LMFDB - Embedded newform 2009.2.a.n.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$16.0419457661$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.633117.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 4x^{2} + 6x - 3 $ x^5 - x^4 - 6x^3 + 4x^2 + 6*x - 3
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			1.5
Root			$-2.03121$ 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)

$f(q)$	$=$	$q+2.03121 q^{2} -3.03121 q^{3} +2.12582 q^{4} +3.82713 q^{5} -6.15703 q^{6} +0.255573 q^{8} +6.18825 q^{9} +O(q^{10})$	\(q+2.03121 q^{2} -3.03121 q^{3} +2.12582 q^{4} +3.82713 q^{5} -6.15703 q^{6} +0.255573 q^{8} +6.18825 q^{9} +7.77372 q^{10} -5.96294 q^{11} -6.44382 q^{12} -1.44574 q^{13} -11.6009 q^{15} -3.73252 q^{16} -6.06148 q^{17} +12.5696 q^{18} +0.0743284 q^{19} +8.13581 q^{20} -12.1120 q^{22} -4.43383 q^{23} -0.774695 q^{24} +9.64695 q^{25} -2.93660 q^{26} -9.66425 q^{27} -1.92662 q^{29} -23.5638 q^{30} -1.76471 q^{31} -8.09269 q^{32} +18.0749 q^{33} -12.3122 q^{34} +13.1551 q^{36} +0.497233 q^{37} +0.150977 q^{38} +4.38234 q^{39} +0.978111 q^{40} +1.00000 q^{41} +4.10393 q^{43} -12.6762 q^{44} +23.6832 q^{45} -9.00606 q^{46} +2.92536 q^{47} +11.3141 q^{48} +19.5950 q^{50} +18.3736 q^{51} -3.07338 q^{52} +3.08431 q^{53} -19.6301 q^{54} -22.8210 q^{55} -0.225305 q^{57} -3.91337 q^{58} -11.4408 q^{59} -24.6614 q^{60} -2.94851 q^{61} -3.58450 q^{62} -8.97293 q^{64} -5.53303 q^{65} +36.7140 q^{66} -1.12488 q^{67} -12.8856 q^{68} +13.4399 q^{69} +5.87671 q^{71} +1.58155 q^{72} -15.7737 q^{73} +1.00999 q^{74} -29.2420 q^{75} +0.158009 q^{76} +8.90146 q^{78} -14.5736 q^{79} -14.2849 q^{80} +10.7297 q^{81} +2.03121 q^{82} +14.4941 q^{83} -23.1981 q^{85} +8.33596 q^{86} +5.83998 q^{87} -1.52396 q^{88} -0.670099 q^{89} +48.1057 q^{90} -9.42555 q^{92} +5.34921 q^{93} +5.94203 q^{94} +0.284465 q^{95} +24.5307 q^{96} +10.5587 q^{97} -36.9002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9}+O(q^{10}) $ 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9	$ 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9} + 2 q^{11} + 2 q^{12} - 5 q^{13} - 5 q^{15} - q^{16} - 13 q^{17} + 21 q^{18} + 23 q^{20} + q^{22} + 2 q^{23} - 2 q^{24} + 22 q^{25} - 10 q^{27} - 5 q^{29} - 33 q^{30} - 17 q^{31} - 12 q^{32} - 3 q^{33} + 8 q^{34} + 15 q^{36} - 7 q^{37} + 3 q^{38} + 5 q^{39} - 7 q^{40} + 5 q^{41} + q^{43} - 47 q^{44} + 23 q^{45} - 24 q^{46} - 9 q^{47} + 19 q^{48} + 2 q^{50} + 5 q^{51} - 20 q^{52} + 5 q^{53} - 2 q^{54} - 33 q^{55} - 3 q^{57} - 27 q^{58} - 7 q^{59} - 16 q^{60} - 22 q^{61} + 28 q^{62} - 3 q^{64} - 31 q^{65} + 42 q^{66} - 3 q^{67} - 17 q^{68} + 22 q^{69} - 24 q^{71} - 12 q^{72} - 40 q^{73} - 5 q^{74} - 24 q^{75} + 19 q^{76} + 30 q^{78} - 42 q^{79} - 24 q^{80} + 9 q^{81} - q^{82} + 12 q^{83} - 23 q^{85} + 16 q^{86} + 32 q^{87} + 26 q^{88} - 8 q^{89} + 59 q^{90} + 12 q^{92} - 11 q^{93} + 23 q^{94} - 17 q^{95} + 17 q^{96} - 16 q^{97} - 45 q^{99}+O(q^{100}) $ 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9 + 2 * q^11 + 2 * q^12 - 5 * q^13 - 5 * q^15 - q^16 - 13 * q^17 + 21 * q^18 + 23 * q^20 + q^22 + 2 * q^23 - 2 * q^24 + 22 * q^25 - 10 * q^27 - 5 * q^29 - 33 * q^30 - 17 * q^31 - 12 * q^32 - 3 * q^33 + 8 * q^34 + 15 * q^36 - 7 * q^37 + 3 * q^38 + 5 * q^39 - 7 * q^40 + 5 * q^41 + q^43 - 47 * q^44 + 23 * q^45 - 24 * q^46 - 9 * q^47 + 19 * q^48 + 2 * q^50 + 5 * q^51 - 20 * q^52 + 5 * q^53 - 2 * q^54 - 33 * q^55 - 3 * q^57 - 27 * q^58 - 7 * q^59 - 16 * q^60 - 22 * q^61 + 28 * q^62 - 3 * q^64 - 31 * q^65 + 42 * q^66 - 3 * q^67 - 17 * q^68 + 22 * q^69 - 24 * q^71 - 12 * q^72 - 40 * q^73 - 5 * q^74 - 24 * q^75 + 19 * q^76 + 30 * q^78 - 42 * q^79 - 24 * q^80 + 9 * q^81 - q^82 + 12 * q^83 - 23 * q^85 + 16 * q^86 + 32 * q^87 + 26 * q^88 - 8 * q^89 + 59 * q^90 + 12 * q^92 - 11 * q^93 + 23 * q^94 - 17 * q^95 + 17 * q^96 - 16 * q^97 - 45 * 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 $

$2$	2.03121	1.43628	0.718142	−	0.695897i	$-0.244993\pi$
$2$	2.03121	1.43628	0.718142	+	0.695897i	$0.244993\pi$
$3$	−3.03121	−1.75007	−0.875036	−	0.484059i	$-0.839162\pi$
$3$	−3.03121	−1.75007	−0.875036	+	0.484059i	$0.839162\pi$
$4$	2.12582	1.06291
$5$	3.82713	1.71155	0.855773	−	0.517351i	$-0.173082\pi$
$5$	3.82713	1.71155	0.855773	+	0.517351i	$0.173082\pi$
$6$	−6.15703	−2.51360
$7$	0	0
$7$	0	0
$8$	0.255573	0.0903586
$9$	6.18825	2.06275
$10$	7.77372	2.45827
$11$	−5.96294	−1.79789	−0.898947	−	0.438057i	$-0.855667\pi$
$11$	−5.96294	−1.79789	−0.898947	+	0.438057i	$0.855667\pi$
$12$	−6.44382	−1.86017
$13$	−1.44574	−0.400976	−0.200488	−	0.979696i	$-0.564253\pi$
$13$	−1.44574	−0.400976	−0.200488	+	0.979696i	$0.564253\pi$
$14$	0	0
$15$	−11.6009	−2.99533
$16$	−3.73252	−0.933131
$17$	−6.06148	−1.47012	−0.735062	−	0.677999i	$-0.762847\pi$
$17$	−6.06148	−1.47012	−0.735062	+	0.677999i	$0.762847\pi$
$18$	12.5696	2.96269
$19$	0.0743284	0.0170521	0.00852605	−	0.999964i	$-0.497286\pi$
$19$	0.0743284	0.0170521	0.00852605	+	0.999964i	$0.497286\pi$
$20$	8.13581	1.81922
$21$	0	0
$22$	−12.1120	−2.58229
$23$	−4.43383	−0.924518	−0.462259	−	0.886745i	$-0.652961\pi$
$23$	−4.43383	−0.924518	−0.462259	+	0.886745i	$0.652961\pi$
$24$	−0.774695	−0.158134
$25$	9.64695	1.92939
$26$	−2.93660	−0.575915
$27$	−9.66425	−1.85989
$28$	0	0
$29$	−1.92662	−0.357764	−0.178882	−	0.983871i	$-0.557248\pi$
$29$	−1.92662	−0.357764	−0.178882	+	0.983871i	$0.557248\pi$
$30$	−23.5638	−4.30214
$31$	−1.76471	−0.316951	−0.158476	−	0.987363i	$-0.550658\pi$
$31$	−1.76471	−0.316951	−0.158476	+	0.987363i	$0.550658\pi$
$32$	−8.09269	−1.43060
$33$	18.0749	3.14644
$34$	−12.3122	−2.11152
$35$	0	0
$36$	13.1551	2.19252
$37$	0.497233	0.0817446	0.0408723	−	0.999164i	$-0.486986\pi$
$37$	0.497233	0.0817446	0.0408723	+	0.999164i	$0.486986\pi$
