LMFDB - Embedded newform 2009.2.a.s.1.6

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			1.6
Root			$-0.972044$ 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)

$f(q)$	$=$	$q-0.972044 q^{2} +1.50665 q^{3} -1.05513 q^{4} +2.83631 q^{5} -1.46453 q^{6} +2.96972 q^{8} -0.730003 q^{9} +O(q^{10})$	\(q-0.972044 q^{2} +1.50665 q^{3} -1.05513 q^{4} +2.83631 q^{5} -1.46453 q^{6} +2.96972 q^{8} -0.730003 q^{9} -2.75702 q^{10} +3.37175 q^{11} -1.58971 q^{12} +6.81273 q^{13} +4.27332 q^{15} -0.776442 q^{16} +0.331605 q^{17} +0.709595 q^{18} +8.31072 q^{19} -2.99267 q^{20} -3.27749 q^{22} -5.67273 q^{23} +4.47433 q^{24} +3.04464 q^{25} -6.62228 q^{26} -5.61981 q^{27} -1.34200 q^{29} -4.15386 q^{30} +0.541567 q^{31} -5.18471 q^{32} +5.08004 q^{33} -0.322335 q^{34} +0.770248 q^{36} -4.20990 q^{37} -8.07839 q^{38} +10.2644 q^{39} +8.42304 q^{40} +1.00000 q^{41} -11.7203 q^{43} -3.55763 q^{44} -2.07051 q^{45} +5.51415 q^{46} +5.46775 q^{47} -1.16983 q^{48} -2.95952 q^{50} +0.499613 q^{51} -7.18832 q^{52} -4.07775 q^{53} +5.46271 q^{54} +9.56331 q^{55} +12.5214 q^{57} +1.30448 q^{58} +15.2272 q^{59} -4.50891 q^{60} -0.720959 q^{61} -0.526427 q^{62} +6.59265 q^{64} +19.3230 q^{65} -4.93803 q^{66} -4.26647 q^{67} -0.349886 q^{68} -8.54682 q^{69} -3.70138 q^{71} -2.16791 q^{72} +11.4928 q^{73} +4.09221 q^{74} +4.58721 q^{75} -8.76889 q^{76} -9.97746 q^{78} +8.47238 q^{79} -2.20223 q^{80} -6.27709 q^{81} -0.972044 q^{82} -7.88767 q^{83} +0.940534 q^{85} +11.3926 q^{86} -2.02193 q^{87} +10.0131 q^{88} -2.31660 q^{89} +2.01263 q^{90} +5.98547 q^{92} +0.815952 q^{93} -5.31490 q^{94} +23.5718 q^{95} -7.81154 q^{96} -13.3398 q^{97} -2.46139 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.972044	−0.687339	−0.343670	−	0.939091i	$-0.611670\pi$
$2$	−0.972044	−0.687339	−0.343670	+	0.939091i	$0.611670\pi$
$3$	1.50665	0.869865	0.434933	−	0.900463i	$-0.356772\pi$
$3$	1.50665	0.869865	0.434933	+	0.900463i	$0.356772\pi$
$4$	−1.05513	−0.527565
$5$	2.83631	1.26844	0.634218	−	0.773155i	$-0.281322\pi$
$5$	2.83631	1.26844	0.634218	+	0.773155i	$0.281322\pi$
$6$	−1.46453	−0.597892
$7$	0	0
$7$	0	0
$8$	2.96972	1.04996
$9$	−0.730003	−0.243334
$10$	−2.75702	−0.871845
$11$	3.37175	1.01662	0.508310	−	0.861174i	$-0.330270\pi$
$11$	3.37175	1.01662	0.508310	+	0.861174i	$0.330270\pi$
$12$	−1.58971	−0.458910
$13$	6.81273	1.88951	0.944756	−	0.327774i	$-0.106298\pi$
$13$	6.81273	1.88951	0.944756	+	0.327774i	$0.106298\pi$
$14$	0	0
$15$	4.27332	1.10337
$16$	−0.776442	−0.194110
$17$	0.331605	0.0804260	0.0402130	−	0.999191i	$-0.487196\pi$
$17$	0.331605	0.0804260	0.0402130	+	0.999191i	$0.487196\pi$
$18$	0.709595	0.167253
$19$	8.31072	1.90661	0.953305	−	0.302009i	$-0.0976574\pi$
$19$	8.31072	1.90661	0.953305	+	0.302009i	$0.0976574\pi$
$20$	−2.99267	−0.669182
$21$	0	0
$22$	−3.27749	−0.698763
$23$	−5.67273	−1.18285	−0.591423	−	0.806361i	$-0.701434\pi$
$23$	−5.67273	−1.18285	−0.591423	+	0.806361i	$0.701434\pi$
$24$	4.47433	0.913320
$25$	3.04464	0.608928
$26$	−6.62228	−1.29874
$27$	−5.61981	−1.08153
$28$	0	0
$29$	−1.34200	−0.249203	−0.124602	−	0.992207i	$-0.539765\pi$
$29$	−1.34200	−0.249203	−0.124602	+	0.992207i	$0.539765\pi$
$30$	−4.15386	−0.758388
$31$	0.541567	0.0972683	0.0486341	−	0.998817i	$-0.484513\pi$
$31$	0.541567	0.0972683	0.0486341	+	0.998817i	$0.484513\pi$
$32$	−5.18471	−0.916535
$33$	5.08004	0.884322
$34$	−0.322335	−0.0552800
$35$	0	0
$36$	0.770248	0.128375
$37$	−4.20990	−0.692104	−0.346052	−	0.938215i	$-0.612478\pi$
$37$	−4.20990	−0.692104	−0.346052	+	0.938215i	$0.612478\pi$
$38$	−8.07839	−1.31049
$39$	10.2644	1.64362
$40$	8.42304	1.33180
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−11.7203	−1.78732	−0.893662	−	0.448741i	$-0.851872\pi$
$43$	−11.7203	−1.78732	−0.893662	+	0.448741i	$0.851872\pi$
$44$	−3.55763	−0.536333
$45$	−2.07051	−0.308654
$46$	5.51415	0.813016
$47$	5.46775	0.797554	0.398777	−	0.917048i	$-0.369435\pi$
$47$	5.46775	0.797554	0.398777	+	0.917048i	$0.369435\pi$
$48$	−1.16983	−0.168850
$49$	0	0
$50$	−2.95952	−0.418540
$51$	0.499613	0.0699598
$52$	−7.18832	−0.996840
$53$	−4.07775	−0.560122	−0.280061	−	0.959982i	$-0.590355\pi$
$53$	−4.07775	−0.560122	−0.280061	+	0.959982i	$0.590355\pi$
$54$	5.46271	0.743380
$55$	9.56331	1.28952
$56$	0	0
$57$	12.5214	1.65849
$58$	1.30448	0.171287
$59$	15.2272	1.98241	0.991206	−	0.132328i	$-0.0422452\pi$
$59$	15.2272	1.98241	0.991206	+	0.132328i	$0.0422452\pi$
$60$	−4.50891	−0.582098
$61$	−0.720959	−0.0923094	−0.0461547	−	0.998934i	$-0.514697\pi$
$61$	−0.720959	−0.0923094	−0.0461547	+	0.998934i	$0.514697\pi$
$62$	−0.526427	−0.0668563
$63$	0	0
$64$	6.59265	0.824081
$65$	19.3230	2.39672
$66$	−4.93803	−0.607829
$67$	−4.26647	−0.521232	−0.260616	−	0.965443i	$-0.583926\pi$
$67$	−4.26647	−0.521232	−0.260616	+	0.965443i	$0.583926\pi$
$68$	−0.349886	−0.0424299
$69$	−8.54682	−1.02892
$70$	0	0
$71$	−3.70138	−0.439273	−0.219636	−	0.975582i	$-0.570487\pi$
$71$	−3.70138	−0.439273	−0.219636	+	0.975582i	$0.570487\pi$
$72$	−2.16791	−0.255490
$73$	11.4928	1.34512	0.672562	−	0.740040i	$-0.265194\pi$
$73$	11.4928	1.34512	0.672562	+	0.740040i	$0.265194\pi$
$74$	4.09221	0.475710
$75$	4.58721	0.529685
$76$	−8.76889	−1.00586
$77$	0	0
$78$	−9.97746	−1.12973
$79$	8.47238	0.953217	0.476608	−	0.879116i	$-0.341866\pi$
