LMFDB - Embedded newform 7203.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7203,2,Mod(1,7203)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7203, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7203.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7203 = 3 \cdot 7^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7203.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:	$57.5162445759$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} - 27 x^{16} + 85 x^{15} + 287 x^{14} - 973 x^{13} - 1504 x^{12} + 5775 x^{11} + \cdots + 351 $ x^18 - 3x^17 - 27x^16 + 85x^15 + 287x^14 - 973x^13 - 1504x^12 + 5775x^11 + 3877x^10 - 18987x^9 - 3525x^8 + 34209x^7 - 3492x^6 - 30947x^5 + 8197x^4 + 11327x^3 - 3405x^2 - 1350*x + 351
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 147)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.43438$ of defining polynomial
Character	$\chi$	$=$	7203.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.43438 q^{2} -1.00000 q^{3} +0.0574538 q^{4} +1.15146 q^{5} +1.43438 q^{6} +2.78635 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.43438 q^{2} -1.00000 q^{3} +0.0574538 q^{4} +1.15146 q^{5} +1.43438 q^{6} +2.78635 q^{8} +1.00000 q^{9} -1.65164 q^{10} -5.46824 q^{11} -0.0574538 q^{12} +3.89595 q^{13} -1.15146 q^{15} -4.11161 q^{16} +2.32680 q^{17} -1.43438 q^{18} -5.93712 q^{19} +0.0661560 q^{20} +7.84354 q^{22} -5.85685 q^{23} -2.78635 q^{24} -3.67413 q^{25} -5.58828 q^{26} -1.00000 q^{27} -5.85187 q^{29} +1.65164 q^{30} -3.41224 q^{31} +0.324908 q^{32} +5.46824 q^{33} -3.33752 q^{34} +0.0574538 q^{36} -6.92148 q^{37} +8.51610 q^{38} -3.89595 q^{39} +3.20839 q^{40} +9.22634 q^{41} +4.36604 q^{43} -0.314171 q^{44} +1.15146 q^{45} +8.40096 q^{46} -7.26869 q^{47} +4.11161 q^{48} +5.27011 q^{50} -2.32680 q^{51} +0.223837 q^{52} +6.20459 q^{53} +1.43438 q^{54} -6.29648 q^{55} +5.93712 q^{57} +8.39382 q^{58} +4.37412 q^{59} -0.0661560 q^{60} -4.44248 q^{61} +4.89445 q^{62} +7.75717 q^{64} +4.48605 q^{65} -7.84354 q^{66} -12.5372 q^{67} +0.133683 q^{68} +5.85685 q^{69} -0.568351 q^{71} +2.78635 q^{72} +14.6453 q^{73} +9.92806 q^{74} +3.67413 q^{75} -0.341110 q^{76} +5.58828 q^{78} +9.54103 q^{79} -4.73437 q^{80} +1.00000 q^{81} -13.2341 q^{82} -4.13806 q^{83} +2.67923 q^{85} -6.26257 q^{86} +5.85187 q^{87} -15.2364 q^{88} +2.47805 q^{89} -1.65164 q^{90} -0.336498 q^{92} +3.41224 q^{93} +10.4261 q^{94} -6.83638 q^{95} -0.324908 q^{96} -11.7472 q^{97} -5.46824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} - 18 q^{3} + 27 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 - 18 * q^3 + 27 * q^4 + 2 * q^5 - 3 * q^6 + 3 * q^8 + 18 * q^9	$ 18 q + 3 q^{2} - 18 q^{3} + 27 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{8} + 18 q^{9} + 2 q^{10} - 27 q^{12} - q^{13} - 2 q^{15} + 37 q^{16} + 5 q^{17} + 3 q^{18} - 3 q^{19} + 19 q^{20} + 4 q^{23} - 3 q^{24} + 34 q^{25} - 3 q^{26} - 18 q^{27} + 10 q^{29} - 2 q^{30} - 8 q^{31} - q^{32} - 3 q^{34} + 27 q^{36} + 9 q^{37} - 5 q^{38} + q^{39} + 14 q^{40} - q^{41} + 4 q^{43} - 13 q^{44} + 2 q^{45} - 2 q^{46} + 21 q^{47} - 37 q^{48} + 118 q^{50} - 5 q^{51} - 108 q^{52} + 89 q^{53} - 3 q^{54} - 2 q^{55} + 3 q^{57} + 103 q^{58} - 17 q^{59} - 19 q^{60} - 77 q^{61} + 37 q^{62} + 35 q^{64} + 103 q^{65} - 11 q^{67} + 55 q^{68} - 4 q^{69} - 3 q^{71} + 3 q^{72} + 9 q^{73} + 110 q^{74} - 34 q^{75} - 121 q^{76} + 3 q^{78} - 7 q^{79} + 56 q^{80} + 18 q^{81} - q^{82} + q^{83} + 104 q^{85} - 20 q^{86} - 10 q^{87} - 17 q^{88} + 15 q^{89} + 2 q^{90} - 7 q^{92} + 8 q^{93} + 6 q^{94} - 19 q^{95} + q^{96} - 86 q^{97}+O(q^{100}) $ 18 * q + 3 * q^2 - 18 * q^3 + 27 * q^4 + 2 * q^5 - 3 * q^6 + 3 * q^8 + 18 * q^9 + 2 * q^10 - 27 * q^12 - q^13 - 2 * q^15 + 37 * q^16 + 5 * q^17 + 3 * q^18 - 3 * q^19 + 19 * q^20 + 4 * q^23 - 3 * q^24 + 34 * q^25 - 3 * q^26 - 18 * q^27 + 10 * q^29 - 2 * q^30 - 8 * q^31 - q^32 - 3 * q^34 + 27 * q^36 + 9 * q^37 - 5 * q^38 + q^39 + 14 * q^40 - q^41 + 4 * q^43 - 13 * q^44 + 2 * q^45 - 2 * q^46 + 21 * q^47 - 37 * q^48 + 118 * q^50 - 5 * q^51 - 108 * q^52 + 89 * q^53 - 3 * q^54 - 2 * q^55 + 3 * q^57 + 103 * q^58 - 17 * q^59 - 19 * q^60 - 77 * q^61 + 37 * q^62 + 35 * q^64 + 103 * q^65 - 11 * q^67 + 55 * q^68 - 4 * q^69 - 3 * q^71 + 3 * q^72 + 9 * q^73 + 110 * q^74 - 34 * q^75 - 121 * q^76 + 3 * q^78 - 7 * q^79 + 56 * q^80 + 18 * q^81 - q^82 + q^83 + 104 * q^85 - 20 * q^86 - 10 * q^87 - 17 * q^88 + 15 * q^89 + 2 * q^90 - 7 * q^92 + 8 * q^93 + 6 * q^94 - 19 * q^95 + q^96 - 86 * q^97

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 $

$2$	−1.43438	−1.01426	−0.507131	−	0.861869i	$-0.669294\pi$
$2$	−1.43438	−1.01426	−0.507131	+	0.861869i	$0.669294\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.0574538	0.0287269
$5$	1.15146	0.514951	0.257475	−	0.966285i	$-0.417109\pi$
$5$	1.15146	0.514951	0.257475	+	0.966285i	$0.417109\pi$
$6$	1.43438	0.585584
$7$	0	0
$7$	0	0
$8$	2.78635	0.985125
$9$	1.00000	0.333333
$10$	−1.65164	−0.522295
$11$	−5.46824	−1.64874	−0.824368	−	0.566055i	$-0.808469\pi$
$11$	−5.46824	−1.64874	−0.824368	+	0.566055i	$0.808469\pi$
$12$	−0.0574538	−0.0165855
$13$	3.89595	1.08054	0.540271	−	0.841491i	$-0.318322\pi$
$13$	3.89595	1.08054	0.540271	+	0.841491i	$0.318322\pi$
$14$	0	0
$15$	−1.15146	−0.297307
$16$	−4.11161	−1.02790
$17$	2.32680	0.564332	0.282166	−	0.959366i	$-0.408947\pi$
$17$	2.32680	0.564332	0.282166	+	0.959366i	$0.408947\pi$
$18$	−1.43438	−0.338087
$19$	−5.93712	−1.36207	−0.681034	−	0.732252i	$-0.738469\pi$
$19$	−5.93712	−1.36207	−0.681034	+	0.732252i	$0.738469\pi$
$20$	0.0661560	0.0147929
$21$	0	0
$22$	7.84354	1.67225
$23$	−5.85685	−1.22124	−0.610618	−	0.791925i	$-0.709079\pi$
$23$	−5.85685	−1.22124	−0.610618	+	0.791925i	$0.709079\pi$
$24$	−2.78635	−0.568762
$25$	−3.67413	−0.734826
$26$	−5.58828	−1.09595
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−5.85187	−1.08666	−0.543332	−	0.839518i	$-0.682838\pi$
