LMFDB - Embedded newform 2736.2.bm.o.1855.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(559,2736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2736, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))

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

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

chi := DirichletCharacter("2736.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.bm (of order $6$, degree $2$, minimal)

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:	no
Analytic conductor:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 912)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1855.1
Root			$-1.62241 - 0.606458i$ of defining polynomial
Character	$\chi$	$=$	2736.1855
Dual form			2736.2.bm.o.559.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33641 - 2.31473i) q^{5} +3.93569i q^{7} +O(q^{10})$	$q+(-1.33641 - 2.31473i) q^{5} +3.93569i q^{7} -2.20364i q^{11} +(-3.60083 - 2.07894i) q^{13} +(0.571993 + 0.990721i) q^{17} +(4.24482 + 0.990721i) q^{19} +(3.19243 + 1.84315i) q^{23} +(-1.07199 + 1.85675i) q^{25} +(2.10083 + 1.21292i) q^{29} -3.67282 q^{31} +(9.11007 - 5.25970i) q^{35} -10.0478i q^{37} +(-8.01847 + 4.62947i) q^{41} +(0.490764 - 0.283343i) q^{43} +(-10.6336 - 6.13932i) q^{47} -8.48963 q^{49} +(-4.09159 - 2.36228i) q^{53} +(-5.10083 + 2.94497i) q^{55} +(-1.33641 - 2.31473i) q^{59} +(-6.41764 + 11.1157i) q^{61} +11.1133i q^{65} +(-1.73558 + 3.00612i) q^{67} +(-6.24482 - 10.8163i) q^{71} +(1.35601 + 2.34868i) q^{73} +8.67282 q^{77} +(3.50924 + 6.07817i) q^{79} -1.98144i q^{83} +(1.52884 - 2.64802i) q^{85} +(-12.9269 - 7.46334i) q^{89} +(8.18206 - 14.1717i) q^{91} +(-3.37957 - 11.1496i) q^{95} +(2.91764 - 1.68450i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{5}+O(q^{10}) $ 6 * q + 2 * q^5	$ 6 q + 2 q^{5} - 3 q^{13} + 2 q^{17} + 4 q^{19} + 12 q^{23} - 5 q^{25} - 6 q^{29} - 2 q^{31} + 6 q^{35} + 12 q^{41} + 33 q^{43} - 18 q^{47} - 8 q^{49} - 36 q^{53} - 12 q^{55} + 2 q^{59} + 3 q^{61} - 19 q^{67} - 16 q^{71} + 11 q^{73} + 32 q^{77} - 9 q^{79} - 8 q^{85} - 6 q^{89} - q^{91} - 26 q^{95} - 24 q^{97}+O(q^{100}) $ 6 * q + 2 * q^5 - 3 * q^13 + 2 * q^17 + 4 * q^19 + 12 * q^23 - 5 * q^25 - 6 * q^29 - 2 * q^31 + 6 * q^35 + 12 * q^41 + 33 * q^43 - 18 * q^47 - 8 * q^49 - 36 * q^53 - 12 * q^55 + 2 * q^59 + 3 * q^61 - 19 * q^67 - 16 * q^71 + 11 * q^73 + 32 * q^77 - 9 * q^79 - 8 * q^85 - 6 * q^89 - q^91 - 26 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.33641	−	2.31473i	−0.597662	−	1.03518i	−0.993165	−	0.116716i	$-0.962763\pi$
$5$	−1.33641	−	2.31473i	−0.597662	−	1.03518i	0.395504	−	0.918464i	$-0.370570\pi$
$6$		0			0
$7$			3.93569i			1.48755i	0.668430	+	0.743775i	$0.266967\pi$
$7$			3.93569i			1.48755i	−0.668430	+	0.743775i	$0.733033\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	2.20364i		−	0.664421i	−0.943205	−	0.332211i	$-0.892205\pi$
$11$		−	2.20364i		−	0.664421i	0.943205	−	0.332211i	$-0.107795\pi$
$12$		0			0
$13$	−3.60083	−	2.07894i	−0.998691	−	0.576594i	−0.0908300	−	0.995866i	$-0.528952\pi$
$13$	−3.60083	−	2.07894i	−0.998691	−	0.576594i	−0.907861	+	0.419272i	$0.862285\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.571993	+	0.990721i	0.138729	+	0.240285i	0.927016	−	0.375023i	$-0.122365\pi$
$17$	0.571993	+	0.990721i	0.138729	+	0.240285i	−0.788287	+	0.615308i	$0.789032\pi$
$18$		0			0
$19$	4.24482	+	0.990721i	0.973828	+	0.227287i
$19$	4.24482	+	0.990721i	0.973828	+	0.227287i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.19243	+	1.84315i	0.665667	+	0.384323i	0.794433	−	0.607352i	$-0.207768\pi$
$23$	3.19243	+	1.84315i	0.665667	+	0.384323i	−0.128766	+	0.991675i	$0.541102\pi$
$24$		0			0
$25$	−1.07199	+	1.85675i	−0.214399	+	0.371349i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.10083	+	1.21292i	0.390114	+	0.225233i	0.682210	−	0.731157i	$-0.261019\pi$
$29$	2.10083	+	1.21292i	0.390114	+	0.225233i	−0.292095	+	0.956389i	$0.594352\pi$
$30$		0			0
$31$	−3.67282			−0.659659			−0.329829	−	0.944041i	$-0.606991\pi$
$31$	−3.67282			−0.659659			−0.329829	+	0.944041i	$0.606991\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	9.11007	−	5.25970i	1.53988	−	0.889051i
$36$		0			0
$37$		−	10.0478i		−	1.65185i	−0.563780	−	0.825925i	$-0.690653\pi$
$37$		−	10.0478i		−	1.65185i	0.563780	−	0.825925i	$-0.309347\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.01847	+	4.62947i	−1.25227	+	0.723001i	−0.971561	−	0.236790i	$-0.923905\pi$
$41$	−8.01847	+	4.62947i	−1.25227	+	0.723001i	−0.280714	+	0.959791i	$0.590571\pi$
$42$		0			0
$43$	0.490764	−	0.283343i	0.0748409	−	0.0432094i	−0.462113	−	0.886821i	$-0.652908\pi$
$43$	0.490764	−	0.283343i	0.0748409	−	0.0432094i	0.536953	+	0.843612i	$0.319575\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−10.6336	−	6.13932i	−1.55107	−	0.895512i	−0.998055	−	0.0623432i	$-0.980143\pi$
$47$	−10.6336	−	6.13932i	−1.55107	−	0.895512i	−0.553018	−	0.833169i	$-0.686524\pi$
$48$		0			0
$49$	−8.48963			−1.21280
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.09159	−	2.36228i	−0.562024	−	0.324485i	0.191934	−	0.981408i	$-0.438524\pi$
$53$	−4.09159	−	2.36228i	−0.562024	−	0.324485i	−0.753957	+	0.656923i	$0.771858\pi$
$54$		0			0
$55$	−5.10083	+	2.94497i	−0.687796	+	0.397099i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.33641	−	2.31473i	−0.173986	−	0.301353i	0.765824	−	0.643050i	$-0.222331\pi$
$59$	−1.33641	−	2.31473i	−0.173986	−	0.301353i	−0.939810	+	0.341698i	$0.888998\pi$
$60$		0			0
$61$	−6.41764	+	11.1157i	−0.821695	+	1.42322i	0.0827247	+	0.996572i	$0.473638\pi$
$61$	−6.41764	+	11.1157i	−0.821695	+	1.42322i	−0.904419	+	0.426645i	$0.859696\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			11.1133i			1.37843i
$66$		0			0
$67$	−1.73558	+	3.00612i	−0.212035	+	0.367255i	−0.952351	−	0.305003i	$-0.901342\pi$
