LMFDB - Embedded newform 2009.2.a.s.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$16.0419457661$
Analytic rank:	$0$
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			1.5
Root			$-1.66890$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.66890 q^{2} -0.213548 q^{3} +0.785231 q^{4} +1.00334 q^{5} +0.356391 q^{6} +2.02733 q^{8} -2.95440 q^{9} +O(q^{10})$	\(q-1.66890 q^{2} -0.213548 q^{3} +0.785231 q^{4} +1.00334 q^{5} +0.356391 q^{6} +2.02733 q^{8} -2.95440 q^{9} -1.67447 q^{10} -3.51567 q^{11} -0.167685 q^{12} -5.76131 q^{13} -0.214261 q^{15} -4.95387 q^{16} +4.86583 q^{17} +4.93060 q^{18} -3.94670 q^{19} +0.787850 q^{20} +5.86730 q^{22} +3.88735 q^{23} -0.432933 q^{24} -3.99332 q^{25} +9.61506 q^{26} +1.27155 q^{27} -5.00025 q^{29} +0.357580 q^{30} +3.40548 q^{31} +4.21287 q^{32} +0.750765 q^{33} -8.12060 q^{34} -2.31988 q^{36} +6.80132 q^{37} +6.58665 q^{38} +1.23032 q^{39} +2.03409 q^{40} +1.00000 q^{41} +1.87465 q^{43} -2.76061 q^{44} -2.96425 q^{45} -6.48761 q^{46} +5.91355 q^{47} +1.05789 q^{48} +6.66445 q^{50} -1.03909 q^{51} -4.52396 q^{52} +10.5343 q^{53} -2.12209 q^{54} -3.52739 q^{55} +0.842811 q^{57} +8.34492 q^{58} +2.78359 q^{59} -0.168244 q^{60} +3.20869 q^{61} -5.68341 q^{62} +2.87689 q^{64} -5.78053 q^{65} -1.25295 q^{66} +7.35906 q^{67} +3.82080 q^{68} -0.830138 q^{69} -12.7360 q^{71} -5.98954 q^{72} -12.2349 q^{73} -11.3507 q^{74} +0.852767 q^{75} -3.09907 q^{76} -2.05328 q^{78} -8.37815 q^{79} -4.97040 q^{80} +8.59165 q^{81} -1.66890 q^{82} -14.9762 q^{83} +4.88206 q^{85} -3.12860 q^{86} +1.06779 q^{87} -7.12742 q^{88} +5.58193 q^{89} +4.94704 q^{90} +3.05247 q^{92} -0.727234 q^{93} -9.86913 q^{94} -3.95986 q^{95} -0.899651 q^{96} +18.3180 q^{97} +10.3867 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.66890	−1.18009	−0.590046	−	0.807370i	$-0.700890\pi$
$2$	−1.66890	−1.18009	−0.590046	+	0.807370i	$0.700890\pi$
$3$	−0.213548	−0.123292	−0.0616461	−	0.998098i	$-0.519635\pi$
$3$	−0.213548	−0.123292	−0.0616461	+	0.998098i	$0.519635\pi$
$4$	0.785231	0.392616
$5$	1.00334	0.448705	0.224353	−	0.974508i	$-0.427973\pi$
$5$	1.00334	0.448705	0.224353	+	0.974508i	$0.427973\pi$
$6$	0.356391	0.145496
$7$	0	0
$7$	0	0
$8$	2.02733	0.716769
$9$	−2.95440	−0.984799
$10$	−1.67447	−0.529513
$11$	−3.51567	−1.06001	−0.530007	−	0.847993i	$-0.677811\pi$
$11$	−3.51567	−1.06001	−0.530007	+	0.847993i	$0.677811\pi$
$12$	−0.167685	−0.0484064
$13$	−5.76131	−1.59790	−0.798950	−	0.601397i	$-0.794611\pi$
$13$	−5.76131	−1.59790	−0.798950	+	0.601397i	$0.794611\pi$
$14$	0	0
$15$	−0.214261	−0.0553219
$16$	−4.95387	−1.23847
$17$	4.86583	1.18014	0.590069	−	0.807353i	$-0.299101\pi$
$17$	4.86583	1.18014	0.590069	+	0.807353i	$0.299101\pi$
$18$	4.93060	1.16215
$19$	−3.94670	−0.905434	−0.452717	−	0.891654i	$-0.649545\pi$
$19$	−3.94670	−0.905434	−0.452717	+	0.891654i	$0.649545\pi$
$20$	0.787850	0.176169
$21$	0	0
$22$	5.86730	1.25091
$23$	3.88735	0.810569	0.405285	−	0.914191i	$-0.367172\pi$
$23$	3.88735	0.810569	0.405285	+	0.914191i	$0.367172\pi$
$24$	−0.432933	−0.0883721
$25$	−3.99332	−0.798664
$26$	9.61506	1.88567
$27$	1.27155	0.244710
$28$	0	0
$29$	−5.00025	−0.928523	−0.464261	−	0.885698i	$-0.653680\pi$
$29$	−5.00025	−0.928523	−0.464261	+	0.885698i	$0.653680\pi$
$30$	0.357580	0.0652849
$31$	3.40548	0.611642	0.305821	−	0.952089i	$-0.401069\pi$
$31$	3.40548	0.611642	0.305821	+	0.952089i	$0.401069\pi$
$32$	4.21287	0.744737
$33$	0.750765	0.130691
$34$	−8.12060	−1.39267
$35$	0	0
$36$	−2.31988	−0.386647
$37$	6.80132	1.11813	0.559065	−	0.829124i	$-0.311160\pi$
$37$	6.80132	1.11813	0.559065	+	0.829124i	$0.311160\pi$
$38$	6.58665	1.06850
$39$	1.23032	0.197009
$40$	2.03409	0.321618
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	1.87465	0.285881	0.142940	−	0.989731i	$-0.454344\pi$
$43$	1.87465	0.285881	0.142940	+	0.989731i	$0.454344\pi$
$44$	−2.76061	−0.416178
$45$	−2.96425	−0.441885
$46$	−6.48761	−0.956546
$47$	5.91355	0.862580	0.431290	−	0.902213i	$-0.358059\pi$
$47$	5.91355	0.862580	0.431290	+	0.902213i	$0.358059\pi$
$48$	1.05789	0.152694
$49$	0	0
$50$	6.66445	0.942496
$51$	−1.03909	−0.145502
$52$	−4.52396	−0.627361
$53$	10.5343	1.44700	0.723498	−	0.690327i	$-0.242533\pi$
$53$	10.5343	1.44700	0.723498	+	0.690327i	$0.242533\pi$
$54$	−2.12209	−0.288780
$55$	−3.52739	−0.475634
$56$	0	0
$57$	0.842811	0.111633
$58$	8.34492	1.09574
$59$	2.78359	0.362393	0.181196	−	0.983447i	$-0.442003\pi$
$59$	2.78359	0.362393	0.181196	+	0.983447i	$0.442003\pi$
$60$	−0.168244	−0.0217202
$61$	3.20869	0.410831	0.205415	−	0.978675i	$-0.434146\pi$
$61$	3.20869	0.410831	0.205415	+	0.978675i	$0.434146\pi$
$62$	−5.68341	−0.721793
$63$	0	0
$64$	2.87689	0.359611
$65$	−5.78053	−0.716986
$66$	−1.25295	−0.154228
$67$	7.35906	0.899052	0.449526	−	0.893267i	$-0.351593\pi$
$67$	7.35906	0.899052	0.449526	+	0.893267i	$0.351593\pi$
$68$	3.82080	0.463341
$69$	−0.830138	−0.0999369
$70$	0	0
$71$	−12.7360	−1.51149	−0.755745	−	0.654866i	$-0.772725\pi$
$71$	−12.7360	−1.51149	−0.755745	+	0.654866i	$0.772725\pi$
$72$	−5.98954	−0.705874
$73$	−12.2349	−1.43198	−0.715992	−	0.698109i	$-0.754025\pi$
$73$	−12.2349	−1.43198	−0.715992	+	0.698109i	$0.754025\pi$
$74$	−11.3507	−1.31950
$75$	0.852767	0.0984690
$76$	−3.09907	−0.355488
$77$	0	0
$78$	−2.05328	−0.232488
