LMFDB - Embedded newform 2009.2.a.s.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$16.0419457661$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 25 x^{15} + 77 x^{14} + 247 x^{13} - 790 x^{12} - 1231 x^{11} + 4173 x^{10} + \cdots - 464 $ x^17 - 3x^16 - 25x^15 + 77x^14 + 247x^13 - 790x^12 - 1231x^11 + 4173x^10 + 3251x^9 - 12183x^8 - 4259x^7 + 19567x^6 + 2029x^5 - 16136x^4 + 299x^3 + 5775x^2 - 312x - 464
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$2.36949$ 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)

$f(q)$	$=$	$q+2.36949 q^{2} -1.64632 q^{3} +3.61450 q^{4} -4.02976 q^{5} -3.90094 q^{6} +3.82554 q^{8} -0.289637 q^{9} +O(q^{10})$	\(q+2.36949 q^{2} -1.64632 q^{3} +3.61450 q^{4} -4.02976 q^{5} -3.90094 q^{6} +3.82554 q^{8} -0.289637 q^{9} -9.54849 q^{10} -2.19931 q^{11} -5.95061 q^{12} +2.49374 q^{13} +6.63427 q^{15} +1.83560 q^{16} +4.73767 q^{17} -0.686293 q^{18} +0.560182 q^{19} -14.5656 q^{20} -5.21126 q^{22} +7.86888 q^{23} -6.29806 q^{24} +11.2390 q^{25} +5.90890 q^{26} +5.41579 q^{27} +1.33395 q^{29} +15.7199 q^{30} +4.18735 q^{31} -3.30164 q^{32} +3.62077 q^{33} +11.2259 q^{34} -1.04689 q^{36} +8.64873 q^{37} +1.32735 q^{38} -4.10549 q^{39} -15.4160 q^{40} +1.00000 q^{41} +2.23622 q^{43} -7.94941 q^{44} +1.16717 q^{45} +18.6453 q^{46} +3.19625 q^{47} -3.02199 q^{48} +26.6307 q^{50} -7.79972 q^{51} +9.01362 q^{52} -13.7317 q^{53} +12.8327 q^{54} +8.86270 q^{55} -0.922238 q^{57} +3.16079 q^{58} -14.1655 q^{59} +23.9796 q^{60} -6.40980 q^{61} +9.92190 q^{62} -11.4944 q^{64} -10.0492 q^{65} +8.57938 q^{66} +0.699489 q^{67} +17.1243 q^{68} -12.9547 q^{69} -5.49009 q^{71} -1.10802 q^{72} +6.06987 q^{73} +20.4931 q^{74} -18.5029 q^{75} +2.02478 q^{76} -9.72793 q^{78} +0.250356 q^{79} -7.39705 q^{80} -8.04720 q^{81} +2.36949 q^{82} +7.93567 q^{83} -19.0917 q^{85} +5.29871 q^{86} -2.19611 q^{87} -8.41356 q^{88} +5.57677 q^{89} +2.76560 q^{90} +28.4421 q^{92} -6.89371 q^{93} +7.57350 q^{94} -2.25740 q^{95} +5.43554 q^{96} +9.96956 q^{97} +0.637002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) $ 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9	$ 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9} - 2 q^{10} + 15 q^{11} + 4 q^{12} - 5 q^{13} + 24 q^{15} + 33 q^{16} + 4 q^{17} + 10 q^{18} + 5 q^{19} - 26 q^{20} + 16 q^{22} + 12 q^{23} + 16 q^{24} + 24 q^{25} + 31 q^{26} - 11 q^{27} + 14 q^{29} - 33 q^{30} - 3 q^{31} + 16 q^{32} + 4 q^{33} - 24 q^{34} + 57 q^{36} + 24 q^{37} + 45 q^{39} + 36 q^{40} + 17 q^{41} + 14 q^{43} - 9 q^{44} - 21 q^{45} + 44 q^{46} + 19 q^{47} - 60 q^{48} - 4 q^{50} + 2 q^{51} - 25 q^{52} + 4 q^{53} + 68 q^{54} + 9 q^{55} - 12 q^{57} - q^{58} - 27 q^{59} + 66 q^{60} - q^{61} - 23 q^{62} + 75 q^{64} + 22 q^{65} - 16 q^{66} + 49 q^{67} + 45 q^{68} + 12 q^{69} + 40 q^{71} - 23 q^{72} - 14 q^{73} + 33 q^{74} + 27 q^{75} - 9 q^{76} - 12 q^{78} + 61 q^{79} - 82 q^{80} + 53 q^{81} + 3 q^{82} - 18 q^{83} - 13 q^{85} - 4 q^{86} - 17 q^{87} + 74 q^{88} + 18 q^{89} - 20 q^{90} + 28 q^{92} - 36 q^{93} - 5 q^{94} + 20 q^{95} + 148 q^{96} + 26 q^{97} + 38 q^{99}+O(q^{100}) $ 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9 - 2 * q^10 + 15 * q^11 + 4 * q^12 - 5 * q^13 + 24 * q^15 + 33 * q^16 + 4 * q^17 + 10 * q^18 + 5 * q^19 - 26 * q^20 + 16 * q^22 + 12 * q^23 + 16 * q^24 + 24 * q^25 + 31 * q^26 - 11 * q^27 + 14 * q^29 - 33 * q^30 - 3 * q^31 + 16 * q^32 + 4 * q^33 - 24 * q^34 + 57 * q^36 + 24 * q^37 + 45 * q^39 + 36 * q^40 + 17 * q^41 + 14 * q^43 - 9 * q^44 - 21 * q^45 + 44 * q^46 + 19 * q^47 - 60 * q^48 - 4 * q^50 + 2 * q^51 - 25 * q^52 + 4 * q^53 + 68 * q^54 + 9 * q^55 - 12 * q^57 - q^58 - 27 * q^59 + 66 * q^60 - q^61 - 23 * q^62 + 75 * q^64 + 22 * q^65 - 16 * q^66 + 49 * q^67 + 45 * q^68 + 12 * q^69 + 40 * q^71 - 23 * q^72 - 14 * q^73 + 33 * q^74 + 27 * q^75 - 9 * q^76 - 12 * q^78 + 61 * q^79 - 82 * q^80 + 53 * q^81 + 3 * q^82 - 18 * q^83 - 13 * q^85 - 4 * q^86 - 17 * q^87 + 74 * q^88 + 18 * q^89 - 20 * q^90 + 28 * q^92 - 36 * q^93 - 5 * q^94 + 20 * q^95 + 148 * q^96 + 26 * q^97 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.36949	1.67548	0.837742	−	0.546066i	$-0.183875\pi$
$2$	2.36949	1.67548	0.837742	+	0.546066i	$0.183875\pi$
$3$	−1.64632	−0.950502	−0.475251	−	0.879850i	$-0.657643\pi$
$3$	−1.64632	−0.950502	−0.475251	+	0.879850i	$0.657643\pi$
$4$	3.61450	1.80725
$5$	−4.02976	−1.80216	−0.901082	−	0.433649i	$-0.857226\pi$
$5$	−4.02976	−1.80216	−0.901082	+	0.433649i	$0.857226\pi$
$6$	−3.90094	−1.59255
$7$	0	0
$7$	0	0
$8$	3.82554	1.35253
$9$	−0.289637	−0.0965457
$10$	−9.54849	−3.01950
$11$	−2.19931	−0.663118	−0.331559	−	0.943435i	$-0.607575\pi$
$11$	−2.19931	−0.663118	−0.331559	+	0.943435i	$0.607575\pi$
$12$	−5.95061	−1.71779
$13$	2.49374	0.691639	0.345819	−	0.938301i	$-0.387601\pi$
$13$	2.49374	0.691639	0.345819	+	0.938301i	$0.387601\pi$
$14$	0	0
$15$	6.63427	1.71296
$16$	1.83560	0.458901
$17$	4.73767	1.14905	0.574527	−	0.818485i	$-0.305186\pi$
$17$	4.73767	1.14905	0.574527	+	0.818485i	$0.305186\pi$
$18$	−0.686293	−0.161761
$19$	0.560182	0.128515	0.0642573	−	0.997933i	$-0.479532\pi$
$19$	0.560182	0.128515	0.0642573	+	0.997933i	$0.479532\pi$
$20$	−14.5656	−3.25696
$21$	0	0
$22$	−5.21126	−1.11104
$23$	7.86888	1.64077	0.820387	−	0.571808i	$-0.193758\pi$
$23$	7.86888	1.64077	0.820387	+	0.571808i	$0.193758\pi$
$24$	−6.29806	−1.28559
$25$	11.2390	2.24780
$26$	5.90890	1.15883
$27$	5.41579	1.04227
$28$	0	0
$29$	1.33395	0.247708	0.123854	−	0.992300i	$-0.460474\pi$
$29$	1.33395	0.247708	0.123854	+	0.992300i	$0.460474\pi$
$30$	15.7199	2.87004
$31$	4.18735	0.752071	0.376035	−	0.926605i	$-0.377287\pi$
$31$	4.18735	0.752071	0.376035	+	0.926605i	$0.377287\pi$
$32$	−3.30164	−0.583653
$33$	3.62077	0.630295
$34$	11.2259	1.92522