$67$	−1.73558	+	3.00612i	−0.212035	+	0.367255i	0.740316	+	0.672259i	$0.234676\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.24482	−	10.8163i	−0.741123	−	1.28366i	−0.951984	−	0.306147i	$-0.900960\pi$
$71$	−6.24482	−	10.8163i	−0.741123	−	1.28366i	0.210861	−	0.977516i	$-0.432373\pi$
$72$		0			0
$73$	1.35601	+	2.34868i	0.158709	+	0.274893i	0.934404	−	0.356216i	$-0.115933\pi$
$73$	1.35601	+	2.34868i	0.158709	+	0.274893i	−0.775694	+	0.631109i	$0.782600\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.67282			0.988360
$78$		0			0
$79$	3.50924	+	6.07817i	0.394820	+	0.683848i	0.993078	−	0.117455i	$-0.0374737\pi$
$79$	3.50924	+	6.07817i	0.394820	+	0.683848i	−0.598258	+	0.801303i	$0.704140\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	1.98144i		−	0.217492i	−0.994070	−	0.108746i	$-0.965317\pi$
$83$		−	1.98144i		−	0.217492i	0.994070	−	0.108746i	$-0.0346835\pi$
$84$		0			0
$85$	1.52884	−	2.64802i	0.165826	−	0.287218i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−12.9269	−	7.46334i	−1.37025	−	0.791112i	−0.379287	−	0.925279i	$-0.623831\pi$
$89$	−12.9269	−	7.46334i	−1.37025	−	0.791112i	−0.990959	+	0.134167i	$0.957164\pi$
$90$		0			0
$91$	8.18206	−	14.1717i	0.857713	−	1.48560i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.37957	−	11.1496i	−0.346736	−	1.14393i
$96$		0			0
$97$	2.91764	−	1.68450i	0.296242	−	0.171035i	−0.344512	−	0.938782i	$-0.611956\pi$
$97$	2.91764	−	1.68450i	0.296242	−	0.171035i	0.640753	+	0.767747i	$0.278622\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.10083	−	8.83490i	0.507552	−	0.879105i	−0.492410	−	0.870363i	$-0.663884\pi$
$101$	5.10083	−	8.83490i	0.507552	−	0.879105i	0.999962	−	0.00874190i	$-0.00278267\pi$
$102$		0			0
$103$	−16.4504			−1.62091			−0.810455	−	0.585802i	$-0.800780\pi$
$103$	−16.4504			−1.62091			−0.810455	+	0.585802i	$0.800780\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.85601			−0.469449			−0.234724	−	0.972062i	$-0.575419\pi$
$107$	−4.85601			−0.469449			−0.234724	+	0.972062i	$0.575419\pi$
$108$		0			0
$109$	−12.7345	+	7.35224i	−1.21974	+	0.704217i	−0.964862	−	0.262757i	$-0.915368\pi$
$109$	−12.7345	+	7.35224i	−1.21974	+	0.704217i	−0.254877	+	0.966973i	$0.582035\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			14.4823i			1.36238i	0.732107	+	0.681189i	$0.238537\pi$
$113$			14.4823i			1.36238i	−0.732107	+	0.681189i	$0.761463\pi$
$114$		0			0
$115$		−	9.85282i		−	0.918780i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.89917	+	2.25119i	−0.357436	+	0.206366i
$120$		0			0
$121$	6.14399			0.558544
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−7.63362			−0.682772
$126$		0			0
$127$	5.81681	−	10.0750i	0.516158	−	0.894013i	−0.483666	−	0.875253i	$-0.660695\pi$
$127$	5.81681	−	10.0750i	0.516158	−	0.894013i	0.999824	−	0.0187598i	$-0.00597177\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	10.7160	−	6.18687i	0.936260	−	0.540550i	0.0474737	−	0.998872i	$-0.484883\pi$
$131$	10.7160	−	6.18687i	0.936260	−	0.540550i	0.888786	+	0.458323i	$0.151550\pi$
$132$		0			0
$133$	−3.89917	+	16.7063i	−0.338101	+	1.44862i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.71598	+	8.16832i	−0.402913	+	0.697866i	−0.994076	−	0.108686i	$-0.965336\pi$
$137$	−4.71598	+	8.16832i	−0.402913	+	0.697866i	0.591163	+	0.806552i	$0.298669\pi$
$138$		0			0
$139$	−11.8941	−	6.86705i	−1.00884	−	0.582456i	−0.0979905	−	0.995187i	$-0.531241\pi$
$139$	−11.8941	−	6.86705i	−1.00884	−	0.582456i	−0.910853	+	0.412731i	$0.864575\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.58123	+	7.93492i	−0.383102	+	0.663551i
$144$		0			0
$145$		−	6.48382i		−	0.538452i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.15322	−	14.1218i	−0.667938	−	1.15690i	−0.978480	−	0.206343i	$-0.933844\pi$
$149$	−8.15322	−	14.1218i	−0.667938	−	1.15690i	0.310542	−	0.950560i	$-0.399490\pi$
$150$		0			0
$151$	7.05767			0.574345			0.287173	−	0.957879i	$-0.407285\pi$
$151$	7.05767			0.574345			0.287173	+	0.957879i	$0.407285\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.90841	+	8.50161i	0.394253	+	0.682866i
$156$		0			0
$157$	5.66246	+	9.80766i	0.451913	+	0.782737i	0.998505	−	0.0546625i	$-0.0174083\pi$
$157$	5.66246	+	9.80766i	0.451913	+	0.782737i	−0.546592	+	0.837399i	$0.684075\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−7.25405	+	12.5644i	−0.571699	+	0.990212i
$162$		0			0
$163$			0.915973i			0.0717445i	0.999356	+	0.0358723i	$0.0114209\pi$
$163$			0.915973i			0.0717445i	−0.999356	+	0.0358723i	$0.988579\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.192425	−	0.333290i	0.0148903	−	0.0257908i	−0.858484	−	0.512840i	$-0.828593\pi$
$167$	0.192425	−	0.333290i	0.0148903	−	0.0257908i	0.873375	+	0.487049i	$0.161927\pi$
$168$		0			0
$169$	2.14399	+	3.71349i	0.164922	+	0.285653i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.34960	+	5.39799i	−0.710837	+	0.410402i	−0.811371	−	0.584532i	$-0.801278\pi$
$173$	−9.34960	+	5.39799i	−0.710837	+	0.410402i	0.100534	+	0.994934i	$0.467945\pi$
$174$		0			0
$175$	−7.30757	−	4.21903i	−0.552401	−	0.318929i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.03920			0.0776737			0.0388368	−	0.999246i	$-0.487635\pi$
$179$	1.03920			0.0776737			0.0388368	+	0.999246i	$0.487635\pi$
$180$		0			0
$181$	−6.73445	−	3.88814i	−0.500568	−	0.289003i	0.228380	−	0.973572i	$-0.426657\pi$
$181$	−6.73445	−	3.88814i	−0.500568	−	0.289003i	−0.728948	+	0.684569i	$0.759990\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−23.2580	+	13.4280i	−1.70996	+	0.987247i
$186$		0			0
$187$	2.18319	−	1.26047i	0.159651	−	0.0921743i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			26.2621i			1.90026i	0.311851	+	0.950131i	$0.399051\pi$
$191$			26.2621i			1.90026i	−0.311851	+	0.950131i	$0.600949\pi$
$192$		0			0
$193$	8.23445	−	4.75416i	0.592729	−	0.342212i	−0.173447	−	0.984843i	$-0.555491\pi$
$193$	8.23445	−	4.75416i	0.592729	−	0.342212i	0.766176	+	0.642631i	$0.222157\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−27.9322			−1.99008			−0.995042	−	0.0994560i	$-0.968290\pi$