$79$	−8.37815	−0.942615	−0.471308	−	0.881969i	$-0.656218\pi$
$79$	−8.37815	−0.942615	−0.471308	+	0.881969i	$0.656218\pi$
$80$	−4.97040	−0.555707
$81$	8.59165	0.954628
$82$	−1.66890	−0.184299
$83$	−14.9762	−1.64385	−0.821923	−	0.569599i	$-0.807099\pi$
$83$	−14.9762	−1.64385	−0.821923	+	0.569599i	$0.807099\pi$
$84$	0	0
$85$	4.88206	0.529534
$86$	−3.12860	−0.337365
$87$	1.06779	0.114480
$88$	−7.12742	−0.759785
$89$	5.58193	0.591683	0.295842	−	0.955237i	$-0.404400\pi$
$89$	5.58193	0.591683	0.295842	+	0.955237i	$0.404400\pi$
$90$	4.94704	0.521464
$91$	0	0
$92$	3.05247	0.318242
$93$	−0.727234	−0.0754107
$94$	−9.86913	−1.01792
$95$	−3.95986	−0.406273
$96$	−0.899651	−0.0918203
$97$	18.3180	1.85991	0.929957	−	0.367668i	$-0.119844\pi$
$97$	18.3180	1.85991	0.929957	+	0.367668i	$0.119844\pi$
$98$	0	0
$99$	10.3867	1.04390
$100$	−3.13568	−0.313568
$101$	−3.99630	−0.397647	−0.198824	−	0.980035i	$-0.563712\pi$
$101$	−3.99630	−0.397647	−0.198824	+	0.980035i	$0.563712\pi$
$102$	1.73414	0.171705
$103$	−2.96969	−0.292612	−0.146306	−	0.989239i	$-0.546738\pi$
$103$	−2.96969	−0.292612	−0.146306	+	0.989239i	$0.546738\pi$
$104$	−11.6801	−1.14533
$105$	0	0
$106$	−17.5807	−1.70759
$107$	11.7066	1.13172	0.565861	−	0.824501i	$-0.308544\pi$
$107$	11.7066	1.13172	0.565861	+	0.824501i	$0.308544\pi$
$108$	0.998462	0.0960771
$109$	14.5578	1.39438	0.697191	−	0.716886i	$-0.254433\pi$
$109$	14.5578	1.39438	0.697191	+	0.716886i	$0.254433\pi$
$110$	5.88687	0.561291
$111$	−1.45241	−0.137857
$112$	0	0
$113$	10.1579	0.955576	0.477788	−	0.878475i	$-0.341439\pi$
$113$	10.1579	0.955576	0.477788	+	0.878475i	$0.341439\pi$
$114$	−1.40657	−0.131737
$115$	3.90032	0.363707
$116$	−3.92635	−0.364553
$117$	17.0212	1.57361
$118$	−4.64554	−0.427657
$119$	0	0
$120$	−0.434377	−0.0396530
$121$	1.35992	0.123629
$122$	−5.35498	−0.484818
$123$	−0.213548	−0.0192550
$124$	2.67409	0.240140
$125$	−9.02332	−0.807070
$126$	0	0
$127$	12.0850	1.07237	0.536186	−	0.844100i	$-0.319865\pi$
$127$	12.0850	1.07237	0.536186	+	0.844100i	$0.319865\pi$
$128$	−13.2270	−1.16911
$129$	−0.400327	−0.0352469
$130$	9.64713	0.846109
$131$	−8.60961	−0.752225	−0.376113	−	0.926574i	$-0.622739\pi$
$131$	−8.60961	−0.752225	−0.376113	+	0.926574i	$0.622739\pi$
$132$	0.589524	0.0513115
$133$	0	0
$134$	−12.2815	−1.06096
$135$	1.27579	0.109803
$136$	9.86465	0.845886
$137$	−0.172461	−0.0147344	−0.00736718	−	0.999973i	$-0.502345\pi$
$137$	−0.172461	−0.0147344	−0.00736718	+	0.999973i	$0.502345\pi$
$138$	1.38542	0.117935
$139$	8.79715	0.746164	0.373082	−	0.927798i	$-0.378301\pi$
$139$	8.79715	0.746164	0.373082	+	0.927798i	$0.378301\pi$
$140$	0	0
$141$	−1.26283	−0.106349
$142$	21.2552	1.78370
$143$	20.2549	1.69380
$144$	14.6357	1.21964
$145$	−5.01693	−0.416633
$146$	20.4188	1.68987
$147$	0	0
$148$	5.34061	0.438995
$149$	0.687011	0.0562822	0.0281411	−	0.999604i	$-0.491041\pi$
$149$	0.687011	0.0562822	0.0281411	+	0.999604i	$0.491041\pi$
$150$	−1.42318	−0.116202
$151$	8.90640	0.724792	0.362396	−	0.932024i	$-0.381959\pi$
$151$	8.90640	0.724792	0.362396	+	0.932024i	$0.381959\pi$
$152$	−8.00125	−0.648987
$153$	−14.3756	−1.16220
$154$	0	0
$155$	3.41684	0.274447
$156$	0.966085	0.0773487
$157$	−15.9049	−1.26935	−0.634676	−	0.772779i	$-0.718866\pi$
$157$	−15.9049	−1.26935	−0.634676	+	0.772779i	$0.718866\pi$
$158$	13.9823	1.11237
$159$	−2.24958	−0.178403
$160$	4.22692	0.334167
$161$	0	0
$162$	−14.3386	−1.12655
$163$	20.2552	1.58651	0.793254	−	0.608890i	$-0.208385\pi$
$163$	20.2552	1.58651	0.793254	+	0.608890i	$0.208385\pi$
$164$	0.785231	0.0613163
$165$	0.753270	0.0586420
$166$	24.9937	1.93989
$167$	16.9622	1.31258	0.656288	−	0.754511i	$-0.272126\pi$
$167$	16.9622	1.31258	0.656288	+	0.754511i	$0.272126\pi$
$168$	0	0
$169$	20.1927	1.55329
$170$	−8.14768	−0.624899
$171$	11.6601	0.891671
$172$	1.47203	0.112241
$173$	−13.8683	−1.05439	−0.527195	−	0.849745i	$-0.676756\pi$
$173$	−13.8683	−1.05439	−0.527195	+	0.849745i	$0.676756\pi$
$174$	−1.78204	−0.135096
$175$	0	0
$176$	17.4162	1.31279
$177$	−0.594431	−0.0446802
$178$	−9.31568	−0.698240
$179$	12.3020	0.919495	0.459747	−	0.888050i	$-0.347940\pi$
$179$	12.3020	0.919495	0.459747	+	0.888050i	$0.347940\pi$
$180$	−2.32762	−0.173491
$181$	−1.79830	−0.133666	−0.0668332	−	0.997764i	$-0.521290\pi$
$181$	−1.79830	−0.133666	−0.0668332	+	0.997764i	$0.521290\pi$
$182$	0	0
$183$	−0.685210	−0.0506522
$184$	7.88095	0.580991
$185$	6.82401	0.501711
$186$	1.21368	0.0889915
$187$	−17.1067	−1.25096
$188$	4.64351	0.338662
$189$	0	0
$190$	6.60862	0.479439
$191$	−2.16556	−0.156694	−0.0783472	−	0.996926i	$-0.524964\pi$
$191$	−2.16556	−0.156694	−0.0783472	+	0.996926i	$0.524964\pi$
$192$	−0.614355	−0.0443372
$193$	7.03513	0.506400	0.253200	−	0.967414i	$-0.418517\pi$
$193$	7.03513	0.506400	0.253200	+	0.967414i	$0.418517\pi$
$194$	−30.5710	−2.19487
$195$	1.23442	0.0883988
$196$	0	0
$197$	−9.47409	−0.675001	−0.337500	−	0.941325i	$-0.609581\pi$
$197$	−9.47409	−0.675001	−0.337500	+	0.941325i	$0.609581\pi$
$198$	−17.3343	−1.23190
$199$	3.55753	0.252187	0.126093	−	0.992018i	$-0.459756\pi$
$199$	3.55753	0.252187	0.126093	+	0.992018i	$0.459756\pi$
$200$	−8.09577	−0.572457
$201$	−1.57151	−0.110846
$202$	6.66944	0.469260
$203$	0	0
$204$	−0.815927	−0.0571263
$205$	1.00334	0.0700760
$206$	4.95612	0.345309