$38$	0.150977	0.0244917
$39$	4.38234	0.701736
$40$	0.978111	0.154653
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	4.10393	0.625844	0.312922	−	0.949779i	$-0.398692\pi$
$43$	4.10393	0.625844	0.312922	+	0.949779i	$0.398692\pi$
$44$	−12.6762	−1.91100
$45$	23.6832	3.53049
$46$	−9.00606	−1.32787
$47$	2.92536	0.426708	0.213354	−	0.976975i	$-0.431561\pi$
$47$	2.92536	0.426708	0.213354	+	0.976975i	$0.431561\pi$
$48$	11.3141	1.63305
$49$	0	0
$50$	19.5950	2.77115
$51$	18.3736	2.57282
$52$	−3.07338	−0.426202
$53$	3.08431	0.423663	0.211832	−	0.977306i	$-0.432057\pi$
$53$	3.08431	0.423663	0.211832	+	0.977306i	$0.432057\pi$
$54$	−19.6301	−2.67132
$55$	−22.8210	−3.07718
$56$	0	0
$57$	−0.225305	−0.0298424
$58$	−3.91337	−0.513850
$59$	−11.4408	−1.48947	−0.744735	−	0.667360i	$-0.767424\pi$
$59$	−11.4408	−1.48947	−0.744735	+	0.667360i	$0.767424\pi$
$60$	−24.6614	−3.18377
$61$	−2.94851	−0.377517	−0.188759	−	0.982023i	$-0.560446\pi$
$61$	−2.94851	−0.377517	−0.188759	+	0.982023i	$0.560446\pi$
$62$	−3.58450	−0.455232
$63$	0	0
$64$	−8.97293	−1.12162
$65$	−5.53303	−0.686288
$66$	36.7140	4.51919
$67$	−1.12488	−0.137426	−0.0687129	−	0.997636i	$-0.521889\pi$
$67$	−1.12488	−0.137426	−0.0687129	+	0.997636i	$0.521889\pi$
$68$	−12.8856	−1.56261
$69$	13.4399	1.61797
$70$	0	0
$71$	5.87671	0.697437	0.348719	−	0.937227i	$-0.386617\pi$
$71$	5.87671	0.697437	0.348719	+	0.937227i	$0.386617\pi$
$72$	1.58155	0.186387
$73$	−15.7737	−1.84617	−0.923087	−	0.384591i	$-0.874343\pi$
$73$	−15.7737	−1.84617	−0.923087	+	0.384591i	$0.874343\pi$
$74$	1.00999	0.117408
$75$	−29.2420	−3.37657
$76$	0.158009	0.0181249
$77$	0	0
$78$	8.90146	1.00789
$79$	−14.5736	−1.63965	−0.819827	−	0.572611i	$-0.805931\pi$
$79$	−14.5736	−1.63965	−0.819827	+	0.572611i	$0.805931\pi$
$80$	−14.2849	−1.59710
$81$	10.7297	1.19218
$82$	2.03121	0.224310
$83$	14.4941	1.59093	0.795465	−	0.606000i	$-0.207227\pi$
$83$	14.4941	1.59093	0.795465	+	0.606000i	$0.207227\pi$
$84$	0	0
$85$	−23.1981	−2.51619
$86$	8.33596	0.898890
$87$	5.83998	0.626112
$88$	−1.52396	−0.162455
$89$	−0.670099	−0.0710303	−0.0355152	−	0.999369i	$-0.511307\pi$
$89$	−0.670099	−0.0710303	−0.0355152	+	0.999369i	$0.511307\pi$
$90$	48.1057	5.07079
$91$	0	0
$92$	−9.42555	−0.982681
$93$	5.34921	0.554687
$94$	5.94203	0.612873
$95$	0.284465	0.0291855
$96$	24.5307	2.50365
$97$	10.5587	1.07207	0.536036	−	0.844195i	$-0.319921\pi$
$97$	10.5587	1.07207	0.536036	+	0.844195i	$0.319921\pi$
$98$	0	0
$99$	−36.9002	−3.70861
$100$	20.5077	2.05077
$101$	3.20947	0.319355	0.159677	−	0.987169i	$-0.448955\pi$
$101$	3.20947	0.319355	0.159677	+	0.987169i	$0.448955\pi$
$102$	37.3207	3.69530
$103$	−5.79008	−0.570513	−0.285257	−	0.958451i	$-0.592079\pi$
$103$	−5.79008	−0.570513	−0.285257	+	0.958451i	$0.592079\pi$
$104$	−0.369491	−0.0362316
$105$	0	0
$106$	6.26490	0.608500
$107$	−5.90146	−0.570516	−0.285258	−	0.958451i	$-0.592079\pi$
$107$	−5.90146	−0.570516	−0.285258	+	0.958451i	$0.592079\pi$
$108$	−20.5445	−1.97689
$109$	−13.4426	−1.28756	−0.643782	−	0.765209i	$-0.722636\pi$
$109$	−13.4426	−1.28756	−0.643782	+	0.765209i	$0.722636\pi$
$110$	−46.3542	−4.41970
$111$	−1.50722	−0.143059
$112$	0	0
$113$	6.01283	0.565639	0.282820	−	0.959173i	$-0.408730\pi$
$113$	6.01283	0.565639	0.282820	+	0.959173i	$0.408730\pi$
$114$	−0.457643	−0.0428622
$115$	−16.9689	−1.58236
$116$	−4.09564	−0.380271
$117$	−8.94659	−0.827112
$118$	−23.2388	−2.13930
$119$	0	0
$120$	−2.96486	−0.270654
$121$	24.5567	2.23242
$122$	−5.98904	−0.542222
$123$	−3.03121	−0.273315
$124$	−3.75146	−0.336891
$125$	17.7845	1.59070
$126$	0	0
$127$	−6.27284	−0.556625	−0.278312	−	0.960491i	$-0.589775\pi$
$127$	−6.27284	−0.556625	−0.278312	+	0.960491i	$0.589775\pi$
$128$	−2.04053	−0.180360
$129$	−12.4399	−1.09527
$130$	−11.2388	−0.985705
$131$	−12.0382	−1.05178	−0.525892	−	0.850551i	$-0.676268\pi$
$131$	−12.0382	−1.05178	−0.525892	+	0.850551i	$0.676268\pi$
$132$	38.4241	3.34439
$133$	0	0
$134$	−2.28487	−0.197382
$135$	−36.9864	−3.18328
$136$	−1.54915	−0.132838
$137$	6.46697	0.552510	0.276255	−	0.961084i	$-0.410907\pi$
$137$	6.46697	0.552510	0.276255	+	0.961084i	$0.410907\pi$
$138$	27.2993	2.32387
$139$	8.66331	0.734812	0.367406	−	0.930061i	$-0.380246\pi$
$139$	8.66331	0.734812	0.367406	+	0.930061i	$0.380246\pi$
$140$	0	0
$141$	−8.86739	−0.746769
$142$	11.9368	1.00172
$143$	8.62085	0.720912
$144$	−23.0978	−1.92481
$145$	−7.37342	−0.612329
$146$	−32.0398	−2.65163
$147$	0	0
$148$	1.05703	0.0868872
$149$	8.01997	0.657022	0.328511	−	0.944500i	$-0.393453\pi$
$149$	8.01997	0.657022	0.328511	+	0.944500i	$0.393453\pi$
$150$	−59.3966	−4.84971
$151$	−4.83256	−0.393268	−0.196634	−	0.980477i	$-0.563001\pi$
$151$	−4.83256	−0.393268	−0.196634	+	0.980477i	$0.563001\pi$
$152$	0.0189963	0.00154080
$153$	−37.5099	−3.03250
$154$	0	0
$155$	−6.75378	−0.542477
$156$	9.31608	0.745883
$157$	10.2117	0.814982	0.407491	−	0.913209i	$-0.366404\pi$
$157$	10.2117	0.814982	0.407491	+	0.913209i	$0.366404\pi$
$158$	−29.6020	−2.35501
$159$	−9.34921	−0.741441
$160$	−30.9718	−2.44854
$161$	0	0
$162$	21.7942	1.71232
$163$	−19.2954	−1.51133	−0.755665	−	0.654958i	$-0.772686\pi$
$163$	−19.2954	−1.51133	−0.755665	+	0.654958i	$0.772686\pi$
$164$	2.12582	0.165999
$165$	69.1752	5.38528
$166$	29.4405	2.28503
$167$	−2.42397	−0.187572	−0.0937861	−	0.995592i	$-0.529897\pi$
$167$	−2.42397	−0.187572	−0.0937861	+	0.995592i	$0.529897\pi$
$168$	0	0
$169$	−10.9098	−0.839218
$170$	−47.1202	−3.61396
$171$	0.459963	0.0351742
$172$	8.72423	0.665217
$173$	8.79388	0.668587	0.334293	−	0.942469i	$-0.391502\pi$
$173$	8.79388	0.668587	0.334293	+	0.942469i	$0.391502\pi$
$174$	11.8622	0.899274
$175$	0	0
$176$	22.2568	1.67767
$177$	34.6796	2.60668
$178$	−1.36111	−0.102020
$179$	14.4831	1.08252	0.541259	−	0.840856i	$-0.317948\pi$
