LMFDB - Embedded newform 1617.2.a.n.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
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			$1.41421$ 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)

$f(q)$	$=$	$q+0.414214 q^{2} +1.00000 q^{3} -1.82843 q^{4} -2.00000 q^{5} +0.414214 q^{6} -1.58579 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.414214 q^{2} +1.00000 q^{3} -1.82843 q^{4} -2.00000 q^{5} +0.414214 q^{6} -1.58579 q^{8} +1.00000 q^{9} -0.828427 q^{10} +1.00000 q^{11} -1.82843 q^{12} +4.82843 q^{13} -2.00000 q^{15} +3.00000 q^{16} -1.58579 q^{17} +0.414214 q^{18} -1.24264 q^{19} +3.65685 q^{20} +0.414214 q^{22} -7.00000 q^{23} -1.58579 q^{24} -1.00000 q^{25} +2.00000 q^{26} +1.00000 q^{27} -5.24264 q^{29} -0.828427 q^{30} -5.65685 q^{31} +4.41421 q^{32} +1.00000 q^{33} -0.656854 q^{34} -1.82843 q^{36} +7.48528 q^{37} -0.514719 q^{38} +4.82843 q^{39} +3.17157 q^{40} -6.82843 q^{41} -11.2426 q^{43} -1.82843 q^{44} -2.00000 q^{45} -2.89949 q^{46} +4.17157 q^{47} +3.00000 q^{48} -0.414214 q^{50} -1.58579 q^{51} -8.82843 q^{52} -12.8284 q^{53} +0.414214 q^{54} -2.00000 q^{55} -1.24264 q^{57} -2.17157 q^{58} +2.65685 q^{59} +3.65685 q^{60} -4.00000 q^{61} -2.34315 q^{62} -4.17157 q^{64} -9.65685 q^{65} +0.414214 q^{66} -8.82843 q^{67} +2.89949 q^{68} -7.00000 q^{69} -9.82843 q^{71} -1.58579 q^{72} +11.6569 q^{73} +3.10051 q^{74} -1.00000 q^{75} +2.27208 q^{76} +2.00000 q^{78} -9.31371 q^{79} -6.00000 q^{80} +1.00000 q^{81} -2.82843 q^{82} +2.82843 q^{83} +3.17157 q^{85} -4.65685 q^{86} -5.24264 q^{87} -1.58579 q^{88} +14.1421 q^{89} -0.828427 q^{90} +12.7990 q^{92} -5.65685 q^{93} +1.72792 q^{94} +2.48528 q^{95} +4.41421 q^{96} +5.48528 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 4 * q^5 - 2 * q^6 - 6 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} - 6 q^{8} + 2 q^{9} + 4 q^{10} + 2 q^{11} + 2 q^{12} + 4 q^{13} - 4 q^{15} + 6 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 14 q^{23} - 6 q^{24} - 2 q^{25} + 4 q^{26} + 2 q^{27} - 2 q^{29} + 4 q^{30} + 6 q^{32} + 2 q^{33} + 10 q^{34} + 2 q^{36} - 2 q^{37} - 18 q^{38} + 4 q^{39} + 12 q^{40} - 8 q^{41} - 14 q^{43} + 2 q^{44} - 4 q^{45} + 14 q^{46} + 14 q^{47} + 6 q^{48} + 2 q^{50} - 6 q^{51} - 12 q^{52} - 20 q^{53} - 2 q^{54} - 4 q^{55} + 6 q^{57} - 10 q^{58} - 6 q^{59} - 4 q^{60} - 8 q^{61} - 16 q^{62} - 14 q^{64} - 8 q^{65} - 2 q^{66} - 12 q^{67} - 14 q^{68} - 14 q^{69} - 14 q^{71} - 6 q^{72} + 12 q^{73} + 26 q^{74} - 2 q^{75} + 30 q^{76} + 4 q^{78} + 4 q^{79} - 12 q^{80} + 2 q^{81} + 12 q^{85} + 2 q^{86} - 2 q^{87} - 6 q^{88} + 4 q^{90} - 14 q^{92} - 22 q^{94} - 12 q^{95} + 6 q^{96} - 6 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 4 * q^5 - 2 * q^6 - 6 * q^8 + 2 * q^9 + 4 * q^10 + 2 * q^11 + 2 * q^12 + 4 * q^13 - 4 * q^15 + 6 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 - 4 * q^20 - 2 * q^22 - 14 * q^23 - 6 * q^24 - 2 * q^25 + 4 * q^26 + 2 * q^27 - 2 * q^29 + 4 * q^30 + 6 * q^32 + 2 * q^33 + 10 * q^34 + 2 * q^36 - 2 * q^37 - 18 * q^38 + 4 * q^39 + 12 * q^40 - 8 * q^41 - 14 * q^43 + 2 * q^44 - 4 * q^45 + 14 * q^46 + 14 * q^47 + 6 * q^48 + 2 * q^50 - 6 * q^51 - 12 * q^52 - 20 * q^53 - 2 * q^54 - 4 * q^55 + 6 * q^57 - 10 * q^58 - 6 * q^59 - 4 * q^60 - 8 * q^61 - 16 * q^62 - 14 * q^64 - 8 * q^65 - 2 * q^66 - 12 * q^67 - 14 * q^68 - 14 * q^69 - 14 * q^71 - 6 * q^72 + 12 * q^73 + 26 * q^74 - 2 * q^75 + 30 * q^76 + 4 * q^78 + 4 * q^79 - 12 * q^80 + 2 * q^81 + 12 * q^85 + 2 * q^86 - 2 * q^87 - 6 * q^88 + 4 * q^90 - 14 * q^92 - 22 * q^94 - 12 * q^95 + 6 * q^96 - 6 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.414214	0.292893	0.146447	−	0.989219i	$-0.453216\pi$
$2$	0.414214	0.292893	0.146447	+	0.989219i	$0.453216\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.82843	−0.914214
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	0.414214	0.169102
$7$	0	0
$7$	0	0
$8$	−1.58579	−0.560660
$9$	1.00000	0.333333
$10$	−0.828427	−0.261972
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.82843	−0.527821
$13$	4.82843	1.33916	0.669582	−	0.742738i	$-0.266473\pi$
$13$	4.82843	1.33916	0.669582	+	0.742738i	$0.266473\pi$
$14$	0	0
$15$	−2.00000	−0.516398
$16$	3.00000	0.750000
$17$	−1.58579	−0.384610	−0.192305	−	0.981335i	$-0.561596\pi$
$17$	−1.58579	−0.384610	−0.192305	+	0.981335i	$0.561596\pi$
$18$	0.414214	0.0976311
$19$	−1.24264	−0.285081	−0.142541	−	0.989789i	$-0.545527\pi$
$19$	−1.24264	−0.285081	−0.142541	+	0.989789i	$0.545527\pi$
$20$	3.65685	0.817697
$21$	0	0
$22$	0.414214	0.0883106
$23$	−7.00000	−1.45960	−0.729800	−	0.683660i	$-0.760387\pi$
$23$	−7.00000	−1.45960	−0.729800	+	0.683660i	$0.760387\pi$
$24$	−1.58579	−0.323697
$25$	−1.00000	−0.200000
$26$	2.00000	0.392232
$27$	1.00000	0.192450
$28$	0	0
$29$	−5.24264	−0.973534	−0.486767	−	0.873532i	$-0.661824\pi$
$29$	−5.24264	−0.973534	−0.486767	+	0.873532i	$0.661824\pi$
$30$	−0.828427	−0.151249
$31$	−5.65685	−1.01600	−0.508001	−	0.861357i	$-0.669615\pi$
$31$	−5.65685	−1.01600	−0.508001	+	0.861357i	$0.669615\pi$
$32$	4.41421	0.780330
$33$	1.00000	0.174078
$34$	−0.656854	−0.112650
$35$	0	0
$36$	−1.82843	−0.304738
$37$	7.48528	1.23057	0.615286	−	0.788304i	$-0.289040\pi$
$37$	7.48528	1.23057	0.615286	+	0.788304i	$0.289040\pi$
$38$	−0.514719	−0.0834984
$39$	4.82843	0.773167
$40$	3.17157	0.501470
$41$	−6.82843	−1.06642	−0.533211	−	0.845983i	$-0.679015\pi$
$41$	−6.82843	−1.06642	−0.533211	+	0.845983i	$0.679015\pi$
$42$	0	0
$43$	−11.2426	−1.71449	−0.857243	−	0.514912i	$-0.827825\pi$
$43$	−11.2426	−1.71449	−0.857243	+	0.514912i	$0.827825\pi$
$44$	−1.82843	−0.275646
$45$	−2.00000	−0.298142
$46$	−2.89949	−0.427507
$47$	4.17157	0.608486	0.304243	−	0.952594i	$-0.401596\pi$
$47$	4.17157	0.608486	0.304243	+	0.952594i	$0.401596\pi$