$35$	0	0
$36$	−1.04689	−0.174482
$37$	8.64873	1.42184	0.710921	−	0.703272i	$-0.248278\pi$
$37$	8.64873	1.42184	0.710921	+	0.703272i	$0.248278\pi$
$38$	1.32735	0.215324
$39$	−4.10549	−0.657404
$40$	−15.4160	−2.43749
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	2.23622	0.341020	0.170510	−	0.985356i	$-0.445458\pi$
$43$	2.23622	0.341020	0.170510	+	0.985356i	$0.445458\pi$
$44$	−7.94941	−1.19842
$45$	1.16717	0.173991
$46$	18.6453	2.74909
$47$	3.19625	0.466221	0.233111	−	0.972450i	$-0.425110\pi$
$47$	3.19625	0.466221	0.233111	+	0.972450i	$0.425110\pi$
$48$	−3.02199	−0.436186
$49$	0	0
$50$	26.6307	3.76615
$51$	−7.79972	−1.09218
$52$	9.01362	1.24996
$53$	−13.7317	−1.88620	−0.943100	−	0.332511i	$-0.892104\pi$
$53$	−13.7317	−1.88620	−0.943100	+	0.332511i	$0.892104\pi$
$54$	12.8327	1.74631
$55$	8.86270	1.19505
$56$	0	0
$57$	−0.922238	−0.122153
$58$	3.16079	0.415032
$59$	−14.1655	−1.84419	−0.922094	−	0.386967i	$-0.873523\pi$
$59$	−14.1655	−1.84419	−0.922094	+	0.386967i	$0.873523\pi$
$60$	23.9796	3.09575
$61$	−6.40980	−0.820690	−0.410345	−	0.911930i	$-0.634592\pi$
$61$	−6.40980	−0.820690	−0.410345	+	0.911930i	$0.634592\pi$
$62$	9.92190	1.26008
$63$	0	0
$64$	−11.4944	−1.43680
$65$	−10.0492	−1.24645
$66$	8.57938	1.05605
$67$	0.699489	0.0854562	0.0427281	−	0.999087i	$-0.486395\pi$
$67$	0.699489	0.0854562	0.0427281	+	0.999087i	$0.486395\pi$
$68$	17.1243	2.07663
$69$	−12.9547	−1.55956
$70$	0	0
$71$	−5.49009	−0.651553	−0.325777	−	0.945447i	$-0.605626\pi$
$71$	−5.49009	−0.651553	−0.325777	+	0.945447i	$0.605626\pi$
$72$	−1.10802	−0.130581
$73$	6.06987	0.710424	0.355212	−	0.934786i	$-0.384409\pi$
$73$	6.06987	0.710424	0.355212	+	0.934786i	$0.384409\pi$
$74$	20.4931	2.38227
$75$	−18.5029	−2.13653
$76$	2.02478	0.232258
$77$	0	0
$78$	−9.72793	−1.10147
$79$	0.250356	0.0281673	0.0140836	−	0.999901i	$-0.495517\pi$
$79$	0.250356	0.0281673	0.0140836	+	0.999901i	$0.495517\pi$
$80$	−7.39705	−0.827015
$81$	−8.04720	−0.894133
$82$	2.36949	0.261667
$83$	7.93567	0.871053	0.435527	−	0.900176i	$-0.356562\pi$
$83$	7.93567	0.871053	0.435527	+	0.900176i	$0.356562\pi$
$84$	0	0
$85$	−19.0917	−2.07079
$86$	5.29871	0.571375
$87$	−2.19611	−0.235447
$88$	−8.41356	−0.896889
$89$	5.57677	0.591137	0.295568	−	0.955322i	$-0.404491\pi$
$89$	5.57677	0.591137	0.295568	+	0.955322i	$0.404491\pi$
$90$	2.76560	0.291520
$91$	0	0
$92$	28.4421	2.96529
$93$	−6.89371	−0.714845
$94$	7.57350	0.781147
$95$	−2.25740	−0.231604
$96$	5.43554	0.554763
$97$	9.96956	1.01226	0.506128	−	0.862458i	$-0.331076\pi$
$97$	9.96956	1.01226	0.506128	+	0.862458i	$0.331076\pi$
$98$	0	0
$99$	0.637002	0.0640212
$100$	40.6233	4.06233
$101$	1.97257	0.196278	0.0981390	−	0.995173i	$-0.468711\pi$
$101$	1.97257	0.196278	0.0981390	+	0.995173i	$0.468711\pi$
$102$	−18.4814	−1.82993
$103$	19.6162	1.93284	0.966420	−	0.256968i	$-0.0827234\pi$
$103$	19.6162	1.93284	0.966420	+	0.256968i	$0.0827234\pi$
$104$	9.53991	0.935465
$105$	0	0
$106$	−32.5373	−3.16030
$107$	3.57459	0.345569	0.172785	−	0.984960i	$-0.444724\pi$
$107$	3.57459	0.345569	0.172785	+	0.984960i	$0.444724\pi$
$108$	19.5754	1.88364
$109$	9.43771	0.903969	0.451984	−	0.892026i	$-0.350716\pi$
$109$	9.43771	0.903969	0.451984	+	0.892026i	$0.350716\pi$
$110$	21.0001	2.00228
$111$	−14.2386	−1.35146
$112$	0	0
$113$	6.51816	0.613177	0.306588	−	0.951842i	$-0.400813\pi$
$113$	6.51816	0.613177	0.306588	+	0.951842i	$0.400813\pi$
$114$	−2.18524	−0.204666
$115$	−31.7097	−2.95695
$116$	4.82156	0.447671
$117$	−0.722279	−0.0667748
$118$	−33.5650	−3.08991
$119$	0	0
$120$	25.3797	2.31684
$121$	−6.16303	−0.560275
$122$	−15.1880	−1.37505
$123$	−1.64632	−0.148443
$124$	15.1352	1.35918
$125$	−25.1416	−2.24873
$126$	0	0
$127$	11.4657	1.01742	0.508709	−	0.860939i	$-0.330123\pi$
$127$	11.4657	1.01742	0.508709	+	0.860939i	$0.330123\pi$
$128$	−20.6327	−1.82369
$129$	−3.68153	−0.324141
$130$	−23.8114	−2.08840
$131$	−1.75198	−0.153071	−0.0765356	−	0.997067i	$-0.524386\pi$
$131$	−1.75198	−0.153071	−0.0765356	+	0.997067i	$0.524386\pi$
$132$	13.0873	1.13910
$133$	0	0
$134$	1.65743	0.143181
$135$	−21.8243	−1.87834
$136$	18.1242	1.55414
$137$	12.7023	1.08523	0.542615	−	0.839982i	$-0.317434\pi$
$137$	12.7023	1.08523	0.542615	+	0.839982i	$0.317434\pi$
$138$	−30.6960	−2.61302
$139$	3.13302	0.265739	0.132869	−	0.991134i	$-0.457581\pi$
$139$	3.13302	0.265739	0.132869	+	0.991134i	$0.457581\pi$
$140$	0	0
$141$	−5.26205	−0.443144
$142$	−13.0087	−1.09167
$143$	−5.48451	−0.458638
$144$	−0.531659	−0.0443049
$145$	−5.37550	−0.446411
$146$	14.3825	1.19030
$147$	0	0
$148$	31.2608	2.56962
$149$	10.0205	0.820913	0.410456	−	0.911880i	$-0.365369\pi$
$149$	10.0205	0.820913	0.410456	+	0.911880i	$0.365369\pi$
$150$	−43.8426	−3.57973
$151$	12.0013	0.976651	0.488326	−	0.872661i	$-0.337608\pi$
$151$	12.0013	0.976651	0.488326	+	0.872661i	$0.337608\pi$
$152$	2.14300	0.173820
$153$	−1.37221	−0.110936
$154$	0	0
$155$	−16.8740	−1.35535
$156$	−14.8393	−1.18809
$157$	−14.2547	−1.13765	−0.568826	−	0.822458i	$-0.692602\pi$
$157$	−14.2547	−1.13765	−0.568826	+	0.822458i	$0.692602\pi$
$158$	0.593218	0.0471939
$159$	22.6068	1.79284
$160$	13.3048	1.05184
$161$	0	0
$162$	−19.0678	−1.49811
$163$	−7.26280	−0.568867	−0.284433	−	0.958696i	$-0.591805\pi$
$163$	−7.26280	−0.568867	−0.284433	+	0.958696i	$0.591805\pi$
$164$	3.61450	0.282245
$165$	−14.5908	−1.13589
$166$	18.8035	1.45944
$167$	−2.96940	−0.229779	−0.114890	−	0.993378i	$-0.536651\pi$
$167$	−2.96940	−0.229779	−0.114890	+	0.993378i	$0.536651\pi$
$168$	0	0
$169$	−6.78127	−0.521636
$170$	−45.2376	−3.46957
$171$	−0.162250	−0.0124075
$172$	8.08282	0.616309
$173$	20.3386	1.54632	0.773158	−	0.634213i	$-0.218676\pi$
$173$	20.3386	1.54632	0.773158	+	0.634213i	$0.218676\pi$
$174$	−5.20366	−0.394488
$175$	0	0
$176$	−4.03707	−0.304305
