LMFDB - Embedded newform 1617.2.a.ba.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1617.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.3676752.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 8x^{3} + 14x^{2} + 11x - 10 $ x^5 - 2x^4 - 8x^3 + 14x^2 + 11x - 10
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.06884$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.06884 q^{2} -1.00000 q^{3} -0.857576 q^{4} -2.69184 q^{5} +1.06884 q^{6} +3.05430 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.06884 q^{2} -1.00000 q^{3} -0.857576 q^{4} -2.69184 q^{5} +1.06884 q^{6} +3.05430 q^{8} +1.00000 q^{9} +2.87715 q^{10} +1.00000 q^{11} +0.857576 q^{12} -3.28888 q^{13} +2.69184 q^{15} -1.54941 q^{16} -1.06884 q^{17} -1.06884 q^{18} -6.35772 q^{19} +2.30845 q^{20} -1.06884 q^{22} -1.54941 q^{23} -3.05430 q^{24} +2.24599 q^{25} +3.51529 q^{26} -1.00000 q^{27} -8.57566 q^{29} -2.87715 q^{30} +3.85758 q^{31} -4.45252 q^{32} -1.00000 q^{33} +1.14242 q^{34} -0.857576 q^{36} +7.82952 q^{37} +6.79540 q^{38} +3.28888 q^{39} -8.22168 q^{40} -6.87715 q^{41} -2.76571 q^{43} -0.857576 q^{44} -2.69184 q^{45} +1.65608 q^{46} -9.13295 q^{47} +1.54941 q^{48} -2.40061 q^{50} +1.06884 q^{51} +2.82046 q^{52} -3.55444 q^{53} +1.06884 q^{54} -2.69184 q^{55} +6.35772 q^{57} +9.16603 q^{58} -1.54941 q^{59} -2.30845 q^{60} +12.3694 q^{61} -4.12314 q^{62} +7.85787 q^{64} +8.85313 q^{65} +1.06884 q^{66} -8.10386 q^{67} +0.916613 q^{68} +1.54941 q^{69} +10.4350 q^{71} +3.05430 q^{72} +14.2500 q^{73} -8.36853 q^{74} -2.24599 q^{75} +5.45223 q^{76} -3.51529 q^{78} +9.38741 q^{79} +4.17077 q^{80} +1.00000 q^{81} +7.35059 q^{82} +2.46916 q^{83} +2.87715 q^{85} +2.95611 q^{86} +8.57566 q^{87} +3.05430 q^{88} -11.6300 q^{89} +2.87715 q^{90} +1.32874 q^{92} -3.85758 q^{93} +9.76168 q^{94} +17.1140 q^{95} +4.45252 q^{96} +12.6644 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} - 5 q^{3} + 10 q^{4} - 4 q^{5} - 2 q^{6} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 - 5 * q^3 + 10 * q^4 - 4 * q^5 - 2 * q^6 + 6 * q^8 + 5 * q^9	$ 5 q + 2 q^{2} - 5 q^{3} + 10 q^{4} - 4 q^{5} - 2 q^{6} + 6 q^{8} + 5 q^{9} + 2 q^{10} + 5 q^{11} - 10 q^{12} + 5 q^{13} + 4 q^{15} + 16 q^{16} + 2 q^{17} + 2 q^{18} - 3 q^{19} - 8 q^{20} + 2 q^{22} + 16 q^{23} - 6 q^{24} + 7 q^{25} - 10 q^{26} - 5 q^{27} - 2 q^{30} + 5 q^{31} + 4 q^{32} - 5 q^{33} + 20 q^{34} + 10 q^{36} + 15 q^{37} + 6 q^{38} - 5 q^{39} - 6 q^{40} - 22 q^{41} + 3 q^{43} + 10 q^{44} - 4 q^{45} + 16 q^{46} - 2 q^{47} - 16 q^{48} + 34 q^{50} - 2 q^{51} + 40 q^{52} + 6 q^{53} - 2 q^{54} - 4 q^{55} + 3 q^{57} + 12 q^{58} + 16 q^{59} + 8 q^{60} + 12 q^{61} - 4 q^{62} - 4 q^{64} - 28 q^{65} - 2 q^{66} + 7 q^{67} + 10 q^{68} - 16 q^{69} + 24 q^{71} + 6 q^{72} + 17 q^{73} - 36 q^{74} - 7 q^{75} + 30 q^{76} + 10 q^{78} + 7 q^{79} + 16 q^{80} + 5 q^{81} + 8 q^{82} - 12 q^{83} + 2 q^{85} - 18 q^{86} + 6 q^{88} - 6 q^{89} + 2 q^{90} + 68 q^{92} - 5 q^{93} + 82 q^{94} - 18 q^{95} - 4 q^{96} - 14 q^{97} + 5 q^{99}+O(q^{100}) $ 5 * q + 2 * q^2 - 5 * q^3 + 10 * q^4 - 4 * q^5 - 2 * q^6 + 6 * q^8 + 5 * q^9 + 2 * q^10 + 5 * q^11 - 10 * q^12 + 5 * q^13 + 4 * q^15 + 16 * q^16 + 2 * q^17 + 2 * q^18 - 3 * q^19 - 8 * q^20 + 2 * q^22 + 16 * q^23 - 6 * q^24 + 7 * q^25 - 10 * q^26 - 5 * q^27 - 2 * q^30 + 5 * q^31 + 4 * q^32 - 5 * q^33 + 20 * q^34 + 10 * q^36 + 15 * q^37 + 6 * q^38 - 5 * q^39 - 6 * q^40 - 22 * q^41 + 3 * q^43 + 10 * q^44 - 4 * q^45 + 16 * q^46 - 2 * q^47 - 16 * q^48 + 34 * q^50 - 2 * q^51 + 40 * q^52 + 6 * q^53 - 2 * q^54 - 4 * q^55 + 3 * q^57 + 12 * q^58 + 16 * q^59 + 8 * q^60 + 12 * q^61 - 4 * q^62 - 4 * q^64 - 28 * q^65 - 2 * q^66 + 7 * q^67 + 10 * q^68 - 16 * q^69 + 24 * q^71 + 6 * q^72 + 17 * q^73 - 36 * q^74 - 7 * q^75 + 30 * q^76 + 10 * q^78 + 7 * q^79 + 16 * q^80 + 5 * q^81 + 8 * q^82 - 12 * q^83 + 2 * q^85 - 18 * q^86 + 6 * q^88 - 6 * q^89 + 2 * q^90 + 68 * q^92 - 5 * q^93 + 82 * q^94 - 18 * q^95 - 4 * q^96 - 14 * q^97 + 5 * 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 $

$2$	−1.06884	−0.755786	−0.377893	−	0.925849i	$-0.623351\pi$
$2$	−1.06884	−0.755786	−0.377893	+	0.925849i	$0.623351\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.857576	−0.428788
$5$	−2.69184	−1.20383	−0.601913	−	0.798562i	$-0.705595\pi$
$5$	−2.69184	−1.20383	−0.601913	+	0.798562i	$0.705595\pi$
$6$	1.06884	0.436353
$7$	0	0
$7$	0	0
$8$	3.05430	1.07986
$9$	1.00000	0.333333
$10$	2.87715	0.909835
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.857576	0.247561
$13$	−3.28888	−0.912171	−0.456085	−	0.889936i	$-0.650749\pi$
$13$	−3.28888	−0.912171	−0.456085	+	0.889936i	$0.650749\pi$
$14$	0	0
$15$	2.69184	0.695030
$16$	−1.54941	−0.387353
$17$	−1.06884	−0.259232	−0.129616	−	0.991564i	$-0.541375\pi$
$17$	−1.06884	−0.259232	−0.129616	+	0.991564i	$0.541375\pi$
$18$	−1.06884	−0.251929
$19$	−6.35772	−1.45856	−0.729281	−	0.684215i	$-0.760145\pi$
$19$	−6.35772	−1.45856	−0.729281	+	0.684215i	$0.760145\pi$
$20$	2.30845	0.516186
$21$	0	0
$22$	−1.06884	−0.227878
$23$	−1.54941	−0.323075	−0.161537	−	0.986867i	$-0.551645\pi$
$23$	−1.54941	−0.323075	−0.161537	+	0.986867i	$0.551645\pi$
$24$	−3.05430	−0.623456
$25$	2.24599	0.449198
$26$	3.51529	0.689406
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−8.57566	−1.59246	−0.796230	−	0.604994i	$-0.793175\pi$
$29$	−8.57566	−1.59246	−0.796230	+	0.604994i	$0.793175\pi$
$30$	−2.87715	−0.525293
$31$	3.85758	0.692841	0.346421	−	0.938079i	$-0.387397\pi$
$31$	3.85758	0.692841	0.346421	+	0.938079i	$0.387397\pi$
$32$	−4.45252	−0.787101
$33$	−1.00000	−0.174078
$34$	1.14242	0.195924
$35$	0	0
$36$	−0.857576	−0.142929
$37$	7.82952	1.28717	0.643583	−	0.765376i	$-0.277447\pi$
$37$	7.82952	1.28717	0.643583	+	0.765376i	$0.277447\pi$
$38$	6.79540	1.10236
$39$	3.28888	0.526642
$40$	−8.22168	−1.29996