$79$	8.47238	0.953217	0.476608	+	0.879116i	$0.341866\pi$
$80$	−2.20223	−0.246216
$81$	−6.27709	−0.697454
$82$	−0.972044	−0.107344
$83$	−7.88767	−0.865784	−0.432892	−	0.901446i	$-0.642507\pi$
$83$	−7.88767	−0.865784	−0.432892	+	0.901446i	$0.642507\pi$
$84$	0	0
$85$	0.940534	0.102015
$86$	11.3926	1.22850
$87$	−2.02193	−0.216773
$88$	10.0131	1.06741
$89$	−2.31660	−0.245559	−0.122779	−	0.992434i	$-0.539181\pi$
$89$	−2.31660	−0.245559	−0.122779	+	0.992434i	$0.539181\pi$
$90$	2.01263	0.212150
$91$	0	0
$92$	5.98547	0.624028
$93$	0.815952	0.0846103
$94$	−5.31490	−0.548190
$95$	23.5718	2.41841
$96$	−7.81154	−0.797262
$97$	−13.3398	−1.35445	−0.677227	−	0.735774i	$-0.736819\pi$
$97$	−13.3398	−1.35445	−0.677227	+	0.735774i	$0.736819\pi$
$98$	0	0
$99$	−2.46139	−0.247379
$100$	−3.21249	−0.321249
$101$	1.63761	0.162948	0.0814740	−	0.996675i	$-0.474037\pi$
$101$	1.63761	0.162948	0.0814740	+	0.996675i	$0.474037\pi$
$102$	−0.485646	−0.0480861
$103$	−4.36078	−0.429681	−0.214840	−	0.976649i	$-0.568923\pi$
$103$	−4.36078	−0.429681	−0.214840	+	0.976649i	$0.568923\pi$
$104$	20.2319	1.98390
$105$	0	0
$106$	3.96375	0.384994
$107$	7.49183	0.724263	0.362131	−	0.932127i	$-0.382049\pi$
$107$	7.49183	0.724263	0.362131	+	0.932127i	$0.382049\pi$
$108$	5.92963	0.570579
$109$	3.40171	0.325825	0.162913	−	0.986641i	$-0.447911\pi$
$109$	3.40171	0.325825	0.162913	+	0.986641i	$0.447911\pi$
$110$	−9.29596	−0.886335
$111$	−6.34286	−0.602037
$112$	0	0
$113$	−3.53846	−0.332870	−0.166435	−	0.986052i	$-0.553226\pi$
$113$	−3.53846	−0.332870	−0.166435	+	0.986052i	$0.553226\pi$
$114$	−12.1713	−1.13995
$115$	−16.0896	−1.50036
$116$	1.41598	0.131471
$117$	−4.97332	−0.459783
$118$	−14.8015	−1.36259
$119$	0	0
$120$	12.6906	1.15849
$121$	0.368672	0.0335157
$122$	0.700804	0.0634478
$123$	1.50665	0.135850
$124$	−0.571423	−0.0513153
$125$	−5.54600	−0.496050
$126$	0	0
$127$	6.67447	0.592264	0.296132	−	0.955147i	$-0.404303\pi$
$127$	6.67447	0.592264	0.296132	+	0.955147i	$0.404303\pi$
$128$	3.96107	0.350112
$129$	−17.6583	−1.55473
$130$	−18.7828	−1.64736
$131$	−9.63117	−0.841480	−0.420740	−	0.907181i	$-0.638229\pi$
$131$	−9.63117	−0.841480	−0.420740	+	0.907181i	$0.638229\pi$
$132$	−5.36011	−0.466537
$133$	0	0
$134$	4.14720	0.358263
$135$	−15.9395	−1.37186
$136$	0.984774	0.0844437
$137$	−2.60314	−0.222401	−0.111200	−	0.993798i	$-0.535470\pi$
$137$	−2.60314	−0.222401	−0.111200	+	0.993798i	$0.535470\pi$
$138$	8.30789	0.707215
$139$	12.2923	1.04262	0.521312	−	0.853366i	$-0.325443\pi$
$139$	12.2923	1.04262	0.521312	+	0.853366i	$0.325443\pi$
$140$	0	0
$141$	8.23799	0.693764
$142$	3.59790	0.301929
$143$	22.9708	1.92092
$144$	0.566805	0.0472337
$145$	−3.80633	−0.316098
$146$	−11.1715	−0.924557
$147$	0	0
$148$	4.44199	0.365130
$149$	15.0702	1.23460	0.617299	−	0.786729i	$-0.288227\pi$
$149$	15.0702	1.23460	0.617299	+	0.786729i	$0.288227\pi$
$150$	−4.45897	−0.364073
$151$	15.4873	1.26034	0.630170	−	0.776457i	$-0.282985\pi$
$151$	15.4873	1.26034	0.630170	+	0.776457i	$0.282985\pi$
$152$	24.6805	2.00185
$153$	−0.242073	−0.0195704
$154$	0	0
$155$	1.53605	0.123378
$156$	−10.8303	−0.867117
$157$	−11.8671	−0.947097	−0.473549	−	0.880768i	$-0.657027\pi$
$157$	−11.8671	−0.947097	−0.473549	+	0.880768i	$0.657027\pi$
$158$	−8.23552	−0.655183
$159$	−6.14374	−0.487230
$160$	−14.7054	−1.16257
$161$	0	0
$162$	6.10161	0.479387
$163$	−11.5865	−0.907529	−0.453764	−	0.891122i	$-0.649919\pi$
$163$	−11.5865	−0.907529	−0.453764	+	0.891122i	$0.649919\pi$
$164$	−1.05513	−0.0823918
$165$	14.4086	1.12171
$166$	7.66717	0.595087
$167$	18.7665	1.45219	0.726096	−	0.687593i	$-0.241333\pi$
$167$	18.7665	1.45219	0.726096	+	0.687593i	$0.241333\pi$
$168$	0	0
$169$	33.4133	2.57026
$170$	−0.914240	−0.0701190
$171$	−6.06685	−0.463944
$172$	12.3664	0.942929
$173$	14.0176	1.06573	0.532867	−	0.846199i	$-0.321114\pi$
$173$	14.0176	1.06573	0.532867	+	0.846199i	$0.321114\pi$
$174$	1.96540	0.148997
$175$	0	0
$176$	−2.61796	−0.197336
$177$	22.9421	1.72443
$178$	2.25184	0.168782
$179$	−16.9595	−1.26762	−0.633808	−	0.773491i	$-0.718509\pi$
$179$	−16.9595	−1.26762	−0.633808	+	0.773491i	$0.718509\pi$
$180$	2.18466	0.162835
$181$	3.63296	0.270036	0.135018	−	0.990843i	$-0.456891\pi$
$181$	3.63296	0.270036	0.135018	+	0.990843i	$0.456891\pi$
$182$	0	0
$183$	−1.08623	−0.0802967
$184$	−16.8464	−1.24194
$185$	−11.9406	−0.877889
$186$	−0.793142	−0.0581560
$187$	1.11809	0.0817627
$188$	−5.76919	−0.420761
$189$	0	0
$190$	−22.9128	−1.66227
$191$	−21.1423	−1.52980	−0.764901	−	0.644148i	$-0.777212\pi$
$191$	−21.1423	−1.52980	−0.764901	+	0.644148i	$0.777212\pi$
$192$	9.93282	0.716840
$193$	−2.18593	−0.157347	−0.0786734	−	0.996900i	$-0.525068\pi$
$193$	−2.18593	−0.157347	−0.0786734	+	0.996900i	$0.525068\pi$
$194$	12.9669	0.930970
$195$	29.1130	2.08483
$196$	0	0
$197$	0.415984	0.0296376	0.0148188	−	0.999890i	$-0.495283\pi$
$197$	0.415984	0.0296376	0.0148188	+	0.999890i	$0.495283\pi$
$198$	2.39258	0.170033
$199$	0.337056	0.0238933	0.0119466	−	0.999929i	$-0.496197\pi$
$199$	0.337056	0.0238933	0.0119466	+	0.999929i	$0.496197\pi$
$200$	9.04173	0.639347
$201$	−6.42808	−0.453402
$202$	−1.59183	−0.112001
$203$	0	0
$204$	−0.527156	−0.0369083
$205$	2.83631	0.198096
$206$	4.23888	0.295337
$207$	4.14111	0.287827
$208$	−5.28969	−0.366774
