LMFDB - Embedded newform 3024.2.cx.b.559.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(559,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.559"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cx (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,0,-3,0,-4,0,0,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3024.559
Dual form			3024.2.cx.b.2575.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.50000 + 0.866025i) q^{11} +(-4.50000 + 2.59808i) q^{13} -6.92820i q^{17} -4.00000 q^{19} +(4.50000 - 2.59808i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(-4.50000 + 7.79423i) q^{29} +(-3.50000 - 6.06218i) q^{31} +(1.50000 - 4.33013i) q^{35} +10.0000 q^{37} +(4.50000 - 2.59808i) q^{41} +(-7.50000 - 4.33013i) q^{43} +(-1.50000 + 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} +6.00000 q^{53} -3.00000 q^{55} +(1.50000 + 2.59808i) q^{59} +(1.50000 + 0.866025i) q^{61} +(4.50000 - 7.79423i) q^{65} +(7.50000 - 4.33013i) q^{67} -3.46410i q^{71} +6.92820i q^{73} +(-4.50000 + 0.866025i) q^{77} +(4.50000 + 2.59808i) q^{79} +(4.50000 - 7.79423i) q^{83} +(6.00000 + 10.3923i) q^{85} -6.92820i q^{89} +(4.50000 - 12.9904i) q^{91} +(6.00000 - 3.46410i) q^{95} +(-4.50000 - 2.59808i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{5} - 4 q^{7} + 3 q^{11} - 9 q^{13} - 8 q^{19} + 9 q^{23} - 2 q^{25} - 9 q^{29} - 7 q^{31} + 3 q^{35} + 20 q^{37} + 9 q^{41} - 15 q^{43} - 3 q^{47} + 2 q^{49} + 12 q^{53} - 6 q^{55} + 3 q^{59}+ \cdots - 9 q^{97}+O(q^{100}) $ 2 * q - 3 * q^5 - 4 * q^7 + 3 * q^11 - 9 * q^13 - 8 * q^19 + 9 * q^23 - 2 * q^25 - 9 * q^29 - 7 * q^31 + 3 * q^35 + 20 * q^37 + 9 * q^41 - 15 * q^43 - 3 * q^47 + 2 * q^49 + 12 * q^53 - 6 * q^55 + 3 * q^59 + 3 * q^61 + 9 * q^65 + 15 * q^67 - 9 * q^77 + 9 * q^79 + 9 * q^83 + 12 * q^85 + 9 * q^91 + 12 * q^95 - 9 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

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
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	0.125567	+	0.992085i	$0.459925\pi$
$6$		0			0
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	0.708787	−	0.705422i	$-0.249243\pi$
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	−0.256520	+	0.966539i	$0.582576\pi$
$12$		0			0
$13$	−4.50000	+	2.59808i	−1.24808	+	0.720577i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−4.50000	+	2.59808i	−1.24808	+	0.720577i	−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	6.92820i		−	1.68034i	−0.542326	−	0.840168i	$-0.682456\pi$
$17$		−	6.92820i		−	1.68034i	0.542326	−	0.840168i	$-0.317544\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.50000	−	2.59808i	0.938315	−	0.541736i	0.0488832	−	0.998805i	$-0.484434\pi$
$23$	4.50000	−	2.59808i	0.938315	−	0.541736i	0.889432	+	0.457068i	$0.151100\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	0.0578882	+	0.998323i	$0.481563\pi$
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	−0.893517	+	0.449029i	$0.851770\pi$
$30$		0			0
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	0.359211	−	0.933257i	$-0.383046\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.50000	−	4.33013i	0.253546	−	0.731925i
$36$		0			0
$37$	10.0000			1.64399			0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000			1.64399			0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	−0.105601	−	0.994409i	$-0.533677\pi$
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	0.808383	+	0.588657i	$0.200343\pi$
$42$		0			0
$43$	−7.50000	−	4.33013i	−1.14374	−	0.660338i	−0.196385	−	0.980527i	$-0.562920\pi$
$43$	−7.50000	−	4.33013i	−1.14374	−	0.660338i	−0.947354	+	0.320189i	$0.896254\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	−0.954441	−	0.298401i	$-0.903547\pi$