$29$	−5.85187	−1.08666	−0.543332	+	0.839518i	$0.682838\pi$
$30$	1.65164	0.301547
$31$	−3.41224	−0.612856	−0.306428	−	0.951894i	$-0.599134\pi$
$31$	−3.41224	−0.612856	−0.306428	+	0.951894i	$0.599134\pi$
$32$	0.324908	0.0574362
$33$	5.46824	0.951898
$34$	−3.33752	−0.572380
$35$	0	0
$36$	0.0574538	0.00957563
$37$	−6.92148	−1.13789	−0.568943	−	0.822377i	$-0.692647\pi$
$37$	−6.92148	−1.13789	−0.568943	+	0.822377i	$0.692647\pi$
$38$	8.51610	1.38149
$39$	−3.89595	−0.623851
$40$	3.20839	0.507291
$41$	9.22634	1.44091	0.720456	−	0.693500i	$-0.243932\pi$
$41$	9.22634	1.44091	0.720456	+	0.693500i	$0.243932\pi$
$42$	0	0
$43$	4.36604	0.665815	0.332907	−	0.942960i	$-0.391970\pi$
$43$	4.36604	0.665815	0.332907	+	0.942960i	$0.391970\pi$
$44$	−0.314171	−0.0473630
$45$	1.15146	0.171650
$46$	8.40096	1.23865
$47$	−7.26869	−1.06025	−0.530124	−	0.847920i	$-0.677855\pi$
$47$	−7.26869	−1.06025	−0.530124	+	0.847920i	$0.677855\pi$
$48$	4.11161	0.593459
$49$	0	0
$50$	5.27011	0.745306
$51$	−2.32680	−0.325817
$52$	0.223837	0.0310406
$53$	6.20459	0.852265	0.426133	−	0.904661i	$-0.359876\pi$
$53$	6.20459	0.852265	0.426133	+	0.904661i	$0.359876\pi$
$54$	1.43438	0.195195
$55$	−6.29648	−0.849017
$56$	0	0
$57$	5.93712	0.786390
$58$	8.39382	1.10216
$59$	4.37412	0.569462	0.284731	−	0.958607i	$-0.408096\pi$
$59$	4.37412	0.569462	0.284731	+	0.958607i	$0.408096\pi$
$60$	−0.0661560	−0.00854070
$61$	−4.44248	−0.568801	−0.284400	−	0.958706i	$-0.591795\pi$
$61$	−4.44248	−0.568801	−0.284400	+	0.958706i	$0.591795\pi$
$62$	4.89445	0.621596
$63$	0	0
$64$	7.75717	0.969646
$65$	4.48605	0.556426
$66$	−7.84354	−0.965474
$67$	−12.5372	−1.53166	−0.765829	−	0.643044i	$-0.777671\pi$
$67$	−12.5372	−1.53166	−0.765829	+	0.643044i	$0.777671\pi$
$68$	0.133683	0.0162115
$69$	5.85685	0.705081
$70$	0	0
$71$	−0.568351	−0.0674509	−0.0337254	−	0.999431i	$-0.510737\pi$
$71$	−0.568351	−0.0674509	−0.0337254	+	0.999431i	$0.510737\pi$
$72$	2.78635	0.328375
$73$	14.6453	1.71410	0.857049	−	0.515236i	$-0.172296\pi$
$73$	14.6453	1.71410	0.857049	+	0.515236i	$0.172296\pi$
$74$	9.92806	1.15411
$75$	3.67413	0.424252
$76$	−0.341110	−0.0391280
$77$	0	0
$78$	5.58828	0.632748
$79$	9.54103	1.07345	0.536725	−	0.843757i	$-0.319661\pi$
$79$	9.54103	1.07345	0.536725	+	0.843757i	$0.319661\pi$
$80$	−4.73437	−0.529319
$81$	1.00000	0.111111
$82$	−13.2341	−1.46146
$83$	−4.13806	−0.454211	−0.227106	−	0.973870i	$-0.572926\pi$
$83$	−4.13806	−0.454211	−0.227106	+	0.973870i	$0.572926\pi$
$84$	0	0
$85$	2.67923	0.290603
$86$	−6.26257	−0.675310
$87$	5.85187	0.627386
$88$	−15.2364	−1.62421
$89$	2.47805	0.262673	0.131336	−	0.991338i	$-0.458073\pi$
$89$	2.47805	0.262673	0.131336	+	0.991338i	$0.458073\pi$
$90$	−1.65164	−0.174098
$91$	0	0
$92$	−0.336498	−0.0350823
$93$	3.41224	0.353833
$94$	10.4261	1.07537
$95$	−6.83638	−0.701398
$96$	−0.324908	−0.0331608
$97$	−11.7472	−1.19275	−0.596374	−	0.802707i	$-0.703392\pi$
$97$	−11.7472	−1.19275	−0.596374	+	0.802707i	$0.703392\pi$
$98$	0	0
$99$	−5.46824	−0.549578
$100$	−0.211093	−0.0211093
$101$	8.54432	0.850192	0.425096	−	0.905148i	$-0.360240\pi$
$101$	8.54432	0.850192	0.425096	+	0.905148i	$0.360240\pi$
$102$	3.33752	0.330464
$103$	−1.30532	−0.128617	−0.0643086	−	0.997930i	$-0.520484\pi$
$103$	−1.30532	−0.128617	−0.0643086	+	0.997930i	$0.520484\pi$
$104$	10.8555	1.06447
$105$	0	0
$106$	−8.89975	−0.864420
$107$	9.27267	0.896423	0.448212	−	0.893928i	$-0.352061\pi$
$107$	9.27267	0.896423	0.448212	+	0.893928i	$0.352061\pi$
$108$	−0.0574538	−0.00552849
$109$	−0.596913	−0.0571739	−0.0285869	−	0.999591i	$-0.509101\pi$
$109$	−0.596913	−0.0571739	−0.0285869	+	0.999591i	$0.509101\pi$
$110$	9.03156	0.861126
$111$	6.92148	0.656958
$112$	0	0
$113$	1.38877	0.130644	0.0653221	−	0.997864i	$-0.479193\pi$
$113$	1.38877	0.130644	0.0653221	+	0.997864i	$0.479193\pi$
$114$	−8.51610	−0.797606
$115$	−6.74395	−0.628877
$116$	−0.336212	−0.0312165
$117$	3.89595	0.360181
$118$	−6.27417	−0.577584
$119$	0	0
$120$	−3.20839	−0.292884
$121$	18.9016	1.71833
$122$	6.37221	0.576913
$123$	−9.22634	−0.831911
$124$	−0.196046	−0.0176054
$125$	−9.98795	−0.893350
$126$	0	0
$127$	2.81024	0.249368	0.124684	−	0.992196i	$-0.460208\pi$
$127$	2.81024	0.249368	0.124684	+	0.992196i	$0.460208\pi$
$128$	−11.7766	−1.04091
$129$	−4.36604	−0.384408
$130$	−6.43471	−0.564361
$131$	−3.38836	−0.296042	−0.148021	−	0.988984i	$-0.547290\pi$
$131$	−3.38836	−0.296042	−0.148021	+	0.988984i	$0.547290\pi$
$132$	0.314171	0.0273451
$133$	0	0
$134$	17.9831	1.55350
$135$	−1.15146	−0.0991023
$136$	6.48329	0.555938
$137$	−8.19970	−0.700547	−0.350274	−	0.936647i	$-0.613911\pi$
$137$	−8.19970	−0.700547	−0.350274	+	0.936647i	$0.613911\pi$
$138$	−8.40096	−0.715137
$139$	−5.66803	−0.480756	−0.240378	−	0.970679i	$-0.577271\pi$
$139$	−5.66803	−0.480756	−0.240378	+	0.970679i	$0.577271\pi$
$140$	0	0
$141$	7.26869	0.612134
$142$	0.815233	0.0684129
$143$	−21.3040	−1.78153
$144$	−4.11161	−0.342634
$145$	−6.73822	−0.559578
$146$	−21.0069	−1.73854
$147$	0	0
$148$	−0.397665	−0.0326879
$149$	−8.53222	−0.698986	−0.349493	−	0.936939i	$-0.613646\pi$
$149$	−8.53222	−0.698986	−0.349493	+	0.936939i	$0.613646\pi$
$150$	−5.27011	−0.430302
$151$	−0.238990	−0.0194487	−0.00972435	−	0.999953i	$-0.503095\pi$
$151$	−0.238990	−0.0194487	−0.00972435	+	0.999953i	$0.503095\pi$
$152$	−16.5429	−1.34181
$153$	2.32680	0.188111
$154$	0	0
$155$	−3.92907	−0.315591
$156$	−0.223837	−0.0179213
$157$	−5.13848	−0.410096	−0.205048	−	0.978752i	$-0.565735\pi$
$157$	−5.13848	−0.410096	−0.205048	+	0.978752i	$0.565735\pi$
$158$	−13.6855	−1.08876
$159$	−6.20459	−0.492056
$160$	0.374120	0.0295768
$161$	0	0
$162$	−1.43438	−0.112696
$163$	18.0278	1.41205	0.706025	−	0.708187i	$-0.250487\pi$
$163$	18.0278	1.41205	0.706025	+	0.708187i	$0.250487\pi$
$164$	0.530088	0.0413929
$165$	6.29648	0.490180
$166$	5.93556	0.460689
$167$	−3.87874	−0.300146	−0.150073	−	0.988675i	$-0.547951\pi$