$179$	14.4831	1.08252	0.541259	+	0.840856i	$0.317948\pi$
$180$	50.3464	3.75260
$181$	3.07539	0.228592	0.114296	−	0.993447i	$-0.463539\pi$
$181$	3.07539	0.228592	0.114296	+	0.993447i	$0.463539\pi$
$182$	0	0
$183$	8.93755	0.660682
$184$	−1.13317	−0.0835382
$185$	1.90298	0.139910
$186$	10.8654	0.796688
$187$	36.1442	2.64313
$188$	6.21880	0.453552
$189$	0	0
$190$	0.577808	0.0419186
$191$	4.90956	0.355243	0.177622	−	0.984099i	$-0.443160\pi$
$191$	4.90956	0.355243	0.177622	+	0.984099i	$0.443160\pi$
$192$	27.1988	1.96291
$193$	11.3050	0.813754	0.406877	−	0.913483i	$-0.366618\pi$
$193$	11.3050	0.813754	0.406877	+	0.913483i	$0.366618\pi$
$194$	21.4469	1.53980
$195$	16.7718	1.20105
$196$	0	0
$197$	−17.8594	−1.27243	−0.636215	−	0.771512i	$-0.719501\pi$
$197$	−17.8594	−1.27243	−0.636215	+	0.771512i	$0.719501\pi$
$198$	−74.9520	−5.32661
$199$	−13.6330	−0.966419	−0.483209	−	0.875505i	$-0.660529\pi$
$199$	−13.6330	−0.966419	−0.483209	+	0.875505i	$0.660529\pi$
$200$	2.46550	0.174337
$201$	3.40974	0.240505
$202$	6.51912	0.458684
$203$	0	0
$204$	39.0591	2.73468
$205$	3.82713	0.267299
$206$	−11.7609	−0.819419
$207$	−27.4377	−1.90705
$208$	5.39625	0.374163
$209$	−0.443216	−0.0306579
$210$	0	0
$211$	22.4460	1.54525	0.772625	−	0.634863i	$-0.218944\pi$
$211$	22.4460	1.54525	0.772625	+	0.634863i	$0.218944\pi$
$212$	6.55670	0.450316
$213$	−17.8136	−1.22056
$214$	−11.9871	−0.819423
$215$	15.7063	1.07116
$216$	−2.46992	−0.168057
$217$	0	0
$218$	−27.3047	−1.84931
$219$	47.8135	3.23094
$220$	−48.5133	−3.27077
$221$	8.76331	0.589484
$222$	−3.06148	−0.205473
$223$	−4.08663	−0.273661	−0.136831	−	0.990594i	$-0.543692\pi$
$223$	−4.08663	−0.273661	−0.136831	+	0.990594i	$0.543692\pi$
$224$	0	0
$225$	59.6977	3.97985
$226$	12.2133	0.812419
$227$	19.5310	1.29632	0.648158	−	0.761506i	$-0.275540\pi$
$227$	19.5310	1.29632	0.648158	+	0.761506i	$0.275540\pi$
$228$	−0.478959	−0.0317198
$229$	−23.0456	−1.52290	−0.761449	−	0.648225i	$-0.775512\pi$
$229$	−23.0456	−1.52290	−0.761449	+	0.648225i	$0.775512\pi$
$230$	−34.4674	−2.27271
$231$	0	0
$232$	−0.492390	−0.0323270
$233$	7.69494	0.504112	0.252056	−	0.967713i	$-0.418893\pi$
$233$	7.69494	0.504112	0.252056	+	0.967713i	$0.418893\pi$
$234$	−18.1724	−1.18797
$235$	11.1957	0.730330
$236$	−24.3212	−1.58317
$237$	44.1756	2.86951
$238$	0	0
$239$	−12.2279	−0.790960	−0.395480	−	0.918475i	$-0.629422\pi$
$239$	−12.2279	−0.790960	−0.395480	+	0.918475i	$0.629422\pi$
$240$	43.3005	2.79503
$241$	3.68209	0.237184	0.118592	−	0.992943i	$-0.462162\pi$
$241$	3.68209	0.237184	0.118592	+	0.992943i	$0.462162\pi$
$242$	49.8798	3.20640
$243$	−3.53112	−0.226521
$244$	−6.26800	−0.401268
$245$	0	0
$246$	−6.15703	−0.392558
$247$	−0.107459	−0.00683748
$248$	−0.451011	−0.0286393
$249$	−43.9346	−2.78424
$250$	36.1241	2.28469
$251$	27.1519	1.71381	0.856907	−	0.515472i	$-0.172383\pi$
$251$	27.1519	1.71381	0.856907	+	0.515472i	$0.172383\pi$
$252$	0	0
$253$	26.4387	1.66219
$254$	−12.7415	−0.799471
$255$	70.3183	4.40351
$256$	13.8011	0.862568
$257$	4.46344	0.278422	0.139211	−	0.990263i	$-0.455543\pi$
$257$	4.46344	0.278422	0.139211	+	0.990263i	$0.455543\pi$
$258$	−25.2681	−1.57312
$259$	0	0
$260$	−11.7623	−0.729464
$261$	−11.9224	−0.737977
$262$	−24.4522	−1.51066
$263$	16.6595	1.02727	0.513633	−	0.858010i	$-0.328299\pi$
$263$	16.6595	1.02727	0.513633	+	0.858010i	$0.328299\pi$
$264$	4.61946	0.284308
$265$	11.8041	0.725119
$266$	0	0
$267$	2.03121	0.124308
$268$	−2.39129	−0.146071
$269$	−3.43160	−0.209229	−0.104614	−	0.994513i	$-0.533361\pi$
$269$	−3.43160	−0.209229	−0.104614	+	0.994513i	$0.533361\pi$
$270$	−75.1272	−4.57210
$271$	−27.8083	−1.68924	−0.844618	−	0.535370i	$-0.820172\pi$
$271$	−27.8083	−1.68924	−0.844618	+	0.535370i	$0.820172\pi$
$272$	22.6246	1.37182
$273$	0	0
$274$	13.1358	0.793561
$275$	−57.5242	−3.46884
$276$	28.5708	1.71976
$277$	−13.5938	−0.816774	−0.408387	−	0.912809i	$-0.633909\pi$
$277$	−13.5938	−0.816774	−0.408387	+	0.912809i	$0.633909\pi$
$278$	17.5970	1.05540
$279$	−10.9205	−0.653791
$280$	0	0
$281$	2.37494	0.141677	0.0708384	−	0.997488i	$-0.477433\pi$
$281$	2.37494	0.141677	0.0708384	+	0.997488i	$0.477433\pi$
$282$	−18.0115	−1.07257
$283$	22.9301	1.36305	0.681526	−	0.731794i	$-0.261317\pi$
$283$	22.9301	1.36305	0.681526	+	0.731794i	$0.261317\pi$
$284$	12.4928	0.741314
$285$	−0.862273	−0.0510767
$286$	17.5108	1.03543
$287$	0	0
$288$	−50.0796	−2.95097
$289$	19.7415	1.16127
$290$	−14.9770	−0.879478
$291$	−32.0056	−1.87620
$292$	−33.5321	−1.96232
$293$	7.30314	0.426654	0.213327	−	0.976981i	$-0.431570\pi$
$293$	7.30314	0.426654	0.213327	+	0.976981i	$0.431570\pi$
$294$	0	0
$295$	−43.7856	−2.54930
$296$	0.127079	0.00738632
$297$	57.6274	3.34388
$298$	16.2903	0.943670
$299$	6.41016	0.370709
$300$	−62.1632	−3.58900
$301$	0	0
$302$	−9.81595	−0.564845
$303$	−9.72860	−0.558893
$304$	−0.277433	−0.0159118
$305$	−11.2843	−0.646139
$306$	−76.1906	−4.35553
$307$	−16.2292	−0.926247	−0.463124	−	0.886294i	$-0.653271\pi$
$307$	−16.2292	−0.926247	−0.463124	+	0.886294i	$0.653271\pi$
$308$	0	0
$309$	17.5509	0.998439
$310$	−13.7184	−0.779150
$311$	−24.8162	−1.40720	−0.703599	−	0.710598i	$-0.748425\pi$
$311$	−24.8162	−1.40720	−0.703599	+	0.710598i	$0.748425\pi$
$312$	1.12001	0.0634079
$313$	−1.00459	−0.0567828	−0.0283914	−	0.999597i	$-0.509038\pi$
$313$	−1.00459	−0.0567828	−0.0283914	+	0.999597i	$0.509038\pi$
$314$	20.7421	1.17055
$315$	0	0
$316$	−30.9808	−1.74281
$317$	−29.9777	−1.68372	−0.841859	−	0.539697i	$-0.818539\pi$
$317$	−29.9777	−1.68372	−0.841859	+	0.539697i	$0.818539\pi$
$318$	−18.9902	−1.06492
$319$	11.4883	0.643221
$320$	−34.3406	−1.91970
$321$	17.8886	0.998443
$322$	0	0
$323$	−0.450540	−0.0250687
$324$	22.8094	1.26719
$325$	−13.9470	−0.773639