$48$	3.00000	0.433013
$49$	0	0
$50$	−0.414214	−0.0585786
$51$	−1.58579	−0.222055
$52$	−8.82843	−1.22428
$53$	−12.8284	−1.76212	−0.881060	−	0.473005i	$-0.843169\pi$
$53$	−12.8284	−1.76212	−0.881060	+	0.473005i	$0.843169\pi$
$54$	0.414214	0.0563673
$55$	−2.00000	−0.269680
$56$	0	0
$57$	−1.24264	−0.164592
$58$	−2.17157	−0.285141
$59$	2.65685	0.345893	0.172946	−	0.984931i	$-0.444671\pi$
$59$	2.65685	0.345893	0.172946	+	0.984931i	$0.444671\pi$
$60$	3.65685	0.472098
$61$	−4.00000	−0.512148	−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000	−0.512148	−0.256074	+	0.966657i	$0.582429\pi$
$62$	−2.34315	−0.297580
$63$	0	0
$64$	−4.17157	−0.521447
$65$	−9.65685	−1.19779
$66$	0.414214	0.0509862
$67$	−8.82843	−1.07856	−0.539282	−	0.842125i	$-0.681304\pi$
$67$	−8.82843	−1.07856	−0.539282	+	0.842125i	$0.681304\pi$
$68$	2.89949	0.351615
$69$	−7.00000	−0.842701
$70$	0	0
$71$	−9.82843	−1.16642	−0.583210	−	0.812322i	$-0.698203\pi$
$71$	−9.82843	−1.16642	−0.583210	+	0.812322i	$0.698203\pi$
$72$	−1.58579	−0.186887
$73$	11.6569	1.36433	0.682166	−	0.731198i	$-0.261038\pi$
$73$	11.6569	1.36433	0.682166	+	0.731198i	$0.261038\pi$
$74$	3.10051	0.360426
$75$	−1.00000	−0.115470
$76$	2.27208	0.260625
$77$	0	0
$78$	2.00000	0.226455
$79$	−9.31371	−1.04787	−0.523937	−	0.851757i	$-0.675537\pi$
$79$	−9.31371	−1.04787	−0.523937	+	0.851757i	$0.675537\pi$
$80$	−6.00000	−0.670820
$81$	1.00000	0.111111
$82$	−2.82843	−0.312348
$83$	2.82843	0.310460	0.155230	−	0.987878i	$-0.450388\pi$
$83$	2.82843	0.310460	0.155230	+	0.987878i	$0.450388\pi$
$84$	0	0
$85$	3.17157	0.344005
$86$	−4.65685	−0.502162
$87$	−5.24264	−0.562070
$88$	−1.58579	−0.169045
$89$	14.1421	1.49906	0.749532	−	0.661968i	$-0.230279\pi$
$89$	14.1421	1.49906	0.749532	+	0.661968i	$0.230279\pi$
$90$	−0.828427	−0.0873239
$91$	0	0
$92$	12.7990	1.33439
$93$	−5.65685	−0.586588
$94$	1.72792	0.178222
$95$	2.48528	0.254984
$96$	4.41421	0.450524
$97$	5.48528	0.556946	0.278473	−	0.960444i	$-0.410172\pi$
$97$	5.48528	0.556946	0.278473	+	0.960444i	$0.410172\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	1.82843	0.182843
$101$	−14.8995	−1.48256	−0.741278	−	0.671199i	$-0.765780\pi$
$101$	−14.8995	−1.48256	−0.741278	+	0.671199i	$0.765780\pi$
$102$	−0.656854	−0.0650383
$103$	−4.48528	−0.441948	−0.220974	−	0.975280i	$-0.570924\pi$
$103$	−4.48528	−0.441948	−0.220974	+	0.975280i	$0.570924\pi$
$104$	−7.65685	−0.750816
$105$	0	0
$106$	−5.31371	−0.516113
$107$	−1.65685	−0.160174	−0.0800871	−	0.996788i	$-0.525520\pi$
$107$	−1.65685	−0.160174	−0.0800871	+	0.996788i	$0.525520\pi$
$108$	−1.82843	−0.175940
$109$	−1.17157	−0.112216	−0.0561082	−	0.998425i	$-0.517869\pi$
$109$	−1.17157	−0.112216	−0.0561082	+	0.998425i	$0.517869\pi$
$110$	−0.828427	−0.0789874
$111$	7.48528	0.710471
$112$	0	0
$113$	3.65685	0.344008	0.172004	−	0.985096i	$-0.444976\pi$
$113$	3.65685	0.344008	0.172004	+	0.985096i	$0.444976\pi$
$114$	−0.514719	−0.0482078
$115$	14.0000	1.30551
$116$	9.58579	0.890018
$117$	4.82843	0.446388
$118$	1.10051	0.101310
$119$	0	0
$120$	3.17157	0.289524
$121$	1.00000	0.0909091
$122$	−1.65685	−0.150005
$123$	−6.82843	−0.615699
$124$	10.3431	0.928842
$125$	12.0000	1.07331
$126$	0	0
$127$	−1.92893	−0.171165	−0.0855825	−	0.996331i	$-0.527275\pi$
$127$	−1.92893	−0.171165	−0.0855825	+	0.996331i	$0.527275\pi$
$128$	−10.5563	−0.933058
$129$	−11.2426	−0.989859
$130$	−4.00000	−0.350823
$131$	−10.8284	−0.946084	−0.473042	−	0.881040i	$-0.656844\pi$
$131$	−10.8284	−0.946084	−0.473042	+	0.881040i	$0.656844\pi$
$132$	−1.82843	−0.159144
$133$	0	0
$134$	−3.65685	−0.315904
$135$	−2.00000	−0.172133
$136$	2.51472	0.215635
$137$	−16.4853	−1.40843	−0.704216	−	0.709985i	$-0.748701\pi$
$137$	−16.4853	−1.40843	−0.704216	+	0.709985i	$0.748701\pi$
$138$	−2.89949	−0.246821
$139$	5.58579	0.473780	0.236890	−	0.971536i	$-0.423872\pi$
$139$	5.58579	0.473780	0.236890	+	0.971536i	$0.423872\pi$
$140$	0	0
$141$	4.17157	0.351310
$142$	−4.07107	−0.341636
$143$	4.82843	0.403773
$144$	3.00000	0.250000
$145$	10.4853	0.870755
$146$	4.82843	0.399603
$147$	0	0
$148$	−13.6863	−1.12501
$149$	20.2132	1.65593	0.827965	−	0.560780i	$-0.189499\pi$
$149$	20.2132	1.65593	0.827965	+	0.560780i	$0.189499\pi$
$150$	−0.414214	−0.0338204
$151$	0.899495	0.0731999	0.0365999	−	0.999330i	$-0.488347\pi$
$151$	0.899495	0.0731999	0.0365999	+	0.999330i	$0.488347\pi$
$152$	1.97056	0.159834
$153$	−1.58579	−0.128203
$154$	0	0
$155$	11.3137	0.908739
$156$	−8.82843	−0.706840
$157$	7.00000	0.558661	0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000	0.558661	0.279330	+	0.960195i	$0.409888\pi$
$158$	−3.85786	−0.306915
$159$	−12.8284	−1.01736
$160$	−8.82843	−0.697948
$161$	0	0
$162$	0.414214	0.0325437
$163$	12.9706	1.01593	0.507966	−	0.861377i	$-0.330397\pi$
$163$	12.9706	1.01593	0.507966	+	0.861377i	$0.330397\pi$
$164$	12.4853	0.974937
$165$	−2.00000	−0.155700
$166$	1.17157	0.0909317
$167$	10.8284	0.837929	0.418964	−	0.908003i	$-0.362393\pi$
$167$	10.8284	0.837929	0.418964	+	0.908003i	$0.362393\pi$
$168$	0	0
$169$	10.3137	0.793362
$170$	1.31371	0.100757
$171$	−1.24264	−0.0950271
$172$	20.5563	1.56741
$173$	−9.17157	−0.697302	−0.348651	−	0.937253i	$-0.613360\pi$
$173$	−9.17157	−0.697302	−0.348651	+	0.937253i	$0.613360\pi$
$174$	−2.17157	−0.164627
$175$	0	0
$176$	3.00000	0.226134
$177$	2.65685	0.199701
$178$	5.85786	0.439065
$179$	12.1716	0.909746	0.454873	−	0.890556i	$-0.349685\pi$
$179$	12.1716	0.909746	0.454873	+	0.890556i	$0.349685\pi$
$180$	3.65685	0.272566
$181$	−0.343146	−0.0255058	−0.0127529	−	0.999919i	$-0.504059\pi$
$181$	−0.343146	−0.0255058	−0.0127529	+	0.999919i	$0.504059\pi$
$182$	0	0
$183$	−4.00000	−0.295689
$184$	11.1005	0.818340
$185$	−14.9706	−1.10066
$186$	−2.34315	−0.171808
$187$	−1.58579	−0.115964