$167$	−3.87874	−0.300146	−0.150073	+	0.988675i	$0.547951\pi$
$168$	0	0
$169$	2.17841	0.167570
$170$	−3.84304	−0.294748
$171$	−5.93712	−0.454023
$172$	0.250845	0.0191268
$173$	12.9576	0.985146	0.492573	−	0.870271i	$-0.336057\pi$
$173$	12.9576	0.985146	0.492573	+	0.870271i	$0.336057\pi$
$174$	−8.39382	−0.636334
$175$	0	0
$176$	22.4832	1.69474
$177$	−4.37412	−0.328779
$178$	−3.55447	−0.266419
$179$	6.36522	0.475759	0.237879	−	0.971295i	$-0.423548\pi$
$179$	6.36522	0.475759	0.237879	+	0.971295i	$0.423548\pi$
$180$	0.0661560	0.00493098
$181$	25.0480	1.86180	0.930901	−	0.365273i	$-0.119024\pi$
$181$	25.0480	1.86180	0.930901	+	0.365273i	$0.119024\pi$
$182$	0	0
$183$	4.44248	0.328397
$184$	−16.3193	−1.20307
$185$	−7.96984	−0.585955
$186$	−4.89445	−0.358879
$187$	−12.7235	−0.930434
$188$	−0.417614	−0.0304576
$189$	0	0
$190$	9.80599	0.711401
$191$	27.0727	1.95891	0.979456	−	0.201657i	$-0.0646328\pi$
$191$	27.0727	1.95891	0.979456	+	0.201657i	$0.0646328\pi$
$192$	−7.75717	−0.559826
$193$	−14.4968	−1.04350	−0.521750	−	0.853098i	$-0.674721\pi$
$193$	−14.4968	−1.04350	−0.521750	+	0.853098i	$0.674721\pi$
$194$	16.8500	1.20976
$195$	−4.48605	−0.321252
$196$	0	0
$197$	5.61172	0.399818	0.199909	−	0.979814i	$-0.435935\pi$
$197$	5.61172	0.399818	0.199909	+	0.979814i	$0.435935\pi$
$198$	7.84354	0.557416
$199$	14.0135	0.993393	0.496697	−	0.867924i	$-0.334546\pi$
$199$	14.0135	0.993393	0.496697	+	0.867924i	$0.334546\pi$
$200$	−10.2374	−0.723895
$201$	12.5372	0.884303
$202$	−12.2558	−0.862317
$203$	0	0
$204$	−0.133683	−0.00935971
$205$	10.6238	0.741999
$206$	1.87233	0.130452
$207$	−5.85685	−0.407079
$208$	−16.0186	−1.11069
$209$	32.4656	2.24569
$210$	0	0
$211$	6.63286	0.456625	0.228312	−	0.973588i	$-0.426679\pi$
$211$	6.63286	0.456625	0.228312	+	0.973588i	$0.426679\pi$
$212$	0.356477	0.0244829
$213$	0.568351	0.0389428
$214$	−13.3006	−0.909208
$215$	5.02734	0.342862
$216$	−2.78635	−0.189587
$217$	0	0
$218$	0.856202	0.0579893
$219$	−14.6453	−0.989635
$220$	−0.361757	−0.0243896
$221$	9.06509	0.609784
$222$	−9.92806	−0.666328
$223$	−22.2229	−1.48815	−0.744077	−	0.668094i	$-0.767110\pi$
$223$	−22.2229	−1.48815	−0.744077	+	0.668094i	$0.767110\pi$
$224$	0	0
$225$	−3.67413	−0.244942
$226$	−1.99202	−0.132507
$227$	−10.5400	−0.699567	−0.349784	−	0.936831i	$-0.613745\pi$
$227$	−10.5400	−0.699567	−0.349784	+	0.936831i	$0.613745\pi$
$228$	0.341110	0.0225905
$229$	10.5427	0.696681	0.348340	−	0.937368i	$-0.386745\pi$
$229$	10.5427	0.696681	0.348340	+	0.937368i	$0.386745\pi$
$230$	9.67341	0.637846
$231$	0	0
$232$	−16.3054	−1.07050
$233$	13.7552	0.901134	0.450567	−	0.892743i	$-0.351222\pi$
$233$	13.7552	0.901134	0.450567	+	0.892743i	$0.351222\pi$
$234$	−5.58828	−0.365317
$235$	−8.36964	−0.545975
$236$	0.251310	0.0163589
$237$	−9.54103	−0.619757
$238$	0	0
$239$	−7.70997	−0.498716	−0.249358	−	0.968411i	$-0.580220\pi$
$239$	−7.70997	−0.498716	−0.249358	+	0.968411i	$0.580220\pi$
$240$	4.73437	0.305602
$241$	−28.5587	−1.83963	−0.919815	−	0.392353i	$-0.871661\pi$
$241$	−28.5587	−1.83963	−0.919815	+	0.392353i	$0.871661\pi$
$242$	−27.1121	−1.74283
$243$	−1.00000	−0.0641500
$244$	−0.255237	−0.0163399
$245$	0	0
$246$	13.2341	0.843776
$247$	−23.1307	−1.47177
$248$	−9.50770	−0.603740
$249$	4.13806	0.262239
$250$	14.3265	0.906090
$251$	3.22940	0.203838	0.101919	−	0.994793i	$-0.467502\pi$
$251$	3.22940	0.203838	0.101919	+	0.994793i	$0.467502\pi$
$252$	0	0
$253$	32.0266	2.01350
$254$	−4.03096	−0.252925
$255$	−2.67923	−0.167780
$256$	1.37776	0.0861102
$257$	16.3779	1.02162	0.510812	−	0.859693i	$-0.329345\pi$
$257$	16.3779	1.02162	0.510812	+	0.859693i	$0.329345\pi$
$258$	6.26257	0.389891
$259$	0	0
$260$	0.257740	0.0159844
$261$	−5.85187	−0.362221
$262$	4.86020	0.300264
$263$	−31.4275	−1.93790	−0.968950	−	0.247257i	$-0.920471\pi$
$263$	−31.4275	−1.93790	−0.968950	+	0.247257i	$0.920471\pi$
$264$	15.2364	0.937739
$265$	7.14436	0.438875
$266$	0	0
$267$	−2.47805	−0.151654
$268$	−0.720307	−0.0439998
$269$	22.5834	1.37693	0.688466	−	0.725268i	$-0.258284\pi$
$269$	22.5834	1.37693	0.688466	+	0.725268i	$0.258284\pi$
$270$	1.65164	0.100516
$271$	−8.85120	−0.537672	−0.268836	−	0.963186i	$-0.586639\pi$
$271$	−8.85120	−0.537672	−0.268836	+	0.963186i	$0.586639\pi$
$272$	−9.56689	−0.580078
$273$	0	0
$274$	11.7615	0.710538
$275$	20.0910	1.21153
$276$	0.336498	0.0202548
$277$	19.9888	1.20101	0.600504	−	0.799622i	$-0.294967\pi$
$277$	19.9888	1.20101	0.600504	+	0.799622i	$0.294967\pi$
$278$	8.13012	0.487612
$279$	−3.41224	−0.204285
$280$	0	0
$281$	−7.29078	−0.434931	−0.217466	−	0.976068i	$-0.569779\pi$
$281$	−7.29078	−0.434931	−0.217466	+	0.976068i	$0.569779\pi$
$282$	−10.4261	−0.620864
$283$	11.1335	0.661815	0.330908	−	0.943663i	$-0.392645\pi$
$283$	11.1335	0.661815	0.330908	+	0.943663i	$0.392645\pi$
$284$	−0.0326539	−0.00193765
$285$	6.83638	0.404952
$286$	30.5580	1.80694
$287$	0	0
$288$	0.324908	0.0191454
$289$	−11.5860	−0.681529
$290$	9.66518	0.567559
$291$	11.7472	0.688633
$292$	0.841425	0.0492407
$293$	5.67555	0.331569	0.165785	−	0.986162i	$-0.446984\pi$
$293$	5.67555	0.331569	0.165785	+	0.986162i	$0.446984\pi$
$294$	0	0
$295$	5.03665	0.293245
$296$	−19.2857	−1.12096
$297$	5.46824	0.317299
$298$	12.2385	0.708955
$299$	−22.8180	−1.31960
$300$	0.211093	0.0121874
$301$	0	0
$302$	0.342802	0.0197261
$303$	−8.54432	−0.490859
$304$	24.4111	1.40007
$305$	−5.11535	−0.292904
$306$	−3.33752	−0.190793
$307$	−11.0354	−0.629824	−0.314912	−	0.949121i	$-0.601975\pi$
$307$	−11.0354	−0.629824	−0.314912	+	0.949121i	$0.601975\pi$
$308$	0	0
$309$	1.30532	0.0742572
$310$	5.63579	0.320091
$311$	9.57688	0.543055	0.271527	−	0.962431i	$-0.412471\pi$
$311$	9.57688	0.543055	0.271527	+	0.962431i	$0.412471\pi$
$312$	−10.8555	−0.614571
$313$	−24.7541	−1.39918	−0.699592	−	0.714543i	$-0.746635\pi$
$313$	−24.7541	−1.39918	−0.699592	+	0.714543i	$0.746635\pi$
$314$	7.37055	0.415944
$315$	0	0
$316$	0.548168	0.0308369
$317$	−4.18530	−0.235070	−0.117535	−	0.993069i	$-0.537499\pi$
