LMFDB - Embedded newform 6027.2.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 123)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.81361$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} +1.10278 q^{5} -1.81361 q^{6} +1.28917 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} +1.10278 q^{5} -1.81361 q^{6} +1.28917 q^{8} +1.00000 q^{9} -2.00000 q^{10} +0.813607 q^{11} +1.28917 q^{12} -5.10278 q^{13} +1.10278 q^{15} -4.91638 q^{16} -3.39194 q^{17} -1.81361 q^{18} -3.10278 q^{19} +1.42166 q^{20} -1.47556 q^{22} -0.897225 q^{23} +1.28917 q^{24} -3.78389 q^{25} +9.25443 q^{26} +1.00000 q^{27} +4.44082 q^{29} -2.00000 q^{30} +8.96526 q^{31} +6.33804 q^{32} +0.813607 q^{33} +6.15165 q^{34} +1.28917 q^{36} +2.08362 q^{37} +5.62721 q^{38} -5.10278 q^{39} +1.42166 q^{40} -1.00000 q^{41} +9.07306 q^{43} +1.04888 q^{44} +1.10278 q^{45} +1.62721 q^{46} +0.235269 q^{47} -4.91638 q^{48} +6.86248 q^{50} -3.39194 q^{51} -6.57834 q^{52} +13.8328 q^{53} -1.81361 q^{54} +0.897225 q^{55} -3.10278 q^{57} -8.05390 q^{58} -1.04888 q^{59} +1.42166 q^{60} -1.91638 q^{61} -16.2594 q^{62} -1.66196 q^{64} -5.62721 q^{65} -1.47556 q^{66} -10.0383 q^{67} -4.37279 q^{68} -0.897225 q^{69} -12.8136 q^{71} +1.28917 q^{72} -4.75971 q^{73} -3.77886 q^{74} -3.78389 q^{75} -4.00000 q^{76} +9.25443 q^{78} -15.8328 q^{79} -5.42166 q^{80} +1.00000 q^{81} +1.81361 q^{82} +7.68111 q^{83} -3.74055 q^{85} -16.4550 q^{86} +4.44082 q^{87} +1.04888 q^{88} -13.2544 q^{89} -2.00000 q^{90} -1.15667 q^{92} +8.96526 q^{93} -0.426686 q^{94} -3.42166 q^{95} +6.33804 q^{96} -2.72999 q^{97} +0.813607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} + 3 q^{4} - 4 q^{5} + q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 + 3 * q^4 - 4 * q^5 + q^6 + 3 * q^8 + 3 * q^9	$ 3 q + q^{2} + 3 q^{3} + 3 q^{4} - 4 q^{5} + q^{6} + 3 q^{8} + 3 q^{9} - 6 q^{10} - 4 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{15} - q^{16} - 2 q^{17} + q^{18} - 2 q^{19} + 6 q^{20} - 10 q^{22} - 10 q^{23} + 3 q^{24} + 5 q^{25} + 2 q^{26} + 3 q^{27} - 6 q^{29} - 6 q^{30} + 2 q^{31} + 7 q^{32} - 4 q^{33} + 3 q^{36} + 20 q^{37} + 4 q^{38} - 8 q^{39} + 6 q^{40} - 3 q^{41} + 10 q^{43} - 8 q^{44} - 4 q^{45} - 8 q^{46} - 4 q^{47} - q^{48} + 3 q^{50} - 2 q^{51} - 18 q^{52} + 14 q^{53} + q^{54} + 10 q^{55} - 2 q^{57} - 28 q^{58} + 8 q^{59} + 6 q^{60} + 8 q^{61} - 38 q^{62} - 17 q^{64} - 4 q^{65} - 10 q^{66} + 12 q^{67} - 26 q^{68} - 10 q^{69} - 32 q^{71} + 3 q^{72} - 4 q^{73} + 20 q^{74} + 5 q^{75} - 12 q^{76} + 2 q^{78} - 20 q^{79} - 18 q^{80} + 3 q^{81} - q^{82} + 14 q^{83} - 22 q^{85} + 6 q^{86} - 6 q^{87} - 8 q^{88} - 14 q^{89} - 6 q^{90} + 2 q^{93} - 18 q^{94} - 12 q^{95} + 7 q^{96} + 12 q^{97} - 4 q^{99}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 + 3 * q^4 - 4 * q^5 + q^6 + 3 * q^8 + 3 * q^9 - 6 * q^10 - 4 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^15 - q^16 - 2 * q^17 + q^18 - 2 * q^19 + 6 * q^20 - 10 * q^22 - 10 * q^23 + 3 * q^24 + 5 * q^25 + 2 * q^26 + 3 * q^27 - 6 * q^29 - 6 * q^30 + 2 * q^31 + 7 * q^32 - 4 * q^33 + 3 * q^36 + 20 * q^37 + 4 * q^38 - 8 * q^39 + 6 * q^40 - 3 * q^41 + 10 * q^43 - 8 * q^44 - 4 * q^45 - 8 * q^46 - 4 * q^47 - q^48 + 3 * q^50 - 2 * q^51 - 18 * q^52 + 14 * q^53 + q^54 + 10 * q^55 - 2 * q^57 - 28 * q^58 + 8 * q^59 + 6 * q^60 + 8 * q^61 - 38 * q^62 - 17 * q^64 - 4 * q^65 - 10 * q^66 + 12 * q^67 - 26 * q^68 - 10 * q^69 - 32 * q^71 + 3 * q^72 - 4 * q^73 + 20 * q^74 + 5 * q^75 - 12 * q^76 + 2 * q^78 - 20 * q^79 - 18 * q^80 + 3 * q^81 - q^82 + 14 * q^83 - 22 * q^85 + 6 * q^86 - 6 * q^87 - 8 * q^88 - 14 * q^89 - 6 * q^90 + 2 * q^93 - 18 * q^94 - 12 * q^95 + 7 * q^96 + 12 * q^97 - 4 * 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 $

$2$	−1.81361	−1.28241	−0.641207	−	0.767368i	$-0.721566\pi$
$2$	−1.81361	−1.28241	−0.641207	+	0.767368i	$0.721566\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.28917	0.644584
$5$	1.10278	0.493176	0.246588	−	0.969120i	$-0.420691\pi$
$5$	1.10278	0.493176	0.246588	+	0.969120i	$0.420691\pi$
$6$	−1.81361	−0.740402
$7$	0	0
$7$	0	0
$8$	1.28917	0.455790
$9$	1.00000	0.333333
$10$	−2.00000	−0.632456
$11$	0.813607	0.245312	0.122656	−	0.992449i	$-0.460859\pi$
$11$	0.813607	0.245312	0.122656	+	0.992449i	$0.460859\pi$
$12$	1.28917	0.372151
$13$	−5.10278	−1.41526	−0.707628	−	0.706586i	$-0.750235\pi$
$13$	−5.10278	−1.41526	−0.707628	+	0.706586i	$0.750235\pi$
$14$	0	0
$15$	1.10278	0.284735
$16$	−4.91638	−1.22910
$17$	−3.39194	−0.822667	−0.411334	−	0.911485i	$-0.634937\pi$
$17$	−3.39194	−0.822667	−0.411334	+	0.911485i	$0.634937\pi$
$18$	−1.81361	−0.427471
$19$	−3.10278	−0.711825	−0.355913	−	0.934519i	$-0.615830\pi$
$19$	−3.10278	−0.711825	−0.355913	+	0.934519i	$0.615830\pi$
$20$	1.42166	0.317893
$21$	0	0
$22$	−1.47556	−0.314591
$23$	−0.897225	−0.187084	−0.0935422	−	0.995615i	$-0.529819\pi$
$23$	−0.897225	−0.187084	−0.0935422	+	0.995615i	$0.529819\pi$
$24$	1.28917	0.263150
$25$	−3.78389	−0.756777
$26$	9.25443	1.81494
$27$	1.00000	0.192450
$28$	0	0
$29$	4.44082	0.824639	0.412320	−	0.911039i	$-0.364719\pi$
$29$	4.44082	0.824639	0.412320	+	0.911039i	$0.364719\pi$
$30$	−2.00000	−0.365148
$31$	8.96526	1.61021	0.805104	−	0.593134i	$-0.202110\pi$
$31$	8.96526	1.61021	0.805104	+	0.593134i	$0.202110\pi$
$32$	6.33804	1.12042
$33$	0.813607	0.141631
$34$	6.15165	1.05500
$35$	0	0
$36$	1.28917	0.214861
$37$	2.08362	0.342545	0.171272	−	0.985224i	$-0.445212\pi$
$37$	2.08362	0.342545	0.171272	+	0.985224i	$0.445212\pi$
$38$	5.62721	0.912854
$39$	−5.10278	−0.817098
$40$	1.42166	0.224785
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	9.07306	1.38363	0.691814	−	0.722076i	$-0.256812\pi$
$43$	9.07306	1.38363	0.691814	+	0.722076i	$0.256812\pi$
$44$	1.04888	0.158124
$45$	1.10278	0.164392
$46$	1.62721	0.239919