$188$	−7.62742	−0.556287
$189$	0	0
$190$	1.02944	0.0746832
$191$	−10.3431	−0.748404	−0.374202	−	0.927347i	$-0.622083\pi$
$191$	−10.3431	−0.748404	−0.374202	+	0.927347i	$0.622083\pi$
$192$	−4.17157	−0.301057
$193$	16.1421	1.16194	0.580968	−	0.813926i	$-0.302674\pi$
$193$	16.1421	1.16194	0.580968	+	0.813926i	$0.302674\pi$
$194$	2.27208	0.163126
$195$	−9.65685	−0.691542
$196$	0	0
$197$	−13.5858	−0.967947	−0.483974	−	0.875083i	$-0.660807\pi$
$197$	−13.5858	−0.967947	−0.483974	+	0.875083i	$0.660807\pi$
$198$	0.414214	0.0294369
$199$	19.7990	1.40351	0.701757	−	0.712417i	$-0.252399\pi$
$199$	19.7990	1.40351	0.701757	+	0.712417i	$0.252399\pi$
$200$	1.58579	0.112132
$201$	−8.82843	−0.622709
$202$	−6.17157	−0.434230
$203$	0	0
$204$	2.89949	0.203005
$205$	13.6569	0.953836
$206$	−1.85786	−0.129444
$207$	−7.00000	−0.486534
$208$	14.4853	1.00437
$209$	−1.24264	−0.0859553
$210$	0	0
$211$	−18.9706	−1.30599	−0.652994	−	0.757363i	$-0.726487\pi$
$211$	−18.9706	−1.30599	−0.652994	+	0.757363i	$0.726487\pi$
$212$	23.4558	1.61095
$213$	−9.82843	−0.673433
$214$	−0.686292	−0.0469139
$215$	22.4853	1.53348
$216$	−1.58579	−0.107899
$217$	0	0
$218$	−0.485281	−0.0328674
$219$	11.6569	0.787697
$220$	3.65685	0.246545
$221$	−7.65685	−0.515056
$222$	3.10051	0.208092
$223$	10.9706	0.734643	0.367322	−	0.930094i	$-0.380275\pi$
$223$	10.9706	0.734643	0.367322	+	0.930094i	$0.380275\pi$
$224$	0	0
$225$	−1.00000	−0.0666667
$226$	1.51472	0.100758
$227$	−18.9706	−1.25912	−0.629560	−	0.776952i	$-0.716765\pi$
$227$	−18.9706	−1.25912	−0.629560	+	0.776952i	$0.716765\pi$
$228$	2.27208	0.150472
$229$	−4.34315	−0.287003	−0.143502	−	0.989650i	$-0.545836\pi$
$229$	−4.34315	−0.287003	−0.143502	+	0.989650i	$0.545836\pi$
$230$	5.79899	0.382374
$231$	0	0
$232$	8.31371	0.545822
$233$	7.58579	0.496961	0.248481	−	0.968637i	$-0.420069\pi$
$233$	7.58579	0.496961	0.248481	+	0.968637i	$0.420069\pi$
$234$	2.00000	0.130744
$235$	−8.34315	−0.544247
$236$	−4.85786	−0.316220
$237$	−9.31371	−0.604990
$238$	0	0
$239$	10.4853	0.678236	0.339118	−	0.940744i	$-0.389871\pi$
$239$	10.4853	0.678236	0.339118	+	0.940744i	$0.389871\pi$
$240$	−6.00000	−0.387298
$241$	−15.3137	−0.986443	−0.493221	−	0.869904i	$-0.664181\pi$
$241$	−15.3137	−0.986443	−0.493221	+	0.869904i	$0.664181\pi$
$242$	0.414214	0.0266267
$243$	1.00000	0.0641500
$244$	7.31371	0.468212
$245$	0	0
$246$	−2.82843	−0.180334
$247$	−6.00000	−0.381771
$248$	8.97056	0.569631
$249$	2.82843	0.179244
$250$	4.97056	0.314366
$251$	−19.4853	−1.22990	−0.614950	−	0.788566i	$-0.710824\pi$
$251$	−19.4853	−1.22990	−0.614950	+	0.788566i	$0.710824\pi$
$252$	0	0
$253$	−7.00000	−0.440086
$254$	−0.798990	−0.0501331
$255$	3.17157	0.198612
$256$	3.97056	0.248160
$257$	−29.4558	−1.83741	−0.918703	−	0.394950i	$-0.870762\pi$
$257$	−29.4558	−1.83741	−0.918703	+	0.394950i	$0.870762\pi$
$258$	−4.65685	−0.289923
$259$	0	0
$260$	17.6569	1.09503
$261$	−5.24264	−0.324511
$262$	−4.48528	−0.277102
$263$	18.0000	1.10993	0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000	1.10993	0.554964	+	0.831875i	$0.312732\pi$
$264$	−1.58579	−0.0975984
$265$	25.6569	1.57609
$266$	0	0
$267$	14.1421	0.865485
$268$	16.1421	0.986038
$269$	11.7990	0.719397	0.359699	−	0.933069i	$-0.382880\pi$
$269$	11.7990	0.719397	0.359699	+	0.933069i	$0.382880\pi$
$270$	−0.828427	−0.0504165
$271$	10.9706	0.666414	0.333207	−	0.942854i	$-0.391869\pi$
$271$	10.9706	0.666414	0.333207	+	0.942854i	$0.391869\pi$
$272$	−4.75736	−0.288457
$273$	0	0
$274$	−6.82843	−0.412520
$275$	−1.00000	−0.0603023
$276$	12.7990	0.770409
$277$	−14.3431	−0.861796	−0.430898	−	0.902401i	$-0.641803\pi$
$277$	−14.3431	−0.861796	−0.430898	+	0.902401i	$0.641803\pi$
$278$	2.31371	0.138767
$279$	−5.65685	−0.338667
$280$	0	0
$281$	11.5858	0.691150	0.345575	−	0.938391i	$-0.387684\pi$
$281$	11.5858	0.691150	0.345575	+	0.938391i	$0.387684\pi$
$282$	1.72792	0.102896
$283$	31.6569	1.88180	0.940902	−	0.338678i	$-0.109980\pi$
$283$	31.6569	1.88180	0.940902	+	0.338678i	$0.109980\pi$
$284$	17.9706	1.06636
$285$	2.48528	0.147215
$286$	2.00000	0.118262
$287$	0	0
$288$	4.41421	0.260110
$289$	−14.4853	−0.852075
$290$	4.34315	0.255038
$291$	5.48528	0.321553
$292$	−21.3137	−1.24729
$293$	−19.7279	−1.15252	−0.576259	−	0.817267i	$-0.695488\pi$
$293$	−19.7279	−1.15252	−0.576259	+	0.817267i	$0.695488\pi$
$294$	0	0
$295$	−5.31371	−0.309376
$296$	−11.8701	−0.689933
$297$	1.00000	0.0580259
$298$	8.37258	0.485011
$299$	−33.7990	−1.95465
$300$	1.82843	0.105564
$301$	0	0
$302$	0.372583	0.0214397
$303$	−14.8995	−0.855954
$304$	−3.72792	−0.213811
$305$	8.00000	0.458079
$306$	−0.656854	−0.0375499
$307$	5.31371	0.303269	0.151635	−	0.988437i	$-0.451546\pi$
$307$	5.31371	0.303269	0.151635	+	0.988437i	$0.451546\pi$
$308$	0	0
$309$	−4.48528	−0.255159
$310$	4.68629	0.266163
$311$	−15.6274	−0.886150	−0.443075	−	0.896485i	$-0.646112\pi$
$311$	−15.6274	−0.886150	−0.443075	+	0.896485i	$0.646112\pi$
$312$	−7.65685	−0.433484
$313$	−34.7990	−1.96696	−0.983478	−	0.181030i	$-0.942057\pi$
$313$	−34.7990	−1.96696	−0.983478	+	0.181030i	$0.942057\pi$
$314$	2.89949	0.163628
$315$	0	0
$316$	17.0294	0.957981
$317$	−2.68629	−0.150877	−0.0754386	−	0.997150i	$-0.524036\pi$
$317$	−2.68629	−0.150877	−0.0754386	+	0.997150i	$0.524036\pi$
$318$	−5.31371	−0.297978
$319$	−5.24264	−0.293532
$320$	8.34315	0.466396
$321$	−1.65685	−0.0924766
$322$	0	0
$323$	1.97056	0.109645
$324$	−1.82843	−0.101579
$325$	−4.82843	−0.267833
$326$	5.37258	0.297560
$327$	−1.17157	−0.0647881
$328$	10.8284	0.597900
$329$	0	0
$330$	−0.828427	−0.0456034
$331$	5.51472	0.303116	0.151558	−	0.988448i	$-0.451571\pi$
$331$	5.51472	0.303116	0.151558	+	0.988448i	$0.451571\pi$
$332$	−5.17157	−0.283827
$333$	7.48528	0.410191
$334$	4.48528	0.245424
$335$	17.6569	0.964697