$317$	−4.18530	−0.235070	−0.117535	+	0.993069i	$0.537499\pi$
$318$	8.89975	0.499073
$319$	31.9994	1.79162
$320$	8.93211	0.499320
$321$	−9.27267	−0.517550
$322$	0	0
$323$	−13.8145	−0.768659
$324$	0.0574538	0.00319188
$325$	−14.3142	−0.794010
$326$	−25.8588	−1.43219
$327$	0.596913	0.0330094
$328$	25.7079	1.41948
$329$	0	0
$330$	−9.03156	−0.497171
$331$	−0.861764	−0.0473668	−0.0236834	−	0.999720i	$-0.507539\pi$
$331$	−0.861764	−0.0473668	−0.0236834	+	0.999720i	$0.507539\pi$
$332$	−0.237747	−0.0130481
$333$	−6.92148	−0.379295
$334$	5.56359	0.304426
$335$	−14.4361	−0.788728
$336$	0	0
$337$	−16.3632	−0.891362	−0.445681	−	0.895192i	$-0.647038\pi$
$337$	−16.3632	−0.891362	−0.445681	+	0.895192i	$0.647038\pi$
$338$	−3.12468	−0.169960
$339$	−1.38877	−0.0754275
$340$	0.153932	0.00834812
$341$	18.6589	1.01044
$342$	8.51610	0.460498
$343$	0	0
$344$	12.1653	0.655911
$345$	6.74395	0.363082
$346$	−18.5861	−0.999195
$347$	31.5737	1.69497	0.847483	−	0.530822i	$-0.178117\pi$
$347$	31.5737	1.69497	0.847483	+	0.530822i	$0.178117\pi$
$348$	0.336212	0.0180228
$349$	−20.1598	−1.07913	−0.539565	−	0.841944i	$-0.681411\pi$
$349$	−20.1598	−1.07913	−0.539565	+	0.841944i	$0.681411\pi$
$350$	0	0
$351$	−3.89595	−0.207950
$352$	−1.77667	−0.0946970
$353$	24.1873	1.28736	0.643681	−	0.765294i	$-0.277406\pi$
$353$	24.1873	1.28736	0.643681	+	0.765294i	$0.277406\pi$
$354$	6.27417	0.333468
$355$	−0.654436	−0.0347339
$356$	0.142373	0.00754577
$357$	0	0
$358$	−9.13016	−0.482544
$359$	−25.8327	−1.36340	−0.681699	−	0.731632i	$-0.738759\pi$
$359$	−25.8327	−1.36340	−0.681699	+	0.731632i	$0.738759\pi$
$360$	3.20839	0.169097
$361$	16.2494	0.855230
$362$	−35.9284	−1.88835
$363$	−18.9016	−0.992077
$364$	0	0
$365$	16.8635	0.882675
$366$	−6.37221	−0.333081
$367$	−32.7640	−1.71027	−0.855133	−	0.518409i	$-0.826525\pi$
$367$	−32.7640	−1.71027	−0.855133	+	0.518409i	$0.826525\pi$
$368$	24.0810	1.25531
$369$	9.22634	0.480304
$370$	11.4318	0.594311
$371$	0	0
$372$	0.196046	0.0101645
$373$	−9.40984	−0.487223	−0.243612	−	0.969873i	$-0.578332\pi$
$373$	−9.40984	−0.487223	−0.243612	+	0.969873i	$0.578332\pi$
$374$	18.2504	0.943704
$375$	9.98795	0.515776
$376$	−20.2532	−1.04448
$377$	−22.7986	−1.17419
$378$	0	0
$379$	20.8879	1.07294	0.536471	−	0.843919i	$-0.319757\pi$
$379$	20.8879	1.07294	0.536471	+	0.843919i	$0.319757\pi$
$380$	−0.392776	−0.0201490
$381$	−2.81024	−0.143973
$382$	−38.8326	−1.98685
$383$	19.3806	0.990305	0.495152	−	0.868806i	$-0.335112\pi$
$383$	19.3806	0.990305	0.495152	+	0.868806i	$0.335112\pi$
$384$	11.7766	0.600970
$385$	0	0
$386$	20.7939	1.05838
$387$	4.36604	0.221938
$388$	−0.674921	−0.0342639
$389$	17.7415	0.899531	0.449765	−	0.893147i	$-0.351508\pi$
$389$	17.7415	0.899531	0.449765	+	0.893147i	$0.351508\pi$
$390$	6.43471	0.325834
$391$	−13.6277	−0.689183
$392$	0	0
$393$	3.38836	0.170920
$394$	−8.04935	−0.405521
$395$	10.9862	0.552774
$396$	−0.314171	−0.0157877
$397$	−12.0773	−0.606142	−0.303071	−	0.952968i	$-0.598012\pi$
$397$	−12.0773	−0.606142	−0.303071	+	0.952968i	$0.598012\pi$
$398$	−20.1008	−1.00756
$399$	0	0
$400$	15.1066	0.755329
$401$	−8.37717	−0.418336	−0.209168	−	0.977880i	$-0.567076\pi$
$401$	−8.37717	−0.418336	−0.209168	+	0.977880i	$0.567076\pi$
$402$	−17.9831	−0.896915
$403$	−13.2939	−0.662216
$404$	0.490904	0.0244234
$405$	1.15146	0.0572167
$406$	0	0
$407$	37.8483	1.87607
$408$	−6.48329	−0.320971
$409$	−29.9214	−1.47952	−0.739758	−	0.672873i	$-0.765060\pi$
$409$	−29.9214	−1.47952	−0.739758	+	0.672873i	$0.765060\pi$
$410$	−15.2386	−0.752581
$411$	8.19970	0.404461
$412$	−0.0749957	−0.00369477
$413$	0	0
$414$	8.40096	0.412885
$415$	−4.76483	−0.233896
$416$	1.26582	0.0620622
$417$	5.66803	0.277564
$418$	−46.5680	−2.27772
$419$	−21.0211	−1.02695	−0.513474	−	0.858105i	$-0.671642\pi$
$419$	−21.0211	−1.02695	−0.513474	+	0.858105i	$0.671642\pi$
$420$	0	0
$421$	19.1823	0.934886	0.467443	−	0.884023i	$-0.345175\pi$
$421$	19.1823	0.934886	0.467443	+	0.884023i	$0.345175\pi$
$422$	−9.51405	−0.463137
$423$	−7.26869	−0.353416
$424$	17.2882	0.839588
$425$	−8.54897	−0.414686
$426$	−0.815233	−0.0394982
$427$	0	0
$428$	0.532750	0.0257514
$429$	21.3040	1.02857
$430$	−7.21113	−0.347751
$431$	11.7822	0.567530	0.283765	−	0.958894i	$-0.408416\pi$
$431$	11.7822	0.567530	0.283765	+	0.958894i	$0.408416\pi$
$432$	4.11161	0.197820
$433$	26.8358	1.28965	0.644824	−	0.764331i	$-0.276931\pi$
$433$	26.8358	1.28965	0.644824	+	0.764331i	$0.276931\pi$
$434$	0	0
$435$	6.73822	0.323073
$436$	−0.0342949	−0.00164243
$437$	34.7728	1.66341
$438$	21.0069	1.00375
$439$	−6.48509	−0.309516	−0.154758	−	0.987952i	$-0.549460\pi$
$439$	−6.48509	−0.309516	−0.154758	+	0.987952i	$0.549460\pi$
$440$	−17.5442	−0.836388
$441$	0	0
$442$	−13.0028	−0.618481
$443$	38.3017	1.81977	0.909884	−	0.414862i	$-0.136170\pi$
$443$	38.3017	1.81977	0.909884	+	0.414862i	$0.136170\pi$
$444$	0.397665	0.0188724
$445$	2.85339	0.135264
$446$	31.8761	1.50938
$447$	8.53222	0.403560
$448$	0	0
$449$	17.7531	0.837820	0.418910	−	0.908028i	$-0.362412\pi$
$449$	17.7531	0.837820	0.418910	+	0.908028i	$0.362412\pi$
$450$	5.27011	0.248435
$451$	−50.4518	−2.37568
$452$	0.0797899	0.00375300
$453$	0.238990	0.0112287
$454$	15.1185	0.709544
$455$	0	0
$456$	16.5429	0.774693
$457$	15.8713	0.742427	0.371214	−	0.928547i	$-0.378942\pi$
$457$	15.8713	0.742427	0.371214	+	0.928547i	$0.378942\pi$
$458$	−15.1223	−0.706616
$459$	−2.32680	−0.108606
$460$	−0.387465	−0.0180657
$461$	−18.3932	−0.856657	−0.428329	−	0.903623i	$-0.640897\pi$
$461$	−18.3932	−0.856657	−0.428329	+	0.903623i	$0.640897\pi$
$462$	0	0
$463$	−0.107657	−0.00500322	−0.00250161	−	0.999997i	$-0.500796\pi$
$463$	−0.107657	−0.00500322	−0.00250161	+	0.999997i	$0.500796\pi$
$464$	24.0606	1.11698
$465$	3.92907	0.182206
$466$	−19.7302	−0.913986
$467$	32.4582	1.50199	0.750993	−	0.660310i	$-0.229575\pi$
$467$	32.4582	1.50199	0.750993	+	0.660310i	$0.229575\pi$
$468$	0.223837	0.0103469