$177$	23.3209	1.75290
$178$	13.2141	0.990441
$179$	16.2809	1.21689	0.608444	−	0.793597i	$-0.291794\pi$
$179$	16.2809	1.21689	0.608444	+	0.793597i	$0.291794\pi$
$180$	4.21873	0.314446
$181$	−10.2189	−0.759567	−0.379783	−	0.925075i	$-0.624001\pi$
$181$	−10.2189	−0.759567	−0.379783	+	0.925075i	$0.624001\pi$
$182$	0	0
$183$	10.5526	0.780068
$184$	30.1027	2.21920
$185$	−34.8523	−2.56239
$186$	−16.3346	−1.19771
$187$	−10.4196	−0.761958
$188$	11.5529	0.842578
$189$	0	0
$190$	−5.34889	−0.388050
$191$	−11.0381	−0.798690	−0.399345	−	0.916801i	$-0.630762\pi$
$191$	−11.0381	−0.798690	−0.399345	+	0.916801i	$0.630762\pi$
$192$	18.9235	1.36568
$193$	20.4877	1.47474	0.737369	−	0.675491i	$-0.236068\pi$
$193$	20.4877	1.47474	0.737369	+	0.675491i	$0.236068\pi$
$194$	23.6228	1.69602
$195$	16.5441	1.18475
$196$	0	0
$197$	−2.42929	−0.173079	−0.0865397	−	0.996248i	$-0.527581\pi$
$197$	−2.42929	−0.173079	−0.0865397	+	0.996248i	$0.527581\pi$
$198$	1.50937	0.107266
$199$	−1.81542	−0.128692	−0.0643458	−	0.997928i	$-0.520496\pi$
$199$	−1.81542	−0.128692	−0.0643458	+	0.997928i	$0.520496\pi$
$200$	42.9952	3.04022
$201$	−1.15158	−0.0812263
$202$	4.67399	0.328861
$203$	0	0
$204$	−28.1921	−1.97384
$205$	−4.02976	−0.281451
$206$	46.4804	3.23844
$207$	−2.27912	−0.158410
$208$	4.57752	0.317394
$209$	−1.23201	−0.0852203
$210$	0	0
$211$	17.1401	1.17997	0.589986	−	0.807414i	$-0.299133\pi$
$211$	17.1401	1.17997	0.589986	+	0.807414i	$0.299133\pi$
$212$	−49.6333	−3.40883
$213$	9.03843	0.619303
$214$	8.46998	0.578996
$215$	−9.01144	−0.614575
$216$	20.7183	1.40970
$217$	0	0
$218$	22.3626	1.51459
$219$	−9.99293	−0.675260
$220$	32.0342	2.15975
$221$	11.8145	0.794731
$222$	−33.7382	−2.26436
$223$	−13.3594	−0.894612	−0.447306	−	0.894381i	$-0.647616\pi$
$223$	−13.3594	−0.894612	−0.447306	+	0.894381i	$0.647616\pi$
$224$	0	0
$225$	−3.25522	−0.217015
$226$	15.4447	1.02737
$227$	11.1902	0.742718	0.371359	−	0.928489i	$-0.378892\pi$
$227$	11.1902	0.742718	0.371359	+	0.928489i	$0.378892\pi$
$228$	−3.33343	−0.220762
$229$	0.994453	0.0657153	0.0328576	−	0.999460i	$-0.489539\pi$
$229$	0.994453	0.0657153	0.0328576	+	0.999460i	$0.489539\pi$
$230$	−75.1359	−4.95432
$231$	0	0
$232$	5.10309	0.335034
$233$	21.9655	1.43901	0.719503	−	0.694489i	$-0.244370\pi$
$233$	21.9655	1.43901	0.719503	+	0.694489i	$0.244370\pi$
$234$	−1.71144	−0.111880
$235$	−12.8801	−0.840207
$236$	−51.2011	−3.33291
$237$	−0.412166	−0.0267731
$238$	0	0
$239$	−16.3177	−1.05550	−0.527752	−	0.849399i	$-0.676965\pi$
$239$	−16.3177	−1.05550	−0.527752	+	0.849399i	$0.676965\pi$
$240$	12.1779	0.786079
$241$	1.66463	0.107229	0.0536143	−	0.998562i	$-0.482926\pi$
$241$	1.66463	0.107229	0.0536143	+	0.998562i	$0.482926\pi$
$242$	−14.6033	−0.938733
$243$	−2.99912	−0.192394
$244$	−23.1682	−1.48319
$245$	0	0
$246$	−3.90094	−0.248715
$247$	1.39695	0.0888857
$248$	16.0189	1.01720
$249$	−13.0646	−0.827938
$250$	−59.5728	−3.76772
$251$	−17.0667	−1.07724	−0.538620	−	0.842549i	$-0.681054\pi$
$251$	−17.0667	−1.07724	−0.538620	+	0.842549i	$0.681054\pi$
$252$	0	0
$253$	−17.3061	−1.08803
$254$	27.1679	1.70467
$255$	31.4310	1.96829
$256$	−25.9001	−1.61876
$257$	−24.0970	−1.50313	−0.751566	−	0.659658i	$-0.770701\pi$
$257$	−24.0970	−1.50313	−0.751566	+	0.659658i	$0.770701\pi$
$258$	−8.72336	−0.543093
$259$	0	0
$260$	−36.3227	−2.25264
$261$	−0.386362	−0.0239152
$262$	−4.15131	−0.256469
$263$	3.30837	0.204003	0.102001	−	0.994784i	$-0.467475\pi$
$263$	3.30837	0.204003	0.102001	+	0.994784i	$0.467475\pi$
$264$	13.8514	0.852495
$265$	55.3356	3.39924
$266$	0	0
$267$	−9.18114	−0.561877
$268$	2.52830	0.154441
$269$	11.6261	0.708853	0.354426	−	0.935084i	$-0.384676\pi$
$269$	11.6261	0.708853	0.354426	+	0.935084i	$0.384676\pi$
$270$	−51.7126	−3.14713
$271$	−27.3193	−1.65953	−0.829765	−	0.558113i	$-0.811526\pi$
$271$	−27.3193	−1.65953	−0.829765	+	0.558113i	$0.811526\pi$
$272$	8.69649	0.527302
$273$	0	0
$274$	30.0980	1.81829
$275$	−24.7180	−1.49055
$276$	−46.8247	−2.81851
$277$	−24.8441	−1.49274	−0.746370	−	0.665531i	$-0.768205\pi$
$277$	−24.8441	−1.49274	−0.746370	+	0.665531i	$0.768205\pi$
$278$	7.42366	0.445242
$279$	−1.21281	−0.0726092
$280$	0	0
$281$	−9.03067	−0.538725	−0.269362	−	0.963039i	$-0.586813\pi$
$281$	−9.03067	−0.538725	−0.269362	+	0.963039i	$0.586813\pi$
$282$	−12.4684	−0.742482
$283$	−16.3934	−0.974489	−0.487244	−	0.873266i	$-0.661998\pi$
$283$	−16.3934	−0.974489	−0.487244	+	0.873266i	$0.661998\pi$
$284$	−19.8439	−1.17752
$285$	3.71640	0.220140
$286$	−12.9955	−0.768441
$287$	0	0
$288$	0.956277	0.0563491
$289$	5.44556	0.320327
$290$	−12.7372	−0.747955
$291$	−16.4131	−0.962151
$292$	21.9395	1.28391
$293$	17.5786	1.02695	0.513476	−	0.858104i	$-0.328358\pi$
$293$	17.5786	1.02695	0.513476	+	0.858104i	$0.328358\pi$
$294$	0	0
$295$	57.0835	3.32353
$296$	33.0861	1.92309
$297$	−11.9110	−0.691147
$298$	23.7435	1.37543
$299$	19.6229	1.13482
$300$	−66.8788	−3.86125
$301$	0	0
$302$	28.4370	1.63636
$303$	−3.24748	−0.186563
$304$	1.02827	0.0589755
$305$	25.8299	1.47902
$306$	−3.25143	−0.185872
$307$	16.4924	0.941273	0.470637	−	0.882327i	$-0.344024\pi$
$307$	16.4924	0.941273	0.470637	+	0.882327i	$0.344024\pi$
$308$	0	0
$309$	−32.2945	−1.83717
$310$	−39.9829	−2.27088
$311$	−24.6211	−1.39614	−0.698068	−	0.716032i	$-0.745957\pi$
$311$	−24.6211	−1.39614	−0.698068	+	0.716032i	$0.745957\pi$
$312$	−15.7057	−0.889161
$313$	2.99860	0.169491	0.0847455	−	0.996403i	$-0.472992\pi$
$313$	2.99860	0.169491	0.0847455	+	0.996403i	$0.472992\pi$
$314$	−33.7765	−1.90612
$315$	0	0
$316$	0.904913	0.0509053
$317$	9.18359	0.515802	0.257901	−	0.966171i	$-0.416969\pi$
$317$	9.18359	0.515802	0.257901	+	0.966171i	$0.416969\pi$
$318$	53.5667	3.00387
$319$	−2.93377	−0.164260
$320$	46.3197	2.58935
$321$	−5.88492	−0.328464
$322$	0	0