$41$	−6.87715	−1.07403	−0.537015	−	0.843573i	$-0.680448\pi$
$41$	−6.87715	−1.07403	−0.537015	+	0.843573i	$0.680448\pi$
$42$	0	0
$43$	−2.76571	−0.421767	−0.210884	−	0.977511i	$-0.567634\pi$
$43$	−2.76571	−0.421767	−0.210884	+	0.977511i	$0.567634\pi$
$44$	−0.857576	−0.129284
$45$	−2.69184	−0.401275
$46$	1.65608	0.244176
$47$	−9.13295	−1.33218	−0.666089	−	0.745873i	$-0.732033\pi$
$47$	−9.13295	−1.33218	−0.666089	+	0.745873i	$0.732033\pi$
$48$	1.54941	0.223639
$49$	0	0
$50$	−2.40061	−0.339498
$51$	1.06884	0.149668
$52$	2.82046	0.391128
$53$	−3.55444	−0.488240	−0.244120	−	0.969745i	$-0.578499\pi$
$53$	−3.55444	−0.488240	−0.244120	+	0.969745i	$0.578499\pi$
$54$	1.06884	0.145451
$55$	−2.69184	−0.362967
$56$	0	0
$57$	6.35772	0.842101
$58$	9.16603	1.20356
$59$	−1.54941	−0.201716	−0.100858	−	0.994901i	$-0.532159\pi$
$59$	−1.54941	−0.201716	−0.100858	+	0.994901i	$0.532159\pi$
$60$	−2.30845	−0.298020
$61$	12.3694	1.58374	0.791871	−	0.610688i	$-0.209107\pi$
$61$	12.3694	1.58374	0.791871	+	0.610688i	$0.209107\pi$
$62$	−4.12314	−0.523639
$63$	0	0
$64$	7.85787	0.982233
$65$	8.85313	1.09810
$66$	1.06884	0.131565
$67$	−8.10386	−0.990044	−0.495022	−	0.868881i	$-0.664840\pi$
$67$	−8.10386	−0.990044	−0.495022	+	0.868881i	$0.664840\pi$
$68$	0.916613	0.111156
$69$	1.54941	0.186527
$70$	0	0
$71$	10.4350	1.23841	0.619206	−	0.785229i	$-0.287455\pi$
$71$	10.4350	1.23841	0.619206	+	0.785229i	$0.287455\pi$
$72$	3.05430	0.359953
$73$	14.2500	1.66784	0.833919	−	0.551886i	$-0.186092\pi$
$73$	14.2500	1.66784	0.833919	+	0.551886i	$0.186092\pi$
$74$	−8.36853	−0.972822
$75$	−2.24599	−0.259345
$76$	5.45223	0.625413
$77$	0	0
$78$	−3.51529	−0.398029
$79$	9.38741	1.05617	0.528083	−	0.849193i	$-0.322911\pi$
$79$	9.38741	1.05617	0.528083	+	0.849193i	$0.322911\pi$
$80$	4.17077	0.466306
$81$	1.00000	0.111111
$82$	7.35059	0.811737
$83$	2.46916	0.271026	0.135513	−	0.990776i	$-0.456732\pi$
$83$	2.46916	0.271026	0.135513	+	0.990776i	$0.456732\pi$
$84$	0	0
$85$	2.87715	0.312071
$86$	2.95611	0.318766
$87$	8.57566	0.919407
$88$	3.05430	0.325589
$89$	−11.6300	−1.23277	−0.616387	−	0.787444i	$-0.711404\pi$
$89$	−11.6300	−1.23277	−0.616387	+	0.787444i	$0.711404\pi$
$90$	2.87715	0.303278
$91$	0	0
$92$	1.32874	0.138531
$93$	−3.85758	−0.400012
$94$	9.76168	1.00684
$95$	17.1140	1.75585
$96$	4.45252	0.454433
$97$	12.6644	1.28587	0.642936	−	0.765920i	$-0.277716\pi$
$97$	12.6644	1.28587	0.642936	+	0.765920i	$0.277716\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	−1.92611	−0.192611
$101$	−5.47683	−0.544965	−0.272483	−	0.962161i	$-0.587845\pi$
$101$	−5.47683	−0.544965	−0.272483	+	0.962161i	$0.587845\pi$
$102$	−1.14242	−0.113117
$103$	−6.32653	−0.623372	−0.311686	−	0.950185i	$-0.600894\pi$
$103$	−6.32653	−0.623372	−0.311686	+	0.950185i	$0.600894\pi$
$104$	−10.0452	−0.985015
$105$	0	0
$106$	3.79914	0.369005
$107$	−3.50682	−0.339017	−0.169508	−	0.985529i	$-0.554218\pi$
$107$	−3.50682	−0.339017	−0.169508	+	0.985529i	$0.554218\pi$
$108$	0.857576	0.0825202
$109$	3.80995	0.364927	0.182463	−	0.983213i	$-0.441593\pi$
$109$	3.80995	0.364927	0.182463	+	0.983213i	$0.441593\pi$
$110$	2.87715	0.274326
$111$	−7.82952	−0.743145
$112$	0	0
$113$	11.1319	1.04720	0.523601	−	0.851964i	$-0.324588\pi$
$113$	11.1319	1.04720	0.523601	+	0.851964i	$0.324588\pi$
$114$	−6.79540	−0.636448
$115$	4.17077	0.388926
$116$	7.35428	0.682827
$117$	−3.28888	−0.304057
$118$	1.65608	0.152454
$119$	0	0
$120$	8.22168	0.750533
$121$	1.00000	0.0909091
$122$	−13.2210	−1.19697
$123$	6.87715	0.620092
$124$	−3.30816	−0.297082
$125$	7.41335	0.663070
$126$	0	0
$127$	12.6951	1.12650	0.563252	−	0.826285i	$-0.309550\pi$
$127$	12.6951	1.12650	0.563252	+	0.826285i	$0.309550\pi$
$128$	0.506213	0.0447433
$129$	2.76571	0.243507
$130$	−9.46260	−0.829925
$131$	6.54568	0.571898	0.285949	−	0.958245i	$-0.407691\pi$
$131$	6.54568	0.571898	0.285949	+	0.958245i	$0.407691\pi$
$132$	0.857576	0.0746424
$133$	0	0
$134$	8.66175	0.748261
$135$	2.69184	0.231677
$136$	−3.26456	−0.279934
$137$	21.4133	1.82947	0.914733	−	0.404059i	$-0.132401\pi$
$137$	21.4133	1.82947	0.914733	+	0.404059i	$0.132401\pi$
$138$	−1.65608	−0.140975
$139$	0.850905	0.0721728	0.0360864	−	0.999349i	$-0.488511\pi$
$139$	0.850905	0.0721728	0.0360864	+	0.999349i	$0.488511\pi$
$140$	0	0
$141$	9.13295	0.769133
$142$	−11.1534	−0.935974
$143$	−3.28888	−0.275030
$144$	−1.54941	−0.129118
$145$	23.0843	1.91705
$146$	−15.2310	−1.26053
$147$	0	0
$148$	−6.71441	−0.551921
$149$	−15.7843	−1.29310	−0.646550	−	0.762872i	$-0.723789\pi$
$149$	−15.7843	−1.29310	−0.646550	+	0.762872i	$0.723789\pi$
$150$	2.40061	0.196009
$151$	−17.0594	−1.38827	−0.694136	−	0.719844i	$-0.744213\pi$
$151$	−17.0594	−1.38827	−0.694136	+	0.719844i	$0.744213\pi$
$152$	−19.4184	−1.57504
$153$	−1.06884	−0.0864108
$154$	0	0
$155$	−10.3840	−0.834060
$156$	−2.82046	−0.225818
$157$	−18.2188	−1.45402	−0.727010	−	0.686627i	$-0.759091\pi$
$157$	−18.2188	−1.45402	−0.727010	+	0.686627i	$0.759091\pi$
$158$	−10.0337	−0.798236
$159$	3.55444	0.281886
$160$	11.9855	0.947533
$161$	0	0
$162$	−1.06884	−0.0839762
$163$	9.91501	0.776603	0.388302	−	0.921532i	$-0.373062\pi$
$163$	9.91501	0.776603	0.388302	+	0.921532i	$0.373062\pi$
$164$	5.89768	0.460531
$165$	2.69184	0.209559
$166$	−2.63914	−0.204837
$167$	−0.193790	−0.0149960	−0.00749798	−	0.999972i	$-0.502387\pi$
$167$	−0.193790	−0.0149960	−0.00749798	+	0.999972i	$0.502387\pi$
$168$	0	0
$169$	−2.18328	−0.167944
$170$	−3.07522	−0.235859
$171$	−6.35772	−0.486187
$172$	2.37181	0.180849
$173$	9.02818	0.686400	0.343200	−	0.939262i	$-0.388489\pi$
$173$	9.02818	0.686400	0.343200	+	0.939262i	$0.388489\pi$
$174$	−9.16603	−0.694875
$175$	0	0
$176$	−1.54941	−0.116791
$177$	1.54941	0.116461
$178$	12.4306	0.931712
$179$	12.2243	0.913687	0.456843	−	0.889547i	$-0.348980\pi$
$179$	12.2243	0.913687	0.456843	+	0.889547i	$0.348980\pi$
