LMFDB - Embedded newform 2009.2.a.r.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:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 25 x^{15} + 77 x^{14} + 247 x^{13} - 790 x^{12} - 1231 x^{11} + 4173 x^{10} + \cdots - 464 $ x^17 - 3x^16 - 25x^15 + 77x^14 + 247x^13 - 790x^12 - 1231x^11 + 4173x^10 + 3251x^9 - 12183x^8 - 4259x^7 + 19567x^6 + 2029x^5 - 16136x^4 + 299x^3 + 5775x^2 - 312x - 464
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			$-2.48154$ 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)

$f(q)$	$=$	$q-2.48154 q^{2} -1.40932 q^{3} +4.15802 q^{4} +1.01447 q^{5} +3.49728 q^{6} -5.35521 q^{8} -1.01382 q^{9} +O(q^{10})$	\(q-2.48154 q^{2} -1.40932 q^{3} +4.15802 q^{4} +1.01447 q^{5} +3.49728 q^{6} -5.35521 q^{8} -1.01382 q^{9} -2.51746 q^{10} -5.25436 q^{11} -5.85999 q^{12} -3.75990 q^{13} -1.42972 q^{15} +4.97311 q^{16} -7.45725 q^{17} +2.51582 q^{18} -4.15386 q^{19} +4.21821 q^{20} +13.0389 q^{22} -8.16729 q^{23} +7.54721 q^{24} -3.97084 q^{25} +9.33034 q^{26} +5.65675 q^{27} +0.264385 q^{29} +3.54790 q^{30} -0.457773 q^{31} -1.63052 q^{32} +7.40507 q^{33} +18.5054 q^{34} -4.21547 q^{36} +3.90164 q^{37} +10.3079 q^{38} +5.29891 q^{39} -5.43273 q^{40} -1.00000 q^{41} +8.82356 q^{43} -21.8477 q^{44} -1.02849 q^{45} +20.2674 q^{46} -6.34286 q^{47} -7.00870 q^{48} +9.85379 q^{50} +10.5096 q^{51} -15.6338 q^{52} -0.762475 q^{53} -14.0374 q^{54} -5.33041 q^{55} +5.85412 q^{57} -0.656081 q^{58} +7.76331 q^{59} -5.94481 q^{60} +4.34168 q^{61} +1.13598 q^{62} -5.90001 q^{64} -3.81433 q^{65} -18.3760 q^{66} +1.34131 q^{67} -31.0074 q^{68} +11.5103 q^{69} +14.8510 q^{71} +5.42920 q^{72} -8.36734 q^{73} -9.68206 q^{74} +5.59619 q^{75} -17.2718 q^{76} -13.1494 q^{78} +9.72739 q^{79} +5.04509 q^{80} -4.93073 q^{81} +2.48154 q^{82} -9.69101 q^{83} -7.56519 q^{85} -21.8960 q^{86} -0.372603 q^{87} +28.1382 q^{88} -3.01789 q^{89} +2.55224 q^{90} -33.9598 q^{92} +0.645149 q^{93} +15.7400 q^{94} -4.21398 q^{95} +2.29793 q^{96} +0.317155 q^{97} +5.32695 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 3 q^{2} - q^{3} + 25 q^{4} + q^{5} - 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) $ 17 * q + 3 * q^2 - q^3 + 25 * q^4 + q^5 - 2 * q^6 + 9 * q^8 + 26 * q^9	$ 17 q + 3 q^{2} - q^{3} + 25 q^{4} + q^{5} - 2 q^{6} + 9 q^{8} + 26 q^{9} + 2 q^{10} + 15 q^{11} - 4 q^{12} + 5 q^{13} + 24 q^{15} + 33 q^{16} - 4 q^{17} + 10 q^{18} - 5 q^{19} + 26 q^{20} + 16 q^{22} + 12 q^{23} - 16 q^{24} + 24 q^{25} - 31 q^{26} + 11 q^{27} + 14 q^{29} - 33 q^{30} + 3 q^{31} + 16 q^{32} - 4 q^{33} + 24 q^{34} + 57 q^{36} + 24 q^{37} + 45 q^{39} - 36 q^{40} - 17 q^{41} + 14 q^{43} - 9 q^{44} + 21 q^{45} + 44 q^{46} - 19 q^{47} + 60 q^{48} - 4 q^{50} + 2 q^{51} + 25 q^{52} + 4 q^{53} - 68 q^{54} - 9 q^{55} - 12 q^{57} - q^{58} + 27 q^{59} + 66 q^{60} + q^{61} + 23 q^{62} + 75 q^{64} + 22 q^{65} + 16 q^{66} + 49 q^{67} - 45 q^{68} - 12 q^{69} + 40 q^{71} - 23 q^{72} + 14 q^{73} + 33 q^{74} - 27 q^{75} + 9 q^{76} - 12 q^{78} + 61 q^{79} + 82 q^{80} + 53 q^{81} - 3 q^{82} + 18 q^{83} - 13 q^{85} - 4 q^{86} + 17 q^{87} + 74 q^{88} - 18 q^{89} + 20 q^{90} + 28 q^{92} - 36 q^{93} + 5 q^{94} + 20 q^{95} - 148 q^{96} - 26 q^{97} + 38 q^{99}+O(q^{100}) $ 17 * q + 3 * q^2 - q^3 + 25 * q^4 + q^5 - 2 * q^6 + 9 * q^8 + 26 * q^9 + 2 * q^10 + 15 * q^11 - 4 * q^12 + 5 * q^13 + 24 * q^15 + 33 * q^16 - 4 * q^17 + 10 * q^18 - 5 * q^19 + 26 * q^20 + 16 * q^22 + 12 * q^23 - 16 * q^24 + 24 * q^25 - 31 * q^26 + 11 * q^27 + 14 * q^29 - 33 * q^30 + 3 * q^31 + 16 * q^32 - 4 * q^33 + 24 * q^34 + 57 * q^36 + 24 * q^37 + 45 * q^39 - 36 * q^40 - 17 * q^41 + 14 * q^43 - 9 * q^44 + 21 * q^45 + 44 * q^46 - 19 * q^47 + 60 * q^48 - 4 * q^50 + 2 * q^51 + 25 * q^52 + 4 * q^53 - 68 * q^54 - 9 * q^55 - 12 * q^57 - q^58 + 27 * q^59 + 66 * q^60 + q^61 + 23 * q^62 + 75 * q^64 + 22 * q^65 + 16 * q^66 + 49 * q^67 - 45 * q^68 - 12 * q^69 + 40 * q^71 - 23 * q^72 + 14 * q^73 + 33 * q^74 - 27 * q^75 + 9 * q^76 - 12 * q^78 + 61 * q^79 + 82 * q^80 + 53 * q^81 - 3 * q^82 + 18 * q^83 - 13 * q^85 - 4 * q^86 + 17 * q^87 + 74 * q^88 - 18 * q^89 + 20 * q^90 + 28 * q^92 - 36 * q^93 + 5 * q^94 + 20 * q^95 - 148 * q^96 - 26 * q^97 + 38 * 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 $

$2$	−2.48154	−1.75471	−0.877356	−	0.479841i	$-0.840694\pi$
$2$	−2.48154	−1.75471	−0.877356	+	0.479841i	$0.840694\pi$
$3$	−1.40932	−0.813671	−0.406836	−	0.913501i	$-0.633368\pi$
$3$	−1.40932	−0.813671	−0.406836	+	0.913501i	$0.633368\pi$
$4$	4.15802	2.07901
$5$	1.01447	0.453687	0.226843	−	0.973931i	$-0.427159\pi$
$5$	1.01447	0.453687	0.226843	+	0.973931i	$0.427159\pi$
$6$	3.49728	1.42776
$7$	0	0
$7$	0	0
$8$	−5.35521	−1.89335
$9$	−1.01382	−0.337939
$10$	−2.51746	−0.796089
$11$	−5.25436	−1.58425	−0.792124	−	0.610360i	$-0.791025\pi$
$11$	−5.25436	−1.58425	−0.792124	+	0.610360i	$0.791025\pi$
$12$	−5.85999	−1.69163
$13$	−3.75990	−1.04281	−0.521405	−	0.853309i	$-0.674592\pi$
$13$	−3.75990	−1.04281	−0.521405	+	0.853309i	$0.674592\pi$
$14$	0	0
$15$	−1.42972	−0.369152
$16$	4.97311	1.24328
$17$	−7.45725	−1.80865	−0.904324	−	0.426847i	$-0.859624\pi$
$17$	−7.45725	−1.80865	−0.904324	+	0.426847i	$0.859624\pi$
$18$	2.51582	0.592985
$19$	−4.15386	−0.952960	−0.476480	−	0.879185i	$-0.658088\pi$
$19$	−4.15386	−0.952960	−0.476480	+	0.879185i	$0.658088\pi$
$20$	4.21821	0.943220
$21$	0	0
$22$	13.0389	2.77990
$23$	−8.16729	−1.70300	−0.851499	−	0.524357i	$-0.824306\pi$
$23$	−8.16729	−1.70300	−0.851499	+	0.524357i	$0.824306\pi$
$24$	7.54721	1.54057
$25$	−3.97084	−0.794168
$26$	9.33034	1.82983
$27$	5.65675	1.08864
$28$	0	0
$29$	0.264385	0.0490951	0.0245475	−	0.999699i	$-0.492185\pi$
$29$	0.264385	0.0490951	0.0245475	+	0.999699i	$0.492185\pi$
$30$	3.54790	0.647755
$31$	−0.457773	−0.0822184	−0.0411092	−	0.999155i	$-0.513089\pi$