$47$	0.235269	0.0343176	0.0171588	−	0.999853i	$-0.494538\pi$
$47$	0.235269	0.0343176	0.0171588	+	0.999853i	$0.494538\pi$
$48$	−4.91638	−0.709619
$49$	0	0
$50$	6.86248	0.970502
$51$	−3.39194	−0.474967
$52$	−6.57834	−0.912251
$53$	13.8328	1.90008	0.950038	−	0.312134i	$-0.101044\pi$
$53$	13.8328	1.90008	0.950038	+	0.312134i	$0.101044\pi$
$54$	−1.81361	−0.246801
$55$	0.897225	0.120982
$56$	0	0
$57$	−3.10278	−0.410973
$58$	−8.05390	−1.05753
$59$	−1.04888	−0.136552	−0.0682760	−	0.997666i	$-0.521750\pi$
$59$	−1.04888	−0.136552	−0.0682760	+	0.997666i	$0.521750\pi$
$60$	1.42166	0.183536
$61$	−1.91638	−0.245368	−0.122684	−	0.992446i	$-0.539150\pi$
$61$	−1.91638	−0.245368	−0.122684	+	0.992446i	$0.539150\pi$
$62$	−16.2594	−2.06495
$63$	0	0
$64$	−1.66196	−0.207744
$65$	−5.62721	−0.697970
$66$	−1.47556	−0.181629
$67$	−10.0383	−1.22638	−0.613188	−	0.789937i	$-0.710113\pi$
$67$	−10.0383	−1.22638	−0.613188	+	0.789937i	$0.710113\pi$
$68$	−4.37279	−0.530278
$69$	−0.897225	−0.108013
$70$	0	0
$71$	−12.8136	−1.52070	−0.760348	−	0.649516i	$-0.774971\pi$
$71$	−12.8136	−1.52070	−0.760348	+	0.649516i	$0.774971\pi$
$72$	1.28917	0.151930
$73$	−4.75971	−0.557082	−0.278541	−	0.960424i	$-0.589851\pi$
$73$	−4.75971	−0.557082	−0.278541	+	0.960424i	$0.589851\pi$
$74$	−3.77886	−0.439284
$75$	−3.78389	−0.436926
$76$	−4.00000	−0.458831
$77$	0	0
$78$	9.25443	1.04786
$79$	−15.8328	−1.78133	−0.890663	−	0.454665i	$-0.849759\pi$
$79$	−15.8328	−1.78133	−0.890663	+	0.454665i	$0.849759\pi$
$80$	−5.42166	−0.606160
$81$	1.00000	0.111111
$82$	1.81361	0.200279
$83$	7.68111	0.843112	0.421556	−	0.906802i	$-0.361484\pi$
$83$	7.68111	0.843112	0.421556	+	0.906802i	$0.361484\pi$
$84$	0	0
$85$	−3.74055	−0.405720
$86$	−16.4550	−1.77438
$87$	4.44082	0.476106
$88$	1.04888	0.111811
$89$	−13.2544	−1.40497	−0.702483	−	0.711700i	$-0.747925\pi$
$89$	−13.2544	−1.40497	−0.702483	+	0.711700i	$0.747925\pi$
$90$	−2.00000	−0.210819
$91$	0	0
$92$	−1.15667	−0.120592
$93$	8.96526	0.929654
$94$	−0.426686	−0.0440093
$95$	−3.42166	−0.351055
$96$	6.33804	0.646874
$97$	−2.72999	−0.277188	−0.138594	−	0.990349i	$-0.544258\pi$
$97$	−2.72999	−0.277188	−0.138594	+	0.990349i	$0.544258\pi$
$98$	0	0
$99$	0.813607	0.0817705
$100$	−4.87807	−0.487807
$101$	11.8625	1.18036	0.590181	−	0.807271i	$-0.299057\pi$
$101$	11.8625	1.18036	0.590181	+	0.807271i	$0.299057\pi$
$102$	6.15165	0.609104
$103$	0.494719	0.0487461	0.0243730	−	0.999703i	$-0.492241\pi$
$103$	0.494719	0.0487461	0.0243730	+	0.999703i	$0.492241\pi$
$104$	−6.57834	−0.645059
$105$	0	0
$106$	−25.0872	−2.43668
$107$	−15.0872	−1.45853	−0.729267	−	0.684229i	$-0.760139\pi$
$107$	−15.0872	−1.45853	−0.729267	+	0.684229i	$0.760139\pi$
$108$	1.28917	0.124050
$109$	5.10278	0.488757	0.244379	−	0.969680i	$-0.421416\pi$
$109$	5.10278	0.488757	0.244379	+	0.969680i	$0.421416\pi$
$110$	−1.62721	−0.155149
$111$	2.08362	0.197768
$112$	0	0
$113$	−17.5139	−1.64757	−0.823783	−	0.566905i	$-0.808141\pi$
$113$	−17.5139	−1.64757	−0.823783	+	0.566905i	$0.808141\pi$
$114$	5.62721	0.527037
$115$	−0.989437	−0.0922655
$116$	5.72496	0.531550
$117$	−5.10278	−0.471752
$118$	1.90225	0.175116
$119$	0	0
$120$	1.42166	0.129779
$121$	−10.3380	−0.939822
$122$	3.47556	0.314663
$123$	−1.00000	−0.0901670
$124$	11.5577	1.03791
$125$	−9.68665	−0.866400
$126$	0	0
$127$	12.8816	1.14306	0.571530	−	0.820581i	$-0.306350\pi$
$127$	12.8816	1.14306	0.571530	+	0.820581i	$0.306350\pi$
$128$	−9.66196	−0.854004
$129$	9.07306	0.798838
$130$	10.2056	0.895086
$131$	6.35720	0.555431	0.277716	−	0.960663i	$-0.410423\pi$
$131$	6.35720	0.555431	0.277716	+	0.960663i	$0.410423\pi$
$132$	1.04888	0.0912929
$133$	0	0
$134$	18.2056	1.57272
$135$	1.10278	0.0949118
$136$	−4.37279	−0.374963
$137$	−17.4897	−1.49425	−0.747123	−	0.664686i	$-0.768565\pi$
$137$	−17.4897	−1.49425	−0.747123	+	0.664686i	$0.768565\pi$
$138$	1.62721	0.138518
$139$	−15.7250	−1.33377	−0.666887	−	0.745159i	$-0.732374\pi$
$139$	−15.7250	−1.33377	−0.666887	+	0.745159i	$0.732374\pi$
$140$	0	0
$141$	0.235269	0.0198133
$142$	23.2388	1.95016
$143$	−4.15165	−0.347178
$144$	−4.91638	−0.409698
$145$	4.89722	0.406692
$146$	8.63224	0.714409
$147$	0	0
$148$	2.68614	0.220799
$149$	11.5678	0.947669	0.473835	−	0.880614i	$-0.342869\pi$
$149$	11.5678	0.947669	0.473835	+	0.880614i	$0.342869\pi$
$150$	6.86248	0.560319
$151$	19.2544	1.56690	0.783451	−	0.621453i	$-0.213457\pi$
$151$	19.2544	1.56690	0.783451	+	0.621453i	$0.213457\pi$
$152$	−4.00000	−0.324443
$153$	−3.39194	−0.274222
$154$	0	0
$155$	9.88666	0.794116
$156$	−6.57834	−0.526688
$157$	20.9200	1.66959	0.834797	−	0.550558i	$-0.185585\pi$
$157$	20.9200	1.66959	0.834797	+	0.550558i	$0.185585\pi$
$158$	28.7144	2.28440
$159$	13.8328	1.09701
$160$	6.98944	0.552564
$161$	0	0
$162$	−1.81361	−0.142490
$163$	−12.7980	−1.00242	−0.501209	−	0.865326i	$-0.667111\pi$
$163$	−12.7980	−1.00242	−0.501209	+	0.865326i	$0.667111\pi$
$164$	−1.28917	−0.100667
$165$	0.897225	0.0698489
$166$	−13.9305	−1.08122
$167$	−9.62721	−0.744976	−0.372488	−	0.928037i	$-0.621495\pi$
$167$	−9.62721	−0.744976	−0.372488	+	0.928037i	$0.621495\pi$
$168$	0	0
$169$	13.0383	1.00295
$170$	6.78389	0.520300
$171$	−3.10278	−0.237275
$172$	11.6967	0.891865
$173$	−11.9461	−0.908245	−0.454123	−	0.890939i	$-0.650047\pi$
$173$	−11.9461	−0.908245	−0.454123	+	0.890939i	$0.650047\pi$
$174$	−8.05390	−0.610565
$175$	0	0
$176$	−4.00000	−0.301511
$177$	−1.04888	−0.0788383
$178$	24.0383	1.80175
$179$	−2.13752	−0.159766	−0.0798828	−	0.996804i	$-0.525455\pi$
$179$	−2.13752	−0.159766	−0.0798828	+	0.996804i	$0.525455\pi$
$180$	1.42166	0.105964
$181$	1.83276	0.136228	0.0681141	−	0.997678i	$-0.478302\pi$
$181$	1.83276	0.136228	0.0681141	+	0.997678i	$0.478302\pi$
$182$	0	0
$183$	−1.91638	−0.141663
$184$	−1.15667	−0.0852712
$185$	2.29776	0.168935
$186$	−16.2594	−1.19220
$187$	−2.75971	−0.201810