$207$	−11.4848	−0.798248
$208$	28.5408	1.97895
$209$	13.8753	0.959773
$210$	0	0
$211$	21.6699	1.49182	0.745908	−	0.666049i	$-0.232016\pi$
$211$	21.6699	1.49182	0.745908	+	0.666049i	$0.232016\pi$
$212$	8.27185	0.568113
$213$	2.71976	0.186355
$214$	−19.5372	−1.33554
$215$	1.88090	0.128276
$216$	2.57785	0.175401
$217$	0	0
$218$	−24.2955	−1.64550
$219$	2.61274	0.176552
$220$	−2.76982	−0.186741
$221$	−28.0336	−1.88574
$222$	2.42393	0.162684
$223$	8.57235	0.574047	0.287023	−	0.957924i	$-0.407334\pi$
$223$	8.57235	0.574047	0.287023	+	0.957924i	$0.407334\pi$
$224$	0	0
$225$	11.7978	0.786523
$226$	−16.9526	−1.12767
$227$	−12.5669	−0.834092	−0.417046	−	0.908885i	$-0.636935\pi$
$227$	−12.5669	−0.834092	−0.417046	+	0.908885i	$0.636935\pi$
$228$	0.661801	0.0438289
$229$	19.8200	1.30974	0.654870	−	0.755742i	$-0.272724\pi$
$229$	19.8200	1.30974	0.654870	+	0.755742i	$0.272724\pi$
$230$	−6.50925	−0.429207
$231$	0	0
$232$	−10.1371	−0.665536
$233$	24.6603	1.61555	0.807776	−	0.589490i	$-0.200671\pi$
$233$	24.6603	1.61555	0.807776	+	0.589490i	$0.200671\pi$
$234$	−28.4067	−1.85700
$235$	5.93328	0.387044
$236$	2.18576	0.142281
$237$	1.78914	0.116217
$238$	0	0
$239$	22.9924	1.48726	0.743629	−	0.668593i	$-0.233103\pi$
$239$	22.9924	1.48726	0.743629	+	0.668593i	$0.233103\pi$
$240$	1.06142	0.0685144
$241$	−17.1819	−1.10679	−0.553393	−	0.832920i	$-0.686667\pi$
$241$	−17.1819	−1.10679	−0.553393	+	0.832920i	$0.686667\pi$
$242$	−2.26957	−0.145894
$243$	−5.64939	−0.362409
$244$	2.51956	0.161298
$245$	0	0
$246$	0.356391	0.0227227
$247$	22.7381	1.44679
$248$	6.90403	0.438406
$249$	3.19813	0.202673
$250$	15.0590	0.952416
$251$	23.4755	1.48176	0.740879	−	0.671638i	$-0.234409\pi$
$251$	23.4755	1.48176	0.740879	+	0.671638i	$0.234409\pi$
$252$	0	0
$253$	−13.6666	−0.859215
$254$	−20.1687	−1.26550
$255$	−1.04256	−0.0652875
$256$	16.3207	1.02005
$257$	−13.9131	−0.867878	−0.433939	−	0.900942i	$-0.642877\pi$
$257$	−13.9131	−0.867878	−0.433939	+	0.900942i	$0.642877\pi$
$258$	0.668107	0.0415945
$259$	0	0
$260$	−4.53905	−0.281500
$261$	14.7727	0.914408
$262$	14.3686	0.887695
$263$	21.3325	1.31542	0.657709	−	0.753272i	$-0.271526\pi$
$263$	21.3325	1.31542	0.657709	+	0.753272i	$0.271526\pi$
$264$	1.52205	0.0936756
$265$	10.5694	0.649275
$266$	0	0
$267$	−1.19201	−0.0729499
$268$	5.77856	0.352982
$269$	−27.2721	−1.66281	−0.831406	−	0.555666i	$-0.812463\pi$
$269$	−27.2721	−1.66281	−0.831406	+	0.555666i	$0.812463\pi$
$270$	−2.12917	−0.129577
$271$	−24.3261	−1.47771	−0.738854	−	0.673866i	$-0.764633\pi$
$271$	−24.3261	−1.47771	−0.738854	+	0.673866i	$0.764633\pi$
$272$	−24.1047	−1.46156
$273$	0	0
$274$	0.287821	0.0173879
$275$	14.0392	0.846594
$276$	−0.651850	−0.0392368
$277$	−1.22146	−0.0733906	−0.0366953	−	0.999327i	$-0.511683\pi$
$277$	−1.22146	−0.0733906	−0.0366953	+	0.999327i	$0.511683\pi$
$278$	−14.6816	−0.880542
$279$	−10.0611	−0.602344
$280$	0	0
$281$	−16.7952	−1.00192	−0.500960	−	0.865470i	$-0.667020\pi$
$281$	−16.7952	−1.00192	−0.500960	+	0.865470i	$0.667020\pi$
$282$	2.10754	0.125502
$283$	2.73856	0.162791	0.0813953	−	0.996682i	$-0.474062\pi$
$283$	2.73856	0.162791	0.0813953	+	0.996682i	$0.474062\pi$
$284$	−10.0007	−0.593434
$285$	0.845622	0.0500903
$286$	−33.8034	−1.99883
$287$	0	0
$288$	−12.4465	−0.733416
$289$	6.67634	0.392726
$290$	8.37276	0.491665
$291$	−3.91179	−0.229313
$292$	−9.60720	−0.562219
$293$	7.34300	0.428983	0.214491	−	0.976726i	$-0.431191\pi$
$293$	7.34300	0.428983	0.214491	+	0.976726i	$0.431191\pi$
$294$	0	0
$295$	2.79288	0.162608
$296$	13.7885	0.801441
$297$	−4.47035	−0.259396
$298$	−1.14655	−0.0664181
$299$	−22.3963	−1.29521
$300$	0.669619	0.0386605
$301$	0	0
$302$	−14.8639	−0.855321
$303$	0.853404	0.0490268
$304$	19.5514	1.12135
$305$	3.21939	0.184342
$306$	23.9915	1.37150
$307$	−30.3452	−1.73189	−0.865945	−	0.500139i	$-0.833282\pi$
$307$	−30.3452	−1.73189	−0.865945	+	0.500139i	$0.833282\pi$
$308$	0	0
$309$	0.634173	0.0360768
$310$	−5.70236	−0.323873
$311$	6.92286	0.392560	0.196280	−	0.980548i	$-0.437114\pi$
$311$	6.92286	0.392560	0.196280	+	0.980548i	$0.437114\pi$
$312$	2.49426	0.141210
$313$	30.7555	1.73840	0.869201	−	0.494458i	$-0.164634\pi$
$313$	30.7555	1.73840	0.869201	+	0.494458i	$0.164634\pi$
$314$	26.5438	1.49795
$315$	0	0
$316$	−6.57878	−0.370085
$317$	2.90604	0.163219	0.0816096	−	0.996664i	$-0.473994\pi$
$317$	2.90604	0.163219	0.0816096	+	0.996664i	$0.473994\pi$
$318$	3.75433	0.210532
$319$	17.5792	0.984247
$320$	2.88648	0.161359
$321$	−2.49993	−0.139533
$322$	0	0
$323$	−19.2040	−1.06854
$324$	6.74643	0.374802
$325$	23.0067	1.27618
$326$	−33.8039	−1.87223
$327$	−3.10879	−0.171916
$328$	2.02733	0.111941
$329$	0	0
$330$	−1.25713	−0.0692029
$331$	4.65475	0.255848	0.127924	−	0.991784i	$-0.459169\pi$
$331$	4.65475	0.255848	0.127924	+	0.991784i	$0.459169\pi$
$332$	−11.7597	−0.645400
$333$	−20.0938	−1.10113
$334$	−28.3083	−1.54896
$335$	7.38360	0.403409
$336$	0	0
$337$	23.8266	1.29792	0.648960	−	0.760823i	$-0.275204\pi$
$337$	23.8266	1.29792	0.648960	+	0.760823i	$0.275204\pi$
$338$	−33.6996	−1.83302
$339$	−2.16921	−0.117815
$340$	3.83355	0.207903
$341$	−11.9725	−0.648349
$342$	−19.4596	−1.05225
$343$	0	0
$344$	3.80052	0.204910
$345$	−0.832907	−0.0448422
$346$	23.1449	1.24428
$347$	−17.1799	−0.922264	−0.461132	−	0.887331i	$-0.652557\pi$