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	0.735643	+	0.677369i	$0.236880\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$		0			0
$61$	1.50000	+	0.866025i	0.192055	+	0.110883i	0.592944	−	0.805243i	$-0.297965\pi$
$61$	1.50000	+	0.866025i	0.192055	+	0.110883i	−0.400889	+	0.916127i	$0.631299\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.50000	−	7.79423i	0.558156	−	0.966755i
$66$		0			0
$67$	7.50000	−	4.33013i	0.916271	−	0.529009i	0.0338274	−	0.999428i	$-0.489230\pi$
$67$	7.50000	−	4.33013i	0.916271	−	0.529009i	0.882443	+	0.470418i	$0.155897\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	3.46410i		−	0.411113i	−0.978645	−	0.205557i	$-0.934100\pi$
$71$		−	3.46410i		−	0.411113i	0.978645	−	0.205557i	$-0.0659005\pi$
$72$		0			0
$73$			6.92820i			0.810885i	0.914121	+	0.405442i	$0.132883\pi$
$73$			6.92820i			0.810885i	−0.914121	+	0.405442i	$0.867117\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.50000	+	0.866025i	−0.512823	+	0.0986928i
$78$		0			0
$79$	4.50000	+	2.59808i	0.506290	+	0.292306i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	4.50000	+	2.59808i	0.506290	+	0.292306i	−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$		0			0
$85$	6.00000	+	10.3923i	0.650791	+	1.12720i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	6.92820i		−	0.734388i	−0.930144	−	0.367194i	$-0.880318\pi$
$89$		−	6.92820i		−	0.734388i	0.930144	−	0.367194i	$-0.119682\pi$
$90$		0			0
$91$	4.50000	−	12.9904i	0.471728	−	1.36176i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	6.00000	−	3.46410i	0.615587	−	0.355409i
$96$		0			0
$97$	−4.50000	−	2.59808i	−0.456906	−	0.263795i	0.253837	−	0.967247i	$-0.418307\pi$
$97$	−4.50000	−	2.59808i	−0.456906	−	0.263795i	−0.710742	+	0.703452i	$0.751641\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	16.5000	+	9.52628i	1.64181	+	0.947900i	0.980189	+	0.198063i	$0.0634650\pi$
$101$	16.5000	+	9.52628i	1.64181	+	0.947900i	0.661622	+	0.749838i	$0.269868\pi$
$102$		0			0
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	17.3205i		−	1.67444i	−0.546869	−	0.837218i	$-0.684180\pi$
$107$		−	17.3205i		−	1.67444i	0.546869	−	0.837218i	$-0.315820\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$		0			0
$115$	−4.50000	+	7.79423i	−0.419627	+	0.726816i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	12.0000	+	13.8564i	1.10004	+	1.27021i
$120$		0			0
$121$	−4.00000	−	6.92820i	−0.363636	−	0.629837i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$		−	17.3205i		−	1.53695i	−0.639882	−	0.768473i	$-0.721017\pi$
$127$		−	17.3205i		−	1.53695i	0.639882	−	0.768473i	$-0.278983\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−10.5000	−	18.1865i	−0.917389	−	1.58896i	−0.803365	−	0.595487i	$-0.796959\pi$
$131$	−10.5000	−	18.1865i	−0.917389	−	1.58896i	−0.114024	−	0.993478i	$-0.536374\pi$
$132$		0			0
$133$	8.00000	−	6.92820i	0.693688	−	0.600751i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−9.00000			−0.752618
$144$		0			0
$145$		−	15.5885i		−	1.29455i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$		0			0
$151$	−19.5000	−	11.2583i	−1.58689	−	0.916190i	−0.993816	−	0.111040i	$-0.964582\pi$
$151$	−19.5000	−	11.2583i	−1.58689	−	0.916190i	−0.593072	−	0.805150i	$-0.702085\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	10.5000	+	6.06218i	0.843380	+	0.486926i
$156$		0			0
$157$	1.50000	−	0.866025i	0.119713	−	0.0691164i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	1.50000	−	0.866025i	0.119713	−	0.0691164i	0.558661	+	0.829396i	$0.311315\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4.50000	+	12.9904i	−0.354650	+	1.02379i