$323$	2.65396	0.147670
$324$	−29.0866	−1.61592
$325$	28.0271	1.55466
$326$	−17.2092	−0.953127
$327$	−15.5375	−0.859224
$328$	3.82554	0.211230
$329$	0	0
$330$	−34.5729	−1.90317
$331$	29.8994	1.64342	0.821710	−	0.569905i	$-0.193020\pi$
$331$	29.8994	1.64342	0.821710	+	0.569905i	$0.193020\pi$
$332$	28.6835	1.57421
$333$	−2.50499	−0.137273
$334$	−7.03598	−0.384992
$335$	−2.81877	−0.154006
$336$	0	0
$337$	−17.8607	−0.972937	−0.486468	−	0.873698i	$-0.661715\pi$
$337$	−17.8607	−0.972937	−0.486468	+	0.873698i	$0.661715\pi$
$338$	−16.0682	−0.873993
$339$	−10.7310	−0.582826
$340$	−69.0069	−3.74243
$341$	−9.20929	−0.498711
$342$	−0.384449	−0.0207886
$343$	0	0
$344$	8.55476	0.461242
$345$	52.2043	2.81058
$346$	48.1922	2.59083
$347$	11.0928	0.595492	0.297746	−	0.954645i	$-0.403765\pi$
$347$	11.0928	0.595492	0.297746	+	0.954645i	$0.403765\pi$
$348$	−7.93782	−0.425512
$349$	34.6956	1.85721	0.928607	−	0.371064i	$-0.121007\pi$
$349$	34.6956	1.85721	0.928607	+	0.371064i	$0.121007\pi$
$350$	0	0
$351$	13.5056	0.720874
$352$	7.26133	0.387030
$353$	−30.9905	−1.64946	−0.824729	−	0.565527i	$-0.808673\pi$
$353$	−30.9905	−1.64946	−0.824729	+	0.565527i	$0.808673\pi$
$354$	55.2586	2.93696
$355$	22.1237	1.17421
$356$	20.1572	1.06833
$357$	0	0
$358$	38.5774	2.03888
$359$	−0.773684	−0.0408335	−0.0204167	−	0.999792i	$-0.506499\pi$
$359$	−0.773684	−0.0408335	−0.0204167	+	0.999792i	$0.506499\pi$
$360$	4.46505	0.235329
$361$	−18.6862	−0.983484
$362$	−24.2137	−1.27264
$363$	10.1463	0.532543
$364$	0	0
$365$	−24.4601	−1.28030
$366$	25.0042	1.30699
$367$	22.1629	1.15689	0.578446	−	0.815721i	$-0.303659\pi$
$367$	22.1629	1.15689	0.578446	+	0.815721i	$0.303659\pi$
$368$	14.4441	0.752953
$369$	−0.289637	−0.0150779
$370$	−82.5823	−4.29325
$371$	0	0
$372$	−24.9173	−1.29190
$373$	9.78259	0.506523	0.253262	−	0.967398i	$-0.418497\pi$
$373$	9.78259	0.506523	0.253262	+	0.967398i	$0.418497\pi$
$374$	−24.6892	−1.27665
$375$	41.3910	2.13742
$376$	12.2274	0.630580
$377$	3.32652	0.171325
$378$	0	0
$379$	23.5584	1.21011	0.605056	−	0.796183i	$-0.293151\pi$
$379$	23.5584	1.21011	0.605056	+	0.796183i	$0.293151\pi$
$380$	−8.15937	−0.418567
$381$	−18.8762	−0.967057
$382$	−26.1547	−1.33819
$383$	16.4700	0.841579	0.420789	−	0.907158i	$-0.361753\pi$
$383$	16.4700	0.841579	0.420789	+	0.907158i	$0.361753\pi$
$384$	33.9679	1.73342
$385$	0	0
$386$	48.5455	2.47090
$387$	−0.647693	−0.0329241
$388$	36.0350	1.82940
$389$	0.797624	0.0404412	0.0202206	−	0.999796i	$-0.493563\pi$
$389$	0.797624	0.0404412	0.0202206	+	0.999796i	$0.493563\pi$
$390$	39.2012	1.98503
$391$	37.2802	1.88534
$392$	0	0
$393$	2.88432	0.145495
$394$	−5.75618	−0.289992
$395$	−1.00888	−0.0507621
$396$	2.30244	0.115702
$397$	17.0149	0.853953	0.426977	−	0.904263i	$-0.359579\pi$
$397$	17.0149	0.853953	0.426977	+	0.904263i	$0.359579\pi$
$398$	−4.30162	−0.215621
$399$	0	0
$400$	20.6303	1.03152
$401$	−24.7268	−1.23480	−0.617399	−	0.786650i	$-0.711814\pi$
$401$	−24.7268	−1.23480	−0.617399	+	0.786650i	$0.711814\pi$
$402$	−2.72866	−0.136093
$403$	10.4422	0.520161
$404$	7.12985	0.354723
$405$	32.4283	1.61137
$406$	0	0
$407$	−19.0212	−0.942848
$408$	−29.8382	−1.47721
$409$	7.66164	0.378844	0.189422	−	0.981896i	$-0.439339\pi$
$409$	7.66164	0.378844	0.189422	+	0.981896i	$0.439339\pi$
$410$	−9.54849	−0.471566
$411$	−20.9120	−1.03151
$412$	70.9027	3.49312
$413$	0	0
$414$	−5.40036	−0.265413
$415$	−31.9789	−1.56978
$416$	−8.23342	−0.403677
$417$	−5.15794	−0.252585
$418$	−2.91925	−0.142785
$419$	−13.6434	−0.666524	−0.333262	−	0.942834i	$-0.608149\pi$
$419$	−13.6434	−0.666524	−0.333262	+	0.942834i	$0.608149\pi$
$420$	0	0
$421$	−36.1007	−1.75944	−0.879720	−	0.475492i	$-0.842270\pi$
$421$	−36.1007	−1.75944	−0.879720	+	0.475492i	$0.842270\pi$
$422$	40.6133	1.97702
$423$	−0.925753	−0.0450117
$424$	−52.5314	−2.55115
$425$	53.2466	2.58284
$426$	21.4165	1.03763
$427$	0	0
$428$	12.9204	0.624530
$429$	9.02925	0.435936
$430$	−21.3525	−1.02971
$431$	6.08039	0.292882	0.146441	−	0.989219i	$-0.453218\pi$
$431$	6.08039	0.292882	0.146441	+	0.989219i	$0.453218\pi$
$432$	9.94124	0.478298
$433$	−13.6259	−0.654817	−0.327409	−	0.944883i	$-0.606175\pi$
$433$	−13.6259	−0.654817	−0.327409	+	0.944883i	$0.606175\pi$
$434$	0	0
$435$	8.84978	0.424315
$436$	34.1126	1.63370
$437$	4.40800	0.210863
$438$	−23.6782	−1.13139
$439$	24.9201	1.18937	0.594686	−	0.803958i	$-0.297276\pi$
$439$	24.9201	1.18937	0.594686	+	0.803958i	$0.297276\pi$
$440$	33.9047	1.61634
$441$	0	0
$442$	27.9944	1.33156
$443$	18.9391	0.899826	0.449913	−	0.893072i	$-0.351455\pi$
$443$	18.9391	0.899826	0.449913	+	0.893072i	$0.351455\pi$
$444$	−51.4652	−2.44243
$445$	−22.4731	−1.06533
$446$	−31.6550	−1.49891
$447$	−16.4970	−0.780279
$448$	0	0
$449$	−11.0724	−0.522540	−0.261270	−	0.965266i	$-0.584141\pi$
$449$	−11.0724	−0.522540	−0.261270	+	0.965266i	$0.584141\pi$
$450$	−7.71323	−0.363605
$451$	−2.19931	−0.103562
$452$	23.5599	1.10816
$453$	−19.7579	−0.928309
$454$	26.5151	1.24441
$455$	0	0
$456$	−3.52806	−0.165217
$457$	−20.5825	−0.962810	−0.481405	−	0.876498i	$-0.659873\pi$
$457$	−20.5825	−0.962810	−0.481405	+	0.876498i	$0.659873\pi$
$458$	2.35635	0.110105
$459$	25.6582	1.19762
$460$	−114.615	−5.34394
$461$	−6.29857	−0.293354	−0.146677	−	0.989184i	$-0.546858\pi$
$461$	−6.29857	−0.293354	−0.146677	+	0.989184i	$0.546858\pi$
$462$	0	0
$463$	19.5859	0.910234	0.455117	−	0.890432i	$-0.349597\pi$
$463$	19.5859	0.910234	0.455117	+	0.890432i	$0.349597\pi$
$464$	2.44860	0.113674
$465$	27.7800	1.28827
$466$	52.0470	2.41103
$467$	−33.8609	−1.56690	−0.783448	−	0.621457i	$-0.786541\pi$
$467$	−33.8609	−1.56690	−0.783448	+	0.621457i	$0.786541\pi$
$468$	−2.61068	−0.120679
$469$	0	0
$470$	−30.5194	−1.40775
$471$	23.4678	1.08134
$472$	−54.1906	−2.49433
$473$	−4.91815	−0.226137