$31$	−0.457773	−0.0822184	−0.0411092	+	0.999155i	$0.513089\pi$
$32$	−1.63052	−0.288238
$33$	7.40507	1.28906
$34$	18.5054	3.17365
$35$	0	0
$36$	−4.21547	−0.702579
$37$	3.90164	0.641426	0.320713	−	0.947176i	$-0.396078\pi$
$37$	3.90164	0.641426	0.320713	+	0.947176i	$0.396078\pi$
$38$	10.3079	1.67217
$39$	5.29891	0.848504
$40$	−5.43273	−0.858990
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	8.82356	1.34558	0.672790	−	0.739833i	$-0.265096\pi$
$43$	8.82356	1.34558	0.672790	+	0.739833i	$0.265096\pi$
$44$	−21.8477	−3.29367
$45$	−1.02849	−0.153318
$46$	20.2674	2.98827
$47$	−6.34286	−0.925201	−0.462601	−	0.886567i	$-0.653084\pi$
$47$	−6.34286	−0.925201	−0.462601	+	0.886567i	$0.653084\pi$
$48$	−7.00870	−1.01162
$49$	0	0
$50$	9.85379	1.39354
$51$	10.5096	1.47164
$52$	−15.6338	−2.16801
$53$	−0.762475	−0.104734	−0.0523670	−	0.998628i	$-0.516677\pi$
$53$	−0.762475	−0.104734	−0.0523670	+	0.998628i	$0.516677\pi$
$54$	−14.0374	−1.91025
$55$	−5.33041	−0.718753
$56$	0	0
$57$	5.85412	0.775397
$58$	−0.656081	−0.0861477
$59$	7.76331	1.01070	0.505348	−	0.862915i	$-0.331364\pi$
$59$	7.76331	1.01070	0.505348	+	0.862915i	$0.331364\pi$
$60$	−5.94481	−0.767471
$61$	4.34168	0.555895	0.277947	−	0.960596i	$-0.410346\pi$
$61$	4.34168	0.555895	0.277947	+	0.960596i	$0.410346\pi$
$62$	1.13598	0.144270
$63$	0	0
$64$	−5.90001	−0.737502
$65$	−3.81433	−0.473109
$66$	−18.3760	−2.26192
$67$	1.34131	0.163867	0.0819336	−	0.996638i	$-0.473890\pi$
$67$	1.34131	0.163867	0.0819336	+	0.996638i	$0.473890\pi$
$68$	−31.0074	−3.76020
$69$	11.5103	1.38568
$70$	0	0
$71$	14.8510	1.76249	0.881246	−	0.472658i	$-0.156705\pi$
$71$	14.8510	1.76249	0.881246	+	0.472658i	$0.156705\pi$
$72$	5.42920	0.639838
$73$	−8.36734	−0.979323	−0.489661	−	0.871913i	$-0.662880\pi$
$73$	−8.36734	−0.979323	−0.489661	+	0.871913i	$0.662880\pi$
$74$	−9.68206	−1.12552
$75$	5.59619	0.646192
$76$	−17.2718	−1.98122
$77$	0	0
$78$	−13.1494	−1.48888
$79$	9.72739	1.09442	0.547208	−	0.836996i	$-0.315691\pi$
$79$	9.72739	1.09442	0.547208	+	0.836996i	$0.315691\pi$
$80$	5.04509	0.564058
$81$	−4.93073	−0.547859
$82$	2.48154	0.274040
$83$	−9.69101	−1.06373	−0.531864	−	0.846830i	$-0.678508\pi$
$83$	−9.69101	−1.06373	−0.531864	+	0.846830i	$0.678508\pi$
$84$	0	0
$85$	−7.56519	−0.820560
$86$	−21.8960	−2.36111
$87$	−0.372603	−0.0399473
$88$	28.1382	2.99954
$89$	−3.01789	−0.319896	−0.159948	−	0.987125i	$-0.551133\pi$
$89$	−3.01789	−0.319896	−0.159948	+	0.987125i	$0.551133\pi$
$90$	2.55224	0.269030
$91$	0	0
$92$	−33.9598	−3.54055
$93$	0.645149	0.0668988
$94$	15.7400	1.62346
$95$	−4.21398	−0.432346
$96$	2.29793	0.234531
$97$	0.317155	0.0322022	0.0161011	−	0.999870i	$-0.494875\pi$
$97$	0.317155	0.0322022	0.0161011	+	0.999870i	$0.494875\pi$
$98$	0	0
$99$	5.32695	0.535379
$100$	−16.5108	−1.65108
$101$	6.20307	0.617228	0.308614	−	0.951187i	$-0.400135\pi$
$101$	6.20307	0.617228	0.308614	+	0.951187i	$0.400135\pi$
$102$	−26.0801	−2.58231
$103$	−10.4187	−1.02659	−0.513295	−	0.858212i	$-0.671575\pi$
$103$	−10.4187	−1.02659	−0.513295	+	0.858212i	$0.671575\pi$
$104$	20.1351	1.97441
$105$	0	0
$106$	1.89211	0.183778
$107$	5.81878	0.562522	0.281261	−	0.959631i	$-0.409247\pi$
$107$	5.81878	0.562522	0.281261	+	0.959631i	$0.409247\pi$
$108$	23.5209	2.26330
$109$	−4.04343	−0.387291	−0.193645	−	0.981072i	$-0.562031\pi$
$109$	−4.04343	−0.387291	−0.193645	+	0.981072i	$0.562031\pi$
$110$	13.2276	1.26120
$111$	−5.49866	−0.521910
$112$	0	0
$113$	−8.11145	−0.763061	−0.381531	−	0.924356i	$-0.624603\pi$
$113$	−8.11145	−0.763061	−0.381531	+	0.924356i	$0.624603\pi$
$114$	−14.5272	−1.36060
$115$	−8.28551	−0.772628
$116$	1.09932	0.102069
$117$	3.81185	0.352406
$118$	−19.2649	−1.77348
$119$	0	0
$120$	7.65645	0.698935
$121$	16.6083	1.50984
$122$	−10.7740	−0.975434
$123$	1.40932	0.127074
$124$	−1.90343	−0.170933
$125$	−9.10069	−0.813991
$126$	0	0
$127$	−1.25266	−0.111156	−0.0555780	−	0.998454i	$-0.517700\pi$
$127$	−1.25266	−0.111156	−0.0555780	+	0.998454i	$0.517700\pi$
$128$	17.9021	1.58234
$129$	−12.4352	−1.09486
$130$	9.46539	0.830170
$131$	−10.3433	−0.903696	−0.451848	−	0.892095i	$-0.649235\pi$
$131$	−10.3433	−0.903696	−0.451848	+	0.892095i	$0.649235\pi$
$132$	30.7905	2.67996
$133$	0	0
$134$	−3.32851	−0.287540
$135$	5.73863	0.493903
$136$	39.9351	3.42441
$137$	−10.7983	−0.922557	−0.461279	−	0.887255i	$-0.652609\pi$
$137$	−10.7983	−0.922557	−0.461279	+	0.887255i	$0.652609\pi$
$138$	−28.5633	−2.43147
$139$	10.7249	0.909672	0.454836	−	0.890575i	$-0.349698\pi$
$139$	10.7249	0.909672	0.454836	+	0.890575i	$0.349698\pi$
$140$	0	0
$141$	8.93912	0.752810
$142$	−36.8533	−3.09266
$143$	19.7559	1.65207
$144$	−5.04182	−0.420151
$145$	0.268212	0.0222738
$146$	20.7638	1.71843
$147$	0	0
$148$	16.2231	1.33353
$149$	−4.58155	−0.375335	−0.187668	−	0.982233i	$-0.560093\pi$
$149$	−4.58155	−0.375335	−0.187668	+	0.982233i	$0.560093\pi$
$150$	−13.8871	−1.13388
$151$	15.0593	1.22551	0.612756	−	0.790272i	$-0.290061\pi$
$151$	15.0593	1.22551	0.612756	+	0.790272i	$0.290061\pi$
$152$	22.2448	1.80429
$153$	7.56028	0.611212
$154$	0	0
$155$	−0.464399	−0.0373014
$156$	22.0330	1.76405
$157$	10.9728	0.875721	0.437861	−	0.899043i	$-0.355736\pi$
$157$	10.9728	0.875721	0.437861	+	0.899043i	$0.355736\pi$
$158$	−24.1389	−1.92039
$159$	1.07457	0.0852190
$160$	−1.65412	−0.130770
$161$	0	0
$162$	12.2358	0.961333
$163$	14.2612	1.11703	0.558513	−	0.829496i	$-0.311372\pi$
$163$	14.2612	1.11703	0.558513	+	0.829496i	$0.311372\pi$
$164$	−4.15802	−0.324687
$165$	7.51226	0.584828
$166$	24.0486	1.86653
$167$	−16.3462	−1.26490	−0.632452	−	0.774599i	$-0.717952\pi$
$167$	−16.3462	−1.26490	−0.632452	+	0.774599i	$0.717952\pi$
$168$	0	0
$169$	1.13688	0.0874521
$170$	18.7733	1.43985
$171$	4.21125	0.322042
$172$	36.6886	2.79748
$173$	−0.848058	−0.0644766	−0.0322383	−	0.999480i	$-0.510264\pi$