$347$	−17.1799	−0.922264	−0.461132	+	0.887331i	$0.652557\pi$
$348$	0.838466	0.0449465
$349$	10.7991	0.578063	0.289031	−	0.957320i	$-0.406667\pi$
$349$	10.7991	0.578063	0.289031	+	0.957320i	$0.406667\pi$
$350$	0	0
$351$	−7.32581	−0.391023
$352$	−14.8110	−0.789431
$353$	4.21898	0.224553	0.112277	−	0.993677i	$-0.464186\pi$
$353$	4.21898	0.224553	0.112277	+	0.993677i	$0.464186\pi$
$354$	0.992047	0.0527267
$355$	−12.7785	−0.678213
$356$	4.38310	0.232304
$357$	0	0
$358$	−20.5308	−1.08509
$359$	1.95478	0.103169	0.0515846	−	0.998669i	$-0.483573\pi$
$359$	1.95478	0.103169	0.0515846	+	0.998669i	$0.483573\pi$
$360$	−6.00951	−0.316729
$361$	−3.42359	−0.180189
$362$	3.00118	0.157739
$363$	−0.290409	−0.0152425
$364$	0	0
$365$	−12.2757	−0.642538
$366$	1.14355	0.0597742
$367$	2.14267	0.111847	0.0559233	−	0.998435i	$-0.482190\pi$
$367$	2.14267	0.111847	0.0559233	+	0.998435i	$0.482190\pi$
$368$	−19.2575	−1.00386
$369$	−2.95440	−0.153800
$370$	−11.3886	−0.592065
$371$	0	0
$372$	−0.571047	−0.0296074
$373$	−8.98831	−0.465397	−0.232698	−	0.972549i	$-0.574756\pi$
$373$	−8.98831	−0.465397	−0.232698	+	0.972549i	$0.574756\pi$
$374$	28.5493	1.47625
$375$	1.92691	0.0995054
$376$	11.9887	0.618271
$377$	28.8080	1.48369
$378$	0	0
$379$	25.3654	1.30293	0.651467	−	0.758677i	$-0.274154\pi$
$379$	25.3654	1.30293	0.651467	+	0.758677i	$0.274154\pi$
$380$	−3.10941	−0.159509
$381$	−2.58074	−0.132215
$382$	3.61411	0.184914
$383$	24.5582	1.25486	0.627432	−	0.778671i	$-0.284106\pi$
$383$	24.5582	1.25486	0.627432	+	0.778671i	$0.284106\pi$
$384$	2.82460	0.144142
$385$	0	0
$386$	−11.7409	−0.597598
$387$	−5.53845	−0.281535
$388$	14.3839	0.730231
$389$	−23.3272	−1.18274	−0.591368	−	0.806402i	$-0.701412\pi$
$389$	−23.3272	−1.18274	−0.591368	+	0.806402i	$0.701412\pi$
$390$	−2.06013	−0.104319
$391$	18.9152	0.956584
$392$	0	0
$393$	1.83857	0.0927435
$394$	15.8113	0.796562
$395$	−8.40609	−0.422956
$396$	8.15594	0.409852
$397$	−17.8817	−0.897458	−0.448729	−	0.893668i	$-0.648123\pi$
$397$	−17.8817	−0.897458	−0.448729	+	0.893668i	$0.648123\pi$
$398$	−5.93717	−0.297604
$399$	0	0
$400$	19.7824	0.989120
$401$	−21.8846	−1.09287	−0.546433	−	0.837503i	$-0.684015\pi$
$401$	−21.8846	−1.09287	−0.546433	+	0.837503i	$0.684015\pi$
$402$	2.62270	0.130809
$403$	−19.6200	−0.977343
$404$	−3.13802	−0.156122
$405$	8.62031	0.428347
$406$	0	0
$407$	−23.9112	−1.18523
$408$	−2.10658	−0.104291
$409$	17.5006	0.865351	0.432675	−	0.901550i	$-0.357570\pi$
$409$	17.5006	0.865351	0.432675	+	0.901550i	$0.357570\pi$
$410$	−1.67447	−0.0826961
$411$	0.0368288	0.00181663
$412$	−2.33190	−0.114884
$413$	0	0
$414$	19.1670	0.942006
$415$	−15.0261	−0.737602
$416$	−24.2716	−1.19002
$417$	−1.87862	−0.0919962
$418$	−23.1565	−1.13262
$419$	7.23185	0.353299	0.176649	−	0.984274i	$-0.443474\pi$
$419$	7.23185	0.353299	0.176649	+	0.984274i	$0.443474\pi$
$420$	0	0
$421$	3.50247	0.170700	0.0853500	−	0.996351i	$-0.472799\pi$
$421$	3.50247	0.170700	0.0853500	+	0.996351i	$0.472799\pi$
$422$	−36.1649	−1.76048
$423$	−17.4710	−0.849468
$424$	21.3565	1.03716
$425$	−19.4308	−0.942533
$426$	−4.53901	−0.219916
$427$	0	0
$428$	9.19241	0.444332
$429$	−4.32539	−0.208832
$430$	−3.13903	−0.151378
$431$	11.0528	0.532395	0.266197	−	0.963919i	$-0.414233\pi$
$431$	11.0528	0.532395	0.266197	+	0.963919i	$0.414233\pi$
$432$	−6.29911	−0.303066
$433$	−32.5407	−1.56381	−0.781904	−	0.623399i	$-0.785751\pi$
$433$	−32.5407	−1.56381	−0.781904	+	0.623399i	$0.785751\pi$
$434$	0	0
$435$	1.07136	0.0513676
$436$	11.4312	0.547456
$437$	−15.3422	−0.733917
$438$	−4.36040	−0.208348
$439$	17.5965	0.839837	0.419918	−	0.907562i	$-0.362059\pi$
$439$	17.5965	0.839837	0.419918	+	0.907562i	$0.362059\pi$
$440$	−7.15119	−0.340920
$441$	0	0
$442$	46.7853	2.22535
$443$	−23.5571	−1.11923	−0.559615	−	0.828753i	$-0.689051\pi$
$443$	−23.5571	−1.11923	−0.559615	+	0.828753i	$0.689051\pi$
$444$	−1.14048	−0.0541247
$445$	5.60055	0.265491
$446$	−14.3064	−0.677428
$447$	−0.146710	−0.00693915
$448$	0	0
$449$	−8.18594	−0.386318	−0.193159	−	0.981167i	$-0.561873\pi$
$449$	−8.18594	−0.386318	−0.193159	+	0.981167i	$0.561873\pi$
$450$	−19.6894	−0.928169
$451$	−3.51567	−0.165546
$452$	7.97631	0.375174
$453$	−1.90195	−0.0893613
$454$	20.9729	0.984305
$455$	0	0
$456$	1.70865	0.0800151
$457$	−9.87038	−0.461717	−0.230859	−	0.972987i	$-0.574153\pi$
$457$	−9.87038	−0.461717	−0.230859	+	0.972987i	$0.574153\pi$
$458$	−33.0775	−1.54561
$459$	6.18716	0.288792
$460$	3.06265	0.142797
$461$	−6.23960	−0.290607	−0.145304	−	0.989387i	$-0.546416\pi$
$461$	−6.23960	−0.290607	−0.145304	+	0.989387i	$0.546416\pi$
$462$	0	0
$463$	−31.4838	−1.46317	−0.731587	−	0.681748i	$-0.761220\pi$
$463$	−31.4838	−1.46317	−0.731587	+	0.681748i	$0.761220\pi$
$464$	24.7706	1.14995
$465$	−0.729660	−0.0338372
$466$	−41.1556	−1.90650
$467$	0.420564	0.0194614	0.00973070	−	0.999953i	$-0.496903\pi$
$467$	0.420564	0.0194614	0.00973070	+	0.999953i	$0.496903\pi$
$468$	13.3656	0.617824
$469$	0	0
$470$	−9.90205	−0.456748
$471$	3.39647	0.156501
$472$	5.64326	0.259752
$473$	−6.59063	−0.303037
$474$	−2.98590	−0.137147
$475$	15.7604	0.723137
$476$	0	0
$477$	−31.1225	−1.42500
$478$	−38.3721	−1.75510
$479$	27.9255	1.27595	0.637975	−	0.770057i	$-0.279773\pi$
$479$	27.9255	1.27595	0.637975	+	0.770057i	$0.279773\pi$