$474$	−0.976625	−0.0448579
$475$	6.29587	0.288874
$476$	0	0
$477$	3.97722	0.182104
$478$	−38.6646	−1.76848
$479$	3.71014	0.169520	0.0847602	−	0.996401i	$-0.472988\pi$
$479$	3.71014	0.169520	0.0847602	+	0.996401i	$0.472988\pi$
$480$	−21.9039	−0.999774
$481$	21.5677	0.983401
$482$	3.94434	0.179660
$483$	0	0
$484$	−22.2763	−1.01256
$485$	−40.1750	−1.82425
$486$	−7.10639	−0.322352
$487$	2.78838	0.126354	0.0631769	−	0.998002i	$-0.479877\pi$
$487$	2.78838	0.126354	0.0631769	+	0.998002i	$0.479877\pi$
$488$	−24.5210	−1.11001
$489$	11.9569	0.540709
$490$	0	0
$491$	−16.3264	−0.736799	−0.368400	−	0.929668i	$-0.620094\pi$
$491$	−16.3264	−0.736799	−0.368400	+	0.929668i	$0.620094\pi$
$492$	−5.95061	−0.268274
$493$	6.31982	0.284630
$494$	3.31006	0.148927
$495$	−2.56697	−0.115377
$496$	7.68632	0.345126
$497$	0	0
$498$	−30.9566	−1.38720
$499$	3.46195	0.154978	0.0774890	−	0.996993i	$-0.475310\pi$
$499$	3.46195	0.154978	0.0774890	+	0.996993i	$0.475310\pi$
$500$	−90.8742	−4.06402
$501$	4.88858	0.218406
$502$	−40.4394	−1.80490
$503$	2.36485	0.105444	0.0527218	−	0.998609i	$-0.483210\pi$
$503$	2.36485	0.105444	0.0527218	+	0.998609i	$0.483210\pi$
$504$	0	0
$505$	−7.94898	−0.353725
$506$	−41.0067	−1.82297
$507$	11.1641	0.495816
$508$	41.4428	1.83873
$509$	−35.4055	−1.56932	−0.784660	−	0.619926i	$-0.787162\pi$
$509$	−35.4055	−1.56932	−0.784660	+	0.619926i	$0.787162\pi$
$510$	74.4756	3.29783
$511$	0	0
$512$	−20.1049	−0.888518
$513$	3.03383	0.133947
$514$	−57.0978	−2.51848
$515$	−79.0485	−3.48329
$516$	−13.3069	−0.585803
$517$	−7.02956	−0.309160
$518$	0	0
$519$	−33.4838	−1.46978
$520$	−38.4436	−1.68586
$521$	−1.94629	−0.0852686	−0.0426343	−	0.999091i	$-0.513575\pi$
$521$	−1.94629	−0.0852686	−0.0426343	+	0.999091i	$0.513575\pi$
$522$	−0.915481	−0.0400695
$523$	22.8204	0.997866	0.498933	−	0.866641i	$-0.333725\pi$
$523$	22.8204	0.997866	0.498933	+	0.866641i	$0.333725\pi$
$524$	−6.33253	−0.276638
$525$	0	0
$526$	7.83916	0.341804
$527$	19.8383	0.864170
$528$	6.64629	0.289243
$529$	38.9193	1.69214
$530$	131.117	5.69538
$531$	4.10285	0.178048
$532$	0	0
$533$	2.49374	0.108016
$534$	−21.7547	−0.941416
$535$	−14.4048	−0.622772
$536$	2.67593	0.115582
$537$	−26.8035	−1.15665
$538$	27.5479	1.18767
$539$	0	0
$540$	−78.8840	−3.39463
$541$	10.3637	0.445572	0.222786	−	0.974867i	$-0.428485\pi$
$541$	10.3637	0.445572	0.222786	+	0.974867i	$0.428485\pi$
$542$	−64.7329	−2.78052
$543$	16.8236	0.721970
$544$	−15.6421	−0.670649
$545$	−38.0317	−1.62910
$546$	0	0
$547$	−34.3321	−1.46793	−0.733967	−	0.679186i	$-0.762333\pi$
$547$	−34.3321	−1.46793	−0.733967	+	0.679186i	$0.762333\pi$
$548$	45.9124	1.96128
$549$	1.85651	0.0792341
$550$	−58.5692	−2.49740
$551$	0.747255	0.0318341
$552$	−49.5587	−2.10936
$553$	0	0
$554$	−58.8680	−2.50106
$555$	57.3780	2.43556
$556$	11.3243	0.480257
$557$	34.0592	1.44314	0.721568	−	0.692343i	$-0.243422\pi$
$557$	34.0592	1.44314	0.721568	+	0.692343i	$0.243422\pi$
$558$	−2.87375	−0.121656
$559$	5.57655	0.235863
$560$	0	0
$561$	17.1540	0.724243
$562$	−21.3981	−0.902625
$563$	29.2923	1.23452	0.617261	−	0.786758i	$-0.288242\pi$
$563$	29.2923	1.23452	0.617261	+	0.786758i	$0.288242\pi$
$564$	−19.0197	−0.800872
$565$	−26.2666	−1.10505
$566$	−38.8441	−1.63274
$567$	0	0
$568$	−21.0026	−0.881248
$569$	−25.0155	−1.04871	−0.524353	−	0.851501i	$-0.675693\pi$
$569$	−25.0155	−1.04871	−0.524353	+	0.851501i	$0.675693\pi$
$570$	8.80598	0.368842
$571$	43.9291	1.83838	0.919188	−	0.393819i	$-0.128846\pi$
$571$	43.9291	1.83838	0.919188	+	0.393819i	$0.128846\pi$
$572$	−19.8238	−0.828873
$573$	18.1722	0.759156
$574$	0	0
$575$	88.4381	3.68813
$576$	3.32921	0.138717
$577$	19.0451	0.792856	0.396428	−	0.918066i	$-0.370250\pi$
$577$	19.0451	0.792856	0.396428	+	0.918066i	$0.370250\pi$
$578$	12.9032	0.536703
$579$	−33.7293	−1.40174
$580$	−19.4297	−0.806776
$581$	0	0
$582$	−38.8907	−1.61207
$583$	30.2004	1.25077
$584$	23.2205	0.960873
$585$	2.91061	0.120339
$586$	41.6523	1.72064
$587$	−17.0503	−0.703740	−0.351870	−	0.936049i	$-0.614454\pi$
$587$	−17.0503	−0.703740	−0.351870	+	0.936049i	$0.614454\pi$
$588$	0	0
$589$	2.34568	0.0966520
$590$	135.259	5.56852
$591$	3.99938	0.164512
$592$	15.8756	0.652485
$593$	6.49376	0.266667	0.133333	−	0.991071i	$-0.457432\pi$
$593$	6.49376	0.266667	0.133333	+	0.991071i	$0.457432\pi$
$594$	−28.2231	−1.15801
$595$	0	0
$596$	36.2191	1.48359
$597$	2.98876	0.122322
$598$	46.4964	1.90138
$599$	−40.5694	−1.65762	−0.828810	−	0.559531i	$-0.810981\pi$
$599$	−40.5694	−1.65762	−0.828810	+	0.559531i	$0.810981\pi$
$600$	−70.7838	−2.88974
$601$	5.64601	0.230305	0.115153	−	0.993348i	$-0.463264\pi$
$601$	5.64601	0.230305	0.115153	+	0.993348i	$0.463264\pi$
$602$	0	0
$603$	−0.202598	−0.00825043
$604$	43.3787	1.76505
$605$	24.8355	1.00971
$606$	−7.69487	−0.312583
$607$	3.54837	0.144024	0.0720119	−	0.997404i	$-0.477058\pi$
$607$	3.54837	0.144024	0.0720119	+	0.997404i	$0.477058\pi$
$608$	−1.84952	−0.0750078
$609$	0	0
$610$	61.2039	2.47807
$611$	7.97062	0.322457
$612$	−4.95984	−0.200490
$613$	−17.4634	−0.705342	−0.352671	−	0.935747i	$-0.614726\pi$
$613$	−17.4634	−0.705342	−0.352671	+	0.935747i	$0.614726\pi$
$614$	39.0787	1.57709
$615$	6.63427	0.267520
$616$	0	0
$617$	13.6489	0.549485	0.274742	−	0.961518i	$-0.411407\pi$
$617$	13.6489	0.549485	0.274742	+	0.961518i	$0.411407\pi$
$618$	−76.5215	−3.07815
$619$	7.27570	0.292435	0.146217	−	0.989252i	$-0.453290\pi$
$619$	7.27570	0.292435	0.146217	+	0.989252i	$0.453290\pi$
$620$	−60.9912	−2.44946
$621$	42.6162	1.71013
$622$	−58.3396	−2.33920
$623$	0	0
$624$	−7.53605	−0.301683
$625$	45.1197	1.80479
$626$	7.10517	0.283980
$627$	2.02829	0.0810020
$628$	−51.5238	−2.05602
$629$	40.9749	1.63377
$630$	0	0
$631$	18.3434	0.730240	0.365120	−	0.930960i	$-0.381028\pi$