$180$	2.30845	0.172062
$181$	−18.5108	−1.37590	−0.687950	−	0.725758i	$-0.741489\pi$
$181$	−18.5108	−1.37590	−0.687950	+	0.725758i	$0.741489\pi$
$182$	0	0
$183$	−12.3694	−0.914374
$184$	−4.73237	−0.348875
$185$	−21.0758	−1.54952
$186$	4.12314	0.302323
$187$	−1.06884	−0.0781615
$188$	7.83219	0.571221
$189$	0	0
$190$	−18.2921	−1.32705
$191$	18.4655	1.33612	0.668060	−	0.744107i	$-0.267125\pi$
$191$	18.4655	1.33612	0.668060	+	0.744107i	$0.267125\pi$
$192$	−7.85787	−0.567093
$193$	−17.0420	−1.22671	−0.613354	−	0.789808i	$-0.710180\pi$
$193$	−17.0420	−1.22671	−0.613354	+	0.789808i	$0.710180\pi$
$194$	−13.5362	−0.971844
$195$	−8.85313	−0.633986
$196$	0	0
$197$	5.45281	0.388497	0.194248	−	0.980952i	$-0.437773\pi$
$197$	5.45281	0.388497	0.194248	+	0.980952i	$0.437773\pi$
$198$	−1.06884	−0.0759593
$199$	4.33148	0.307050	0.153525	−	0.988145i	$-0.450937\pi$
$199$	4.33148	0.307050	0.153525	+	0.988145i	$0.450937\pi$
$200$	6.85992	0.485070
$201$	8.10386	0.571602
$202$	5.85387	0.411877
$203$	0	0
$204$	−0.916613	−0.0641758
$205$	18.5122	1.29295
$206$	6.76207	0.471136
$207$	−1.54941	−0.107692
$208$	5.09583	0.353332
$209$	−6.35772	−0.439773
$210$	0	0
$211$	26.0751	1.79508	0.897542	−	0.440929i	$-0.145351\pi$
$211$	26.0751	1.79508	0.897542	+	0.440929i	$0.145351\pi$
$212$	3.04820	0.209352
$213$	−10.4350	−0.714997
$214$	3.74823	0.256224
$215$	7.44485	0.507734
$216$	−3.05430	−0.207819
$217$	0	0
$218$	−4.07223	−0.275807
$219$	−14.2500	−0.962927
$220$	2.30845	0.155636
$221$	3.51529	0.236464
$222$	8.36853	0.561659
$223$	13.3681	0.895196	0.447598	−	0.894235i	$-0.352280\pi$
$223$	13.3681	0.895196	0.447598	+	0.894235i	$0.352280\pi$
$224$	0	0
$225$	2.24599	0.149733
$226$	−11.8983	−0.791460
$227$	−22.7579	−1.51049	−0.755247	−	0.655441i	$-0.772483\pi$
$227$	−22.7579	−1.51049	−0.755247	+	0.655441i	$0.772483\pi$
$228$	−5.45223	−0.361083
$229$	25.5630	1.68925	0.844627	−	0.535356i	$-0.179822\pi$
$229$	25.5630	1.68925	0.844627	+	0.535356i	$0.179822\pi$
$230$	−4.45790	−0.293945
$231$	0	0
$232$	−26.1926	−1.71963
$233$	−22.4676	−1.47190	−0.735952	−	0.677033i	$-0.763265\pi$
$233$	−22.4676	−1.47190	−0.735952	+	0.677033i	$0.763265\pi$
$234$	3.51529	0.229802
$235$	24.5844	1.60371
$236$	1.32874	0.0864935
$237$	−9.38741	−0.609778
$238$	0	0
$239$	−13.1701	−0.851900	−0.425950	−	0.904747i	$-0.640060\pi$
$239$	−13.1701	−0.851900	−0.425950	+	0.904747i	$0.640060\pi$
$240$	−4.17077	−0.269222
$241$	14.5507	0.937296	0.468648	−	0.883385i	$-0.344741\pi$
$241$	14.5507	0.937296	0.468648	+	0.883385i	$0.344741\pi$
$242$	−1.06884	−0.0687078
$243$	−1.00000	−0.0641500
$244$	−10.6077	−0.679089
$245$	0	0
$246$	−7.35059	−0.468657
$247$	20.9098	1.33046
$248$	11.7822	0.748170
$249$	−2.46916	−0.156477
$250$	−7.92370	−0.501139
$251$	−5.15996	−0.325694	−0.162847	−	0.986651i	$-0.552068\pi$
$251$	−5.15996	−0.325694	−0.162847	+	0.986651i	$0.552068\pi$
$252$	0	0
$253$	−1.54941	−0.0974108
$254$	−13.5690	−0.851396
$255$	−2.87715	−0.180174
$256$	−16.2568	−1.01605
$257$	14.8235	0.924662	0.462331	−	0.886707i	$-0.347013\pi$
$257$	14.8235	0.924662	0.462331	+	0.886707i	$0.347013\pi$
$258$	−2.95611	−0.184039
$259$	0	0
$260$	−7.59223	−0.470850
$261$	−8.57566	−0.530820
$262$	−6.99630	−0.432233
$263$	15.4689	0.953851	0.476926	−	0.878944i	$-0.341751\pi$
$263$	15.4689	0.953851	0.476926	+	0.878944i	$0.341751\pi$
$264$	−3.05430	−0.187979
$265$	9.56799	0.587757
$266$	0	0
$267$	11.6300	0.711742
$268$	6.94967	0.424519
$269$	−5.91442	−0.360609	−0.180304	−	0.983611i	$-0.557708\pi$
$269$	−5.91442	−0.360609	−0.180304	+	0.983611i	$0.557708\pi$
$270$	−2.87715	−0.175098
$271$	−9.29021	−0.564340	−0.282170	−	0.959364i	$-0.591054\pi$
$271$	−9.29021	−0.564340	−0.282170	+	0.959364i	$0.591054\pi$
$272$	1.65608	0.100415
$273$	0	0
$274$	−22.8875	−1.38268
$275$	2.24599	0.135438
$276$	−1.32874	−0.0799807
$277$	9.56666	0.574805	0.287402	−	0.957810i	$-0.407208\pi$
$277$	9.56666	0.574805	0.287402	+	0.957810i	$0.407208\pi$
$278$	−0.909484	−0.0545472
$279$	3.85758	0.230947
$280$	0	0
$281$	−13.0057	−0.775853	−0.387927	−	0.921690i	$-0.626809\pi$
$281$	−13.0057	−0.775853	−0.387927	+	0.921690i	$0.626809\pi$
$282$	−9.76168	−0.581300
$283$	24.2236	1.43994	0.719971	−	0.694004i	$-0.244155\pi$
$283$	24.2236	1.43994	0.719971	+	0.694004i	$0.244155\pi$
$284$	−8.94884	−0.531016
$285$	−17.1140	−1.01374
$286$	3.51529	0.207864
$287$	0	0
$288$	−4.45252	−0.262367
$289$	−15.8576	−0.932799
$290$	−24.6735	−1.44888
$291$	−12.6644	−0.742398
$292$	−12.2205	−0.715149
$293$	3.05010	0.178189	0.0890944	−	0.996023i	$-0.471603\pi$
$293$	3.05010	0.178189	0.0890944	+	0.996023i	$0.471603\pi$
$294$	0	0
$295$	4.17077	0.242832
$296$	23.9137	1.38996
$297$	−1.00000	−0.0580259
$298$	16.8709	0.977306
$299$	5.09583	0.294700
$300$	1.92611	0.111204
$301$	0	0
$302$	18.2338	1.04924
$303$	5.47683	0.314636
$304$	9.85074	0.564979
$305$	−33.2965	−1.90655
$306$	1.14242	0.0653081
$307$	20.5254	1.17145	0.585723	−	0.810511i	$-0.300811\pi$
$307$	20.5254	1.17145	0.585723	+	0.810511i	$0.300811\pi$
$308$	0	0
$309$	6.32653	0.359904
$310$	11.0988	0.630371
$311$	7.99535	0.453375	0.226687	−	0.973968i	$-0.427210\pi$
$311$	7.99535	0.453375	0.226687	+	0.973968i	$0.427210\pi$
$312$	10.0452	0.568698
$313$	15.9147	0.899553	0.449776	−	0.893141i	$-0.351504\pi$
$313$	15.9147	0.899553	0.449776	+	0.893141i	$0.351504\pi$
$314$	19.4730	1.09893
$315$	0	0
$316$	−8.05042	−0.452871
$317$	26.7915	1.50476	0.752381	−	0.658728i	$-0.228905\pi$
$317$	26.7915	1.50476	0.752381	+	0.658728i	$0.228905\pi$
$318$	−3.79914	−0.213045
$319$	−8.57566	−0.480145
$320$	−21.1521	−1.18244
$321$	3.50682	0.195731
$322$	0	0
$323$	6.79540	0.378106
$324$	−0.857576	−0.0476431
$325$	−7.38679	−0.409745
$326$	−10.5976	−0.586946
$327$	−3.80995	−0.210691
$328$	−21.0049	−1.15980
$329$	0	0
$330$	−2.87715	−0.158382
$331$	−10.1227	−0.556393	−0.278196	−	0.960524i	$-0.589737\pi$