$162$		0			0
$163$			3.46410i			0.271329i	0.990755	+	0.135665i	$0.0433170\pi$
$163$			3.46410i			0.271329i	−0.990755	+	0.135665i	$0.956683\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	0.918208	−	0.396098i	$-0.129636\pi$
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	−0.802135	+	0.597143i	$0.796303\pi$
$168$		0			0
$169$	7.00000	−	12.1244i	0.538462	−	0.932643i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.50000	+	2.59808i	0.342129	+	0.197528i	0.661213	−	0.750198i	$-0.270042\pi$
$173$	4.50000	+	2.59808i	0.342129	+	0.197528i	−0.319084	+	0.947726i	$0.603375\pi$
$174$		0			0
$175$	−1.00000	−	5.19615i	−0.0755929	−	0.392792i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	3.46410i		−	0.258919i	−0.991585	−	0.129460i	$-0.958676\pi$
$179$		−	3.46410i		−	0.258919i	0.991585	−	0.129460i	$-0.0413242\pi$
$180$		0			0
$181$		−	13.8564i		−	1.02994i	−0.857209	−	0.514969i	$-0.827803\pi$
$181$		−	13.8564i		−	1.02994i	0.857209	−	0.514969i	$-0.172197\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−15.0000	+	8.66025i	−1.10282	+	0.636715i
$186$		0			0
$187$	6.00000	−	10.3923i	0.438763	−	0.759961i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.5000	−	6.06218i	−0.759753	−	0.438644i	0.0694538	−	0.997585i	$-0.477874\pi$
$191$	−10.5000	−	6.06218i	−0.759753	−	0.438644i	−0.829207	+	0.558941i	$0.811208\pi$
$192$		0			0
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	0.941865	−	0.335993i	$-0.109072\pi$
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	−0.761911	+	0.647682i	$0.775738\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.50000	−	23.3827i	−0.315838	−	1.64114i
$204$		0			0
$205$	−4.50000	+	7.79423i	−0.314294	+	0.544373i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.00000	−	3.46410i	−0.415029	−	0.239617i
$210$		0			0
$211$	−4.50000	+	2.59808i	−0.309793	+	0.178859i	−0.646834	−	0.762631i	$-0.723907\pi$
$211$	−4.50000	+	2.59808i	−0.309793	+	0.178859i	0.337041	+	0.941490i	$0.390574\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	15.0000			1.02299
$216$		0			0
$217$	17.5000	+	6.06218i	1.18798	+	0.411527i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	18.0000	+	31.1769i	1.21081	+	2.09719i
$222$		0			0
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	−0.350100	−	0.936713i	$-0.613852\pi$
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	0.986267	−	0.165161i	$-0.0528144\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	−0.911502	−	0.411296i	$-0.865076\pi$
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	0.811943	+	0.583736i	$0.198410\pi$
$228$		0			0
$229$	1.50000	−	0.866025i	0.0991228	−	0.0572286i	−0.449619	−	0.893220i	$-0.648440\pi$
$229$	1.50000	−	0.866025i	0.0991228	−	0.0572286i	0.548742	+	0.835992i	$0.315107\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$		−	5.19615i		−	0.338960i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	16.5000	−	9.52628i	1.06730	−	0.616204i	0.139855	−	0.990172i	$-0.455336\pi$
$239$	16.5000	−	9.52628i	1.06730	−	0.616204i	0.927442	+	0.373968i	$0.122003\pi$
$240$		0			0
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	−0.450910	+	0.892570i	$0.648900\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.50000	+	11.2583i	0.287494	+	0.719268i
$246$		0			0
$247$	18.0000	−	10.3923i	1.14531	−	0.661247i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.5000	+	7.79423i	−0.842107	+	0.486191i	−0.857980	−	0.513683i	$-0.828281\pi$
$257$	−13.5000	+	7.79423i	−0.842107	+	0.486191i	0.0158730	+	0.999874i	$0.494947\pi$
$258$		0			0