$336$	0	0
$337$	32.1421	1.75089	0.875447	−	0.483314i	$-0.160567\pi$
$337$	32.1421	1.75089	0.875447	+	0.483314i	$0.160567\pi$
$338$	4.27208	0.232370
$339$	3.65685	0.198613
$340$	−5.79899	−0.314494
$341$	−5.65685	−0.306336
$342$	−0.514719	−0.0278328
$343$	0	0
$344$	17.8284	0.961244
$345$	14.0000	0.753735
$346$	−3.79899	−0.204235
$347$	−18.9706	−1.01839	−0.509197	−	0.860650i	$-0.670057\pi$
$347$	−18.9706	−1.01839	−0.509197	+	0.860650i	$0.670057\pi$
$348$	9.58579	0.513852
$349$	−22.9706	−1.22959	−0.614793	−	0.788688i	$-0.710760\pi$
$349$	−22.9706	−1.22959	−0.614793	+	0.788688i	$0.710760\pi$
$350$	0	0
$351$	4.82843	0.257722
$352$	4.41421	0.235278
$353$	−9.31371	−0.495719	−0.247859	−	0.968796i	$-0.579727\pi$
$353$	−9.31371	−0.495719	−0.247859	+	0.968796i	$0.579727\pi$
$354$	1.10051	0.0584912
$355$	19.6569	1.04328
$356$	−25.8579	−1.37046
$357$	0	0
$358$	5.04163	0.266458
$359$	−8.00000	−0.422224	−0.211112	−	0.977462i	$-0.567708\pi$
$359$	−8.00000	−0.422224	−0.211112	+	0.977462i	$0.567708\pi$
$360$	3.17157	0.167157
$361$	−17.4558	−0.918729
$362$	−0.142136	−0.00747048
$363$	1.00000	0.0524864
$364$	0	0
$365$	−23.3137	−1.22030
$366$	−1.65685	−0.0866052
$367$	24.1421	1.26021	0.630105	−	0.776510i	$-0.283012\pi$
$367$	24.1421	1.26021	0.630105	+	0.776510i	$0.283012\pi$
$368$	−21.0000	−1.09470
$369$	−6.82843	−0.355474
$370$	−6.20101	−0.322375
$371$	0	0
$372$	10.3431	0.536267
$373$	9.65685	0.500013	0.250006	−	0.968244i	$-0.419567\pi$
$373$	9.65685	0.500013	0.250006	+	0.968244i	$0.419567\pi$
$374$	−0.656854	−0.0339651
$375$	12.0000	0.619677
$376$	−6.61522	−0.341154
$377$	−25.3137	−1.30372
$378$	0	0
$379$	13.1716	0.676578	0.338289	−	0.941042i	$-0.390152\pi$
$379$	13.1716	0.676578	0.338289	+	0.941042i	$0.390152\pi$
$380$	−4.54416	−0.233110
$381$	−1.92893	−0.0988222
$382$	−4.28427	−0.219202
$383$	−20.3137	−1.03798	−0.518991	−	0.854780i	$-0.673692\pi$
$383$	−20.3137	−1.03798	−0.518991	+	0.854780i	$0.673692\pi$
$384$	−10.5563	−0.538701
$385$	0	0
$386$	6.68629	0.340323
$387$	−11.2426	−0.571496
$388$	−10.0294	−0.509168
$389$	27.7990	1.40946	0.704732	−	0.709473i	$-0.251067\pi$
$389$	27.7990	1.40946	0.704732	+	0.709473i	$0.251067\pi$
$390$	−4.00000	−0.202548
$391$	11.1005	0.561377
$392$	0	0
$393$	−10.8284	−0.546222
$394$	−5.62742	−0.283505
$395$	18.6274	0.937247
$396$	−1.82843	−0.0918819
$397$	0.514719	0.0258330	0.0129165	−	0.999917i	$-0.495888\pi$
$397$	0.514719	0.0258330	0.0129165	+	0.999917i	$0.495888\pi$
$398$	8.20101	0.411079
$399$	0	0
$400$	−3.00000	−0.150000
$401$	24.4853	1.22274	0.611368	−	0.791346i	$-0.290619\pi$
$401$	24.4853	1.22274	0.611368	+	0.791346i	$0.290619\pi$
$402$	−3.65685	−0.182387
$403$	−27.3137	−1.36059
$404$	27.2426	1.35537
$405$	−2.00000	−0.0993808
$406$	0	0
$407$	7.48528	0.371032
$408$	2.51472	0.124497
$409$	31.7990	1.57236	0.786179	−	0.617998i	$-0.212056\pi$
$409$	31.7990	1.57236	0.786179	+	0.617998i	$0.212056\pi$
$410$	5.65685	0.279372
$411$	−16.4853	−0.813159
$412$	8.20101	0.404035
$413$	0	0
$414$	−2.89949	−0.142502
$415$	−5.65685	−0.277684
$416$	21.3137	1.04499
$417$	5.58579	0.273537
$418$	−0.514719	−0.0251757
$419$	−24.7990	−1.21151	−0.605755	−	0.795651i	$-0.707129\pi$
$419$	−24.7990	−1.21151	−0.605755	+	0.795651i	$0.707129\pi$
$420$	0	0
$421$	−7.00000	−0.341159	−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000	−0.341159	−0.170580	+	0.985344i	$0.554564\pi$
$422$	−7.85786	−0.382515
$423$	4.17157	0.202829
$424$	20.3431	0.987950
$425$	1.58579	0.0769219
$426$	−4.07107	−0.197244
$427$	0	0
$428$	3.02944	0.146433
$429$	4.82843	0.233119
$430$	9.31371	0.449147
$431$	−26.9706	−1.29913	−0.649563	−	0.760308i	$-0.725048\pi$
$431$	−26.9706	−1.29913	−0.649563	+	0.760308i	$0.725048\pi$
$432$	3.00000	0.144338
$433$	29.1421	1.40048	0.700241	−	0.713907i	$-0.253076\pi$
$433$	29.1421	1.40048	0.700241	+	0.713907i	$0.253076\pi$
$434$	0	0
$435$	10.4853	0.502731
$436$	2.14214	0.102590
$437$	8.69848	0.416105
$438$	4.82843	0.230711
$439$	11.1005	0.529798	0.264899	−	0.964276i	$-0.414661\pi$
$439$	11.1005	0.529798	0.264899	+	0.964276i	$0.414661\pi$
$440$	3.17157	0.151199
$441$	0	0
$442$	−3.17157	−0.150856
$443$	−11.6274	−0.552435	−0.276218	−	0.961095i	$-0.589081\pi$
$443$	−11.6274	−0.552435	−0.276218	+	0.961095i	$0.589081\pi$
$444$	−13.6863	−0.649523
$445$	−28.2843	−1.34080
$446$	4.54416	0.215172
$447$	20.2132	0.956052
$448$	0	0
$449$	−4.00000	−0.188772	−0.0943858	−	0.995536i	$-0.530089\pi$
$449$	−4.00000	−0.188772	−0.0943858	+	0.995536i	$0.530089\pi$
$450$	−0.414214	−0.0195262
$451$	−6.82843	−0.321538
$452$	−6.68629	−0.314497
$453$	0.899495	0.0422620
$454$	−7.85786	−0.368788
$455$	0	0
$456$	1.97056	0.0922801
$457$	13.1716	0.616140	0.308070	−	0.951364i	$-0.400317\pi$
$457$	13.1716	0.616140	0.308070	+	0.951364i	$0.400317\pi$
$458$	−1.79899	−0.0840613
$459$	−1.58579	−0.0740182
$460$	−25.5980	−1.19351
$461$	15.2426	0.709921	0.354960	−	0.934881i	$-0.384494\pi$
$461$	15.2426	0.709921	0.354960	+	0.934881i	$0.384494\pi$
$462$	0	0
$463$	−26.6274	−1.23748	−0.618741	−	0.785595i	$-0.712357\pi$
$463$	−26.6274	−1.23748	−0.618741	+	0.785595i	$0.712357\pi$
$464$	−15.7279	−0.730150
$465$	11.3137	0.524661
$466$	3.14214	0.145557
$467$	14.3137	0.662359	0.331180	−	0.943568i	$-0.392553\pi$
$467$	14.3137	0.662359	0.331180	+	0.943568i	$0.392553\pi$
$468$	−8.82843	−0.408094
$469$	0	0
$470$	−3.45584	−0.159406
$471$	7.00000	0.322543
$472$	−4.21320	−0.193928
$473$	−11.2426	−0.516937
$474$	−3.85786	−0.177198
$475$	1.24264	0.0570163
$476$	0	0
$477$	−12.8284	−0.587373
$478$	4.34315	0.198651
$479$	14.0000	0.639676	0.319838	−	0.947472i	$-0.396371\pi$
$479$	14.0000	0.639676	0.319838	+	0.947472i	$0.396371\pi$
$480$	−8.82843	−0.402961
$481$	36.1421	1.64794
$482$	−6.34315	−0.288922
$483$	0	0