$173$	−0.848058	−0.0644766	−0.0322383	+	0.999480i	$0.510264\pi$
$174$	0.924628	0.0700959
$175$	0	0
$176$	−26.1305	−1.96966
$177$	−10.9410	−0.822375
$178$	7.48900	0.561325
$179$	15.3327	1.14602	0.573010	−	0.819549i	$-0.305776\pi$
$179$	15.3327	1.14602	0.573010	+	0.819549i	$0.305776\pi$
$180$	−4.27649	−0.318751
$181$	−7.53427	−0.560018	−0.280009	−	0.959997i	$-0.590337\pi$
$181$	−7.53427	−0.560018	−0.280009	+	0.959997i	$0.590337\pi$
$182$	0	0
$183$	−6.11881	−0.452315
$184$	43.7376	3.22438
$185$	3.95812	0.291007
$186$	−1.60096	−0.117388
$187$	39.1830	2.86535
$188$	−26.3738	−1.92350
$189$	0	0
$190$	10.4572	0.758642
$191$	18.6681	1.35077	0.675387	−	0.737463i	$-0.263977\pi$
$191$	18.6681	1.35077	0.675387	+	0.737463i	$0.263977\pi$
$192$	8.31501	0.600084
$193$	10.3641	0.746026	0.373013	−	0.927826i	$-0.378325\pi$
$193$	10.3641	0.746026	0.373013	+	0.927826i	$0.378325\pi$
$194$	−0.787032	−0.0565056
$195$	5.37561	0.384955
$196$	0	0
$197$	−7.76991	−0.553583	−0.276792	−	0.960930i	$-0.589271\pi$
$197$	−7.76991	−0.553583	−0.276792	+	0.960930i	$0.589271\pi$
$198$	−13.2190	−0.939435
$199$	−14.9397	−1.05905	−0.529525	−	0.848294i	$-0.677630\pi$
$199$	−14.9397	−1.05905	−0.529525	+	0.848294i	$0.677630\pi$
$200$	21.2647	1.50364
$201$	−1.89034	−0.133334
$202$	−15.3931	−1.08306
$203$	0	0
$204$	43.6994	3.05957
$205$	−1.01447	−0.0708540
$206$	25.8545	1.80137
$207$	8.28013	0.575509
$208$	−18.6984	−1.29650
$209$	21.8258	1.50973
$210$	0	0
$211$	−14.3885	−0.990548	−0.495274	−	0.868737i	$-0.664932\pi$
$211$	−14.3885	−0.990548	−0.495274	+	0.868737i	$0.664932\pi$
$212$	−3.17039	−0.217743
$213$	−20.9298	−1.43409
$214$	−14.4395	−0.987064
$215$	8.95128	0.610472
$216$	−30.2931	−2.06118
$217$	0	0
$218$	10.0339	0.679583
$219$	11.7923	0.796847
$220$	−22.1640	−1.49429
$221$	28.0385	1.88608
$222$	13.6451	0.915801
$223$	13.0474	0.873718	0.436859	−	0.899530i	$-0.356091\pi$
$223$	13.0474	0.873718	0.436859	+	0.899530i	$0.356091\pi$
$224$	0	0
$225$	4.02570	0.268380
$226$	20.1289	1.33895
$227$	−29.3223	−1.94619	−0.973094	−	0.230408i	$-0.925994\pi$
$227$	−29.3223	−1.94619	−0.973094	+	0.230408i	$0.925994\pi$
$228$	24.3415	1.61206
$229$	−7.51012	−0.496283	−0.248141	−	0.968724i	$-0.579820\pi$
$229$	−7.51012	−0.496283	−0.248141	+	0.968724i	$0.579820\pi$
$230$	20.5608	1.35574
$231$	0	0
$232$	−1.41584	−0.0929543
$233$	−16.4892	−1.08025	−0.540123	−	0.841586i	$-0.681622\pi$
$233$	−16.4892	−1.08025	−0.540123	+	0.841586i	$0.681622\pi$
$234$	−9.45925	−0.618371
$235$	−6.43467	−0.419752
$236$	32.2800	2.10125
$237$	−13.7090	−0.890496
$238$	0	0
$239$	0.692747	0.0448101	0.0224050	−	0.999749i	$-0.492868\pi$
$239$	0.692747	0.0448101	0.0224050	+	0.999749i	$0.492868\pi$
$240$	−7.11015	−0.458958
$241$	−8.43104	−0.543091	−0.271546	−	0.962426i	$-0.587535\pi$
$241$	−8.43104	−0.543091	−0.271546	+	0.962426i	$0.587535\pi$
$242$	−41.2140	−2.64934
$243$	−10.0213	−0.642866
$244$	18.0528	1.15571
$245$	0	0
$246$	−3.49728	−0.222978
$247$	15.6181	0.993756
$248$	2.45147	0.155669
$249$	13.6577	0.865524
$250$	22.5837	1.42832
$251$	−9.32963	−0.588881	−0.294440	−	0.955670i	$-0.595133\pi$
$251$	−9.32963	−0.588881	−0.294440	+	0.955670i	$0.595133\pi$
$252$	0	0
$253$	42.9138	2.69797
$254$	3.10853	0.195047
$255$	10.6618	0.667666
$256$	−32.6248	−2.03905
$257$	−4.73517	−0.295372	−0.147686	−	0.989034i	$-0.547182\pi$
$257$	−4.73517	−0.295372	−0.147686	+	0.989034i	$0.547182\pi$
$258$	30.8585	1.92116
$259$	0	0
$260$	−15.8601	−0.983599
$261$	−0.268038	−0.0165911
$262$	25.6672	1.58573
$263$	−26.1310	−1.61130	−0.805652	−	0.592389i	$-0.798185\pi$
$263$	−26.1310	−1.61130	−0.805652	+	0.592389i	$0.798185\pi$
$264$	−39.6557	−2.44064
$265$	−0.773511	−0.0475164
$266$	0	0
$267$	4.25317	0.260290
$268$	5.57720	0.340682
$269$	6.63873	0.404770	0.202385	−	0.979306i	$-0.435131\pi$
$269$	6.63873	0.404770	0.202385	+	0.979306i	$0.435131\pi$
$270$	−14.2406	−0.866657
$271$	14.9285	0.906844	0.453422	−	0.891296i	$-0.350203\pi$
$271$	14.9285	0.906844	0.453422	+	0.891296i	$0.350203\pi$
$272$	−37.0857	−2.24865
$273$	0	0
$274$	26.7963	1.61882
$275$	20.8642	1.25816
$276$	47.8602	2.88084
$277$	15.2060	0.913638	0.456819	−	0.889560i	$-0.348989\pi$
$277$	15.2060	0.913638	0.456819	+	0.889560i	$0.348989\pi$
$278$	−26.6142	−1.59621
$279$	0.464098	0.0277848
$280$	0	0
$281$	−8.69712	−0.518827	−0.259413	−	0.965766i	$-0.583529\pi$
$281$	−8.69712	−0.518827	−0.259413	+	0.965766i	$0.583529\pi$
$282$	−22.1828	−1.32096
$283$	−20.3047	−1.20699	−0.603495	−	0.797367i	$-0.706226\pi$
$283$	−20.3047	−1.20699	−0.603495	+	0.797367i	$0.706226\pi$
$284$	61.7509	3.66424
$285$	5.93885	0.351787
$286$	−49.0249	−2.89890
$287$	0	0
$288$	1.65305	0.0974069
$289$	38.6105	2.27121
$290$	−0.665578	−0.0390841
$291$	−0.446973	−0.0262020
$292$	−34.7916	−2.03602
$293$	−15.7908	−0.922507	−0.461254	−	0.887268i	$-0.652600\pi$
$293$	−15.7908	−0.922507	−0.461254	+	0.887268i	$0.652600\pi$
$294$	0	0
$295$	7.87568	0.458540
$296$	−20.8941	−1.21445
$297$	−29.7226	−1.72468
$298$	11.3693	0.658605
$299$	30.7082	1.77590
$300$	23.2691	1.34344
$301$	0	0
$302$	−37.3703	−2.15042
$303$	−8.74211	−0.502221
$304$	−20.6576	−1.18479
$305$	4.40452	0.252202
$306$	−18.7611	−1.07250
$307$	−12.2219	−0.697540	−0.348770	−	0.937208i	$-0.613401\pi$
$307$	−12.2219	−0.697540	−0.348770	+	0.937208i	$0.613401\pi$
$308$	0	0
$309$	14.6833	0.835306
$310$	1.15242	0.0654532
$311$	−11.0350	−0.625735	−0.312868	−	0.949797i	$-0.601290\pi$
$311$	−11.0350	−0.625735	−0.312868	+	0.949797i	$0.601290\pi$
$312$	−28.3768	−1.60652
$313$	2.40000	0.135656	0.0678280	−	0.997697i	$-0.478393\pi$
$313$	2.40000	0.135656	0.0678280	+	0.997697i	$0.478393\pi$
$314$	−27.2293	−1.53664
$315$	0	0
$316$	40.4467	2.27531
$317$	−20.7361	−1.16466	−0.582328	−	0.812954i	$-0.697858\pi$
$317$	−20.7361	−1.16466	−0.582328	+	0.812954i	$0.697858\pi$
$318$	−2.66659	−0.149535