$469$	0	0
$470$	12.0053	0.553762
$471$	5.13848	0.236769
$472$	12.1879	0.560992
$473$	−23.8745	−1.09775
$474$	13.6855	0.628595
$475$	21.8137	1.00088
$476$	0	0
$477$	6.20459	0.284088
$478$	11.0590	0.505829
$479$	16.8627	0.770476	0.385238	−	0.922817i	$-0.374119\pi$
$479$	16.8627	0.770476	0.385238	+	0.922817i	$0.374119\pi$
$480$	−0.374120	−0.0170762
$481$	−26.9657	−1.22953
$482$	40.9642	1.86587
$483$	0	0
$484$	1.08597	0.0493622
$485$	−13.5265	−0.614206
$486$	1.43438	0.0650649
$487$	34.8054	1.57718	0.788591	−	0.614918i	$-0.210811\pi$
$487$	34.8054	1.57718	0.788591	+	0.614918i	$0.210811\pi$
$488$	−12.3783	−0.560340
$489$	−18.0278	−0.815247
$490$	0	0
$491$	18.6284	0.840689	0.420344	−	0.907365i	$-0.361909\pi$
$491$	18.6284	0.840689	0.420344	+	0.907365i	$0.361909\pi$
$492$	−0.530088	−0.0238982
$493$	−13.6161	−0.613239
$494$	33.1783	1.49276
$495$	−6.29648	−0.283006
$496$	14.0298	0.629956
$497$	0	0
$498$	−5.93556	−0.265979
$499$	−22.1337	−0.990840	−0.495420	−	0.868653i	$-0.664986\pi$
$499$	−22.1337	−0.990840	−0.495420	+	0.868653i	$0.664986\pi$
$500$	−0.573845	−0.0256631
$501$	3.87874	0.173289
$502$	−4.63220	−0.206745
$503$	−16.6139	−0.740776	−0.370388	−	0.928877i	$-0.620775\pi$
$503$	−16.6139	−0.740776	−0.370388	+	0.928877i	$0.620775\pi$
$504$	0	0
$505$	9.83849	0.437807
$506$	−45.9384	−2.04221
$507$	−2.17841	−0.0967468
$508$	0.161459	0.00716358
$509$	35.5269	1.57470	0.787352	−	0.616504i	$-0.211452\pi$
$509$	35.5269	1.57470	0.787352	+	0.616504i	$0.211452\pi$
$510$	3.84304	0.170173
$511$	0	0
$512$	21.5769	0.953573
$513$	5.93712	0.262130
$514$	−23.4921	−1.03619
$515$	−1.50303	−0.0662315
$516$	−0.250845	−0.0110429
$517$	39.7469	1.74807
$518$	0	0
$519$	−12.9576	−0.568774
$520$	12.4997	0.548149
$521$	34.4241	1.50815	0.754074	−	0.656790i	$-0.228086\pi$
$521$	34.4241	1.50815	0.754074	+	0.656790i	$0.228086\pi$
$522$	8.39382	0.367387
$523$	32.6781	1.42891	0.714457	−	0.699679i	$-0.246674\pi$
$523$	32.6781	1.42891	0.714457	+	0.699679i	$0.246674\pi$
$524$	−0.194674	−0.00850437
$525$	0	0
$526$	45.0790	1.96554
$527$	−7.93960	−0.345854
$528$	−22.4832	−0.978457
$529$	11.3026	0.491419
$530$	−10.2477	−0.445134
$531$	4.37412	0.189821
$532$	0	0
$533$	35.9454	1.55697
$534$	3.55447	0.153817
$535$	10.6772	0.461614
$536$	−34.9330	−1.50887
$537$	−6.36522	−0.274680
$538$	−32.3932	−1.39657
$539$	0	0
$540$	−0.0661560	−0.00284690
$541$	29.3356	1.26124	0.630618	−	0.776093i	$-0.282801\pi$
$541$	29.3356	1.26124	0.630618	+	0.776093i	$0.282801\pi$
$542$	12.6960	0.545340
$543$	−25.0480	−1.07491
$544$	0.755996	0.0324131
$545$	−0.687324	−0.0294417
$546$	0	0
$547$	−2.50343	−0.107039	−0.0535194	−	0.998567i	$-0.517044\pi$
$547$	−2.50343	−0.107039	−0.0535194	+	0.998567i	$0.517044\pi$
$548$	−0.471103	−0.0201245
$549$	−4.44248	−0.189600
$550$	−28.8182	−1.22881
$551$	34.7432	1.48011
$552$	16.3193	0.694593
$553$	0	0
$554$	−28.6715	−1.21814
$555$	7.96984	0.338301
$556$	−0.325649	−0.0138106
$557$	16.4674	0.697745	0.348872	−	0.937170i	$-0.386565\pi$
$557$	16.4674	0.697745	0.348872	+	0.937170i	$0.386565\pi$
$558$	4.89445	0.207199
$559$	17.0099	0.719441
$560$	0	0
$561$	12.7235	0.537186
$562$	10.4578	0.441134
$563$	−2.87622	−0.121218	−0.0606092	−	0.998162i	$-0.519304\pi$
$563$	−2.87622	−0.121218	−0.0606092	+	0.998162i	$0.519304\pi$
$564$	0.417614	0.0175847
$565$	1.59912	0.0672753
$566$	−15.9696	−0.671254
$567$	0	0
$568$	−1.58363	−0.0664476
$569$	9.02763	0.378458	0.189229	−	0.981933i	$-0.439401\pi$
$569$	9.02763	0.378458	0.189229	+	0.981933i	$0.439401\pi$
$570$	−9.80599	−0.410728
$571$	−8.25549	−0.345482	−0.172741	−	0.984967i	$-0.555262\pi$
$571$	−8.25549	−0.345482	−0.172741	+	0.984967i	$0.555262\pi$
$572$	−1.22399	−0.0511777
$573$	−27.0727	−1.13098
$574$	0	0
$575$	21.5188	0.897396
$576$	7.75717	0.323215
$577$	−27.6193	−1.14981	−0.574903	−	0.818222i	$-0.694960\pi$
$577$	−27.6193	−1.14981	−0.574903	+	0.818222i	$0.694960\pi$
$578$	16.6188	0.691249
$579$	14.4968	0.602465
$580$	−0.387136	−0.0160749
$581$	0	0
$582$	−16.8500	−0.698454
$583$	−33.9281	−1.40516
$584$	40.8069	1.68860
$585$	4.48605	0.185475
$586$	−8.14091	−0.336298
$587$	23.2756	0.960686	0.480343	−	0.877081i	$-0.340512\pi$
$587$	23.2756	0.960686	0.480343	+	0.877081i	$0.340512\pi$
$588$	0	0
$589$	20.2589	0.834752
$590$	−7.22448	−0.297427
$591$	−5.61172	−0.230835
$592$	28.4584	1.16963
$593$	6.73276	0.276481	0.138241	−	0.990399i	$-0.455855\pi$
$593$	6.73276	0.276481	0.138241	+	0.990399i	$0.455855\pi$
$594$	−7.84354	−0.321825
$595$	0	0
$596$	−0.490208	−0.0200797
$597$	−14.0135	−0.573536
$598$	32.7297	1.33842
$599$	7.81935	0.319490	0.159745	−	0.987158i	$-0.448933\pi$
$599$	7.81935	0.319490	0.159745	+	0.987158i	$0.448933\pi$
$600$	10.2374	0.417941
$601$	−8.17879	−0.333620	−0.166810	−	0.985989i	$-0.553347\pi$
$601$	−8.17879	−0.333620	−0.166810	+	0.985989i	$0.553347\pi$
$602$	0	0
$603$	−12.5372	−0.510553
$604$	−0.0137308	−0.000558700 0
$605$	21.7645	0.884854
$606$	12.2558	0.497859
$607$	46.8789	1.90276	0.951378	−	0.308025i	$-0.0996681\pi$
$607$	46.8789	1.90276	0.951378	+	0.308025i	$0.0996681\pi$
$608$	−1.92902	−0.0782320
$609$	0	0
$610$	7.33738	0.297082
$611$	−28.3185	−1.14564
$612$	0.133683	0.00540383
$613$	10.1787	0.411112	0.205556	−	0.978645i	$-0.434100\pi$
$613$	10.1787	0.411112	0.205556	+	0.978645i	$0.434100\pi$
$614$	15.8290	0.638806
$615$	−10.6238	−0.428393
$616$	0	0
$617$	−13.9667	−0.562279	−0.281140	−	0.959667i	$-0.590712\pi$
$617$	−13.9667	−0.562279	−0.281140	+	0.959667i	$0.590712\pi$
$618$	−1.87233	−0.0753163
$619$	10.9377	0.439624	0.219812	−	0.975542i	$-0.429456\pi$
$619$	10.9377	0.439624	0.219812	+	0.975542i	$0.429456\pi$
$620$	−0.225740	−0.00906593
$621$	5.85685	0.235027
$622$	−13.7369	−0.550800
$623$	0	0
$624$	16.0186	0.641258
$625$	6.86987	0.274795
$626$	35.5068	1.41914
$627$	−32.4656	−1.29655
$628$	−0.295225	−0.0117808
$629$	−16.1049	−0.642145
$630$	0	0
$631$	10.7302	0.427163	0.213582	−	0.976925i	$-0.431487\pi$