$326$	−39.1930	−2.17070
$327$	40.7473	2.25333
$328$	0.255573	0.0141116
$329$	0	0
$330$	140.510	7.73480
$331$	−25.1471	−1.38221	−0.691106	−	0.722754i	$-0.742876\pi$
$331$	−25.1471	−1.38221	−0.691106	+	0.722754i	$0.742876\pi$
$332$	30.8118	1.69102
$333$	3.07700	0.168619
$334$	−4.92359	−0.269407
$335$	−4.30506	−0.235210
$336$	0	0
$337$	1.81608	0.0989285	0.0494642	−	0.998776i	$-0.484249\pi$
$337$	1.81608	0.0989285	0.0494642	+	0.998776i	$0.484249\pi$
$338$	−22.1602	−1.20536
$339$	−18.2262	−0.989909
$340$	−49.3150	−2.67448
$341$	10.5229	0.569845
$342$	0.934282	0.0505202
$343$	0	0
$344$	1.04885	0.0565504
$345$	51.4363	2.76924
$346$	17.8622	0.960280
$347$	23.5712	1.26537	0.632685	−	0.774409i	$-0.281953\pi$
$347$	23.5712	1.26537	0.632685	+	0.774409i	$0.281953\pi$
$348$	12.4148	0.665501
$349$	−22.3613	−1.19697	−0.598486	−	0.801133i	$-0.704231\pi$
$349$	−22.3613	−1.19697	−0.598486	+	0.801133i	$0.704231\pi$
$350$	0	0
$351$	13.9720	0.745769
$352$	48.2562	2.57207
$353$	−12.0297	−0.640277	−0.320139	−	0.947371i	$-0.603729\pi$
$353$	−12.0297	−0.640277	−0.320139	+	0.947371i	$0.603729\pi$
$354$	70.4416	3.74393
$355$	22.4910	1.19370
$356$	−1.42451	−0.0754990
$357$	0	0
$358$	29.4182	1.55480
$359$	−29.0810	−1.53483	−0.767417	−	0.641148i	$-0.778459\pi$
$359$	−29.0810	−1.53483	−0.767417	+	0.641148i	$0.778459\pi$
$360$	6.05279	0.319010
$361$	−18.9945	−0.999709
$362$	6.24677	0.328323
$363$	−74.4365	−3.90690
$364$	0	0
$365$	−60.3681	−3.15981
$366$	18.1541	0.948928
$367$	34.9839	1.82615	0.913073	−	0.407796i	$-0.133702\pi$
$367$	34.9839	1.82615	0.913073	+	0.407796i	$0.133702\pi$
$368$	16.5494	0.862697
$369$	6.18825	0.322147
$370$	3.86535	0.200950
$371$	0	0
$372$	11.3715	0.589583
$373$	25.0688	1.29801	0.649006	−	0.760783i	$-0.275185\pi$
$373$	25.0688	1.29801	0.649006	+	0.760783i	$0.275185\pi$
$374$	73.4166	3.79628
$375$	−53.9086	−2.78383
$376$	0.747642	0.0385567
$377$	2.78538	0.143455
$378$	0	0
$379$	16.2692	0.835695	0.417848	−	0.908517i	$-0.362785\pi$
$379$	16.2692	0.835695	0.417848	+	0.908517i	$0.362785\pi$
$380$	0.604722	0.0310216
$381$	19.0143	0.974133
$382$	9.97235	0.510230
$383$	7.88034	0.402667	0.201333	−	0.979523i	$-0.435473\pi$
$383$	7.88034	0.402667	0.201333	+	0.979523i	$0.435473\pi$
$384$	6.18529	0.315642
$385$	0	0
$386$	22.9629	1.16878
$387$	25.3962	1.29096
$388$	22.4459	1.13952
$389$	28.0477	1.42208	0.711038	−	0.703154i	$-0.248225\pi$
$389$	28.0477	1.42208	0.711038	+	0.703154i	$0.248225\pi$
$390$	34.0671	1.72505
$391$	26.8756	1.35916
$392$	0	0
$393$	36.4904	1.84070
$394$	−36.2762	−1.82757
$395$	−55.7750	−2.80634
$396$	−78.4432	−3.94192
$397$	−12.8210	−0.643466	−0.321733	−	0.946830i	$-0.604265\pi$
$397$	−12.8210	−0.643466	−0.321733	+	0.946830i	$0.604265\pi$
$398$	−27.6915	−1.38805
$399$	0	0
$400$	−36.0075	−1.80037
$401$	−1.81684	−0.0907285	−0.0453643	−	0.998971i	$-0.514445\pi$
$401$	−1.81684	−0.0907285	−0.0453643	+	0.998971i	$0.514445\pi$
$402$	6.92591	0.345433
$403$	2.55131	0.127090
$404$	6.82277	0.339446
$405$	41.0638	2.04048
$406$	0	0
$407$	−2.96497	−0.146968
$408$	4.69580	0.232477
$409$	35.2528	1.74314	0.871569	−	0.490273i	$-0.163103\pi$
$409$	35.2528	1.74314	0.871569	+	0.490273i	$0.163103\pi$
$410$	7.77372	0.383917
$411$	−19.6027	−0.966932
$412$	−12.3087	−0.606405
$413$	0	0
$414$	−55.7317	−2.73906
$415$	55.4707	2.72295
$416$	11.6999	0.573636
$417$	−26.2603	−1.28597
$418$	−0.900266	−0.0440334
$419$	−16.1804	−0.790464	−0.395232	−	0.918581i	$-0.629336\pi$
$419$	−16.1804	−0.790464	−0.395232	+	0.918581i	$0.629336\pi$
$420$	0	0
$421$	−8.95139	−0.436264	−0.218132	−	0.975919i	$-0.569996\pi$
$421$	−8.95139	−0.436264	−0.218132	+	0.975919i	$0.569996\pi$
$422$	45.5927	2.21942
$423$	18.1028	0.880191
$424$	0.788266	0.0382816
$425$	−58.4748	−2.83644
$426$	−36.1831	−1.75308
$427$	0	0
$428$	−12.5455	−0.606408
$429$	−26.1316	−1.26165
$430$	31.9028	1.53849
$431$	12.5790	0.605907	0.302954	−	0.953005i	$-0.402027\pi$
$431$	12.5790	0.605907	0.302954	+	0.953005i	$0.402027\pi$
$432$	36.0720	1.73552
$433$	−16.4245	−0.789309	−0.394654	−	0.918830i	$-0.629136\pi$
$433$	−16.4245	−0.789309	−0.394654	+	0.918830i	$0.629136\pi$
$434$	0	0
$435$	22.3504	1.07162
$436$	−28.5765	−1.36857
$437$	−0.329560	−0.0157650
$438$	97.1193	4.64054
$439$	25.2770	1.20640	0.603202	−	0.797589i	$-0.293891\pi$
$439$	25.2770	1.20640	0.603202	+	0.797589i	$0.293891\pi$
$440$	−5.83242	−0.278050
$441$	0	0
$442$	17.8002	0.846667
$443$	−0.450540	−0.0214058	−0.0107029	−	0.999943i	$-0.503407\pi$
$443$	−0.450540	−0.0214058	−0.0107029	+	0.999943i	$0.503407\pi$
$444$	−3.20408	−0.152059
$445$	−2.56456	−0.121572
$446$	−8.30082	−0.393055
$447$	−24.3102	−1.14983
$448$	0	0
$449$	−18.2531	−0.861418	−0.430709	−	0.902491i	$-0.641736\pi$
$449$	−18.2531	−0.861418	−0.430709	+	0.902491i	$0.641736\pi$
$450$	121.259	5.71619
$451$	−5.96294	−0.280784
$452$	12.7822	0.601224
$453$	14.6485	0.688247
$454$	39.6716	1.86188
$455$	0	0
$456$	−0.0575818	−0.00269652
$457$	28.5308	1.33461	0.667307	−	0.744783i	$-0.267447\pi$
$457$	28.5308	1.33461	0.667307	+	0.744783i	$0.267447\pi$
$458$	−46.8105	−2.18731
$459$	58.5797	2.73426
$460$	−36.0728	−1.68190
$461$	7.30314	0.340141	0.170071	−	0.985432i	$-0.445600\pi$
$461$	7.30314	0.340141	0.170071	+	0.985432i	$0.445600\pi$
$462$	0	0
$463$	−16.5369	−0.768535	−0.384268	−	0.923222i	$-0.625546\pi$
$463$	−16.5369	−0.768535	−0.384268	+	0.923222i	$0.625546\pi$
$464$	7.19114	0.333840
$465$	20.4721	0.949373
$466$	15.6301	0.724048
$467$	16.6909	0.772363	0.386181	−	0.922423i	$-0.373794\pi$
$467$	16.6909	0.772363	0.386181	+	0.922423i	$0.373794\pi$
$468$	−19.0189	−0.879147
$469$	0	0
$470$	22.7409	1.04896
$471$	−30.9538	−1.42628
$472$	−2.92396	−0.134586
$473$	−24.4715	−1.12520
$474$	89.7300	4.12143
$475$	0.717043	0.0329002
$476$	0	0
