LMFDB - Embedded newform 2009.2.a.k.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:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.44504 q^{2} -1.55496 q^{3} +0.0881460 q^{4} -3.60388 q^{5} -2.24698 q^{6} -2.76271 q^{8} -0.582105 q^{9} +O(q^{10})$	\(q+1.44504 q^{2} -1.55496 q^{3} +0.0881460 q^{4} -3.60388 q^{5} -2.24698 q^{6} -2.76271 q^{8} -0.582105 q^{9} -5.20775 q^{10} -4.49396 q^{11} -0.137063 q^{12} -4.13706 q^{13} +5.60388 q^{15} -4.16852 q^{16} -2.02177 q^{17} -0.841166 q^{18} +8.29590 q^{19} -0.317667 q^{20} -6.49396 q^{22} -1.06100 q^{23} +4.29590 q^{24} +7.98792 q^{25} -5.97823 q^{26} +5.57002 q^{27} +6.98792 q^{29} +8.09783 q^{30} -9.48188 q^{31} -0.498271 q^{32} +6.98792 q^{33} -2.92154 q^{34} -0.0513102 q^{36} -3.74094 q^{37} +11.9879 q^{38} +6.43296 q^{39} +9.95646 q^{40} -1.00000 q^{41} -0.515729 q^{43} -0.396125 q^{44} +2.09783 q^{45} -1.53319 q^{46} -2.75302 q^{47} +6.48188 q^{48} +11.5429 q^{50} +3.14377 q^{51} -0.364666 q^{52} -3.50604 q^{53} +8.04892 q^{54} +16.1957 q^{55} -12.8998 q^{57} +10.0978 q^{58} +0.933624 q^{59} +0.493959 q^{60} +6.59179 q^{61} -13.7017 q^{62} +7.61702 q^{64} +14.9095 q^{65} +10.0978 q^{66} -15.3840 q^{67} -0.178211 q^{68} +1.64981 q^{69} +5.20775 q^{71} +1.60819 q^{72} +0.219833 q^{73} -5.40581 q^{74} -12.4209 q^{75} +0.731250 q^{76} +9.29590 q^{78} +6.21983 q^{79} +15.0228 q^{80} -6.91484 q^{81} -1.44504 q^{82} -10.1957 q^{83} +7.28621 q^{85} -0.745251 q^{86} -10.8659 q^{87} +12.4155 q^{88} +17.0465 q^{89} +3.03146 q^{90} -0.0935228 q^{92} +14.7439 q^{93} -3.97823 q^{94} -29.8974 q^{95} +0.774791 q^{96} -0.841166 q^{97} +2.61596 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 4 q^{2} - 5 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 9 q^{8} + 4 q^{9}+O(q^{10}) $ 3 * q + 4 * q^2 - 5 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 9 * q^8 + 4 * q^9	$ 3 q + 4 q^{2} - 5 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 9 q^{8} + 4 q^{9} + 2 q^{10} - 4 q^{11} + 5 q^{12} - 7 q^{13} + 8 q^{15} + 18 q^{16} - 3 q^{17} - 11 q^{18} + 11 q^{19} + 16 q^{20} - 10 q^{22} - 13 q^{23} - q^{24} + 5 q^{25} - 21 q^{26} - 8 q^{27} + 2 q^{29} + 6 q^{30} + 27 q^{32} + 2 q^{33} + 17 q^{34} - 32 q^{36} + 3 q^{37} + 17 q^{38} + 36 q^{40} - 3 q^{41} + 11 q^{43} - 10 q^{44} - 12 q^{45} - 8 q^{46} - 13 q^{47} - 9 q^{48} + 16 q^{50} + 26 q^{51} - 35 q^{52} - 20 q^{53} + 15 q^{54} + 12 q^{55} - 16 q^{57} + 12 q^{58} - 4 q^{59} - 8 q^{60} - 8 q^{61} - 14 q^{62} + 49 q^{64} + 12 q^{66} - 36 q^{67} + 52 q^{68} + 31 q^{69} - 2 q^{71} - 23 q^{72} + 2 q^{73} - 3 q^{74} + q^{75} + 10 q^{76} + 14 q^{78} + 20 q^{79} + 58 q^{80} + 27 q^{81} - 4 q^{82} + 6 q^{83} + 30 q^{85} + 31 q^{86} + 6 q^{87} + 2 q^{88} + q^{89} - 16 q^{90} - q^{92} - 14 q^{93} - 15 q^{94} - 26 q^{95} + 4 q^{96} - 11 q^{97} + 18 q^{99}+O(q^{100}) $ 3 * q + 4 * q^2 - 5 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 9 * q^8 + 4 * q^9 + 2 * q^10 - 4 * q^11 + 5 * q^12 - 7 * q^13 + 8 * q^15 + 18 * q^16 - 3 * q^17 - 11 * q^18 + 11 * q^19 + 16 * q^20 - 10 * q^22 - 13 * q^23 - q^24 + 5 * q^25 - 21 * q^26 - 8 * q^27 + 2 * q^29 + 6 * q^30 + 27 * q^32 + 2 * q^33 + 17 * q^34 - 32 * q^36 + 3 * q^37 + 17 * q^38 + 36 * q^40 - 3 * q^41 + 11 * q^43 - 10 * q^44 - 12 * q^45 - 8 * q^46 - 13 * q^47 - 9 * q^48 + 16 * q^50 + 26 * q^51 - 35 * q^52 - 20 * q^53 + 15 * q^54 + 12 * q^55 - 16 * q^57 + 12 * q^58 - 4 * q^59 - 8 * q^60 - 8 * q^61 - 14 * q^62 + 49 * q^64 + 12 * q^66 - 36 * q^67 + 52 * q^68 + 31 * q^69 - 2 * q^71 - 23 * q^72 + 2 * q^73 - 3 * q^74 + q^75 + 10 * q^76 + 14 * q^78 + 20 * q^79 + 58 * q^80 + 27 * q^81 - 4 * q^82 + 6 * q^83 + 30 * q^85 + 31 * q^86 + 6 * q^87 + 2 * q^88 + q^89 - 16 * q^90 - q^92 - 14 * q^93 - 15 * q^94 - 26 * q^95 + 4 * q^96 - 11 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.44504	1.02180	0.510899	−	0.859640i	$-0.329312\pi$
$2$	1.44504	1.02180	0.510899	+	0.859640i	$0.329312\pi$
$3$	−1.55496	−0.897755	−0.448878	−	0.893593i	$-0.648176\pi$
$3$	−1.55496	−0.897755	−0.448878	+	0.893593i	$0.648176\pi$
$4$	0.0881460	0.0440730
$5$	−3.60388	−1.61170	−0.805851	−	0.592118i	$-0.798292\pi$
$5$	−3.60388	−1.61170	−0.805851	+	0.592118i	$0.798292\pi$
$6$	−2.24698	−0.917326
$7$	0	0
$7$	0	0
$8$	−2.76271	−0.976765
$9$	−0.582105	−0.194035
$10$	−5.20775	−1.64684
$11$	−4.49396	−1.35498	−0.677490	−	0.735532i	$-0.736932\pi$
$11$	−4.49396	−1.35498	−0.677490	+	0.735532i	$0.736932\pi$
$12$	−0.137063	−0.0395668
$13$	−4.13706	−1.14741	−0.573707	−	0.819060i	$-0.694495\pi$
$13$	−4.13706	−1.14741	−0.573707	+	0.819060i	$0.694495\pi$
$14$	0	0
$15$	5.60388	1.44691
$16$	−4.16852	−1.04213
$17$	−2.02177	−0.490351	−0.245176	−	0.969479i	$-0.578846\pi$
$17$	−2.02177	−0.490351	−0.245176	+	0.969479i	$0.578846\pi$
$18$	−0.841166	−0.198265
$19$	8.29590	1.90321	0.951605	−	0.307325i	$-0.0994338\pi$
$19$	8.29590	1.90321	0.951605	+	0.307325i	$0.0994338\pi$
$20$	−0.317667	−0.0710325
$21$	0	0
$22$	−6.49396	−1.38452
$23$	−1.06100	−0.221234	−0.110617	−	0.993863i	$-0.535283\pi$
$23$	−1.06100	−0.221234	−0.110617	+	0.993863i	$0.535283\pi$
$24$	4.29590	0.876896
$25$	7.98792	1.59758
$26$	−5.97823	−1.17243
$27$	5.57002	1.07195
$28$	0	0
$29$	6.98792	1.29762	0.648812	−	0.760949i	$-0.275266\pi$
$29$	6.98792	1.29762	0.648812	+	0.760949i	$0.275266\pi$
$30$	8.09783	1.47846
$31$	−9.48188	−1.70300	−0.851498	−	0.524358i	$-0.824305\pi$
$31$	−9.48188	−1.70300	−0.851498	+	0.524358i	$0.824305\pi$
$32$	−0.498271	−0.0880827
$33$	6.98792	1.21644
$34$	−2.92154	−0.501040
$35$	0	0
$36$	−0.0513102	−0.00855171
$37$	−3.74094	−0.615007	−0.307503	−	0.951547i	$-0.599494\pi$
$37$	−3.74094	−0.615007	−0.307503	+	0.951547i	$0.599494\pi$
$38$	11.9879	1.94470
$39$	6.43296	1.03010
$40$	9.95646	1.57425
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−0.515729	−0.0786480	−0.0393240	−	0.999227i	$-0.512520\pi$