$319$	−1.38917	−0.0777788
$320$	−5.98541	−0.334595
$321$	−8.20052	−0.457708
$322$	0	0
$323$	30.9763	1.72357
$324$	−20.5021	−1.13900
$325$	14.9300	0.828166
$326$	−35.3898	−1.96006
$327$	5.69849	0.315127
$328$	5.35521	0.295692
$329$	0	0
$330$	−18.6419	−1.02621
$331$	8.40745	0.462115	0.231058	−	0.972940i	$-0.425781\pi$
$331$	8.40745	0.462115	0.231058	+	0.972940i	$0.425781\pi$
$332$	−40.2955	−2.21150
$333$	−3.95555	−0.216763
$334$	40.5636	2.21954
$335$	1.36073	0.0743444
$336$	0	0
$337$	−4.08624	−0.222592	−0.111296	−	0.993787i	$-0.535500\pi$
$337$	−4.08624	−0.222592	−0.111296	+	0.993787i	$0.535500\pi$
$338$	−2.82120	−0.153453
$339$	11.4316	0.620881
$340$	−31.4562	−1.70595
$341$	2.40530	0.130254
$342$	−10.4504	−0.565091
$343$	0	0
$344$	−47.2520	−2.54766
$345$	11.6769	0.628665
$346$	2.10449	0.113138
$347$	19.9001	1.06830	0.534148	−	0.845391i	$-0.320633\pi$
$347$	19.9001	1.06830	0.534148	+	0.845391i	$0.320633\pi$
$348$	−1.54929	−0.0830508
$349$	−25.1660	−1.34711	−0.673553	−	0.739139i	$-0.735233\pi$
$349$	−25.1660	−1.34711	−0.673553	+	0.739139i	$0.735233\pi$
$350$	0	0
$351$	−21.2688	−1.13525
$352$	8.56735	0.456641
$353$	13.6046	0.724097	0.362049	−	0.932159i	$-0.382077\pi$
$353$	13.6046	0.724097	0.362049	+	0.932159i	$0.382077\pi$
$354$	27.1505	1.44303
$355$	15.0660	0.799619
$356$	−12.5485	−0.665067
$357$	0	0
$358$	−38.0486	−2.01093
$359$	4.26958	0.225340	0.112670	−	0.993632i	$-0.464060\pi$
$359$	4.26958	0.225340	0.112670	+	0.993632i	$0.464060\pi$
$360$	5.50779	0.290286
$361$	−1.74547	−0.0918667
$362$	18.6966	0.982670
$363$	−23.4064	−1.22852
$364$	0	0
$365$	−8.48845	−0.444306
$366$	15.1841	0.793683
$367$	31.2622	1.63187	0.815937	−	0.578141i	$-0.196222\pi$
$367$	31.2622	1.63187	0.815937	+	0.578141i	$0.196222\pi$
$368$	−40.6168	−2.11730
$369$	1.01382	0.0527772
$370$	−9.82221	−0.510632
$371$	0	0
$372$	2.68254	0.139083
$373$	−20.2661	−1.04934	−0.524671	−	0.851305i	$-0.675812\pi$
$373$	−20.2661	−1.04934	−0.524671	+	0.851305i	$0.675812\pi$
$374$	−97.2341	−5.02786
$375$	12.8258	0.662321
$376$	33.9674	1.75173
$377$	−0.994062	−0.0511968
$378$	0	0
$379$	−4.19409	−0.215436	−0.107718	−	0.994181i	$-0.534354\pi$
$379$	−4.19409	−0.215436	−0.107718	+	0.994181i	$0.534354\pi$
$380$	−17.5218	−0.898851
$381$	1.76540	0.0904444
$382$	−46.3255	−2.37022
$383$	−1.84647	−0.0943504	−0.0471752	−	0.998887i	$-0.515022\pi$
$383$	−1.84647	−0.0943504	−0.0471752	+	0.998887i	$0.515022\pi$
$384$	−25.2299	−1.28751
$385$	0	0
$386$	−25.7190	−1.30906
$387$	−8.94547	−0.454724
$388$	1.31874	0.0669488
$389$	−14.7145	−0.746053	−0.373026	−	0.927821i	$-0.621680\pi$
$389$	−14.7145	−0.746053	−0.373026	+	0.927821i	$0.621680\pi$
$390$	−13.3398	−0.675485
$391$	60.9055	3.08012
$392$	0	0
$393$	14.5770	0.735312
$394$	19.2813	0.971379
$395$	9.86819	0.496523
$396$	22.1496	1.11306
$397$	−13.0761	−0.656271	−0.328135	−	0.944631i	$-0.606420\pi$
$397$	−13.0761	−0.656271	−0.328135	+	0.944631i	$0.606420\pi$
$398$	37.0735	1.85833
$399$	0	0
$400$	−19.7474	−0.987371
$401$	33.3330	1.66457	0.832285	−	0.554349i	$-0.187033\pi$
$401$	33.3330	1.66457	0.832285	+	0.554349i	$0.187033\pi$
$402$	4.69094	0.233963
$403$	1.72118	0.0857382
$404$	25.7925	1.28322
$405$	−5.00210	−0.248556
$406$	0	0
$407$	−20.5006	−1.01618
$408$	−56.2814	−2.78634
$409$	−16.3431	−0.808114	−0.404057	−	0.914734i	$-0.632400\pi$
$409$	−16.3431	−0.808114	−0.404057	+	0.914734i	$0.632400\pi$
$410$	2.51746	0.124328
$411$	15.2182	0.750658
$412$	−43.3214	−2.13429
$413$	0	0
$414$	−20.5474	−1.00985
$415$	−9.83129	−0.482599
$416$	6.13061	0.300578
$417$	−15.1148	−0.740174
$418$	−54.1616	−2.64913
$419$	14.5565	0.711131	0.355566	−	0.934651i	$-0.384288\pi$
$419$	14.5565	0.711131	0.355566	+	0.934651i	$0.384288\pi$
$420$	0	0
$421$	−16.0444	−0.781957	−0.390979	−	0.920400i	$-0.627863\pi$
$421$	−16.0444	−0.781957	−0.390979	+	0.920400i	$0.627863\pi$
$422$	35.7057	1.73813
$423$	6.43050	0.312661
$424$	4.08321	0.198298
$425$	29.6115	1.43637
$426$	51.9382	2.51641
$427$	0	0
$428$	24.1946	1.16949
$429$	−27.8424	−1.34424
$430$	−22.2129	−1.07120
$431$	33.5871	1.61783	0.808917	−	0.587923i	$-0.200054\pi$
$431$	33.5871	1.61783	0.808917	+	0.587923i	$0.200054\pi$
$432$	28.1316	1.35348
$433$	23.7405	1.14090	0.570449	−	0.821333i	$-0.306769\pi$
$433$	23.7405	1.14090	0.570449	+	0.821333i	$0.306769\pi$
$434$	0	0
$435$	−0.377997	−0.0181235
$436$	−16.8127	−0.805182
$437$	33.9258	1.62289
$438$	−29.2629	−1.39824
$439$	−32.1612	−1.53497	−0.767486	−	0.641066i	$-0.778493\pi$
$439$	−32.1612	−1.53497	−0.767486	+	0.641066i	$0.778493\pi$
$440$	28.5455	1.36085
$441$	0	0
$442$	−69.5786	−3.30952
$443$	5.93198	0.281837	0.140918	−	0.990021i	$-0.454995\pi$
$443$	5.93198	0.281837	0.140918	+	0.990021i	$0.454995\pi$
$444$	−22.8636	−1.08506
$445$	−3.06157	−0.145133
$446$	−32.3776	−1.53312
$447$	6.45687	0.305399
$448$	0	0
$449$	17.1624	0.809945	0.404972	−	0.914329i	$-0.367281\pi$
$449$	17.1624	0.809945	0.404972	+	0.914329i	$0.367281\pi$
$450$	−9.98993	−0.470930
$451$	5.25436	0.247418
$452$	−33.7276	−1.58641
$453$	−21.2234	−0.997163
$454$	72.7643	3.41500
$455$	0	0
$456$	−31.3500	−1.46810
$457$	−41.0148	−1.91859	−0.959297	−	0.282401i	$-0.908869\pi$
$457$	−41.0148	−1.91859	−0.959297	+	0.282401i	$0.908869\pi$
$458$	18.6366	0.870833
$459$	−42.1838	−1.96897
$460$	−34.4513	−1.60630
$461$	−40.1685	−1.87083	−0.935416	−	0.353550i	$-0.884974\pi$
$461$	−40.1685	−1.87083	−0.935416	+	0.353550i	$0.884974\pi$
$462$	0	0
$463$	−25.8876	−1.20310	−0.601549	−	0.798836i	$-0.705449\pi$
$463$	−25.8876	−1.20310	−0.601549	+	0.798836i	$0.705449\pi$
$464$	1.31482	0.0610388
$465$	0.654487	0.0303511
$466$	40.9187	1.89552
$467$	22.2641	1.03026	0.515129	−	0.857113i	$-0.327744\pi$
$467$	22.2641	1.03026	0.515129	+	0.857113i	$0.327744\pi$
$468$	15.8498	0.732656
$469$	0	0
$470$	15.9679	0.736543
$471$	−15.4641	−0.712549