$188$	0.303302	0.0221206
$189$	0	0
$190$	6.20555	0.450198
$191$	−18.6167	−1.34705	−0.673527	−	0.739163i	$-0.735221\pi$
$191$	−18.6167	−1.34705	−0.673527	+	0.739163i	$0.735221\pi$
$192$	−1.66196	−0.119941
$193$	15.6116	1.12375	0.561875	−	0.827222i	$-0.310080\pi$
$193$	15.6116	1.12375	0.561875	+	0.827222i	$0.310080\pi$
$194$	4.95112	0.355470
$195$	−5.62721	−0.402973
$196$	0	0
$197$	−5.21057	−0.371238	−0.185619	−	0.982622i	$-0.559429\pi$
$197$	−5.21057	−0.371238	−0.185619	+	0.982622i	$0.559429\pi$
$198$	−1.47556	−0.104864
$199$	−2.05390	−0.145597	−0.0727985	−	0.997347i	$-0.523193\pi$
$199$	−2.05390	−0.145597	−0.0727985	+	0.997347i	$0.523193\pi$
$200$	−4.87807	−0.344932
$201$	−10.0383	−0.708048
$202$	−21.5139	−1.51371
$203$	0	0
$204$	−4.37279	−0.306156
$205$	−1.10278	−0.0770212
$206$	−0.897225	−0.0625126
$207$	−0.897225	−0.0623614
$208$	25.0872	1.73948
$209$	−2.52444	−0.174619
$210$	0	0
$211$	−9.04888	−0.622950	−0.311475	−	0.950254i	$-0.600823\pi$
$211$	−9.04888	−0.622950	−0.311475	+	0.950254i	$0.600823\pi$
$212$	17.8328	1.22476
$213$	−12.8136	−0.877974
$214$	27.3622	1.87044
$215$	10.0055	0.682372
$216$	1.28917	0.0877168
$217$	0	0
$218$	−9.25443	−0.626789
$219$	−4.75971	−0.321631
$220$	1.15667	0.0779830
$221$	17.3083	1.16428
$222$	−3.77886	−0.253621
$223$	−24.8222	−1.66222	−0.831109	−	0.556110i	$-0.812293\pi$
$223$	−24.8222	−1.66222	−0.831109	+	0.556110i	$0.812293\pi$
$224$	0	0
$225$	−3.78389	−0.252259
$226$	31.7633	2.11286
$227$	−16.6464	−1.10486	−0.552429	−	0.833560i	$-0.686299\pi$
$227$	−16.6464	−1.10486	−0.552429	+	0.833560i	$0.686299\pi$
$228$	−4.00000	−0.264906
$229$	15.7789	1.04270	0.521348	−	0.853344i	$-0.325429\pi$
$229$	15.7789	1.04270	0.521348	+	0.853344i	$0.325429\pi$
$230$	1.79445	0.118323
$231$	0	0
$232$	5.72496	0.375862
$233$	−24.9200	−1.63256	−0.816280	−	0.577656i	$-0.803967\pi$
$233$	−24.9200	−1.63256	−0.816280	+	0.577656i	$0.803967\pi$
$234$	9.25443	0.604981
$235$	0.259449	0.0169246
$236$	−1.35218	−0.0880193
$237$	−15.8328	−1.02845
$238$	0	0
$239$	−2.95112	−0.190892	−0.0954462	−	0.995435i	$-0.530428\pi$
$239$	−2.95112	−0.190892	−0.0954462	+	0.995435i	$0.530428\pi$
$240$	−5.42166	−0.349967
$241$	16.5925	1.06881	0.534407	−	0.845227i	$-0.320535\pi$
$241$	16.5925	1.06881	0.534407	+	0.845227i	$0.320535\pi$
$242$	18.7491	1.20524
$243$	1.00000	0.0641500
$244$	−2.47054	−0.158160
$245$	0	0
$246$	1.81361	0.115631
$247$	15.8328	1.00741
$248$	11.5577	0.733916
$249$	7.68111	0.486771
$250$	17.5678	1.11108
$251$	20.1361	1.27098	0.635489	−	0.772110i	$-0.280799\pi$
$251$	20.1361	1.27098	0.635489	+	0.772110i	$0.280799\pi$
$252$	0	0
$253$	−0.729988	−0.0458940
$254$	−23.3622	−1.46588
$255$	−3.74055	−0.234242
$256$	20.8469	1.30293
$257$	−25.9008	−1.61565	−0.807824	−	0.589424i	$-0.799355\pi$
$257$	−25.9008	−1.61565	−0.807824	+	0.589424i	$0.799355\pi$
$258$	−16.4550	−1.02444
$259$	0	0
$260$	−7.25443	−0.449900
$261$	4.44082	0.274880
$262$	−11.5295	−0.712292
$263$	−22.4408	−1.38376	−0.691880	−	0.722012i	$-0.743217\pi$
$263$	−22.4408	−1.38376	−0.691880	+	0.722012i	$0.743217\pi$
$264$	1.04888	0.0645538
$265$	15.2544	0.937072
$266$	0	0
$267$	−13.2544	−0.811158
$268$	−12.9411	−0.790502
$269$	−7.62721	−0.465039	−0.232520	−	0.972592i	$-0.574697\pi$
$269$	−7.62721	−0.465039	−0.232520	+	0.972592i	$0.574697\pi$
$270$	−2.00000	−0.121716
$271$	−19.9164	−1.20983	−0.604917	−	0.796289i	$-0.706794\pi$
$271$	−19.9164	−1.20983	−0.604917	+	0.796289i	$0.706794\pi$
$272$	16.6761	1.01114
$273$	0	0
$274$	31.7194	1.91624
$275$	−3.07860	−0.185646
$276$	−1.15667	−0.0696236
$277$	−17.6413	−1.05997	−0.529983	−	0.848008i	$-0.677802\pi$
$277$	−17.6413	−1.05997	−0.529983	+	0.848008i	$0.677802\pi$
$278$	28.5189	1.71045
$279$	8.96526	0.536736
$280$	0	0
$281$	−0.0297193	−0.00177291	−0.000886453	−	1.00000i	$-0.500282\pi$
$281$	−0.0297193	−0.00177291	−0.000886453		1.00000i	$0.500282\pi$
$282$	−0.426686	−0.0254088
$283$	10.1814	0.605220	0.302610	−	0.953115i	$-0.402142\pi$
$283$	10.1814	0.605220	0.302610	+	0.953115i	$0.402142\pi$
$284$	−16.5189	−0.980216
$285$	−3.42166	−0.202682
$286$	7.52946	0.445226
$287$	0	0
$288$	6.33804	0.373473
$289$	−5.49472	−0.323219
$290$	−8.88164	−0.521548
$291$	−2.72999	−0.160035
$292$	−6.13607	−0.359086
$293$	−3.14808	−0.183913	−0.0919564	−	0.995763i	$-0.529312\pi$
$293$	−3.14808	−0.183913	−0.0919564	+	0.995763i	$0.529312\pi$
$294$	0	0
$295$	−1.15667	−0.0673442
$296$	2.68614	0.156128
$297$	0.813607	0.0472102
$298$	−20.9794	−1.21530
$299$	4.57834	0.264772
$300$	−4.87807	−0.281635
$301$	0	0
$302$	−34.9200	−2.00942
$303$	11.8625	0.681482
$304$	15.2544	0.874901
$305$	−2.11334	−0.121009
$306$	6.15165	0.351666
$307$	12.7980	0.730422	0.365211	−	0.930925i	$-0.380997\pi$
$307$	12.7980	0.730422	0.365211	+	0.930925i	$0.380997\pi$
$308$	0	0
$309$	0.494719	0.0281436
$310$	−17.9305	−1.01838
$311$	−26.6167	−1.50929	−0.754646	−	0.656132i	$-0.772191\pi$
$311$	−26.6167	−1.50929	−0.754646	+	0.656132i	$0.772191\pi$
$312$	−6.57834	−0.372425
$313$	3.00502	0.169854	0.0849270	−	0.996387i	$-0.472934\pi$
$313$	3.00502	0.169854	0.0849270	+	0.996387i	$0.472934\pi$
$314$	−37.9406	−2.14111
$315$	0	0
$316$	−20.4111	−1.14821
$317$	−4.33302	−0.243367	−0.121683	−	0.992569i	$-0.538829\pi$
$317$	−4.33302	−0.243367	−0.121683	+	0.992569i	$0.538829\pi$
$318$	−25.0872	−1.40682
$319$	3.61308	0.202294
$320$	−1.83276	−0.102455
$321$	−15.0872	−0.842085
$322$	0	0
$323$	10.5244	0.585595
$324$	1.28917	0.0716205
$325$	19.3083	1.07103
$326$	23.2106	1.28551
$327$	5.10278	0.282184
$328$	−1.28917	−0.0711824
$329$	0	0
$330$	−1.62721	−0.0895751
$331$	5.53500	0.304231	0.152116	−	0.988363i	$-0.451391\pi$
$331$	5.53500	0.304231	0.152116	+	0.988363i	$0.451391\pi$
$332$	9.90225	0.543456
$333$	2.08362	0.114182
$334$	17.4600	0.955367
$335$	−11.0700	−0.604819
$336$	0	0