$43$	−0.515729	−0.0786480	−0.0393240	+	0.999227i	$0.512520\pi$
$44$	−0.396125	−0.0597180
$45$	2.09783	0.312727
$46$	−1.53319	−0.226056
$47$	−2.75302	−0.401569	−0.200785	−	0.979635i	$-0.564349\pi$
$47$	−2.75302	−0.401569	−0.200785	+	0.979635i	$0.564349\pi$
$48$	6.48188	0.935578
$49$	0	0
$50$	11.5429	1.63241
$51$	3.14377	0.440216
$52$	−0.364666	−0.0505700
$53$	−3.50604	−0.481592	−0.240796	−	0.970576i	$-0.577408\pi$
$53$	−3.50604	−0.481592	−0.240796	+	0.970576i	$0.577408\pi$
$54$	8.04892	1.09532
$55$	16.1957	2.18382
$56$	0	0
$57$	−12.8998	−1.70862
$58$	10.0978	1.32591
$59$	0.933624	0.121548	0.0607738	−	0.998152i	$-0.480643\pi$
$59$	0.933624	0.121548	0.0607738	+	0.998152i	$0.480643\pi$
$60$	0.493959	0.0637699
$61$	6.59179	0.843993	0.421996	−	0.906598i	$-0.361329\pi$
$61$	6.59179	0.843993	0.421996	+	0.906598i	$0.361329\pi$
$62$	−13.7017	−1.74012
$63$	0	0
$64$	7.61702	0.952128
$65$	14.9095	1.84929
$66$	10.0978	1.24296
$67$	−15.3840	−1.87946	−0.939730	−	0.341917i	$-0.888924\pi$
$67$	−15.3840	−1.87946	−0.939730	+	0.341917i	$0.888924\pi$
$68$	−0.178211	−0.0216113
$69$	1.64981	0.198614
$70$	0	0
$71$	5.20775	0.618046	0.309023	−	0.951055i	$-0.399998\pi$
$71$	5.20775	0.618046	0.309023	+	0.951055i	$0.399998\pi$
$72$	1.60819	0.189527
$73$	0.219833	0.0257295	0.0128647	−	0.999917i	$-0.495905\pi$
$73$	0.219833	0.0257295	0.0128647	+	0.999917i	$0.495905\pi$
$74$	−5.40581	−0.628413
$75$	−12.4209	−1.43424
$76$	0.731250	0.0838801
$77$	0	0
$78$	9.29590	1.05255
$79$	6.21983	0.699786	0.349893	−	0.936790i	$-0.386218\pi$
$79$	6.21983	0.699786	0.349893	+	0.936790i	$0.386218\pi$
$80$	15.0228	1.67960
$81$	−6.91484	−0.768315
$82$	−1.44504	−0.159578
$83$	−10.1957	−1.11912	−0.559560	−	0.828790i	$-0.689030\pi$
$83$	−10.1957	−1.11912	−0.559560	+	0.828790i	$0.689030\pi$
$84$	0	0
$85$	7.28621	0.790300
$86$	−0.745251	−0.0803624
$87$	−10.8659	−1.16495
$88$	12.4155	1.32350
$89$	17.0465	1.80693	0.903464	−	0.428664i	$-0.141016\pi$
$89$	17.0465	1.80693	0.903464	+	0.428664i	$0.141016\pi$
$90$	3.03146	0.319544
$91$	0	0
$92$	−0.0935228	−0.00975043
$93$	14.7439	1.52887
$94$	−3.97823	−0.410323
$95$	−29.8974	−3.06741
$96$	0.774791	0.0790767
$97$	−0.841166	−0.0854075	−0.0427038	−	0.999088i	$-0.513597\pi$
$97$	−0.841166	−0.0854075	−0.0427038	+	0.999088i	$0.513597\pi$
$98$	0	0
$99$	2.61596	0.262914
$100$	0.704103	0.0704103
$101$	−16.2446	−1.61640	−0.808198	−	0.588910i	$-0.799557\pi$
$101$	−16.2446	−1.61640	−0.808198	+	0.588910i	$0.799557\pi$
$102$	4.54288	0.449812
$103$	−10.3177	−1.01663	−0.508315	−	0.861171i	$-0.669731\pi$
$103$	−10.3177	−1.01663	−0.508315	+	0.861171i	$0.669731\pi$
$104$	11.4295	1.12075
$105$	0	0
$106$	−5.06638	−0.492090
$107$	−6.29590	−0.608647	−0.304324	−	0.952569i	$-0.598430\pi$
$107$	−6.29590	−0.608647	−0.304324	+	0.952569i	$0.598430\pi$
$108$	0.490975	0.0472441
$109$	10.8116	1.03557	0.517783	−	0.855512i	$-0.326757\pi$
$109$	10.8116	1.03557	0.517783	+	0.855512i	$0.326757\pi$
$110$	23.4034	2.23143
$111$	5.81700	0.552126
$112$	0	0
$113$	−2.76271	−0.259894	−0.129947	−	0.991521i	$-0.541481\pi$
$113$	−2.76271	−0.259894	−0.129947	+	0.991521i	$0.541481\pi$
$114$	−18.6407	−1.74586
$115$	3.82371	0.356563
$116$	0.615957	0.0571902
$117$	2.40821	0.222639
$118$	1.34913	0.124197
$119$	0	0
$120$	−15.4819	−1.41330
$121$	9.19567	0.835970
$122$	9.52542	0.862391
$123$	1.55496	0.140206
$124$	−0.835790	−0.0750561
$125$	−10.7681	−0.963127
$126$	0	0
$127$	17.5646	1.55861	0.779305	−	0.626645i	$-0.215572\pi$
$127$	17.5646	1.55861	0.779305	+	0.626645i	$0.215572\pi$
$128$	12.0035	1.06097
$129$	0.801938	0.0706067
$130$	21.5448	1.88960
$131$	−4.31767	−0.377236	−0.188618	−	0.982051i	$-0.560401\pi$
$131$	−4.31767	−0.377236	−0.188618	+	0.982051i	$0.560401\pi$
$132$	0.615957	0.0536122
$133$	0	0
$134$	−22.2306	−1.92043
$135$	−20.0737	−1.72767
$136$	5.58556	0.478958
$137$	−3.50604	−0.299541	−0.149771	−	0.988721i	$-0.547854\pi$
$137$	−3.50604	−0.299541	−0.149771	+	0.988721i	$0.547854\pi$
$138$	2.38404	0.202943
$139$	−19.5254	−1.65612	−0.828062	−	0.560636i	$-0.810557\pi$
$139$	−19.5254	−1.65612	−0.828062	+	0.560636i	$0.810557\pi$
$140$	0	0
$141$	4.28083	0.360511
$142$	7.52542	0.631519
$143$	18.5918	1.55472
$144$	2.42652	0.202210
$145$	−25.1836	−2.09138
$146$	0.317667	0.0262903
$147$	0	0
$148$	−0.329749	−0.0271052
$149$	−13.7995	−1.13050	−0.565251	−	0.824919i	$-0.691221\pi$
$149$	−13.7995	−1.13050	−0.565251	+	0.824919i	$0.691221\pi$
$150$	−17.9487	−1.46550
$151$	13.4276	1.09272	0.546361	−	0.837550i	$-0.316013\pi$
$151$	13.4276	1.09272	0.546361	+	0.837550i	$0.316013\pi$
$152$	−22.9191	−1.85899
$153$	1.17688	0.0951454
$154$	0	0
$155$	34.1715	2.74472
$156$	0.567040	0.0453995
$157$	18.3696	1.46605	0.733026	−	0.680201i	$-0.238108\pi$
$157$	18.3696	1.46605	0.733026	+	0.680201i	$0.238108\pi$
$158$	8.98792	0.715040
$159$	5.45175	0.432352
$160$	1.79571	0.141963
$161$	0	0
$162$	−9.99223	−0.785064
$163$	9.25667	0.725038	0.362519	−	0.931976i	$-0.381917\pi$
$163$	9.25667	0.725038	0.362519	+	0.931976i	$0.381917\pi$
$164$	−0.0881460	−0.00688305
$165$	−25.1836	−1.96054
$166$	−14.7332	−1.14352
$167$	9.48427	0.733915	0.366957	−	0.930238i	$-0.380399\pi$
$167$	9.48427	0.733915	0.366957	+	0.930238i	$0.380399\pi$
$168$	0	0
$169$	4.11529	0.316561
$170$	10.5289	0.807528
$171$	−4.82908	−0.369289
$172$	−0.0454595	−0.00346625
$173$	−0.933624	−0.0709821	−0.0354911	−	0.999370i	$-0.511300\pi$
$173$	−0.933624	−0.0709821	−0.0354911	+	0.999370i	$0.511300\pi$
$174$	−15.7017	−1.19034
$175$	0	0
$176$	18.7332	1.41207
$177$	−1.45175	−0.109120
$178$	24.6329	1.84632
$179$	−15.3056	−1.14399	−0.571997	−	0.820256i	$-0.693831\pi$
$179$	−15.3056	−1.14399	−0.571997	+	0.820256i	$0.693831\pi$
$180$	0.184916	0.0137828
$181$	8.14675	0.605543	0.302772	−	0.953063i	$-0.402088\pi$