$259$	−20.0000	+	17.3205i	−1.24274	+	1.07624i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−16.5000	−	9.52628i	−1.01743	−	0.587416i	−0.104074	−	0.994570i	$-0.533188\pi$
$263$	−16.5000	−	9.52628i	−1.01743	−	0.587416i	−0.913360	+	0.407154i	$0.866521\pi$
$264$		0			0
$265$	−9.00000	+	5.19615i	−0.552866	+	0.319197i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.00000	+	1.73205i	−0.180907	+	0.104447i
$276$		0			0
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	0.425684	+	0.904872i	$0.360033\pi$
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	−0.996484	+	0.0837823i	$0.973300\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	−0.110717	−	0.993852i	$-0.535315\pi$
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	0.916060	−	0.401042i	$-0.131352\pi$
$282$		0			0
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	0.991960	−	0.126550i	$-0.0403903\pi$
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	−0.605575	+	0.795788i	$0.707057\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.50000	+	12.9904i	−0.265627	+	0.766798i
$288$		0			0
$289$	−31.0000			−1.82353
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−13.5000	+	7.79423i	−0.788678	+	0.455344i	−0.839497	−	0.543364i	$-0.817150\pi$
$293$	−13.5000	+	7.79423i	−0.788678	+	0.455344i	0.0508187	+	0.998708i	$0.483817\pi$
$294$		0			0
$295$	−4.50000	−	2.59808i	−0.262000	−	0.151266i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−13.5000	+	23.3827i	−0.780725	+	1.35226i
$300$		0			0
$301$	22.5000	−	4.33013i	1.29688	−	0.249584i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.00000			−0.171780
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.50000	−	7.79423i	−0.255172	−	0.441970i	0.709771	−	0.704433i	$-0.248799\pi$
$311$	−4.50000	−	7.79423i	−0.255172	−	0.441970i	−0.964942	+	0.262463i	$0.915465\pi$
$312$		0			0
$313$	1.50000	+	0.866025i	0.0847850	+	0.0489506i	0.541793	−	0.840512i	$-0.317746\pi$
$313$	1.50000	+	0.866025i	0.0847850	+	0.0489506i	−0.457008	+	0.889463i	$0.651079\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.50000	+	7.79423i	−0.252745	+	0.437767i	−0.964281	−	0.264883i	$-0.914667\pi$
$317$	−4.50000	+	7.79423i	−0.252745	+	0.437767i	0.711535	+	0.702650i	$0.248000\pi$
$318$		0			0
$319$	−13.5000	+	7.79423i	−0.755855	+	0.436393i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			27.7128i			1.54198i
$324$		0			0
$325$		−	10.3923i		−	0.576461i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.50000	−	7.79423i	−0.0826977	−	0.429710i
$330$		0			0
$331$	22.5000	+	12.9904i	1.23671	+	0.714016i	0.968421	−	0.249322i	$-0.0802077\pi$
$331$	22.5000	+	12.9904i	1.23671	+	0.714016i	0.268291	+	0.963338i	$0.413541\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−7.50000	+	12.9904i	−0.409769	+	0.709740i
$336$		0			0
$337$	−11.5000	−	19.9186i	−0.626445	−	1.08503i	−0.988260	−	0.152784i	$-0.951176\pi$
$337$	−11.5000	−	19.9186i	−0.626445	−	1.08503i	0.361815	−	0.932250i	$-0.382157\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	12.1244i		−	0.656571i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.50000	+	4.33013i	−0.402621	+	0.232453i	−0.687614	−	0.726076i	$-0.741342\pi$
$347$	−7.50000	+	4.33013i	−0.402621	+	0.232453i	0.284993	+	0.958530i	$0.408009\pi$
$348$		0			0
$349$	−28.5000	−	16.4545i	−1.52557	−	0.880788i	−0.999540	−	0.0303222i	$-0.990347\pi$
$349$	−28.5000	−	16.4545i	−1.52557	−	0.880788i	−0.526030	−	0.850466i	$-0.676320\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	16.5000	+	9.52628i	0.878206	+	0.507033i	0.870067	−	0.492934i	$-0.164076\pi$
$353$	16.5000	+	9.52628i	0.878206	+	0.507033i	0.00813978	+	0.999967i	$0.497409\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	24.2487i		−	1.27980i	−0.768459	−	0.639899i	$-0.778976\pi$