$472$	−41.5742	−1.91361
$473$	−46.3621	−2.13173
$474$	34.0194	1.56256
$475$	16.4943	0.756811
$476$	0	0
$477$	0.773010	0.0353937
$478$	−1.71908	−0.0786288
$479$	29.7682	1.36015	0.680073	−	0.733145i	$-0.261948\pi$
$479$	29.7682	1.36015	0.680073	+	0.733145i	$0.261948\pi$
$480$	2.33119	0.106404
$481$	−14.6698	−0.668885
$482$	20.9219	0.952968
$483$	0	0
$484$	69.0575	3.13898
$485$	0.321746	0.0146097
$486$	24.8682	1.12804
$487$	16.7135	0.757363	0.378682	−	0.925527i	$-0.376378\pi$
$487$	16.7135	0.757363	0.378682	+	0.925527i	$0.376378\pi$
$488$	−23.2506	−1.05250
$489$	−20.0986	−0.908892
$490$	0	0
$491$	−27.0953	−1.22279	−0.611396	−	0.791325i	$-0.709392\pi$
$491$	−27.0953	−1.22279	−0.611396	+	0.791325i	$0.709392\pi$
$492$	5.85999	0.264189
$493$	−1.97158	−0.0887957
$494$	−38.7569	−1.74376
$495$	5.40406	0.242894
$496$	−2.27655	−0.102220
$497$	0	0
$498$	−33.8922	−1.51875
$499$	−28.7606	−1.28750	−0.643751	−	0.765235i	$-0.722623\pi$
$499$	−28.7606	−1.28750	−0.643751	+	0.765235i	$0.722623\pi$
$500$	−37.8409	−1.69230
$501$	23.0370	1.02922
$502$	23.1518	1.03332
$503$	−8.89437	−0.396580	−0.198290	−	0.980143i	$-0.563539\pi$
$503$	−8.89437	−0.396580	−0.198290	+	0.980143i	$0.563539\pi$
$504$	0	0
$505$	6.29285	0.280028
$506$	−106.492	−4.73416
$507$	−1.60222	−0.0711573
$508$	−5.20860	−0.231094
$509$	−30.3963	−1.34729	−0.673646	−	0.739054i	$-0.735273\pi$
$509$	−30.3963	−1.34729	−0.673646	+	0.739054i	$0.735273\pi$
$510$	−26.4576	−1.17156
$511$	0	0
$512$	45.1553	1.99560
$513$	−23.4973	−1.03743
$514$	11.7505	0.518292
$515$	−10.5696	−0.465750
$516$	−51.7059	−2.27623
$517$	33.3277	1.46575
$518$	0	0
$519$	1.19518	0.0524628
$520$	20.4265	0.895763
$521$	4.28263	0.187625	0.0938127	−	0.995590i	$-0.470095\pi$
$521$	4.28263	0.187625	0.0938127	+	0.995590i	$0.470095\pi$
$522$	0.665146	0.0291126
$523$	−15.2026	−0.664762	−0.332381	−	0.943145i	$-0.607852\pi$
$523$	−15.2026	−0.664762	−0.332381	+	0.943145i	$0.607852\pi$
$524$	−43.0076	−1.87879
$525$	0	0
$526$	64.8449	2.82737
$527$	3.41372	0.148704
$528$	36.8262	1.60266
$529$	43.7046	1.90020
$530$	1.91950	0.0833776
$531$	−7.87057	−0.341554
$532$	0	0
$533$	3.75990	0.162860
$534$	−10.5544	−0.456734
$535$	5.90300	0.255209
$536$	−7.18301	−0.310259
$537$	−21.6087	−0.932483
$538$	−16.4742	−0.710255
$539$	0	0
$540$	23.8614	1.02683
$541$	9.86849	0.424279	0.212140	−	0.977239i	$-0.431957\pi$
$541$	9.86849	0.424279	0.212140	+	0.977239i	$0.431957\pi$
$542$	−37.0457	−1.59125
$543$	10.6182	0.455671
$544$	12.1592	0.521322
$545$	−4.10196	−0.175709
$546$	0	0
$547$	−1.77390	−0.0758466	−0.0379233	−	0.999281i	$-0.512074\pi$
$547$	−1.77390	−0.0758466	−0.0379233	+	0.999281i	$0.512074\pi$
$548$	−44.8994	−1.91801
$549$	−4.40166	−0.187858
$550$	−51.7753	−2.20771
$551$	−1.09822	−0.0467856
$552$	−61.6402	−2.62358
$553$	0	0
$554$	−37.7342	−1.60317
$555$	−5.57825	−0.236784
$556$	44.5943	1.89122
$557$	−21.9654	−0.930705	−0.465352	−	0.885126i	$-0.654072\pi$
$557$	−21.9654	−0.930705	−0.465352	+	0.885126i	$0.654072\pi$
$558$	−1.15168	−0.0487543
$559$	−33.1757	−1.40318
$560$	0	0
$561$	−55.2214	−2.33145
$562$	21.5822	0.910391
$563$	43.6484	1.83956	0.919780	−	0.392434i	$-0.128367\pi$
$563$	43.6484	1.83956	0.919780	+	0.392434i	$0.128367\pi$
$564$	37.1691	1.56510
$565$	−8.22886	−0.346191
$566$	50.3869	2.11792
$567$	0	0
$568$	−79.5304	−3.33702
$569$	28.9235	1.21254	0.606269	−	0.795260i	$-0.292665\pi$
$569$	28.9235	1.21254	0.606269	+	0.795260i	$0.292665\pi$
$570$	−14.7375	−0.617285
$571$	−3.28763	−0.137583	−0.0687916	−	0.997631i	$-0.521914\pi$
$571$	−3.28763	−0.137583	−0.0687916	+	0.997631i	$0.521914\pi$
$572$	82.1454	3.43467
$573$	−26.3093	−1.09909
$574$	0	0
$575$	32.4310	1.35247
$576$	5.98153	0.249230
$577$	35.7021	1.48630	0.743149	−	0.669126i	$-0.233331\pi$
$577$	35.7021	1.48630	0.743149	+	0.669126i	$0.233331\pi$
$578$	−95.8134	−3.98531
$579$	−14.6064	−0.607020
$580$	1.11523	0.0463075
$581$	0	0
$582$	1.10918	0.0459770
$583$	4.00631	0.165925
$584$	44.8089	1.85420
$585$	3.86703	0.159882
$586$	39.1854	1.61873
$587$	37.3851	1.54305	0.771524	−	0.636200i	$-0.219495\pi$
$587$	37.3851	1.54305	0.771524	+	0.636200i	$0.219495\pi$
$588$	0	0
$589$	1.90152	0.0783509
$590$	−19.5438	−0.804605
$591$	10.9503	0.450435
$592$	19.4033	0.797470
$593$	36.2967	1.49053	0.745263	−	0.666770i	$-0.232324\pi$
$593$	36.2967	1.49053	0.745263	+	0.666770i	$0.232324\pi$
$594$	73.7577	3.02632
$595$	0	0
$596$	−19.0502	−0.780326
$597$	21.0549	0.861719
$598$	−76.2036	−3.11620
$599$	−0.260042	−0.0106250	−0.00531252	−	0.999986i	$-0.501691\pi$
$599$	−0.260042	−0.0106250	−0.00531252	+	0.999986i	$0.501691\pi$
$600$	−29.9688	−1.22347
$601$	18.1572	0.740648	0.370324	−	0.928903i	$-0.379247\pi$
$601$	18.1572	0.740648	0.370324	+	0.928903i	$0.379247\pi$
$602$	0	0
$603$	−1.35984	−0.0553771
$604$	62.6171	2.54785
$605$	16.8487	0.684995
$606$	21.6939	0.881253
$607$	4.95145	0.200973	0.100487	−	0.994938i	$-0.467960\pi$
$607$	4.95145	0.200973	0.100487	+	0.994938i	$0.467960\pi$
$608$	6.77296	0.274680
$609$	0	0
$610$	−10.9300	−0.442542
$611$	23.8485	0.964809
$612$	31.4358	1.27072
$613$	−6.55127	−0.264603	−0.132302	−	0.991210i	$-0.542237\pi$
$613$	−6.55127	−0.264603	−0.132302	+	0.991210i	$0.542237\pi$
$614$	30.3291	1.22398
$615$	1.42972	0.0576519
$616$	0	0
$617$	1.05131	0.0423241	0.0211620	−	0.999776i	$-0.493263\pi$
$617$	1.05131	0.0423241	0.0211620	+	0.999776i	$0.493263\pi$
$618$	−36.4373	−1.46572
$619$	−0.0534770	−0.00214942	−0.00107471	−	0.999999i	$-0.500342\pi$
$619$	−0.0534770	−0.00214942	−0.00107471	+	0.999999i	$0.500342\pi$
$620$	−1.93098	−0.0775501
$621$	−46.2003	−1.85396
$622$	27.3837	1.09798
$623$	0	0
$624$	26.3520	1.05493
$625$	10.6218	0.424871
$626$	−5.95569	−0.238037
$627$	−30.7596	−1.22842
$628$	45.6250	1.82063
$629$	−29.0955	−1.16011
$630$	0	0
$631$	37.0619	1.47541	0.737706	−	0.675122i	$-0.235909\pi$