$631$	10.7302	0.427163	0.213582	+	0.976925i	$0.431487\pi$
$632$	26.5847	1.05748
$633$	−6.63286	−0.263632
$634$	6.00332	0.238422
$635$	3.23589	0.128412
$636$	−0.356477	−0.0141352
$637$	0	0
$638$	−45.8994	−1.81717
$639$	−0.568351	−0.0224836
$640$	−13.5603	−0.536018
$641$	36.1947	1.42960	0.714802	−	0.699327i	$-0.246517\pi$
$641$	36.1947	1.42960	0.714802	+	0.699327i	$0.246517\pi$
$642$	13.3006	0.524931
$643$	−26.7210	−1.05377	−0.526886	−	0.849936i	$-0.676641\pi$
$643$	−26.7210	−1.05377	−0.526886	+	0.849936i	$0.676641\pi$
$644$	0	0
$645$	−5.02734	−0.197951
$646$	19.8153	0.779621
$647$	−39.4109	−1.54940	−0.774702	−	0.632326i	$-0.782100\pi$
$647$	−39.4109	−1.54940	−0.774702	+	0.632326i	$0.782100\pi$
$648$	2.78635	0.109458
$649$	−23.9187	−0.938893
$650$	20.5321	0.805334
$651$	0	0
$652$	1.03577	0.0405638
$653$	43.9896	1.72145	0.860724	−	0.509072i	$-0.170011\pi$
$653$	43.9896	1.72145	0.860724	+	0.509072i	$0.170011\pi$
$654$	−0.856202	−0.0334801
$655$	−3.90158	−0.152447
$656$	−37.9351	−1.48112
$657$	14.6453	0.571366
$658$	0	0
$659$	−31.3694	−1.22198	−0.610989	−	0.791639i	$-0.709228\pi$
$659$	−31.3694	−1.22198	−0.610989	+	0.791639i	$0.709228\pi$
$660$	0.361757	0.0140814
$661$	−3.95557	−0.153854	−0.0769269	−	0.997037i	$-0.524511\pi$
$661$	−3.95557	−0.153854	−0.0769269	+	0.997037i	$0.524511\pi$
$662$	1.23610	0.0480424
$663$	−9.06509	−0.352059
$664$	−11.5301	−0.447455
$665$	0	0
$666$	9.92806	0.384704
$667$	34.2735	1.32707
$668$	−0.222848	−0.00862225
$669$	22.2229	0.859186
$670$	20.7069	0.799977
$671$	24.2925	0.937802
$672$	0	0
$673$	−25.6097	−0.987183	−0.493591	−	0.869694i	$-0.664316\pi$
$673$	−25.6097	−0.987183	−0.493591	+	0.869694i	$0.664316\pi$
$674$	23.4711	0.904075
$675$	3.67413	0.141417
$676$	0.125158	0.00481377
$677$	−12.7449	−0.489825	−0.244913	−	0.969545i	$-0.578759\pi$
$677$	−12.7449	−0.489825	−0.244913	+	0.969545i	$0.578759\pi$
$678$	1.99202	0.0765032
$679$	0	0
$680$	7.46528	0.286280
$681$	10.5400	0.403895
$682$	−26.7640	−1.02485
$683$	13.2270	0.506117	0.253059	−	0.967451i	$-0.418563\pi$
$683$	13.2270	0.506117	0.253059	+	0.967451i	$0.418563\pi$
$684$	−0.341110	−0.0130427
$685$	−9.44166	−0.360747
$686$	0	0
$687$	−10.5427	−0.402229
$688$	−17.9514	−0.684392
$689$	24.1727	0.920908
$690$	−9.67341	−0.368260
$691$	−30.1337	−1.14634	−0.573169	−	0.819437i	$-0.694286\pi$
$691$	−30.1337	−1.14634	−0.573169	+	0.819437i	$0.694286\pi$
$692$	0.744461	0.0283002
$693$	0	0
$694$	−45.2888	−1.71914
$695$	−6.52653	−0.247565
$696$	16.3054	0.618054
$697$	21.4679	0.813153
$698$	28.9169	1.09452
$699$	−13.7552	−0.520270
$700$	0	0
$701$	1.84844	0.0698147	0.0349074	−	0.999391i	$-0.488886\pi$
$701$	1.84844	0.0698147	0.0349074	+	0.999391i	$0.488886\pi$
$702$	5.58828	0.210916
$703$	41.0937	1.54988
$704$	−42.4180	−1.59869
$705$	8.36964	0.315219
$706$	−34.6939	−1.30572
$707$	0	0
$708$	−0.251310	−0.00944480
$709$	17.6375	0.662389	0.331195	−	0.943562i	$-0.392548\pi$
$709$	17.6375	0.662389	0.331195	+	0.943562i	$0.392548\pi$
$710$	0.938712	0.0352292
$711$	9.54103	0.357817
$712$	6.90473	0.258766
$713$	19.9849	0.748442
$714$	0	0
$715$	−24.5308	−0.917399
$716$	0.365706	0.0136671
$717$	7.70997	0.287934
$718$	37.0540	1.38284
$719$	−20.4423	−0.762371	−0.381185	−	0.924499i	$-0.624484\pi$
$719$	−20.4423	−0.762371	−0.381185	+	0.924499i	$0.624484\pi$
$720$	−4.73437	−0.176440
$721$	0	0
$722$	−23.3078	−0.867427
$723$	28.5587	1.06211
$724$	1.43910	0.0534837
$725$	21.5005	0.798509
$726$	27.1121	1.00623
$727$	31.2788	1.16006	0.580032	−	0.814593i	$-0.303040\pi$
$727$	31.2788	1.16006	0.580032	+	0.814593i	$0.303040\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−24.1887	−0.895264
$731$	10.1589	0.375741
$732$	0.255237	0.00943383
$733$	−48.1316	−1.77778	−0.888891	−	0.458119i	$-0.848523\pi$
$733$	−48.1316	−1.77778	−0.888891	+	0.458119i	$0.848523\pi$
$734$	46.9961	1.73466
$735$	0	0
$736$	−1.90294	−0.0701431
$737$	68.5562	2.52530
$738$	−13.2341	−0.487154
$739$	−14.1257	−0.519621	−0.259810	−	0.965660i	$-0.583660\pi$
$739$	−14.1257	−0.519621	−0.259810	+	0.965660i	$0.583660\pi$
$740$	−0.457898	−0.0168326
$741$	23.1307	0.849728
$742$	0	0
$743$	18.0584	0.662500	0.331250	−	0.943543i	$-0.392530\pi$
$743$	18.0584	0.662500	0.331250	+	0.943543i	$0.392530\pi$
$744$	9.50770	0.348569
$745$	−9.82455	−0.359944
$746$	13.4973	0.494172
$747$	−4.13806	−0.151404
$748$	−0.731013	−0.0267285
$749$	0	0
$750$	−14.3265	−0.523132
$751$	25.7201	0.938540	0.469270	−	0.883055i	$-0.344517\pi$
$751$	25.7201	0.938540	0.469270	+	0.883055i	$0.344517\pi$
$752$	29.8860	1.08983
$753$	−3.22940	−0.117686
$754$	32.7019	1.19093
$755$	−0.275188	−0.0100151
$756$	0	0
$757$	−1.04597	−0.0380164	−0.0190082	−	0.999819i	$-0.506051\pi$
$757$	−1.04597	−0.0380164	−0.0190082	+	0.999819i	$0.506051\pi$
$758$	−29.9613	−1.08824
$759$	−32.0266	−1.16249
$760$	−19.0486	−0.690965
$761$	34.0927	1.23586	0.617930	−	0.786233i	$-0.287972\pi$
$761$	34.0927	1.23586	0.617930	+	0.786233i	$0.287972\pi$
$762$	4.03096	0.146026
$763$	0	0
$764$	1.55543	0.0562734
$765$	2.67923	0.0968677
$766$	−27.7993	−1.00443
$767$	17.0414	0.615328
$768$	−1.37776	−0.0497158
$769$	23.5305	0.848532	0.424266	−	0.905538i	$-0.360532\pi$
$769$	23.5305	0.848532	0.424266	+	0.905538i	$0.360532\pi$
$770$	0	0
$771$	−16.3779	−0.589834
$772$	−0.832894	−0.0299765
$773$	−10.2175	−0.367499	−0.183749	−	0.982973i	$-0.558823\pi$
$773$	−10.2175	−0.367499	−0.183749	+	0.982973i	$0.558823\pi$
$774$	−6.26257	−0.225103
$775$	12.5370	0.450342
$776$	−32.7319	−1.17501
$777$	0	0
$778$	−25.4481	−0.912360
$779$	−54.7779	−1.96262
$780$	−0.257740	−0.00922858
$781$	3.10788	0.111209
$782$	19.5474	0.699012
$783$	5.85187	0.209129
$784$	0	0
$785$	−5.91678	−0.211179
$786$	−4.86020	−0.173358
$787$	6.58366	0.234682	0.117341	−	0.993092i	$-0.462563\pi$
$787$	6.58366	0.234682	0.117341	+	0.993092i	$0.462563\pi$
$788$	0.322414	0.0114855
$789$	31.4275	1.11885
$790$	−15.7584	−0.560657
$791$	0	0
$792$	−15.2364	−0.541404
$793$	−17.3077	−0.614613