$197$	−27.9322			−1.99008			−0.995042	+	0.0994560i	$0.968290\pi$
$198$		0			0
$199$	6.87562	+	3.96964i	0.487399	+	0.281400i	0.723495	−	0.690330i	$-0.242534\pi$
$199$	6.87562	+	3.96964i	0.487399	+	0.281400i	−0.236096	+	0.971730i	$0.575868\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.77365	+	8.26821i	−0.335045	+	0.580315i
$204$		0			0
$205$	21.4320	+	12.3737i	1.49687	+	0.864220i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.18319	−	9.35403i	0.151014	−	0.647032i
$210$		0			0
$211$	−4.32605	−	7.49293i	−0.297817	−	0.515835i	0.677819	−	0.735229i	$-0.262925\pi$
$211$	−4.32605	−	7.49293i	−0.297817	−	0.515835i	−0.975636	+	0.219394i	$0.929592\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.31173	−	0.757326i	−0.0894590	−	0.0516492i
$216$		0			0
$217$		−	14.4551i		−	0.981275i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	4.75656i		−	0.319961i
$222$		0			0
$223$	−7.18206	−	12.4397i	−0.480946	−	0.833023i	0.518815	−	0.854887i	$-0.326373\pi$
$223$	−7.18206	−	12.4397i	−0.480946	−	0.833023i	−0.999761	+	0.0218634i	$0.993040\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.1832			−0.941371			−0.470686	−	0.882301i	$-0.655993\pi$
$227$	−14.1832			−0.941371			−0.470686	+	0.882301i	$0.655993\pi$
$228$		0			0
$229$	−16.5473			−1.09348			−0.546738	−	0.837303i	$-0.684131\pi$
$229$	−16.5473			−1.09348			−0.546738	+	0.837303i	$0.684131\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−13.1193	−	22.7233i	−0.859474	−	1.48865i	−0.872431	−	0.488737i	$-0.837458\pi$
$233$	−13.1193	−	22.7233i	−0.859474	−	1.48865i	0.0129574	−	0.999916i	$-0.495875\pi$
$234$		0			0
$235$			32.8187i			2.14085i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			1.26047i			0.0815327i	0.999169	+	0.0407664i	$0.0129799\pi$
$239$			1.26047i			0.0815327i	−0.999169	+	0.0407664i	$0.987020\pi$
$240$		0			0
$241$	−18.1336	−	10.4695i	−1.16809	−	0.674397i	−0.214860	−	0.976645i	$-0.568930\pi$
$241$	−18.1336	−	10.4695i	−1.16809	−	0.674397i	−0.953229	+	0.302248i	$0.902263\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	11.3456	+	19.6512i	0.724847	+	1.25547i
$246$		0			0
$247$	−13.2252	−	12.3921i	−0.841500	−	0.788493i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	24.6521	+	14.2329i	1.55603	+	0.898372i	0.997631	+	0.0687973i	$0.0219162\pi$
$251$	24.6521	+	14.2329i	1.55603	+	0.898372i	0.558396	+	0.829575i	$0.311417\pi$
$252$		0			0
$253$	4.06163	−	7.03494i	0.255352	−	0.442283i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.4764	−	6.04858i	−0.653503	−	0.377300i	0.136294	−	0.990668i	$-0.456481\pi$
$257$	−10.4764	−	6.04858i	−0.653503	−	0.377300i	−0.789797	+	0.613368i	$0.789814\pi$
$258$		0			0
$259$	39.5450			2.45721
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.11930	+	0.646229i	−0.0690191	+	0.0398482i	−0.534112	−	0.845413i	$-0.679354\pi$
$263$	−1.11930	+	0.646229i	−0.0690191	+	0.0398482i	0.465093	+	0.885262i	$0.346021\pi$
$264$		0			0
$265$			12.6279i			0.775728i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	24.5420	−	14.1693i	1.49635	−	0.863920i	0.496363	−	0.868115i	$-0.334669\pi$
$269$	24.5420	−	14.1693i	1.49635	−	0.863920i	0.999991	+	0.00419513i	$0.00133536\pi$
$270$		0			0
$271$	13.2017	−	7.62198i	0.801944	−	0.463002i	−0.0422066	−	0.999109i	$-0.513439\pi$
$271$	13.2017	−	7.62198i	0.801944	−	0.463002i	0.844150	+	0.536106i	$0.180105\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.09159	+	2.36228i	0.246732	+	0.142451i
$276$		0			0
$277$	−15.8353			−0.951450			−0.475725	−	0.879594i	$-0.657814\pi$
$277$	−15.8353			−0.951450			−0.475725	+	0.879594i	$0.657814\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	15.8445	+	9.14784i	0.945205	+	0.545714i	0.891588	−	0.452847i	$-0.149592\pi$
$281$	15.8445	+	9.14784i	0.945205	+	0.545714i	0.0536166	+	0.998562i	$0.482925\pi$
$282$		0			0
$283$	25.4218	−	14.6773i	1.51117	−	0.872474i	0.511254	−	0.859430i	$-0.329181\pi$
$283$	25.4218	−	14.6773i	1.51117	−	0.872474i	0.999915	−	0.0130439i	$-0.00415212\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−18.2201	−	31.5582i	−1.07550	−	1.86282i
$288$		0			0
$289$	7.84565	−	13.5891i	0.461509	−	0.799356i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			19.6512i			1.14804i	0.818842	+	0.574019i	$0.194616\pi$
$293$			19.6512i			1.14804i	−0.818842	+	0.574019i	$0.805384\pi$
$294$		0			0
$295$	−3.57199	+	6.18687i	−0.207969	+	0.360214i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.66359	−	13.2737i	−0.443197	−	0.767639i
$300$		0			0
$301$	1.11515	+	1.93150i	0.0642761	+	0.111330i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	34.3064			1.96438
$306$		0			0
$307$	3.59046	+	6.21887i	0.204919	+	0.354929i	0.950107	−	0.311925i	$-0.100974\pi$
$307$	3.59046	+	6.21887i	0.204919	+	0.354929i	−0.745188	+	0.666854i	$0.767640\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			29.1868i			1.65503i	0.561444	+	0.827515i	$0.310246\pi$
$311$			29.1868i			1.65503i	−0.561444	+	0.827515i	$0.689754\pi$
$312$		0			0
$313$	7.24482	−	12.5484i	0.409501	−	0.709277i	−0.585333	−	0.810793i	$-0.699036\pi$
$313$	7.24482	−	12.5484i	0.409501	−	0.709277i	0.994834	+	0.101516i	$0.0323694\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.37562	+	1.37156i	0.133428	+	0.0770346i	0.565228	−	0.824935i	$-0.308788\pi$
$317$	2.37562	+	1.37156i	0.133428	+	0.0770346i	−0.431800	+	0.901969i	$0.642121\pi$
$318$		0			0
$319$	2.67282	−	4.62947i	0.149649	−	0.259200i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.44648	+	4.77212i	0.0804842	+	0.265528i
$324$		0			0
$325$	7.72013	−	4.45722i	0.428236	−	0.247242i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	24.1625	−	41.8506i	1.33212	−	2.30730i
$330$		0			0
$331$	−10.0761			−0.553835			−0.276918	−	0.960894i	$-0.589313\pi$
$331$	−10.0761			−0.553835			−0.276918	+	0.960894i	$0.589313\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	9.27781			0.506901
$336$		0			0