$209$	28.0216	1.93830
$210$	0	0
$211$	0.691323	0.0475926	0.0237963	−	0.999717i	$-0.492425\pi$
$211$	0.691323	0.0475926	0.0237963	+	0.999717i	$0.492425\pi$
$212$	4.30255	0.295501
$213$	−5.57669	−0.382108
$214$	−7.28239	−0.497814
$215$	−33.2423	−2.26710
$216$	−16.6893	−1.13556
$217$	0	0
$218$	−3.30662	−0.223952
$219$	17.3156	1.17008
$220$	−10.0905	−0.680303
$221$	2.25914	0.151966
$222$	6.16554	0.413804
$223$	−21.9932	−1.47278	−0.736388	−	0.676559i	$-0.763470\pi$
$223$	−21.9932	−1.47278	−0.736388	+	0.676559i	$0.763470\pi$
$224$	0	0
$225$	−2.22260	−0.148173
$226$	3.43954	0.228795
$227$	17.3296	1.15021	0.575104	−	0.818080i	$-0.304961\pi$
$227$	17.3296	1.15021	0.575104	+	0.818080i	$0.304961\pi$
$228$	−13.2117	−0.874963
$229$	−1.83524	−0.121276	−0.0606379	−	0.998160i	$-0.519313\pi$
$229$	−1.83524	−0.121276	−0.0606379	+	0.998160i	$0.519313\pi$
$230$	15.6398	1.03126
$231$	0	0
$232$	−3.98537	−0.261652
$233$	−6.65061	−0.435696	−0.217848	−	0.975983i	$-0.569904\pi$
$233$	−6.65061	−0.435696	−0.217848	+	0.975983i	$0.569904\pi$
$234$	4.83429	0.316027
$235$	15.5082	1.01164
$236$	−16.0667	−1.04585
$237$	12.7649	0.829170
$238$	0	0
$239$	3.99934	0.258696	0.129348	−	0.991599i	$-0.458712\pi$
$239$	3.99934	0.258696	0.129348	+	0.991599i	$0.458712\pi$
$240$	−3.31799	−0.214175
$241$	−10.6402	−0.685394	−0.342697	−	0.939446i	$-0.611340\pi$
$241$	−10.6402	−0.685394	−0.342697	+	0.939446i	$0.611340\pi$
$242$	−0.358366	−0.0230366
$243$	7.40206	0.474842
$244$	0.760706	0.0486992
$245$	0	0
$246$	−1.46453	−0.0933751
$247$	56.6187	3.60256
$248$	1.60830	0.102127
$249$	−11.8840	−0.753116
$250$	5.39096	0.340954
$251$	3.83177	0.241859	0.120929	−	0.992661i	$-0.461413\pi$
$251$	3.83177	0.241859	0.120929	+	0.992661i	$0.461413\pi$
$252$	0	0
$253$	−19.1270	−1.20250
$254$	−6.48788	−0.407086
$255$	1.41706	0.0887395
$256$	−17.0356	−1.06473
$257$	5.17306	0.322686	0.161343	−	0.986898i	$-0.448417\pi$
$257$	5.17306	0.322686	0.161343	+	0.986898i	$0.448417\pi$
$258$	17.1647	1.06863
$259$	0	0
$260$	−20.3883	−1.26443
$261$	0.979665	0.0606397
$262$	9.36193	0.578382
$263$	−4.84048	−0.298477	−0.149238	−	0.988801i	$-0.547682\pi$
$263$	−4.84048	−0.298477	−0.149238	+	0.988801i	$0.547682\pi$
$264$	15.0863	0.928499
$265$	−11.5657	−0.710478
$266$	0	0
$267$	−3.49030	−0.213603
$268$	4.50168	0.274984
$269$	7.59794	0.463255	0.231627	−	0.972805i	$-0.425595\pi$
$269$	7.59794	0.463255	0.231627	+	0.972805i	$0.425595\pi$
$270$	15.4939	0.942930
$271$	4.15646	0.252487	0.126244	−	0.991999i	$-0.459708\pi$
$271$	4.15646	0.252487	0.126244	+	0.991999i	$0.459708\pi$
$272$	−0.257472	−0.0156115
$273$	0	0
$274$	2.53036	0.152865
$275$	10.2658	0.619048
$276$	9.01801	0.542820
$277$	−23.1228	−1.38931	−0.694657	−	0.719341i	$-0.744444\pi$
$277$	−23.1228	−1.38931	−0.694657	+	0.719341i	$0.744444\pi$
$278$	−11.9487	−0.716636
$279$	−0.395345	−0.0236687
$280$	0	0
$281$	−29.7735	−1.77614	−0.888069	−	0.459710i	$-0.847953\pi$
$281$	−29.7735	−1.77614	−0.888069	+	0.459710i	$0.847953\pi$
$282$	−8.00769	−0.476851
$283$	22.9591	1.36478	0.682389	−	0.730989i	$-0.260941\pi$
$283$	22.9591	1.36478	0.682389	+	0.730989i	$0.260941\pi$
$284$	3.90544	0.231745
$285$	35.5144	2.10369
$286$	−22.3286	−1.32032
$287$	0	0
$288$	3.78485	0.223025
$289$	−16.8900	−0.993532
$290$	3.69992	0.217267
$291$	−20.0985	−1.17819
$292$	−12.1263	−0.709641
$293$	0.201056	0.0117458	0.00587291	−	0.999983i	$-0.498131\pi$
$293$	0.201056	0.0117458	0.00587291	+	0.999983i	$0.498131\pi$
$294$	0	0
$295$	43.1890	2.51456
$296$	−12.5022	−0.726678
$297$	−18.9486	−1.09951
$298$	−14.6489	−0.848587
$299$	−38.6468	−2.23500
$300$	−4.84010	−0.279443
$301$	0	0
$302$	−15.0544	−0.866281
$303$	2.46730	0.141743
$304$	−6.45279	−0.370093
$305$	−2.04486	−0.117088
$306$	0.235305	0.0134515
$307$	2.34525	0.133850	0.0669252	−	0.997758i	$-0.478681\pi$
$307$	2.34525	0.133850	0.0669252	+	0.997758i	$0.478681\pi$
$308$	0	0
$309$	−6.57018	−0.373765
$310$	−1.49311	−0.0848029
$311$	−25.8769	−1.46734	−0.733672	−	0.679504i	$-0.762195\pi$
$311$	−25.8769	−1.46734	−0.733672	+	0.679504i	$0.762195\pi$
$312$	30.4824	1.72573
$313$	6.52508	0.368819	0.184410	−	0.982849i	$-0.440963\pi$
$313$	6.52508	0.368819	0.184410	+	0.982849i	$0.440963\pi$
$314$	11.5353	0.650977
$315$	0	0
$316$	−8.93945	−0.502884
$317$	−0.895862	−0.0503166	−0.0251583	−	0.999683i	$-0.508009\pi$
$317$	−0.895862	−0.0503166	−0.0251583	+	0.999683i	$0.508009\pi$
$318$	5.97199	0.334893
$319$	−4.52489	−0.253345
$320$	18.6988	1.04529
$321$	11.2876	0.630011
$322$	0	0
$323$	2.75588	0.153341
$324$	6.62314	0.367952
$325$	20.7423	1.15058
$326$	11.2626	0.623780
$327$	5.12520	0.283424
$328$	2.96972	0.163975
$329$	0	0
$330$	−14.0058	−0.770992
$331$	27.6100	1.51758	0.758790	−	0.651335i	$-0.225791\pi$
$331$	27.6100	1.51758	0.758790	+	0.651335i	$0.225791\pi$
$332$	8.32252	0.456757
$333$	3.07324	0.168413
$334$	−18.2418	−0.998149
$335$	−12.1010	−0.661149
$336$	0	0
$337$	19.7958	1.07834	0.539172	−	0.842196i	$-0.318737\pi$
$337$	19.7958	1.07834	0.539172	+	0.842196i	$0.318737\pi$
$338$	−32.4793	−1.76664
$339$	−5.33123	−0.289552
$340$	−0.992385	−0.0538196
$341$	1.82603	0.0988848
$342$	5.89725	0.318887
$343$	0	0
$344$	−34.8059	−1.87661
$345$	−24.2414	−1.30511
$346$	−13.6257	−0.732521
$347$	−18.5953	−0.998249	−0.499125	−	0.866530i	$-0.666345\pi$