$477$	19.0865	0.873911
$478$	−24.8376	−1.13604
$479$	−7.64133	−0.349141	−0.174571	−	0.984645i	$-0.555854\pi$
$479$	−7.64133	−0.349141	−0.174571	+	0.984645i	$0.555854\pi$
$480$	93.8821	4.28511
$481$	−0.718869	−0.0327776
$482$	7.47911	0.340664
$483$	0	0
$484$	52.2031	2.37287
$485$	40.4095	1.83490
$486$	−7.17245	−0.325349
$487$	−11.6260	−0.526825	−0.263412	−	0.964683i	$-0.584848\pi$
$487$	−11.6260	−0.526825	−0.263412	+	0.964683i	$0.584848\pi$
$488$	−0.753557	−0.0341119
$489$	58.4884	2.64494
$490$	0	0
$491$	25.9788	1.17241	0.586204	−	0.810164i	$-0.300622\pi$
$491$	25.9788	1.17241	0.586204	+	0.810164i	$0.300622\pi$
$492$	−6.44382	−0.290510
$493$	11.6781	0.525957
$494$	−0.218273	−0.00982056
$495$	−141.222	−6.34745
$496$	6.58682	0.295757
$497$	0	0
$498$	−89.2404	−3.99896
$499$	−23.1920	−1.03821	−0.519107	−	0.854709i	$-0.673736\pi$
$499$	−23.1920	−1.03821	−0.519107	+	0.854709i	$0.673736\pi$
$500$	37.8067	1.69077
$501$	7.34756	0.328265
$502$	55.1513	2.46152
$503$	−10.6434	−0.474564	−0.237282	−	0.971441i	$-0.576257\pi$
$503$	−10.6434	−0.474564	−0.237282	+	0.971441i	$0.576257\pi$
$504$	0	0
$505$	12.2831	0.546590
$506$	53.7026	2.38737
$507$	33.0700	1.46869
$508$	−13.3350	−0.591643
$509$	−1.33530	−0.0591860	−0.0295930	−	0.999562i	$-0.509421\pi$
$509$	−1.33530	−0.0591860	−0.0295930	+	0.999562i	$0.509421\pi$
$510$	142.831	6.32468
$511$	0	0
$512$	32.1140	1.41925
$513$	−0.718329	−0.0317150
$514$	9.06619	0.399893
$515$	−22.1594	−0.976460
$516$	−26.4450	−1.16418
$517$	−17.4438	−0.767175
$518$	0	0
$519$	−26.6561	−1.17007
$520$	−1.41409	−0.0620120
$521$	−26.5594	−1.16359	−0.581795	−	0.813335i	$-0.697649\pi$
$521$	−26.5594	−1.16359	−0.581795	+	0.813335i	$0.697649\pi$
$522$	−24.2169	−1.05994
$523$	9.41507	0.411692	0.205846	−	0.978584i	$-0.434005\pi$
$523$	9.41507	0.411692	0.205846	+	0.978584i	$0.434005\pi$
$524$	−25.5911	−1.11795
$525$	0	0
$526$	33.8389	1.47545
$527$	10.6968	0.465958
$528$	−67.4651	−2.93604
$529$	−3.34111	−0.145266
$530$	23.9766	1.04148
$531$	−70.7987	−3.07240
$532$	0	0
$533$	−1.44574	−0.0626219
$534$	4.12582	0.178542
$535$	−22.5857	−0.976464
$536$	−0.287488	−0.0124176
$537$	−43.9013	−1.89448
$538$	−6.97032	−0.300512
$539$	0	0
$540$	−78.6265	−3.38355
$541$	−8.71416	−0.374651	−0.187325	−	0.982298i	$-0.559982\pi$
$541$	−8.71416	−0.374651	−0.187325	+	0.982298i	$0.559982\pi$
$542$	−56.4846	−2.42622
$543$	−9.32217	−0.400052
$544$	49.0537	2.10316
$545$	−51.4465	−2.20373
$546$	0	0
$547$	−16.6541	−0.712079	−0.356040	−	0.934471i	$-0.615873\pi$
$547$	−16.6541	−0.712079	−0.356040	+	0.934471i	$0.615873\pi$
$548$	13.7476	0.587269
$549$	−18.2461	−0.778724
$550$	−116.844	−4.98224
$551$	−0.143202	−0.00610062
$552$	3.43487	0.146198
$553$	0	0
$554$	−27.6119	−1.17312
$555$	−5.76833	−0.244852
$556$	18.4167	0.781040
$557$	8.98351	0.380643	0.190322	−	0.981722i	$-0.439047\pi$
$557$	8.98351	0.380643	0.190322	+	0.981722i	$0.439047\pi$
$558$	−22.1818	−0.939029
$559$	−5.93321	−0.250948
$560$	0	0
$561$	−109.561	−4.62566
$562$	4.82400	0.203488
$563$	6.35931	0.268013	0.134007	−	0.990980i	$-0.457216\pi$
$563$	6.35931	0.268013	0.134007	+	0.990980i	$0.457216\pi$
$564$	−18.8505	−0.793749
$565$	23.0119	0.968118
$566$	46.5759	1.95773
$567$	0	0
$568$	1.50193	0.0630194
$569$	−5.92160	−0.248246	−0.124123	−	0.992267i	$-0.539612\pi$
$569$	−5.92160	−0.248246	−0.124123	+	0.992267i	$0.539612\pi$
$570$	−1.75146	−0.0733606
$571$	45.8163	1.91735	0.958676	−	0.284502i	$-0.0918281\pi$
$571$	45.8163	1.91735	0.958676	+	0.284502i	$0.0918281\pi$
$572$	18.3264	0.766266
$573$	−14.8819	−0.621701
$574$	0	0
$575$	−42.7730	−1.78376
$576$	−55.5267	−2.31361
$577$	−37.9400	−1.57946	−0.789731	−	0.613453i	$-0.789780\pi$
$577$	−37.9400	−1.57946	−0.789731	+	0.613453i	$0.789780\pi$
$578$	40.0992	1.66791
$579$	−34.2679	−1.42413
$580$	−15.6746	−0.650852
$581$	0	0
$582$	−65.0102	−2.69476
$583$	−18.3916	−0.761702
$584$	−4.03133	−0.166818
$585$	−34.2398	−1.41564
$586$	14.8342	0.612796
$587$	−5.81661	−0.240077	−0.120039	−	0.992769i	$-0.538302\pi$
$587$	−5.81661	−0.240077	−0.120039	+	0.992769i	$0.538302\pi$
$588$	0	0
$589$	−0.131168	−0.00540469
$590$	−88.9379	−3.66151
$591$	54.1357	2.22684
$592$	−1.85593	−0.0762784
$593$	16.7778	0.688980	0.344490	−	0.938790i	$-0.388052\pi$
$593$	16.7778	0.688980	0.344490	+	0.938790i	$0.388052\pi$
$594$	117.053	4.80276
$595$	0	0
$596$	17.0490	0.698356
$597$	41.3245	1.69130
$598$	13.0204	0.532444
$599$	−13.8344	−0.565260	−0.282630	−	0.959229i	$-0.591207\pi$
$599$	−13.8344	−0.565260	−0.282630	+	0.959229i	$0.591207\pi$
$600$	−7.47344	−0.305102
$601$	−22.2486	−0.907539	−0.453769	−	0.891119i	$-0.649921\pi$
$601$	−22.2486	−0.907539	−0.453769	+	0.891119i	$0.649921\pi$
$602$	0	0
$603$	−6.96102	−0.283475
$604$	−10.2732	−0.418009
$605$	93.9817	3.82090
$606$	−19.7608	−0.802729
$607$	2.39107	0.0970505	0.0485252	−	0.998822i	$-0.484548\pi$
$607$	2.39107	0.0970505	0.0485252	+	0.998822i	$0.484548\pi$
$608$	−0.601517	−0.0243947
$609$	0	0
$610$	−22.9209	−0.928038
$611$	−4.22931	−0.171099
$612$	−79.7395	−3.22328
$613$	38.0777	1.53795	0.768973	−	0.639282i	$-0.220768\pi$
$613$	38.0777	1.53795	0.768973	+	0.639282i	$0.220768\pi$
$614$	−32.9649	−1.33035
$615$	−11.6009	−0.467792
$616$	0	0
$617$	−22.6988	−0.913819	−0.456910	−	0.889513i	$-0.651044\pi$
$617$	−22.6988	−0.913819	−0.456910	+	0.889513i	$0.651044\pi$
$618$	35.6497	1.43404
$619$	33.3077	1.33875	0.669376	−	0.742924i	$-0.266562\pi$
$619$	33.3077	1.33875	0.669376	+	0.742924i	$0.266562\pi$
$620$	−14.3573	−0.576605
$621$	42.8497	1.71950
$622$	−50.4070	−2.02113
$623$	0	0
$624$	−16.3572	−0.654811
$625$	19.8289	0.793158
$626$	−2.04053	−0.0815562
$627$	1.34348	0.0536535
$628$	21.7083	0.866254
$629$	−3.01397	−0.120175
$630$	0	0
$631$	−5.52118	−0.219795	−0.109897	−	0.993943i	$-0.535052\pi$