$181$	8.14675	0.605543	0.302772	+	0.953063i	$0.402088\pi$
$182$	0	0
$183$	−10.2500	−0.757699
$184$	2.93123	0.216093
$185$	13.4819	0.991207
$186$	21.3056	1.56220
$187$	9.08575	0.664416
$188$	−0.242668	−0.0176984
$189$	0	0
$190$	−43.2030	−3.13427
$191$	9.70171	0.701991	0.350996	−	0.936377i	$-0.385843\pi$
$191$	9.70171	0.701991	0.350996	+	0.936377i	$0.385843\pi$
$192$	−11.8442	−0.854778
$193$	12.6160	0.908116	0.454058	−	0.890972i	$-0.349976\pi$
$193$	12.6160	0.908116	0.454058	+	0.890972i	$0.349976\pi$
$194$	−1.21552	−0.0872693
$195$	−23.1836	−1.66021
$196$	0	0
$197$	−13.1618	−0.937741	−0.468870	−	0.883267i	$-0.655339\pi$
$197$	−13.1618	−0.937741	−0.468870	+	0.883267i	$0.655339\pi$
$198$	3.78017	0.268645
$199$	18.9487	1.34324	0.671619	−	0.740897i	$-0.265599\pi$
$199$	18.9487	1.34324	0.671619	+	0.740897i	$0.265599\pi$
$200$	−22.0683	−1.56046
$201$	23.9215	1.68730
$202$	−23.4741	−1.65163
$203$	0	0
$204$	0.277111	0.0194016
$205$	3.60388	0.251706
$206$	−14.9095	−1.03879
$207$	0.617613	0.0429271
$208$	17.2454	1.19576
$209$	−37.2814	−2.57881
$210$	0	0
$211$	14.2392	0.980268	0.490134	−	0.871647i	$-0.336948\pi$
$211$	14.2392	0.980268	0.490134	+	0.871647i	$0.336948\pi$
$212$	−0.309043	−0.0212252
$213$	−8.09783	−0.554854
$214$	−9.09783	−0.621915
$215$	1.85862	0.126757
$216$	−15.3884	−1.04704
$217$	0	0
$218$	15.6233	1.05814
$219$	−0.341830	−0.0230988
$220$	1.42758	0.0962477
$221$	8.36419	0.562636
$222$	8.40581	0.564161
$223$	8.12200	0.543889	0.271945	−	0.962313i	$-0.412333\pi$
$223$	8.12200	0.543889	0.271945	+	0.962313i	$0.412333\pi$
$224$	0	0
$225$	−4.64981	−0.309987
$226$	−3.99223	−0.265559
$227$	15.2078	1.00937	0.504687	−	0.863302i	$-0.331608\pi$
$227$	15.2078	1.00937	0.504687	+	0.863302i	$0.331608\pi$
$228$	−1.13706	−0.0753039
$229$	−22.9041	−1.51354	−0.756772	−	0.653679i	$-0.773225\pi$
$229$	−22.9041	−1.51354	−0.756772	+	0.653679i	$0.773225\pi$
$230$	5.52542	0.364335
$231$	0	0
$232$	−19.3056	−1.26747
$233$	−4.19567	−0.274867	−0.137434	−	0.990511i	$-0.543885\pi$
$233$	−4.19567	−0.274867	−0.137434	+	0.990511i	$0.543885\pi$
$234$	3.47996	0.227492
$235$	9.92154	0.647210
$236$	0.0822952	0.00535696
$237$	−9.67158	−0.628237
$238$	0	0
$239$	−15.5254	−1.00426	−0.502128	−	0.864793i	$-0.667449\pi$
$239$	−15.5254	−1.00426	−0.502128	+	0.864793i	$0.667449\pi$
$240$	−23.3599	−1.50787
$241$	6.58104	0.423922	0.211961	−	0.977278i	$-0.432015\pi$
$241$	6.58104	0.423922	0.211961	+	0.977278i	$0.432015\pi$
$242$	13.2881	0.854193
$243$	−5.95779	−0.382192
$244$	0.581040	0.0371973
$245$	0	0
$246$	2.24698	0.143262
$247$	−34.3207	−2.18377
$248$	26.1957	1.66343
$249$	15.8538	1.00470
$250$	−15.5603	−0.984122
$251$	3.90217	0.246302	0.123151	−	0.992388i	$-0.460700\pi$
$251$	3.90217	0.246302	0.123151	+	0.992388i	$0.460700\pi$
$252$	0	0
$253$	4.76809	0.299767
$254$	25.3817	1.59259
$255$	−11.3297	−0.709496
$256$	2.11146	0.131966
$257$	1.81833	0.113424	0.0567122	−	0.998391i	$-0.481938\pi$
$257$	1.81833	0.113424	0.0567122	+	0.998391i	$0.481938\pi$
$258$	1.15883	0.0721458
$259$	0	0
$260$	1.31421	0.0815038
$261$	−4.06770	−0.251785
$262$	−6.23921	−0.385460
$263$	−7.30559	−0.450482	−0.225241	−	0.974303i	$-0.572317\pi$
$263$	−7.30559	−0.450482	−0.225241	+	0.974303i	$0.572317\pi$
$264$	−19.3056	−1.18818
$265$	12.6353	0.776182
$266$	0	0
$267$	−26.5066	−1.62218
$268$	−1.35604	−0.0828334
$269$	−10.3612	−0.631734	−0.315867	−	0.948803i	$-0.602295\pi$
$269$	−10.3612	−0.631734	−0.315867	+	0.948803i	$0.602295\pi$
$270$	−29.0073	−1.76533
$271$	13.4082	0.814491	0.407245	−	0.913319i	$-0.366489\pi$
$271$	13.4082	0.814491	0.407245	+	0.913319i	$0.366489\pi$
$272$	8.42779	0.511010
$273$	0	0
$274$	−5.06638	−0.306071
$275$	−35.8974	−2.16469
$276$	0.145424	0.00875350
$277$	7.65279	0.459812	0.229906	−	0.973213i	$-0.426158\pi$
$277$	7.65279	0.459812	0.229906	+	0.973213i	$0.426158\pi$
$278$	−28.2150	−1.69223
$279$	5.51945	0.330441
$280$	0	0
$281$	−22.1280	−1.32004	−0.660022	−	0.751246i	$-0.729453\pi$
$281$	−22.1280	−1.32004	−0.660022	+	0.751246i	$0.729453\pi$
$282$	6.18598	0.368370
$283$	−11.5603	−0.687191	−0.343595	−	0.939118i	$-0.611645\pi$
$283$	−11.5603	−0.687191	−0.343595	+	0.939118i	$0.611645\pi$
$284$	0.459042	0.0272392
$285$	46.4892	2.75378
$286$	26.8659	1.58862
$287$	0	0
$288$	0.290046	0.0170911
$289$	−12.9124	−0.759556
$290$	−36.3913	−2.13697
$291$	1.30798	0.0766751
$292$	0.0193774	0.00113397
$293$	−6.19567	−0.361955	−0.180977	−	0.983487i	$-0.557926\pi$
$293$	−6.19567	−0.361955	−0.180977	+	0.983487i	$0.557926\pi$
$294$	0	0
$295$	−3.36467	−0.195898
$296$	10.3351	0.600717
$297$	−25.0315	−1.45247
$298$	−19.9409	−1.15515
$299$	4.38942	0.253847
$300$	−1.09485	−0.0632112
$301$	0	0
$302$	19.4034	1.11654
$303$	25.2597	1.45113
$304$	−34.5816	−1.98339
$305$	−23.7560	−1.36026
$306$	1.70065	0.0972194
$307$	2.51812	0.143717	0.0718584	−	0.997415i	$-0.477107\pi$
$307$	2.51812	0.143717	0.0718584	+	0.997415i	$0.477107\pi$
$308$	0	0
$309$	16.0435	0.912685
$310$	49.3793	2.80455
$311$	10.8683	0.616286	0.308143	−	0.951340i	$-0.400293\pi$
$311$	10.8683	0.616286	0.308143	+	0.951340i	$0.400293\pi$
$312$	−17.7724	−1.00616
$313$	−17.3817	−0.982469	−0.491234	−	0.871027i	$-0.663454\pi$
$313$	−17.3817	−0.982469	−0.491234	+	0.871027i	$0.663454\pi$
$314$	26.5448	1.49801
$315$	0	0
$316$	0.548253	0.0308417
$317$	−8.96854	−0.503723	−0.251862	−	0.967763i	$-0.581043\pi$
$317$	−8.96854	−0.503723	−0.251862	+	0.967763i	$0.581043\pi$
$318$	7.87800	0.441776
$319$	−31.4034	−1.75825
$320$	−27.4508	−1.53455
$321$	9.78986	0.546416
$322$	0	0
$323$	−16.7724	−0.933241
$324$	−0.609515	−0.0338620
$325$	−33.0465	−1.83309
$326$	13.3763	0.740843
$327$	−16.8116	−0.929685
$328$	2.76271	0.152545
$329$	0	0
$330$	−36.3913	−2.00328
$331$	−27.9517	−1.53636	−0.768181	−	0.640232i	$-0.778838\pi$
$331$	−27.9517	−1.53636	−0.768181	+	0.640232i	$0.778838\pi$