$631$	18.3434	0.730240	0.365120	+	0.930960i	$0.381028\pi$
$632$	0.957749	0.0380972
$633$	−28.2180	−1.12157
$634$	21.7604	0.864218
$635$	−46.2041	−1.83355
$636$	81.7123	3.24010
$637$	0	0
$638$	−6.95155	−0.275215
$639$	1.59013	0.0629047
$640$	83.1447	3.28658
$641$	17.8380	0.704559	0.352279	−	0.935895i	$-0.385407\pi$
$641$	17.8380	0.704559	0.352279	+	0.935895i	$0.385407\pi$
$642$	−13.9443	−0.550337
$643$	−9.75440	−0.384676	−0.192338	−	0.981329i	$-0.561607\pi$
$643$	−9.75440	−0.384676	−0.192338	+	0.981329i	$0.561607\pi$
$644$	0	0
$645$	14.8357	0.584155
$646$	6.28854	0.247419
$647$	−8.46942	−0.332967	−0.166484	−	0.986044i	$-0.553241\pi$
$647$	−8.46942	−0.332967	−0.166484	+	0.986044i	$0.553241\pi$
$648$	−30.7849	−1.20935
$649$	31.1543	1.22291
$650$	66.4100	2.60481
$651$	0	0
$652$	−26.2514	−1.02808
$653$	−8.93922	−0.349819	−0.174909	−	0.984585i	$-0.555963\pi$
$653$	−8.93922	−0.349819	−0.174909	+	0.984585i	$0.555963\pi$
$654$	−36.8159	−1.43962
$655$	7.06006	0.275860
$656$	1.83560	0.0716683
$657$	−1.75806	−0.0685884
$658$	0	0
$659$	41.0753	1.60006	0.800032	−	0.599957i	$-0.204816\pi$
$659$	41.0753	1.60006	0.800032	+	0.599957i	$0.204816\pi$
$660$	−52.7385	−2.05284
$661$	−2.89008	−0.112411	−0.0562055	−	0.998419i	$-0.517900\pi$
$661$	−2.89008	−0.112411	−0.0562055	+	0.998419i	$0.517900\pi$
$662$	70.8465	2.75353
$663$	−19.4505	−0.755393
$664$	30.3583	1.17813
$665$	0	0
$666$	−5.93556	−0.229998
$667$	10.4967	0.406434
$668$	−10.7329	−0.415268
$669$	21.9938	0.850330
$670$	−6.67907	−0.258035
$671$	14.0971	0.544214
$672$	0	0
$673$	2.39313	0.0922482	0.0461241	−	0.998936i	$-0.485313\pi$
$673$	2.39313	0.0922482	0.0461241	+	0.998936i	$0.485313\pi$
$674$	−42.3209	−1.63014
$675$	60.8679	2.34281
$676$	−24.5109	−0.942726
$677$	−40.8530	−1.57011	−0.785054	−	0.619427i	$-0.787365\pi$
$677$	−40.8530	−1.57011	−0.785054	+	0.619427i	$0.787365\pi$
$678$	−25.4269	−0.976516
$679$	0	0
$680$	−73.0361	−2.80081
$681$	−18.4226	−0.705955
$682$	−21.8214	−0.835583
$683$	4.19752	0.160613	0.0803067	−	0.996770i	$-0.474410\pi$
$683$	4.19752	0.160613	0.0803067	+	0.996770i	$0.474410\pi$
$684$	−0.586451	−0.0224235
$685$	−51.1872	−1.95576
$686$	0	0
$687$	−1.63719	−0.0624625
$688$	4.10482	0.156495
$689$	−34.2434	−1.30457
$690$	123.698	4.70909
$691$	−30.7030	−1.16800	−0.583999	−	0.811755i	$-0.698513\pi$
$691$	−30.7030	−1.16800	−0.583999	+	0.811755i	$0.698513\pi$
$692$	73.5139	2.79458
$693$	0	0
$694$	26.2843	0.997739
$695$	−12.6253	−0.478905
$696$	−8.40130	−0.318450
$697$	4.73767	0.179452
$698$	82.2111	3.11173
$699$	−36.1622	−1.36778
$700$	0	0
$701$	−42.2453	−1.59558	−0.797792	−	0.602933i	$-0.793999\pi$
$701$	−42.2453	−1.59558	−0.797792	+	0.602933i	$0.793999\pi$
$702$	32.0013	1.20781
$703$	4.84486	0.182727
$704$	25.2798	0.952769
$705$	21.2048	0.798619
$706$	−73.4318	−2.76364
$707$	0	0
$708$	84.2933	3.16793
$709$	−49.4445	−1.85693	−0.928464	−	0.371421i	$-0.878871\pi$
$709$	−49.4445	−1.85693	−0.928464	+	0.371421i	$0.878871\pi$
$710$	52.4220	1.96736
$711$	−0.0725125	−0.00271943
$712$	21.3342	0.799533
$713$	32.9498	1.23398
$714$	0	0
$715$	22.1013	0.826541
$716$	58.8471	2.19922
$717$	26.8641	1.00326
$718$	−1.83324	−0.0684158
$719$	33.8765	1.26338	0.631690	−	0.775221i	$-0.282362\pi$
$719$	33.8765	1.26338	0.631690	+	0.775221i	$0.282362\pi$
$720$	2.14246	0.0798447
$721$	0	0
$722$	−44.2768	−1.64781
$723$	−2.74052	−0.101921
$724$	−36.9363	−1.37273
$725$	14.9922	0.556798
$726$	24.0416	0.892267
$727$	19.3374	0.717186	0.358593	−	0.933494i	$-0.383257\pi$
$727$	19.3374	0.717186	0.358593	+	0.933494i	$0.383257\pi$
$728$	0	0
$729$	29.0791	1.07700
$730$	−57.9581	−2.14512
$731$	10.5945	0.391851
$732$	38.1422	1.40978
$733$	−25.9226	−0.957473	−0.478736	−	0.877959i	$-0.658905\pi$
$733$	−25.9226	−0.957473	−0.478736	+	0.877959i	$0.658905\pi$
$734$	52.5148	1.93836
$735$	0	0
$736$	−25.9802	−0.957642
$737$	−1.53839	−0.0566675
$738$	−0.686293	−0.0252628
$739$	−4.29392	−0.157954	−0.0789771	−	0.996876i	$-0.525165\pi$
$739$	−4.29392	−0.157954	−0.0789771	+	0.996876i	$0.525165\pi$
$740$	−125.974	−4.63088
$741$	−2.29982	−0.0844860
$742$	0	0
$743$	−3.57081	−0.131000	−0.0655002	−	0.997853i	$-0.520864\pi$
$743$	−3.57081	−0.131000	−0.0655002	+	0.997853i	$0.520864\pi$
$744$	−26.3722	−0.966852
$745$	−40.3803	−1.47942
$746$	23.1798	0.848672
$747$	−2.29846	−0.0840964
$748$	−37.6617	−1.37705
$749$	0	0
$750$	98.0758	3.58122
$751$	42.9984	1.56904	0.784518	−	0.620106i	$-0.212911\pi$
$751$	42.9984	1.56904	0.784518	+	0.620106i	$0.212911\pi$
$752$	5.86705	0.213949
$753$	28.0972	1.02392
$754$	7.88218	0.287052
$755$	−48.3623	−1.76009
$756$	0	0
$757$	−11.1293	−0.404501	−0.202251	−	0.979334i	$-0.564826\pi$
$757$	−11.1293	−0.404501	−0.202251	+	0.979334i	$0.564826\pi$
$758$	55.8214	2.02752
$759$	28.4914	1.03417
$760$	−8.63578	−0.313253
$761$	−7.40224	−0.268331	−0.134165	−	0.990959i	$-0.542835\pi$
$761$	−7.40224	−0.268331	−0.134165	+	0.990959i	$0.542835\pi$
$762$	−44.7270	−1.62029
$763$	0	0
$764$	−39.8972	−1.44343
$765$	5.52966	0.199925
$766$	39.0256	1.41005
$767$	−35.3250	−1.27551
$768$	42.6399	1.53863
$769$	−6.22010	−0.224302	−0.112151	−	0.993691i	$-0.535774\pi$
$769$	−6.22010	−0.224302	−0.112151	+	0.993691i	$0.535774\pi$
$770$	0	0
$771$	39.6714	1.42873
$772$	74.0528	2.66522
$773$	−1.12543	−0.0404788	−0.0202394	−	0.999795i	$-0.506443\pi$
$773$	−1.12543	−0.0404788	−0.0202394	+	0.999795i	$0.506443\pi$
$774$	−1.53470	−0.0551638
$775$	47.0616	1.69050
$776$	38.1390	1.36911
$777$	0	0
$778$	1.88997	0.0677585
$779$	0.560182	0.0200706
$780$	59.7988	2.14114
$781$	12.0744	0.432056
$782$	88.3351	3.15886
$783$	7.22439	0.258179
$784$	0	0
$785$	57.4432	2.05024
$786$	6.83437	0.243774
$787$	−11.3018	−0.402867	−0.201433	−	0.979502i	$-0.564560\pi$
$787$	−11.3018	−0.402867	−0.201433	+	0.979502i	$0.564560\pi$
$788$	−8.78065	−0.312798