$331$	−10.1227	−0.556393	−0.278196	+	0.960524i	$0.589737\pi$
$332$	−2.11749	−0.116212
$333$	7.82952	0.429055
$334$	0.207131	0.0113337
$335$	21.8143	1.19184
$336$	0	0
$337$	1.36539	0.0743777	0.0371889	−	0.999308i	$-0.488160\pi$
$337$	1.36539	0.0743777	0.0371889	+	0.999308i	$0.488160\pi$
$338$	2.33358	0.126930
$339$	−11.1319	−0.604602
$340$	−2.46737	−0.133812
$341$	3.85758	0.208899
$342$	6.79540	0.367453
$343$	0	0
$344$	−8.44731	−0.455448
$345$	−4.17077	−0.224547
$346$	−9.64970	−0.518771
$347$	−25.3077	−1.35859	−0.679295	−	0.733865i	$-0.737715\pi$
$347$	−25.3077	−1.35859	−0.679295	+	0.733865i	$0.737715\pi$
$348$	−7.35428	−0.394231
$349$	−5.48986	−0.293866	−0.146933	−	0.989146i	$-0.546940\pi$
$349$	−5.48986	−0.293866	−0.146933	+	0.989146i	$0.546940\pi$
$350$	0	0
$351$	3.28888	0.175547
$352$	−4.45252	−0.237320
$353$	17.3437	0.923112	0.461556	−	0.887111i	$-0.347291\pi$
$353$	17.3437	0.923112	0.461556	+	0.887111i	$0.347291\pi$
$354$	−1.65608	−0.0880196
$355$	−28.0894	−1.49083
$356$	9.97357	0.528598
$357$	0	0
$358$	−13.0658	−0.690552
$359$	9.54538	0.503786	0.251893	−	0.967755i	$-0.418947\pi$
$359$	9.54538	0.503786	0.251893	+	0.967755i	$0.418947\pi$
$360$	−8.22168	−0.433320
$361$	21.4206	1.12740
$362$	19.7852	1.03989
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	−38.3587	−2.00779
$366$	13.2210	0.691071
$367$	6.61745	0.345428	0.172714	−	0.984972i	$-0.444746\pi$
$367$	6.61745	0.345428	0.172714	+	0.984972i	$0.444746\pi$
$368$	2.40068	0.125144
$369$	−6.87715	−0.358010
$370$	22.5267	1.17111
$371$	0	0
$372$	3.30816	0.171520
$373$	−32.7150	−1.69392	−0.846959	−	0.531658i	$-0.821569\pi$
$373$	−32.7150	−1.69392	−0.846959	+	0.531658i	$0.821569\pi$
$374$	1.14242	0.0590734
$375$	−7.41335	−0.382824
$376$	−27.8947	−1.43856
$377$	28.2043	1.45260
$378$	0	0
$379$	−7.69346	−0.395186	−0.197593	−	0.980284i	$-0.563312\pi$
$379$	−7.69346	−0.395186	−0.197593	+	0.980284i	$0.563312\pi$
$380$	−14.6765	−0.752889
$381$	−12.6951	−0.650388
$382$	−19.7368	−1.00982
$383$	−6.45806	−0.329992	−0.164996	−	0.986294i	$-0.552761\pi$
$383$	−6.45806	−0.329992	−0.164996	+	0.986294i	$0.552761\pi$
$384$	−0.506213	−0.0258326
$385$	0	0
$386$	18.2152	0.927129
$387$	−2.76571	−0.140589
$388$	−10.8607	−0.551366
$389$	5.52556	0.280157	0.140078	−	0.990140i	$-0.455265\pi$
$389$	5.52556	0.280157	0.140078	+	0.990140i	$0.455265\pi$
$390$	9.46260	0.479157
$391$	1.65608	0.0837515
$392$	0	0
$393$	−6.54568	−0.330186
$394$	−5.82820	−0.293620
$395$	−25.2694	−1.27144
$396$	−0.857576	−0.0430948
$397$	32.5455	1.63341	0.816707	−	0.577052i	$-0.195797\pi$
$397$	32.5455	1.63341	0.816707	+	0.577052i	$0.195797\pi$
$398$	−4.62967	−0.232064
$399$	0	0
$400$	−3.47997	−0.173998
$401$	−32.1805	−1.60702	−0.803509	−	0.595293i	$-0.797036\pi$
$401$	−32.1805	−1.60702	−0.803509	+	0.595293i	$0.797036\pi$
$402$	−8.66175	−0.432009
$403$	−12.6871	−0.631989
$404$	4.69680	0.233674
$405$	−2.69184	−0.133758
$406$	0	0
$407$	7.82952	0.388095
$408$	3.26456	0.161620
$409$	−2.18057	−0.107822	−0.0539112	−	0.998546i	$-0.517169\pi$
$409$	−2.18057	−0.107822	−0.0539112	+	0.998546i	$0.517169\pi$
$410$	−19.7866	−0.977191
$411$	−21.4133	−1.05624
$412$	5.42548	0.267294
$413$	0	0
$414$	1.65608	0.0813918
$415$	−6.64658	−0.326268
$416$	14.6438	0.717971
$417$	−0.850905	−0.0416690
$418$	6.79540	0.332374
$419$	−36.7377	−1.79475	−0.897376	−	0.441266i	$-0.854530\pi$
$419$	−36.7377	−1.79475	−0.897376	+	0.441266i	$0.854530\pi$
$420$	0	0
$421$	−36.6439	−1.78591	−0.892957	−	0.450142i	$-0.851373\pi$
$421$	−36.6439	−1.78591	−0.892957	+	0.450142i	$0.851373\pi$
$422$	−27.8702	−1.35670
$423$	−9.13295	−0.444059
$424$	−10.8563	−0.527230
$425$	−2.40061	−0.116447
$426$	11.1534	0.540385
$427$	0	0
$428$	3.00736	0.145366
$429$	3.28888	0.158789
$430$	−7.95737	−0.383738
$431$	25.8282	1.24410	0.622051	−	0.782977i	$-0.286300\pi$
$431$	25.8282	1.24410	0.622051	+	0.782977i	$0.286300\pi$
$432$	1.54941	0.0745462
$433$	−4.81228	−0.231263	−0.115632	−	0.993292i	$-0.536889\pi$
$433$	−4.81228	−0.231263	−0.115632	+	0.993292i	$0.536889\pi$
$434$	0	0
$435$	−23.0843	−1.10681
$436$	−3.26732	−0.156476
$437$	9.85074	0.471225
$438$	15.2310	0.727767
$439$	27.2860	1.30229	0.651146	−	0.758953i	$-0.274289\pi$
$439$	27.2860	1.30229	0.651146	+	0.758953i	$0.274289\pi$
$440$	−8.22168	−0.391953
$441$	0	0
$442$	−3.75730	−0.178716
$443$	−27.1307	−1.28902	−0.644510	−	0.764596i	$-0.722939\pi$
$443$	−27.1307	−1.28902	−0.644510	+	0.764596i	$0.722939\pi$
$444$	6.71441	0.318652
$445$	31.3060	1.48404
$446$	−14.2884	−0.676577
$447$	15.7843	0.746571
$448$	0	0
$449$	4.27537	0.201767	0.100884	−	0.994898i	$-0.467833\pi$
$449$	4.27537	0.201767	0.100884	+	0.994898i	$0.467833\pi$
$450$	−2.40061	−0.113166
$451$	−6.87715	−0.323832
$452$	−9.54645	−0.449027
$453$	17.0594	0.801519
$454$	24.3246	1.14161
$455$	0	0
$456$	19.4184	0.909349
$457$	29.0995	1.36122	0.680609	−	0.732646i	$-0.261715\pi$
$457$	29.0995	1.36122	0.680609	+	0.732646i	$0.261715\pi$
$458$	−27.3229	−1.27671
$459$	1.06884	0.0498893
$460$	−3.57675	−0.166767
$461$	−2.96972	−0.138314	−0.0691569	−	0.997606i	$-0.522031\pi$
$461$	−2.96972	−0.138314	−0.0691569	+	0.997606i	$0.522031\pi$
$462$	0	0
$463$	−20.3076	−0.943773	−0.471887	−	0.881659i	$-0.656427\pi$
$463$	−20.3076	−0.943773	−0.471887	+	0.881659i	$0.656427\pi$
$464$	13.2872	0.616845
$465$	10.3840	0.481545
$466$	24.0144	1.11244
$467$	37.1349	1.71840	0.859200	−	0.511640i	$-0.170962\pi$
$467$	37.1349	1.71840	0.859200	+	0.511640i	$0.170962\pi$
$468$	2.82046	0.130376
$469$	0	0
$470$	−26.2769	−1.21206
$471$	18.2188	0.839479
$472$	−4.73237	−0.217825
$473$	−2.76571	−0.127168
$474$	10.0337	0.460862
$475$	−14.2794	−0.655183
$476$	0	0
$477$	−3.55444	−0.162747
$478$	14.0767	0.643854
$479$	18.3686	0.839284	0.419642	−	0.907690i	$-0.362156\pi$
$479$	18.3686	0.839284	0.419642	+	0.907690i	$0.362156\pi$