$347$	−18.5953	−0.998249	−0.499125	+	0.866530i	$0.666345\pi$
$348$	2.13339	0.114362
$349$	8.32941	0.445863	0.222932	−	0.974834i	$-0.428437\pi$
$349$	8.32941	0.445863	0.222932	+	0.974834i	$0.428437\pi$
$350$	0	0
$351$	−38.2863	−2.04357
$352$	−17.4815	−0.931768
$353$	−24.9111	−1.32588	−0.662942	−	0.748671i	$-0.730692\pi$
$353$	−24.9111	−1.32588	−0.662942	+	0.748671i	$0.730692\pi$
$354$	−22.3007	−1.18527
$355$	−10.4982	−0.557189
$356$	2.44431	0.129548
$357$	0	0
$358$	16.4854	0.871282
$359$	17.7466	0.936629	0.468315	−	0.883562i	$-0.344861\pi$
$359$	17.7466	0.936629	0.468315	+	0.883562i	$0.344861\pi$
$360$	−6.14885	−0.324073
$361$	50.0681	2.63516
$362$	−3.53140	−0.185606
$363$	0.555460	0.0291541
$364$	0	0
$365$	32.5970	1.70620
$366$	1.05587	0.0551911
$367$	3.48842	0.182094	0.0910469	−	0.995847i	$-0.470979\pi$
$367$	3.48842	0.182094	0.0910469	+	0.995847i	$0.470979\pi$
$368$	4.40454	0.229603
$369$	−0.730003	−0.0380024
$370$	11.6068	0.603407
$371$	0	0
$372$	−0.860935	−0.0446374
$373$	15.3021	0.792314	0.396157	−	0.918183i	$-0.370344\pi$
$373$	15.3021	0.792314	0.396157	+	0.918183i	$0.370344\pi$
$374$	−1.08683	−0.0561987
$375$	−8.35589	−0.431496
$376$	16.2377	0.837395
$377$	−9.14269	−0.470873
$378$	0	0
$379$	20.3028	1.04289	0.521443	−	0.853286i	$-0.325394\pi$
$379$	20.3028	1.04289	0.521443	+	0.853286i	$0.325394\pi$
$380$	−24.8713	−1.27587
$381$	10.0561	0.515190
$382$	20.5512	1.05149
$383$	−23.5717	−1.20446	−0.602229	−	0.798323i	$-0.705721\pi$
$383$	−23.5717	−1.20446	−0.602229	+	0.798323i	$0.705721\pi$
$384$	5.96795	0.304550
$385$	0	0
$386$	2.12482	0.108151
$387$	8.55583	0.434917
$388$	14.0753	0.714563
$389$	2.13713	0.108357	0.0541783	−	0.998531i	$-0.482746\pi$
$389$	2.13713	0.108357	0.0541783	+	0.998531i	$0.482746\pi$
$390$	−28.2992	−1.43298
$391$	−1.88111	−0.0951316
$392$	0	0
$393$	−14.5108	−0.731974
$394$	−0.404354	−0.0203711
$395$	24.0303	1.20909
$396$	2.59708	0.130508
$397$	−9.66326	−0.484985	−0.242492	−	0.970153i	$-0.577965\pi$
$397$	−9.66326	−0.484985	−0.242492	+	0.970153i	$0.577965\pi$
$398$	−0.327633	−0.0164228
$399$	0	0
$400$	−2.36398	−0.118199
$401$	−30.3369	−1.51495	−0.757477	−	0.652862i	$-0.773568\pi$
$401$	−30.3369	−1.51495	−0.757477	+	0.652862i	$0.773568\pi$
$402$	6.24838	0.311641
$403$	3.68955	0.183790
$404$	−1.72789	−0.0859656
$405$	−17.8037	−0.884675
$406$	0	0
$407$	−14.1947	−0.703607
$408$	1.48371	0.0734547
$409$	−0.503834	−0.0249130	−0.0124565	−	0.999922i	$-0.503965\pi$
$409$	−0.503834	−0.0249130	−0.0124565	+	0.999922i	$0.503965\pi$
$410$	−2.75702	−0.136159
$411$	−3.92202	−0.193459
$412$	4.60119	0.226685
$413$	0	0
$414$	−4.02534	−0.197835
$415$	−22.3719	−1.09819
$416$	−35.3220	−1.73181
$417$	18.5203	0.906942
$418$	−27.2383	−1.33227
$419$	9.33151	0.455874	0.227937	−	0.973676i	$-0.426802\pi$
$419$	9.33151	0.455874	0.227937	+	0.973676i	$0.426802\pi$
$420$	0	0
$421$	−8.74829	−0.426365	−0.213183	−	0.977012i	$-0.568383\pi$
$421$	−8.74829	−0.426365	−0.213183	+	0.977012i	$0.568383\pi$
$422$	−0.671996	−0.0327123
$423$	−3.99148	−0.194072
$424$	−12.1098	−0.588103
$425$	1.00962	0.0489736
$426$	5.42079	0.262638
$427$	0	0
$428$	−7.90485	−0.382095
$429$	34.6090	1.67094
$430$	32.3130	1.55827
$431$	−19.4807	−0.938350	−0.469175	−	0.883105i	$-0.655449\pi$
$431$	−19.4807	−0.938350	−0.469175	+	0.883105i	$0.655449\pi$
$432$	4.36346	0.209937
$433$	27.2600	1.31003	0.655015	−	0.755616i	$-0.272662\pi$
$433$	27.2600	1.31003	0.655015	+	0.755616i	$0.272662\pi$
$434$	0	0
$435$	−5.73480	−0.274963
$436$	−3.58925	−0.171894
$437$	−47.1445	−2.25523
$438$	−16.8315	−0.804240
$439$	−31.5366	−1.50516	−0.752581	−	0.658500i	$-0.771191\pi$
$439$	−31.5366	−1.50516	−0.752581	+	0.658500i	$0.771191\pi$
$440$	28.4004	1.35393
$441$	0	0
$442$	−2.19598	−0.104452
$443$	22.3752	1.06308	0.531538	−	0.847034i	$-0.321614\pi$
$443$	22.3752	1.06308	0.531538	+	0.847034i	$0.321614\pi$
$444$	6.69254	0.317614
$445$	−6.57058	−0.311475
$446$	21.3784	1.01230
$447$	22.7055	1.07393
$448$	0	0
$449$	−26.3703	−1.24449	−0.622245	−	0.782822i	$-0.713779\pi$
$449$	−26.3703	−1.24449	−0.622245	+	0.782822i	$0.713779\pi$
$450$	2.16046	0.101845
$451$	3.37175	0.158769
$452$	3.73354	0.175611
$453$	23.3340	1.09633
$454$	−16.8452	−0.790583
$455$	0	0
$456$	37.1849	1.74134
$457$	−28.3861	−1.32785	−0.663923	−	0.747801i	$-0.731110\pi$
$457$	−28.3861	−1.32785	−0.663923	+	0.747801i	$0.731110\pi$
$458$	1.78393	0.0833576
$459$	−1.86356	−0.0869834
$460$	16.9766	0.791539
$461$	−10.2874	−0.479132	−0.239566	−	0.970880i	$-0.577005\pi$
$461$	−10.2874	−0.479132	−0.239566	+	0.970880i	$0.577005\pi$
$462$	0	0
$463$	−6.49216	−0.301716	−0.150858	−	0.988555i	$-0.548204\pi$
$463$	−6.49216	−0.301716	−0.150858	+	0.988555i	$0.548204\pi$
$464$	1.04199	0.0483729
$465$	2.31429	0.107323
$466$	6.46469	0.299471
$467$	31.3680	1.45154	0.725769	−	0.687938i	$-0.241484\pi$
$467$	31.3680	1.45154	0.725769	+	0.687938i	$0.241484\pi$
$468$	5.24750	0.242566
$469$	0	0
$470$	−15.0747	−0.695343
$471$	−17.8796	−0.823847
$472$	45.2205	2.08144
$473$	−39.5178	−1.81703
$474$	−12.4081	−0.569921
$475$	25.3031	1.16099
$476$	0	0
$477$	2.97677	0.136297
$478$	−3.88754	−0.177812
$479$	3.06503	0.140045	0.0700224	−	0.997545i	$-0.477693\pi$
$479$	3.06503	0.140045	0.0700224	+	0.997545i	$0.477693\pi$
$480$	−22.1559	−1.01128