$631$	−5.52118	−0.219795	−0.109897	+	0.993943i	$0.535052\pi$
$632$	−3.72461	−0.148157
$633$	−68.0387	−2.70430
$634$	−60.8912	−2.41830
$635$	−24.0070	−0.952689
$636$	−19.8748	−0.788086
$637$	0	0
$638$	23.3352	0.923848
$639$	36.3665	1.43864
$640$	−7.80940	−0.308694
$641$	12.7799	0.504775	0.252387	−	0.967626i	$-0.418784\pi$
$641$	12.7799	0.504775	0.252387	+	0.967626i	$0.418784\pi$
$642$	36.3355	1.43405
$643$	−19.0687	−0.751998	−0.375999	−	0.926620i	$-0.622700\pi$
$643$	−19.0687	−0.751998	−0.375999	+	0.926620i	$0.622700\pi$
$644$	0	0
$645$	−47.6091	−1.87461
$646$	−0.915143	−0.0360058
$647$	−20.9933	−0.825331	−0.412665	−	0.910883i	$-0.635402\pi$
$647$	−20.9933	−0.825331	−0.412665	+	0.910883i	$0.635402\pi$
$648$	2.74221	0.107724
$649$	68.2210	2.67791
$650$	−28.3293	−1.11116
$651$	0	0
$652$	−41.0185	−1.60641
$653$	−36.4523	−1.42649	−0.713244	−	0.700916i	$-0.752775\pi$
$653$	−36.4523	−1.42649	−0.713244	+	0.700916i	$0.752775\pi$
$654$	82.7663	3.23642
$655$	−46.0719	−1.80018
$656$	−3.73252	−0.145731
$657$	−97.6117	−3.80819
$658$	0	0
$659$	−20.9058	−0.814373	−0.407187	−	0.913345i	$-0.633490\pi$
$659$	−20.9058	−0.814373	−0.407187	+	0.913345i	$0.633490\pi$
$660$	147.054	5.72408
$661$	−51.0624	−1.98610	−0.993048	−	0.117709i	$-0.962445\pi$
$661$	−51.0624	−1.98610	−0.993048	+	0.117709i	$0.962445\pi$
$662$	−51.0792	−1.98525
$663$	−26.5635	−1.03164
$664$	3.70428	0.143754
$665$	0	0
$666$	6.25004	0.242184
$667$	8.54230	0.330759
$668$	−5.15293	−0.199373
$669$	12.3875	0.478927
$670$	−8.74449	−0.337829
$671$	17.5818	0.678737
$672$	0	0
$673$	42.4278	1.63547	0.817736	−	0.575594i	$-0.195229\pi$
$673$	42.4278	1.63547	0.817736	+	0.575594i	$0.195229\pi$
$674$	3.68885	0.142089
$675$	−93.2306	−3.58845
$676$	−23.1924	−0.892015
$677$	−15.1486	−0.582209	−0.291105	−	0.956691i	$-0.594023\pi$
$677$	−15.1486	−0.582209	−0.291105	+	0.956691i	$0.594023\pi$
$678$	−37.0212	−1.42179
$679$	0	0
$680$	−5.92880	−0.227359
$681$	−59.2025	−2.26865
$682$	21.3742	0.818459
$683$	8.69113	0.332557	0.166278	−	0.986079i	$-0.446825\pi$
$683$	8.69113	0.332557	0.166278	+	0.986079i	$0.446825\pi$
$684$	0.977799	0.0373871
$685$	24.7499	0.945647
$686$	0	0
$687$	69.8562	2.66518
$688$	−15.3180	−0.583994
$689$	−4.45911	−0.169879
$690$	104.478	3.97741
$691$	−24.8701	−0.946102	−0.473051	−	0.881035i	$-0.656847\pi$
$691$	−24.8701	−0.946102	−0.473051	+	0.881035i	$0.656847\pi$
$692$	18.6942	0.710648
$693$	0	0
$694$	47.8782	1.81743
$695$	33.1556	1.25767
$696$	1.49254	0.0565746
$697$	−6.06148	−0.229595
$698$	−45.4205	−1.71919
$699$	−23.3250	−0.882233
$700$	0	0
$701$	38.5821	1.45723	0.728613	−	0.684926i	$-0.240165\pi$
$701$	38.5821	1.45723	0.728613	+	0.684926i	$0.240165\pi$
$702$	28.3801	1.07114
$703$	0.0369585	0.00139392
$704$	53.5050	2.01655
$705$	−33.9367	−1.27813
$706$	−24.4349	−0.919620
$707$	0	0
$708$	73.7227	2.77067
$709$	13.3306	0.500642	0.250321	−	0.968163i	$-0.419464\pi$
$709$	13.3306	0.500642	0.250321	+	0.968163i	$0.419464\pi$
$710$	45.6839	1.71449
$711$	−90.1848	−3.38220
$712$	−0.171259	−0.00641820
$713$	7.82443	0.293027
$714$	0	0
$715$	32.9932	1.23387
$716$	30.7885	1.15062
$717$	37.0655	1.38424
$718$	−59.0696	−2.20446
$719$	−19.0012	−0.708625	−0.354312	−	0.935127i	$-0.615285\pi$
$719$	−19.0012	−0.708625	−0.354312	+	0.935127i	$0.615285\pi$
$720$	−88.3983	−3.29441
$721$	0	0
$722$	−38.5818	−1.43587
$723$	−11.1612	−0.415090
$724$	6.53774	0.242973
$725$	−18.5860	−0.690266
$726$	−151.196	−5.61142
$727$	−19.0336	−0.705916	−0.352958	−	0.935639i	$-0.614824\pi$
$727$	−19.0336	−0.705916	−0.352958	+	0.935639i	$0.614824\pi$
$728$	0	0
$729$	−21.4854	−0.795756
$730$	−122.620	−4.53839
$731$	−24.8759	−0.920069
$732$	18.9996	0.702247
$733$	−50.7508	−1.87452	−0.937261	−	0.348628i	$-0.886648\pi$
$733$	−50.7508	−1.87452	−0.937261	+	0.348628i	$0.886648\pi$
$734$	71.0598	2.62286
$735$	0	0
$736$	35.8817	1.32262
$737$	6.70758	0.247077
$738$	12.5696	0.462695
$739$	−6.70443	−0.246626	−0.123313	−	0.992368i	$-0.539352\pi$
$739$	−6.70443	−0.246626	−0.123313	+	0.992368i	$0.539352\pi$
$740$	4.04539	0.148712
$741$	0.325732	0.0119661
$742$	0	0
$743$	30.7597	1.12846	0.564232	−	0.825617i	$-0.309173\pi$
$743$	30.7597	1.12846	0.564232	+	0.825617i	$0.309173\pi$
$744$	1.36711	0.0501207
$745$	30.6935	1.12452
$746$	50.9200	1.86432
$747$	89.6928	3.28169
$748$	76.8363	2.80941
$749$	0	0
$750$	−109.500	−3.99837
$751$	−38.8738	−1.41852	−0.709262	−	0.704945i	$-0.750972\pi$
$751$	−38.8738	−1.41852	−0.709262	+	0.704945i	$0.750972\pi$
$752$	−10.9190	−0.398174
$753$	−82.3032	−2.99930
$754$	5.65770	0.206041
$755$	−18.4948	−0.673096
$756$	0	0
$757$	3.89914	0.141717	0.0708583	−	0.997486i	$-0.477426\pi$
$757$	3.89914	0.141717	0.0708583	+	0.997486i	$0.477426\pi$
$758$	33.0463	1.20030
$759$	−80.1413	−2.90894
$760$	0.0727014	0.00263716
$761$	−13.9575	−0.505959	−0.252979	−	0.967472i	$-0.581410\pi$
$761$	−13.9575	−0.505959	−0.252979	+	0.967472i	$0.581410\pi$
$762$	38.6221	1.39913
$763$	0	0
$764$	10.4369	0.377592
$765$	−143.556	−5.19026
$766$	16.0067	0.578344
$767$	16.5405	0.597241
$768$	−41.8340	−1.50956
$769$	−9.40607	−0.339192	−0.169596	−	0.985514i	$-0.554246\pi$
$769$	−9.40607	−0.339192	−0.169596	+	0.985514i	$0.554246\pi$
$770$	0	0
$771$	−13.5296	−0.487258
$772$	24.0325	0.864948
$773$	−6.38151	−0.229527	−0.114764	−	0.993393i	$-0.536611\pi$
$773$	−6.38151	−0.229527	−0.114764	+	0.993393i	$0.536611\pi$
$774$	51.5850	1.85418
$775$	−17.0241	−0.611523
$776$	2.69851	0.0968709
$777$	0	0
$778$	56.9709	2.04250
$779$	0.0743284	0.00266309
$780$	35.6539	1.27661
$781$	−35.0425	−1.25392
$782$	54.5900	1.95214
$783$	18.6193	0.665400
$784$	0	0
$785$	39.0815	1.39488
$786$	74.1197	2.64376
$787$	31.4514	1.12112	0.560561	−	0.828113i	$-0.310586\pi$
$787$	31.4514	1.12112	0.560561	+	0.828113i	$0.310586\pi$