$480$	−11.9855	−0.547059
$481$	−25.7504	−1.17411
$482$	−15.5525	−0.708395
$483$	0	0
$484$	−0.857576	−0.0389807
$485$	−34.0904	−1.54797
$486$	1.06884	0.0484837
$487$	−20.1247	−0.911936	−0.455968	−	0.889996i	$-0.650707\pi$
$487$	−20.1247	−0.911936	−0.455968	+	0.889996i	$0.650707\pi$
$488$	37.7799	1.71022
$489$	−9.91501	−0.448372
$490$	0	0
$491$	15.0288	0.678238	0.339119	−	0.940743i	$-0.389871\pi$
$491$	15.0288	0.678238	0.339119	+	0.940743i	$0.389871\pi$
$492$	−5.89768	−0.265888
$493$	9.16603	0.412817
$494$	−22.3493	−1.00554
$495$	−2.69184	−0.120989
$496$	−5.97698	−0.268374
$497$	0	0
$498$	2.63914	0.118263
$499$	2.14242	0.0959081	0.0479540	−	0.998850i	$-0.484730\pi$
$499$	2.14242	0.0959081	0.0479540	+	0.998850i	$0.484730\pi$
$500$	−6.35751	−0.284316
$501$	0.193790	0.00865792
$502$	5.51519	0.246155
$503$	6.30359	0.281063	0.140532	−	0.990076i	$-0.455119\pi$
$503$	6.30359	0.281063	0.140532	+	0.990076i	$0.455119\pi$
$504$	0	0
$505$	14.7427	0.656044
$506$	1.65608	0.0736217
$507$	2.18328	0.0969627
$508$	−10.8870	−0.483031
$509$	−24.7033	−1.09495	−0.547477	−	0.836820i	$-0.684412\pi$
$509$	−24.7033	−1.09495	−0.547477	+	0.836820i	$0.684412\pi$
$510$	3.07522	0.136173
$511$	0	0
$512$	16.3635	0.723173
$513$	6.35772	0.280700
$514$	−15.8439	−0.698846
$515$	17.0300	0.750432
$516$	−2.37181	−0.104413
$517$	−9.13295	−0.401667
$518$	0	0
$519$	−9.02818	−0.396293
$520$	27.0401	1.18579
$521$	3.65318	0.160049	0.0800244	−	0.996793i	$-0.474500\pi$
$521$	3.65318	0.160049	0.0800244	+	0.996793i	$0.474500\pi$
$522$	9.16603	0.401186
$523$	−7.66278	−0.335070	−0.167535	−	0.985866i	$-0.553581\pi$
$523$	−7.66278	−0.335070	−0.167535	+	0.985866i	$0.553581\pi$
$524$	−5.61341	−0.245223
$525$	0	0
$526$	−16.5338	−0.720907
$527$	−4.12314	−0.179607
$528$	1.54941	0.0674296
$529$	−20.5993	−0.895623
$530$	−10.2267	−0.444218
$531$	−1.54941	−0.0672388
$532$	0	0
$533$	22.6181	0.979699
$534$	−12.4306	−0.537924
$535$	9.43978	0.408117
$536$	−24.7516	−1.06911
$537$	−12.2243	−0.527517
$538$	6.32159	0.272543
$539$	0	0
$540$	−2.30845	−0.0993400
$541$	−14.4857	−0.622787	−0.311394	−	0.950281i	$-0.600796\pi$
$541$	−14.4857	−0.622787	−0.311394	+	0.950281i	$0.600796\pi$
$542$	9.92977	0.426520
$543$	18.5108	0.794376
$544$	4.75904	0.204042
$545$	−10.2558	−0.439309
$546$	0	0
$547$	6.15312	0.263089	0.131544	−	0.991310i	$-0.458006\pi$
$547$	6.15312	0.263089	0.131544	+	0.991310i	$0.458006\pi$
$548$	−18.3636	−0.784453
$549$	12.3694	0.527914
$550$	−2.40061	−0.102362
$551$	54.5217	2.32270
$552$	4.73237	0.201423
$553$	0	0
$554$	−10.2253	−0.434429
$555$	21.0758	0.894618
$556$	−0.729715	−0.0309468
$557$	−19.8018	−0.839030	−0.419515	−	0.907748i	$-0.637800\pi$
$557$	−19.8018	−0.839030	−0.419515	+	0.907748i	$0.637800\pi$
$558$	−4.12314	−0.174546
$559$	9.09609	0.384724
$560$	0	0
$561$	1.06884	0.0451266
$562$	13.9010	0.586379
$563$	5.84416	0.246302	0.123151	−	0.992388i	$-0.460700\pi$
$563$	5.84416	0.246302	0.123151	+	0.992388i	$0.460700\pi$
$564$	−7.83219	−0.329795
$565$	−29.9653	−1.26065
$566$	−25.8912	−1.08829
$567$	0	0
$568$	31.8717	1.33731
$569$	−34.3484	−1.43996	−0.719979	−	0.693996i	$-0.755849\pi$
$569$	−34.3484	−1.43996	−0.719979	+	0.693996i	$0.755849\pi$
$570$	18.2921	0.766173
$571$	9.65620	0.404100	0.202050	−	0.979375i	$-0.435240\pi$
$571$	9.65620	0.404100	0.202050	+	0.979375i	$0.435240\pi$
$572$	2.82046	0.117929
$573$	−18.4655	−0.771409
$574$	0	0
$575$	−3.47997	−0.145125
$576$	7.85787	0.327411
$577$	−34.6524	−1.44260	−0.721299	−	0.692624i	$-0.756455\pi$
$577$	−34.6524	−1.44260	−0.721299	+	0.692624i	$0.756455\pi$
$578$	16.9493	0.704996
$579$	17.0420	0.708240
$580$	−19.7965	−0.822006
$581$	0	0
$582$	13.5362	0.561094
$583$	−3.55444	−0.147210
$584$	43.5238	1.80103
$585$	8.85313	0.366032
$586$	−3.26008	−0.134673
$587$	−15.4442	−0.637451	−0.318726	−	0.947847i	$-0.603255\pi$
$587$	−15.4442	−0.637451	−0.318726	+	0.947847i	$0.603255\pi$
$588$	0	0
$589$	−24.5254	−1.01055
$590$	−4.45790	−0.183529
$591$	−5.45281	−0.224299
$592$	−12.1312	−0.498588
$593$	−5.56789	−0.228646	−0.114323	−	0.993444i	$-0.536470\pi$
$593$	−5.56789	−0.228646	−0.114323	+	0.993444i	$0.536470\pi$
$594$	1.06884	0.0438551
$595$	0	0
$596$	13.5362	0.554465
$597$	−4.33148	−0.177275
$598$	−5.44664	−0.222730
$599$	27.5490	1.12562	0.562810	−	0.826586i	$-0.309720\pi$
$599$	27.5490	1.12562	0.562810	+	0.826586i	$0.309720\pi$
$600$	−6.85992	−0.280055
$601$	15.6408	0.638000	0.319000	−	0.947755i	$-0.396653\pi$
$601$	15.6408	0.638000	0.319000	+	0.947755i	$0.396653\pi$
$602$	0	0
$603$	−8.10386	−0.330015
$604$	14.6297	0.595274
$605$	−2.69184	−0.109439
$606$	−5.85387	−0.237797
$607$	11.4510	0.464782	0.232391	−	0.972623i	$-0.425345\pi$
$607$	11.4510	0.464782	0.232391	+	0.972623i	$0.425345\pi$
$608$	28.3079	1.14804
$609$	0	0
$610$	35.5887	1.44094
$611$	30.0372	1.21517
$612$	0.916613	0.0370519
$613$	14.9151	0.602415	0.301208	−	0.953559i	$-0.402610\pi$
$613$	14.9151	0.602415	0.301208	+	0.953559i	$0.402610\pi$
$614$	−21.9384	−0.885362
$615$	−18.5122	−0.746483
$616$	0	0
$617$	27.8601	1.12161	0.560803	−	0.827949i	$-0.310493\pi$
$617$	27.8601	1.12161	0.560803	+	0.827949i	$0.310493\pi$
$618$	−6.76207	−0.272010
$619$	1.29794	0.0521686	0.0260843	−	0.999660i	$-0.491696\pi$
$619$	1.29794	0.0521686	0.0260843	+	0.999660i	$0.491696\pi$
$620$	8.90504	0.357635
$621$	1.54941	0.0621758
$622$	−8.54577	−0.342654
$623$	0	0
$624$	−5.09583	−0.203997
$625$	−31.1855	−1.24742
$626$	−17.0103	−0.679869
$627$	6.35772	0.253903
$628$	15.6240	0.623466
$629$	−8.36853	−0.333675
$630$	0	0
$631$	45.9952	1.83104	0.915519	−	0.402274i	$-0.131780\pi$
$631$	45.9952	1.83104	0.915519	+	0.402274i	$0.131780\pi$
$632$	28.6720	1.14051
$633$	−26.0751	−1.03639
$634$	−28.6359	−1.13728
$635$	−34.1730	−1.35612
$636$	−3.04820	−0.120869
$637$	0	0
$638$	9.16603	0.362887
$639$	10.4350	0.412804