$337$	3.76555	−	2.17404i	0.205123	−	0.118428i	−0.393920	−	0.919145i	$-0.628881\pi$
$337$	3.76555	−	2.17404i	0.205123	−	0.118428i	0.599043	+	0.800717i	$0.295548\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			8.09357i			0.438291i
$342$		0			0
$343$		−	5.86273i		−	0.316558i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.542026	−	0.312939i	0.0290975	−	0.0167994i	−0.485381	−	0.874303i	$-0.661319\pi$
$347$	0.542026	−	0.312939i	0.0290975	−	0.0167994i	0.514478	+	0.857503i	$0.327986\pi$
$348$		0			0
$349$	6.79834			0.363907			0.181953	−	0.983307i	$-0.441758\pi$
$349$	6.79834			0.363907			0.181953	+	0.983307i	$0.441758\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−20.0185			−1.06548			−0.532738	−	0.846280i	$-0.678837\pi$
$353$	−20.0185			−1.06548			−0.532738	+	0.846280i	$0.678837\pi$
$354$		0			0
$355$	−16.6913	+	28.9102i	−0.885882	+	1.53439i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	14.7882	−	8.53796i	0.780490	−	0.450616i	−0.0561140	−	0.998424i	$-0.517871\pi$
$359$	14.7882	−	8.53796i	0.780490	−	0.450616i	0.836604	+	0.547808i	$0.184538\pi$
$360$		0			0
$361$	17.0369	+	8.41086i	0.896681	+	0.442677i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.62438	−	6.27762i	0.189709	−	0.328586i
$366$		0			0
$367$	−25.5277	−	14.7384i	−1.33254	−	0.769340i	−0.346848	−	0.937921i	$-0.612748\pi$
$367$	−25.5277	−	14.7384i	−1.33254	−	0.769340i	−0.985688	+	0.168582i	$0.946081\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	9.29721	−	16.1032i	0.482687	−	0.836038i
$372$		0			0
$373$		−	26.6745i		−	1.38116i	−0.723258	−	0.690578i	$-0.757356\pi$
$373$		−	26.6745i		−	1.38116i	0.723258	−	0.690578i	$-0.242644\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.04316	−	8.73500i	−0.259736	−	0.449876i
$378$		0			0
$379$	−6.80890			−0.349750			−0.174875	−	0.984591i	$-0.555952\pi$
$379$	−6.80890			−0.349750			−0.174875	+	0.984591i	$0.555952\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−5.23558	−	9.06829i	−0.267526	−	0.463368i	0.700697	−	0.713459i	$-0.252873\pi$
$383$	−5.23558	−	9.06829i	−0.267526	−	0.463368i	−0.968222	+	0.250091i	$0.919539\pi$
$384$		0			0
$385$	−11.5905	−	20.0753i	−0.590705	−	1.02313i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.25405	−	2.17208i	0.0635830	−	0.110129i	−0.832482	−	0.554053i	$-0.813081\pi$
$389$	1.25405	−	2.17208i	0.0635830	−	0.110129i	0.896065	+	0.443924i	$0.146414\pi$
$390$		0			0
$391$			4.21707i			0.213267i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	9.37957	−	16.2459i	0.471937	−	0.817419i
$396$		0			0
$397$	−4.54316	−	7.86898i	−0.228014	−	0.394933i	0.729205	−	0.684295i	$-0.239890\pi$
$397$	−4.54316	−	7.86898i	−0.228014	−	0.394933i	−0.957220	+	0.289363i	$0.906557\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.97399	−	5.75848i	0.498077	−	0.287565i	−0.229842	−	0.973228i	$-0.573821\pi$
$401$	9.97399	−	5.75848i	0.498077	−	0.287565i	0.727919	+	0.685663i	$0.240488\pi$
$402$		0			0
$403$	13.2252	+	7.63558i	0.658795	+	0.380355i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−22.1417			−1.09752
$408$		0			0
$409$	16.1664	+	9.33368i	0.799378	+	0.461521i	0.843253	−	0.537516i	$-0.180637\pi$
$409$	16.1664	+	9.33368i	0.799378	+	0.461521i	−0.0438759	+	0.999037i	$0.513971\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	9.11007	−	5.25970i	0.448277	−	0.258813i
$414$		0			0
$415$	−4.58651	+	2.64802i	−0.225143	+	0.129986i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	27.2053i		−	1.32907i	−0.747259	−	0.664533i	$-0.768630\pi$
$419$		−	27.2053i		−	1.32907i	0.747259	−	0.664533i	$-0.231370\pi$
$420$		0			0
$421$	−1.11930	+	0.646229i	−0.0545514	+	0.0314953i	−0.527028	−	0.849848i	$-0.676694\pi$
$421$	−1.11930	+	0.646229i	−0.0545514	+	0.0314953i	0.472476	+	0.881343i	$0.343360\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.45269			−0.118973
$426$		0			0
$427$	−43.7478	−	25.2578i	−2.11711	−	1.22231i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.6336	−	18.4180i	0.512203	−	0.887162i	−0.487696	−	0.873013i	$-0.662163\pi$
$431$	10.6336	−	18.4180i	0.512203	−	0.887162i	0.999900	−	0.0141492i	$-0.00450397\pi$
$432$		0			0
$433$	33.3890	+	19.2771i	1.60457	+	0.926401i	0.990556	+	0.137108i	$0.0437807\pi$
$433$	33.3890	+	19.2771i	1.60457	+	0.926401i	0.614017	+	0.789293i	$0.289553\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	11.7252	+	10.9866i	0.560893	+	0.525562i
$438$		0			0
$439$	12.3692	+	21.4241i	0.590350	+	1.02252i	0.994185	+	0.107684i	$0.0343435\pi$
$439$	12.3692	+	21.4241i	0.590350	+	1.02252i	−0.403835	+	0.914832i	$0.632323\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	31.5513	+	18.2161i	1.49905	+	0.865474i	0.999999	−	0.00110093i	$-0.000350438\pi$
$443$	31.5513	+	18.2161i	1.49905	+	0.865474i	0.499046	+	0.866575i	$0.333684\pi$
$444$		0			0
$445$			39.8964i			1.89127i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			28.9509i			1.36628i	0.730289	+	0.683138i	$0.239385\pi$
$449$			28.9509i			1.36628i	−0.730289	+	0.683138i	$0.760615\pi$
$450$		0			0
$451$	10.2017	+	17.6698i	0.480377	+	0.832038i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−43.7384			−2.05049
$456$		0			0
$457$	−14.2224			−0.665295			−0.332648	−	0.943051i	$-0.607942\pi$
$457$	−14.2224			−0.665295			−0.332648	+	0.943051i	$0.607942\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	18.1677	+	31.4674i	0.846156	+	1.46559i	0.884613	+	0.466325i	$0.154422\pi$
$461$	18.1677	+	31.4674i	0.846156	+	1.46559i	−0.0384575	+	0.999260i	$0.512244\pi$
$462$		0			0
$463$			29.6264i			1.37685i	0.725306	+	0.688427i	$0.241698\pi$
$463$			29.6264i			1.37685i	−0.725306	+	0.688427i	$0.758302\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			30.4879i			1.41081i	0.708803	+	0.705407i	$0.249236\pi$
$467$			30.4879i			1.41081i	−0.708803	+	0.705407i	$0.750764\pi$
$468$		0			0
$469$	−11.8311	−	6.83071i	−0.546311	−	0.315413i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.624385	−	1.08147i	−0.0287092	−	0.0497259i