$481$	−28.6810	−1.30774
$482$	10.3427	0.471098
$483$	0	0
$484$	−0.388997	−0.0176817
$485$	−37.8359	−1.71804
$486$	−7.19513	−0.326378
$487$	−13.6638	−0.619164	−0.309582	−	0.950873i	$-0.600189\pi$
$487$	−13.6638	−0.619164	−0.309582	+	0.950873i	$0.600189\pi$
$488$	−2.14105	−0.0969207
$489$	−17.4569	−0.789428
$490$	0	0
$491$	−18.3020	−0.825960	−0.412980	−	0.910740i	$-0.635512\pi$
$491$	−18.3020	−0.825960	−0.412980	+	0.910740i	$0.635512\pi$
$492$	−1.58971	−0.0716698
$493$	−0.445014	−0.0200424
$494$	−55.0359	−2.47618
$495$	−6.98125	−0.313784
$496$	−0.420495	−0.0188808
$497$	0	0
$498$	11.5517	0.517646
$499$	13.4350	0.601432	0.300716	−	0.953714i	$-0.402774\pi$
$499$	13.4350	0.601432	0.300716	+	0.953714i	$0.402774\pi$
$500$	5.85175	0.261698
$501$	28.2745	1.26321
$502$	−3.72465	−0.166239
$503$	−29.1869	−1.30138	−0.650691	−	0.759343i	$-0.725521\pi$
$503$	−29.1869	−1.30138	−0.650691	+	0.759343i	$0.725521\pi$
$504$	0	0
$505$	4.64476	0.206689
$506$	18.5923	0.826528
$507$	50.3422	2.23578
$508$	−7.04244	−0.312458
$509$	−26.4308	−1.17153	−0.585763	−	0.810483i	$-0.699205\pi$
$509$	−26.4308	−1.17153	−0.585763	+	0.810483i	$0.699205\pi$
$510$	−1.37744	−0.0609941
$511$	0	0
$512$	8.63725	0.381716
$513$	−46.7047	−2.06206
$514$	−5.02844	−0.221795
$515$	−12.3685	−0.545022
$516$	18.6318	0.820221
$517$	18.4359	0.810809
$518$	0	0
$519$	21.1196	0.927046
$520$	57.3840	2.51645
$521$	−4.20510	−0.184229	−0.0921143	−	0.995748i	$-0.529363\pi$
$521$	−4.20510	−0.184229	−0.0921143	+	0.995748i	$0.529363\pi$
$522$	−0.952278	−0.0416801
$523$	−17.8954	−0.782511	−0.391256	−	0.920282i	$-0.627959\pi$
$523$	−17.8954	−0.782511	−0.391256	+	0.920282i	$0.627959\pi$
$524$	10.1621	0.443935
$525$	0	0
$526$	4.70516	0.205155
$527$	0.179586	0.00782290
$528$	−3.94436	−0.171656
$529$	9.17987	0.399125
$530$	11.2424	0.488339
$531$	−11.1159	−0.482389
$532$	0	0
$533$	6.81273	0.295092
$534$	3.39273	0.146818
$535$	21.2491	0.918680
$536$	−12.6702	−0.547270
$537$	−25.5521	−1.10265
$538$	−7.38554	−0.318413
$539$	0	0
$540$	16.8183	0.723743
$541$	−5.56542	−0.239276	−0.119638	−	0.992818i	$-0.538173\pi$
$541$	−5.56542	−0.239276	−0.119638	+	0.992818i	$0.538173\pi$
$542$	−4.04027	−0.173544
$543$	5.47360	0.234895
$544$	−1.71927	−0.0737133
$545$	9.64831	0.413288
$546$	0	0
$547$	−11.4571	−0.489871	−0.244935	−	0.969539i	$-0.578767\pi$
$547$	−11.4571	−0.489871	−0.244935	+	0.969539i	$0.578767\pi$
$548$	2.74665	0.117331
$549$	0.526303	0.0224620
$550$	−9.97876	−0.425496
$551$	−11.1530	−0.475133
$552$	−25.3817	−1.08032
$553$	0	0
$554$	22.4764	0.954930
$555$	−17.9903	−0.763645
$556$	−12.9700	−0.550051
$557$	−37.9483	−1.60792	−0.803960	−	0.594683i	$-0.797277\pi$
$557$	−37.9483	−1.60792	−0.803960	+	0.594683i	$0.797277\pi$
$558$	0.384293	0.0162684
$559$	−79.8470	−3.37717
$560$	0	0
$561$	1.68457	0.0711225
$562$	28.9412	1.22081
$563$	−1.36123	−0.0573688	−0.0286844	−	0.999589i	$-0.509132\pi$
$563$	−1.36123	−0.0573688	−0.0286844	+	0.999589i	$0.509132\pi$
$564$	−8.69215	−0.366006
$565$	−10.0362	−0.422225
$566$	−22.3173	−0.938066
$567$	0	0
$568$	−10.9921	−0.461217
$569$	11.5745	0.485229	0.242615	−	0.970123i	$-0.421995\pi$
$569$	11.5745	0.485229	0.242615	+	0.970123i	$0.421995\pi$
$570$	−34.5216	−1.44595
$571$	24.1491	1.01061	0.505304	−	0.862941i	$-0.331380\pi$
$571$	24.1491	1.01061	0.505304	+	0.862941i	$0.331380\pi$
$572$	−24.2372	−1.01341
$573$	−31.8541	−1.33072
$574$	0	0
$575$	−17.2714	−0.720268
$576$	−4.81265	−0.200527
$577$	−6.24104	−0.259818	−0.129909	−	0.991526i	$-0.541469\pi$
$577$	−6.24104	−0.259818	−0.129909	+	0.991526i	$0.541469\pi$
$578$	16.4179	0.682893
$579$	−3.29344	−0.136871
$580$	4.01617	0.166762
$581$	0	0
$582$	19.5366	0.809818
$583$	−13.7491	−0.569431
$584$	34.1303	1.41232
$585$	−14.1059	−0.583205
$586$	−0.195435	−0.00807336
$587$	−3.24155	−0.133793	−0.0668966	−	0.997760i	$-0.521310\pi$
$587$	−3.24155	−0.133793	−0.0668966	+	0.997760i	$0.521310\pi$
$588$	0	0
$589$	4.50081	0.185453
$590$	−41.9816	−1.72836
$591$	0.626742	0.0257807
$592$	3.26874	0.134345
$593$	17.6268	0.723845	0.361922	−	0.932208i	$-0.382121\pi$
$593$	17.6268	0.723845	0.361922	+	0.932208i	$0.382121\pi$
$594$	18.4189	0.755735
$595$	0	0
$596$	−15.9010	−0.651330
$597$	0.507826	0.0207839
$598$	37.5664	1.53620
$599$	18.6071	0.760265	0.380132	−	0.924932i	$-0.375878\pi$
$599$	18.6071	0.760265	0.380132	+	0.924932i	$0.375878\pi$
$600$	13.6227	0.556146
$601$	9.19988	0.375271	0.187635	−	0.982239i	$-0.439918\pi$
$601$	9.19988	0.375271	0.187635	+	0.982239i	$0.439918\pi$
$602$	0	0
$603$	3.11453	0.126834
$604$	−16.3411	−0.664911
$605$	1.04567	0.0425124
$606$	−2.39833	−0.0974254
$607$	−2.04211	−0.0828868	−0.0414434	−	0.999141i	$-0.513196\pi$
$607$	−2.04211	−0.0828868	−0.0414434	+	0.999141i	$0.513196\pi$
$608$	−43.0887	−1.74748
$609$	0	0
$610$	1.98770	0.0804795
$611$	37.2503	1.50699
$612$	0.255418	0.0103247
$613$	−3.55365	−0.143530	−0.0717652	−	0.997422i	$-0.522863\pi$
$613$	−3.55365	−0.143530	−0.0717652	+	0.997422i	$0.522863\pi$
$614$	−2.27969	−0.0920006
$615$	4.27332	0.172317
$616$	0	0
$617$	−14.2917	−0.575363	−0.287681	−	0.957726i	$-0.592884\pi$
$617$	−14.2917	−0.575363	−0.287681	+	0.957726i	$0.592884\pi$
$618$	6.38651	0.256903
$619$	5.82312	0.234051	0.117025	−	0.993129i	$-0.462664\pi$
$619$	5.82312	0.234051	0.117025	+	0.993129i	$0.462664\pi$