$337$	−3.71083	−0.202142	−0.101071	−	0.994879i	$-0.532227\pi$
$337$	−3.71083	−0.202142	−0.101071	+	0.994879i	$0.532227\pi$
$338$	−23.6464	−1.28619
$339$	−17.5139	−0.951223
$340$	−4.82220	−0.261521
$341$	7.29419	0.395003
$342$	5.62721	0.304285
$343$	0	0
$344$	11.6967	0.630644
$345$	−0.989437	−0.0532695
$346$	21.6655	1.16475
$347$	3.07860	0.165268	0.0826338	−	0.996580i	$-0.473667\pi$
$347$	3.07860	0.165268	0.0826338	+	0.996580i	$0.473667\pi$
$348$	5.72496	0.306890
$349$	−14.7980	−0.792120	−0.396060	−	0.918225i	$-0.629623\pi$
$349$	−14.7980	−0.792120	−0.396060	+	0.918225i	$0.629623\pi$
$350$	0	0
$351$	−5.10278	−0.272366
$352$	5.15667	0.274852
$353$	−26.8222	−1.42760	−0.713801	−	0.700349i	$-0.753028\pi$
$353$	−26.8222	−1.42760	−0.713801	+	0.700349i	$0.753028\pi$
$354$	1.90225	0.101103
$355$	−14.1305	−0.749970
$356$	−17.0872	−0.905619
$357$	0	0
$358$	3.87662	0.204886
$359$	2.35720	0.124408	0.0622042	−	0.998063i	$-0.480187\pi$
$359$	2.35720	0.124408	0.0622042	+	0.998063i	$0.480187\pi$
$360$	1.42166	0.0749282
$361$	−9.37279	−0.493305
$362$	−3.32391	−0.174701
$363$	−10.3380	−0.542607
$364$	0	0
$365$	−5.24889	−0.274739
$366$	3.47556	0.181671
$367$	−23.1708	−1.20951	−0.604753	−	0.796413i	$-0.706728\pi$
$367$	−23.1708	−1.20951	−0.604753	+	0.796413i	$0.706728\pi$
$368$	4.41110	0.229944
$369$	−1.00000	−0.0520579
$370$	−4.16724	−0.216644
$371$	0	0
$372$	11.5577	0.599240
$373$	35.2091	1.82306	0.911530	−	0.411235i	$-0.134902\pi$
$373$	35.2091	1.82306	0.911530	+	0.411235i	$0.134902\pi$
$374$	5.00502	0.258804
$375$	−9.68665	−0.500217
$376$	0.303302	0.0156416
$377$	−22.6605	−1.16708
$378$	0	0
$379$	−26.0383	−1.33750	−0.668749	−	0.743488i	$-0.733170\pi$
$379$	−26.0383	−1.33750	−0.668749	+	0.743488i	$0.733170\pi$
$380$	−4.41110	−0.226285
$381$	12.8816	0.659946
$382$	33.7633	1.72748
$383$	−15.3819	−0.785978	−0.392989	−	0.919543i	$-0.628559\pi$
$383$	−15.3819	−0.785978	−0.392989	+	0.919543i	$0.628559\pi$
$384$	−9.66196	−0.493060
$385$	0	0
$386$	−28.3133	−1.44111
$387$	9.07306	0.461209
$388$	−3.51941	−0.178671
$389$	4.46500	0.226384	0.113192	−	0.993573i	$-0.463892\pi$
$389$	4.46500	0.226384	0.113192	+	0.993573i	$0.463892\pi$
$390$	10.2056	0.516778
$391$	3.04334	0.153908
$392$	0	0
$393$	6.35720	0.320678
$394$	9.44993	0.476081
$395$	−17.4600	−0.878507
$396$	1.04888	0.0527080
$397$	10.5628	0.530129	0.265065	−	0.964231i	$-0.414607\pi$
$397$	10.5628	0.530129	0.265065	+	0.964231i	$0.414607\pi$
$398$	3.72496	0.186716
$399$	0	0
$400$	18.6030	0.930152
$401$	13.0872	0.653543	0.326772	−	0.945103i	$-0.394039\pi$
$401$	13.0872	0.653543	0.326772	+	0.945103i	$0.394039\pi$
$402$	18.2056	0.908010
$403$	−45.7477	−2.27885
$404$	15.2927	0.760842
$405$	1.10278	0.0547973
$406$	0	0
$407$	1.69525	0.0840302
$408$	−4.37279	−0.216485
$409$	18.5542	0.917444	0.458722	−	0.888580i	$-0.348307\pi$
$409$	18.5542	0.917444	0.458722	+	0.888580i	$0.348307\pi$
$410$	2.00000	0.0987730
$411$	−17.4897	−0.862703
$412$	0.637776	0.0314210
$413$	0	0
$414$	1.62721	0.0799732
$415$	8.47054	0.415802
$416$	−32.3416	−1.58568
$417$	−15.7250	−0.770055
$418$	4.57834	0.223934
$419$	25.6116	1.25121	0.625605	−	0.780140i	$-0.284852\pi$
$419$	25.6116	1.25121	0.625605	+	0.780140i	$0.284852\pi$
$420$	0	0
$421$	−8.67609	−0.422847	−0.211423	−	0.977395i	$-0.567810\pi$
$421$	−8.67609	−0.422847	−0.211423	+	0.977395i	$0.567810\pi$
$422$	16.4111	0.798880
$423$	0.235269	0.0114392
$424$	17.8328	0.866036
$425$	12.8347	0.622576
$426$	23.2388	1.12593
$427$	0	0
$428$	−19.4499	−0.940148
$429$	−4.15165	−0.200444
$430$	−18.1461	−0.875083
$431$	7.10278	0.342129	0.171064	−	0.985260i	$-0.445279\pi$
$431$	7.10278	0.342129	0.171064	+	0.985260i	$0.445279\pi$
$432$	−4.91638	−0.236540
$433$	11.0247	0.529813	0.264907	−	0.964274i	$-0.414659\pi$
$433$	11.0247	0.529813	0.264907	+	0.964274i	$0.414659\pi$
$434$	0	0
$435$	4.89722	0.234804
$436$	6.57834	0.315045
$437$	2.78389	0.133171
$438$	8.63224	0.412464
$439$	1.32391	0.0631868	0.0315934	−	0.999501i	$-0.489942\pi$
$439$	1.32391	0.0631868	0.0315934	+	0.999501i	$0.489942\pi$
$440$	1.15667	0.0551423
$441$	0	0
$442$	−31.3905	−1.49309
$443$	15.5889	0.740651	0.370325	−	0.928902i	$-0.379246\pi$
$443$	15.5889	0.740651	0.370325	+	0.928902i	$0.379246\pi$
$444$	2.68614	0.127478
$445$	−14.6167	−0.692896
$446$	45.0177	2.13165
$447$	11.5678	0.547137
$448$	0	0
$449$	−32.7839	−1.54717	−0.773584	−	0.633694i	$-0.781538\pi$
$449$	−32.7839	−1.54717	−0.773584	+	0.633694i	$0.781538\pi$
$450$	6.86248	0.323501
$451$	−0.813607	−0.0383112
$452$	−22.5783	−1.06200
$453$	19.2544	0.904652
$454$	30.1900	1.41689
$455$	0	0
$456$	−4.00000	−0.187317
$457$	−14.1672	−0.662715	−0.331358	−	0.943505i	$-0.607507\pi$
$457$	−14.1672	−0.662715	−0.331358	+	0.943505i	$0.607507\pi$
$458$	−28.6167	−1.33717
$459$	−3.39194	−0.158322
$460$	−1.27555	−0.0594729
$461$	30.0766	1.40081	0.700404	−	0.713747i	$-0.253003\pi$
$461$	30.0766	1.40081	0.700404	+	0.713747i	$0.253003\pi$
$462$	0	0
$463$	−23.8766	−1.10964	−0.554820	−	0.831970i	$-0.687213\pi$
$463$	−23.8766	−1.10964	−0.554820	+	0.831970i	$0.687213\pi$
$464$	−21.8328	−1.01356
$465$	9.88666	0.458483
$466$	45.1950	2.09362
$467$	9.73501	0.450483	0.225241	−	0.974303i	$-0.427683\pi$
$467$	9.73501	0.450483	0.225241	+	0.974303i	$0.427683\pi$
$468$	−6.57834	−0.304084
$469$	0	0
$470$	−0.470539	−0.0217043
$471$	20.9200	0.963941
$472$	−1.35218	−0.0622390
$473$	7.38190	0.339420
$474$	28.7144	1.31890
$475$	11.7406	0.538693
$476$	0	0
$477$	13.8328	0.633359
$478$	5.35218	0.244803
$479$	1.17635	0.0537487	0.0268743	−	0.999639i	$-0.491445\pi$
$479$	1.17635	0.0537487	0.0268743	+	0.999639i	$0.491445\pi$
$480$	6.98944	0.319023
$481$	−10.6322	−0.484788
$482$	−30.0922	−1.37066
$483$	0	0
$484$	−13.3275	−0.605795
$485$	−3.01056	−0.136703
$486$	−1.81361	−0.0822669
$487$	20.6025	0.933589	0.466795	−	0.884366i	$-0.345409\pi$