$474$		0			0
$475$	−6.38993	+	6.81950i	−0.293190	+	0.312900i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−20.5882	−	11.8866i	−0.940699	−	0.543113i	−0.0505196	−	0.998723i	$-0.516088\pi$
$479$	−20.5882	−	11.8866i	−0.940699	−	0.543113i	−0.890179	+	0.455610i	$0.849421\pi$
$480$		0			0
$481$	−20.8888	+	36.1805i	−0.952447	+	1.64969i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.79834	−	4.50237i	−0.354104	−	0.204442i
$486$		0			0
$487$	10.2880			0.466193			0.233096	−	0.972454i	$-0.425114\pi$
$487$	10.2880			0.466193			0.233096	+	0.972454i	$0.425114\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	28.5513	−	16.4841i	1.28850	−	0.743916i	0.310114	−	0.950699i	$-0.399633\pi$
$491$	28.5513	−	16.4841i	1.28850	−	0.743916i	0.978387	+	0.206783i	$0.0662996\pi$
$492$		0			0
$493$			2.77512i			0.124985i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	42.5697	−	24.5776i	1.90951	−	1.10246i
$498$		0			0
$499$	14.2067	−	8.20227i	0.635981	−	0.367184i	−0.147084	−	0.989124i	$-0.546989\pi$
$499$	14.2067	−	8.20227i	0.635981	−	0.367184i	0.783065	+	0.621940i	$0.213655\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12.8521	−	7.42014i	−0.573045	−	0.330848i	0.185320	−	0.982678i	$-0.440668\pi$
$503$	−12.8521	−	7.42014i	−0.573045	−	0.330848i	−0.758365	+	0.651831i	$0.774001\pi$
$504$		0			0
$505$	−27.2672			−1.21338
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−24.8168	−	14.3280i	−1.09999	−	0.635077i	−0.163769	−	0.986499i	$-0.552365\pi$
$509$	−24.8168	−	14.3280i	−1.09999	−	0.635077i	−0.936217	+	0.351422i	$0.885698\pi$
$510$		0			0
$511$	−9.24369	+	5.33684i	−0.408917	+	0.236088i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	21.9846	+	38.0784i	0.968755	+	1.67793i
$516$		0			0
$517$	−13.5288	+	23.4326i	−0.594998	+	1.03057i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			0.911178i			0.0399194i	0.999801	+	0.0199597i	$0.00635380\pi$
$521$			0.911178i			0.0399194i	−0.999801	+	0.0199597i	$0.993646\pi$
$522$		0			0
$523$	−5.12043	+	8.86885i	−0.223901	+	0.387808i	−0.955989	−	0.293402i	$-0.905213\pi$
$523$	−5.12043	+	8.86885i	−0.223901	+	0.387808i	0.732088	+	0.681210i	$0.238546\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.10083	−	3.63875i	−0.0915136	−	0.158506i
$528$		0			0
$529$	−4.70561	−	8.15036i	−0.204592	−	0.354364i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	38.4975			1.66751
$534$		0			0
$535$	6.48963	+	11.2404i	0.280571	+	0.485964i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			18.7081i			0.805813i
$540$		0			0
$541$	19.6233	−	33.9885i	0.843670	−	1.46128i	−0.0431020	−	0.999071i	$-0.513724\pi$
$541$	19.6233	−	33.9885i	0.843670	−	1.46128i	0.886772	−	0.462208i	$-0.152943\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	34.0369	+	19.6512i	1.45798	+	0.841767i
$546$		0			0
$547$	−5.81794	+	10.0770i	−0.248757	+	0.430860i	−0.963181	−	0.268853i	$-0.913355\pi$
$547$	−5.81794	+	10.0770i	−0.248757	+	0.430860i	0.714424	+	0.699713i	$0.246689\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.71598	+	7.22994i	0.328712	+	0.308006i
$552$		0			0
$553$	−23.9218	+	13.8113i	−1.01726	+	0.587314i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.514319	−	0.890827i	0.0217924	−	0.0377455i	−0.854924	−	0.518754i	$-0.826396\pi$
$557$	0.514319	−	0.890827i	0.0217924	−	0.0377455i	0.876716	+	0.481008i	$0.159729\pi$
$558$		0			0
$559$	−2.35621			−0.0996572
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.29588			0.181050			0.0905249	−	0.995894i	$-0.471146\pi$
$563$	4.29588			0.181050			0.0905249	+	0.995894i	$0.471146\pi$
$564$		0			0
$565$	33.5226	−	19.3543i	1.41031	−	0.814241i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	25.9992i		−	1.08995i	−0.838454	−	0.544973i	$-0.816540\pi$
$569$		−	25.9992i		−	1.08995i	0.838454	−	0.544973i	$-0.183460\pi$
$570$		0			0
$571$			35.2310i			1.47437i	0.675691	+	0.737185i	$0.263846\pi$
$571$			35.2310i			1.47437i	−0.675691	+	0.737185i	$0.736154\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−6.84452	+	3.95168i	−0.285436	+	0.164797i
$576$		0			0
$577$	9.51037			0.395922			0.197961	−	0.980210i	$-0.436568\pi$
$577$	9.51037			0.395922			0.197961	+	0.980210i	$0.436568\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	7.79834			0.323530
$582$		0			0
$583$	−5.20561	+	9.01639i	−0.215594	+	0.373421i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.84452	+	5.68373i	−0.406327	+	0.234593i	−0.689210	−	0.724561i	$-0.742042\pi$
$587$	−9.84452	+	5.68373i	−0.406327	+	0.234593i	0.282884	+	0.959154i	$0.408709\pi$
$588$		0			0
$589$	−15.5905	−	3.63875i	−0.642394	−	0.149932i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−12.9269	+	22.3900i	−0.530843	+	0.919447i	0.468509	+	0.883459i	$0.344791\pi$
$593$	−12.9269	+	22.3900i	−0.530843	+	0.919447i	−0.999352	+	0.0359886i	$0.988542\pi$
$594$		0			0
$595$	10.4218	+	6.01702i	0.427252	+	0.246674i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2.56276	+	4.43883i	−0.104711	+	0.181366i	−0.913620	−	0.406569i	$-0.866725\pi$
$599$	−2.56276	+	4.43883i	−0.104711	+	0.181366i	0.808909	+	0.587934i	$0.200059\pi$
$600$		0			0
$601$			12.7822i			0.521398i	0.965420	+	0.260699i	$0.0839530\pi$
$601$			12.7822i			0.521398i	−0.965420	+	0.260699i	$0.916047\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−8.21090	−	14.2217i	−0.333820	−	0.578194i
$606$		0			0
$607$	31.7882			1.29024			0.645121	−	0.764080i	$-0.276807\pi$
$607$	31.7882			1.29024			0.645121	+	0.764080i	$0.276807\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	25.5266	+	44.2133i	1.03269	+	1.78868i
$612$		0			0
$613$	−21.1664	−	36.6613i	−0.854903	−	1.48074i	−0.876735	−	0.480974i	$-0.840283\pi$
$613$	−21.1664	−	36.6613i	−0.854903	−	1.48074i	0.0218315	−	0.999762i	$-0.493050\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	10.1717	−	17.6179i	0.409497	−	0.709270i	−0.585336	−	0.810791i	$-0.699038\pi$
$617$	10.1717	−	17.6179i	0.409497	−	0.709270i	0.994833	+	0.101521i	$0.0323709\pi$