$480$	−0.902652	−0.0412002
$481$	−39.1845	−1.78666
$482$	28.6749	1.30611
$483$	0	0
$484$	1.06785	0.0485388
$485$	18.3791	0.834554
$486$	9.42827	0.427675
$487$	18.3288	0.830558	0.415279	−	0.909694i	$-0.363684\pi$
$487$	18.3288	0.830558	0.415279	+	0.909694i	$0.363684\pi$
$488$	6.50507	0.294471
$489$	−4.32546	−0.195604
$490$	0	0
$491$	−8.43902	−0.380848	−0.190424	−	0.981702i	$-0.560986\pi$
$491$	−8.43902	−0.380848	−0.190424	+	0.981702i	$0.560986\pi$
$492$	−0.167685	−0.00755982
$493$	−24.3304	−1.09579
$494$	−37.9477	−1.70735
$495$	10.4213	0.468404
$496$	−16.8703	−0.757499
$497$	0	0
$498$	−5.33737	−0.239173
$499$	6.32026	0.282934	0.141467	−	0.989943i	$-0.454818\pi$
$499$	6.32026	0.282934	0.141467	+	0.989943i	$0.454818\pi$
$500$	−7.08539	−0.316868
$501$	−3.62225	−0.161830
$502$	−39.1782	−1.74861
$503$	−25.8395	−1.15213	−0.576063	−	0.817405i	$-0.695412\pi$
$503$	−25.8395	−1.15213	−0.576063	+	0.817405i	$0.695412\pi$
$504$	0	0
$505$	−4.00963	−0.178426
$506$	22.8083	1.01395
$507$	−4.31212	−0.191508
$508$	9.48953	0.421030
$509$	7.06142	0.312992	0.156496	−	0.987679i	$-0.449980\pi$
$509$	7.06142	0.312992	0.156496	+	0.987679i	$0.449980\pi$
$510$	1.73992	0.0770452
$511$	0	0
$512$	−0.783754	−0.0346373
$513$	−5.01843	−0.221569
$514$	23.2197	1.02418
$515$	−2.97960	−0.131297
$516$	−0.314350	−0.0138385
$517$	−20.7901	−0.914347
$518$	0	0
$519$	2.96156	0.129998
$520$	−11.7190	−0.513914
$521$	19.5315	0.855689	0.427845	−	0.903852i	$-0.359273\pi$
$521$	19.5315	0.855689	0.427845	+	0.903852i	$0.359273\pi$
$522$	−24.6542	−1.07909
$523$	5.74833	0.251357	0.125679	−	0.992071i	$-0.459889\pi$
$523$	5.74833	0.251357	0.125679	+	0.992071i	$0.459889\pi$
$524$	−6.76054	−0.295335
$525$	0	0
$526$	−35.6018	−1.55231
$527$	16.5705	0.721822
$528$	−3.71920	−0.161857
$529$	−7.88847	−0.342977
$530$	−17.6393	−0.766204
$531$	−8.22383	−0.356884
$532$	0	0
$533$	−5.76131	−0.249550
$534$	1.98935	0.0860876
$535$	11.7457	0.507810
$536$	14.9192	0.644413
$537$	−2.62707	−0.113367
$538$	45.5145	1.96227
$539$	0	0
$540$	1.00179	0.0431103
$541$	−35.6312	−1.53191	−0.765953	−	0.642897i	$-0.777732\pi$
$541$	−35.6312	−1.53191	−0.765953	+	0.642897i	$0.777732\pi$
$542$	40.5979	1.74383
$543$	0.384024	0.0164800
$544$	20.4991	0.878892
$545$	14.6063	0.625667
$546$	0	0
$547$	3.65967	0.156476	0.0782381	−	0.996935i	$-0.475071\pi$
$547$	3.65967	0.156476	0.0782381	+	0.996935i	$0.475071\pi$
$548$	−0.135422	−0.00578494
$549$	−9.47974	−0.404585
$550$	−23.4300	−0.999059
$551$	19.7345	0.840716
$552$	−1.68296	−0.0716317
$553$	0	0
$554$	2.03850	0.0866076
$555$	−1.45726	−0.0618571
$556$	6.90779	0.292956
$557$	−28.4879	−1.20707	−0.603536	−	0.797336i	$-0.706242\pi$
$557$	−28.4879	−1.20707	−0.603536	+	0.797336i	$0.706242\pi$
$558$	16.7910	0.710821
$559$	−10.8004	−0.456809
$560$	0	0
$561$	3.65310	0.154234
$562$	28.0296	1.18236
$563$	3.96557	0.167129	0.0835644	−	0.996502i	$-0.473370\pi$
$563$	3.96557	0.167129	0.0835644	+	0.996502i	$0.473370\pi$
$564$	−0.991613	−0.0417544
$565$	10.1918	0.428772
$566$	−4.57039	−0.192108
$567$	0	0
$568$	−25.8201	−1.08339
$569$	9.25968	0.388186	0.194093	−	0.980983i	$-0.437824\pi$
$569$	9.25968	0.388186	0.194093	+	0.980983i	$0.437824\pi$
$570$	−1.41126	−0.0591112
$571$	19.4629	0.814496	0.407248	−	0.913318i	$-0.366488\pi$
$571$	19.4629	0.814496	0.407248	+	0.913318i	$0.366488\pi$
$572$	15.9047	0.665011
$573$	0.462452	0.0193192
$574$	0	0
$575$	−15.5234	−0.647372
$576$	−8.49947	−0.354144
$577$	35.2059	1.46564	0.732820	−	0.680422i	$-0.238204\pi$
$577$	35.2059	1.46564	0.732820	+	0.680422i	$0.238204\pi$
$578$	−11.1421	−0.463452
$579$	−1.50234	−0.0624352
$580$	−3.93945	−0.163577
$581$	0	0
$582$	6.52839	0.270610
$583$	−37.0351	−1.53384
$584$	−24.8041	−1.02640
$585$	17.0780	0.706087
$586$	−12.2547	−0.506239
$587$	−11.7669	−0.485673	−0.242836	−	0.970067i	$-0.578078\pi$
$587$	−11.7669	−0.485673	−0.242836	+	0.970067i	$0.578078\pi$
$588$	0	0
$589$	−13.4404	−0.553802
$590$	−4.66104	−0.191892
$591$	2.02318	0.0832223
$592$	−33.6929	−1.38477
$593$	38.9481	1.59941	0.799703	−	0.600395i	$-0.204990\pi$
$593$	38.9481	1.59941	0.799703	+	0.600395i	$0.204990\pi$
$594$	7.46058	0.306111
$595$	0	0
$596$	0.539463	0.0220973
$597$	−0.759706	−0.0310927
$598$	37.3771	1.52847
$599$	−43.9150	−1.79432	−0.897158	−	0.441709i	$-0.854372\pi$
$599$	−43.9150	−1.79432	−0.897158	+	0.441709i	$0.854372\pi$
$600$	1.72884	0.0705795
$601$	−28.3881	−1.15798	−0.578988	−	0.815336i	$-0.696552\pi$
$601$	−28.3881	−1.15798	−0.578988	+	0.815336i	$0.696552\pi$
$602$	0	0
$603$	−21.7416	−0.885385
$604$	6.99358	0.284565
$605$	1.36446	0.0554731
$606$	−1.42425	−0.0578561
$607$	−7.00170	−0.284190	−0.142095	−	0.989853i	$-0.545384\pi$
$607$	−7.00170	−0.284190	−0.142095	+	0.989853i	$0.545384\pi$
$608$	−16.6269	−0.674310
$609$	0	0
$610$	−5.37285	−0.217540
$611$	−34.0698	−1.37832
$612$	−11.2882	−0.456297
$613$	10.0887	0.407479	0.203740	−	0.979025i	$-0.434690\pi$
$613$	10.0887	0.407479	0.203740	+	0.979025i	$0.434690\pi$
$614$	50.6431	2.04379
$615$	−0.214261	−0.00863983
$616$	0	0
$617$	−18.3132	−0.737262	−0.368631	−	0.929576i	$-0.620173\pi$
$617$	−18.3132	−0.737262	−0.368631	+	0.929576i	$0.620173\pi$
$618$	−1.05837	−0.0425740
$619$	12.6255	0.507461	0.253730	−	0.967275i	$-0.418342\pi$
$619$	12.6255	0.507461	0.253730	+	0.967275i	$0.418342\pi$