$788$	−37.9659	−1.35248
$789$	−50.4984	−1.79779
$790$	−113.291	−4.03071
$791$	0	0
$792$	−9.43067	−0.335104
$793$	4.26277	0.151375
$794$	−26.0421	−0.924200
$795$	−35.7807	−1.26901
$796$	−28.9814	−1.02722
$797$	12.7701	0.452339	0.226170	−	0.974088i	$-0.427380\pi$
$797$	12.7701	0.452339	0.226170	+	0.974088i	$0.427380\pi$
$798$	0	0
$799$	−17.7320	−0.627313
$800$	−78.0698	−2.76018
$801$	−4.14674	−0.146518
$802$	−3.69038	−0.130312
$803$	94.0578	3.31923
$804$	7.24851	0.255635
$805$	0	0
$806$	5.18225	0.182537
$807$	10.4019	0.366165
$808$	0.820254	0.0288564
$809$	37.8116	1.32939	0.664693	−	0.747117i	$-0.268563\pi$
$809$	37.8116	1.32939	0.664693	+	0.747117i	$0.268563\pi$
$810$	83.4094	2.93071
$811$	29.0566	1.02031	0.510157	−	0.860081i	$-0.329587\pi$
$811$	29.0566	1.02031	0.510157	+	0.860081i	$0.329587\pi$
$812$	0	0
$813$	84.2929	2.95628
$814$	−6.02248	−0.211088
$815$	−73.8460	−2.58671
$816$	−68.5800	−2.40078
$817$	0.305039	0.0106720
$818$	71.6059	2.50364
$819$	0	0
$820$	8.13581	0.284115
$821$	−22.1598	−0.773381	−0.386691	−	0.922209i	$-0.626382\pi$
$821$	−22.1598	−0.773381	−0.386691	+	0.922209i	$0.626382\pi$
$822$	−39.8173	−1.38879
$823$	−44.5895	−1.55429	−0.777147	−	0.629319i	$-0.783334\pi$
$823$	−44.5895	−1.55429	−0.777147	+	0.629319i	$0.783334\pi$
$824$	−1.47978	−0.0515507
$825$	174.368	6.07072
$826$	0	0
$827$	17.7093	0.615814	0.307907	−	0.951416i	$-0.400371\pi$
$827$	17.7093	0.615814	0.307907	+	0.951416i	$0.400371\pi$
$828$	−58.3276	−2.02702
$829$	−29.8270	−1.03594	−0.517968	−	0.855400i	$-0.673311\pi$
$829$	−29.8270	−1.03594	−0.517968	+	0.855400i	$0.673311\pi$
$830$	112.673	3.91093
$831$	41.2058	1.42941
$832$	12.9725	0.449741
$833$	0	0
$834$	−53.3403	−1.84702
$835$	−9.27685	−0.321039
$836$	−0.942199	−0.0325866
$837$	17.0546	0.589493
$838$	−32.8658	−1.13533
$839$	−31.3123	−1.08102	−0.540511	−	0.841337i	$-0.681769\pi$
$839$	−31.3123	−1.08102	−0.540511	+	0.841337i	$0.681769\pi$
$840$	0	0
$841$	−25.2881	−0.872005
$842$	−18.1822	−0.626599
$843$	−7.19894	−0.247945
$844$	47.7163	1.64246
$845$	−41.7534	−1.43636
$846$	36.7707	1.26420
$847$	0	0
$848$	−11.5123	−0.395333
$849$	−69.5060	−2.38544
$850$	−118.775	−4.07394
$851$	−2.20465	−0.0755744
$852$	−37.8685	−1.29735
$853$	−33.0949	−1.13315	−0.566574	−	0.824011i	$-0.691731\pi$
$853$	−33.0949	−1.13315	−0.566574	+	0.824011i	$0.691731\pi$
$854$	0	0
$855$	1.76034	0.0602023
$856$	−1.50825	−0.0515510
$857$	20.0025	0.683272	0.341636	−	0.939832i	$-0.389019\pi$
$857$	20.0025	0.683272	0.341636	+	0.939832i	$0.389019\pi$
$858$	−53.0789	−1.81208
$859$	37.3721	1.27512	0.637559	−	0.770401i	$-0.279944\pi$
$859$	37.3721	1.27512	0.637559	+	0.770401i	$0.279944\pi$
$860$	33.3888	1.13855
$861$	0	0
$862$	25.5505	0.870255
$863$	46.4668	1.58175	0.790875	−	0.611978i	$-0.209626\pi$
$863$	46.4668	1.58175	0.790875	+	0.611978i	$0.209626\pi$
$864$	78.2098	2.66075
$865$	33.6554	1.14432
$866$	−33.3615	−1.13367
$867$	−59.8408	−2.03230
$868$	0	0
$869$	86.9013	2.94793
$870$	45.3984	1.53915
$871$	1.62628	0.0551044
$872$	−3.43555	−0.116342
$873$	65.3397	2.21142
$874$	−0.669406	−0.0226430
$875$	0	0
$876$	101.643	3.43420
$877$	−10.5546	−0.356404	−0.178202	−	0.983994i	$-0.557028\pi$
$877$	−10.5546	−0.356404	−0.178202	+	0.983994i	$0.557028\pi$
$878$	51.3429	1.73274
$879$	−22.1374	−0.746675
$880$	85.1798	2.87141
$881$	25.0214	0.842993	0.421497	−	0.906830i	$-0.361505\pi$
$881$	25.0214	0.842993	0.421497	+	0.906830i	$0.361505\pi$
$882$	0	0
$883$	14.4626	0.486704	0.243352	−	0.969938i	$-0.421753\pi$
$883$	14.4626	0.486704	0.243352	+	0.969938i	$0.421753\pi$
$884$	18.6293	0.626570
$885$	132.723	4.46145
$886$	−0.915143	−0.0307448
$887$	5.65795	0.189975	0.0949877	−	0.995478i	$-0.469719\pi$
$887$	5.65795	0.189975	0.0949877	+	0.995478i	$0.469719\pi$
$888$	−0.385204	−0.0129266
$889$	0	0
$890$	−5.20916	−0.174612
$891$	−63.9803	−2.14342
$892$	−8.68746	−0.290878
$893$	0.217437	0.00727626
$894$	−49.3792	−1.65149
$895$	55.4288	1.85278
$896$	0	0
$897$	−19.4306	−0.648768
$898$	−37.0759	−1.23724
$899$	3.39992	0.113394
$900$	126.907	4.23023
$901$	−18.6955	−0.622838
$902$	−12.1120	−0.403285
$903$	0	0
$904$	1.53671	0.0511104
$905$	11.7699	0.391246
$906$	29.7542	0.988518
$907$	−45.9050	−1.52425	−0.762126	−	0.647429i	$-0.775844\pi$
$907$	−45.9050	−1.52425	−0.762126	+	0.647429i	$0.775844\pi$
$908$	41.5194	1.37787
$909$	19.8610	0.658748
$910$	0	0
$911$	42.5495	1.40973	0.704864	−	0.709342i	$-0.251008\pi$
$911$	42.5495	1.40973	0.704864	+	0.709342i	$0.251008\pi$
$912$	0.840957	0.0278469
$913$	−86.4272	−2.86032
$914$	57.9521	1.91688
$915$	34.2052	1.13079
$916$	−48.9909	−1.61870
$917$	0	0
$918$	118.988	3.92718
$919$	−25.1999	−0.831269	−0.415634	−	0.909532i	$-0.636440\pi$
$919$	−25.1999	−0.831269	−0.415634	+	0.909532i	$0.636440\pi$
$920$	−4.33678	−0.142979
$921$	49.1940	1.62100
$922$	14.8342	0.488539
$923$	−8.49618	−0.279655
$924$	0	0
$925$	4.79678	0.157717
$926$	−33.5900	−1.10384
$927$	−35.8304	−1.17683
$928$	15.5915	0.511816
$929$	−37.0410	−1.21528	−0.607639	−	0.794214i	$-0.707883\pi$
$929$	−37.0410	−1.21528	−0.607639	+	0.794214i	$0.707883\pi$
$930$	41.5833	1.36357
$931$	0	0
$932$	16.3581	0.535827
$933$	75.2231	2.46270
$934$	33.9027	1.10933
$935$	138.329	4.52384
$936$	−2.28650	−0.0747367
$937$	−24.4307	−0.798115	−0.399058	−	0.916926i	$-0.630663\pi$
$937$	−24.4307	−0.798115	−0.399058	+	0.916926i	$0.630663\pi$
$938$	0	0
$939$	3.04512	0.0993739
$940$	23.8002	0.776276
$941$	42.4153	1.38270	0.691350	−	0.722520i	$-0.257016\pi$
$941$	42.4153	1.38270	0.691350	+	0.722520i	$0.257016\pi$
$942$	−62.8738	−2.04854
$943$	−4.43383	−0.144386
$944$	42.7032	1.38987
$945$	0	0
$946$	−49.7068	−1.61611
$947$	−10.0783	−0.327501	−0.163750	−	0.986502i	$-0.552359\pi$
$947$	−10.0783	−0.327501	−0.163750	+	0.986502i	$0.552359\pi$