$618$		0			0
$619$			13.1402i			0.528150i	0.964502	+	0.264075i	$0.0850667\pi$
$619$			13.1402i			0.528150i	−0.964502	+	0.264075i	$0.914933\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	29.3734	−	50.8761i	1.17682	−	2.03831i
$624$		0			0
$625$	15.5616	+	26.9535i	0.622465	+	1.07814i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	9.95458	−	5.74728i	0.396915	−	0.229159i
$630$		0			0
$631$	−3.57312	−	2.06294i	−0.142244	−	0.0821245i	0.427189	−	0.904162i	$-0.359504\pi$
$631$	−3.57312	−	2.06294i	−0.142244	−	0.0821245i	−0.569433	+	0.822038i	$0.692837\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−31.0946			−1.23395
$636$		0			0
$637$	30.5697	+	17.6494i	1.21122	+	0.699296i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−31.9714	+	18.4587i	−1.26279	+	0.729074i	−0.973614	−	0.228201i	$-0.926716\pi$
$641$	−31.9714	+	18.4587i	−1.26279	+	0.729074i	−0.289179	+	0.957275i	$0.593382\pi$
$642$		0			0
$643$	−6.62854	+	3.82699i	−0.261404	+	0.150922i	−0.624975	−	0.780645i	$-0.714891\pi$
$643$	−6.62854	+	3.82699i	−0.261404	+	0.150922i	0.363571	+	0.931567i	$0.381557\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			26.5387i			1.04335i	0.853146	+	0.521673i	$0.174692\pi$
$647$			26.5387i			1.04335i	−0.853146	+	0.521673i	$0.825308\pi$
$648$		0			0
$649$	−5.10083	+	2.94497i	−0.200225	+	0.115600i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.23860			0.0876033			0.0438017	−	0.999040i	$-0.486053\pi$
$653$	2.23860			0.0876033			0.0438017	+	0.999040i	$0.486053\pi$
$654$		0			0
$655$	−28.6419	−	16.5364i	−1.11913	−	0.646132i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.43724	−	5.95348i	0.133896	−	0.231915i	−0.791279	−	0.611455i	$-0.790585\pi$
$659$	3.43724	−	5.95348i	0.133896	−	0.231915i	0.925175	+	0.379540i	$0.123918\pi$
$660$		0			0
$661$	32.2386	+	18.6130i	1.25394	+	0.723960i	0.971889	−	0.235440i	$-0.0756531\pi$
$661$	32.2386	+	18.6130i	1.25394	+	0.723960i	0.282047	+	0.959400i	$0.408986\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	43.8815	−	13.3009i	1.70165	−	0.515788i
$666$		0			0
$667$	4.47116	+	7.74428i	0.173124	+	0.299860i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	24.4949	+	14.1421i	0.945616	+	0.545952i
$672$		0			0
$673$		−	40.4406i		−	1.55887i	−0.626482	−	0.779436i	$-0.715506\pi$
$673$		−	40.4406i		−	1.55887i	0.626482	−	0.779436i	$-0.284494\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			14.1650i			0.544405i	0.962240	+	0.272202i	$0.0877520\pi$
$677$			14.1650i			0.544405i	−0.962240	+	0.272202i	$0.912248\pi$
$678$		0			0
$679$	6.62967	+	11.4829i	0.254423	+	0.440674i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−23.8952			−0.914325			−0.457163	−	0.889383i	$-0.651134\pi$
$683$	−23.8952			−0.914325			−0.457163	+	0.889383i	$0.651134\pi$
$684$		0			0
$685$	25.2100			0.963223
$686$		0			0
$687$		0			0
$688$		0			0
$689$	9.82209	+	17.0124i	0.374192	+	0.648119i
$690$		0			0
$691$		−	19.0166i		−	0.723427i	−0.932289	−	0.361714i	$-0.882192\pi$
$691$		−	19.0166i		−	0.723427i	0.932289	−	0.361714i	$-0.117808\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			36.7088i			1.39245i
$696$		0			0
$697$	−9.17302	−	5.29605i	−0.347453	−	0.200602i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−14.2109	−	24.6140i	−0.536738	−	0.929658i	−0.999077	−	0.0429544i	$-0.986323\pi$
$701$	−14.2109	−	24.6140i	−0.536738	−	0.929658i	0.462339	−	0.886703i	$-0.347010\pi$
$702$		0			0
$703$	9.95458	−	42.6511i	0.375444	−	1.60862i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	34.7714	+	20.0753i	1.30771	+	0.755008i
$708$		0			0
$709$	13.8681	−	24.0202i	0.520826	−	0.902098i	−0.478880	−	0.877880i	$-0.658957\pi$
$709$	13.8681	−	24.0202i	0.520826	−	0.902098i	0.999707	−	0.0242175i	$-0.00770943\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−11.7252	−	6.76956i	−0.439113	−	0.253522i
$714$		0			0
$715$	24.4896			0.915860
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.844517	+	0.487582i	−0.0314952	+	0.0181837i	−0.515665	−	0.856790i	$-0.672455\pi$
$719$	−0.844517	+	0.487582i	−0.0314952	+	0.0181837i	0.484170	+	0.874974i	$0.339122\pi$
$720$		0			0
$721$		−	64.7438i		−	2.41118i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.50415	+	2.60047i	−0.167280	+	0.0965792i
$726$		0			0
$727$	−22.6924	+	13.1015i	−0.841615	+	0.485907i	−0.857813	−	0.513962i	$-0.828177\pi$
$727$	−22.6924	+	13.1015i	−0.841615	+	0.485907i	0.0161975	+	0.999869i	$0.494844\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.561428	+	0.324141i	0.0207652	+	0.0119888i
$732$		0			0
$733$	27.2751			1.00743			0.503715	−	0.863870i	$-0.331966\pi$
$733$	27.2751			1.00743			0.503715	+	0.863870i	$0.331966\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.62438	+	3.82459i	0.244012	+	0.140881i
$738$		0			0
$739$	21.2908	−	12.2922i	0.783195	−	0.452178i	−0.0543667	−	0.998521i	$-0.517314\pi$
$739$	21.2908	−	12.2922i	0.783195	−	0.452178i	0.837561	+	0.546343i	$0.183981\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	24.1101	+	41.7599i	0.884513	+	1.53202i	0.846271	+	0.532752i	$0.178842\pi$
$743$	24.1101	+	41.7599i	0.884513	+	1.53202i	0.0382412	+	0.999269i	$0.487824\pi$
$744$		0			0
$745$	−21.7921	+	37.7451i	−0.798402	+	1.38287i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	19.1118i		−	0.698328i
$750$		0			0
$751$	16.2437	−	28.1349i	0.592741	−	1.02666i	−0.401121	−	0.916025i	$-0.631379\pi$
$751$	16.2437	−	28.1349i	0.592741	−	1.02666i	0.993861	−	0.110632i	$-0.0352874\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−9.43196	−	16.3366i	−0.343264	−	0.594551i
$756$		0			0
$757$	−11.5801	−	20.0573i	−0.420886	−	0.728996i	0.575141	−	0.818055i	$-0.304947\pi$
$757$	−11.5801	−	20.0573i	−0.420886	−	0.728996i	−0.996026	+	0.0890590i	$0.971614\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	18.5496			0.672421			0.336211	−	0.941787i	$-0.390855\pi$
$761$	18.5496			0.672421			0.336211	+	0.941787i	$0.390855\pi$