$332$	−0.898707	−0.0493230
$333$	2.17762	0.119333
$334$	13.7052	0.749913
$335$	55.4422	3.02913
$336$	0	0
$337$	23.4571	1.27779	0.638895	−	0.769294i	$-0.279392\pi$
$337$	23.4571	1.27779	0.638895	+	0.769294i	$0.279392\pi$
$338$	5.94677	0.323462
$339$	4.29590	0.233321
$340$	0.642250	0.0348309
$341$	42.6112	2.30752
$342$	−6.97823	−0.377339
$343$	0	0
$344$	1.42481	0.0768206
$345$	−5.94571	−0.320106
$346$	−1.34913	−0.0725295
$347$	−14.6160	−0.784626	−0.392313	−	0.919832i	$-0.628325\pi$
$347$	−14.6160	−0.784626	−0.392313	+	0.919832i	$0.628325\pi$
$348$	−0.957787	−0.0513428
$349$	35.8538	1.91921	0.959606	−	0.281347i	$-0.0907813\pi$
$349$	35.8538	1.91921	0.959606	+	0.281347i	$0.0907813\pi$
$350$	0	0
$351$	−23.0435	−1.22997
$352$	2.23921	0.119350
$353$	−4.56166	−0.242793	−0.121396	−	0.992604i	$-0.538737\pi$
$353$	−4.56166	−0.242793	−0.121396	+	0.992604i	$0.538737\pi$
$354$	−2.09783	−0.111499
$355$	−18.7681	−0.996107
$356$	1.50258	0.0796367
$357$	0	0
$358$	−22.1172	−1.16893
$359$	21.0465	1.11079	0.555397	−	0.831586i	$-0.312566\pi$
$359$	21.0465	1.11079	0.555397	+	0.831586i	$0.312566\pi$
$360$	−5.79571	−0.305461
$361$	49.8219	2.62221
$362$	11.7724	0.618743
$363$	−14.2989	−0.750497
$364$	0	0
$365$	−0.792249	−0.0414682
$366$	−14.8116	−0.774216
$367$	17.8431	0.931401	0.465701	−	0.884942i	$-0.345802\pi$
$367$	17.8431	0.931401	0.465701	+	0.884942i	$0.345802\pi$
$368$	4.42280	0.230554
$369$	0.582105	0.0303032
$370$	19.4819	1.01281
$371$	0	0
$372$	1.29962	0.0673820
$373$	6.83340	0.353820	0.176910	−	0.984227i	$-0.443390\pi$
$373$	6.83340	0.353820	0.176910	+	0.984227i	$0.443390\pi$
$374$	13.1293	0.678900
$375$	16.7439	0.864652
$376$	7.60579	0.392239
$377$	−28.9095	−1.48891
$378$	0	0
$379$	8.47517	0.435340	0.217670	−	0.976022i	$-0.430154\pi$
$379$	8.47517	0.435340	0.217670	+	0.976022i	$0.430154\pi$
$380$	−2.63533	−0.135190
$381$	−27.3123	−1.39925
$382$	14.0194	0.717294
$383$	−11.5308	−0.589196	−0.294598	−	0.955621i	$-0.595186\pi$
$383$	−11.5308	−0.589196	−0.294598	+	0.955621i	$0.595186\pi$
$384$	−18.6649	−0.952488
$385$	0	0
$386$	18.2306	0.927912
$387$	0.300209	0.0152605
$388$	−0.0741455	−0.00376417
$389$	−8.72886	−0.442571	−0.221285	−	0.975209i	$-0.571025\pi$
$389$	−8.72886	−0.442571	−0.221285	+	0.975209i	$0.571025\pi$
$390$	−33.5013	−1.69640
$391$	2.14510	0.108482
$392$	0	0
$393$	6.71379	0.338666
$394$	−19.0194	−0.958182
$395$	−22.4155	−1.12785
$396$	0.230586	0.0115874
$397$	12.6112	0.632937	0.316468	−	0.948603i	$-0.397503\pi$
$397$	12.6112	0.632937	0.316468	+	0.948603i	$0.397503\pi$
$398$	27.3817	1.37252
$399$	0	0
$400$	−33.2978	−1.66489
$401$	−5.24698	−0.262022	−0.131011	−	0.991381i	$-0.541822\pi$
$401$	−5.24698	−0.262022	−0.131011	+	0.991381i	$0.541822\pi$
$402$	34.5676	1.72408
$403$	39.2271	1.95404
$404$	−1.43190	−0.0712395
$405$	24.9202	1.23830
$406$	0	0
$407$	16.8116	0.833321
$408$	−8.68532	−0.429987
$409$	29.2271	1.44519	0.722594	−	0.691272i	$-0.242950\pi$
$409$	29.2271	1.44519	0.722594	+	0.691272i	$0.242950\pi$
$410$	5.20775	0.257192
$411$	5.45175	0.268915
$412$	−0.909461	−0.0448059
$413$	0	0
$414$	0.892477	0.0438628
$415$	36.7439	1.80369
$416$	2.06138	0.101067
$417$	30.3612	1.48679
$418$	−53.8732	−2.63503
$419$	−6.67025	−0.325863	−0.162932	−	0.986637i	$-0.552095\pi$
$419$	−6.67025	−0.325863	−0.162932	+	0.986637i	$0.552095\pi$
$420$	0	0
$421$	23.1943	1.13042	0.565212	−	0.824946i	$-0.308795\pi$
$421$	23.1943	1.13042	0.565212	+	0.824946i	$0.308795\pi$
$422$	20.5763	1.00164
$423$	1.60255	0.0779185
$424$	9.68617	0.470402
$425$	−16.1497	−0.783377
$426$	−11.7017	−0.566950
$427$	0	0
$428$	−0.554958	−0.0268249
$429$	−28.9095	−1.39576
$430$	2.68579	0.129520
$431$	34.4155	1.65774	0.828868	−	0.559444i	$-0.188985\pi$
$431$	34.4155	1.65774	0.828868	+	0.559444i	$0.188985\pi$
$432$	−23.2188	−1.11711
$433$	−35.8431	−1.72251	−0.861254	−	0.508174i	$-0.830321\pi$
$433$	−35.8431	−1.72251	−0.861254	+	0.508174i	$0.830321\pi$
$434$	0	0
$435$	39.1594	1.87755
$436$	0.953002	0.0456405
$437$	−8.80194	−0.421054
$438$	−0.493959	−0.0236023
$439$	7.78554	0.371584	0.185792	−	0.982589i	$-0.440515\pi$
$439$	7.78554	0.371584	0.185792	+	0.982589i	$0.440515\pi$
$440$	−44.7439	−2.13308
$441$	0	0
$442$	12.0866	0.574901
$443$	−36.7241	−1.74481	−0.872407	−	0.488781i	$-0.837442\pi$
$443$	−36.7241	−1.74481	−0.872407	+	0.488781i	$0.837442\pi$
$444$	0.512746	0.0243338
$445$	−61.4336	−2.91223
$446$	11.7366	0.555745
$447$	21.4577	1.01492
$448$	0	0
$449$	11.7614	0.555054	0.277527	−	0.960718i	$-0.410485\pi$
$449$	11.7614	0.555054	0.277527	+	0.960718i	$0.410485\pi$
$450$	−6.71917	−0.316745
$451$	4.49396	0.211612
$452$	−0.243522	−0.0114543
$453$	−20.8793	−0.980997
$454$	21.9758	1.03138
$455$	0	0
$456$	35.6383	1.66892
$457$	−35.4771	−1.65955	−0.829774	−	0.558099i	$-0.811531\pi$
$457$	−35.4771	−1.65955	−0.829774	+	0.558099i	$0.811531\pi$
$458$	−33.0974	−1.54654
$459$	−11.2613	−0.525633
$460$	0.337045	0.0157148
$461$	−22.7439	−1.05929	−0.529645	−	0.848219i	$-0.677675\pi$
$461$	−22.7439	−1.05929	−0.529645	+	0.848219i	$0.677675\pi$
$462$	0	0
$463$	7.46250	0.346812	0.173406	−	0.984850i	$-0.444523\pi$
$463$	7.46250	0.346812	0.173406	+	0.984850i	$0.444523\pi$
$464$	−29.1293	−1.35229
$465$	−53.1353	−2.46409
$466$	−6.06292	−0.280859
$467$	0.469796	0.0217396	0.0108698	−	0.999941i	$-0.496540\pi$
$467$	0.469796	0.0217396	0.0108698	+	0.999941i	$0.496540\pi$
$468$	0.212274	0.00981236
$469$	0	0
$470$	14.3370	0.661319
$471$	−28.5639	−1.31616
$472$	−2.57933	−0.118723
$473$	2.31767	0.106566
$474$	−13.9758	−0.641931
$475$	66.2669	3.04054
$476$	0	0
$477$	2.04088	0.0934457
$478$	−22.4349	−1.02615
$479$	4.02954	0.184114	0.0920572	−	0.995754i	$-0.470656\pi$
$479$	4.02954	0.184114	0.0920572	+	0.995754i	$0.470656\pi$
$480$	−2.79225	−0.127448
$481$	15.4765	0.705668