$487$	20.6025	0.933589	0.466795	+	0.884366i	$0.345409\pi$
$488$	−2.47054	−0.111836
$489$	−12.7980	−0.578746
$490$	0	0
$491$	14.1900	0.640384	0.320192	−	0.947353i	$-0.396253\pi$
$491$	14.1900	0.640384	0.320192	+	0.947353i	$0.396253\pi$
$492$	−1.28917	−0.0581202
$493$	−15.0630	−0.678404
$494$	−28.7144	−1.29192
$495$	0.897225	0.0403273
$496$	−44.0766	−1.97910
$497$	0	0
$498$	−13.9305	−0.624241
$499$	−21.4600	−0.960680	−0.480340	−	0.877082i	$-0.659487\pi$
$499$	−21.4600	−0.960680	−0.480340	+	0.877082i	$0.659487\pi$
$500$	−12.4877	−0.558468
$501$	−9.62721	−0.430112
$502$	−36.5189	−1.62992
$503$	15.5491	0.693302	0.346651	−	0.937994i	$-0.387319\pi$
$503$	15.5491	0.693302	0.346651	+	0.937994i	$0.387319\pi$
$504$	0	0
$505$	13.0816	0.582126
$506$	1.32391	0.0588550
$507$	13.0383	0.579052
$508$	16.6066	0.736799
$509$	−22.7542	−1.00856	−0.504280	−	0.863540i	$-0.668242\pi$
$509$	−22.7542	−1.00856	−0.504280	+	0.863540i	$0.668242\pi$
$510$	6.78389	0.300396
$511$	0	0
$512$	−18.4842	−0.816892
$513$	−3.10278	−0.136991
$514$	46.9739	2.07193
$515$	0.545563	0.0240404
$516$	11.6967	0.514918
$517$	0.191417	0.00841850
$518$	0	0
$519$	−11.9461	−0.524376
$520$	−7.25443	−0.318128
$521$	38.7230	1.69649	0.848243	−	0.529608i	$-0.177661\pi$
$521$	38.7230	1.69649	0.848243	+	0.529608i	$0.177661\pi$
$522$	−8.05390	−0.352510
$523$	−6.56829	−0.287211	−0.143606	−	0.989635i	$-0.545870\pi$
$523$	−6.56829	−0.287211	−0.143606	+	0.989635i	$0.545870\pi$
$524$	8.19550	0.358022
$525$	0	0
$526$	40.6988	1.77455
$527$	−30.4096	−1.32467
$528$	−4.00000	−0.174078
$529$	−22.1950	−0.964999
$530$	−27.6655	−1.20171
$531$	−1.04888	−0.0455173
$532$	0	0
$533$	5.10278	0.221026
$534$	24.0383	1.04024
$535$	−16.6378	−0.719314
$536$	−12.9411	−0.558969
$537$	−2.13752	−0.0922407
$538$	13.8328	0.596373
$539$	0	0
$540$	1.42166	0.0611786
$541$	42.0766	1.80902	0.904508	−	0.426457i	$-0.140239\pi$
$541$	42.0766	1.80902	0.904508	+	0.426457i	$0.140239\pi$
$542$	36.1205	1.55151
$543$	1.83276	0.0786514
$544$	−21.4983	−0.921732
$545$	5.62721	0.241043
$546$	0	0
$547$	19.9688	0.853805	0.426903	−	0.904298i	$-0.359605\pi$
$547$	19.9688	0.853805	0.426903	+	0.904298i	$0.359605\pi$
$548$	−22.5472	−0.963167
$549$	−1.91638	−0.0817892
$550$	5.58336	0.238075
$551$	−13.7789	−0.586999
$552$	−1.15667	−0.0492313
$553$	0	0
$554$	31.9945	1.35931
$555$	2.29776	0.0975346
$556$	−20.2721	−0.859730
$557$	13.5491	0.574095	0.287048	−	0.957916i	$-0.407326\pi$
$557$	13.5491	0.574095	0.287048	+	0.957916i	$0.407326\pi$
$558$	−16.2594	−0.688317
$559$	−46.2978	−1.95819
$560$	0	0
$561$	−2.75971	−0.116515
$562$	0.0538991	0.00227360
$563$	−9.75468	−0.411111	−0.205555	−	0.978645i	$-0.565900\pi$
$563$	−9.75468	−0.411111	−0.205555	+	0.978645i	$0.565900\pi$
$564$	0.303302	0.0127713
$565$	−19.3139	−0.812540
$566$	−18.4650	−0.776142
$567$	0	0
$568$	−16.5189	−0.693118
$569$	−21.4544	−0.899417	−0.449708	−	0.893175i	$-0.648472\pi$
$569$	−21.4544	−0.899417	−0.449708	+	0.893175i	$0.648472\pi$
$570$	6.20555	0.259922
$571$	20.9411	0.876357	0.438178	−	0.898888i	$-0.355624\pi$
$571$	20.9411	0.876357	0.438178	+	0.898888i	$0.355624\pi$
$572$	−5.35218	−0.223786
$573$	−18.6167	−0.777722
$574$	0	0
$575$	3.39500	0.141581
$576$	−1.66196	−0.0692481
$577$	−18.4705	−0.768939	−0.384469	−	0.923138i	$-0.625616\pi$
$577$	−18.4705	−0.768939	−0.384469	+	0.923138i	$0.625616\pi$
$578$	9.96526	0.414500
$579$	15.6116	0.648797
$580$	6.31335	0.262148
$581$	0	0
$582$	4.95112	0.205231
$583$	11.2544	0.466111
$584$	−6.13607	−0.253912
$585$	−5.62721	−0.232657
$586$	5.70938	0.235852
$587$	0.127471	0.00526130	0.00263065	−	0.999997i	$-0.499163\pi$
$587$	0.127471	0.00526130	0.00263065	+	0.999997i	$0.499163\pi$
$588$	0	0
$589$	−27.8172	−1.14619
$590$	2.09775	0.0863631
$591$	−5.21057	−0.214334
$592$	−10.2439	−0.421020
$593$	27.2841	1.12043	0.560213	−	0.828349i	$-0.310719\pi$
$593$	27.2841	1.12043	0.560213	+	0.828349i	$0.310719\pi$
$594$	−1.47556	−0.0605430
$595$	0	0
$596$	14.9128	0.610853
$597$	−2.05390	−0.0840605
$598$	−8.30330	−0.339547
$599$	−42.3260	−1.72939	−0.864697	−	0.502293i	$-0.832490\pi$
$599$	−42.3260	−1.72939	−0.864697	+	0.502293i	$0.832490\pi$
$600$	−4.87807	−0.199146
$601$	15.6756	0.639420	0.319710	−	0.947515i	$-0.396415\pi$
$601$	15.6756	0.639420	0.319710	+	0.947515i	$0.396415\pi$
$602$	0	0
$603$	−10.0383	−0.408792
$604$	24.8222	1.01000
$605$	−11.4005	−0.463498
$606$	−21.5139	−0.873941
$607$	1.93051	0.0783572	0.0391786	−	0.999232i	$-0.487526\pi$
$607$	1.93051	0.0783572	0.0391786	+	0.999232i	$0.487526\pi$
$608$	−19.6655	−0.797542
$609$	0	0
$610$	3.83276	0.155184
$611$	−1.20053	−0.0485681
$612$	−4.37279	−0.176759
$613$	−0.372787	−0.0150567	−0.00752836	−	0.999972i	$-0.502396\pi$
$613$	−0.372787	−0.0150567	−0.00752836	+	0.999972i	$0.502396\pi$
$614$	−23.2106	−0.936703
$615$	−1.10278	−0.0444682
$616$	0	0
$617$	31.3083	1.26043	0.630213	−	0.776422i	$-0.282968\pi$
$617$	31.3083	1.26043	0.630213	+	0.776422i	$0.282968\pi$
$618$	−0.897225	−0.0360917
$619$	−34.3658	−1.38128	−0.690639	−	0.723200i	$-0.742671\pi$
$619$	−34.3658	−1.38128	−0.690639	+	0.723200i	$0.742671\pi$
$620$	12.7456	0.511875
$621$	−0.897225	−0.0360044
$622$	48.2721	1.93554
$623$	0	0
$624$	25.0872	1.00429
$625$	8.23724	0.329490
$626$	−5.44993	−0.217823
$627$	−2.52444	−0.100816
$628$	26.9693	1.07619
$629$	−7.06752	−0.281800
$630$	0	0
$631$	7.33804	0.292123	0.146061	−	0.989276i	$-0.453340\pi$
$631$	7.33804	0.292123	0.146061	+	0.989276i	$0.453340\pi$
$632$	−20.4111	−0.811910
$633$	−9.04888	−0.359661
$634$	7.85840	0.312097
$635$	14.2056	0.563730
$636$	17.8328	0.707115
$637$	0	0
$638$	−6.55270	−0.259424
$639$	−12.8136	−0.506898
$640$	−10.6550	−0.421174
$641$	−31.5764	−1.24719	−0.623596	−	0.781747i	$-0.714329\pi$
$641$	−31.5764	−1.24719	−0.623596	+	0.781747i	$0.714329\pi$
$642$	27.3622	1.07990