$762$		0			0
$763$	−28.9361	−	50.1188i	−1.04756	−	1.81442i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			11.1133i			0.401277i
$768$		0			0
$769$	−18.8249	+	32.6057i	−0.678844	+	1.17579i	0.296486	+	0.955037i	$0.404185\pi$
$769$	−18.8249	+	32.6057i	−0.678844	+	1.17579i	−0.975329	+	0.220755i	$0.929148\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.981529	+	0.566686i	0.0353031	+	0.0203823i	0.517548	−	0.855654i	$-0.326845\pi$
$773$	0.981529	+	0.566686i	0.0353031	+	0.0203823i	−0.482245	+	0.876037i	$0.660178\pi$
$774$		0			0
$775$	3.93724	−	6.81950i	0.141430	−	0.244964i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−38.6235	+	11.7072i	−1.38383	+	0.419453i
$780$		0			0
$781$	−23.8353	+	13.7613i	−0.852893	+	0.492418i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	15.1348	−	26.2142i	0.540182	−	0.935623i
$786$		0			0
$787$	−13.9687			−0.497930			−0.248965	−	0.968512i	$-0.580090\pi$
$787$	−13.9687			−0.497930			−0.248965	+	0.968512i	$0.580090\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−56.9977			−2.02661
$792$		0			0
$793$	46.2177	−	26.6838i	1.64124	−	0.947569i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			10.2972i			0.364746i	0.983229	+	0.182373i	$0.0583778\pi$
$797$			10.2972i			0.364746i	−0.983229	+	0.182373i	$0.941622\pi$
$798$		0			0
$799$		−	14.0466i		−	0.496933i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	5.17565	−	2.98816i	0.182645	−	0.105450i
$804$		0			0
$805$	38.7776			1.36673
$806$		0			0
$807$		0			0
$808$		0			0
$809$	26.1338			0.918816			0.459408	−	0.888225i	$-0.348062\pi$
$809$	26.1338			0.918816			0.459408	+	0.888225i	$0.348062\pi$
$810$		0			0
$811$	18.0185	−	31.2089i	0.632714	−	1.09589i	−0.354280	−	0.935139i	$-0.615274\pi$
$811$	18.0185	−	31.2089i	0.632714	−	1.09589i	0.986995	−	0.160754i	$-0.0513925\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.12023	−	1.22412i	0.0742685	−	0.0428789i
$816$		0			0
$817$	2.36392	−	0.716528i	0.0827031	−	0.0250682i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.89917	−	6.75356i	0.136082	−	0.235701i	−0.789928	−	0.613199i	$-0.789882\pi$
$821$	3.89917	−	6.75356i	0.136082	−	0.235701i	0.926010	+	0.377498i	$0.123216\pi$
$822$		0			0
$823$	−23.8824	−	13.7885i	−0.832488	−	0.480637i	0.0222159	−	0.999753i	$-0.492928\pi$
$823$	−23.8824	−	13.7885i	−0.832488	−	0.480637i	−0.854704	+	0.519116i	$0.826261\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.99605	−	3.45726i	0.0694094	−	0.120221i	−0.829232	−	0.558904i	$-0.811222\pi$
$827$	1.99605	−	3.45726i	0.0694094	−	0.120221i	0.898641	+	0.438684i	$0.144555\pi$
$828$		0			0
$829$		−	50.8873i		−	1.76739i	−0.468063	−	0.883695i	$-0.655048\pi$
$829$		−	50.8873i		−	1.76739i	0.468063	−	0.883695i	$-0.344952\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.85601	−	8.41086i	−0.168251	−	0.291419i
$834$		0			0
$835$	−1.02864			−0.0355975
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−25.3117	−	43.8412i	−0.873858	−	1.51357i	−0.857974	−	0.513692i	$-0.828277\pi$
$839$	−25.3117	−	43.8412i	−0.873858	−	1.51357i	−0.0158834	−	0.999874i	$-0.505056\pi$
$840$		0			0
$841$	−11.5577	−	20.0185i	−0.398540	−	0.690292i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.73050	−	9.92551i	0.197135	−	0.341448i
$846$		0			0
$847$			24.1808i			0.830862i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	18.5196	−	32.0769i	0.634844	−	1.09958i
$852$		0			0
$853$	10.3745	+	17.9691i	0.355216	+	0.615251i	0.987155	−	0.159766i	$-0.0510741\pi$
$853$	10.3745	+	17.9691i	0.355216	+	0.615251i	−0.631939	+	0.775018i	$0.717741\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−24.6521	+	14.2329i	−0.842099	+	0.486186i	−0.857977	−	0.513688i	$-0.828279\pi$
$857$	−24.6521	+	14.2329i	−0.842099	+	0.486186i	0.0158779	+	0.999874i	$0.494946\pi$
$858$		0			0
$859$	43.4453	+	25.0832i	1.48234	+	0.855827i	0.999799	−	0.0200484i	$-0.00638202\pi$
$859$	43.4453	+	25.0832i	1.48234	+	0.855827i	0.482537	+	0.875876i	$0.339715\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	39.5922			1.34773			0.673866	−	0.738853i	$-0.264632\pi$
$863$	39.5922			1.34773			0.673866	+	0.738853i	$0.264632\pi$
$864$		0			0
$865$	24.9898	+	14.4279i	0.849680	+	0.490563i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	13.3941	−	7.73308i	0.454363	−	0.262327i
$870$		0			0
$871$	12.4991	−	7.21634i	0.423515	−	0.244516i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		−	30.0435i		−	1.01566i
$876$		0			0
$877$	−41.5924	+	24.0134i	−1.40447	+	0.810873i	−0.994848	−	0.101380i	$-0.967674\pi$
$877$	−41.5924	+	24.0134i	−1.40447	+	0.810873i	−0.409626	+	0.912253i	$0.634341\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−27.9815			−0.942722			−0.471361	−	0.881940i	$-0.656237\pi$
$881$	−27.9815			−0.942722			−0.471361	+	0.881940i	$0.656237\pi$
$882$		0			0
$883$	26.3445	+	15.2100i	0.886564	+	0.511858i	0.872817	−	0.488048i	$-0.162291\pi$
$883$	26.3445	+	15.2100i	0.886564	+	0.511858i	0.0137467	+	0.999906i	$0.495624\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.09555	+	3.62960i	−0.0703616	+	0.121870i	−0.899060	−	0.437826i	$-0.855749\pi$
$887$	−2.09555	+	3.62960i	−0.0703616	+	0.121870i	0.828698	+	0.559696i	$0.189082\pi$
$888$		0			0
$889$	39.6521	+	22.8931i	1.32989	+	0.767811i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−39.0554	−	36.5953i	−1.30694	−	1.22461i
$894$		0			0
$895$	−1.38880	−	2.40548i	−0.0464226	−	0.0804063i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−7.71598	−	4.45482i	−0.257342	−	0.148577i
$900$		0			0
$901$		−	5.40484i		−	0.180061i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			20.7846i			0.690904i
$906$		0			0
$907$	−4.38485	−	7.59478i	−0.145597	−	0.252181i	0.783999	−	0.620762i	$-0.213177\pi$
$907$	−4.38485	−	7.59478i	−0.145597	−	0.252181i	−0.929595	+	0.368582i	$0.879843\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.95854			0.0648892			0.0324446	−	0.999474i	$-0.489671\pi$