$789$	−5.44663	−0.193905
$790$	−2.39053	−0.0850511
$791$	0	0
$792$	2.43688	0.0865908
$793$	−15.9844	−0.567621
$794$	40.3167	1.43079
$795$	−91.1000	−3.23098
$796$	−6.56183	−0.232578
$797$	−2.55391	−0.0904642	−0.0452321	−	0.998977i	$-0.514403\pi$
$797$	−2.55391	−0.0904642	−0.0452321	+	0.998977i	$0.514403\pi$
$798$	0	0
$799$	15.1428	0.535714
$800$	−37.1070	−1.31193
$801$	−1.61524	−0.0570717
$802$	−58.5900	−2.06889
$803$	−13.3495	−0.471095
$804$	−4.16239	−0.146796
$805$	0	0
$806$	24.7426	0.871522
$807$	−19.1402	−0.673766
$808$	7.54615	0.265473
$809$	−53.6737	−1.88707	−0.943533	−	0.331278i	$-0.892520\pi$
$809$	−53.6737	−1.88707	−0.943533	+	0.331278i	$0.892520\pi$
$810$	76.8386	2.69983
$811$	3.54969	0.124646	0.0623232	−	0.998056i	$-0.480149\pi$
$811$	3.54969	0.124646	0.0623232	+	0.998056i	$0.480149\pi$
$812$	0	0
$813$	44.9763	1.57739
$814$	−45.0707	−1.57973
$815$	29.2674	1.02519
$816$	−14.3172	−0.501202
$817$	1.25269	0.0438261
$818$	18.1542	0.634747
$819$	0	0
$820$	−14.5656	−0.508652
$821$	−27.2250	−0.950159	−0.475080	−	0.879943i	$-0.657581\pi$
$821$	−27.2250	−0.950159	−0.475080	+	0.879943i	$0.657581\pi$
$822$	−49.5509	−1.72828
$823$	9.93648	0.346364	0.173182	−	0.984890i	$-0.444595\pi$
$823$	9.93648	0.346364	0.173182	+	0.984890i	$0.444595\pi$
$824$	75.0426	2.61423
$825$	40.6937	1.41677
$826$	0	0
$827$	−52.7777	−1.83526	−0.917631	−	0.397434i	$-0.869901\pi$
$827$	−52.7777	−1.83526	−0.917631	+	0.397434i	$0.869901\pi$
$828$	−8.23787	−0.286286
$829$	−28.6819	−0.996165	−0.498082	−	0.867130i	$-0.665962\pi$
$829$	−28.6819	−0.996165	−0.498082	+	0.867130i	$0.665962\pi$
$830$	−75.7737	−2.63014
$831$	40.9014	1.41885
$832$	−28.6641	−0.993748
$833$	0	0
$834$	−12.2217	−0.423203
$835$	11.9660	0.414100
$836$	−4.45312	−0.154014
$837$	22.6778	0.783860
$838$	−32.3280	−1.11675
$839$	−13.8280	−0.477396	−0.238698	−	0.971094i	$-0.576721\pi$
$839$	−13.8280	−0.477396	−0.238698	+	0.971094i	$0.576721\pi$
$840$	0	0
$841$	−27.2206	−0.938641
$842$	−85.5403	−2.94791
$843$	14.8674	0.512059
$844$	61.9528	2.13250
$845$	27.3269	0.940073
$846$	−2.19357	−0.0754164
$847$	0	0
$848$	−25.2060	−0.865578
$849$	26.9888	0.926254
$850$	126.167	4.32751
$851$	68.0558	2.33292
$852$	32.6694	1.11923
$853$	7.82689	0.267988	0.133994	−	0.990982i	$-0.457220\pi$
$853$	7.82689	0.267988	0.133994	+	0.990982i	$0.457220\pi$
$854$	0	0
$855$	0.653827	0.0223604
$856$	13.6748	0.467394
$857$	22.6177	0.772607	0.386304	−	0.922372i	$-0.373752\pi$
$857$	22.6177	0.772607	0.386304	+	0.922372i	$0.373752\pi$
$858$	21.3947	0.730404
$859$	−3.61610	−0.123380	−0.0616899	−	0.998095i	$-0.519649\pi$
$859$	−3.61610	−0.123380	−0.0616899	+	0.998095i	$0.519649\pi$
$860$	−32.5718	−1.11069
$861$	0	0
$862$	14.4075	0.490720
$863$	5.93685	0.202093	0.101046	−	0.994882i	$-0.467781\pi$
$863$	5.93685	0.202093	0.101046	+	0.994882i	$0.467781\pi$
$864$	−17.8810	−0.608323
$865$	−81.9598	−2.78672
$866$	−32.2864	−1.09714
$867$	−8.96512	−0.304471
$868$	0	0
$869$	−0.550612	−0.0186782
$870$	20.9695	0.710933
$871$	1.74434	0.0591048
$872$	36.1044	1.22265
$873$	−2.88756	−0.0977289
$874$	10.4447	0.353298
$875$	0	0
$876$	−36.1194	−1.22036
$877$	−5.42132	−0.183065	−0.0915324	−	0.995802i	$-0.529177\pi$
$877$	−5.42132	−0.183065	−0.0915324	+	0.995802i	$0.529177\pi$
$878$	59.0481	1.99278
$879$	−28.9399	−0.976120
$880$	16.2684	0.548408
$881$	30.2288	1.01843	0.509217	−	0.860638i	$-0.329935\pi$
$881$	30.2288	1.01843	0.509217	+	0.860638i	$0.329935\pi$
$882$	0	0
$883$	0.723881	0.0243605	0.0121803	−	0.999926i	$-0.496123\pi$
$883$	0.723881	0.0243605	0.0121803	+	0.999926i	$0.496123\pi$
$884$	42.7036	1.43628
$885$	−93.9775	−3.15902
$886$	44.8762	1.50764
$887$	30.3422	1.01879	0.509396	−	0.860532i	$-0.329869\pi$
$887$	30.3422	1.01879	0.509396	+	0.860532i	$0.329869\pi$
$888$	−54.4702	−1.82790
$889$	0	0
$890$	−53.2498	−1.78494
$891$	17.6983	0.592915
$892$	−48.2875	−1.61679
$893$	1.79048	0.0599162
$894$	−39.0894	−1.30735
$895$	−65.6079	−2.19303
$896$	0	0
$897$	−32.3056	−1.07865
$898$	−26.2360	−0.875507
$899$	5.58572	0.186294
$900$	−11.7660	−0.392200
$901$	−65.0565	−2.16735
$902$	−5.21126	−0.173516
$903$	0	0
$904$	24.9355	0.829342
$905$	41.1798	1.36886
$906$	−46.8163	−1.55537
$907$	−14.2072	−0.471744	−0.235872	−	0.971784i	$-0.575795\pi$
$907$	−14.2072	−0.471744	−0.235872	+	0.971784i	$0.575795\pi$
$908$	40.4469	1.34228
$909$	−0.571329	−0.0189498
$910$	0	0
$911$	−1.26559	−0.0419309	−0.0209655	−	0.999780i	$-0.506674\pi$
$911$	−1.26559	−0.0419309	−0.0209655	+	0.999780i	$0.506674\pi$
$912$	−1.69286	−0.0560563
$913$	−17.4530	−0.577611
$914$	−48.7702	−1.61317
$915$	−42.5243	−1.40581
$916$	3.59445	0.118764
$917$	0	0
$918$	60.7970	2.00660
$919$	−8.63415	−0.284814	−0.142407	−	0.989808i	$-0.545484\pi$
$919$	−8.63415	−0.284814	−0.142407	+	0.989808i	$0.545484\pi$
$920$	−121.307	−3.99937
$921$	−27.1518	−0.894682
$922$	−14.9244	−0.491510
$923$	−13.6908	−0.450639
$924$	0	0
$925$	97.2028	3.19601
$926$	46.4087	1.52508
$927$	−5.68157	−0.186607
$928$	−4.40422	−0.144576
$929$	−15.4951	−0.508376	−0.254188	−	0.967155i	$-0.581808\pi$
$929$	−15.4951	−0.508376	−0.254188	+	0.967155i	$0.581808\pi$
$930$	65.8246	2.15847
$931$	0	0
$932$	79.3942	2.60064
$933$	40.5342	1.32703
$934$	−80.2332	−2.62531
$935$	41.9886	1.37317
$936$	−2.76311	−0.0903151
$937$	19.9639	0.652192	0.326096	−	0.945337i	$-0.394267\pi$
$937$	19.9639	0.652192	0.326096	+	0.945337i	$0.394267\pi$
$938$	0	0
$939$	−4.93665	−0.161102
$940$	−46.5552	−1.51846
$941$	0.844408	0.0275269	0.0137635	−	0.999905i	$-0.495619\pi$
$941$	0.844408	0.0275269	0.0137635	+	0.999905i	$0.495619\pi$
$942$	55.6069	1.81177
$943$	7.86888	0.256246
$944$	−26.0022	−0.846299
$945$	0	0
$946$	−11.6535	−0.378889
$947$	−30.0548	−0.976650	−0.488325	−	0.872662i	$-0.662392\pi$