$643$	4.51890	0.178208	0.0891040	−	0.996022i	$-0.471600\pi$
$643$	4.51890	0.178208	0.0891040	+	0.996022i	$0.471600\pi$
$644$	0	0
$645$	10.0055	0.393968
$646$	−19.0872	−0.750975
$647$	20.6705	0.812643	0.406322	−	0.913730i	$-0.366811\pi$
$647$	20.6705	0.812643	0.406322	+	0.913730i	$0.366811\pi$
$648$	1.28917	0.0506433
$649$	−0.853372	−0.0334978
$650$	−35.0177	−1.37351
$651$	0	0
$652$	−16.4988	−0.646143
$653$	0.381381	0.0149246	0.00746229	−	0.999972i	$-0.497625\pi$
$653$	0.381381	0.0149246	0.00746229	+	0.999972i	$0.497625\pi$
$654$	−9.25443	−0.361877
$655$	7.01056	0.273925
$656$	4.91638	0.191952
$657$	−4.75971	−0.185694
$658$	0	0
$659$	13.4600	0.524326	0.262163	−	0.965024i	$-0.415564\pi$
$659$	13.4600	0.524326	0.262163	+	0.965024i	$0.415564\pi$
$660$	1.15667	0.0450235
$661$	−30.7738	−1.19696	−0.598482	−	0.801136i	$-0.704229\pi$
$661$	−30.7738	−1.19696	−0.598482	+	0.801136i	$0.704229\pi$
$662$	−10.0383	−0.390150
$663$	17.3083	0.672200
$664$	9.90225	0.384282
$665$	0	0
$666$	−3.77886	−0.146428
$667$	−3.98441	−0.154277
$668$	−12.4111	−0.480200
$669$	−24.8222	−0.959682
$670$	20.0766	0.775628
$671$	−1.55918	−0.0601915
$672$	0	0
$673$	1.48110	0.0570923	0.0285461	−	0.999592i	$-0.490912\pi$
$673$	1.48110	0.0570923	0.0285461	+	0.999592i	$0.490912\pi$
$674$	6.72999	0.259229
$675$	−3.78389	−0.145642
$676$	16.8086	0.646484
$677$	−45.3749	−1.74390	−0.871950	−	0.489596i	$-0.837144\pi$
$677$	−45.3749	−1.74390	−0.871950	+	0.489596i	$0.837144\pi$
$678$	31.7633	1.21986
$679$	0	0
$680$	−4.82220	−0.184923
$681$	−16.6464	−0.637890
$682$	−13.2288	−0.506557
$683$	−0.0594386	−0.00227436	−0.00113718	−	0.999999i	$-0.500362\pi$
$683$	−0.0594386	−0.00227436	−0.00113718	+	0.999999i	$0.500362\pi$
$684$	−4.00000	−0.152944
$685$	−19.2872	−0.736926
$686$	0	0
$687$	15.7789	0.602001
$688$	−44.6066	−1.70061
$689$	−70.5855	−2.68909
$690$	1.79445	0.0683135
$691$	18.9355	0.720342	0.360171	−	0.932886i	$-0.382718\pi$
$691$	18.9355	0.720342	0.360171	+	0.932886i	$0.382718\pi$
$692$	−15.4005	−0.585441
$693$	0	0
$694$	−5.58336	−0.211941
$695$	−17.3411	−0.657785
$696$	5.72496	0.217004
$697$	3.39194	0.128479
$698$	26.8378	1.01583
$699$	−24.9200	−0.942559
$700$	0	0
$701$	−0.540024	−0.0203964	−0.0101982	−	0.999948i	$-0.503246\pi$
$701$	−0.540024	−0.0203964	−0.0101982	+	0.999948i	$0.503246\pi$
$702$	9.25443	0.349286
$703$	−6.46500	−0.243832
$704$	−1.35218	−0.0509621
$705$	0.259449	0.00977142
$706$	48.6449	1.83078
$707$	0	0
$708$	−1.35218	−0.0508180
$709$	28.0867	1.05482	0.527409	−	0.849612i	$-0.323164\pi$
$709$	28.0867	1.05482	0.527409	+	0.849612i	$0.323164\pi$
$710$	25.6272	0.961772
$711$	−15.8328	−0.593775
$712$	−17.0872	−0.640369
$713$	−8.04385	−0.301245
$714$	0	0
$715$	−4.57834	−0.171220
$716$	−2.75562	−0.102982
$717$	−2.95112	−0.110212
$718$	−4.27504	−0.159543
$719$	−9.86248	−0.367809	−0.183904	−	0.982944i	$-0.558874\pi$
$719$	−9.86248	−0.367809	−0.183904	+	0.982944i	$0.558874\pi$
$720$	−5.42166	−0.202053
$721$	0	0
$722$	16.9985	0.632620
$723$	16.5925	0.617081
$724$	2.36274	0.0878106
$725$	−16.8036	−0.624069
$726$	18.7491	0.695846
$727$	30.4650	1.12988	0.564942	−	0.825131i	$-0.308898\pi$
$727$	30.4650	1.12988	0.564942	+	0.825131i	$0.308898\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	9.51941	0.352329
$731$	−30.7753	−1.13827
$732$	−2.47054	−0.0913137
$733$	−27.5436	−1.01735	−0.508673	−	0.860960i	$-0.669864\pi$
$733$	−27.5436	−1.01735	−0.508673	+	0.860960i	$0.669864\pi$
$734$	42.0227	1.55109
$735$	0	0
$736$	−5.68665	−0.209613
$737$	−8.16724	−0.300844
$738$	1.81361	0.0667598
$739$	13.1013	0.481940	0.240970	−	0.970533i	$-0.422534\pi$
$739$	13.1013	0.481940	0.240970	+	0.970533i	$0.422534\pi$
$740$	2.96220	0.108893
$741$	15.8328	0.581631
$742$	0	0
$743$	34.7527	1.27495	0.637477	−	0.770470i	$-0.279978\pi$
$743$	34.7527	1.27495	0.637477	+	0.770470i	$0.279978\pi$
$744$	11.5577	0.423727
$745$	12.7567	0.467368
$746$	−63.8555	−2.33792
$747$	7.68111	0.281037
$748$	−3.55773	−0.130083
$749$	0	0
$750$	17.5678	0.641484
$751$	32.7738	1.19593	0.597967	−	0.801521i	$-0.295975\pi$
$751$	32.7738	1.19593	0.597967	+	0.801521i	$0.295975\pi$
$752$	−1.15667	−0.0421796
$753$	20.1361	0.733799
$754$	41.0972	1.49667
$755$	21.2333	0.772759
$756$	0	0
$757$	−32.2978	−1.17388	−0.586941	−	0.809630i	$-0.699668\pi$
$757$	−32.2978	−1.17388	−0.586941	+	0.809630i	$0.699668\pi$
$758$	47.2233	1.71523
$759$	−0.729988	−0.0264969
$760$	−4.41110	−0.160007
$761$	−44.4494	−1.61129	−0.805645	−	0.592399i	$-0.798181\pi$
$761$	−44.4494	−1.61129	−0.805645	+	0.592399i	$0.798181\pi$
$762$	−23.3622	−0.846324
$763$	0	0
$764$	−24.0000	−0.868290
$765$	−3.74055	−0.135240
$766$	27.8967	1.00795
$767$	5.35218	0.193256
$768$	20.8469	0.752248
$769$	19.7108	0.710791	0.355395	−	0.934716i	$-0.384346\pi$
$769$	19.7108	0.710791	0.355395	+	0.934716i	$0.384346\pi$
$770$	0	0
$771$	−25.9008	−0.932794
$772$	20.1260	0.724351
$773$	−43.2530	−1.55570	−0.777851	−	0.628449i	$-0.783690\pi$
$773$	−43.2530	−1.55570	−0.777851	+	0.628449i	$0.783690\pi$
$774$	−16.4550	−0.591461
$775$	−33.9235	−1.21857
$776$	−3.51941	−0.126340
$777$	0	0
$778$	−8.09775	−0.290318
$779$	3.10278	0.111168
$780$	−7.25443	−0.259750
$781$	−10.4252	−0.373044
$782$	−5.51941	−0.197374
$783$	4.44082	0.158702
$784$	0	0
$785$	23.0700	0.823404
$786$	−11.5295	−0.411242
$787$	21.4358	0.764104	0.382052	−	0.924141i	$-0.375218\pi$
$787$	21.4358	0.764104	0.382052	+	0.924141i	$0.375218\pi$
$788$	−6.71731	−0.239294
$789$	−22.4408	−0.798914
$790$	31.6655	1.12661
$791$	0	0
$792$	1.04888	0.0372702
$793$	9.77886	0.347258
$794$	−19.1567	−0.679845
$795$	15.2544	0.541019
$796$	−2.64782	−0.0938496
$797$	4.40105	0.155893	0.0779467	−	0.996958i	$-0.475164\pi$
$797$	4.40105	0.155893	0.0779467	+	0.996958i	$0.475164\pi$
$798$	0	0
$799$	−0.798021	−0.0282319
$800$	−23.9824	−0.847907
$801$	−13.2544	−0.468322