$794$	17.3235	0.614787
$795$	−7.14436	−0.253384
$796$	0.805131	0.0285371
$797$	5.08134	0.179990	0.0899951	−	0.995942i	$-0.471315\pi$
$797$	5.08134	0.179990	0.0899951	+	0.995942i	$0.471315\pi$
$798$	0	0
$799$	−16.9128	−0.598332
$800$	−1.19375	−0.0422056
$801$	2.47805	0.0875577
$802$	12.0161	0.424302
$803$	−80.0837	−2.82609
$804$	0.720307	0.0254033
$805$	0	0
$806$	19.0685	0.671661
$807$	−22.5834	−0.794972
$808$	23.8075	0.837546
$809$	33.4782	1.17703	0.588516	−	0.808485i	$-0.299712\pi$
$809$	33.4782	1.17703	0.588516	+	0.808485i	$0.299712\pi$
$810$	−1.65164	−0.0580327
$811$	22.7939	0.800401	0.400200	−	0.916428i	$-0.368941\pi$
$811$	22.7939	0.800401	0.400200	+	0.916428i	$0.368941\pi$
$812$	0	0
$813$	8.85120	0.310425
$814$	−54.2890	−1.90283
$815$	20.7584	0.727136
$816$	9.56689	0.334908
$817$	−25.9217	−0.906885
$818$	42.9187	1.50062
$819$	0	0
$820$	0.610378	0.0213153
$821$	−12.0282	−0.419785	−0.209893	−	0.977724i	$-0.567311\pi$
$821$	−12.0282	−0.419785	−0.209893	+	0.977724i	$0.567311\pi$
$822$	−11.7615	−0.410230
$823$	14.8951	0.519211	0.259605	−	0.965715i	$-0.416408\pi$
$823$	14.8951	0.519211	0.259605	+	0.965715i	$0.416408\pi$
$824$	−3.63709	−0.126704
$825$	−20.0910	−0.699479
$826$	0	0
$827$	−15.5772	−0.541672	−0.270836	−	0.962626i	$-0.587300\pi$
$827$	−15.5772	−0.541672	−0.270836	+	0.962626i	$0.587300\pi$
$828$	−0.336498	−0.0116941
$829$	3.81743	0.132585	0.0662924	−	0.997800i	$-0.478883\pi$
$829$	3.81743	0.132585	0.0662924	+	0.997800i	$0.478883\pi$
$830$	6.83459	0.237232
$831$	−19.9888	−0.693403
$832$	30.2215	1.04774
$833$	0	0
$834$	−8.13012	−0.281523
$835$	−4.46623	−0.154560
$836$	1.86527	0.0645117
$837$	3.41224	0.117944
$838$	30.1523	1.04159
$839$	14.0797	0.486085	0.243042	−	0.970016i	$-0.421855\pi$
$839$	14.0797	0.486085	0.243042	+	0.970016i	$0.421855\pi$
$840$	0	0
$841$	5.24434	0.180839
$842$	−27.5147	−0.948219
$843$	7.29078	0.251108
$844$	0.381083	0.0131174
$845$	2.50837	0.0862905
$846$	10.4261	0.358456
$847$	0	0
$848$	−25.5108	−0.876045
$849$	−11.1335	−0.382099
$850$	12.2625	0.420600
$851$	40.5381	1.38963
$852$	0.0326539	0.00111871
$853$	−11.0317	−0.377719	−0.188860	−	0.982004i	$-0.560479\pi$
$853$	−11.0317	−0.377719	−0.188860	+	0.982004i	$0.560479\pi$
$854$	0	0
$855$	−6.83638	−0.233799
$856$	25.8370	0.883089
$857$	−34.3331	−1.17280	−0.586399	−	0.810022i	$-0.699455\pi$
$857$	−34.3331	−1.17280	−0.586399	+	0.810022i	$0.699455\pi$
$858$	−30.5580	−1.04323
$859$	−26.4368	−0.902011	−0.451005	−	0.892521i	$-0.648935\pi$
$859$	−26.4368	−0.902011	−0.451005	+	0.892521i	$0.648935\pi$
$860$	0.288840	0.00984935
$861$	0	0
$862$	−16.9002	−0.575624
$863$	−21.7413	−0.740084	−0.370042	−	0.929015i	$-0.620657\pi$
$863$	−21.7413	−0.740084	−0.370042	+	0.929015i	$0.620657\pi$
$864$	−0.324908	−0.0110536
$865$	14.9202	0.507301
$866$	−38.4928	−1.30804
$867$	11.5860	0.393481
$868$	0	0
$869$	−52.1726	−1.76983
$870$	−9.66518	−0.327680
$871$	−48.8441	−1.65502
$872$	−1.66321	−0.0563234
$873$	−11.7472	−0.397582
$874$	−49.8775	−1.68713
$875$	0	0
$876$	−0.841425	−0.0284291
$877$	−4.03691	−0.136317	−0.0681584	−	0.997675i	$-0.521712\pi$
$877$	−4.03691	−0.136317	−0.0681584	+	0.997675i	$0.521712\pi$
$878$	9.30210	0.313931
$879$	−5.67555	−0.191432
$880$	25.8887	0.872706
$881$	−41.8324	−1.40937	−0.704685	−	0.709520i	$-0.748912\pi$
$881$	−41.8324	−1.40937	−0.704685	+	0.709520i	$0.748912\pi$
$882$	0	0
$883$	50.0791	1.68530	0.842648	−	0.538465i	$-0.180995\pi$
$883$	50.0791	1.68530	0.842648	+	0.538465i	$0.180995\pi$
$884$	0.520824	0.0175172
$885$	−5.03665	−0.169305
$886$	−54.9393	−1.84572
$887$	−21.7805	−0.731316	−0.365658	−	0.930749i	$-0.619156\pi$
$887$	−21.7805	−0.731316	−0.365658	+	0.930749i	$0.619156\pi$
$888$	19.2857	0.647186
$889$	0	0
$890$	−4.09285	−0.137193
$891$	−5.46824	−0.183193
$892$	−1.27679	−0.0427500
$893$	43.1551	1.44413
$894$	−12.2385	−0.409315
$895$	7.32933	0.244992
$896$	0	0
$897$	22.8180	0.761870
$898$	−25.4647	−0.849769
$899$	19.9680	0.665969
$900$	−0.211093	−0.00703642
$901$	14.4368	0.480961
$902$	72.3672	2.40957
$903$	0	0
$904$	3.86960	0.128701
$905$	28.8419	0.958736
$906$	−0.342802	−0.0113888
$907$	−37.2833	−1.23797	−0.618986	−	0.785402i	$-0.712456\pi$
$907$	−37.2833	−1.23797	−0.618986	+	0.785402i	$0.712456\pi$
$908$	−0.605565	−0.0200964
$909$	8.54432	0.283397
$910$	0	0
$911$	54.9701	1.82124	0.910621	−	0.413244i	$-0.135604\pi$
$911$	54.9701	1.82124	0.910621	+	0.413244i	$0.135604\pi$
$912$	−24.4111	−0.808332
$913$	22.6279	0.748874
$914$	−22.7655	−0.753016
$915$	5.11535	0.169108
$916$	0.605717	0.0200135
$917$	0	0
$918$	3.33752	0.110155
$919$	12.2262	0.403307	0.201653	−	0.979457i	$-0.435369\pi$
$919$	12.2262	0.403307	0.201653	+	0.979457i	$0.435369\pi$
$920$	−18.7910	−0.619522
$921$	11.0354	0.363629
$922$	26.3829	0.868875
$923$	−2.21427	−0.0728835
$924$	0	0
$925$	25.4304	0.836147
$926$	0.154421	0.00507458
$927$	−1.30532	−0.0428724
$928$	−1.90132	−0.0624138
$929$	25.8744	0.848911	0.424455	−	0.905449i	$-0.360466\pi$
$929$	25.8744	0.848911	0.424455	+	0.905449i	$0.360466\pi$
$930$	−5.63579	−0.184805
$931$	0	0
$932$	0.790289	0.0258868
$933$	−9.57688	−0.313533
$934$	−46.5575	−1.52341
$935$	−14.6507	−0.479128
$936$	10.8555	0.354823
$937$	2.93657	0.0959335	0.0479667	−	0.998849i	$-0.484726\pi$
$937$	2.93657	0.0959335	0.0479667	+	0.998849i	$0.484726\pi$
$938$	0	0
$939$	24.7541	0.807819
$940$	−0.480867	−0.0156842
$941$	33.6578	1.09721	0.548606	−	0.836081i	$-0.315159\pi$
$941$	33.6578	1.09721	0.548606	+	0.836081i	$0.315159\pi$
$942$	−7.37055	−0.240146
$943$	−54.0373	−1.75970
$944$	−17.9847	−0.585351
$945$	0	0
$946$	34.2452	1.11341
$947$	8.79218	0.285707	0.142854	−	0.989744i	$-0.454372\pi$
$947$	8.79218	0.285707	0.142854	+	0.989744i	$0.454372\pi$
$948$	−0.548168	−0.0178037
$949$	57.0572	1.85215
$950$	−31.2893	−1.01516
$951$	4.18530	0.135718
$952$	0	0
$953$	−30.1768	−0.977524	−0.488762	−	0.872417i	$-0.662551\pi$
$953$	−30.1768	−0.977524	−0.488762	+	0.872417i	$0.662551\pi$
