LMFDB - Embedded newform 7203.2.a.h.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	$-0.582891\pi$
$5$	−1.15146	−0.514951	−0.257475	+	0.966285i	$0.582891\pi$
$6$	−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	$-0.681678\pi$
$13$	−3.89595	−1.08054	−0.540271	+	0.841491i	$0.681678\pi$
$14$	0	0
$15$	−1.15146	−0.297307
$16$	−4.11161	−1.02790
$17$	−2.32680	−0.564332	−0.282166	−	0.959366i	$-0.591053\pi$
$17$	−2.32680	−0.564332	−0.282166	+	0.959366i	$0.591053\pi$
$18$	−1.43438	−0.338087
$19$	5.93712	1.36207	0.681034	−	0.732252i	$-0.261531\pi$
$19$	5.93712	1.36207	0.681034	+	0.732252i	$0.261531\pi$
$20$	−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	$-0.400866\pi$
$31$	3.41224	0.612856	0.306428	+	0.951894i	$0.400866\pi$
$32$	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	$-0.756068\pi$
$41$	−9.22634	−1.44091	−0.720456	+	0.693500i	$0.756068\pi$
$42$	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	$-0.322145\pi$
$47$	7.26869	1.06025	0.530124	+	0.847920i	$0.322145\pi$
$48$	−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	$-0.591904\pi$
$59$	−4.37412	−0.569462	−0.284731	+	0.958607i	$0.591904\pi$
$60$	−0.0661560	−0.00854070
$61$	4.44248	0.568801	0.284400	−	0.958706i	$-0.408205\pi$
$61$	4.44248	0.568801	0.284400	+	0.958706i	$0.408205\pi$
$62$	−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	$-0.827704\pi$
$73$	−14.6453	−1.71410	−0.857049	+	0.515236i	$0.827704\pi$
$74$	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	$-0.427074\pi$
$83$	4.13806	0.454211	0.227106	+	0.973870i	$0.427074\pi$
$84$	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	$-0.541927\pi$
$89$	−2.47805	−0.262673	−0.131336	+	0.991338i	$0.541927\pi$
$90$	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	$-0.296608\pi$
$97$	11.7472	1.19275	0.596374	+	0.802707i	$0.296608\pi$
$98$	0	0
$99$	−5.46824	−0.549578
$100$	−0.211093	−0.0211093
$101$	−8.54432	−0.850192	−0.425096	−	0.905148i	$-0.639760\pi$
$101$	−8.54432	−0.850192	−0.425096	+	0.905148i	$0.639760\pi$
$102$	3.33752	0.330464
$103$	1.30532	0.128617	0.0643086	−	0.997930i	$-0.479516\pi$
$103$	1.30532	0.128617	0.0643086	+	0.997930i	$0.479516\pi$
$104$	−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	$-0.452710\pi$
$131$	3.38836	0.296042	0.148021	+	0.988984i	$0.452710\pi$
$132$	−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	$-0.422729\pi$
$139$	5.66803	0.480756	0.240378	+	0.970679i	$0.422729\pi$
$140$	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	$-0.434265\pi$
$157$	5.13848	0.410096	0.205048	+	0.978752i	$0.434265\pi$
$158$	−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	$-0.452049\pi$
$167$	3.87874	0.300146	0.150073	+	0.988675i	$0.452049\pi$
$168$	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	$-0.663943\pi$
$173$	−12.9576	−0.985146	−0.492573	+	0.870271i	$0.663943\pi$
$174$	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	$-0.880976\pi$
$181$	−25.0480	−1.86180	−0.930901	+	0.365273i	$0.880976\pi$
$182$	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	$-0.665454\pi$
$199$	−14.0135	−0.993393	−0.496697	+	0.867924i	$0.665454\pi$
$200$	−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	$-0.232890\pi$
$223$	22.2229	1.48815	0.744077	+	0.668094i	$0.232890\pi$
$224$	0	0
$225$	−3.67413	−0.244942
$226$	−1.99202	−0.132507
$227$	10.5400	0.699567	0.349784	−	0.936831i	$-0.386255\pi$
$227$	10.5400	0.699567	0.349784	+	0.936831i	$0.386255\pi$
$228$	0.341110	0.0225905
$229$	−10.5427	−0.696681	−0.348340	−	0.937368i	$-0.613255\pi$
$229$	−10.5427	−0.696681	−0.348340	+	0.937368i	$0.613255\pi$
$230$	−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	$-0.128339\pi$
$241$	28.5587	1.83963	0.919815	+	0.392353i	$0.128339\pi$
$242$	−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	$-0.532498\pi$
$251$	−3.22940	−0.203838	−0.101919	+	0.994793i	$0.532498\pi$
$252$	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	$-0.670655\pi$
$257$	−16.3779	−1.02162	−0.510812	+	0.859693i	$0.670655\pi$
$258$	−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	$-0.741716\pi$
$269$	−22.5834	−1.37693	−0.688466	+	0.725268i	$0.741716\pi$
$270$	1.65164	0.100516
$271$	8.85120	0.537672	0.268836	−	0.963186i	$-0.413361\pi$