$802$	−23.7350	−0.838112
$803$	−3.87253	−0.136659
$804$	−12.9411	−0.456397
$805$	0	0
$806$	82.9683	2.92243
$807$	−7.62721	−0.268491
$808$	15.2927	0.537997
$809$	−26.3799	−0.927469	−0.463734	−	0.885974i	$-0.653491\pi$
$809$	−26.3799	−0.927469	−0.463734	+	0.885974i	$0.653491\pi$
$810$	−2.00000	−0.0702728
$811$	−4.96526	−0.174354	−0.0871769	−	0.996193i	$-0.527785\pi$
$811$	−4.96526	−0.174354	−0.0871769	+	0.996193i	$0.527785\pi$
$812$	0	0
$813$	−19.9164	−0.698498
$814$	−3.07451	−0.107761
$815$	−14.1133	−0.494369
$816$	16.6761	0.583780
$817$	−28.1517	−0.984902
$818$	−33.6499	−1.17654
$819$	0	0
$820$	−1.42166	−0.0496466
$821$	−15.7789	−0.550686	−0.275343	−	0.961346i	$-0.588791\pi$
$821$	−15.7789	−0.550686	−0.275343	+	0.961346i	$0.588791\pi$
$822$	31.7194	1.10634
$823$	−8.35166	−0.291121	−0.145560	−	0.989349i	$-0.546498\pi$
$823$	−8.35166	−0.291121	−0.145560	+	0.989349i	$0.546498\pi$
$824$	0.637776	0.0222180
$825$	−3.07860	−0.107183
$826$	0	0
$827$	−18.3925	−0.639568	−0.319784	−	0.947490i	$-0.603610\pi$
$827$	−18.3925	−0.639568	−0.319784	+	0.947490i	$0.603610\pi$
$828$	−1.15667	−0.0401972
$829$	29.4147	1.02161	0.510807	−	0.859695i	$-0.329347\pi$
$829$	29.4147	1.02161	0.510807	+	0.859695i	$0.329347\pi$
$830$	−15.3622	−0.533231
$831$	−17.6413	−0.611972
$832$	8.48059	0.294011
$833$	0	0
$834$	28.5189	0.987529
$835$	−10.6167	−0.367404
$836$	−3.25443	−0.112557
$837$	8.96526	0.309885
$838$	−46.4494	−1.60457
$839$	33.4600	1.15517	0.577583	−	0.816332i	$-0.303996\pi$
$839$	33.4600	1.15517	0.577583	+	0.816332i	$0.303996\pi$
$840$	0	0
$841$	−9.27912	−0.319970
$842$	15.7350	0.542264
$843$	−0.0297193	−0.00102359
$844$	−11.6655	−0.401544
$845$	14.3783	0.494629
$846$	−0.426686	−0.0146698
$847$	0	0
$848$	−68.0071	−2.33537
$849$	10.1814	0.349424
$850$	−23.2772	−0.798400
$851$	−1.86947	−0.0640848
$852$	−16.5189	−0.565928
$853$	−40.4494	−1.38496	−0.692481	−	0.721436i	$-0.743482\pi$
$853$	−40.4494	−1.38496	−0.692481	+	0.721436i	$0.743482\pi$
$854$	0	0
$855$	−3.42166	−0.117018
$856$	−19.4499	−0.664785
$857$	−12.4494	−0.425264	−0.212632	−	0.977132i	$-0.568204\pi$
$857$	−12.4494	−0.425264	−0.212632	+	0.977132i	$0.568204\pi$
$858$	7.52946	0.257052
$859$	21.6514	0.738736	0.369368	−	0.929283i	$-0.379574\pi$
$859$	21.6514	0.738736	0.369368	+	0.929283i	$0.379574\pi$
$860$	12.8988	0.439846
$861$	0	0
$862$	−12.8816	−0.438750
$863$	19.3778	0.659628	0.329814	−	0.944046i	$-0.393014\pi$
$863$	19.3778	0.659628	0.329814	+	0.944046i	$0.393014\pi$
$864$	6.33804	0.215625
$865$	−13.1739	−0.447925
$866$	−19.9945	−0.679439
$867$	−5.49472	−0.186610
$868$	0	0
$869$	−12.8816	−0.436980
$870$	−8.88164	−0.301116
$871$	51.2233	1.73563
$872$	6.57834	0.222771
$873$	−2.72999	−0.0923961
$874$	−5.04888	−0.170781
$875$	0	0
$876$	−6.13607	−0.207318
$877$	−3.08413	−0.104144	−0.0520719	−	0.998643i	$-0.516583\pi$
$877$	−3.08413	−0.104144	−0.0520719	+	0.998643i	$0.516583\pi$
$878$	−2.40105	−0.0810316
$879$	−3.14808	−0.106182
$880$	−4.41110	−0.148698
$881$	34.5783	1.16497	0.582487	−	0.812840i	$-0.302080\pi$
$881$	34.5783	1.16497	0.582487	+	0.812840i	$0.302080\pi$
$882$	0	0
$883$	−9.64280	−0.324506	−0.162253	−	0.986749i	$-0.551876\pi$
$883$	−9.64280	−0.324506	−0.162253	+	0.986749i	$0.551876\pi$
$884$	22.3133	0.750479
$885$	−1.15667	−0.0388812
$886$	−28.2721	−0.949821
$887$	−32.2041	−1.08131	−0.540654	−	0.841245i	$-0.681823\pi$
$887$	−32.2041	−1.08131	−0.540654	+	0.841245i	$0.681823\pi$
$888$	2.68614	0.0901408
$889$	0	0
$890$	26.5089	0.888579
$891$	0.813607	0.0272568
$892$	−32.0000	−1.07144
$893$	−0.729988	−0.0244281
$894$	−20.9794	−0.701656
$895$	−2.35720	−0.0787925
$896$	0	0
$897$	4.57834	0.152866
$898$	59.4571	1.98411
$899$	39.8131	1.32784
$900$	−4.87807	−0.162602
$901$	−46.9200	−1.56313
$902$	1.47556	0.0491308
$903$	0	0
$904$	−22.5783	−0.750944
$905$	2.02113	0.0671845
$906$	−34.9200	−1.16014
$907$	−17.8227	−0.591794	−0.295897	−	0.955220i	$-0.595618\pi$
$907$	−17.8227	−0.591794	−0.295897	+	0.955220i	$0.595618\pi$
$908$	−21.4600	−0.712174
$909$	11.8625	0.393454
$910$	0	0
$911$	−20.7894	−0.688784	−0.344392	−	0.938826i	$-0.611915\pi$
$911$	−20.7894	−0.688784	−0.344392	+	0.938826i	$0.611915\pi$
$912$	15.2544	0.505125
$913$	6.24940	0.206825
$914$	25.6938	0.849875
$915$	−2.11334	−0.0698648
$916$	20.3416	0.672106
$917$	0	0
$918$	6.15165	0.203035
$919$	33.8555	1.11679	0.558395	−	0.829575i	$-0.311417\pi$
$919$	33.8555	1.11679	0.558395	+	0.829575i	$0.311417\pi$
$920$	−1.27555	−0.0420537
$921$	12.7980	0.421709
$922$	−54.5472	−1.79642
$923$	65.3850	2.15217
$924$	0	0
$925$	−7.88418	−0.259230
$926$	43.3028	1.42302
$927$	0.494719	0.0162487
$928$	28.1461	0.923941
$929$	4.10635	0.134725	0.0673624	−	0.997729i	$-0.478542\pi$
$929$	4.10635	0.134725	0.0673624	+	0.997729i	$0.478542\pi$
$930$	−17.9305	−0.587965
$931$	0	0
$932$	−32.1260	−1.05232
$933$	−26.6167	−0.871390
$934$	−17.6555	−0.577705
$935$	−3.04334	−0.0995277
$936$	−6.57834	−0.215020
$937$	−13.3028	−0.434583	−0.217292	−	0.976107i	$-0.569722\pi$
$937$	−13.3028	−0.434583	−0.217292	+	0.976107i	$0.569722\pi$
$938$	0	0
$939$	3.00502	0.0980652
$940$	0.334474	0.0109093
$941$	11.7633	0.383472	0.191736	−	0.981447i	$-0.438588\pi$
$941$	11.7633	0.383472	0.191736	+	0.981447i	$0.438588\pi$
$942$	−37.9406	−1.23617
$943$	0.897225	0.0292177
$944$	5.15667	0.167835
$945$	0	0
$946$	−13.3879	−0.435277
$947$	1.40054	0.0455114	0.0227557	−	0.999741i	$-0.492756\pi$
$947$	1.40054	0.0455114	0.0227557	+	0.999741i	$0.492756\pi$
$948$	−20.4111	−0.662922
$949$	24.2877	0.788413
$950$	−21.2927	−0.690828
$951$	−4.33302	−0.140508
$952$	0	0
$953$	33.7577	1.09352	0.546760	−	0.837289i	$-0.315861\pi$
$953$	33.7577	1.09352	0.546760	+	0.837289i	$0.315861\pi$
$954$	−25.0872	−0.812228
$955$	−20.5300	−0.664334
$956$	−3.80450	−0.123046
$957$	3.61308	0.116794
$958$	−2.13343	−0.0689280
$959$	0	0