$640$	−1.36264	−0.0538632
$641$	−2.52448	−0.0997110	−0.0498555	−	0.998756i	$-0.515876\pi$
$641$	−2.52448	−0.0997110	−0.0498555	+	0.998756i	$0.515876\pi$
$642$	−3.74823	−0.147931
$643$	22.1800	0.874692	0.437346	−	0.899293i	$-0.355919\pi$
$643$	22.1800	0.874692	0.437346	+	0.899293i	$0.355919\pi$
$644$	0	0
$645$	−7.44485	−0.293141
$646$	−7.26322	−0.285767
$647$	23.2965	0.915879	0.457940	−	0.888983i	$-0.348588\pi$
$647$	23.2965	0.915879	0.457940	+	0.888983i	$0.348588\pi$
$648$	3.05430	0.119984
$649$	−1.54941	−0.0608198
$650$	7.89532	0.309680
$651$	0	0
$652$	−8.50287	−0.332998
$653$	37.2377	1.45722	0.728611	−	0.684927i	$-0.240166\pi$
$653$	37.2377	1.45722	0.728611	+	0.684927i	$0.240166\pi$
$654$	4.07223	0.159237
$655$	−17.6199	−0.688466
$656$	10.6555	0.416029
$657$	14.2500	0.555946
$658$	0	0
$659$	−13.8016	−0.537632	−0.268816	−	0.963192i	$-0.586632\pi$
$659$	−13.8016	−0.537632	−0.268816	+	0.963192i	$0.586632\pi$
$660$	−2.30845	−0.0898565
$661$	26.9350	1.04765	0.523825	−	0.851826i	$-0.324505\pi$
$661$	26.9350	1.04765	0.523825	+	0.851826i	$0.324505\pi$
$662$	10.8196	0.420514
$663$	−3.51529	−0.136523
$664$	7.54155	0.292669
$665$	0	0
$666$	−8.36853	−0.324274
$667$	13.2872	0.514484
$668$	0.166190	0.00643008
$669$	−13.3681	−0.516842
$670$	−23.3160	−0.900776
$671$	12.3694	0.477516
$672$	0	0
$673$	24.7186	0.952832	0.476416	−	0.879220i	$-0.341936\pi$
$673$	24.7186	0.952832	0.476416	+	0.879220i	$0.341936\pi$
$674$	−1.45939	−0.0562136
$675$	−2.24599	−0.0864482
$676$	1.87232	0.0720125
$677$	−24.8668	−0.955708	−0.477854	−	0.878439i	$-0.658585\pi$
$677$	−24.8668	−0.955708	−0.477854	+	0.878439i	$0.658585\pi$
$678$	11.8983	0.456950
$679$	0	0
$680$	8.78768	0.336992
$681$	22.7579	0.872084
$682$	−4.12314	−0.157883
$683$	6.12052	0.234195	0.117098	−	0.993120i	$-0.462641\pi$
$683$	6.12052	0.234195	0.117098	+	0.993120i	$0.462641\pi$
$684$	5.45223	0.208471
$685$	−57.6413	−2.20236
$686$	0	0
$687$	−25.5630	−0.975291
$688$	4.28523	0.163373
$689$	11.6901	0.445359
$690$	4.45790	0.169709
$691$	12.4832	0.474885	0.237443	−	0.971402i	$-0.423691\pi$
$691$	12.4832	0.474885	0.237443	+	0.971402i	$0.423691\pi$
$692$	−7.74234	−0.294320
$693$	0	0
$694$	27.0500	1.02680
$695$	−2.29050	−0.0868835
$696$	26.1926	0.992829
$697$	7.35059	0.278424
$698$	5.86780	0.222099
$699$	22.4676	0.849804
$700$	0	0
$701$	−28.0867	−1.06082	−0.530409	−	0.847742i	$-0.677962\pi$
$701$	−28.0867	−1.06082	−0.530409	+	0.847742i	$0.677962\pi$
$702$	−3.51529	−0.132676
$703$	−49.7779	−1.87741
$704$	7.85787	0.296155
$705$	−24.5844	−0.925902
$706$	−18.5377	−0.697675
$707$	0	0
$708$	−1.32874	−0.0499371
$709$	−13.7626	−0.516866	−0.258433	−	0.966029i	$-0.583206\pi$
$709$	−13.7626	−0.516866	−0.258433	+	0.966029i	$0.583206\pi$
$710$	30.0232	1.12675
$711$	9.38741	0.352056
$712$	−35.5214	−1.33122
$713$	−5.97698	−0.223840
$714$	0	0
$715$	8.85313	0.331088
$716$	−10.4833	−0.391778
$717$	13.1701	0.491845
$718$	−10.2025	−0.380754
$719$	30.6448	1.14286	0.571430	−	0.820651i	$-0.306389\pi$
$719$	30.6448	1.14286	0.571430	+	0.820651i	$0.306389\pi$
$720$	4.17077	0.155435
$721$	0	0
$722$	−22.8953	−0.852074
$723$	−14.5507	−0.541148
$724$	15.8744	0.589969
$725$	−19.2608	−0.715330
$726$	1.06884	0.0396685
$727$	28.8508	1.07002	0.535009	−	0.844846i	$-0.320308\pi$
$727$	28.8508	1.07002	0.535009	+	0.844846i	$0.320308\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	40.9995	1.51746
$731$	2.95611	0.109336
$732$	10.6077	0.392072
$733$	8.05237	0.297421	0.148710	−	0.988881i	$-0.452488\pi$
$733$	8.05237	0.297421	0.148710	+	0.988881i	$0.452488\pi$
$734$	−7.07301	−0.261070
$735$	0	0
$736$	6.89879	0.254293
$737$	−8.10386	−0.298509
$738$	7.35059	0.270579
$739$	−15.4562	−0.568567	−0.284283	−	0.958740i	$-0.591756\pi$
$739$	−15.4562	−0.568567	−0.284283	+	0.958740i	$0.591756\pi$
$740$	18.0741	0.664417
$741$	−20.9098	−0.768140
$742$	0	0
$743$	14.1256	0.518216	0.259108	−	0.965848i	$-0.416571\pi$
$743$	14.1256	0.518216	0.259108	+	0.965848i	$0.416571\pi$
$744$	−11.7822	−0.431956
$745$	42.4887	1.55667
$746$	34.9672	1.28024
$747$	2.46916	0.0903419
$748$	0.916613	0.0335147
$749$	0	0
$750$	7.92370	0.289333
$751$	1.87053	0.0682568	0.0341284	−	0.999417i	$-0.489134\pi$
$751$	1.87053	0.0682568	0.0341284	+	0.999417i	$0.489134\pi$
$752$	14.1507	0.516023
$753$	5.15996	0.188039
$754$	−30.1460	−1.09785
$755$	45.9210	1.67124
$756$	0	0
$757$	2.68353	0.0975345	0.0487672	−	0.998810i	$-0.484471\pi$
$757$	2.68353	0.0975345	0.0487672	+	0.998810i	$0.484471\pi$
$758$	8.22309	0.298676
$759$	1.54941	0.0562401
$760$	52.2711	1.89607
$761$	26.2059	0.949963	0.474981	−	0.879996i	$-0.342455\pi$
$761$	26.2059	0.949963	0.474981	+	0.879996i	$0.342455\pi$
$762$	13.5690	0.491554
$763$	0	0
$764$	−15.8356	−0.572912
$765$	2.87715	0.104024
$766$	6.90265	0.249403
$767$	5.09583	0.184000
$768$	16.2568	0.586617
$769$	−14.9106	−0.537689	−0.268844	−	0.963184i	$-0.586642\pi$
$769$	−14.9106	−0.537689	−0.268844	+	0.963184i	$0.586642\pi$
$770$	0	0
$771$	−14.8235	−0.533854
$772$	14.6148	0.525998
$773$	11.0130	0.396112	0.198056	−	0.980191i	$-0.436537\pi$
$773$	11.0130	0.396112	0.198056	+	0.980191i	$0.436537\pi$
$774$	2.95611	0.106255
$775$	8.66408	0.311223
$776$	38.6808	1.38856
$777$	0	0
$778$	−5.90595	−0.211739
$779$	43.7230	1.56654
$780$	7.59223	0.271845
$781$	10.4350	0.373395
$782$	−1.77009	−0.0632982
$783$	8.57566	0.306469
$784$	0	0
$785$	49.0421	1.75039
$786$	6.99630	0.249550
$787$	−41.1852	−1.46809	−0.734046	−	0.679099i	$-0.762370\pi$
$787$	−41.1852	−1.46809	−0.734046	+	0.679099i	$0.762370\pi$
$788$	−4.67620	−0.166583
$789$	−15.4689	−0.550706
$790$	27.0090	0.960937
$791$	0	0
$792$	3.05430	0.108530
$793$	−40.6815	−1.44464
$794$	−34.7861	−1.23451
$795$	−9.56799	−0.339342
$796$	−3.71457	−0.131659
$797$	−21.5389	−0.762947	−0.381473	−	0.924380i	$-0.624583\pi$
$797$	−21.5389	−0.762947	−0.381473	+	0.924380i	$0.624583\pi$