$620$	2.68301	0.107752
$621$	4.94297	0.198355
$622$	−11.5536	−0.463256
$623$	0	0
$624$	−6.09484	−0.243989
$625$	10.9132	0.436527
$626$	−51.3279	−2.05147
$627$	−2.96304	−0.118333
$628$	−12.4890	−0.498367
$629$	33.0941	1.31955
$630$	0	0
$631$	18.6742	0.743409	0.371705	−	0.928351i	$-0.378773\pi$
$631$	18.6742	0.743409	0.371705	+	0.928351i	$0.378773\pi$
$632$	−16.9853	−0.675637
$633$	−4.62757	−0.183929
$634$	−4.84989	−0.192614
$635$	12.1253	0.481179
$636$	−1.76644	−0.0700439
$637$	0	0
$638$	−29.3380	−1.16150
$639$	37.6273	1.48851
$640$	−13.2711	−0.524586
$641$	1.15436	0.0455946	0.0227973	−	0.999740i	$-0.492743\pi$
$641$	1.15436	0.0455946	0.0227973	+	0.999740i	$0.492743\pi$
$642$	4.17214	0.164661
$643$	−25.1954	−0.993611	−0.496806	−	0.867862i	$-0.665494\pi$
$643$	−25.1954	−0.993611	−0.496806	+	0.867862i	$0.665494\pi$
$644$	0	0
$645$	−0.401663	−0.0158155
$646$	32.0495	1.26097
$647$	42.5339	1.67218	0.836090	−	0.548593i	$-0.184836\pi$
$647$	42.5339	1.67218	0.836090	+	0.548593i	$0.184836\pi$
$648$	17.4181	0.684248
$649$	−9.78618	−0.384141
$650$	−38.3960	−1.50601
$651$	0	0
$652$	15.9050	0.622888
$653$	−1.09120	−0.0427019	−0.0213509	−	0.999772i	$-0.506797\pi$
$653$	−1.09120	−0.0427019	−0.0213509	+	0.999772i	$0.506797\pi$
$654$	5.18826	0.202877
$655$	−8.63833	−0.337527
$656$	−4.95387	−0.193416
$657$	36.1467	1.41022
$658$	0	0
$659$	23.5037	0.915573	0.457786	−	0.889062i	$-0.348642\pi$
$659$	23.5037	0.915573	0.457786	+	0.889062i	$0.348642\pi$
$660$	0.591491	0.0230237
$661$	16.6529	0.647722	0.323861	−	0.946105i	$-0.395019\pi$
$661$	16.6529	0.647722	0.323861	+	0.946105i	$0.395019\pi$
$662$	−7.76832	−0.301924
$663$	5.98653	0.232497
$664$	−30.3616	−1.17826
$665$	0	0
$666$	33.5346	1.29944
$667$	−19.4377	−0.752632
$668$	13.3193	0.515338
$669$	−1.83061	−0.0707755
$670$	−12.3225	−0.476060
$671$	−11.2807	−0.435486
$672$	0	0
$673$	40.5668	1.56374	0.781868	−	0.623444i	$-0.214267\pi$
$673$	40.5668	1.56374	0.781868	+	0.623444i	$0.214267\pi$
$674$	−39.7643	−1.53166
$675$	−5.07771	−0.195441
$676$	15.8559	0.609844
$677$	3.71776	0.142885	0.0714425	−	0.997445i	$-0.477240\pi$
$677$	3.71776	0.142885	0.0714425	+	0.997445i	$0.477240\pi$
$678$	3.62019	0.139033
$679$	0	0
$680$	9.89755	0.379554
$681$	2.68363	0.102837
$682$	19.9810	0.765111
$683$	−1.69128	−0.0647151	−0.0323576	−	0.999476i	$-0.510302\pi$
$683$	−1.69128	−0.0647151	−0.0323576	+	0.999476i	$0.510302\pi$
$684$	9.15588	0.350084
$685$	−0.173037	−0.00661139
$686$	0	0
$687$	−4.23252	−0.161481
$688$	−9.28676	−0.354054
$689$	−60.6913	−2.31216
$690$	1.39004	0.0529179
$691$	−24.1479	−0.918628	−0.459314	−	0.888274i	$-0.651905\pi$
$691$	−24.1479	−0.918628	−0.459314	+	0.888274i	$0.651905\pi$
$692$	−10.8898	−0.413970
$693$	0	0
$694$	28.6715	1.08836
$695$	8.82649	0.334808
$696$	2.16477	0.0820555
$697$	4.86583	0.184307
$698$	−18.0226	−0.682167
$699$	−5.26617	−0.199185
$700$	0	0
$701$	−4.80032	−0.181305	−0.0906527	−	0.995883i	$-0.528895\pi$
$701$	−4.80032	−0.181305	−0.0906527	+	0.995883i	$0.528895\pi$
$702$	12.2260	0.461442
$703$	−26.8427	−1.01239
$704$	−10.1142	−0.381193
$705$	−1.26704	−0.0477196
$706$	−7.04105	−0.264994
$707$	0	0
$708$	−0.466766	−0.0175421
$709$	48.0275	1.80371	0.901856	−	0.432038i	$-0.142205\pi$
$709$	48.0275	1.80371	0.901856	+	0.432038i	$0.142205\pi$
$710$	21.3261	0.800354
$711$	24.7524	0.928287
$712$	11.3164	0.424100
$713$	13.2383	0.495778
$714$	0	0
$715$	20.3224	0.760015
$716$	9.65991	0.361008
$717$	−4.91000	−0.183367
$718$	−3.26233	−0.121749
$719$	−11.8437	−0.441696	−0.220848	−	0.975308i	$-0.570883\pi$
$719$	−11.8437	−0.441696	−0.220848	+	0.975308i	$0.570883\pi$
$720$	14.6845	0.547260
$721$	0	0
$722$	5.71363	0.212639
$723$	3.66917	0.136458
$724$	−1.41208	−0.0524796
$725$	19.9676	0.741577
$726$	0.484664	0.0179876
$727$	48.3049	1.79153	0.895765	−	0.444527i	$-0.146628\pi$
$727$	48.3049	1.79153	0.895765	+	0.444527i	$0.146628\pi$
$728$	0	0
$729$	−24.5685	−0.909946
$730$	20.4869	0.758254
$731$	9.12171	0.337379
$732$	−0.538049	−0.0198868
$733$	40.0781	1.48032	0.740159	−	0.672432i	$-0.234750\pi$
$733$	40.0781	1.48032	0.740159	+	0.672432i	$0.234750\pi$
$734$	−3.57591	−0.131989
$735$	0	0
$736$	16.3769	0.603661
$737$	−25.8720	−0.953007
$738$	4.93060	0.181498
$739$	11.7872	0.433600	0.216800	−	0.976216i	$-0.430438\pi$
$739$	11.7872	0.433600	0.216800	+	0.976216i	$0.430438\pi$
$740$	5.35842	0.196980
$741$	−4.85569	−0.178378
$742$	0	0
$743$	8.89729	0.326410	0.163205	−	0.986592i	$-0.447817\pi$
$743$	8.89729	0.326410	0.163205	+	0.986592i	$0.447817\pi$
$744$	−1.47434	−0.0540521
$745$	0.689303	0.0252541
$746$	15.0006	0.549211
$747$	44.2455	1.61886
$748$	−13.4327	−0.491147
$749$	0	0
$750$	−3.21583	−0.117426
$751$	40.1828	1.46629	0.733145	−	0.680072i	$-0.238051\pi$
$751$	40.1828	1.46629	0.733145	+	0.680072i	$0.238051\pi$
$752$	−29.2950	−1.06828
$753$	−5.01315	−0.182689
$754$	−48.0777	−1.75089
$755$	8.93611	0.325218
$756$	0	0
$757$	−36.7228	−1.33471	−0.667357	−	0.744738i	$-0.732574\pi$
$757$	−36.7228	−1.33471	−0.667357	+	0.744738i	$0.732574\pi$
$758$	−42.3324	−1.53758
$759$	2.91849	0.105934
$760$	−8.02794	−0.291204
$761$	−38.1188	−1.38181	−0.690904	−	0.722947i	$-0.742787\pi$
$761$	−38.1188	−1.38181	−0.690904	+	0.722947i	$0.742787\pi$
$762$	4.30699	0.156026
$763$	0	0