$482$	9.50988	0.433163
$483$	0	0
$484$	0.810561	0.0368437
$485$	3.03146	0.137651
$486$	−8.60925	−0.390524
$487$	35.8756	1.62568	0.812840	−	0.582488i	$-0.197921\pi$
$487$	35.8756	1.62568	0.812840	+	0.582488i	$0.197921\pi$
$488$	−18.2112	−0.824383
$489$	−14.3937	−0.650907
$490$	0	0
$491$	−30.3532	−1.36982	−0.684910	−	0.728628i	$-0.740158\pi$
$491$	−30.3532	−1.36982	−0.684910	+	0.728628i	$0.740158\pi$
$492$	0.137063	0.00617929
$493$	−14.1280	−0.636292
$494$	−49.5948	−2.23137
$495$	−9.42758	−0.423738
$496$	39.5254	1.77474
$497$	0	0
$498$	22.9095	1.02660
$499$	34.2258	1.53216	0.766079	−	0.642747i	$-0.222205\pi$
$499$	34.2258	1.53216	0.766079	+	0.642747i	$0.222205\pi$
$500$	−0.949164	−0.0424479
$501$	−14.7476	−0.658876
$502$	5.63879	0.251672
$503$	19.5308	0.870835	0.435418	−	0.900229i	$-0.356601\pi$
$503$	19.5308	0.870835	0.435418	+	0.900229i	$0.356601\pi$
$504$	0	0
$505$	58.5435	2.60515
$506$	6.89008	0.306302
$507$	−6.39911	−0.284194
$508$	1.54825	0.0686926
$509$	20.4198	0.905092	0.452546	−	0.891741i	$-0.350516\pi$
$509$	20.4198	0.905092	0.452546	+	0.891741i	$0.350516\pi$
$510$	−16.3720	−0.724963
$511$	0	0
$512$	−20.9558	−0.926123
$513$	46.2083	2.04015
$514$	2.62756	0.115897
$515$	37.1836	1.63850
$516$	0.0706876	0.00311185
$517$	12.3720	0.544118
$518$	0	0
$519$	1.45175	0.0637246
$520$	−41.1905	−1.80632
$521$	−6.81807	−0.298705	−0.149352	−	0.988784i	$-0.547719\pi$
$521$	−6.81807	−0.298705	−0.149352	+	0.988784i	$0.547719\pi$
$522$	−5.87800	−0.257273
$523$	4.36121	0.190702	0.0953511	−	0.995444i	$-0.469603\pi$
$523$	4.36121	0.190702	0.0953511	+	0.995444i	$0.469603\pi$
$524$	−0.380585	−0.0166259
$525$	0	0
$526$	−10.5569	−0.460302
$527$	19.1702	0.835066
$528$	−29.1293	−1.26769
$529$	−21.8743	−0.951056
$530$	18.2586	0.793102
$531$	−0.543468	−0.0235845
$532$	0	0
$533$	4.13706	0.179196
$534$	−38.3032	−1.65754
$535$	22.6896	0.980958
$536$	42.5016	1.83579
$537$	23.7995	1.02703
$538$	−14.9724	−0.645505
$539$	0	0
$540$	−1.76941	−0.0761434
$541$	−1.44935	−0.0623126	−0.0311563	−	0.999515i	$-0.509919\pi$
$541$	−1.44935	−0.0623126	−0.0311563	+	0.999515i	$0.509919\pi$
$542$	19.3754	0.832246
$543$	−12.6679	−0.543630
$544$	1.00739	0.0431915
$545$	−38.9638	−1.66902
$546$	0	0
$547$	23.0664	0.986247	0.493124	−	0.869959i	$-0.335855\pi$
$547$	23.0664	0.986247	0.493124	+	0.869959i	$0.335855\pi$
$548$	−0.309043	−0.0132017
$549$	−3.83712	−0.163764
$550$	−51.8732	−2.21188
$551$	57.9711	2.46965
$552$	−4.55794	−0.193999
$553$	0	0
$554$	11.0586	0.469835
$555$	−20.9638	−0.889862
$556$	−1.72109	−0.0729904
$557$	15.3599	0.650819	0.325409	−	0.945573i	$-0.394498\pi$
$557$	15.3599	0.650819	0.325409	+	0.945573i	$0.394498\pi$
$558$	7.97584	0.337644
$559$	2.13361	0.0902419
$560$	0	0
$561$	−14.1280	−0.596483
$562$	−31.9758	−1.34882
$563$	23.3884	0.985702	0.492851	−	0.870114i	$-0.335955\pi$
$563$	23.3884	0.985702	0.492851	+	0.870114i	$0.335955\pi$
$564$	0.377338	0.0158888
$565$	9.95646	0.418871
$566$	−16.7052	−0.702171
$567$	0	0
$568$	−14.3875	−0.603686
$569$	−13.6498	−0.572230	−0.286115	−	0.958195i	$-0.592364\pi$
$569$	−13.6498	−0.572230	−0.286115	+	0.958195i	$0.592364\pi$
$570$	67.1788	2.81381
$571$	−2.36121	−0.0988135	−0.0494067	−	0.998779i	$-0.515733\pi$
$571$	−2.36121	−0.0988135	−0.0494067	+	0.998779i	$0.515733\pi$
$572$	1.63879	0.0685213
$573$	−15.0858	−0.630216
$574$	0	0
$575$	−8.47517	−0.353439
$576$	−4.43391	−0.184746
$577$	−21.0368	−0.875775	−0.437887	−	0.899030i	$-0.644273\pi$
$577$	−21.0368	−0.875775	−0.437887	+	0.899030i	$0.644273\pi$
$578$	−18.6590	−0.776113
$579$	−19.6173	−0.815267
$580$	−2.21983	−0.0921735
$581$	0	0
$582$	1.89008	0.0783465
$583$	15.7560	0.652547
$584$	−0.607333	−0.0251316
$585$	−8.67887	−0.358827
$586$	−8.95300	−0.369845
$587$	38.7764	1.60048	0.800238	−	0.599683i	$-0.204707\pi$
$587$	38.7764	1.60048	0.800238	+	0.599683i	$0.204707\pi$
$588$	0	0
$589$	−78.6607	−3.24116
$590$	−4.86208	−0.200169
$591$	20.4661	0.841862
$592$	15.5942	0.640917
$593$	38.9439	1.59923	0.799617	−	0.600510i	$-0.205036\pi$
$593$	38.9439	1.59923	0.799617	+	0.600510i	$0.205036\pi$
$594$	−36.1715	−1.48413
$595$	0	0
$596$	−1.21637	−0.0498246
$597$	−29.4644	−1.20590
$598$	6.34290	0.259380
$599$	−5.29052	−0.216165	−0.108082	−	0.994142i	$-0.534471\pi$
$599$	−5.29052	−0.216165	−0.108082	+	0.994142i	$0.534471\pi$
$600$	34.3153	1.40092
$601$	−8.63773	−0.352340	−0.176170	−	0.984360i	$-0.556371\pi$
$601$	−8.63773	−0.352340	−0.176170	+	0.984360i	$0.556371\pi$
$602$	0	0
$603$	8.95513	0.364681
$604$	1.18359	0.0481595
$605$	−33.1400	−1.34733
$606$	36.5013	1.48276
$607$	−23.4034	−0.949916	−0.474958	−	0.880009i	$-0.657537\pi$
$607$	−23.4034	−0.949916	−0.474958	+	0.880009i	$0.657537\pi$
$608$	−4.13361	−0.167640
$609$	0	0
$610$	−34.3284	−1.38992
$611$	11.3894	0.460767
$612$	0.103738	0.00419334
$613$	21.6770	0.875524	0.437762	−	0.899091i	$-0.355771\pi$
$613$	21.6770	0.875524	0.437762	+	0.899091i	$0.355771\pi$
$614$	3.63879	0.146850
$615$	−5.60388	−0.225970
$616$	0	0
$617$	13.6015	0.547575	0.273788	−	0.961790i	$-0.411723\pi$
$617$	13.6015	0.547575	0.273788	+	0.961790i	$0.411723\pi$
$618$	23.1836	0.932581
$619$	6.02416	0.242132	0.121066	−	0.992644i	$-0.461369\pi$
$619$	6.02416	0.242132	0.121066	+	0.992644i	$0.461369\pi$
$620$	3.01208	0.120968
$621$	−5.90979	−0.237152
$622$	15.7052	0.629720
$623$	0	0
$624$	−26.8159	−1.07350
$625$	−1.13275	−0.0453101
$626$	−25.1172	−1.00389
$627$	57.9711	2.31514
$628$	1.61920	0.0646133
$629$	7.56332	0.301569
$630$	0	0
$631$	−0.685317	−0.0272820	−0.0136410	−	0.999907i	$-0.504342\pi$
$631$	−0.685317	−0.0272820	−0.0136410	+	0.999907i	$0.504342\pi$
$632$	−17.1836	−0.683526
$633$	−22.1414	−0.880041
$634$	−12.9599	−0.514704
$635$	−63.3008	−2.51202
$636$	0.480550	0.0190550
$637$	0	0
$638$	−45.3793	−1.79658
$639$	−3.03146	−0.119923
$640$	−43.2590	−1.70996