$271$	8.85120	0.537672	0.268836	+	0.963186i	$0.413361\pi$
$272$	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	$-0.607355\pi$
$283$	−11.1335	−0.661815	−0.330908	+	0.943663i	$0.607355\pi$
$284$	−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	$-0.553016\pi$
$293$	−5.67555	−0.331569	−0.165785	+	0.986162i	$0.553016\pi$
$294$	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	$-0.398025\pi$
$307$	11.0354	0.629824	0.314912	+	0.949121i	$0.398025\pi$
$308$	0	0
$309$	1.30532	0.0742572
$310$	5.63579	0.320091
$311$	−9.57688	−0.543055	−0.271527	−	0.962431i	$-0.587529\pi$
$311$	−9.57688	−0.543055	−0.271527	+	0.962431i	$0.587529\pi$
$312$	−10.8555	−0.614571
$313$	24.7541	1.39918	0.699592	−	0.714543i	$-0.253365\pi$
$313$	24.7541	1.39918	0.699592	+	0.714543i	$0.253365\pi$
$314$	−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	$-0.318589\pi$
$349$	20.1598	1.07913	0.539565	+	0.841944i	$0.318589\pi$
$350$	0	0
$351$	−3.89595	−0.207950
$352$	−1.77667	−0.0946970
$353$	−24.1873	−1.28736	−0.643681	−	0.765294i	$-0.722594\pi$
$353$	−24.1873	−1.28736	−0.643681	+	0.765294i	$0.722594\pi$
$354$	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	$-0.173475\pi$
$367$	32.7640	1.71027	0.855133	+	0.518409i	$0.173475\pi$
$368$	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	$-0.664888\pi$
$383$	−19.3806	−0.990305	−0.495152	+	0.868806i	$0.664888\pi$
$384$	−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	$-0.401988\pi$
$397$	12.0773	0.606142	0.303071	+	0.952968i	$0.401988\pi$
$398$	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	$-0.234940\pi$
$409$	29.9214	1.47952	0.739758	+	0.672873i	$0.234940\pi$
$410$	−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	$-0.328358\pi$
$419$	21.0211	1.02695	0.513474	+	0.858105i	$0.328358\pi$
$420$	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	$-0.723069\pi$
$433$	−26.8358	−1.28965	−0.644824	+	0.764331i	$0.723069\pi$
$434$	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	$-0.450540\pi$
$439$	6.48509	0.309516	0.154758	+	0.987952i	$0.450540\pi$
$440$	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	$-0.359103\pi$
$461$	18.3932	0.856657	0.428329	+	0.903623i	$0.359103\pi$
$462$	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	$-0.770425\pi$
$467$	−32.4582	−1.50199	−0.750993	+	0.660310i	$0.770425\pi$
$468$	−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	$-0.625881\pi$
$479$	−16.8627	−0.770476	−0.385238	+	0.922817i	$0.625881\pi$
$480$	−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	$-0.379225\pi$
$503$	16.6139	0.740776	0.370388	+	0.928877i	$0.379225\pi$
$504$	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	$-0.788548\pi$
$509$	−35.5269	−1.57470	−0.787352	+	0.616504i	$0.788548\pi$
$510$	−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	$-0.771914\pi$
$521$	−34.4241	−1.50815	−0.754074	+	0.656790i	$0.771914\pi$
$522$	8.39382	0.367387
$523$	−32.6781	−1.42891	−0.714457	−	0.699679i	$-0.753326\pi$
$523$	−32.6781	−1.42891	−0.714457	+	0.699679i	$0.753326\pi$
$524$	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	$-0.480696\pi$
$563$	2.87622	0.121218	0.0606092	+	0.998162i	$0.480696\pi$
$564$	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	$-0.305040\pi$
$577$	27.6193	1.14981	0.574903	+	0.818222i	$0.305040\pi$
$578$	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	$-0.659488\pi$
$587$	−23.2756	−0.960686	−0.480343	+	0.877081i	$0.659488\pi$
$588$	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	$-0.544145\pi$
$593$	−6.73276	−0.276481	−0.138241	+	0.990399i	$0.544145\pi$
$594$	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	$-0.446653\pi$
$601$	8.17879	0.333620	0.166810	+	0.985989i	$0.446653\pi$
$602$	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	$-0.900332\pi$
$607$	−46.8789	−1.90276	−0.951378	+	0.308025i	$0.900332\pi$
$608$	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	$-0.570544\pi$
$619$	−10.9377	−0.439624	−0.219812	+	0.975542i	$0.570544\pi$
$620$	−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	$-0.323359\pi$
$643$	26.7210	1.05377	0.526886	+	0.849936i	$0.323359\pi$
$644$	0	0
$645$	−5.02734	−0.197951
$646$	19.8153	0.779621
$647$	39.4109	1.54940	0.774702	−	0.632326i	$-0.217900\pi$