$764$	−1.70047	−0.0615207
$765$	−14.4236	−0.521485
$766$	−40.9852	−1.48085
$767$	−16.0371	−0.579067
$768$	−3.48527	−0.125764
$769$	−3.22533	−0.116308	−0.0581541	−	0.998308i	$-0.518521\pi$
$769$	−3.22533	−0.116308	−0.0581541	+	0.998308i	$0.518521\pi$
$770$	0	0
$771$	2.97113	0.107003
$772$	5.52420	0.198820
$773$	−43.6247	−1.56907	−0.784536	−	0.620083i	$-0.787099\pi$
$773$	−43.6247	−1.56907	−0.784536	+	0.620083i	$0.787099\pi$
$774$	9.24312	0.332237
$775$	−13.5992	−0.488496
$776$	37.1367	1.33313
$777$	0	0
$778$	38.9308	1.39574
$779$	−3.94670	−0.141405
$780$	0.969307	0.0347068
$781$	44.7757	1.60220
$782$	−31.5676	−1.12886
$783$	−6.35807	−0.227219
$784$	0	0
$785$	−15.9580	−0.569565
$786$	−3.06839	−0.109446
$787$	8.35050	0.297663	0.148832	−	0.988863i	$-0.452449\pi$
$787$	8.35050	0.297663	0.148832	+	0.988863i	$0.452449\pi$
$788$	−7.43935	−0.265016
$789$	−4.55552	−0.162181
$790$	14.0289	0.499127
$791$	0	0
$792$	21.0572	0.748236
$793$	−18.4863	−0.656466
$794$	29.8428	1.05908
$795$	−2.25708	−0.0800505
$796$	2.79349	0.0990125
$797$	−11.5618	−0.409539	−0.204769	−	0.978810i	$-0.565644\pi$
$797$	−11.5618	−0.409539	−0.204769	+	0.978810i	$0.565644\pi$
$798$	0	0
$799$	28.7744	1.01796
$800$	−16.8233	−0.594794
$801$	−16.4912	−0.582689
$802$	36.5233	1.28968
$803$	43.0137	1.51792
$804$	−1.23400	−0.0435199
$805$	0	0
$806$	32.7439	1.15335
$807$	5.82392	0.205012
$808$	−8.10182	−0.285021
$809$	48.7987	1.71567	0.857836	−	0.513924i	$-0.171809\pi$
$809$	48.7987	1.71567	0.857836	+	0.513924i	$0.171809\pi$
$810$	−14.3864	−0.505488
$811$	13.8738	0.487176	0.243588	−	0.969879i	$-0.421676\pi$
$811$	13.8738	0.487176	0.243588	+	0.969879i	$0.421676\pi$
$812$	0	0
$813$	5.19481	0.182190
$814$	39.9054	1.39868
$815$	20.3228	0.711875
$816$	5.14753	0.180199
$817$	−7.39866	−0.258846
$818$	−29.2068	−1.02119
$819$	0	0
$820$	0.787850	0.0275129
$821$	37.1937	1.29807	0.649034	−	0.760760i	$-0.275173\pi$
$821$	37.1937	1.29807	0.649034	+	0.760760i	$0.275173\pi$
$822$	−0.0614637	−0.00214379
$823$	−31.6554	−1.10344	−0.551718	−	0.834031i	$-0.686028\pi$
$823$	−31.6554	−1.10344	−0.551718	+	0.834031i	$0.686028\pi$
$824$	−6.02054	−0.209736
$825$	−2.99804	−0.104378
$826$	0	0
$827$	18.2232	0.633683	0.316842	−	0.948478i	$-0.397378\pi$
$827$	18.2232	0.633683	0.316842	+	0.948478i	$0.397378\pi$
$828$	−9.01821	−0.313405
$829$	7.93087	0.275451	0.137725	−	0.990470i	$-0.456021\pi$
$829$	7.93087	0.275451	0.137725	+	0.990470i	$0.456021\pi$
$830$	25.0771	0.870438
$831$	0.260841	0.00904849
$832$	−16.5746	−0.574622
$833$	0	0
$834$	3.13522	0.108564
$835$	17.0188	0.588960
$836$	10.8953	0.376822
$837$	4.33024	0.149675
$838$	−12.0692	−0.416925
$839$	−3.16668	−0.109326	−0.0546630	−	0.998505i	$-0.517408\pi$
$839$	−3.16668	−0.109326	−0.0546630	+	0.998505i	$0.517408\pi$
$840$	0	0
$841$	−3.99752	−0.137845
$842$	−5.84528	−0.201442
$843$	3.58660	0.123529
$844$	17.0159	0.585710
$845$	20.2601	0.696967
$846$	29.1573	1.00245
$847$	0	0
$848$	−52.1855	−1.79206
$849$	−0.584816	−0.0200708
$850$	32.4281	1.11228
$851$	26.4391	0.906322
$852$	2.13564	0.0731658
$853$	−39.5683	−1.35479	−0.677396	−	0.735618i	$-0.736892\pi$
$853$	−39.5683	−1.35479	−0.677396	+	0.735618i	$0.736892\pi$
$854$	0	0
$855$	11.6990	0.400097
$856$	23.7332	0.811183
$857$	−27.2713	−0.931571	−0.465785	−	0.884898i	$-0.654228\pi$
$857$	−27.2713	−0.931571	−0.465785	+	0.884898i	$0.654228\pi$
$858$	7.21865	0.246441
$859$	−29.6877	−1.01293	−0.506465	−	0.862260i	$-0.669048\pi$
$859$	−29.6877	−1.01293	−0.506465	+	0.862260i	$0.669048\pi$
$860$	1.47694	0.0503632
$861$	0	0
$862$	−18.4460	−0.628275
$863$	30.4503	1.03654	0.518271	−	0.855217i	$-0.326576\pi$
$863$	30.4503	1.03654	0.518271	+	0.855217i	$0.326576\pi$
$864$	5.35688	0.182245
$865$	−13.9146	−0.473110
$866$	54.3073	1.84544
$867$	−1.42572	−0.0484200
$868$	0	0
$869$	29.4548	0.999185
$870$	−1.78799	−0.0606185
$871$	−42.3978	−1.43660
$872$	29.5134	0.999450
$873$	−54.1187	−1.83164
$874$	25.6046	0.866090
$875$	0	0
$876$	2.05160	0.0693172
$877$	−15.3705	−0.519023	−0.259512	−	0.965740i	$-0.583562\pi$
$877$	−15.3705	−0.519023	−0.259512	+	0.965740i	$0.583562\pi$
$878$	−29.3669	−0.991084
$879$	−1.56809	−0.0528902
$880$	17.4743	0.589058
$881$	1.78454	0.0601226	0.0300613	−	0.999548i	$-0.490430\pi$
$881$	1.78454	0.0601226	0.0300613	+	0.999548i	$0.490430\pi$
$882$	0	0
$883$	−16.3164	−0.549090	−0.274545	−	0.961574i	$-0.588527\pi$
$883$	−16.3164	−0.549090	−0.274545	+	0.961574i	$0.588527\pi$
$884$	−22.0128	−0.740372
$885$	−0.596414	−0.0200482
$886$	39.3144	1.32079
$887$	−23.4033	−0.785806	−0.392903	−	0.919580i	$-0.628529\pi$
$887$	−23.4033	−0.785806	−0.392903	+	0.919580i	$0.628529\pi$
$888$	−2.94451	−0.0988114
$889$	0	0
$890$	−9.34676	−0.313304
$891$	−30.2054	−1.01192
$892$	6.73127	0.225380
$893$	−23.3390	−0.781010
$894$	0.244845	0.00818883
$895$	12.3430	0.412582
$896$	0	0
$897$	4.78269	0.159689
$898$	13.6615	0.455891
$899$	−17.0282	−0.567923
$900$	9.26404	0.308801
$901$	51.2581	1.70765
$902$	5.86730	0.195360
$903$	0	0
$904$	20.5934	0.684928
$905$	−1.80430	−0.0599769
$906$	3.17416	0.105454
$907$	54.5579	1.81157	0.905783	−	0.423742i	$-0.139284\pi$
$907$	54.5579	1.81157	0.905783	+	0.423742i	$0.139284\pi$
$908$	−9.86790	−0.327478
$909$	11.8067	0.391603
$910$	0	0
$911$	−6.08564	−0.201626	−0.100813	−	0.994905i	$-0.532144\pi$