$620$	−1.62073	−0.0650902
$621$	31.8797	1.27929
$622$	25.1535	1.00856
$623$	0	0
$624$	−7.96972	−0.319044
$625$	−30.9534	−1.23813
$626$	−6.34267	−0.253504
$627$	42.2188	1.68606
$628$	12.5213	0.499655
$629$	−1.39603	−0.0556632
$630$	0	0
$631$	1.12725	0.0448751	0.0224375	−	0.999748i	$-0.492857\pi$
$631$	1.12725	0.0448751	0.0224375	+	0.999748i	$0.492857\pi$
$632$	25.1606	1.00083
$633$	1.04158	0.0413992
$634$	0.870817	0.0345846
$635$	18.9309	0.751248
$636$	6.48245	0.257046
$637$	0	0
$638$	4.39839	0.174134
$639$	2.70202	0.106890
$640$	11.2348	0.444095
$641$	−13.0592	−0.515808	−0.257904	−	0.966171i	$-0.583032\pi$
$641$	−13.0592	−0.515808	−0.257904	+	0.966171i	$0.583032\pi$
$642$	−10.9720	−0.433031
$643$	23.0738	0.909942	0.454971	−	0.890506i	$-0.349650\pi$
$643$	23.0738	0.909942	0.454971	+	0.890506i	$0.349650\pi$
$644$	0	0
$645$	−50.0845	−1.97207
$646$	−2.67883	−0.105397
$647$	−39.2734	−1.54400	−0.771998	−	0.635625i	$-0.780742\pi$
$647$	−39.2734	−1.54400	−0.771998	+	0.635625i	$0.780742\pi$
$648$	−18.6412	−0.732295
$649$	51.3422	2.01536
$650$	−20.1625	−0.790836
$651$	0	0
$652$	12.2253	0.478780
$653$	−22.3213	−0.873502	−0.436751	−	0.899583i	$-0.643871\pi$
$653$	−22.3213	−0.873502	−0.436751	+	0.899583i	$0.643871\pi$
$654$	−4.98192	−0.194808
$655$	−27.3170	−1.06736
$656$	−0.776442	−0.0303150
$657$	−8.38974	−0.327315
$658$	0	0
$659$	−2.94033	−0.114539	−0.0572695	−	0.998359i	$-0.518239\pi$
$659$	−2.94033	−0.114539	−0.0572695	+	0.998359i	$0.518239\pi$
$660$	−15.2029	−0.591772
$661$	33.7457	1.31256	0.656278	−	0.754519i	$-0.272130\pi$
$661$	33.7457	1.31256	0.656278	+	0.754519i	$0.272130\pi$
$662$	−26.8381	−1.04309
$663$	3.40373	0.132190
$664$	−23.4242	−0.909035
$665$	0	0
$666$	−2.98733	−0.115757
$667$	7.61281	0.294769
$668$	−19.8011	−0.766126
$669$	−33.1361	−1.28112
$670$	11.7627	0.454434
$671$	−2.43089	−0.0938435
$672$	0	0
$673$	−26.4472	−1.01946	−0.509732	−	0.860333i	$-0.670255\pi$
$673$	−26.4472	−1.01946	−0.509732	+	0.860333i	$0.670255\pi$
$674$	−19.2424	−0.741188
$675$	−17.1103	−0.658576
$676$	−35.2554	−1.35598
$677$	−15.3944	−0.591654	−0.295827	−	0.955242i	$-0.595595\pi$
$677$	−15.3944	−0.591654	−0.295827	+	0.955242i	$0.595595\pi$
$678$	5.18219	0.199021
$679$	0	0
$680$	2.79312	0.107111
$681$	26.1097	1.00053
$682$	−1.77498	−0.0679674
$683$	−16.0508	−0.614165	−0.307083	−	0.951683i	$-0.599353\pi$
$683$	−16.0508	−0.614165	−0.307083	+	0.951683i	$0.599353\pi$
$684$	6.40132	0.244760
$685$	−7.38329	−0.282101
$686$	0	0
$687$	−2.76506	−0.105494
$688$	9.10010	0.346938
$689$	−27.7806	−1.05836
$690$	23.5637	0.897056
$691$	9.87960	0.375838	0.187919	−	0.982185i	$-0.439826\pi$
$691$	9.87960	0.375838	0.187919	+	0.982185i	$0.439826\pi$
$692$	−14.7903	−0.562244
$693$	0	0
$694$	18.0755	0.686136
$695$	34.8649	1.32250
$696$	−6.00456	−0.227602
$697$	0.331605	0.0125604
$698$	−8.09656	−0.306459
$699$	−10.0201	−0.378997
$700$	0	0
$701$	40.3563	1.52424	0.762118	−	0.647439i	$-0.224160\pi$
$701$	40.3563	1.52424	0.762118	+	0.647439i	$0.224160\pi$
$702$	37.2160	1.40463
$703$	−34.9873	−1.31957
$704$	22.2287	0.837777
$705$	23.3655	0.879995
$706$	24.2147	0.911332
$707$	0	0
$708$	−24.2069	−0.909749
$709$	12.4902	0.469080	0.234540	−	0.972106i	$-0.424642\pi$
$709$	12.4902	0.469080	0.234540	+	0.972106i	$0.424642\pi$
$710$	10.2048	0.382978
$711$	−6.18486	−0.231950
$712$	−6.87965	−0.257826
$713$	−3.07216	−0.115053
$714$	0	0
$715$	65.1523	2.43656
$716$	17.8945	0.668749
$717$	6.02561	0.225031
$718$	−17.2505	−0.643782
$719$	−11.1277	−0.414995	−0.207497	−	0.978236i	$-0.566532\pi$
$719$	−11.1277	−0.414995	−0.207497	+	0.978236i	$0.566532\pi$
$720$	1.60763	0.0599129
$721$	0	0
$722$	−48.6684	−1.81125
$723$	−16.0310	−0.596201
$724$	−3.83324	−0.142461
$725$	−4.08591	−0.151747
$726$	−0.539932	−0.0200388
$727$	13.3397	0.494743	0.247372	−	0.968921i	$-0.420433\pi$
$727$	13.3397	0.494743	0.247372	+	0.968921i	$0.420433\pi$
$728$	0	0
$729$	29.9836	1.11050
$730$	−31.6857	−1.17274
$731$	−3.88650	−0.143747
$732$	1.14612	0.0423617
$733$	21.5062	0.794349	0.397175	−	0.917743i	$-0.369991\pi$
$733$	21.5062	0.794349	0.397175	+	0.917743i	$0.369991\pi$
$734$	−3.39090	−0.125160
$735$	0	0
$736$	29.4114	1.08412
$737$	−14.3854	−0.529895
$738$	0.709595	0.0261206
$739$	7.06024	0.259715	0.129858	−	0.991533i	$-0.458548\pi$
$739$	7.06024	0.259715	0.129858	+	0.991533i	$0.458548\pi$
$740$	12.5989	0.463143
$741$	85.3046	3.13374
$742$	0	0
$743$	−12.8929	−0.472996	−0.236498	−	0.971632i	$-0.576000\pi$
$743$	−12.8929	−0.472996	−0.236498	+	0.971632i	$0.576000\pi$
$744$	2.42315	0.0888370
$745$	42.7437	1.56601
$746$	−14.8743	−0.544588
$747$	5.75802	0.210675
$748$	−1.17973	−0.0431351
$749$	0	0
$750$	8.12230	0.296584
$751$	6.36078	0.232108	0.116054	−	0.993243i	$-0.462975\pi$
$751$	6.36078	0.232108	0.116054	+	0.993243i	$0.462975\pi$
$752$	−4.24539	−0.154813
$753$	5.77313	0.210385
$754$	8.88710	0.323649
$755$	43.9268	1.59866
$756$	0	0
$757$	−35.7572	−1.29962	−0.649809	−	0.760098i	$-0.725151\pi$
$757$	−35.7572	−1.29962	−0.649809	+	0.760098i	$0.725151\pi$
$758$	−19.7352	−0.716816
$759$	−28.8177	−1.04602
$760$	70.0016	2.53922
$761$	−12.9444	−0.469234	−0.234617	−	0.972088i	$-0.575384\pi$
$761$	−12.9444	−0.469234	−0.234617	+	0.972088i	$0.575384\pi$
$762$	−9.77498	−0.354110
$763$	0	0