$359$		−	24.2487i		−	1.27980i	0.768459	−	0.639899i	$-0.221024\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.00000	−	10.3923i	−0.314054	−	0.543958i
$366$		0			0
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−12.0000	+	10.3923i	−0.623009	+	0.539542i
$372$		0			0
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	0.983783	−	0.179364i	$-0.0574041\pi$
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	−0.647225	+	0.762299i	$0.724071\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	46.7654i		−	2.40854i
$378$		0			0
$379$		−	17.3205i		−	0.889695i	−0.895606	−	0.444847i	$-0.853258\pi$
$379$		−	17.3205i		−	0.889695i	0.895606	−	0.444847i	$-0.146742\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.50000	+	2.59808i	0.0766464	+	0.132755i	0.901801	−	0.432151i	$-0.142245\pi$
$383$	1.50000	+	2.59808i	0.0766464	+	0.132755i	−0.825155	+	0.564907i	$0.808912\pi$
$384$		0			0
$385$	6.00000	−	5.19615i	0.305788	−	0.264820i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	−0.825491	−	0.564416i	$-0.809102\pi$
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	0.901544	+	0.432688i	$0.142435\pi$
$390$		0			0
$391$	−18.0000	−	31.1769i	−0.910299	−	1.57668i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−9.00000			−0.452839
$396$		0			0
$397$			13.8564i			0.695433i	0.937600	+	0.347717i	$0.113043\pi$
$397$			13.8564i			0.695433i	−0.937600	+	0.347717i	$0.886957\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	−0.999598	−	0.0283431i	$-0.990977\pi$
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	0.475253	−	0.879849i	$-0.342356\pi$
$402$		0			0
$403$	31.5000	+	18.1865i	1.56913	+	0.905936i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	15.0000	+	8.66025i	0.743522	+	0.429273i
$408$		0			0
$409$	25.5000	−	14.7224i	1.26089	−	0.727977i	0.287646	−	0.957737i	$-0.407127\pi$
$409$	25.5000	−	14.7224i	1.26089	−	0.727977i	0.973247	+	0.229759i	$0.0737939\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−7.50000	−	2.59808i	−0.369051	−	0.127843i
$414$		0			0
$415$			15.5885i			0.765207i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	0.734919	−	0.678155i	$-0.237220\pi$
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	−0.954759	+	0.297382i	$0.903887\pi$
$420$		0			0
$421$	8.50000	−	14.7224i	0.414265	−	0.717527i	−0.581086	−	0.813842i	$-0.697372\pi$
$421$	8.50000	−	14.7224i	0.414265	−	0.717527i	0.995351	+	0.0963145i	$0.0307055\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.0000	+	6.92820i	0.582086	+	0.336067i
$426$		0			0
$427$	−4.50000	+	0.866025i	−0.217770	+	0.0419099i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			3.46410i			0.166860i	0.996514	+	0.0834300i	$0.0265875\pi$
$431$			3.46410i			0.166860i	−0.996514	+	0.0834300i	$0.973413\pi$
$432$		0			0
$433$			6.92820i			0.332948i	0.986046	+	0.166474i	$0.0532382\pi$
$433$			6.92820i			0.332948i	−0.986046	+	0.166474i	$0.946762\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−18.0000	+	10.3923i	−0.861057	+	0.497131i
$438$		0			0
$439$	3.50000	−	6.06218i	0.167046	−	0.289332i	−0.770334	−	0.637641i	$-0.779911\pi$
$439$	3.50000	−	6.06218i	0.167046	−	0.289332i	0.937380	+	0.348309i	$0.113244\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.50000	+	4.33013i	0.356336	+	0.205731i	0.667472	−	0.744635i	$-0.267376\pi$
$443$	7.50000	+	4.33013i	0.356336	+	0.205731i	−0.311136	+	0.950365i	$0.600710\pi$
$444$		0			0
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	9.00000			0.423793
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.50000	+	23.3827i	0.210963	+	1.09620i
$456$		0			0