$911$	−6.08564	−0.201626	−0.100813	+	0.994905i	$0.532144\pi$
$912$	−4.17518	−0.138254
$913$	52.6512	1.74250
$914$	16.4727	0.544868
$915$	−0.687496	−0.0227279
$916$	15.5632	0.514224
$917$	0	0
$918$	−10.3258	−0.340801
$919$	−12.1478	−0.400720	−0.200360	−	0.979722i	$-0.564211\pi$
$919$	−12.1478	−0.400720	−0.200360	+	0.979722i	$0.564211\pi$
$920$	7.90724	0.260694
$921$	6.48016	0.213529
$922$	10.4133	0.342943
$923$	73.3763	2.41521
$924$	0	0
$925$	−27.1598	−0.893010
$926$	52.5433	1.72668
$927$	8.77365	0.288164
$928$	−21.0654	−0.691505
$929$	0.724653	0.0237751	0.0118875	−	0.999929i	$-0.496216\pi$
$929$	0.724653	0.0237751	0.0118875	+	0.999929i	$0.496216\pi$
$930$	1.21773	0.0399310
$931$	0	0
$932$	19.3641	0.634291
$933$	−1.47837	−0.0483995
$934$	−0.701881	−0.0229662
$935$	−17.1637	−0.561314
$936$	34.5076	1.12792
$937$	54.0177	1.76468	0.882341	−	0.470610i	$-0.155966\pi$
$937$	54.0177	1.76468	0.882341	+	0.470610i	$0.155966\pi$
$938$	0	0
$939$	−6.56778	−0.214332
$940$	4.65899	0.151960
$941$	−54.1628	−1.76566	−0.882828	−	0.469697i	$-0.844363\pi$
$941$	−54.1628	−1.76566	−0.882828	+	0.469697i	$0.844363\pi$
$942$	−5.66838	−0.184686
$943$	3.88735	0.126590
$944$	−13.7896	−0.448812
$945$	0	0
$946$	10.9991	0.357612
$947$	41.0213	1.33301	0.666506	−	0.745500i	$-0.267789\pi$
$947$	41.0213	1.33301	0.666506	+	0.745500i	$0.267789\pi$
$948$	1.40489	0.0456287
$949$	70.4889	2.28817
$950$	−26.3026	−0.853368
$951$	−0.620579	−0.0201237
$952$	0	0
$953$	−50.6204	−1.63976	−0.819879	−	0.572537i	$-0.805959\pi$
$953$	−50.6204	−1.63976	−0.819879	+	0.572537i	$0.805959\pi$
$954$	51.9403	1.68163
$955$	−2.17278	−0.0703096
$956$	18.0544	0.583921
$957$	−3.75401	−0.121350
$958$	−46.6049	−1.50574
$959$	0	0
$960$	−0.616404	−0.0198944
$961$	−19.4027	−0.625894
$962$	65.3951	2.10842
$963$	−34.5860	−1.11452
$964$	−13.4918	−0.434541
$965$	7.05860	0.227224
$966$	0	0
$967$	56.5914	1.81986	0.909928	−	0.414766i	$-0.136137\pi$
$967$	56.5914	1.81986	0.909928	+	0.414766i	$0.136137\pi$
$968$	2.75701	0.0886136
$969$	4.10098	0.131742
$970$	−30.6730	−0.984849
$971$	−37.3602	−1.19895	−0.599473	−	0.800395i	$-0.704623\pi$
$971$	−37.3602	−1.19895	−0.599473	+	0.800395i	$0.704623\pi$
$972$	−4.43608	−0.142287
$973$	0	0
$974$	−30.5890	−0.980134
$975$	−4.91305	−0.157344
$976$	−15.8954	−0.508801
$977$	−5.18757	−0.165965	−0.0829826	−	0.996551i	$-0.526445\pi$
$977$	−5.18757	−0.165965	−0.0829826	+	0.996551i	$0.526445\pi$
$978$	7.21877	0.230831
$979$	−19.6242	−0.627192
$980$	0	0
$981$	−43.0094	−1.37319
$982$	14.0839	0.449435
$983$	−46.2680	−1.47572	−0.737860	−	0.674954i	$-0.764164\pi$
$983$	−46.2680	−1.47572	−0.737860	+	0.674954i	$0.764164\pi$
$984$	−0.432933	−0.0138014
$985$	−9.50569	−0.302876
$986$	40.6050	1.29313
$987$	0	0
$988$	17.8547	0.568034
$989$	7.28741	0.231726
$990$	−17.3922	−0.552759
$991$	16.9356	0.537977	0.268989	−	0.963143i	$-0.413311\pi$
$991$	16.9356	0.537977	0.268989	+	0.963143i	$0.413311\pi$
$992$	14.3468	0.455512
$993$	−0.994014	−0.0315441
$994$	0	0
$995$	3.56940	0.113158
$996$	2.51127	0.0795727
$997$	−22.3438	−0.707636	−0.353818	−	0.935314i	$-0.615117\pi$
$997$	−22.3438	−0.707636	−0.353818	+	0.935314i	$0.615117\pi$
$998$	−10.5479	−0.333888
$999$	8.64823	0.273618

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.s.1.5		17
7.2	even	3		287.2.e.d.165.13	✓	34
7.4	even	3		287.2.e.d.247.13	yes	34
7.6	odd	2		2009.2.a.r.1.5		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.13	✓	34	7.2	even	3
287.2.e.d.247.13	yes	34	7.4	even	3
2009.2.a.r.1.5		17	7.6	odd	2
2009.2.a.s.1.5		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)

\(f(q)\)	\(=\)	\(q-1.66890 q^{2} -0.213548 q^{3} +0.785231 q^{4} +1.00334 q^{5} +0.356391 q^{6} +2.02733 q^{8} -2.95440 q^{9} +O(q^{10})\)	\(q-1.66890 q^{2} -0.213548 q^{3} +0.785231 q^{4} +1.00334 q^{5} +0.356391 q^{6} +2.02733 q^{8} -2.95440 q^{9} -1.67447 q^{10} -3.51567 q^{11} -0.167685 q^{12} -5.76131 q^{13} -0.214261 q^{15} -4.95387 q^{16} +4.86583 q^{17} +4.93060 q^{18} -3.94670 q^{19} +0.787850 q^{20} +5.86730 q^{22} +3.88735 q^{23} -0.432933 q^{24} -3.99332 q^{25} +9.61506 q^{26} +1.27155 q^{27} -5.00025 q^{29} +0.357580 q^{30} +3.40548 q^{31} +4.21287 q^{32} +0.750765 q^{33} -8.12060 q^{34} -2.31988 q^{36} +6.80132 q^{37} +6.58665 q^{38} +1.23032 q^{39} +2.03409 q^{40} +1.00000 q^{41} +1.87465 q^{43} -2.76061 q^{44} -2.96425 q^{45} -6.48761 q^{46} +5.91355 q^{47} +1.05789 q^{48} +6.66445 q^{50} -1.03909 q^{51} -4.52396 q^{52} +10.5343 q^{53} -2.12209 q^{54} -3.52739 q^{55} +0.842811 q^{57} +8.34492 q^{58} +2.78359 q^{59} -0.168244 q^{60} +3.20869 q^{61} -5.68341 q^{62} +2.87689 q^{64} -5.78053 q^{65} -1.25295 q^{66} +7.35906 q^{67} +3.82080 q^{68} -0.830138 q^{69} -12.7360 q^{71} -5.98954 q^{72} -12.2349 q^{73} -11.3507 q^{74} +0.852767 q^{75} -3.09907 q^{76} -2.05328 q^{78} -8.37815 q^{79} -4.97040 q^{80} +8.59165 q^{81} -1.66890 q^{82} -14.9762 q^{83} +4.88206 q^{85} -3.12860 q^{86} +1.06779 q^{87} -7.12742 q^{88} +5.58193 q^{89} +4.94704 q^{90} +3.05247 q^{92} -0.727234 q^{93} -9.86913 q^{94} -3.95986 q^{95} -0.899651 q^{96} +18.3180 q^{97} +10.3867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 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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