$798$	0	0
$799$	9.76168	0.345343
$800$	−10.0003	−0.353564
$801$	−11.6300	−0.410924
$802$	34.3959	1.21456
$803$	14.2500	0.502872
$804$	−6.94967	−0.245096
$805$	0	0
$806$	13.5605	0.477649
$807$	5.91442	0.208198
$808$	−16.7279	−0.588485
$809$	−28.8671	−1.01491	−0.507456	−	0.861677i	$-0.669414\pi$
$809$	−28.8671	−1.01491	−0.507456	+	0.861677i	$0.669414\pi$
$810$	2.87715	0.101093
$811$	−19.7341	−0.692959	−0.346480	−	0.938057i	$-0.612623\pi$
$811$	−19.7341	−0.692959	−0.346480	+	0.938057i	$0.612623\pi$
$812$	0	0
$813$	9.29021	0.325822
$814$	−8.36853	−0.293317
$815$	−26.6896	−0.934896
$816$	−1.65608	−0.0579744
$817$	17.5836	0.615173
$818$	2.33069	0.0814907
$819$	0	0
$820$	−15.8756	−0.554400
$821$	−2.33854	−0.0816157	−0.0408079	−	0.999167i	$-0.512993\pi$
$821$	−2.33854	−0.0816157	−0.0408079	+	0.999167i	$0.512993\pi$
$822$	22.8875	0.798293
$823$	39.4889	1.37650	0.688248	−	0.725476i	$-0.258380\pi$
$823$	39.4889	1.37650	0.688248	+	0.725476i	$0.258380\pi$
$824$	−19.3231	−0.673153
$825$	−2.24599	−0.0781953
$826$	0	0
$827$	−8.04663	−0.279809	−0.139904	−	0.990165i	$-0.544679\pi$
$827$	−8.04663	−0.279809	−0.139904	+	0.990165i	$0.544679\pi$
$828$	1.32874	0.0461769
$829$	7.01026	0.243477	0.121738	−	0.992562i	$-0.461153\pi$
$829$	7.01026	0.243477	0.121738	+	0.992562i	$0.461153\pi$
$830$	7.10415	0.246589
$831$	−9.56666	−0.331864
$832$	−25.8436	−0.895965
$833$	0	0
$834$	0.909484	0.0314928
$835$	0.521652	0.0180525
$836$	5.45223	0.188569
$837$	−3.85758	−0.133337
$838$	39.2668	1.35645
$839$	22.4205	0.774043	0.387021	−	0.922071i	$-0.373504\pi$
$839$	22.4205	0.774043	0.387021	+	0.922071i	$0.373504\pi$
$840$	0	0
$841$	44.5419	1.53593
$842$	39.1665	1.34977
$843$	13.0057	0.447939
$844$	−22.3614	−0.769710
$845$	5.87702	0.202176
$846$	9.76168	0.335614
$847$	0	0
$848$	5.50730	0.189122
$849$	−24.2236	−0.831351
$850$	2.56587	0.0880088
$851$	−12.1312	−0.415851
$852$	8.94884	0.306582
$853$	−36.0726	−1.23510	−0.617551	−	0.786531i	$-0.711875\pi$
$853$	−36.0726	−1.23510	−0.617551	+	0.786531i	$0.711875\pi$
$854$	0	0
$855$	17.1140	0.585285
$856$	−10.7109	−0.366090
$857$	28.9136	0.987669	0.493835	−	0.869556i	$-0.335595\pi$
$857$	28.9136	0.987669	0.493835	+	0.869556i	$0.335595\pi$
$858$	−3.51529	−0.120010
$859$	−29.1333	−0.994016	−0.497008	−	0.867746i	$-0.665568\pi$
$859$	−29.1333	−0.994016	−0.497008	+	0.867746i	$0.665568\pi$
$860$	−6.38452	−0.217710
$861$	0	0
$862$	−27.6063	−0.940275
$863$	48.6478	1.65599	0.827995	−	0.560736i	$-0.189482\pi$
$863$	48.6478	1.65599	0.827995	+	0.560736i	$0.189482\pi$
$864$	4.45252	0.151478
$865$	−24.3024	−0.826306
$866$	5.14357	0.174785
$867$	15.8576	0.538551
$868$	0	0
$869$	9.38741	0.318446
$870$	24.6735	0.836509
$871$	26.6526	0.903089
$872$	11.6367	0.394069
$873$	12.6644	0.428624
$874$	−10.5289	−0.356145
$875$	0	0
$876$	12.2205	0.412891
$877$	10.5092	0.354870	0.177435	−	0.984133i	$-0.443220\pi$
$877$	10.5092	0.354870	0.177435	+	0.984133i	$0.443220\pi$
$878$	−29.1645	−0.984253
$879$	−3.05010	−0.102877
$880$	4.17077	0.140597
$881$	−18.6650	−0.628841	−0.314420	−	0.949284i	$-0.601810\pi$
$881$	−18.6650	−0.628841	−0.314420	+	0.949284i	$0.601810\pi$
$882$	0	0
$883$	26.2974	0.884980	0.442490	−	0.896774i	$-0.354095\pi$
$883$	26.2974	0.884980	0.442490	+	0.896774i	$0.354095\pi$
$884$	−3.01463	−0.101393
$885$	−4.17077	−0.140199
$886$	28.9985	0.974223
$887$	−46.7766	−1.57060	−0.785302	−	0.619112i	$-0.787493\pi$
$887$	−46.7766	−1.57060	−0.785302	+	0.619112i	$0.787493\pi$
$888$	−23.9137	−0.802491
$889$	0	0
$890$	−33.4611	−1.12162
$891$	1.00000	0.0335013
$892$	−11.4642	−0.383849
$893$	58.0647	1.94306
$894$	−16.8709	−0.564248
$895$	−32.9058	−1.09992
$896$	0	0
$897$	−5.09583	−0.170145
$898$	−4.56970	−0.152493
$899$	−33.0813	−1.10332
$900$	−1.92611	−0.0642035
$901$	3.79914	0.126568
$902$	7.35059	0.244748
$903$	0	0
$904$	34.0002	1.13083
$905$	49.8282	1.65635
$906$	−18.2338	−0.605777
$907$	40.7553	1.35326	0.676629	−	0.736324i	$-0.263440\pi$
$907$	40.7553	1.35326	0.676629	+	0.736324i	$0.263440\pi$
$908$	19.5166	0.647681
$909$	−5.47683	−0.181655
$910$	0	0
$911$	−14.9736	−0.496099	−0.248050	−	0.968747i	$-0.579790\pi$
$911$	−14.9736	−0.496099	−0.248050	+	0.968747i	$0.579790\pi$
$912$	−9.85074	−0.326191
$913$	2.46916	0.0817173
$914$	−31.1028	−1.02879
$915$	33.2965	1.10075
$916$	−21.9222	−0.724331
$917$	0	0
$918$	−1.14242	−0.0377056
$919$	−33.9815	−1.12095	−0.560473	−	0.828173i	$-0.689381\pi$
$919$	−33.9815	−1.12095	−0.560473	+	0.828173i	$0.689381\pi$
$920$	12.7388	0.419985
$921$	−20.5254	−0.676335
$922$	3.17417	0.104536
$923$	−34.3196	−1.12964
$924$	0	0
$925$	17.5850	0.578192
$926$	21.7056	0.713290
$927$	−6.32653	−0.207791
$928$	38.1833	1.25343
$929$	−52.0737	−1.70848	−0.854241	−	0.519878i	$-0.825977\pi$
$929$	−52.0737	−1.70848	−0.854241	+	0.519878i	$0.825977\pi$
$930$	−11.0988	−0.363945
$931$	0	0
$932$	19.2677	0.631135
$933$	−7.99535	−0.261756
$934$	−39.6914	−1.29874
$935$	2.87715	0.0940929
$936$	−10.0452	−0.328338
$937$	−50.0381	−1.63467	−0.817336	−	0.576161i	$-0.804550\pi$
$937$	−50.0381	−1.63467	−0.817336	+	0.576161i	$0.804550\pi$
$938$	0	0
$939$	−15.9147	−0.519357
$940$	−21.0830	−0.687651
$941$	25.4304	0.829007	0.414504	−	0.910048i	$-0.363955\pi$
$941$	25.4304	0.829007	0.414504	+	0.910048i	$0.363955\pi$
$942$	−19.4730	−0.634466
$943$	10.6555	0.346992
$944$	2.40068	0.0781355
$945$	0	0
$946$	2.95611	0.0961114
$947$	20.7035	0.672774	0.336387	−	0.941724i	$-0.390795\pi$
$947$	20.7035	0.672774	0.336387	+	0.941724i	$0.390795\pi$
$948$	8.05042	0.261465
$949$	−46.8666	−1.52135
$950$	15.2624	0.495178
$951$	−26.7915	−0.868775
$952$	0	0
$953$	−4.08220	−0.132235	−0.0661177	−	0.997812i	$-0.521061\pi$
$953$	−4.08220	−0.132235	−0.0661177	+	0.997812i	$0.521061\pi$
$954$	3.79914	0.123002
$955$	−49.7063	−1.60846
$956$	11.2943	0.365284
$957$	8.57566	0.277212