$764$	22.3079	0.807070
$765$	−0.686592	−0.0248238
$766$	22.9127	0.827871
$767$	103.739	3.74579
$768$	−25.6667	−0.926169
$769$	−34.6334	−1.24891	−0.624455	−	0.781060i	$-0.714679\pi$
$769$	−34.6334	−1.24891	−0.624455	+	0.781060i	$0.714679\pi$
$770$	0	0
$771$	7.79399	0.280694
$772$	2.30644	0.0830107
$773$	−5.08516	−0.182901	−0.0914503	−	0.995810i	$-0.529150\pi$
$773$	−5.08516	−0.182901	−0.0914503	+	0.995810i	$0.529150\pi$
$774$	−8.31665	−0.298936
$775$	1.64888	0.0592294
$776$	−39.6156	−1.42212
$777$	0	0
$778$	−2.07738	−0.0744778
$779$	8.31072	0.297762
$780$	−30.7180	−1.09988
$781$	−12.4801	−0.446573
$782$	1.82852	0.0653877
$783$	7.54179	0.269522
$784$	0	0
$785$	−33.6587	−1.20133
$786$	14.1052	0.503114
$787$	34.0261	1.21290	0.606449	−	0.795122i	$-0.292593\pi$
$787$	34.0261	1.21290	0.606449	+	0.795122i	$0.292593\pi$
$788$	−0.438917	−0.0156358
$789$	−7.29291	−0.259634
$790$	−23.3585	−0.831057
$791$	0	0
$792$	−7.30963	−0.259736
$793$	−4.91170	−0.174420
$794$	9.39311	0.333349
$795$	−17.4255	−0.618020
$796$	−0.355638	−0.0126052
$797$	22.0139	0.779771	0.389885	−	0.920863i	$-0.372515\pi$
$797$	22.0139	0.779771	0.389885	+	0.920863i	$0.372515\pi$
$798$	0	0
$799$	1.81313	0.0641441
$800$	−15.7856	−0.558104
$801$	1.69112	0.0597529
$802$	29.4888	1.04129
$803$	38.7506	1.36748
$804$	6.78245	0.239199
$805$	0	0
$806$	−3.58641	−0.126326
$807$	11.4474	0.402969
$808$	4.86324	0.171088
$809$	−16.2143	−0.570063	−0.285032	−	0.958518i	$-0.592004\pi$
$809$	−16.2143	−0.570063	−0.285032	+	0.958518i	$0.592004\pi$
$810$	17.3060	0.608072
$811$	−19.7995	−0.695255	−0.347628	−	0.937633i	$-0.613013\pi$
$811$	−19.7995	−0.695255	−0.347628	+	0.937633i	$0.613013\pi$
$812$	0	0
$813$	6.26234	0.219630
$814$	13.7979	0.483616
$815$	−32.8630	−1.15114
$816$	−0.387920	−0.0135799
$817$	−97.4038	−3.40773
$818$	0.489749	0.0171237
$819$	0	0
$820$	−2.99267	−0.104509
$821$	−23.3808	−0.815994	−0.407997	−	0.912983i	$-0.633773\pi$
$821$	−23.3808	−0.815994	−0.407997	+	0.912983i	$0.633773\pi$
$822$	3.81237	0.132972
$823$	50.5366	1.76160	0.880798	−	0.473492i	$-0.157007\pi$
$823$	50.5366	1.76160	0.880798	+	0.473492i	$0.157007\pi$
$824$	−12.9503	−0.451146
$825$	15.4669	0.538488
$826$	0	0
$827$	13.7609	0.478512	0.239256	−	0.970957i	$-0.423097\pi$
$827$	13.7609	0.478512	0.239256	+	0.970957i	$0.423097\pi$
$828$	−4.36941	−0.151847
$829$	23.8332	0.827763	0.413881	−	0.910331i	$-0.364173\pi$
$829$	23.8332	0.827763	0.413881	+	0.910331i	$0.364173\pi$
$830$	21.7464	0.754830
$831$	−34.8380	−1.20852
$832$	44.9140	1.55711
$833$	0	0
$834$	−18.0025	−0.623377
$835$	53.2275	1.84201
$836$	−29.5665	−1.02258
$837$	−3.04350	−0.105199
$838$	−9.07064	−0.313340
$839$	36.5692	1.26251	0.631254	−	0.775576i	$-0.282541\pi$
$839$	36.5692	1.26251	0.631254	+	0.775576i	$0.282541\pi$
$840$	0	0
$841$	−27.1990	−0.937898
$842$	8.50372	0.293058
$843$	−44.8583	−1.54500
$844$	−0.729435	−0.0251082
$845$	94.7705	3.26020
$846$	3.87989	0.133393
$847$	0	0
$848$	3.16613	0.108725
$849$	34.5914	1.18717
$850$	−0.981393	−0.0336615
$851$	23.8816	0.818652
$852$	5.88413	0.201587
$853$	−0.765299	−0.0262033	−0.0131017	−	0.999914i	$-0.504171\pi$
$853$	−0.765299	−0.0262033	−0.0131017	+	0.999914i	$0.504171\pi$
$854$	0	0
$855$	−17.2075	−0.588483
$856$	22.2486	0.760443
$857$	−7.32125	−0.250089	−0.125045	−	0.992151i	$-0.539907\pi$
$857$	−7.32125	−0.250089	−0.125045	+	0.992151i	$0.539907\pi$
$858$	−33.6415	−1.14850
$859$	−51.4639	−1.75593	−0.877963	−	0.478728i	$-0.841098\pi$
$859$	−51.4639	−1.75593	−0.877963	+	0.478728i	$0.841098\pi$
$860$	35.0749	1.19604
$861$	0	0
$862$	18.9361	0.644965
$863$	−22.7203	−0.773409	−0.386704	−	0.922204i	$-0.626387\pi$
$863$	−22.7203	−0.773409	−0.386704	+	0.922204i	$0.626387\pi$
$864$	29.1371	0.991264
$865$	39.7581	1.35182
$866$	−26.4979	−0.900435
$867$	−25.4474	−0.864239
$868$	0	0
$869$	28.5667	0.969059
$870$	5.57448	0.188993
$871$	−29.0663	−0.984874
$872$	10.1021	0.342102
$873$	9.73812	0.329585
$874$	45.8265	1.55011
$875$	0	0
$876$	−18.2702	−0.617292
$877$	−55.8676	−1.88652	−0.943258	−	0.332061i	$-0.892256\pi$
$877$	−55.8676	−1.88652	−0.943258	+	0.332061i	$0.892256\pi$
$878$	30.6550	1.03456
$879$	0.302921	0.0102173
$880$	−7.42535	−0.250309
$881$	12.8791	0.433909	0.216954	−	0.976182i	$-0.430388\pi$
$881$	12.8791	0.433909	0.216954	+	0.976182i	$0.430388\pi$
$882$	0	0
$883$	46.5706	1.56723	0.783613	−	0.621250i	$-0.213375\pi$
$883$	46.5706	1.56723	0.783613	+	0.621250i	$0.213375\pi$
$884$	−2.38368	−0.0801719
$885$	65.0708	2.18733
$886$	−21.7496	−0.730694
$887$	55.2044	1.85358	0.926791	−	0.375578i	$-0.122556\pi$
$887$	55.2044	1.85358	0.926791	+	0.375578i	$0.122556\pi$
$888$	−18.8365	−0.632112
$889$	0	0
$890$	6.38690	0.214089
$891$	−21.1647	−0.709045
$892$	23.2057	0.776985
$893$	45.4410	1.52062
$894$	−22.0708	−0.738157
$895$	−48.1025	−1.60789
$896$	0	0
$897$	−58.2272	−1.94415
$898$	25.6331	0.855387
$899$	−0.726783	−0.0242396
$900$	2.34513	0.0781709
$901$	−1.35220	−0.0450484
$902$	−3.27749	−0.109128
$903$	0	0
$904$	−10.5082	−0.349499
$905$	10.3042	0.342523
$906$	−22.6817	−0.753548
$907$	−42.5926	−1.41426	−0.707132	−	0.707082i	$-0.750011\pi$
$907$	−42.5926	−1.41426	−0.707132	+	0.707082i	$0.750011\pi$
$908$	−18.2850	−0.606810
$909$	−1.19546	−0.0396509
$910$	0	0
$911$	37.5530	1.24419	0.622093	−	0.782943i	$-0.286283\pi$