$960$	−1.83276	−0.0591522
$961$	49.3758	1.59277
$962$	19.2827	0.621699
$963$	−15.0872	−0.486178
$964$	21.3905	0.688941
$965$	17.2161	0.554206
$966$	0	0
$967$	−10.4806	−0.337033	−0.168516	−	0.985699i	$-0.553898\pi$
$967$	−10.4806	−0.337033	−0.168516	+	0.985699i	$0.553898\pi$
$968$	−13.3275	−0.428361
$969$	10.5244	0.338094
$970$	5.45998	0.175309
$971$	−57.6358	−1.84962	−0.924811	−	0.380428i	$-0.875777\pi$
$971$	−57.6358	−1.84962	−0.924811	+	0.380428i	$0.875777\pi$
$972$	1.28917	0.0413501
$973$	0	0
$974$	−37.3649	−1.19725
$975$	19.3083	0.618361
$976$	9.42166	0.301580
$977$	41.9008	1.34053	0.670263	−	0.742124i	$-0.266181\pi$
$977$	41.9008	1.34053	0.670263	+	0.742124i	$0.266181\pi$
$978$	23.2106	0.742192
$979$	−10.7839	−0.344655
$980$	0	0
$981$	5.10278	0.162919
$982$	−25.7350	−0.821237
$983$	18.4056	0.587046	0.293523	−	0.955952i	$-0.405172\pi$
$983$	18.4056	0.587046	0.293523	+	0.955952i	$0.405172\pi$
$984$	−1.28917	−0.0410972
$985$	−5.74609	−0.183086
$986$	27.3184	0.869994
$987$	0	0
$988$	20.4111	0.649364
$989$	−8.14057	−0.258855
$990$	−1.62721	−0.0517162
$991$	26.0666	0.828032	0.414016	−	0.910270i	$-0.364126\pi$
$991$	26.0666	0.828032	0.414016	+	0.910270i	$0.364126\pi$
$992$	56.8222	1.80411
$993$	5.53500	0.175648
$994$	0	0
$995$	−2.26499	−0.0718050
$996$	9.90225	0.313765
$997$	29.8483	0.945307	0.472653	−	0.881248i	$-0.343296\pi$
$997$	29.8483	0.945307	0.472653	+	0.881248i	$0.343296\pi$
$998$	38.9200	1.23199
$999$	2.08362	0.0659228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.s.1.1		3
7.6	odd	2		123.2.a.d.1.1	✓	3
21.20	even	2		369.2.a.e.1.3		3
28.27	even	2		1968.2.a.w.1.1		3
35.34	odd	2		3075.2.a.t.1.3		3
56.13	odd	2		7872.2.a.bx.1.3		3
56.27	even	2		7872.2.a.bs.1.3		3
84.83	odd	2		5904.2.a.bd.1.3		3
105.104	even	2		9225.2.a.bx.1.1		3
287.286	odd	2		5043.2.a.n.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
123.2.a.d.1.1	✓	3	7.6	odd	2
369.2.a.e.1.3		3	21.20	even	2
1968.2.a.w.1.1		3	28.27	even	2
3075.2.a.t.1.3		3	35.34	odd	2
5043.2.a.n.1.1		3	287.286	odd	2
5904.2.a.bd.1.3		3	84.83	odd	2
6027.2.a.s.1.1		3	1.1	even	1	trivial
7872.2.a.bs.1.3		3	56.27	even	2
7872.2.a.bx.1.3		3	56.13	odd	2
9225.2.a.bx.1.1		3	105.104	even	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} +1.10278 q^{5} -1.81361 q^{6} +1.28917 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} +1.10278 q^{5} -1.81361 q^{6} +1.28917 q^{8} +1.00000 q^{9} -2.00000 q^{10} +0.813607 q^{11} +1.28917 q^{12} -5.10278 q^{13} +1.10278 q^{15} -4.91638 q^{16} -3.39194 q^{17} -1.81361 q^{18} -3.10278 q^{19} +1.42166 q^{20} -1.47556 q^{22} -0.897225 q^{23} +1.28917 q^{24} -3.78389 q^{25} +9.25443 q^{26} +1.00000 q^{27} +4.44082 q^{29} -2.00000 q^{30} +8.96526 q^{31} +6.33804 q^{32} +0.813607 q^{33} +6.15165 q^{34} +1.28917 q^{36} +2.08362 q^{37} +5.62721 q^{38} -5.10278 q^{39} +1.42166 q^{40} -1.00000 q^{41} +9.07306 q^{43} +1.04888 q^{44} +1.10278 q^{45} +1.62721 q^{46} +0.235269 q^{47} -4.91638 q^{48} +6.86248 q^{50} -3.39194 q^{51} -6.57834 q^{52} +13.8328 q^{53} -1.81361 q^{54} +0.897225 q^{55} -3.10278 q^{57} -8.05390 q^{58} -1.04888 q^{59} +1.42166 q^{60} -1.91638 q^{61} -16.2594 q^{62} -1.66196 q^{64} -5.62721 q^{65} -1.47556 q^{66} -10.0383 q^{67} -4.37279 q^{68} -0.897225 q^{69} -12.8136 q^{71} +1.28917 q^{72} -4.75971 q^{73} -3.77886 q^{74} -3.78389 q^{75} -4.00000 q^{76} +9.25443 q^{78} -15.8328 q^{79} -5.42166 q^{80} +1.00000 q^{81} +1.81361 q^{82} +7.68111 q^{83} -3.74055 q^{85} -16.4550 q^{86} +4.44082 q^{87} +1.04888 q^{88} -13.2544 q^{89} -2.00000 q^{90} -1.15667 q^{92} +8.96526 q^{93} -0.426686 q^{94} -3.42166 q^{95} +6.33804 q^{96} -2.72999 q^{97} +0.813607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} + 3 q^{4} - 4 q^{5} + q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 + 3 * q^4 - 4 * q^5 + q^6 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} + 3 q^{4} - 4 q^{5} + q^{6} + 3 q^{8} + 3 q^{9} - 6 q^{10} - 4 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{15} - q^{16} - 2 q^{17} + q^{18} - 2 q^{19} + 6 q^{20} - 10 q^{22} - 10 q^{23} + 3 q^{24} + 5 q^{25} + 2 q^{26} + 3 q^{27} - 6 q^{29} - 6 q^{30} + 2 q^{31} + 7 q^{32} - 4 q^{33} + 3 q^{36} + 20 q^{37} + 4 q^{38} - 8 q^{39} + 6 q^{40} - 3 q^{41} + 10 q^{43} - 8 q^{44} - 4 q^{45} - 8 q^{46} - 4 q^{47} - q^{48} + 3 q^{50} - 2 q^{51} - 18 q^{52} + 14 q^{53} + q^{54} + 10 q^{55} - 2 q^{57} - 28 q^{58} + 8 q^{59} + 6 q^{60} + 8 q^{61} - 38 q^{62} - 17 q^{64} - 4 q^{65} - 10 q^{66} + 12 q^{67} - 26 q^{68} - 10 q^{69} - 32 q^{71} + 3 q^{72} - 4 q^{73} + 20 q^{74} + 5 q^{75} - 12 q^{76} + 2 q^{78} - 20 q^{79} - 18 q^{80} + 3 q^{81} - q^{82} + 14 q^{83} - 22 q^{85} + 6 q^{86} - 6 q^{87} - 8 q^{88} - 14 q^{89} - 6 q^{90} + 2 q^{93} - 18 q^{94} - 12 q^{95} + 7 q^{96} + 12 q^{97} - 4 q^{99}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + 3 * q^4 - 4 * q^5 + q^6 + 3 * q^8 + 3 * q^9 - 6 * q^10 - 4 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^15 - q^16 - 2 * q^17 + q^18 - 2 * q^19 + 6 * q^20 - 10 * q^22 - 10 * q^23 + 3 * q^24 + 5 * q^25 + 2 * q^26 + 3 * q^27 - 6 * q^29 - 6 * q^30 + 2 * q^31 + 7 * q^32 - 4 * q^33 + 3 * q^36 + 20 * q^37 + 4 * q^38 - 8 * q^39 + 6 * q^40 - 3 * q^41 + 10 * q^43 - 8 * q^44 - 4 * q^45 - 8 * q^46 - 4 * q^47 - q^48 + 3 * q^50 - 2 * q^51 - 18 * q^52 + 14 * q^53 + q^54 + 10 * q^55 - 2 * q^57 - 28 * q^58 + 8 * q^59 + 6 * q^60 + 8 * q^61 - 38 * q^62 - 17 * q^64 - 4 * q^65 - 10 * q^66 + 12 * q^67 - 26 * q^68 - 10 * q^69 - 32 * q^71 + 3 * q^72 - 4 * q^73 + 20 * q^74 + 5 * q^75 - 12 * q^76 + 2 * q^78 - 20 * q^79 - 18 * q^80 + 3 * q^81 - q^82 + 14 * q^83 - 22 * q^85 + 6 * q^86 - 6 * q^87 - 8 * q^88 - 14 * q^89 - 6 * q^90 + 2 * q^93 - 18 * q^94 - 12 * q^95 + 7 * q^96 + 12 * q^97 - 4 * q^99

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