$641$	−10.5047	−0.414911	−0.207456	−	0.978244i	$-0.566518\pi$
$641$	−10.5047	−0.414911	−0.207456	+	0.978244i	$0.566518\pi$
$642$	14.1468	0.558328
$643$	17.9608	0.708304	0.354152	−	0.935188i	$-0.384770\pi$
$643$	17.9608	0.708304	0.354152	+	0.935188i	$0.384770\pi$
$644$	0	0
$645$	−2.89008	−0.113797
$646$	−24.2368	−0.953585
$647$	1.52542	0.0599704	0.0299852	−	0.999550i	$-0.490454\pi$
$647$	1.52542	0.0599704	0.0299852	+	0.999550i	$0.490454\pi$
$648$	19.1037	0.750464
$649$	−4.19567	−0.164694
$650$	−47.7536	−1.87305
$651$	0	0
$652$	0.815938	0.0319546
$653$	4.87071	0.190605	0.0953027	−	0.995448i	$-0.469618\pi$
$653$	4.87071	0.190605	0.0953027	+	0.995448i	$0.469618\pi$
$654$	−24.2935	−0.949951
$655$	15.5603	0.607993
$656$	4.16852	0.162753
$657$	−0.127966	−0.00499242
$658$	0	0
$659$	42.9288	1.67227	0.836135	−	0.548524i	$-0.184810\pi$
$659$	42.9288	1.67227	0.836135	+	0.548524i	$0.184810\pi$
$660$	−2.21983	−0.0864069
$661$	−5.18837	−0.201804	−0.100902	−	0.994896i	$-0.532173\pi$
$661$	−5.18837	−0.201804	−0.100902	+	0.994896i	$0.532173\pi$
$662$	−40.3913	−1.56985
$663$	−13.0060	−0.505110
$664$	28.1677	1.09312
$665$	0	0
$666$	3.14675	0.121934
$667$	−7.41417	−0.287078
$668$	0.836001	0.0323458
$669$	−12.6294	−0.488280
$670$	80.1163	3.09516
$671$	−29.6233	−1.14359
$672$	0	0
$673$	31.5254	1.21522	0.607608	−	0.794237i	$-0.292129\pi$
$673$	31.5254	1.21522	0.607608	+	0.794237i	$0.292129\pi$
$674$	33.8965	1.30565
$675$	44.4929	1.71253
$676$	0.362747	0.0139518
$677$	−12.3672	−0.475309	−0.237655	−	0.971350i	$-0.576379\pi$
$677$	−12.3672	−0.475309	−0.237655	+	0.971350i	$0.576379\pi$
$678$	6.20775	0.238407
$679$	0	0
$680$	−20.1297	−0.771938
$681$	−23.6474	−0.906171
$682$	61.5749	2.35783
$683$	4.74871	0.181704	0.0908521	−	0.995864i	$-0.471041\pi$
$683$	4.74871	0.181704	0.0908521	+	0.995864i	$0.471041\pi$
$684$	−0.425665	−0.0162757
$685$	12.6353	0.482771
$686$	0	0
$687$	35.6149	1.35879
$688$	2.14983	0.0819615
$689$	14.5047	0.552586
$690$	−8.59179	−0.327084
$691$	−7.11423	−0.270638	−0.135319	−	0.990802i	$-0.543206\pi$
$691$	−7.11423	−0.270638	−0.135319	+	0.990802i	$0.543206\pi$
$692$	−0.0822952	−0.00312840
$693$	0	0
$694$	−21.1207	−0.801730
$695$	70.3672	2.66918
$696$	30.0194	1.13788
$697$	2.02177	0.0765800
$698$	51.8103	1.96105
$699$	6.52409	0.246764
$700$	0	0
$701$	21.6383	0.817268	0.408634	−	0.912698i	$-0.366005\pi$
$701$	21.6383	0.817268	0.408634	+	0.912698i	$0.366005\pi$
$702$	−33.2989	−1.25679
$703$	−31.0344	−1.17049
$704$	−34.2306	−1.29011
$705$	−15.4276	−0.581036
$706$	−6.59179	−0.248085
$707$	0	0
$708$	−0.127966	−0.00480924
$709$	−14.7332	−0.553316	−0.276658	−	0.960968i	$-0.589227\pi$
$709$	−14.7332	−0.553316	−0.276658	+	0.960968i	$0.589227\pi$
$710$	−27.1207	−1.01782
$711$	−3.62060	−0.135783
$712$	−47.0946	−1.76494
$713$	10.0603	0.376760
$714$	0	0
$715$	−67.0025	−2.50575
$716$	−1.34913	−0.0504192
$717$	24.1414	0.901576
$718$	30.4131	1.13501
$719$	41.4663	1.54643	0.773217	−	0.634142i	$-0.218646\pi$
$719$	41.4663	1.54643	0.773217	+	0.634142i	$0.218646\pi$
$720$	−8.74487	−0.325902
$721$	0	0
$722$	71.9947	2.67937
$723$	−10.2332	−0.380578
$724$	0.718104	0.0266881
$725$	55.8189	2.07306
$726$	−20.6625	−0.766857
$727$	−21.5230	−0.798245	−0.399122	−	0.916898i	$-0.630685\pi$
$727$	−21.5230	−0.798245	−0.399122	+	0.916898i	$0.630685\pi$
$728$	0	0
$729$	30.0086	1.11143
$730$	−1.14483	−0.0423722
$731$	1.04269	0.0385652
$732$	−0.903493	−0.0333941
$733$	3.88876	0.143634	0.0718172	−	0.997418i	$-0.477120\pi$
$733$	3.88876	0.143634	0.0718172	+	0.997418i	$0.477120\pi$
$734$	25.7840	0.951705
$735$	0	0
$736$	0.528665	0.0194869
$737$	69.1353	2.54663
$738$	0.841166	0.0309638
$739$	10.4655	0.384979	0.192490	−	0.981299i	$-0.438344\pi$
$739$	10.4655	0.384979	0.192490	+	0.981299i	$0.438344\pi$
$740$	1.18837	0.0436855
$741$	53.3672	1.96049
$742$	0	0
$743$	41.3903	1.51846	0.759231	−	0.650821i	$-0.225575\pi$
$743$	41.3903	1.51846	0.759231	+	0.650821i	$0.225575\pi$
$744$	−40.7332	−1.49335
$745$	49.7318	1.82203
$746$	9.87454	0.361533
$747$	5.93495	0.217149
$748$	0.800873	0.0292828
$749$	0	0
$750$	24.1957	0.883501
$751$	31.1293	1.13592	0.567962	−	0.823055i	$-0.307732\pi$
$751$	31.1293	1.13592	0.567962	+	0.823055i	$0.307732\pi$
$752$	11.4760	0.418488
$753$	−6.06770	−0.221119
$754$	−41.7754	−1.52137
$755$	−48.3913	−1.76114
$756$	0	0
$757$	−38.2741	−1.39110	−0.695548	−	0.718479i	$-0.744839\pi$
$757$	−38.2741	−1.39110	−0.695548	+	0.718479i	$0.744839\pi$
$758$	12.2470	0.444830
$759$	−7.41417	−0.269117
$760$	82.5978	2.99614
$761$	17.7259	0.642562	0.321281	−	0.946984i	$-0.395887\pi$
$761$	17.7259	0.642562	0.321281	+	0.946984i	$0.395887\pi$
$762$	−39.4674	−1.42975
$763$	0	0
$764$	0.855167	0.0309389
$765$	−4.24134	−0.153346
$766$	−16.6625	−0.602040
$767$	−3.86246	−0.139465
$768$	−3.28322	−0.118473
$769$	−19.4470	−0.701275	−0.350638	−	0.936511i	$-0.614035\pi$
$769$	−19.4470	−0.701275	−0.350638	+	0.936511i	$0.614035\pi$
$770$	0	0
$771$	−2.82743	−0.101827
$772$	1.11205	0.0400234
$773$	32.9807	1.18623	0.593117	−	0.805116i	$-0.297897\pi$
$773$	32.9807	1.18623	0.593117	+	0.805116i	$0.297897\pi$
$774$	0.433814	0.0155931
$775$	−75.7405	−2.72068
$776$	2.32390	0.0834231
$777$	0	0
$778$	−12.6136	−0.452218
$779$	−8.29590	−0.297231
$780$	−2.04354	−0.0731705
$781$	−23.4034	−0.837440
$782$	3.09975	0.110847
$783$	38.9229	1.39099
$784$	0	0
$785$	−66.2016	−2.36284
$786$	9.70171	0.346049
$787$	−48.5387	−1.73022	−0.865109	−	0.501585i	$-0.832751\pi$
$787$	−48.5387	−1.73022	−0.865109	+	0.501585i	$0.832751\pi$
$788$	−1.16016	−0.0413290
$789$	11.3599	0.404422
$790$	−32.3913	−1.15243
$791$	0	0
$792$	−7.22713	−0.256805
$793$	−27.2707	−0.968410
$794$	18.2237	0.646734
$795$	−19.6474	−0.696822
$796$	1.67025	0.0592005
$797$	8.97716	0.317987	0.158994	−	0.987280i	$-0.449175\pi$