$947$	−30.0548	−0.976650	−0.488325	+	0.872662i	$0.662392\pi$
$948$	−1.48977	−0.0483856
$949$	15.1367	0.491357
$950$	14.9180	0.484005
$951$	−15.1191	−0.490271
$952$	0	0
$953$	25.3832	0.822243	0.411122	−	0.911581i	$-0.365137\pi$
$953$	25.3832	0.822243	0.411122	+	0.911581i	$0.365137\pi$
$954$	9.42400	0.305113
$955$	44.4810	1.43937
$956$	−58.9802	−1.90756
$957$	4.82992	0.156129
$958$	8.79114	0.284029
$959$	0	0
$960$	−76.2570	−2.46119
$961$	−13.4661	−0.434390
$962$	51.1044	1.64767
$963$	−1.03534	−0.0333632
$964$	6.01682	0.193789
$965$	−82.5606	−2.65772
$966$	0	0
$967$	24.4940	0.787675	0.393838	−	0.919180i	$-0.371147\pi$
$967$	24.4940	0.787675	0.393838	+	0.919180i	$0.371147\pi$
$968$	−23.5769	−0.757791
$969$	−4.36926	−0.140361
$970$	−95.1943	−3.05650
$971$	19.5636	0.627826	0.313913	−	0.949452i	$-0.398360\pi$
$971$	19.5636	0.627826	0.313913	+	0.949452i	$0.398360\pi$
$972$	−10.8403	−0.347703
$973$	0	0
$974$	6.60706	0.211704
$975$	−46.1415	−1.47771
$976$	−11.7658	−0.376616
$977$	−44.1764	−1.41333	−0.706665	−	0.707548i	$-0.749801\pi$
$977$	−44.1764	−1.41333	−0.706665	+	0.707548i	$0.749801\pi$
$978$	28.3318	0.905950
$979$	−12.2651	−0.391993
$980$	0	0
$981$	−2.73351	−0.0872743
$982$	−38.6852	−1.23450
$983$	11.8953	0.379402	0.189701	−	0.981842i	$-0.439248\pi$
$983$	11.8953	0.379402	0.189701	+	0.981842i	$0.439248\pi$
$984$	−6.29806	−0.200775
$985$	9.78944	0.311918
$986$	14.9748	0.476894
$987$	0	0
$988$	5.04927	0.160639
$989$	17.5966	0.559538
$990$	−6.08241	−0.193312
$991$	31.7041	1.00711	0.503557	−	0.863962i	$-0.332024\pi$
$991$	31.7041	1.00711	0.503557	+	0.863962i	$0.332024\pi$
$992$	−13.8251	−0.438948
$993$	−49.2239	−1.56207
$994$	0	0
$995$	7.31570	0.231923
$996$	−47.2221	−1.49629
$997$	27.0121	0.855482	0.427741	−	0.903901i	$-0.359309\pi$
$997$	27.0121	0.855482	0.427741	+	0.903901i	$0.359309\pi$
$998$	8.20306	0.259663
$999$	46.8397	1.48194

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.s.1.14		17
7.2	even	3		287.2.e.d.165.4	✓	34
7.4	even	3		287.2.e.d.247.4	yes	34
7.6	odd	2		2009.2.a.r.1.14		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.4	✓	34	7.2	even	3
287.2.e.d.247.4	yes	34	7.4	even	3
2009.2.a.r.1.14		17	7.6	odd	2
2009.2.a.s.1.14		17	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+2.36949 q^{2} -1.64632 q^{3} +3.61450 q^{4} -4.02976 q^{5} -3.90094 q^{6} +3.82554 q^{8} -0.289637 q^{9} +O(q^{10})\)	\(q+2.36949 q^{2} -1.64632 q^{3} +3.61450 q^{4} -4.02976 q^{5} -3.90094 q^{6} +3.82554 q^{8} -0.289637 q^{9} -9.54849 q^{10} -2.19931 q^{11} -5.95061 q^{12} +2.49374 q^{13} +6.63427 q^{15} +1.83560 q^{16} +4.73767 q^{17} -0.686293 q^{18} +0.560182 q^{19} -14.5656 q^{20} -5.21126 q^{22} +7.86888 q^{23} -6.29806 q^{24} +11.2390 q^{25} +5.90890 q^{26} +5.41579 q^{27} +1.33395 q^{29} +15.7199 q^{30} +4.18735 q^{31} -3.30164 q^{32} +3.62077 q^{33} +11.2259 q^{34} -1.04689 q^{36} +8.64873 q^{37} +1.32735 q^{38} -4.10549 q^{39} -15.4160 q^{40} +1.00000 q^{41} +2.23622 q^{43} -7.94941 q^{44} +1.16717 q^{45} +18.6453 q^{46} +3.19625 q^{47} -3.02199 q^{48} +26.6307 q^{50} -7.79972 q^{51} +9.01362 q^{52} -13.7317 q^{53} +12.8327 q^{54} +8.86270 q^{55} -0.922238 q^{57} +3.16079 q^{58} -14.1655 q^{59} +23.9796 q^{60} -6.40980 q^{61} +9.92190 q^{62} -11.4944 q^{64} -10.0492 q^{65} +8.57938 q^{66} +0.699489 q^{67} +17.1243 q^{68} -12.9547 q^{69} -5.49009 q^{71} -1.10802 q^{72} +6.06987 q^{73} +20.4931 q^{74} -18.5029 q^{75} +2.02478 q^{76} -9.72793 q^{78} +0.250356 q^{79} -7.39705 q^{80} -8.04720 q^{81} +2.36949 q^{82} +7.93567 q^{83} -19.0917 q^{85} +5.29871 q^{86} -2.19611 q^{87} -8.41356 q^{88} +5.57677 q^{89} +2.76560 q^{90} +28.4421 q^{92} -6.89371 q^{93} +7.57350 q^{94} -2.25740 q^{95} +5.43554 q^{96} +9.96956 q^{97} +0.637002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9	\( 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9} - 2 q^{10} + 15 q^{11} + 4 q^{12} - 5 q^{13} + 24 q^{15} + 33 q^{16} + 4 q^{17} + 10 q^{18} + 5 q^{19} - 26 q^{20} + 16 q^{22} + 12 q^{23} + 16 q^{24} + 24 q^{25} + 31 q^{26} - 11 q^{27} + 14 q^{29} - 33 q^{30} - 3 q^{31} + 16 q^{32} + 4 q^{33} - 24 q^{34} + 57 q^{36} + 24 q^{37} + 45 q^{39} + 36 q^{40} + 17 q^{41} + 14 q^{43} - 9 q^{44} - 21 q^{45} + 44 q^{46} + 19 q^{47} - 60 q^{48} - 4 q^{50} + 2 q^{51} - 25 q^{52} + 4 q^{53} + 68 q^{54} + 9 q^{55} - 12 q^{57} - q^{58} - 27 q^{59} + 66 q^{60} - q^{61} - 23 q^{62} + 75 q^{64} + 22 q^{65} - 16 q^{66} + 49 q^{67} + 45 q^{68} + 12 q^{69} + 40 q^{71} - 23 q^{72} - 14 q^{73} + 33 q^{74} + 27 q^{75} - 9 q^{76} - 12 q^{78} + 61 q^{79} - 82 q^{80} + 53 q^{81} + 3 q^{82} - 18 q^{83} - 13 q^{85} - 4 q^{86} - 17 q^{87} + 74 q^{88} + 18 q^{89} - 20 q^{90} + 28 q^{92} - 36 q^{93} - 5 q^{94} + 20 q^{95} + 148 q^{96} + 26 q^{97} + 38 q^{99}+O(q^{100}) \) 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9 - 2 * q^10 + 15 * q^11 + 4 * q^12 - 5 * q^13 + 24 * q^15 + 33 * q^16 + 4 * q^17 + 10 * q^18 + 5 * q^19 - 26 * q^20 + 16 * q^22 + 12 * q^23 + 16 * q^24 + 24 * q^25 + 31 * q^26 - 11 * q^27 + 14 * q^29 - 33 * q^30 - 3 * q^31 + 16 * q^32 + 4 * q^33 - 24 * q^34 + 57 * q^36 + 24 * q^37 + 45 * q^39 + 36 * q^40 + 17 * q^41 + 14 * q^43 - 9 * q^44 - 21 * q^45 + 44 * q^46 + 19 * q^47 - 60 * q^48 - 4 * q^50 + 2 * q^51 - 25 * q^52 + 4 * q^53 + 68 * q^54 + 9 * q^55 - 12 * q^57 - q^58 - 27 * q^59 + 66 * q^60 - q^61 - 23 * q^62 + 75 * q^64 + 22 * q^65 - 16 * q^66 + 49 * q^67 + 45 * q^68 + 12 * q^69 + 40 * q^71 - 23 * q^72 - 14 * q^73 + 33 * q^74 + 27 * q^75 - 9 * q^76 - 12 * q^78 + 61 * q^79 - 82 * q^80 + 53 * q^81 + 3 * q^82 - 18 * q^83 - 13 * q^85 - 4 * q^86 - 17 * q^87 + 74 * q^88 + 18 * q^89 - 20 * q^90 + 28 * q^92 - 36 * q^93 - 5 * q^94 + 20 * q^95 + 148 * q^96 + 26 * q^97 + 38 * q^99

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