$911$	1.95854			0.0648892			0.0324446	+	0.999474i	$0.489671\pi$
$912$		0			0
$913$	−4.36638			−0.144506
$914$		0			0
$915$		0			0
$916$		0			0
$917$	24.3496	+	42.1747i	0.804095	+	1.39273i
$918$		0			0
$919$			43.4284i			1.43257i	0.697808	+	0.716285i	$0.254159\pi$
$919$			43.4284i			1.43257i	−0.697808	+	0.716285i	$0.745841\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			51.9304i			1.70931i
$924$		0			0
$925$	18.6562	+	10.7712i	0.613414	+	0.354154i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.02997	+	5.24806i	0.0994100	+	0.172183i	0.911441	−	0.411432i	$-0.134971\pi$
$929$	3.02997	+	5.24806i	0.0994100	+	0.172183i	−0.812031	+	0.583615i	$0.801638\pi$
$930$		0			0
$931$	−36.0369	−	8.41086i	−1.18106	−	0.275655i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−5.83528	−	3.36900i	−0.190834	−	0.110178i
$936$		0			0
$937$	−12.1297	+	21.0092i	−0.396259	+	0.686341i	−0.993261	−	0.115899i	$-0.963025\pi$
$937$	−12.1297	+	21.0092i	−0.396259	+	0.686341i	0.597002	+	0.802240i	$0.296358\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−35.6706	−	20.5944i	−1.16283	−	0.671359i	−0.210847	−	0.977519i	$-0.567622\pi$
$941$	−35.6706	−	20.5944i	−1.16283	−	0.671359i	−0.951980	+	0.306160i	$0.900956\pi$
$942$		0			0
$943$	−34.1312			−1.11146
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.88900	+	1.09062i	−0.0613843	+	0.0354403i	−0.530378	−	0.847761i	$-0.677950\pi$
$947$	−1.88900	+	1.09062i	−0.0613843	+	0.0354403i	0.468994	+	0.883201i	$0.344617\pi$
$948$		0			0
$949$		−	11.2763i		−	0.366044i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	21.7974	−	12.5847i	0.706087	−	0.407660i	−0.103523	−	0.994627i	$-0.533012\pi$
$953$	21.7974	−	12.5847i	0.706087	−	0.407660i	0.809611	+	0.586967i	$0.199678\pi$
$954$		0			0
$955$	60.7899	−	35.0970i	1.96711	−	1.13571i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−32.1479	−	18.5606i	−1.03811	−	0.599354i
$960$		0			0
$961$	−17.5104			−0.564851
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−22.0092	−	12.7070i	−0.708502	−	0.409054i
$966$		0			0
$967$	6.65548	−	3.84254i	0.214026	−	0.123568i	−0.389155	−	0.921172i	$-0.627233\pi$
$967$	6.65548	−	3.84254i	0.214026	−	0.123568i	0.603181	+	0.797604i	$0.293900\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	24.3272	+	42.1359i	0.780696	+	1.35221i	0.931537	+	0.363647i	$0.118469\pi$
$971$	24.3272	+	42.1359i	0.780696	+	1.35221i	−0.150840	+	0.988558i	$0.548198\pi$
$972$		0			0
$973$	27.0266	−	46.8114i	0.866432	−	1.50070i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	11.2811i		−	0.360914i	−0.983583	−	0.180457i	$-0.942242\pi$
$977$		−	11.2811i		−	0.360914i	0.983583	−	0.180457i	$-0.0577576\pi$
$978$		0			0
$979$	−16.4465	+	28.4861i	−0.525632	+	0.910421i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	19.8485	+	34.3786i	0.633068	+	1.09651i	0.986921	+	0.161205i	$0.0515379\pi$
$983$	19.8485	+	34.3786i	0.633068	+	1.09651i	−0.353853	+	0.935301i	$0.615129\pi$
$984$		0			0
$985$	37.3289	+	64.6555i	1.18940	+	2.06010i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.08897			0.0664254
$990$		0			0
$991$	7.78930	+	13.4915i	0.247435	+	0.428571i	0.962814	−	0.270167i	$-0.0870789\pi$
$991$	7.78930	+	13.4915i	0.247435	+	0.428571i	−0.715378	+	0.698738i	$0.753746\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	21.2203i		−	0.672728i
$996$		0			0
$997$	16.5185	−	28.6108i	0.523145	−	0.906114i	−0.476492	−	0.879179i	$-0.658092\pi$
$997$	16.5185	−	28.6108i	0.523145	−	0.906114i	0.999637	−	0.0269353i	$-0.00857480\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.bm.o.1855.1		6
3.2	odd	2		912.2.bb.f.31.3	yes	6
4.3	odd	2		2736.2.bm.n.1855.1		6
12.11	even	2		912.2.bb.e.31.3	✓	6
19.8	odd	6		2736.2.bm.n.559.1		6
57.8	even	6		912.2.bb.e.559.3	yes	6
76.27	even	6	inner	2736.2.bm.o.559.1		6
228.179	odd	6		912.2.bb.f.559.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bb.e.31.3	✓	6	12.11	even	2
912.2.bb.e.559.3	yes	6	57.8	even	6
912.2.bb.f.31.3	yes	6	3.2	odd	2
912.2.bb.f.559.3	yes	6	228.179	odd	6
2736.2.bm.n.559.1		6	19.8	odd	6
2736.2.bm.n.1855.1		6	4.3	odd	2
2736.2.bm.o.559.1		6	76.27	even	6	inner
2736.2.bm.o.1855.1		6	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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33641 - 2.31473i) q^{5} +3.93569i q^{7} +O(q^{10})\)	\(q+(-1.33641 - 2.31473i) q^{5} +3.93569i q^{7} -2.20364i q^{11} +(-3.60083 - 2.07894i) q^{13} +(0.571993 + 0.990721i) q^{17} +(4.24482 + 0.990721i) q^{19} +(3.19243 + 1.84315i) q^{23} +(-1.07199 + 1.85675i) q^{25} +(2.10083 + 1.21292i) q^{29} -3.67282 q^{31} +(9.11007 - 5.25970i) q^{35} -10.0478i q^{37} +(-8.01847 + 4.62947i) q^{41} +(0.490764 - 0.283343i) q^{43} +(-10.6336 - 6.13932i) q^{47} -8.48963 q^{49} +(-4.09159 - 2.36228i) q^{53} +(-5.10083 + 2.94497i) q^{55} +(-1.33641 - 2.31473i) q^{59} +(-6.41764 + 11.1157i) q^{61} +11.1133i q^{65} +(-1.73558 + 3.00612i) q^{67} +(-6.24482 - 10.8163i) q^{71} +(1.35601 + 2.34868i) q^{73} +8.67282 q^{77} +(3.50924 + 6.07817i) q^{79} -1.98144i q^{83} +(1.52884 - 2.64802i) q^{85} +(-12.9269 - 7.46334i) q^{89} +(8.18206 - 14.1717i) q^{91} +(-3.37957 - 11.1496i) q^{95} +(2.91764 - 1.68450i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{5}+O(q^{10}) \) 6 * q + 2 * q^5	\( 6 q + 2 q^{5} - 3 q^{13} + 2 q^{17} + 4 q^{19} + 12 q^{23} - 5 q^{25} - 6 q^{29} - 2 q^{31} + 6 q^{35} + 12 q^{41} + 33 q^{43} - 18 q^{47} - 8 q^{49} - 36 q^{53} - 12 q^{55} + 2 q^{59} + 3 q^{61} - 19 q^{67} - 16 q^{71} + 11 q^{73} + 32 q^{77} - 9 q^{79} - 8 q^{85} - 6 q^{89} - q^{91} - 26 q^{95} - 24 q^{97}+O(q^{100}) \) 6 * q + 2 * q^5 - 3 * q^13 + 2 * q^17 + 4 * q^19 + 12 * q^23 - 5 * q^25 - 6 * q^29 - 2 * q^31 + 6 * q^35 + 12 * q^41 + 33 * q^43 - 18 * q^47 - 8 * q^49 - 36 * q^53 - 12 * q^55 + 2 * q^59 + 3 * q^61 - 19 * q^67 - 16 * q^71 + 11 * q^73 + 32 * q^77 - 9 * q^79 - 8 * q^85 - 6 * q^89 - q^91 - 26 * q^95 - 24 * q^97

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