$954$	−8.89975	−0.288140
$955$	31.1733	1.00874
$956$	−0.442967	−0.0143266
$957$	−31.9994	−1.03439
$958$	−24.1876	−0.781464
$959$	0	0
$960$	−8.93211	−0.288283
$961$	−19.3566	−0.624408
$962$	38.6792	1.24707
$963$	9.27267	0.298808
$964$	−1.64081	−0.0528468
$965$	−16.6925	−0.537351
$966$	0	0
$967$	−13.6618	−0.439333	−0.219667	−	0.975575i	$-0.570497\pi$
$967$	−13.6618	−0.439333	−0.219667	+	0.975575i	$0.570497\pi$
$968$	52.6666	1.69277
$969$	13.8145	0.443785
$970$	19.4022	0.622966
$971$	24.3062	0.780022	0.390011	−	0.920810i	$-0.372471\pi$
$971$	24.3062	0.780022	0.390011	+	0.920810i	$0.372471\pi$
$972$	−0.0574538	−0.00184283
$973$	0	0
$974$	−49.9242	−1.59968
$975$	14.3142	0.458422
$976$	18.2657	0.584671
$977$	−24.0007	−0.767851	−0.383926	−	0.923364i	$-0.625428\pi$
$977$	−24.0007	−0.767851	−0.383926	+	0.923364i	$0.625428\pi$
$978$	25.8588	0.826874
$979$	−13.5506	−0.433078
$980$	0	0
$981$	−0.596913	−0.0190580
$982$	−26.7203	−0.852679
$983$	3.39262	0.108208	0.0541039	−	0.998535i	$-0.482770\pi$
$983$	3.39262	0.108208	0.0541039	+	0.998535i	$0.482770\pi$
$984$	−25.7079	−0.819537
$985$	6.46170	0.205887
$986$	19.5307	0.621985
$987$	0	0
$988$	−1.32895	−0.0422794
$989$	−25.5712	−0.813117
$990$	9.03156	0.287042
$991$	37.3537	1.18658	0.593289	−	0.804989i	$-0.297829\pi$
$991$	37.3537	1.18658	0.593289	+	0.804989i	$0.297829\pi$
$992$	−1.10866	−0.0352001
$993$	0.861764	0.0273473
$994$	0	0
$995$	16.1361	0.511549
$996$	0.237747	0.00753331
$997$	22.7499	0.720498	0.360249	−	0.932856i	$-0.382692\pi$
$997$	22.7499	0.720498	0.360249	+	0.932856i	$0.382692\pi$
$998$	31.7482	1.00497
$999$	6.92148	0.218986

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7203.2.a.g.1.6		18
7.6	odd	2		7203.2.a.h.1.6		18
49.20	odd	14		147.2.i.b.106.2	yes	36
49.27	odd	14		147.2.i.b.43.2	✓	36
147.20	even	14		441.2.u.d.253.5		36
147.125	even	14		441.2.u.d.190.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.43.2	✓	36	49.27	odd	14
147.2.i.b.106.2	yes	36	49.20	odd	14
441.2.u.d.190.5		36	147.125	even	14
441.2.u.d.253.5		36	147.20	even	14
7203.2.a.g.1.6		18	1.1	even	1	trivial
7203.2.a.h.1.6		18	7.6	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:	\( N \)	\(=\)	\( 7203 = 3 \cdot 7^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7203.a (trivial)

\(f(q)\)	\(=\)	\(q-1.43438 q^{2} -1.00000 q^{3} +0.0574538 q^{4} +1.15146 q^{5} +1.43438 q^{6} +2.78635 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.43438 q^{2} -1.00000 q^{3} +0.0574538 q^{4} +1.15146 q^{5} +1.43438 q^{6} +2.78635 q^{8} +1.00000 q^{9} -1.65164 q^{10} -5.46824 q^{11} -0.0574538 q^{12} +3.89595 q^{13} -1.15146 q^{15} -4.11161 q^{16} +2.32680 q^{17} -1.43438 q^{18} -5.93712 q^{19} +0.0661560 q^{20} +7.84354 q^{22} -5.85685 q^{23} -2.78635 q^{24} -3.67413 q^{25} -5.58828 q^{26} -1.00000 q^{27} -5.85187 q^{29} +1.65164 q^{30} -3.41224 q^{31} +0.324908 q^{32} +5.46824 q^{33} -3.33752 q^{34} +0.0574538 q^{36} -6.92148 q^{37} +8.51610 q^{38} -3.89595 q^{39} +3.20839 q^{40} +9.22634 q^{41} +4.36604 q^{43} -0.314171 q^{44} +1.15146 q^{45} +8.40096 q^{46} -7.26869 q^{47} +4.11161 q^{48} +5.27011 q^{50} -2.32680 q^{51} +0.223837 q^{52} +6.20459 q^{53} +1.43438 q^{54} -6.29648 q^{55} +5.93712 q^{57} +8.39382 q^{58} +4.37412 q^{59} -0.0661560 q^{60} -4.44248 q^{61} +4.89445 q^{62} +7.75717 q^{64} +4.48605 q^{65} -7.84354 q^{66} -12.5372 q^{67} +0.133683 q^{68} +5.85685 q^{69} -0.568351 q^{71} +2.78635 q^{72} +14.6453 q^{73} +9.92806 q^{74} +3.67413 q^{75} -0.341110 q^{76} +5.58828 q^{78} +9.54103 q^{79} -4.73437 q^{80} +1.00000 q^{81} -13.2341 q^{82} -4.13806 q^{83} +2.67923 q^{85} -6.26257 q^{86} +5.85187 q^{87} -15.2364 q^{88} +2.47805 q^{89} -1.65164 q^{90} -0.336498 q^{92} +3.41224 q^{93} +10.4261 q^{94} -6.83638 q^{95} -0.324908 q^{96} -11.7472 q^{97} -5.46824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} - 18 q^{3} + 27 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 - 18 * q^3 + 27 * q^4 + 2 * q^5 - 3 * q^6 + 3 * q^8 + 18 * q^9	\( 18 q + 3 q^{2} - 18 q^{3} + 27 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{8} + 18 q^{9} + 2 q^{10} - 27 q^{12} - q^{13} - 2 q^{15} + 37 q^{16} + 5 q^{17} + 3 q^{18} - 3 q^{19} + 19 q^{20} + 4 q^{23} - 3 q^{24} + 34 q^{25} - 3 q^{26} - 18 q^{27} + 10 q^{29} - 2 q^{30} - 8 q^{31} - q^{32} - 3 q^{34} + 27 q^{36} + 9 q^{37} - 5 q^{38} + q^{39} + 14 q^{40} - q^{41} + 4 q^{43} - 13 q^{44} + 2 q^{45} - 2 q^{46} + 21 q^{47} - 37 q^{48} + 118 q^{50} - 5 q^{51} - 108 q^{52} + 89 q^{53} - 3 q^{54} - 2 q^{55} + 3 q^{57} + 103 q^{58} - 17 q^{59} - 19 q^{60} - 77 q^{61} + 37 q^{62} + 35 q^{64} + 103 q^{65} - 11 q^{67} + 55 q^{68} - 4 q^{69} - 3 q^{71} + 3 q^{72} + 9 q^{73} + 110 q^{74} - 34 q^{75} - 121 q^{76} + 3 q^{78} - 7 q^{79} + 56 q^{80} + 18 q^{81} - q^{82} + q^{83} + 104 q^{85} - 20 q^{86} - 10 q^{87} - 17 q^{88} + 15 q^{89} + 2 q^{90} - 7 q^{92} + 8 q^{93} + 6 q^{94} - 19 q^{95} + q^{96} - 86 q^{97}+O(q^{100}) \) 18 * q + 3 * q^2 - 18 * q^3 + 27 * q^4 + 2 * q^5 - 3 * q^6 + 3 * q^8 + 18 * q^9 + 2 * q^10 - 27 * q^12 - q^13 - 2 * q^15 + 37 * q^16 + 5 * q^17 + 3 * q^18 - 3 * q^19 + 19 * q^20 + 4 * q^23 - 3 * q^24 + 34 * q^25 - 3 * q^26 - 18 * q^27 + 10 * q^29 - 2 * q^30 - 8 * q^31 - q^32 - 3 * q^34 + 27 * q^36 + 9 * q^37 - 5 * q^38 + q^39 + 14 * q^40 - q^41 + 4 * q^43 - 13 * q^44 + 2 * q^45 - 2 * q^46 + 21 * q^47 - 37 * q^48 + 118 * q^50 - 5 * q^51 - 108 * q^52 + 89 * q^53 - 3 * q^54 - 2 * q^55 + 3 * q^57 + 103 * q^58 - 17 * q^59 - 19 * q^60 - 77 * q^61 + 37 * q^62 + 35 * q^64 + 103 * q^65 - 11 * q^67 + 55 * q^68 - 4 * q^69 - 3 * q^71 + 3 * q^72 + 9 * q^73 + 110 * q^74 - 34 * q^75 - 121 * q^76 + 3 * q^78 - 7 * q^79 + 56 * q^80 + 18 * q^81 - q^82 + q^83 + 104 * q^85 - 20 * q^86 - 10 * q^87 - 17 * q^88 + 15 * q^89 + 2 * q^90 - 7 * q^92 + 8 * q^93 + 6 * q^94 - 19 * q^95 + q^96 - 86 * q^97

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