$948$	93.9095	3.05004
$949$	22.8047	0.740271
$950$	1.45647	0.0472540
$951$	90.8689	2.94663
$952$	0	0
$953$	−50.1799	−1.62549	−0.812743	−	0.582623i	$-0.802026\pi$
$953$	−50.1799	−1.62549	−0.812743	+	0.582623i	$0.802026\pi$
$954$	38.7687	1.25518
$955$	18.7895	0.608015
$956$	−25.9944	−0.840720
$957$	−34.8235	−1.12568
$958$	−15.5212	−0.501466
$959$	0	0
$960$	104.094	3.35961
$961$	−27.8858	−0.899542
$962$	−1.46017	−0.0470779
$963$	−36.5197	−1.17683
$964$	7.82748	0.252106
$965$	43.2659	1.39278
$966$	0	0
$967$	33.4107	1.07441	0.537207	−	0.843450i	$-0.319479\pi$
$967$	33.4107	1.07441	0.537207	+	0.843450i	$0.319479\pi$
$968$	6.27601	0.201719
$969$	1.36568	0.0438721
$970$	82.0803	2.63544
$971$	57.1446	1.83386	0.916929	−	0.399051i	$-0.130660\pi$
$971$	57.1446	1.83386	0.916929	+	0.399051i	$0.130660\pi$
$972$	−7.50653	−0.240772
$973$	0	0
$974$	−23.6149	−0.756670
$975$	42.2762	1.35392
$976$	11.0054	0.352273
$977$	−5.17315	−0.165504	−0.0827519	−	0.996570i	$-0.526371\pi$
$977$	−5.17315	−0.165504	−0.0827519	+	0.996570i	$0.526371\pi$
$978$	118.802	3.79888
$979$	3.99576	0.127705
$980$	0	0
$981$	−83.1859	−2.65592
$982$	52.7685	1.68391
$983$	−53.4989	−1.70635	−0.853175	−	0.521624i	$-0.825326\pi$
$983$	−53.4989	−1.70635	−0.853175	+	0.521624i	$0.825326\pi$
$984$	−0.774695	−0.0246964
$985$	−68.3503	−2.17782
$986$	23.7208	0.755424
$987$	0	0
$988$	−0.228440	−0.00726764
$989$	−18.1962	−0.578604
$990$	−286.852	−9.11674
$991$	16.6924	0.530252	0.265126	−	0.964214i	$-0.414587\pi$
$991$	16.6924	0.530252	0.265126	+	0.964214i	$0.414587\pi$
$992$	14.2813	0.453430
$993$	76.2263	2.41897
$994$	0	0
$995$	−52.1754	−1.65407
$996$	−93.3971	−2.95940
$997$	−0.818514	−0.0259226	−0.0129613	−	0.999916i	$-0.504126\pi$
$997$	−0.818514	−0.0259226	−0.0129613	+	0.999916i	$0.504126\pi$
$998$	−47.1078	−1.49117
$999$	−4.80538	−0.152036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.n.1.5		5
7.6	odd	2		287.2.a.e.1.5	✓	5
21.20	even	2		2583.2.a.r.1.1		5
28.27	even	2		4592.2.a.bb.1.1		5
35.34	odd	2		7175.2.a.n.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.e.1.5	✓	5	7.6	odd	2
2009.2.a.n.1.5		5	1.1	even	1	trivial
2583.2.a.r.1.1		5	21.20	even	2
4592.2.a.bb.1.1		5	28.27	even	2
7175.2.a.n.1.1		5	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)

\(f(q)\)	\(=\)	\(q+2.03121 q^{2} -3.03121 q^{3} +2.12582 q^{4} +3.82713 q^{5} -6.15703 q^{6} +0.255573 q^{8} +6.18825 q^{9} +O(q^{10})\)	\(q+2.03121 q^{2} -3.03121 q^{3} +2.12582 q^{4} +3.82713 q^{5} -6.15703 q^{6} +0.255573 q^{8} +6.18825 q^{9} +7.77372 q^{10} -5.96294 q^{11} -6.44382 q^{12} -1.44574 q^{13} -11.6009 q^{15} -3.73252 q^{16} -6.06148 q^{17} +12.5696 q^{18} +0.0743284 q^{19} +8.13581 q^{20} -12.1120 q^{22} -4.43383 q^{23} -0.774695 q^{24} +9.64695 q^{25} -2.93660 q^{26} -9.66425 q^{27} -1.92662 q^{29} -23.5638 q^{30} -1.76471 q^{31} -8.09269 q^{32} +18.0749 q^{33} -12.3122 q^{34} +13.1551 q^{36} +0.497233 q^{37} +0.150977 q^{38} +4.38234 q^{39} +0.978111 q^{40} +1.00000 q^{41} +4.10393 q^{43} -12.6762 q^{44} +23.6832 q^{45} -9.00606 q^{46} +2.92536 q^{47} +11.3141 q^{48} +19.5950 q^{50} +18.3736 q^{51} -3.07338 q^{52} +3.08431 q^{53} -19.6301 q^{54} -22.8210 q^{55} -0.225305 q^{57} -3.91337 q^{58} -11.4408 q^{59} -24.6614 q^{60} -2.94851 q^{61} -3.58450 q^{62} -8.97293 q^{64} -5.53303 q^{65} +36.7140 q^{66} -1.12488 q^{67} -12.8856 q^{68} +13.4399 q^{69} +5.87671 q^{71} +1.58155 q^{72} -15.7737 q^{73} +1.00999 q^{74} -29.2420 q^{75} +0.158009 q^{76} +8.90146 q^{78} -14.5736 q^{79} -14.2849 q^{80} +10.7297 q^{81} +2.03121 q^{82} +14.4941 q^{83} -23.1981 q^{85} +8.33596 q^{86} +5.83998 q^{87} -1.52396 q^{88} -0.670099 q^{89} +48.1057 q^{90} -9.42555 q^{92} +5.34921 q^{93} +5.94203 q^{94} +0.284465 q^{95} +24.5307 q^{96} +10.5587 q^{97} -36.9002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9}+O(q^{10}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9} + 2 q^{11} + 2 q^{12} - 5 q^{13} - 5 q^{15} - q^{16} - 13 q^{17} + 21 q^{18} + 23 q^{20} + q^{22} + 2 q^{23} - 2 q^{24} + 22 q^{25} - 10 q^{27} - 5 q^{29} - 33 q^{30} - 17 q^{31} - 12 q^{32} - 3 q^{33} + 8 q^{34} + 15 q^{36} - 7 q^{37} + 3 q^{38} + 5 q^{39} - 7 q^{40} + 5 q^{41} + q^{43} - 47 q^{44} + 23 q^{45} - 24 q^{46} - 9 q^{47} + 19 q^{48} + 2 q^{50} + 5 q^{51} - 20 q^{52} + 5 q^{53} - 2 q^{54} - 33 q^{55} - 3 q^{57} - 27 q^{58} - 7 q^{59} - 16 q^{60} - 22 q^{61} + 28 q^{62} - 3 q^{64} - 31 q^{65} + 42 q^{66} - 3 q^{67} - 17 q^{68} + 22 q^{69} - 24 q^{71} - 12 q^{72} - 40 q^{73} - 5 q^{74} - 24 q^{75} + 19 q^{76} + 30 q^{78} - 42 q^{79} - 24 q^{80} + 9 q^{81} - q^{82} + 12 q^{83} - 23 q^{85} + 16 q^{86} + 32 q^{87} + 26 q^{88} - 8 q^{89} + 59 q^{90} + 12 q^{92} - 11 q^{93} + 23 q^{94} - 17 q^{95} + 17 q^{96} - 16 q^{97} - 45 q^{99}+O(q^{100}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9 + 2 * q^11 + 2 * q^12 - 5 * q^13 - 5 * q^15 - q^16 - 13 * q^17 + 21 * q^18 + 23 * q^20 + q^22 + 2 * q^23 - 2 * q^24 + 22 * q^25 - 10 * q^27 - 5 * q^29 - 33 * q^30 - 17 * q^31 - 12 * q^32 - 3 * q^33 + 8 * q^34 + 15 * q^36 - 7 * q^37 + 3 * q^38 + 5 * q^39 - 7 * q^40 + 5 * q^41 + q^43 - 47 * q^44 + 23 * q^45 - 24 * q^46 - 9 * q^47 + 19 * q^48 + 2 * q^50 + 5 * q^51 - 20 * q^52 + 5 * q^53 - 2 * q^54 - 33 * q^55 - 3 * q^57 - 27 * q^58 - 7 * q^59 - 16 * q^60 - 22 * q^61 + 28 * q^62 - 3 * q^64 - 31 * q^65 + 42 * q^66 - 3 * q^67 - 17 * q^68 + 22 * q^69 - 24 * q^71 - 12 * q^72 - 40 * q^73 - 5 * q^74 - 24 * q^75 + 19 * q^76 + 30 * q^78 - 42 * q^79 - 24 * q^80 + 9 * q^81 - q^82 + 12 * q^83 - 23 * q^85 + 16 * q^86 + 32 * q^87 + 26 * q^88 - 8 * q^89 + 59 * q^90 + 12 * q^92 - 11 * q^93 + 23 * q^94 - 17 * q^95 + 17 * q^96 - 16 * q^97 - 45 * q^99

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