$958$	−19.6332	−0.634319
$959$	0	0
$960$	21.1521	0.682681
$961$	−16.1191	−0.519971
$962$	27.5231	0.887379
$963$	−3.50682	−0.113006
$964$	−12.4784	−0.401901
$965$	45.8742	1.47674
$966$	0	0
$967$	−20.6016	−0.662503	−0.331251	−	0.943543i	$-0.607471\pi$
$967$	−20.6016	−0.662503	−0.331251	+	0.943543i	$0.607471\pi$
$968$	3.05430	0.0981689
$969$	−6.79540	−0.218300
$970$	36.4373	1.16993
$971$	−26.2802	−0.843370	−0.421685	−	0.906742i	$-0.638561\pi$
$971$	−26.2802	−0.843370	−0.421685	+	0.906742i	$0.638561\pi$
$972$	0.857576	0.0275067
$973$	0	0
$974$	21.5101	0.689228
$975$	7.38679	0.236567
$976$	−19.1653	−0.613468
$977$	29.1791	0.933523	0.466761	−	0.884383i	$-0.345421\pi$
$977$	29.1791	0.933523	0.466761	+	0.884383i	$0.345421\pi$
$978$	10.5976	0.338873
$979$	−11.6300	−0.371695
$980$	0	0
$981$	3.80995	0.121642
$982$	−16.0634	−0.512603
$983$	46.2067	1.47377	0.736883	−	0.676020i	$-0.236297\pi$
$983$	46.2067	1.47377	0.736883	+	0.676020i	$0.236297\pi$
$984$	21.0049	0.669611
$985$	−14.6781	−0.467682
$986$	−9.79704	−0.312001
$987$	0	0
$988$	−17.9317	−0.570484
$989$	4.28523	0.136262
$990$	2.87715	0.0914419
$991$	−31.5650	−1.00270	−0.501348	−	0.865245i	$-0.667163\pi$
$991$	−31.5650	−1.00270	−0.501348	+	0.865245i	$0.667163\pi$
$992$	−17.1759	−0.545336
$993$	10.1227	0.321234
$994$	0	0
$995$	−11.6596	−0.369635
$996$	2.11749	0.0670953
$997$	18.0835	0.572711	0.286356	−	0.958123i	$-0.407556\pi$
$997$	18.0835	0.572711	0.286356	+	0.958123i	$0.407556\pi$
$998$	−2.28991	−0.0724860
$999$	−7.82952	−0.247715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.ba.1.2		5
3.2	odd	2		4851.2.a.ca.1.4		5
7.2	even	3		231.2.i.f.67.4	✓	10
7.4	even	3		231.2.i.f.100.4	yes	10
7.6	odd	2		1617.2.a.bb.1.2		5
21.2	odd	6		693.2.i.j.298.2		10
21.11	odd	6		693.2.i.j.100.2		10
21.20	even	2		4851.2.a.bz.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.f.67.4	✓	10	7.2	even	3
231.2.i.f.100.4	yes	10	7.4	even	3
693.2.i.j.100.2		10	21.11	odd	6
693.2.i.j.298.2		10	21.2	odd	6
1617.2.a.ba.1.2		5	1.1	even	1	trivial
1617.2.a.bb.1.2		5	7.6	odd	2
4851.2.a.bz.1.4		5	21.20	even	2
4851.2.a.ca.1.4		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-1.06884 q^{2} -1.00000 q^{3} -0.857576 q^{4} -2.69184 q^{5} +1.06884 q^{6} +3.05430 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.06884 q^{2} -1.00000 q^{3} -0.857576 q^{4} -2.69184 q^{5} +1.06884 q^{6} +3.05430 q^{8} +1.00000 q^{9} +2.87715 q^{10} +1.00000 q^{11} +0.857576 q^{12} -3.28888 q^{13} +2.69184 q^{15} -1.54941 q^{16} -1.06884 q^{17} -1.06884 q^{18} -6.35772 q^{19} +2.30845 q^{20} -1.06884 q^{22} -1.54941 q^{23} -3.05430 q^{24} +2.24599 q^{25} +3.51529 q^{26} -1.00000 q^{27} -8.57566 q^{29} -2.87715 q^{30} +3.85758 q^{31} -4.45252 q^{32} -1.00000 q^{33} +1.14242 q^{34} -0.857576 q^{36} +7.82952 q^{37} +6.79540 q^{38} +3.28888 q^{39} -8.22168 q^{40} -6.87715 q^{41} -2.76571 q^{43} -0.857576 q^{44} -2.69184 q^{45} +1.65608 q^{46} -9.13295 q^{47} +1.54941 q^{48} -2.40061 q^{50} +1.06884 q^{51} +2.82046 q^{52} -3.55444 q^{53} +1.06884 q^{54} -2.69184 q^{55} +6.35772 q^{57} +9.16603 q^{58} -1.54941 q^{59} -2.30845 q^{60} +12.3694 q^{61} -4.12314 q^{62} +7.85787 q^{64} +8.85313 q^{65} +1.06884 q^{66} -8.10386 q^{67} +0.916613 q^{68} +1.54941 q^{69} +10.4350 q^{71} +3.05430 q^{72} +14.2500 q^{73} -8.36853 q^{74} -2.24599 q^{75} +5.45223 q^{76} -3.51529 q^{78} +9.38741 q^{79} +4.17077 q^{80} +1.00000 q^{81} +7.35059 q^{82} +2.46916 q^{83} +2.87715 q^{85} +2.95611 q^{86} +8.57566 q^{87} +3.05430 q^{88} -11.6300 q^{89} +2.87715 q^{90} +1.32874 q^{92} -3.85758 q^{93} +9.76168 q^{94} +17.1140 q^{95} +4.45252 q^{96} +12.6644 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} - 5 q^{3} + 10 q^{4} - 4 q^{5} - 2 q^{6} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 - 5 * q^3 + 10 * q^4 - 4 * q^5 - 2 * q^6 + 6 * q^8 + 5 * q^9	\( 5 q + 2 q^{2} - 5 q^{3} + 10 q^{4} - 4 q^{5} - 2 q^{6} + 6 q^{8} + 5 q^{9} + 2 q^{10} + 5 q^{11} - 10 q^{12} + 5 q^{13} + 4 q^{15} + 16 q^{16} + 2 q^{17} + 2 q^{18} - 3 q^{19} - 8 q^{20} + 2 q^{22} + 16 q^{23} - 6 q^{24} + 7 q^{25} - 10 q^{26} - 5 q^{27} - 2 q^{30} + 5 q^{31} + 4 q^{32} - 5 q^{33} + 20 q^{34} + 10 q^{36} + 15 q^{37} + 6 q^{38} - 5 q^{39} - 6 q^{40} - 22 q^{41} + 3 q^{43} + 10 q^{44} - 4 q^{45} + 16 q^{46} - 2 q^{47} - 16 q^{48} + 34 q^{50} - 2 q^{51} + 40 q^{52} + 6 q^{53} - 2 q^{54} - 4 q^{55} + 3 q^{57} + 12 q^{58} + 16 q^{59} + 8 q^{60} + 12 q^{61} - 4 q^{62} - 4 q^{64} - 28 q^{65} - 2 q^{66} + 7 q^{67} + 10 q^{68} - 16 q^{69} + 24 q^{71} + 6 q^{72} + 17 q^{73} - 36 q^{74} - 7 q^{75} + 30 q^{76} + 10 q^{78} + 7 q^{79} + 16 q^{80} + 5 q^{81} + 8 q^{82} - 12 q^{83} + 2 q^{85} - 18 q^{86} + 6 q^{88} - 6 q^{89} + 2 q^{90} + 68 q^{92} - 5 q^{93} + 82 q^{94} - 18 q^{95} - 4 q^{96} - 14 q^{97} + 5 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - 5 * q^3 + 10 * q^4 - 4 * q^5 - 2 * q^6 + 6 * q^8 + 5 * q^9 + 2 * q^10 + 5 * q^11 - 10 * q^12 + 5 * q^13 + 4 * q^15 + 16 * q^16 + 2 * q^17 + 2 * q^18 - 3 * q^19 - 8 * q^20 + 2 * q^22 + 16 * q^23 - 6 * q^24 + 7 * q^25 - 10 * q^26 - 5 * q^27 - 2 * q^30 + 5 * q^31 + 4 * q^32 - 5 * q^33 + 20 * q^34 + 10 * q^36 + 15 * q^37 + 6 * q^38 - 5 * q^39 - 6 * q^40 - 22 * q^41 + 3 * q^43 + 10 * q^44 - 4 * q^45 + 16 * q^46 - 2 * q^47 - 16 * q^48 + 34 * q^50 - 2 * q^51 + 40 * q^52 + 6 * q^53 - 2 * q^54 - 4 * q^55 + 3 * q^57 + 12 * q^58 + 16 * q^59 + 8 * q^60 + 12 * q^61 - 4 * q^62 - 4 * q^64 - 28 * q^65 - 2 * q^66 + 7 * q^67 + 10 * q^68 - 16 * q^69 + 24 * q^71 + 6 * q^72 + 17 * q^73 - 36 * q^74 - 7 * q^75 + 30 * q^76 + 10 * q^78 + 7 * q^79 + 16 * q^80 + 5 * q^81 + 8 * q^82 - 12 * q^83 + 2 * q^85 - 18 * q^86 + 6 * q^88 - 6 * q^89 + 2 * q^90 + 68 * q^92 - 5 * q^93 + 82 * q^94 - 18 * q^95 - 4 * q^96 - 14 * q^97 + 5 * q^99

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