$484$	−1.82843	−0.0831103
$485$	−10.9706	−0.498148
$486$	0.414214	0.0187891
$487$	12.6274	0.572203	0.286101	−	0.958199i	$-0.407641\pi$
$487$	12.6274	0.572203	0.286101	+	0.958199i	$0.407641\pi$
$488$	6.34315	0.287141
$489$	12.9706	0.586549
$490$	0	0
$491$	−18.4853	−0.834229	−0.417115	−	0.908854i	$-0.636959\pi$
$491$	−18.4853	−0.834229	−0.417115	+	0.908854i	$0.636959\pi$
$492$	12.4853	0.562880
$493$	8.31371	0.374431
$494$	−2.48528	−0.111818
$495$	−2.00000	−0.0898933
$496$	−16.9706	−0.762001
$497$	0	0
$498$	1.17157	0.0524994
$499$	7.79899	0.349131	0.174565	−	0.984646i	$-0.444148\pi$
$499$	7.79899	0.349131	0.174565	+	0.984646i	$0.444148\pi$
$500$	−21.9411	−0.981237
$501$	10.8284	0.483778
$502$	−8.07107	−0.360229
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	29.7990	1.32604
$506$	−2.89949	−0.128898
$507$	10.3137	0.458048
$508$	3.52691	0.156481
$509$	−12.0000	−0.531891	−0.265945	−	0.963988i	$-0.585684\pi$
$509$	−12.0000	−0.531891	−0.265945	+	0.963988i	$0.585684\pi$
$510$	1.31371	0.0581720
$511$	0	0
$512$	22.7574	1.00574
$513$	−1.24264	−0.0548639
$514$	−12.2010	−0.538163
$515$	8.97056	0.395290
$516$	20.5563	0.904943
$517$	4.17157	0.183466
$518$	0	0
$519$	−9.17157	−0.402587
$520$	15.3137	0.671551
$521$	36.8284	1.61348	0.806741	−	0.590905i	$-0.201229\pi$
$521$	36.8284	1.61348	0.806741	+	0.590905i	$0.201229\pi$
$522$	−2.17157	−0.0950472
$523$	34.2843	1.49915	0.749573	−	0.661921i	$-0.230259\pi$
$523$	34.2843	1.49915	0.749573	+	0.661921i	$0.230259\pi$
$524$	19.7990	0.864923
$525$	0	0
$526$	7.45584	0.325090
$527$	8.97056	0.390764
$528$	3.00000	0.130558
$529$	26.0000	1.13043
$530$	10.6274	0.461625
$531$	2.65685	0.115298
$532$	0	0
$533$	−32.9706	−1.42811
$534$	5.85786	0.253495
$535$	3.31371	0.143264
$536$	14.0000	0.604708
$537$	12.1716	0.525242
$538$	4.88730	0.210707
$539$	0	0
$540$	3.65685	0.157366
$541$	8.34315	0.358700	0.179350	−	0.983785i	$-0.442601\pi$
$541$	8.34315	0.358700	0.179350	+	0.983785i	$0.442601\pi$
$542$	4.54416	0.195188
$543$	−0.343146	−0.0147258
$544$	−7.00000	−0.300123
$545$	2.34315	0.100369
$546$	0	0
$547$	18.2132	0.778740	0.389370	−	0.921081i	$-0.372693\pi$
$547$	18.2132	0.778740	0.389370	+	0.921081i	$0.372693\pi$
$548$	30.1421	1.28761
$549$	−4.00000	−0.170716
$550$	−0.414214	−0.0176621
$551$	6.51472	0.277536
$552$	11.1005	0.472469
$553$	0	0
$554$	−5.94113	−0.252414
$555$	−14.9706	−0.635465
$556$	−10.2132	−0.433136
$557$	22.5563	0.955743	0.477872	−	0.878430i	$-0.341408\pi$
$557$	22.5563	0.955743	0.477872	+	0.878430i	$0.341408\pi$
$558$	−2.34315	−0.0991933
$559$	−54.2843	−2.29598
$560$	0	0
$561$	−1.58579	−0.0669520
$562$	4.79899	0.202433
$563$	19.1716	0.807985	0.403993	−	0.914762i	$-0.367622\pi$
$563$	19.1716	0.807985	0.403993	+	0.914762i	$0.367622\pi$
$564$	−7.62742	−0.321172
$565$	−7.31371	−0.307690
$566$	13.1127	0.551168
$567$	0	0
$568$	15.5858	0.653965
$569$	−7.24264	−0.303627	−0.151814	−	0.988409i	$-0.548511\pi$
$569$	−7.24264	−0.303627	−0.151814	+	0.988409i	$0.548511\pi$
$570$	1.02944	0.0431184
$571$	−18.0711	−0.756251	−0.378125	−	0.925754i	$-0.623431\pi$
$571$	−18.0711	−0.756251	−0.378125	+	0.925754i	$0.623431\pi$
$572$	−8.82843	−0.369135
$573$	−10.3431	−0.432091
$574$	0	0
$575$	7.00000	0.291920
$576$	−4.17157	−0.173816
$577$	−3.65685	−0.152237	−0.0761184	−	0.997099i	$-0.524253\pi$
$577$	−3.65685	−0.152237	−0.0761184	+	0.997099i	$0.524253\pi$
$578$	−6.00000	−0.249567
$579$	16.1421	0.670844
$580$	−19.1716	−0.796056
$581$	0	0
$582$	2.27208	0.0941807
$583$	−12.8284	−0.531299
$584$	−18.4853	−0.764926
$585$	−9.65685	−0.399262
$586$	−8.17157	−0.337565
$587$	31.3137	1.29246	0.646228	−	0.763145i	$-0.276346\pi$
$587$	31.3137	1.29246	0.646228	+	0.763145i	$0.276346\pi$
$588$	0	0
$589$	7.02944	0.289643
$590$	−2.20101	−0.0906142
$591$	−13.5858	−0.558845
$592$	22.4558	0.922930
$593$	−47.7279	−1.95995	−0.979975	−	0.199118i	$-0.936192\pi$
$593$	−47.7279	−1.95995	−0.979975	+	0.199118i	$0.936192\pi$
$594$	0.414214	0.0169954
$595$	0	0
$596$	−36.9584	−1.51387
$597$	19.7990	0.810319
$598$	−14.0000	−0.572503
$599$	−46.6274	−1.90514	−0.952572	−	0.304312i	$-0.901573\pi$
$599$	−46.6274	−1.90514	−0.952572	+	0.304312i	$0.901573\pi$
$600$	1.58579	0.0647395
$601$	2.48528	0.101377	0.0506884	−	0.998715i	$-0.483858\pi$
$601$	2.48528	0.101377	0.0506884	+	0.998715i	$0.483858\pi$
$602$	0	0
$603$	−8.82843	−0.359521
$604$	−1.64466	−0.0669203
$605$	−2.00000	−0.0813116
$606$	−6.17157	−0.250703
$607$	−41.3137	−1.67687	−0.838436	−	0.545000i	$-0.816530\pi$
$607$	−41.3137	−1.67687	−0.838436	+	0.545000i	$0.816530\pi$
$608$	−5.48528	−0.222458
$609$	0	0
$610$	3.31371	0.134168
$611$	20.1421	0.814864
$612$	2.89949	0.117205
$613$	30.8284	1.24515	0.622574	−	0.782561i	$-0.286087\pi$
$613$	30.8284	1.24515	0.622574	+	0.782561i	$0.286087\pi$
$614$	2.20101	0.0888255
$615$	13.6569	0.550698
$616$	0	0
$617$	18.8284	0.758004	0.379002	−	0.925396i	$-0.376267\pi$
$617$	18.8284	0.758004	0.379002	+	0.925396i	$0.376267\pi$
$618$	−1.85786	−0.0747343
$619$	−10.6274	−0.427152	−0.213576	−	0.976926i	$-0.568511\pi$
$619$	−10.6274	−0.427152	−0.213576	+	0.976926i	$0.568511\pi$
$620$	−20.6863	−0.830781
$621$	−7.00000	−0.280900
$622$	−6.47309	−0.259547
$623$	0	0
$624$	14.4853	0.579875
$625$	−19.0000	−0.760000
$626$	−14.4142	−0.576108
$627$	−1.24264	−0.0496263
$628$	−12.7990	−0.510735
$629$	−11.8701	−0.473290
$630$	0	0
$631$	−30.2843	−1.20560	−0.602799	−	0.797893i	$-0.705948\pi$
$631$	−30.2843	−1.20560	−0.602799	+	0.797893i	$0.705948\pi$
$632$	14.7696	0.587501
$633$	−18.9706	−0.754012
$634$	−1.11270	−0.0441909
$635$	3.85786	0.153095
$636$	23.4558	0.930085
$637$	0	0
$638$	−2.17157	−0.0859734
$639$	−9.82843	−0.388807
$640$	21.1127	0.834553
$641$	4.48528	0.177158	0.0885790	−	0.996069i	$-0.471767\pi$