$631$	37.0619	1.47541	0.737706	+	0.675122i	$0.235909\pi$
$632$	−52.0922	−2.07212
$633$	20.2781	0.805981
$634$	51.4574	2.04363
$635$	−1.27080	−0.0504300
$636$	4.46809	0.177171
$637$	0	0
$638$	3.44728	0.136479
$639$	−15.0562	−0.595614
$640$	18.1613	0.717887
$641$	−18.9766	−0.749532	−0.374766	−	0.927119i	$-0.622277\pi$
$641$	−18.9766	−0.749532	−0.374766	+	0.927119i	$0.622277\pi$
$642$	20.3499	0.803146
$643$	21.9771	0.866693	0.433346	−	0.901227i	$-0.357333\pi$
$643$	21.9771	0.866693	0.433346	+	0.901227i	$0.357333\pi$
$644$	0	0
$645$	−12.6152	−0.496724
$646$	−76.8689	−3.02437
$647$	−36.3748	−1.43004	−0.715020	−	0.699104i	$-0.753582\pi$
$647$	−36.3748	−1.43004	−0.715020	+	0.699104i	$0.753582\pi$
$648$	26.4051	1.03729
$649$	−40.7912	−1.60119
$650$	−37.0493	−1.45319
$651$	0	0
$652$	59.2985	2.32231
$653$	−25.3274	−0.991138	−0.495569	−	0.868569i	$-0.665040\pi$
$653$	−25.3274	−0.991138	−0.495569	+	0.868569i	$0.665040\pi$
$654$	−14.1410	−0.552957
$655$	−10.4930	−0.409995
$656$	−4.97311	−0.194167
$657$	8.48294	0.330951
$658$	0	0
$659$	7.76844	0.302615	0.151308	−	0.988487i	$-0.451652\pi$
$659$	7.76844	0.302615	0.151308	+	0.988487i	$0.451652\pi$
$660$	31.2361	1.21586
$661$	0.350738	0.0136421	0.00682107	−	0.999977i	$-0.497829\pi$
$661$	0.350738	0.0136421	0.00682107	+	0.999977i	$0.497829\pi$
$662$	−20.8634	−0.810879
$663$	−39.5153	−1.53465
$664$	51.8974	2.01401
$665$	0	0
$666$	9.81584	0.380356
$667$	−2.15931	−0.0836088
$668$	−67.9677	−2.62975
$669$	−18.3879	−0.710919
$670$	−3.37669	−0.130453
$671$	−22.8127	−0.880675
$672$	0	0
$673$	−10.3135	−0.397555	−0.198778	−	0.980045i	$-0.563697\pi$
$673$	−10.3135	−0.397555	−0.198778	+	0.980045i	$0.563697\pi$
$674$	10.1402	0.390584
$675$	−22.4621	−0.864565
$676$	4.72716	0.181814
$677$	2.23553	0.0859185	0.0429592	−	0.999077i	$-0.486321\pi$
$677$	2.23553	0.0859185	0.0429592	+	0.999077i	$0.486321\pi$
$678$	−28.3680	−1.08947
$679$	0	0
$680$	40.5132	1.55361
$681$	41.3245	1.58356
$682$	−5.96884	−0.228559
$683$	34.4761	1.31919	0.659595	−	0.751621i	$-0.270728\pi$
$683$	34.4761	1.31919	0.659595	+	0.751621i	$0.270728\pi$
$684$	17.5105	0.669530
$685$	−10.9546	−0.418552
$686$	0	0
$687$	10.5842	0.403811
$688$	43.8805	1.67293
$689$	2.86683	0.109218
$690$	−28.9767	−1.10313
$691$	−9.76177	−0.371355	−0.185678	−	0.982611i	$-0.559448\pi$
$691$	−9.76177	−0.371355	−0.185678	+	0.982611i	$0.559448\pi$
$692$	−3.52624	−0.134048
$693$	0	0
$694$	−49.3829	−1.87455
$695$	10.8801	0.412706
$696$	1.99537	0.0756343
$697$	7.45725	0.282463
$698$	62.4504	2.36378
$699$	23.2386	0.878966
$700$	0	0
$701$	−17.6354	−0.666081	−0.333041	−	0.942913i	$-0.608075\pi$
$701$	−17.6354	−0.666081	−0.333041	+	0.942913i	$0.608075\pi$
$702$	52.7794	1.99203
$703$	−16.2069	−0.611253
$704$	31.0008	1.16839
$705$	9.06851	0.341540
$706$	−33.7602	−1.27058
$707$	0	0
$708$	−45.4929	−1.70973
$709$	15.4989	0.582074	0.291037	−	0.956712i	$-0.406000\pi$
$709$	15.4989	0.582074	0.291037	+	0.956712i	$0.406000\pi$
$710$	−37.3868	−1.40310
$711$	−9.86179	−0.369846
$712$	16.1614	0.605676
$713$	3.73876	0.140018
$714$	0	0
$715$	20.0418	0.749522
$716$	63.7537	2.38259
$717$	−0.976303	−0.0364607
$718$	−10.5951	−0.395406
$719$	21.2526	0.792589	0.396294	−	0.918123i	$-0.370296\pi$
$719$	21.2526	0.792589	0.396294	+	0.918123i	$0.370296\pi$
$720$	−5.11480	−0.190617
$721$	0	0
$722$	4.33144	0.161200
$723$	11.8820	0.441898
$724$	−31.3277	−1.16428
$725$	−1.04983	−0.0389897
$726$	58.0837	2.15569
$727$	19.3154	0.716369	0.358185	−	0.933651i	$-0.383396\pi$
$727$	19.3154	0.716369	0.358185	+	0.933651i	$0.383396\pi$
$728$	0	0
$729$	28.9154	1.07094
$730$	21.0644	0.779628
$731$	−65.7995	−2.43368
$732$	−25.4422	−0.940369
$733$	1.50305	0.0555165	0.0277582	−	0.999615i	$-0.491163\pi$
$733$	1.50305	0.0555165	0.0277582	+	0.999615i	$0.491163\pi$
$734$	−77.5783	−2.86347
$735$	0	0
$736$	13.3169	0.490869
$737$	−7.04773	−0.259606
$738$	−2.51582	−0.0926087
$739$	43.6440	1.60547	0.802735	−	0.596335i	$-0.203377\pi$
$739$	43.6440	1.60547	0.802735	+	0.596335i	$0.203377\pi$
$740$	16.4579	0.605006
$741$	−22.0109	−0.808591
$742$	0	0
$743$	14.6077	0.535906	0.267953	−	0.963432i	$-0.413653\pi$
$743$	14.6077	0.535906	0.267953	+	0.963432i	$0.413653\pi$
$744$	−3.45491	−0.126663
$745$	−4.64787	−0.170285
$746$	50.2912	1.84129
$747$	9.82491	0.359475
$748$	162.924	5.95709
$749$	0	0
$750$	−31.8277	−1.16218
$751$	−44.0504	−1.60742	−0.803711	−	0.595019i	$-0.797144\pi$
$751$	−44.0504	−1.60742	−0.803711	+	0.595019i	$0.797144\pi$
$752$	−31.5437	−1.15028
$753$	13.1484	0.479156
$754$	2.46680	0.0898356
$755$	15.2773	0.555998
$756$	0	0
$757$	7.37561	0.268071	0.134036	−	0.990977i	$-0.457206\pi$
$757$	7.37561	0.268071	0.134036	+	0.990977i	$0.457206\pi$
$758$	10.4078	0.378028
$759$	−60.4793	−2.19526
$760$	22.5668	0.818583
$761$	49.3445	1.78874	0.894368	−	0.447331i	$-0.147625\pi$
$761$	49.3445	1.78874	0.894368	+	0.447331i	$0.147625\pi$
$762$	−4.38092	−0.158704
$763$	0	0
$764$	77.6223	2.80827
$765$	7.66971	0.277299
$766$	4.58209	0.165558
$767$	−29.1893	−1.05396
$768$	45.9788	1.65912
$769$	14.5456	0.524526	0.262263	−	0.964996i	$-0.415531\pi$
$769$	14.5456	0.524526	0.262263	+	0.964996i	$0.415531\pi$
$770$	0	0
$771$	6.67336	0.240335
$772$	43.0943	1.55100
$773$	−39.1871	−1.40946	−0.704731	−	0.709475i	$-0.748932\pi$
$773$	−39.1871	−1.40946	−0.704731	+	0.709475i	$0.748932\pi$
$774$	22.1985	0.797909
$775$	1.81774	0.0652953
$776$	−1.69843	−0.0609702
$777$	0	0
$778$	36.5145	1.30911
$779$	4.15386	0.148827
$780$	22.3519	0.800327
$781$	−78.0326	−2.79222
$782$	−151.139	−5.40472
$783$	1.49556	0.0534470
$784$	0	0
$785$	11.1316	0.397303
$786$	−36.1733	−1.29026
$787$	47.8452	1.70550	0.852749	−	0.522322i	$-0.174934\pi$
$787$	47.8452	1.70550	0.852749	+	0.522322i	$0.174934\pi$
$788$	−32.3075	−1.15091
$789$	36.8269	1.31107
$790$	−24.4883	−0.871254
$791$	0	0