$797$	8.97716	0.317987	0.158994	+	0.987280i	$0.449175\pi$
$798$	0	0
$799$	5.56597	0.196910
$800$	−3.98015	−0.140720
$801$	−9.92287	−0.350607
$802$	−7.58211	−0.267733
$803$	−0.987918	−0.0348629
$804$	2.10859	0.0743642
$805$	0	0
$806$	56.6848	1.99664
$807$	16.1112	0.567143
$808$	44.8791	1.57884
$809$	2.40688	0.0846213	0.0423107	−	0.999105i	$-0.486528\pi$
$809$	2.40688	0.0846213	0.0423107	+	0.999105i	$0.486528\pi$
$810$	36.0108	1.26529
$811$	6.13275	0.215350	0.107675	−	0.994186i	$-0.465659\pi$
$811$	6.13275	0.215350	0.107675	+	0.994186i	$0.465659\pi$
$812$	0	0
$813$	−20.8492	−0.731213
$814$	24.2935	0.851487
$815$	−33.3599	−1.16855
$816$	−13.1049	−0.458762
$817$	−4.27844	−0.149684
$818$	42.2344	1.47669
$819$	0	0
$820$	0.317667	0.0110934
$821$	−15.6472	−0.546089	−0.273045	−	0.962001i	$-0.588031\pi$
$821$	−15.6472	−0.546089	−0.273045	+	0.962001i	$0.588031\pi$
$822$	7.87800	0.274777
$823$	−33.5206	−1.16846	−0.584228	−	0.811590i	$-0.698603\pi$
$823$	−33.5206	−1.16846	−0.584228	+	0.811590i	$0.698603\pi$
$824$	28.5047	0.993009
$825$	55.8189	1.94337
$826$	0	0
$827$	−1.02071	−0.0354934	−0.0177467	−	0.999843i	$-0.505649\pi$
$827$	−1.02071	−0.0354934	−0.0177467	+	0.999843i	$0.505649\pi$
$828$	0.0544401	0.00189192
$829$	−0.469796	−0.0163167	−0.00815835	−	0.999967i	$-0.502597\pi$
$829$	−0.469796	−0.0163167	−0.00815835	+	0.999967i	$0.502597\pi$
$830$	53.0965	1.84301
$831$	−11.8998	−0.412799
$832$	−31.5121	−1.09249
$833$	0	0
$834$	43.8732	1.51921
$835$	−34.1801	−1.18285
$836$	−3.28621	−0.113656
$837$	−52.8143	−1.82553
$838$	−9.63879	−0.332967
$839$	−45.1057	−1.55722	−0.778611	−	0.627507i	$-0.784076\pi$
$839$	−45.1057	−1.55722	−0.778611	+	0.627507i	$0.784076\pi$
$840$	0	0
$841$	19.8310	0.683828
$842$	33.5168	1.15507
$843$	34.4081	1.18508
$844$	1.25513	0.0432033
$845$	−14.8310	−0.510202
$846$	2.31575	0.0796171
$847$	0	0
$848$	14.6150	0.501881
$849$	17.9758	0.616929
$850$	−23.3370	−0.800454
$851$	3.96913	0.136060
$852$	−0.713792	−0.0244541
$853$	−2.00000	−0.0684787	−0.0342393	−	0.999414i	$-0.510901\pi$
$853$	−2.00000	−0.0684787	−0.0342393	+	0.999414i	$0.510901\pi$
$854$	0	0
$855$	17.4034	0.595184
$856$	17.3937	0.594506
$857$	−2.01075	−0.0686860	−0.0343430	−	0.999410i	$-0.510934\pi$
$857$	−2.01075	−0.0686860	−0.0343430	+	0.999410i	$0.510934\pi$
$858$	−41.7754	−1.42619
$859$	33.8926	1.15640	0.578200	−	0.815895i	$-0.303755\pi$
$859$	33.8926	1.15640	0.578200	+	0.815895i	$0.303755\pi$
$860$	0.163830	0.00558657
$861$	0	0
$862$	49.7318	1.69387
$863$	30.3284	1.03239	0.516196	−	0.856471i	$-0.327348\pi$
$863$	30.3284	1.03239	0.516196	+	0.856471i	$0.327348\pi$
$864$	−2.77538	−0.0944204
$865$	3.36467	0.114402
$866$	−51.7948	−1.76006
$867$	20.0783	0.681895
$868$	0	0
$869$	−27.9517	−0.948196
$870$	56.5870	1.91848
$871$	63.6448	2.15652
$872$	−29.8694	−1.01150
$873$	0.489647	0.0165721
$874$	−12.7192	−0.430232
$875$	0	0
$876$	−0.0301310	−0.00101803
$877$	−5.24804	−0.177214	−0.0886069	−	0.996067i	$-0.528242\pi$
$877$	−5.24804	−0.177214	−0.0886069	+	0.996067i	$0.528242\pi$
$878$	11.2504	0.379684
$879$	9.63401	0.324947
$880$	−67.5120	−2.27583
$881$	31.7318	1.06907	0.534536	−	0.845145i	$-0.320486\pi$
$881$	31.7318	1.06907	0.534536	+	0.845145i	$0.320486\pi$
$882$	0	0
$883$	−51.9952	−1.74978	−0.874889	−	0.484323i	$-0.839066\pi$
$883$	−51.9952	−1.74978	−0.874889	+	0.484323i	$0.839066\pi$
$884$	0.737270	0.0247971
$885$	5.23191	0.175869
$886$	−53.0678	−1.78285
$887$	−28.0935	−0.943288	−0.471644	−	0.881789i	$-0.656339\pi$
$887$	−28.0935	−0.943288	−0.471644	+	0.881789i	$0.656339\pi$
$888$	−16.0707	−0.539297
$889$	0	0
$890$	−88.7741	−2.97571
$891$	31.0750	1.04105
$892$	0.715922	0.0239708
$893$	−22.8388	−0.764270
$894$	31.0073	1.03704
$895$	55.1594	1.84378
$896$	0	0
$897$	−6.82536	−0.227892
$898$	16.9957	0.567153
$899$	−66.2586	−2.20985
$900$	−0.409862	−0.0136621
$901$	7.08841	0.236149
$902$	6.49396	0.216225
$903$	0	0
$904$	7.63256	0.253855
$905$	−29.3599	−0.975955
$906$	−30.1715	−1.00238
$907$	29.5733	0.981964	0.490982	−	0.871170i	$-0.336638\pi$
$907$	29.5733	0.981964	0.490982	+	0.871170i	$0.336638\pi$
$908$	1.34050	0.0444861
$909$	9.45606	0.313638
$910$	0	0
$911$	−39.5666	−1.31090	−0.655449	−	0.755239i	$-0.727521\pi$
$911$	−39.5666	−1.31090	−0.655449	+	0.755239i	$0.727521\pi$
$912$	53.7730	1.78060
$913$	45.8189	1.51639
$914$	−51.2659	−1.69572
$915$	36.9396	1.22119
$916$	−2.01890	−0.0667064
$917$	0	0
$918$	−16.2731	−0.537091
$919$	−1.31037	−0.0432252	−0.0216126	−	0.999766i	$-0.506880\pi$
$919$	−1.31037	−0.0432252	−0.0216126	+	0.999766i	$0.506880\pi$
$920$	−10.5638	−0.348278
$921$	−3.91557	−0.129023
$922$	−32.8659	−1.08238
$923$	−21.5448	−0.709156
$924$	0	0
$925$	−29.8823	−0.982524
$926$	10.7836	0.354372
$927$	6.00597	0.197262
$928$	−3.48188	−0.114298
$929$	−27.3653	−0.897825	−0.448912	−	0.893576i	$-0.648189\pi$
$929$	−27.3653	−0.897825	−0.448912	+	0.893576i	$0.648189\pi$
$930$	−76.7827	−2.51780
$931$	0	0
$932$	−0.369831	−0.0121142
$933$	−16.8998	−0.553274
$934$	0.678875	0.0222135
$935$	−32.7439	−1.07084
$936$	−6.65317	−0.217466
$937$	−16.2241	−0.530020	−0.265010	−	0.964246i	$-0.585375\pi$
$937$	−16.2241	−0.530020	−0.265010	+	0.964246i	$0.585375\pi$
$938$	0	0
$939$	27.0277	0.882017
$940$	0.874544	0.0285245
$941$	29.2513	0.953565	0.476782	−	0.879021i	$-0.341803\pi$
$941$	29.2513	0.953565	0.476782	+	0.879021i	$0.341803\pi$
$942$	−41.2760	−1.34485
$943$	1.06100	0.0345509
$944$	−3.89183	−0.126668
$945$	0	0
$946$	3.34913	0.108889
$947$	35.1239	1.14137	0.570687	−	0.821168i	$-0.306677\pi$
$947$	35.1239	1.14137	0.570687	+	0.821168i	$0.306677\pi$
$948$	−0.852511	−0.0276883
$949$	−0.909461	−0.0295224
$950$	95.7585	3.10682
$951$	13.9457	0.452220
$952$	0	0
$953$	−18.5176	−0.599845	−0.299923	−	0.953963i	$-0.596961\pi$
$953$	−18.5176	−0.599845	−0.299923	+	0.953963i	$0.596961\pi$
$954$	2.94916	0.0954827