$911$	37.5530	1.24419	0.622093	+	0.782943i	$0.286283\pi$
$912$	−9.72210	−0.321931
$913$	−26.5952	−0.880173
$914$	27.5926	0.912681
$915$	−3.08089	−0.101851
$916$	1.93641	0.0639808
$917$	0	0
$918$	1.81146	0.0597871
$919$	7.19567	0.237363	0.118682	−	0.992932i	$-0.462133\pi$
$919$	7.19567	0.237363	0.118682	+	0.992932i	$0.462133\pi$
$920$	−47.7817	−1.57531
$921$	3.53347	0.116432
$922$	9.99980	0.329326
$923$	−25.2165	−0.830012
$924$	0	0
$925$	−12.8176	−0.421441
$926$	6.31067	0.207381
$927$	3.18339	0.104556
$928$	6.95788	0.228404
$929$	0.0135113	0.000443291 0	0.000221646	−	1.00000i	$-0.499929\pi$
$929$	0.0135113	0.000443291 0	0.000221646		1.00000i	$0.499929\pi$
$930$	−2.24959	−0.0737671
$931$	0	0
$932$	7.01726	0.229858
$933$	−38.9875	−1.27639
$934$	−30.4911	−0.997699
$935$	3.17124	0.103711
$936$	−14.7694	−0.482752
$937$	2.60567	0.0851234	0.0425617	−	0.999094i	$-0.486448\pi$
$937$	2.60567	0.0851234	0.0425617	+	0.999094i	$0.486448\pi$
$938$	0	0
$939$	9.83101	0.320823
$940$	−16.3632	−0.533708
$941$	0.683229	0.0222726	0.0111363	−	0.999938i	$-0.496455\pi$
$941$	0.683229	0.0222726	0.0111363	+	0.999938i	$0.496455\pi$
$942$	17.3797	0.566262
$943$	−5.67273	−0.184730
$944$	−11.8230	−0.384807
$945$	0	0
$946$	38.4130	1.24891
$947$	−27.3110	−0.887487	−0.443744	−	0.896154i	$-0.646350\pi$
$947$	−27.3110	−0.887487	−0.443744	+	0.896154i	$0.646350\pi$
$948$	−13.4686	−0.437441
$949$	78.2971	2.54163
$950$	−24.5958	−0.797992
$951$	−1.34975	−0.0437687
$952$	0	0
$953$	24.7059	0.800302	0.400151	−	0.916449i	$-0.368958\pi$
$953$	24.7059	0.800302	0.400151	+	0.916449i	$0.368958\pi$
$954$	−2.89355	−0.0936822
$955$	−59.9660	−1.94046
$956$	−4.21983	−0.136479
$957$	−6.81742	−0.220376
$958$	−2.97935	−0.0962583
$959$	0	0
$960$	28.1725	0.909265
$961$	−30.7067	−0.990539
$962$	27.8792	0.898860
$963$	−5.46906	−0.176238
$964$	11.2268	0.361590
$965$	−6.19998	−0.199584
$966$	0	0
$967$	28.1852	0.906375	0.453188	−	0.891415i	$-0.350287\pi$
$967$	28.1852	0.906375	0.453188	+	0.891415i	$0.350287\pi$
$968$	1.09485	0.0351899
$969$	4.15214	0.133386
$970$	36.7781	1.18087
$971$	−49.4938	−1.58833	−0.794166	−	0.607701i	$-0.792092\pi$
$971$	−49.4938	−1.58833	−0.794166	+	0.607701i	$0.792092\pi$
$972$	−7.81013	−0.250510
$973$	0	0
$974$	13.2818	0.425576
$975$	31.2514	1.00085
$976$	0.559783	0.0179182
$977$	−42.8017	−1.36935	−0.684675	−	0.728849i	$-0.740056\pi$
$977$	−42.8017	−1.36935	−0.684675	+	0.728849i	$0.740056\pi$
$978$	16.9689	0.542605
$979$	−7.81098	−0.249640
$980$	0	0
$981$	−2.48326	−0.0792845
$982$	17.7904	0.567715
$983$	21.2934	0.679154	0.339577	−	0.940578i	$-0.389716\pi$
$983$	21.2934	0.679154	0.339577	+	0.940578i	$0.389716\pi$
$984$	4.47433	0.142637
$985$	1.17986	0.0375934
$986$	0.432573	0.0137759
$987$	0	0
$988$	−59.7401	−1.90059
$989$	66.4859	2.11413
$990$	6.78608	0.215676
$991$	22.6584	0.719769	0.359885	−	0.932997i	$-0.382816\pi$
$991$	22.6584	0.719769	0.359885	+	0.932997i	$0.382816\pi$
$992$	−2.80787	−0.0891498
$993$	41.5986	1.32009
$994$	0	0
$995$	0.955994	0.0303070
$996$	12.5391	0.397317
$997$	−58.0474	−1.83838	−0.919190	−	0.393813i	$-0.871156\pi$
$997$	−58.0474	−1.83838	−0.919190	+	0.393813i	$0.871156\pi$
$998$	−13.0594	−0.413387
$999$	23.6589	0.748534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.s.1.6		17
7.2	even	3		287.2.e.d.165.12	✓	34
7.4	even	3		287.2.e.d.247.12	yes	34
7.6	odd	2		2009.2.a.r.1.6		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.12	✓	34	7.2	even	3
287.2.e.d.247.12	yes	34	7.4	even	3
2009.2.a.r.1.6		17	7.6	odd	2
2009.2.a.s.1.6		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)

\(f(q)\)	\(=\)	\(q-0.972044 q^{2} +1.50665 q^{3} -1.05513 q^{4} +2.83631 q^{5} -1.46453 q^{6} +2.96972 q^{8} -0.730003 q^{9} +O(q^{10})\)	\(q-0.972044 q^{2} +1.50665 q^{3} -1.05513 q^{4} +2.83631 q^{5} -1.46453 q^{6} +2.96972 q^{8} -0.730003 q^{9} -2.75702 q^{10} +3.37175 q^{11} -1.58971 q^{12} +6.81273 q^{13} +4.27332 q^{15} -0.776442 q^{16} +0.331605 q^{17} +0.709595 q^{18} +8.31072 q^{19} -2.99267 q^{20} -3.27749 q^{22} -5.67273 q^{23} +4.47433 q^{24} +3.04464 q^{25} -6.62228 q^{26} -5.61981 q^{27} -1.34200 q^{29} -4.15386 q^{30} +0.541567 q^{31} -5.18471 q^{32} +5.08004 q^{33} -0.322335 q^{34} +0.770248 q^{36} -4.20990 q^{37} -8.07839 q^{38} +10.2644 q^{39} +8.42304 q^{40} +1.00000 q^{41} -11.7203 q^{43} -3.55763 q^{44} -2.07051 q^{45} +5.51415 q^{46} +5.46775 q^{47} -1.16983 q^{48} -2.95952 q^{50} +0.499613 q^{51} -7.18832 q^{52} -4.07775 q^{53} +5.46271 q^{54} +9.56331 q^{55} +12.5214 q^{57} +1.30448 q^{58} +15.2272 q^{59} -4.50891 q^{60} -0.720959 q^{61} -0.526427 q^{62} +6.59265 q^{64} +19.3230 q^{65} -4.93803 q^{66} -4.26647 q^{67} -0.349886 q^{68} -8.54682 q^{69} -3.70138 q^{71} -2.16791 q^{72} +11.4928 q^{73} +4.09221 q^{74} +4.58721 q^{75} -8.76889 q^{76} -9.97746 q^{78} +8.47238 q^{79} -2.20223 q^{80} -6.27709 q^{81} -0.972044 q^{82} -7.88767 q^{83} +0.940534 q^{85} +11.3926 q^{86} -2.02193 q^{87} +10.0131 q^{88} -2.31660 q^{89} +2.01263 q^{90} +5.98547 q^{92} +0.815952 q^{93} -5.31490 q^{94} +23.5718 q^{95} -7.81154 q^{96} -13.3398 q^{97} -2.46139 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 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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