$792$	−28.5270	−1.01366
$793$	−16.3243	−0.579692
$794$	32.4488	1.15157
$795$	1.09013	0.0386628
$796$	−62.1198	−2.20178
$797$	−26.1138	−0.924998	−0.462499	−	0.886620i	$-0.653047\pi$
$797$	−26.1138	−0.924998	−0.462499	+	0.886620i	$0.653047\pi$
$798$	0	0
$799$	47.3003	1.67336
$800$	6.47455	0.228910
$801$	3.05959	0.108105
$802$	−82.7170	−2.92084
$803$	43.9650	1.55149
$804$	−7.86007	−0.277203
$805$	0	0
$806$	−4.27118	−0.150446
$807$	−9.35610	−0.329350
$808$	−33.2187	−1.16863
$809$	32.8565	1.15517	0.577587	−	0.816329i	$-0.303994\pi$
$809$	32.8565	1.15517	0.577587	+	0.816329i	$0.303994\pi$
$810$	12.4129	0.436144
$811$	−27.7057	−0.972879	−0.486439	−	0.873714i	$-0.661705\pi$
$811$	−27.7057	−0.972879	−0.486439	+	0.873714i	$0.661705\pi$
$812$	0	0
$813$	−21.0391	−0.737873
$814$	50.8730	1.78310
$815$	14.4677	0.506780
$816$	52.2656	1.82966
$817$	−36.6518	−1.28228
$818$	40.5560	1.41801
$819$	0	0
$820$	−4.21821	−0.147306
$821$	−37.3553	−1.30371	−0.651855	−	0.758344i	$-0.726009\pi$
$821$	−37.3553	−1.30371	−0.651855	+	0.758344i	$0.726009\pi$
$822$	−37.7645	−1.31719
$823$	36.8291	1.28378	0.641891	−	0.766796i	$-0.278150\pi$
$823$	36.8291	1.28378	0.641891	+	0.766796i	$0.278150\pi$
$824$	55.7946	1.94370
$825$	−29.4044	−1.02373
$826$	0	0
$827$	−15.8549	−0.551330	−0.275665	−	0.961254i	$-0.588898\pi$
$827$	−15.8549	−0.551330	−0.275665	+	0.961254i	$0.588898\pi$
$828$	34.4290	1.19649
$829$	31.4052	1.09075	0.545374	−	0.838193i	$-0.316388\pi$
$829$	31.4052	1.09075	0.545374	+	0.838193i	$0.316388\pi$
$830$	24.3967	0.846822
$831$	−21.4301	−0.743401
$832$	22.1835	0.769074
$833$	0	0
$834$	37.5079	1.29879
$835$	−16.5828	−0.573871
$836$	90.7524	3.13874
$837$	−2.58951	−0.0895065
$838$	−36.1225	−1.24783
$839$	−11.1872	−0.386224	−0.193112	−	0.981177i	$-0.561858\pi$
$839$	−11.1872	−0.386224	−0.193112	+	0.981177i	$0.561858\pi$
$840$	0	0
$841$	−28.9301	−0.997590
$842$	39.8148	1.37211
$843$	12.2570	0.422154
$844$	−59.8279	−2.05936
$845$	1.15333	0.0396759
$846$	−15.9575	−0.548631
$847$	0	0
$848$	−3.79187	−0.130213
$849$	28.6158	0.982093
$850$	−73.4821	−2.52042
$851$	−31.8658	−1.09235
$852$	−87.0268	−2.98149
$853$	−11.9114	−0.407840	−0.203920	−	0.978988i	$-0.565368\pi$
$853$	−11.9114	−0.407840	−0.203920	+	0.978988i	$0.565368\pi$
$854$	0	0
$855$	4.27221	0.146106
$856$	−31.1608	−1.06505
$857$	23.1449	0.790615	0.395307	−	0.918549i	$-0.370638\pi$
$857$	23.1449	0.790615	0.395307	+	0.918549i	$0.370638\pi$
$858$	69.0918	2.35876
$859$	18.2362	0.622212	0.311106	−	0.950375i	$-0.399301\pi$
$859$	18.2362	0.622212	0.311106	+	0.950375i	$0.399301\pi$
$860$	37.2196	1.26918
$861$	0	0
$862$	−83.3476	−2.83883
$863$	17.0867	0.581638	0.290819	−	0.956778i	$-0.406072\pi$
$863$	17.0867	0.581638	0.290819	+	0.956778i	$0.406072\pi$
$864$	−9.22346	−0.313789
$865$	−0.860333	−0.0292522
$866$	−58.9130	−2.00195
$867$	−54.4146	−1.84802
$868$	0	0
$869$	−51.1112	−1.73383
$870$	0.938012	0.0318016
$871$	−5.04320	−0.170882
$872$	21.6534	0.733278
$873$	−0.321537	−0.0108824
$874$	−84.1880	−2.84770
$875$	0	0
$876$	49.0325	1.65665
$877$	−10.1529	−0.342840	−0.171420	−	0.985198i	$-0.554836\pi$
$877$	−10.1529	−0.342840	−0.171420	+	0.985198i	$0.554836\pi$
$878$	79.8093	2.69343
$879$	22.2543	0.750618
$880$	−26.5087	−0.893608
$881$	21.9643	0.739997	0.369998	−	0.929032i	$-0.379358\pi$
$881$	21.9643	0.739997	0.369998	+	0.929032i	$0.379358\pi$
$882$	0	0
$883$	1.08924	0.0366558	0.0183279	−	0.999832i	$-0.494166\pi$
$883$	1.08924	0.0366558	0.0183279	+	0.999832i	$0.494166\pi$
$884$	116.585	3.92117
$885$	−11.0994	−0.373101
$886$	−14.7204	−0.494542
$887$	−3.76904	−0.126552	−0.0632760	−	0.997996i	$-0.520155\pi$
$887$	−3.76904	−0.126552	−0.0632760	+	0.997996i	$0.520155\pi$
$888$	29.4465	0.988160
$889$	0	0
$890$	7.59741	0.254666
$891$	25.9078	0.867944
$892$	54.2513	1.81647
$893$	26.3473	0.881680
$894$	−16.0230	−0.535888
$895$	15.5546	0.519934
$896$	0	0
$897$	−43.2777	−1.44500
$898$	−42.5892	−1.42122
$899$	−0.121028	−0.00403652
$900$	16.7390	0.557966
$901$	5.68596	0.189427
$902$	−13.0389	−0.434147
$903$	0	0
$904$	43.4385	1.44474
$905$	−7.64333	−0.254073
$906$	52.6667	1.74973
$907$	−30.8489	−1.02432	−0.512160	−	0.858890i	$-0.671154\pi$
$907$	−30.8489	−1.02432	−0.512160	+	0.858890i	$0.671154\pi$
$908$	−121.923	−4.04615
$909$	−6.28877	−0.208585
$910$	0	0
$911$	34.0614	1.12850	0.564252	−	0.825603i	$-0.309165\pi$
$911$	34.0614	1.12850	0.564252	+	0.825603i	$0.309165\pi$
$912$	29.1131	0.964032
$913$	50.9200	1.68521
$914$	101.780	3.36658
$915$	−6.20738	−0.205210
$916$	−31.2272	−1.03178
$917$	0	0
$918$	104.681	3.45498
$919$	−6.17017	−0.203535	−0.101768	−	0.994808i	$-0.532450\pi$
$919$	−6.17017	−0.203535	−0.101768	+	0.994808i	$0.532450\pi$
$920$	44.3706	1.46286
$921$	17.2246	0.567569
$922$	99.6795	3.28277
$923$	−55.8384	−1.83794
$924$	0	0
$925$	−15.4928	−0.509400
$926$	64.2409	2.11109
$927$	10.5627	0.346924
$928$	−0.431086	−0.0141511
$929$	−47.4777	−1.55769	−0.778846	−	0.627215i	$-0.784195\pi$
$929$	−47.4777	−1.55769	−0.778846	+	0.627215i	$0.784195\pi$
$930$	−1.62413	−0.0532574
$931$	0	0
$932$	−68.5627	−2.24584
$933$	15.5518	0.509143
$934$	−55.2491	−1.80781
$935$	39.7502	1.29997
$936$	−20.4133	−0.667229
$937$	30.9791	1.01204	0.506021	−	0.862521i	$-0.331116\pi$
$937$	30.9791	1.01204	0.506021	+	0.862521i	$0.331116\pi$
$938$	0	0
$939$	−3.38237	−0.110379
$940$	−26.7555	−0.872669
$941$	44.7355	1.45834	0.729168	−	0.684335i	$-0.239907\pi$
$941$	44.7355	1.45834	0.729168	+	0.684335i	$0.239907\pi$
$942$	38.3748	1.25032
$943$	8.16729	0.265964
$944$	38.6078	1.25658
$945$	0	0
$946$	115.049	3.74058
$947$	39.8424	1.29470	0.647352	−	0.762192i	$-0.275877\pi$
$947$	39.8424	1.29470	0.647352	+	0.762192i	$0.275877\pi$
$948$	−57.0024	−1.85135
$949$	31.4604	1.02125
$950$	−40.9312	−1.32798
$951$	29.2238	0.947647
$952$	0	0
$953$	9.16051	0.296738	0.148369	−	0.988932i	$-0.452598\pi$