$641$	4.48528	0.177158	0.0885790	+	0.996069i	$0.471767\pi$
$642$	−0.686292	−0.0270858
$643$	2.00000	0.0788723	0.0394362	−	0.999222i	$-0.487444\pi$
$643$	2.00000	0.0788723	0.0394362	+	0.999222i	$0.487444\pi$
$644$	0	0
$645$	22.4853	0.885357
$646$	0.816234	0.0321143
$647$	3.31371	0.130275	0.0651377	−	0.997876i	$-0.479251\pi$
$647$	3.31371	0.130275	0.0651377	+	0.997876i	$0.479251\pi$
$648$	−1.58579	−0.0622956
$649$	2.65685	0.104291
$650$	−2.00000	−0.0784465
$651$	0	0
$652$	−23.7157	−0.928780
$653$	−31.1127	−1.21753	−0.608767	−	0.793349i	$-0.708336\pi$
$653$	−31.1127	−1.21753	−0.608767	+	0.793349i	$0.708336\pi$
$654$	−0.485281	−0.0189760
$655$	21.6569	0.846203
$656$	−20.4853	−0.799816
$657$	11.6569	0.454777
$658$	0	0
$659$	17.5147	0.682277	0.341138	−	0.940013i	$-0.389188\pi$
$659$	17.5147	0.682277	0.341138	+	0.940013i	$0.389188\pi$
$660$	3.65685	0.142343
$661$	−21.9706	−0.854556	−0.427278	−	0.904120i	$-0.640527\pi$
$661$	−21.9706	−0.854556	−0.427278	+	0.904120i	$0.640527\pi$
$662$	2.28427	0.0887807
$663$	−7.65685	−0.297368
$664$	−4.48528	−0.174063
$665$	0	0
$666$	3.10051	0.120142
$667$	36.6985	1.42097
$668$	−19.7990	−0.766046
$669$	10.9706	0.424146
$670$	7.31371	0.282553
$671$	−4.00000	−0.154418
$672$	0	0
$673$	32.8284	1.26544	0.632721	−	0.774379i	$-0.281938\pi$
$673$	32.8284	1.26544	0.632721	+	0.774379i	$0.281938\pi$
$674$	13.3137	0.512825
$675$	−1.00000	−0.0384900
$676$	−18.8579	−0.725302
$677$	50.0122	1.92212	0.961062	−	0.276332i	$-0.0891188\pi$
$677$	50.0122	1.92212	0.961062	+	0.276332i	$0.0891188\pi$
$678$	1.51472	0.0581724
$679$	0	0
$680$	−5.02944	−0.192870
$681$	−18.9706	−0.726954
$682$	−2.34315	−0.0897237
$683$	42.7990	1.63766	0.818829	−	0.574038i	$-0.194624\pi$
$683$	42.7990	1.63766	0.818829	+	0.574038i	$0.194624\pi$
$684$	2.27208	0.0868751
$685$	32.9706	1.25974
$686$	0	0
$687$	−4.34315	−0.165701
$688$	−33.7279	−1.28586
$689$	−61.9411	−2.35977
$690$	5.79899	0.220764
$691$	39.4558	1.50097	0.750486	−	0.660887i	$-0.229820\pi$
$691$	39.4558	1.50097	0.750486	+	0.660887i	$0.229820\pi$
$692$	16.7696	0.637483
$693$	0	0
$694$	−7.85786	−0.298280
$695$	−11.1716	−0.423762
$696$	8.31371	0.315130
$697$	10.8284	0.410156
$698$	−9.51472	−0.360137
$699$	7.58579	0.286921
$700$	0	0
$701$	16.8995	0.638285	0.319143	−	0.947707i	$-0.396605\pi$
$701$	16.8995	0.638285	0.319143	+	0.947707i	$0.396605\pi$
$702$	2.00000	0.0754851
$703$	−9.30152	−0.350813
$704$	−4.17157	−0.157222
$705$	−8.34315	−0.314221
$706$	−3.85786	−0.145193
$707$	0	0
$708$	−4.85786	−0.182570
$709$	−47.7696	−1.79402	−0.897012	−	0.442007i	$-0.854267\pi$
$709$	−47.7696	−1.79402	−0.897012	+	0.442007i	$0.854267\pi$
$710$	8.14214	0.305569
$711$	−9.31371	−0.349291
$712$	−22.4264	−0.840465
$713$	39.5980	1.48296
$714$	0	0
$715$	−9.65685	−0.361146
$716$	−22.2548	−0.831702
$717$	10.4853	0.391580
$718$	−3.31371	−0.123667
$719$	50.7990	1.89448	0.947241	−	0.320521i	$-0.103858\pi$
$719$	50.7990	1.89448	0.947241	+	0.320521i	$0.103858\pi$
$720$	−6.00000	−0.223607
$721$	0	0
$722$	−7.23045	−0.269089
$723$	−15.3137	−0.569523
$724$	0.627417	0.0233178
$725$	5.24264	0.194707
$726$	0.414214	0.0153729
$727$	−50.0833	−1.85749	−0.928743	−	0.370725i	$-0.879109\pi$
$727$	−50.0833	−1.85749	−0.928743	+	0.370725i	$0.879109\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−9.65685	−0.357416
$731$	17.8284	0.659408
$732$	7.31371	0.270322
$733$	−1.65685	−0.0611973	−0.0305987	−	0.999532i	$-0.509741\pi$
$733$	−1.65685	−0.0611973	−0.0305987	+	0.999532i	$0.509741\pi$
$734$	10.0000	0.369107
$735$	0	0
$736$	−30.8995	−1.13897
$737$	−8.82843	−0.325199
$738$	−2.82843	−0.104116
$739$	−28.3431	−1.04262	−0.521310	−	0.853368i	$-0.674556\pi$
$739$	−28.3431	−1.04262	−0.521310	+	0.853368i	$0.674556\pi$
$740$	27.3726	1.00624
$741$	−6.00000	−0.220416
$742$	0	0
$743$	−5.79899	−0.212744	−0.106372	−	0.994326i	$-0.533923\pi$
$743$	−5.79899	−0.212744	−0.106372	+	0.994326i	$0.533923\pi$
$744$	8.97056	0.328877
$745$	−40.4264	−1.48111
$746$	4.00000	0.146450
$747$	2.82843	0.103487
$748$	2.89949	0.106016
$749$	0	0
$750$	4.97056	0.181499
$751$	−6.68629	−0.243986	−0.121993	−	0.992531i	$-0.538929\pi$
$751$	−6.68629	−0.243986	−0.121993	+	0.992531i	$0.538929\pi$
$752$	12.5147	0.456365
$753$	−19.4853	−0.710083
$754$	−10.4853	−0.381851
$755$	−1.79899	−0.0654719
$756$	0	0
$757$	−30.3137	−1.10177	−0.550885	−	0.834581i	$-0.685710\pi$
$757$	−30.3137	−1.10177	−0.550885	+	0.834581i	$0.685710\pi$
$758$	5.45584	0.198165
$759$	−7.00000	−0.254084
$760$	−3.94113	−0.142960
$761$	−39.7990	−1.44271	−0.721356	−	0.692564i	$-0.756481\pi$
$761$	−39.7990	−1.44271	−0.721356	+	0.692564i	$0.756481\pi$
$762$	−0.798990	−0.0289443
$763$	0	0
$764$	18.9117	0.684201
$765$	3.17157	0.114668
$766$	−8.41421	−0.304018
$767$	12.8284	0.463208
$768$	3.97056	0.143275
$769$	−5.79899	−0.209117	−0.104558	−	0.994519i	$-0.533343\pi$
$769$	−5.79899	−0.209117	−0.104558	+	0.994519i	$0.533343\pi$
$770$	0	0
$771$	−29.4558	−1.06083
$772$	−29.5147	−1.06226
$773$	−40.3431	−1.45104	−0.725521	−	0.688200i	$-0.758401\pi$
$773$	−40.3431	−1.45104	−0.725521	+	0.688200i	$0.758401\pi$
$774$	−4.65685	−0.167387
$775$	5.65685	0.203200
$776$	−8.69848	−0.312257
$777$	0	0
$778$	11.5147	0.412823
$779$	8.48528	0.304017
$780$	17.6569	0.632217
$781$	−9.82843	−0.351689
$782$	4.59798	0.164423
$783$	−5.24264	−0.187357
$784$	0	0
$785$	−14.0000	−0.499681
$786$	−4.48528	−0.159985
$787$	−35.5269	−1.26640	−0.633199	−	0.773989i	$-0.718258\pi$
$787$	−35.5269	−1.26640	−0.633199	+	0.773989i	$0.718258\pi$
$788$	24.8406	0.884910
$789$	18.0000	0.640817
$790$	7.71573	0.274513
$791$	0	0
$792$	−1.58579	−0.0563485
$793$	−19.3137	−0.685850
$794$	0.213203	0.00756631
$795$	25.6569	0.909955
$796$	−36.2010	−1.28311
$797$	16.8284	0.596093	0.298047	−	0.954551i	$-0.403665\pi$