$955$	−34.9638	−1.13140
$956$	−1.36850	−0.0442606
$957$	48.8310	1.57848
$958$	5.82285	0.188128
$959$	0	0
$960$	42.6848	1.37765
$961$	58.9060	1.90019
$962$	22.3642	0.721050
$963$	3.66487	0.118099
$964$	0.580092	0.0186835
$965$	−45.4663	−1.46361
$966$	0	0
$967$	54.5387	1.75385	0.876923	−	0.480631i	$-0.159592\pi$
$967$	54.5387	1.75385	0.876923	+	0.480631i	$0.159592\pi$
$968$	−25.4050	−0.816546
$969$	26.0804	0.837822
$970$	4.38059	0.140652
$971$	−34.3588	−1.10263	−0.551313	−	0.834298i	$-0.685873\pi$
$971$	−34.3588	−1.10263	−0.551313	+	0.834298i	$0.685873\pi$
$972$	−0.525155	−0.0168444
$973$	0	0
$974$	51.8418	1.66112
$975$	51.3860	1.64567
$976$	−27.4780	−0.879551
$977$	−5.48188	−0.175381	−0.0876904	−	0.996148i	$-0.527949\pi$
$977$	−5.48188	−0.175381	−0.0876904	+	0.996148i	$0.527949\pi$
$978$	−20.7995	−0.665096
$979$	−76.6064	−2.44835
$980$	0	0
$981$	−6.29350	−0.200936
$982$	−43.8616	−1.39968
$983$	10.4310	0.332699	0.166349	−	0.986067i	$-0.446802\pi$
$983$	10.4310	0.332699	0.166349	+	0.986067i	$0.446802\pi$
$984$	−4.29590	−0.136948
$985$	47.4336	1.51136
$986$	−20.4155	−0.650162
$987$	0	0
$988$	−3.02523	−0.0962453
$989$	0.547188	0.0173996
$990$	−13.6233	−0.432975
$991$	6.75733	0.214654	0.107327	−	0.994224i	$-0.465771\pi$
$991$	6.75733	0.214654	0.107327	+	0.994224i	$0.465771\pi$
$992$	4.72455	0.150004
$993$	43.4637	1.37928
$994$	0	0
$995$	−68.2887	−2.16490
$996$	1.39745	0.0442800
$997$	−48.9670	−1.55080	−0.775400	−	0.631470i	$-0.782452\pi$
$997$	−48.9670	−1.55080	−0.775400	+	0.631470i	$0.782452\pi$
$998$	49.4577	1.56556
$999$	−20.8371	−0.659257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.k.1.2		3
7.6	odd	2		287.2.a.d.1.2	✓	3
21.20	even	2		2583.2.a.l.1.2		3
28.27	even	2		4592.2.a.r.1.2		3
35.34	odd	2		7175.2.a.i.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.d.1.2	✓	3	7.6	odd	2
2009.2.a.k.1.2		3	1.1	even	1	trivial
2583.2.a.l.1.2		3	21.20	even	2
4592.2.a.r.1.2		3	28.27	even	2
7175.2.a.i.1.2		3	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.44504 q^{2} -1.55496 q^{3} +0.0881460 q^{4} -3.60388 q^{5} -2.24698 q^{6} -2.76271 q^{8} -0.582105 q^{9} +O(q^{10})\)	\(q+1.44504 q^{2} -1.55496 q^{3} +0.0881460 q^{4} -3.60388 q^{5} -2.24698 q^{6} -2.76271 q^{8} -0.582105 q^{9} -5.20775 q^{10} -4.49396 q^{11} -0.137063 q^{12} -4.13706 q^{13} +5.60388 q^{15} -4.16852 q^{16} -2.02177 q^{17} -0.841166 q^{18} +8.29590 q^{19} -0.317667 q^{20} -6.49396 q^{22} -1.06100 q^{23} +4.29590 q^{24} +7.98792 q^{25} -5.97823 q^{26} +5.57002 q^{27} +6.98792 q^{29} +8.09783 q^{30} -9.48188 q^{31} -0.498271 q^{32} +6.98792 q^{33} -2.92154 q^{34} -0.0513102 q^{36} -3.74094 q^{37} +11.9879 q^{38} +6.43296 q^{39} +9.95646 q^{40} -1.00000 q^{41} -0.515729 q^{43} -0.396125 q^{44} +2.09783 q^{45} -1.53319 q^{46} -2.75302 q^{47} +6.48188 q^{48} +11.5429 q^{50} +3.14377 q^{51} -0.364666 q^{52} -3.50604 q^{53} +8.04892 q^{54} +16.1957 q^{55} -12.8998 q^{57} +10.0978 q^{58} +0.933624 q^{59} +0.493959 q^{60} +6.59179 q^{61} -13.7017 q^{62} +7.61702 q^{64} +14.9095 q^{65} +10.0978 q^{66} -15.3840 q^{67} -0.178211 q^{68} +1.64981 q^{69} +5.20775 q^{71} +1.60819 q^{72} +0.219833 q^{73} -5.40581 q^{74} -12.4209 q^{75} +0.731250 q^{76} +9.29590 q^{78} +6.21983 q^{79} +15.0228 q^{80} -6.91484 q^{81} -1.44504 q^{82} -10.1957 q^{83} +7.28621 q^{85} -0.745251 q^{86} -10.8659 q^{87} +12.4155 q^{88} +17.0465 q^{89} +3.03146 q^{90} -0.0935228 q^{92} +14.7439 q^{93} -3.97823 q^{94} -29.8974 q^{95} +0.774791 q^{96} -0.841166 q^{97} +2.61596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 4 q^{2} - 5 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 9 q^{8} + 4 q^{9}+O(q^{10}) \) 3 * q + 4 * q^2 - 5 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 9 * q^8 + 4 * q^9	\( 3 q + 4 q^{2} - 5 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 9 q^{8} + 4 q^{9} + 2 q^{10} - 4 q^{11} + 5 q^{12} - 7 q^{13} + 8 q^{15} + 18 q^{16} - 3 q^{17} - 11 q^{18} + 11 q^{19} + 16 q^{20} - 10 q^{22} - 13 q^{23} - q^{24} + 5 q^{25} - 21 q^{26} - 8 q^{27} + 2 q^{29} + 6 q^{30} + 27 q^{32} + 2 q^{33} + 17 q^{34} - 32 q^{36} + 3 q^{37} + 17 q^{38} + 36 q^{40} - 3 q^{41} + 11 q^{43} - 10 q^{44} - 12 q^{45} - 8 q^{46} - 13 q^{47} - 9 q^{48} + 16 q^{50} + 26 q^{51} - 35 q^{52} - 20 q^{53} + 15 q^{54} + 12 q^{55} - 16 q^{57} + 12 q^{58} - 4 q^{59} - 8 q^{60} - 8 q^{61} - 14 q^{62} + 49 q^{64} + 12 q^{66} - 36 q^{67} + 52 q^{68} + 31 q^{69} - 2 q^{71} - 23 q^{72} + 2 q^{73} - 3 q^{74} + q^{75} + 10 q^{76} + 14 q^{78} + 20 q^{79} + 58 q^{80} + 27 q^{81} - 4 q^{82} + 6 q^{83} + 30 q^{85} + 31 q^{86} + 6 q^{87} + 2 q^{88} + q^{89} - 16 q^{90} - q^{92} - 14 q^{93} - 15 q^{94} - 26 q^{95} + 4 q^{96} - 11 q^{97} + 18 q^{99}+O(q^{100}) \) 3 * q + 4 * q^2 - 5 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 9 * q^8 + 4 * q^9 + 2 * q^10 - 4 * q^11 + 5 * q^12 - 7 * q^13 + 8 * q^15 + 18 * q^16 - 3 * q^17 - 11 * q^18 + 11 * q^19 + 16 * q^20 - 10 * q^22 - 13 * q^23 - q^24 + 5 * q^25 - 21 * q^26 - 8 * q^27 + 2 * q^29 + 6 * q^30 + 27 * q^32 + 2 * q^33 + 17 * q^34 - 32 * q^36 + 3 * q^37 + 17 * q^38 + 36 * q^40 - 3 * q^41 + 11 * q^43 - 10 * q^44 - 12 * q^45 - 8 * q^46 - 13 * q^47 - 9 * q^48 + 16 * q^50 + 26 * q^51 - 35 * q^52 - 20 * q^53 + 15 * q^54 + 12 * q^55 - 16 * q^57 + 12 * q^58 - 4 * q^59 - 8 * q^60 - 8 * q^61 - 14 * q^62 + 49 * q^64 + 12 * q^66 - 36 * q^67 + 52 * q^68 + 31 * q^69 - 2 * q^71 - 23 * q^72 + 2 * q^73 - 3 * q^74 + q^75 + 10 * q^76 + 14 * q^78 + 20 * q^79 + 58 * q^80 + 27 * q^81 - 4 * q^82 + 6 * q^83 + 30 * q^85 + 31 * q^86 + 6 * q^87 + 2 * q^88 + q^89 - 16 * q^90 - q^92 - 14 * q^93 - 15 * q^94 - 26 * q^95 + 4 * q^96 - 11 * q^97 + 18 * q^99

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Database

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