$953$	9.16051	0.296738	0.148369	+	0.988932i	$0.452598\pi$
$954$	−1.91825	−0.0621057
$955$	18.9383	0.612829
$956$	2.88046	0.0931607
$957$	1.95779	0.0632864
$958$	−73.8709	−2.38666
$959$	0	0
$960$	8.43537	0.272250
$961$	−30.7904	−0.993240
$962$	36.4036	1.17370
$963$	−5.89917	−0.190098
$964$	−35.0565	−1.12909
$965$	10.5141	0.338462
$966$	0	0
$967$	3.43523	0.110469	0.0552347	−	0.998473i	$-0.482409\pi$
$967$	3.43523	0.110469	0.0552347	+	0.998473i	$0.482409\pi$
$968$	−88.9407	−2.85866
$969$	−43.6556	−1.40242
$970$	−0.798424	−0.0256359
$971$	45.3254	1.45456	0.727281	−	0.686340i	$-0.240784\pi$
$971$	45.3254	1.45456	0.727281	+	0.686340i	$0.240784\pi$
$972$	−41.6687	−1.33653
$973$	0	0
$974$	−41.4753	−1.32895
$975$	−21.0411	−0.673855
$976$	21.5916	0.691131
$977$	19.8006	0.633476	0.316738	−	0.948513i	$-0.397412\pi$
$977$	19.8006	0.633476	0.316738	+	0.948513i	$0.397412\pi$
$978$	49.8755	1.59484
$979$	15.8571	0.506794
$980$	0	0
$981$	4.09930	0.130881
$982$	67.2379	2.14565
$983$	40.2660	1.28429	0.642143	−	0.766585i	$-0.278045\pi$
$983$	40.2660	1.28429	0.642143	+	0.766585i	$0.278045\pi$
$984$	−7.54721	−0.240596
$985$	−7.88238	−0.251154
$986$	4.89256	0.155811
$987$	0	0
$988$	64.9404	2.06603
$989$	−72.0646	−2.29152
$990$	−13.4104	−0.426210
$991$	−51.9256	−1.64947	−0.824736	−	0.565518i	$-0.808676\pi$
$991$	−51.9256	−1.64947	−0.824736	+	0.565518i	$0.808676\pi$
$992$	0.746409	0.0236985
$993$	−11.8488	−0.376010
$994$	0	0
$995$	−15.1560	−0.480477
$996$	56.7892	1.79943
$997$	−35.1549	−1.11337	−0.556684	−	0.830725i	$-0.687926\pi$
$997$	−35.1549	−1.11337	−0.556684	+	0.830725i	$0.687926\pi$
$998$	71.3705	2.25919
$999$	22.0706	0.698284

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.r.1.2		17
7.3	odd	6		287.2.e.d.247.16	yes	34
7.5	odd	6		287.2.e.d.165.16	✓	34
7.6	odd	2		2009.2.a.s.1.2		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.16	✓	34	7.5	odd	6
287.2.e.d.247.16	yes	34	7.3	odd	6
2009.2.a.r.1.2		17	1.1	even	1	trivial
2009.2.a.s.1.2		17	7.6	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)

\(f(q)\)	\(=\)	\(q-2.48154 q^{2} -1.40932 q^{3} +4.15802 q^{4} +1.01447 q^{5} +3.49728 q^{6} -5.35521 q^{8} -1.01382 q^{9} +O(q^{10})\)	\(q-2.48154 q^{2} -1.40932 q^{3} +4.15802 q^{4} +1.01447 q^{5} +3.49728 q^{6} -5.35521 q^{8} -1.01382 q^{9} -2.51746 q^{10} -5.25436 q^{11} -5.85999 q^{12} -3.75990 q^{13} -1.42972 q^{15} +4.97311 q^{16} -7.45725 q^{17} +2.51582 q^{18} -4.15386 q^{19} +4.21821 q^{20} +13.0389 q^{22} -8.16729 q^{23} +7.54721 q^{24} -3.97084 q^{25} +9.33034 q^{26} +5.65675 q^{27} +0.264385 q^{29} +3.54790 q^{30} -0.457773 q^{31} -1.63052 q^{32} +7.40507 q^{33} +18.5054 q^{34} -4.21547 q^{36} +3.90164 q^{37} +10.3079 q^{38} +5.29891 q^{39} -5.43273 q^{40} -1.00000 q^{41} +8.82356 q^{43} -21.8477 q^{44} -1.02849 q^{45} +20.2674 q^{46} -6.34286 q^{47} -7.00870 q^{48} +9.85379 q^{50} +10.5096 q^{51} -15.6338 q^{52} -0.762475 q^{53} -14.0374 q^{54} -5.33041 q^{55} +5.85412 q^{57} -0.656081 q^{58} +7.76331 q^{59} -5.94481 q^{60} +4.34168 q^{61} +1.13598 q^{62} -5.90001 q^{64} -3.81433 q^{65} -18.3760 q^{66} +1.34131 q^{67} -31.0074 q^{68} +11.5103 q^{69} +14.8510 q^{71} +5.42920 q^{72} -8.36734 q^{73} -9.68206 q^{74} +5.59619 q^{75} -17.2718 q^{76} -13.1494 q^{78} +9.72739 q^{79} +5.04509 q^{80} -4.93073 q^{81} +2.48154 q^{82} -9.69101 q^{83} -7.56519 q^{85} -21.8960 q^{86} -0.372603 q^{87} +28.1382 q^{88} -3.01789 q^{89} +2.55224 q^{90} -33.9598 q^{92} +0.645149 q^{93} +15.7400 q^{94} -4.21398 q^{95} +2.29793 q^{96} +0.317155 q^{97} +5.32695 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} - q^{3} + 25 q^{4} + q^{5} - 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 17 * q + 3 * q^2 - q^3 + 25 * q^4 + q^5 - 2 * q^6 + 9 * q^8 + 26 * q^9	\( 17 q + 3 q^{2} - q^{3} + 25 q^{4} + q^{5} - 2 q^{6} + 9 q^{8} + 26 q^{9} + 2 q^{10} + 15 q^{11} - 4 q^{12} + 5 q^{13} + 24 q^{15} + 33 q^{16} - 4 q^{17} + 10 q^{18} - 5 q^{19} + 26 q^{20} + 16 q^{22} + 12 q^{23} - 16 q^{24} + 24 q^{25} - 31 q^{26} + 11 q^{27} + 14 q^{29} - 33 q^{30} + 3 q^{31} + 16 q^{32} - 4 q^{33} + 24 q^{34} + 57 q^{36} + 24 q^{37} + 45 q^{39} - 36 q^{40} - 17 q^{41} + 14 q^{43} - 9 q^{44} + 21 q^{45} + 44 q^{46} - 19 q^{47} + 60 q^{48} - 4 q^{50} + 2 q^{51} + 25 q^{52} + 4 q^{53} - 68 q^{54} - 9 q^{55} - 12 q^{57} - q^{58} + 27 q^{59} + 66 q^{60} + q^{61} + 23 q^{62} + 75 q^{64} + 22 q^{65} + 16 q^{66} + 49 q^{67} - 45 q^{68} - 12 q^{69} + 40 q^{71} - 23 q^{72} + 14 q^{73} + 33 q^{74} - 27 q^{75} + 9 q^{76} - 12 q^{78} + 61 q^{79} + 82 q^{80} + 53 q^{81} - 3 q^{82} + 18 q^{83} - 13 q^{85} - 4 q^{86} + 17 q^{87} + 74 q^{88} - 18 q^{89} + 20 q^{90} + 28 q^{92} - 36 q^{93} + 5 q^{94} + 20 q^{95} - 148 q^{96} - 26 q^{97} + 38 q^{99}+O(q^{100}) \) 17 * q + 3 * q^2 - q^3 + 25 * q^4 + q^5 - 2 * q^6 + 9 * q^8 + 26 * q^9 + 2 * q^10 + 15 * q^11 - 4 * q^12 + 5 * q^13 + 24 * q^15 + 33 * q^16 - 4 * q^17 + 10 * q^18 - 5 * q^19 + 26 * q^20 + 16 * q^22 + 12 * q^23 - 16 * q^24 + 24 * q^25 - 31 * q^26 + 11 * q^27 + 14 * q^29 - 33 * q^30 + 3 * q^31 + 16 * q^32 - 4 * q^33 + 24 * q^34 + 57 * q^36 + 24 * q^37 + 45 * q^39 - 36 * q^40 - 17 * q^41 + 14 * q^43 - 9 * q^44 + 21 * q^45 + 44 * q^46 - 19 * q^47 + 60 * q^48 - 4 * q^50 + 2 * q^51 + 25 * q^52 + 4 * q^53 - 68 * q^54 - 9 * q^55 - 12 * q^57 - q^58 + 27 * q^59 + 66 * q^60 + q^61 + 23 * q^62 + 75 * q^64 + 22 * q^65 + 16 * q^66 + 49 * q^67 - 45 * q^68 - 12 * q^69 + 40 * q^71 - 23 * q^72 + 14 * q^73 + 33 * q^74 - 27 * q^75 + 9 * q^76 - 12 * q^78 + 61 * q^79 + 82 * q^80 + 53 * q^81 - 3 * q^82 + 18 * q^83 - 13 * q^85 - 4 * q^86 + 17 * q^87 + 74 * q^88 - 18 * q^89 + 20 * q^90 + 28 * q^92 - 36 * q^93 + 5 * q^94 + 20 * q^95 - 148 * q^96 - 26 * q^97 + 38 * q^99

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