$647$	39.4109	1.54940	0.774702	+	0.632326i	$0.217900\pi$
$648$	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	$-0.475489\pi$
$661$	3.95557	0.153854	0.0769269	+	0.997037i	$0.475489\pi$
$662$	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	$-0.421241\pi$
$677$	12.7449	0.489825	0.244913	+	0.969545i	$0.421241\pi$
$678$	−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	$-0.305714\pi$
$691$	30.1337	1.14634	0.573169	+	0.819437i	$0.305714\pi$
$692$	−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	$-0.375516\pi$
$719$	20.4423	0.762371	0.381185	+	0.924499i	$0.375516\pi$
$720$	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	$-0.696960\pi$
$727$	−31.2788	−1.16006	−0.580032	+	0.814593i	$0.696960\pi$
$728$	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	$-0.151477\pi$
$733$	48.1316	1.77778	0.888891	+	0.458119i	$0.151477\pi$
$734$	−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	$-0.712028\pi$
$761$	−34.0927	−1.23586	−0.617930	+	0.786233i	$0.712028\pi$
$762$	−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	$-0.639468\pi$
$769$	−23.5305	−0.848532	−0.424266	+	0.905538i	$0.639468\pi$
$770$	0	0
$771$	−16.3779	−0.589834
$772$	−0.832894	−0.0299765
$773$	10.2175	0.367499	0.183749	−	0.982973i	$-0.441177\pi$
$773$	10.2175	0.367499	0.183749	+	0.982973i	$0.441177\pi$
$774$	−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	$-0.537437\pi$
$787$	−6.58366	−0.234682	−0.117341	+	0.993092i	$0.537437\pi$
$788$	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	$-0.528685\pi$
$797$	−5.08134	−0.179990	−0.0899951	+	0.995942i	$0.528685\pi$
$798$	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	$-0.631059\pi$
$811$	−22.7939	−0.800401	−0.400200	+	0.916428i	$0.631059\pi$
$812$	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	$-0.521117\pi$
$829$	−3.81743	−0.132585	−0.0662924	+	0.997800i	$0.521117\pi$
$830$	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	$-0.578145\pi$
$839$	−14.0797	−0.486085	−0.243042	+	0.970016i	$0.578145\pi$
$840$	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	$-0.439521\pi$
$853$	11.0317	0.377719	0.188860	+	0.982004i	$0.439521\pi$
$854$	0	0
$855$	−6.83638	−0.233799
$856$	25.8370	0.883089
$857$	34.3331	1.17280	0.586399	−	0.810022i	$-0.300545\pi$
$857$	34.3331	1.17280	0.586399	+	0.810022i	$0.300545\pi$
$858$	−30.5580	−1.04323
$859$	26.4368	0.902011	0.451005	−	0.892521i	$-0.351065\pi$
$859$	26.4368	0.902011	0.451005	+	0.892521i	$0.351065\pi$
$860$	−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	$-0.251088\pi$
$881$	41.8324	1.40937	0.704685	+	0.709520i	$0.251088\pi$
$882$	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	$-0.380844\pi$
$887$	21.7805	0.731316	0.365658	+	0.930749i	$0.380844\pi$
$888$	−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	$-0.639534\pi$
$929$	−25.8744	−0.848911	−0.424455	+	0.905449i	$0.639534\pi$
$930$	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	$-0.515274\pi$
$937$	−2.93657	−0.0959335	−0.0479667	+	0.998849i	$0.515274\pi$
$938$	0	0
$939$	24.7541	0.807819
$940$	−0.480867	−0.0156842
$941$	−33.6578	−1.09721	−0.548606	−	0.836081i	$-0.684841\pi$
$941$	−33.6578	−1.09721	−0.548606	+	0.836081i	$0.684841\pi$
$942$	−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	$-0.627529\pi$
$971$	−24.3062	−0.780022	−0.390011	+	0.920810i	$0.627529\pi$
$972$	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	$-0.517230\pi$
$983$	−3.39262	−0.108208	−0.0541039	+	0.998535i	$0.517230\pi$
$984$	−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	$-0.617308\pi$
$997$	−22.7499	−0.720498	−0.360249	+	0.932856i	$0.617308\pi$
$998$	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.h.1.6		18
7.6	odd	2		7203.2.a.g.1.6		18
49.22	even	7		147.2.i.b.43.2	✓	36
49.29	even	7		147.2.i.b.106.2	yes	36
147.29	odd	14		441.2.u.d.253.5		36
147.71	odd	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	49.22	even	7
147.2.i.b.106.2	yes	36	49.29	even	7
441.2.u.d.190.5		36	147.71	odd	14
441.2.u.d.253.5		36	147.29	odd	14
7203.2.a.g.1.6		18	7.6	odd	2
7203.2.a.h.1.6		18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7203 = 3 \cdot 7^{4} \)
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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