$797$	16.8284	0.596093	0.298047	+	0.954551i	$0.403665\pi$
$798$	0	0
$799$	−6.61522	−0.234030
$800$	−4.41421	−0.156066
$801$	14.1421	0.499688
$802$	10.1421	0.358131
$803$	11.6569	0.411361
$804$	16.1421	0.569289
$805$	0	0
$806$	−11.3137	−0.398508
$807$	11.7990	0.415344
$808$	23.6274	0.831210
$809$	5.17157	0.181823	0.0909114	−	0.995859i	$-0.471022\pi$
$809$	5.17157	0.181823	0.0909114	+	0.995859i	$0.471022\pi$
$810$	−0.828427	−0.0291080
$811$	−18.9706	−0.666147	−0.333073	−	0.942901i	$-0.608086\pi$
$811$	−18.9706	−0.666147	−0.333073	+	0.942901i	$0.608086\pi$
$812$	0	0
$813$	10.9706	0.384754
$814$	3.10051	0.108673
$815$	−25.9411	−0.908678
$816$	−4.75736	−0.166541
$817$	13.9706	0.488768
$818$	13.1716	0.460533
$819$	0	0
$820$	−24.9706	−0.872010
$821$	33.1716	1.15770	0.578848	−	0.815436i	$-0.303502\pi$
$821$	33.1716	1.15770	0.578848	+	0.815436i	$0.303502\pi$
$822$	−6.82843	−0.238169
$823$	−38.8284	−1.35347	−0.676737	−	0.736225i	$-0.736607\pi$
$823$	−38.8284	−1.35347	−0.676737	+	0.736225i	$0.736607\pi$
$824$	7.11270	0.247783
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	−14.6863	−0.510692	−0.255346	−	0.966850i	$-0.582189\pi$
$827$	−14.6863	−0.510692	−0.255346	+	0.966850i	$0.582189\pi$
$828$	12.7990	0.444796
$829$	−11.8284	−0.410818	−0.205409	−	0.978676i	$-0.565853\pi$
$829$	−11.8284	−0.410818	−0.205409	+	0.978676i	$0.565853\pi$
$830$	−2.34315	−0.0813318
$831$	−14.3431	−0.497558
$832$	−20.1421	−0.698303
$833$	0	0
$834$	2.31371	0.0801172
$835$	−21.6569	−0.749466
$836$	2.27208	0.0785815
$837$	−5.65685	−0.195529
$838$	−10.2721	−0.354843
$839$	−24.9706	−0.862080	−0.431040	−	0.902333i	$-0.641853\pi$
$839$	−24.9706	−0.862080	−0.431040	+	0.902333i	$0.641853\pi$
$840$	0	0
$841$	−1.51472	−0.0522317
$842$	−2.89949	−0.0999232
$843$	11.5858	0.399036
$844$	34.6863	1.19395
$845$	−20.6274	−0.709605
$846$	1.72792	0.0594072
$847$	0	0
$848$	−38.4853	−1.32159
$849$	31.6569	1.08646
$850$	0.656854	0.0225299
$851$	−52.3970	−1.79614
$852$	17.9706	0.615661
$853$	4.48528	0.153573	0.0767866	−	0.997048i	$-0.475534\pi$
$853$	4.48528	0.153573	0.0767866	+	0.997048i	$0.475534\pi$
$854$	0	0
$855$	2.48528	0.0849948
$856$	2.62742	0.0898033
$857$	26.3553	0.900281	0.450141	−	0.892958i	$-0.351374\pi$
$857$	26.3553	0.900281	0.450141	+	0.892958i	$0.351374\pi$
$858$	2.00000	0.0682789
$859$	−7.51472	−0.256399	−0.128199	−	0.991748i	$-0.540920\pi$
$859$	−7.51472	−0.256399	−0.128199	+	0.991748i	$0.540920\pi$
$860$	−41.1127	−1.40193
$861$	0	0
$862$	−11.1716	−0.380505
$863$	−42.6274	−1.45105	−0.725527	−	0.688194i	$-0.758404\pi$
$863$	−42.6274	−1.45105	−0.725527	+	0.688194i	$0.758404\pi$
$864$	4.41421	0.150175
$865$	18.3431	0.623686
$866$	12.0711	0.410192
$867$	−14.4853	−0.491946
$868$	0	0
$869$	−9.31371	−0.315946
$870$	4.34315	0.147246
$871$	−42.6274	−1.44437
$872$	1.85786	0.0629152
$873$	5.48528	0.185649
$874$	3.60303	0.121874
$875$	0	0
$876$	−21.3137	−0.720123
$877$	−14.4853	−0.489133	−0.244567	−	0.969632i	$-0.578646\pi$
$877$	−14.4853	−0.489133	−0.244567	+	0.969632i	$0.578646\pi$
$878$	4.59798	0.155174
$879$	−19.7279	−0.665406
$880$	−6.00000	−0.202260
$881$	39.3137	1.32451	0.662256	−	0.749277i	$-0.269599\pi$
$881$	39.3137	1.32451	0.662256	+	0.749277i	$0.269599\pi$
$882$	0	0
$883$	28.3431	0.953823	0.476911	−	0.878951i	$-0.341756\pi$
$883$	28.3431	0.953823	0.476911	+	0.878951i	$0.341756\pi$
$884$	14.0000	0.470871
$885$	−5.31371	−0.178618
$886$	−4.81623	−0.161805
$887$	9.31371	0.312724	0.156362	−	0.987700i	$-0.450023\pi$
$887$	9.31371	0.312724	0.156362	+	0.987700i	$0.450023\pi$
$888$	−11.8701	−0.398333
$889$	0	0
$890$	−11.7157	−0.392712
$891$	1.00000	0.0335013
$892$	−20.0589	−0.671621
$893$	−5.18377	−0.173468
$894$	8.37258	0.280021
$895$	−24.3431	−0.813702
$896$	0	0
$897$	−33.7990	−1.12852
$898$	−1.65685	−0.0552899
$899$	29.6569	0.989111
$900$	1.82843	0.0609476
$901$	20.3431	0.677728
$902$	−2.82843	−0.0941763
$903$	0	0
$904$	−5.79899	−0.192872
$905$	0.686292	0.0228131
$906$	0.372583	0.0123782
$907$	−34.4853	−1.14506	−0.572532	−	0.819882i	$-0.694039\pi$
$907$	−34.4853	−1.14506	−0.572532	+	0.819882i	$0.694039\pi$
$908$	34.6863	1.15111
$909$	−14.8995	−0.494185
$910$	0	0
$911$	−21.4853	−0.711839	−0.355920	−	0.934517i	$-0.615832\pi$
$911$	−21.4853	−0.711839	−0.355920	+	0.934517i	$0.615832\pi$
$912$	−3.72792	−0.123444
$913$	2.82843	0.0936073
$914$	5.45584	0.180463
$915$	8.00000	0.264472
$916$	7.94113	0.262382
$917$	0	0
$918$	−0.656854	−0.0216794
$919$	−14.3553	−0.473539	−0.236769	−	0.971566i	$-0.576089\pi$
$919$	−14.3553	−0.473539	−0.236769	+	0.971566i	$0.576089\pi$
$920$	−22.2010	−0.731946
$921$	5.31371	0.175093
$922$	6.31371	0.207931
$923$	−47.4558	−1.56203
$924$	0	0
$925$	−7.48528	−0.246115
$926$	−11.0294	−0.362450
$927$	−4.48528	−0.147316
$928$	−23.1421	−0.759678
$929$	−17.1716	−0.563381	−0.281691	−	0.959505i	$-0.590895\pi$
$929$	−17.1716	−0.563381	−0.281691	+	0.959505i	$0.590895\pi$
$930$	4.68629	0.153670
$931$	0	0
$932$	−13.8701	−0.454329
$933$	−15.6274	−0.511619
$934$	5.92893	0.194001
$935$	3.17157	0.103722
$936$	−7.65685	−0.250272
$937$	34.1421	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$937$	34.1421	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$938$	0	0
$939$	−34.7990	−1.13562
$940$	15.2548	0.497558
$941$	2.07107	0.0675149	0.0337574	−	0.999430i	$-0.489253\pi$
$941$	2.07107	0.0675149	0.0337574	+	0.999430i	$0.489253\pi$
$942$	2.89949	0.0944706
$943$	47.7990	1.55655
$944$	7.97056	0.259420
$945$	0	0
$946$	−4.65685	−0.151407
$947$	20.5147	0.666639	0.333319	−	0.942814i	$-0.391831\pi$
$947$	20.5147	0.666639	0.333319	+	0.942814i	$0.391831\pi$
$948$	17.0294	0.553090
$949$	56.2843	1.82706
$950$	0.514719	0.0166997
$951$	−2.68629	−0.0871090
$952$	0	0
$953$	14.1421	0.458109	0.229054	−	0.973414i	$-0.426437\pi$
