^{9} +6.98792 q^{10} -1.10992 q^{11} -1.15883 q^{12} -5.15883 q^{13} -0.493959 q^{15} +18.5308 q^{16} +6.45473 q^{17} -8.29590 q^{18} +1.86294 q^{19} +14.5918 q^{20} -3.10992 q^{22} -3.08815 q^{23} -2.13706 q^{24} +1.21983 q^{25} -14.4547 q^{26} +1.18060 q^{27} +0.219833 q^{29} -1.38404 q^{30} +0.670251 q^{31} +30.3424 q^{32} +0.219833 q^{33} +18.0858 q^{34} -17.3230 q^{36} +1.33513 q^{37} +5.21983 q^{38} +1.02177 q^{39} +26.9095 q^{40} -1.00000 q^{41} +11.3448 q^{43} -6.49396 q^{44} -7.38404 q^{45} -8.65279 q^{46} -4.44504 q^{47} -3.67025 q^{48} +3.41789 q^{50} -1.27844 q^{51} -30.1836 q^{52} -6.89008 q^{53} +3.30798 q^{54} -2.76809 q^{55} -0.368977 q^{57} +0.615957 q^{58} -13.3056 q^{59} -2.89008 q^{60} -6.27413 q^{61} +1.87800 q^{62} +47.9560 q^{64} -12.8659 q^{65} +0.615957 q^{66} -14.7138 q^{67} +37.7657 q^{68} +0.611645 q^{69} -6.98792 q^{71} -31.9463 q^{72} -5.20775 q^{73} +3.74094 q^{74} -0.241603 q^{75} +10.8998 q^{76} +2.86294 q^{78} +0.792249 q^{79} +46.2150 q^{80} +8.64848 q^{81} -2.80194 q^{82} +8.76809 q^{83} +16.0978 q^{85} +31.7875 q^{86} -0.0435405 q^{87} -11.9758 q^{88} -9.70709 q^{89} -20.6896 q^{90} -18.0683 q^{92} -0.132751 q^{93} -12.4547 q^{94} +4.64609 q^{95} -6.00969 q^{96} -8.29590 q^{97} +3.28621 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 4 q^{2} - 5 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 9 q^{8} + 4 q^{9}+O(q^{10}) \) 3 * q + 4 * q^2 - 5 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 9 * q^8 + 4 * q^9	\( 3 q + 4 q^{2} - 5 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 9 q^{8} + 4 q^{9} + 2 q^{10} - 4 q^{11} + 5 q^{12} - 7 q^{13} + 8 q^{15} + 18 q^{16} - 3 q^{17} - 11 q^{18} + 11 q^{19} + 16 q^{20} - 10 q^{22} - 13 q^{23} - q^{24} + 5 q^{25} - 21 q^{26} - 8 q^{27} + 2 q^{29} + 6 q^{30} + 27 q^{32} + 2 q^{33} + 17 q^{34} - 32 q^{36} + 3 q^{37} + 17 q^{38} + 36 q^{40} - 3 q^{41} + 11 q^{43} - 10 q^{44} - 12 q^{45} - 8 q^{46} - 13 q^{47} - 9 q^{48} + 16 q^{50} + 26 q^{51} - 35 q^{52} - 20 q^{53} + 15 q^{54} + 12 q^{55} - 16 q^{57} + 12 q^{58} - 4 q^{59} - 8 q^{60} - 8 q^{61} - 14 q^{62} + 49 q^{64} + 12 q^{66} - 36 q^{67} + 52 q^{68} + 31 q^{69} - 2 q^{71} - 23 q^{72} + 2 q^{73} - 3 q^{74} + q^{75} + 10 q^{76} + 14 q^{78} + 20 q^{79} + 58 q^{80} + 27 q^{81} - 4 q^{82} + 6 q^{83} + 30 q^{85} + 31 q^{86} + 6 q^{87} + 2 q^{88} + q^{89} - 16 q^{90} - q^{92} - 14 q^{93} - 15 q^{94} - 26 q^{95} + 4 q^{96} - 11 q^{97} + 18 q^{99}+O(q^{100}) \) 3 * q + 4 * q^2 - 5 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 9 * q^8 + 4 * q^9 + 2 * q^10 - 4 * q^11 + 5 * q^12 - 7 * q^13 + 8 * q^15 + 18 * q^16 - 3 * q^17 - 11 * q^18 + 11 * q^19 + 16 * q^20 - 10 * q^22 - 13 * q^23 - q^24 + 5 * q^25 - 21 * q^26 - 8 * q^27 + 2 * q^29 + 6 * q^30 + 27 * q^32 + 2 * q^33 + 17 * q^34 - 32 * q^36 + 3 * q^37 + 17 * q^38 + 36 * q^40 - 3 * q^41 + 11 * q^43 - 10 * q^44 - 12 * q^45 - 8 * q^46 - 13 * q^47 - 9 * q^48 + 16 * q^50 + 26 * q^51 - 35 * q^52 - 20 * q^53 + 15 * q^54 + 12 * q^55 - 16 * q^57 + 12 * q^58 - 4 * q^59 - 8 * q^60 - 8 * q^61 - 14 * q^62 + 49 * q^64 + 12 * q^66 - 36 * q^67 + 52 * q^68 + 31 * q^69 - 2 * q^71 - 23 * q^72 + 2 * q^73 - 3 * q^74 + q^75 + 10 * q^76 + 14 * q^78 + 20 * q^79 + 58 * q^80 + 27 * q^81 - 4 * q^82 + 6 * q^83 + 30 * q^85 + 31 * q^86 + 6 * q^87 + 2 * q^88 + q^89 - 16 * q^90 - q^92 - 14 * q^93 - 15 * q^94 - 26 * q^95 + 4 * q^96 - 11 * q^97 + 18 * q^99

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