$953$	14.1421	0.458109	0.229054	+	0.973414i	$0.426437\pi$
$954$	−5.31371	−0.172038
$955$	20.6863	0.669393
$956$	−19.1716	−0.620053
$957$	−5.24264	−0.169471
$958$	5.79899	0.187357
$959$	0	0
$960$	8.34315	0.269274
$961$	1.00000	0.0322581
$962$	14.9706	0.482670
$963$	−1.65685	−0.0533914
$964$	28.0000	0.901819
$965$	−32.2843	−1.03927
$966$	0	0
$967$	27.0416	0.869600	0.434800	−	0.900527i	$-0.356819\pi$
$967$	27.0416	0.869600	0.434800	+	0.900527i	$0.356819\pi$
$968$	−1.58579	−0.0509691
$969$	1.97056	0.0633036
$970$	−4.54416	−0.145904
$971$	−28.9706	−0.929710	−0.464855	−	0.885387i	$-0.653893\pi$
$971$	−28.9706	−0.929710	−0.464855	+	0.885387i	$0.653893\pi$
$972$	−1.82843	−0.0586468
$973$	0	0
$974$	5.23045	0.167594
$975$	−4.82843	−0.154633
$976$	−12.0000	−0.384111
$977$	−7.17157	−0.229439	−0.114719	−	0.993398i	$-0.536597\pi$
$977$	−7.17157	−0.229439	−0.114719	+	0.993398i	$0.536597\pi$
$978$	5.37258	0.171796
$979$	14.1421	0.451985
$980$	0	0
$981$	−1.17157	−0.0374054
$982$	−7.65685	−0.244340
$983$	−35.9706	−1.14728	−0.573641	−	0.819107i	$-0.694470\pi$
$983$	−35.9706	−1.14728	−0.573641	+	0.819107i	$0.694470\pi$
$984$	10.8284	0.345198
$985$	27.1716	0.865758
$986$	3.44365	0.109668
$987$	0	0
$988$	10.9706	0.349020
$989$	78.6985	2.50247
$990$	−0.828427	−0.0263291
$991$	−47.3137	−1.50297	−0.751485	−	0.659750i	$-0.770662\pi$
$991$	−47.3137	−1.50297	−0.751485	+	0.659750i	$0.770662\pi$
$992$	−24.9706	−0.792816
$993$	5.51472	0.175004
$994$	0	0
$995$	−39.5980	−1.25534
$996$	−5.17157	−0.163868
$997$	38.1421	1.20797	0.603987	−	0.796994i	$-0.293578\pi$
$997$	38.1421	1.20797	0.603987	+	0.796994i	$0.293578\pi$
$998$	3.23045	0.102258
$999$	7.48528	0.236824

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.n.1.2		2
3.2	odd	2		4851.2.a.be.1.1		2
7.2	even	3		231.2.i.d.67.1	✓	4
7.4	even	3		231.2.i.d.100.1	yes	4
7.6	odd	2		1617.2.a.m.1.2		2
21.2	odd	6		693.2.i.f.298.2		4
21.11	odd	6		693.2.i.f.100.2		4
21.20	even	2		4851.2.a.bd.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.d.67.1	✓	4	7.2	even	3
231.2.i.d.100.1	yes	4	7.4	even	3
693.2.i.f.100.2		4	21.11	odd	6
693.2.i.f.298.2		4	21.2	odd	6
1617.2.a.m.1.2		2	7.6	odd	2
1617.2.a.n.1.2		2	1.1	even	1	trivial
4851.2.a.bd.1.1		2	21.20	even	2
4851.2.a.be.1.1		2	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)

\(f(q)\)	\(=\)	\(q+0.414214 q^{2} +1.00000 q^{3} -1.82843 q^{4} -2.00000 q^{5} +0.414214 q^{6} -1.58579 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.414214 q^{2} +1.00000 q^{3} -1.82843 q^{4} -2.00000 q^{5} +0.414214 q^{6} -1.58579 q^{8} +1.00000 q^{9} -0.828427 q^{10} +1.00000 q^{11} -1.82843 q^{12} +4.82843 q^{13} -2.00000 q^{15} +3.00000 q^{16} -1.58579 q^{17} +0.414214 q^{18} -1.24264 q^{19} +3.65685 q^{20} +0.414214 q^{22} -7.00000 q^{23} -1.58579 q^{24} -1.00000 q^{25} +2.00000 q^{26} +1.00000 q^{27} -5.24264 q^{29} -0.828427 q^{30} -5.65685 q^{31} +4.41421 q^{32} +1.00000 q^{33} -0.656854 q^{34} -1.82843 q^{36} +7.48528 q^{37} -0.514719 q^{38} +4.82843 q^{39} +3.17157 q^{40} -6.82843 q^{41} -11.2426 q^{43} -1.82843 q^{44} -2.00000 q^{45} -2.89949 q^{46} +4.17157 q^{47} +3.00000 q^{48} -0.414214 q^{50} -1.58579 q^{51} -8.82843 q^{52} -12.8284 q^{53} +0.414214 q^{54} -2.00000 q^{55} -1.24264 q^{57} -2.17157 q^{58} +2.65685 q^{59} +3.65685 q^{60} -4.00000 q^{61} -2.34315 q^{62} -4.17157 q^{64} -9.65685 q^{65} +0.414214 q^{66} -8.82843 q^{67} +2.89949 q^{68} -7.00000 q^{69} -9.82843 q^{71} -1.58579 q^{72} +11.6569 q^{73} +3.10051 q^{74} -1.00000 q^{75} +2.27208 q^{76} +2.00000 q^{78} -9.31371 q^{79} -6.00000 q^{80} +1.00000 q^{81} -2.82843 q^{82} +2.82843 q^{83} +3.17157 q^{85} -4.65685 q^{86} -5.24264 q^{87} -1.58579 q^{88} +14.1421 q^{89} -0.828427 q^{90} +12.7990 q^{92} -5.65685 q^{93} +1.72792 q^{94} +2.48528 q^{95} +4.41421 q^{96} +5.48528 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 4 * q^5 - 2 * q^6 - 6 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} - 6 q^{8} + 2 q^{9} + 4 q^{10} + 2 q^{11} + 2 q^{12} + 4 q^{13} - 4 q^{15} + 6 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 14 q^{23} - 6 q^{24} - 2 q^{25} + 4 q^{26} + 2 q^{27} - 2 q^{29} + 4 q^{30} + 6 q^{32} + 2 q^{33} + 10 q^{34} + 2 q^{36} - 2 q^{37} - 18 q^{38} + 4 q^{39} + 12 q^{40} - 8 q^{41} - 14 q^{43} + 2 q^{44} - 4 q^{45} + 14 q^{46} + 14 q^{47} + 6 q^{48} + 2 q^{50} - 6 q^{51} - 12 q^{52} - 20 q^{53} - 2 q^{54} - 4 q^{55} + 6 q^{57} - 10 q^{58} - 6 q^{59} - 4 q^{60} - 8 q^{61} - 16 q^{62} - 14 q^{64} - 8 q^{65} - 2 q^{66} - 12 q^{67} - 14 q^{68} - 14 q^{69} - 14 q^{71} - 6 q^{72} + 12 q^{73} + 26 q^{74} - 2 q^{75} + 30 q^{76} + 4 q^{78} + 4 q^{79} - 12 q^{80} + 2 q^{81} + 12 q^{85} + 2 q^{86} - 2 q^{87} - 6 q^{88} + 4 q^{90} - 14 q^{92} - 22 q^{94} - 12 q^{95} + 6 q^{96} - 6 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 4 * q^5 - 2 * q^6 - 6 * q^8 + 2 * q^9 + 4 * q^10 + 2 * q^11 + 2 * q^12 + 4 * q^13 - 4 * q^15 + 6 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 - 4 * q^20 - 2 * q^22 - 14 * q^23 - 6 * q^24 - 2 * q^25 + 4 * q^26 + 2 * q^27 - 2 * q^29 + 4 * q^30 + 6 * q^32 + 2 * q^33 + 10 * q^34 + 2 * q^36 - 2 * q^37 - 18 * q^38 + 4 * q^39 + 12 * q^40 - 8 * q^41 - 14 * q^43 + 2 * q^44 - 4 * q^45 + 14 * q^46 + 14 * q^47 + 6 * q^48 + 2 * q^50 - 6 * q^51 - 12 * q^52 - 20 * q^53 - 2 * q^54 - 4 * q^55 + 6 * q^57 - 10 * q^58 - 6 * q^59 - 4 * q^60 - 8 * q^61 - 16 * q^62 - 14 * q^64 - 8 * q^65 - 2 * q^66 - 12 * q^67 - 14 * q^68 - 14 * q^69 - 14 * q^71 - 6 * q^72 + 12 * q^73 + 26 * q^74 - 2 * q^75 + 30 * q^76 + 4 * q^78 + 4 * q^79 - 12 * q^80 + 2 * q^81 + 12 * q^85 + 2 * q^86 - 2 * q^87 - 6 * q^88 + 4 * q^90 - 14 * q^92 - 22 * q^94 - 12 * q^95 + 6 * q^96 - 6 * q^97 + 2 * q^99

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