$457$	6.50000	−	11.2583i	0.304057	−	0.526642i	−0.672994	−	0.739648i	$-0.734992\pi$
$457$	6.50000	−	11.2583i	0.304057	−	0.526642i	0.977051	+	0.213006i	$0.0683253\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	10.5000	+	6.06218i	0.489034	+	0.282344i	0.724174	−	0.689618i	$-0.242221\pi$
$461$	10.5000	+	6.06218i	0.489034	+	0.282344i	−0.235140	+	0.971962i	$0.575555\pi$
$462$		0			0
$463$	−4.50000	+	2.59808i	−0.209133	+	0.120743i	−0.600908	−	0.799318i	$-0.705194\pi$
$463$	−4.50000	+	2.59808i	−0.209133	+	0.120743i	0.391776	+	0.920061i	$0.371861\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$		0			0
$469$	−7.50000	+	21.6506i	−0.346318	+	0.999733i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.50000	−	12.9904i	−0.344850	−	0.597298i
$474$		0			0
$475$	4.00000	−	6.92820i	0.183533	−	0.317888i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.50000	−	7.79423i	0.205610	−	0.356127i	−0.744717	−	0.667381i	$-0.767415\pi$
$479$	4.50000	−	7.79423i	0.205610	−	0.356127i	0.950327	+	0.311253i	$0.100749\pi$
$480$		0			0
$481$	−45.0000	+	25.9808i	−2.05182	+	1.18462i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	9.00000			0.408669
$486$		0			0
$487$			10.3923i			0.470920i	0.971884	+	0.235460i	$0.0756597\pi$
$487$			10.3923i			0.470920i	−0.971884	+	0.235460i	$0.924340\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−13.5000	+	7.79423i	−0.609246	+	0.351749i	−0.772670	−	0.634807i	$-0.781079\pi$
$491$	−13.5000	+	7.79423i	−0.609246	+	0.351749i	0.163424	+	0.986556i	$0.447746\pi$
$492$		0			0
$493$	54.0000	+	31.1769i	2.43204	+	1.40414i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.00000	+	6.92820i	0.269137	+	0.310772i
$498$		0			0
$499$	−22.5000	+	12.9904i	−1.00724	+	0.581529i	−0.910382	−	0.413769i	$-0.864212\pi$
$499$	−22.5000	+	12.9904i	−1.00724	+	0.581529i	−0.0968564	+	0.995298i	$0.530879\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	36.0000			1.60516			0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000			1.60516			0.802580	+	0.596544i	$0.203460\pi$
$504$		0			0
$505$	−33.0000			−1.46848
$506$		0			0
$507$		0			0
$508$		0			0
$509$	16.5000	−	9.52628i	0.731350	−	0.422245i	−0.0875661	−	0.996159i	$-0.527909\pi$
$509$	16.5000	−	9.52628i	0.731350	−	0.422245i	0.818916	+	0.573914i	$0.194576\pi$
$510$		0			0
$511$	−12.0000	−	13.8564i	−0.530849	−	0.612971i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.50000	−	4.33013i	−0.330489	−	0.190808i
$516$		0			0
$517$	−4.50000	+	2.59808i	−0.197910	+	0.114263i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			27.7128i			1.21412i	0.794656	+	0.607060i	$0.207651\pi$
$521$			27.7128i			1.21412i	−0.794656	+	0.607060i	$0.792349\pi$
$522$		0			0
$523$	−8.00000			−0.349816			−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000			−0.349816			−0.174908	+	0.984585i	$0.555963\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−42.0000	+	24.2487i	−1.82955	+	1.05629i
$528$		0			0
$529$	2.00000	−	3.46410i	0.0869565	−	0.150613i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−13.5000	+	23.3827i	−0.584750	+	1.01282i
$534$		0			0
$535$	15.0000	+	25.9808i	0.648507	+	1.12325i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7.50000	−	9.52628i	0.323048	−	0.410326i
$540$		0			0
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.00000	+	1.73205i	−0.128506	+	0.0741929i
$546$		0			0
$547$	−1.50000	−	0.866025i	−0.0641354	−	0.0370286i	0.467589	−	0.883946i	$-0.345123\pi$
$547$	−1.50000	−	0.866025i	−0.0641354	−	0.0370286i	−0.531725	+	0.846917i	$0.678456\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	18.0000	−	31.1769i	0.766826	−	1.32818i
$552$		0			0
$553$	−13.5000	+	2.59808i	−0.574078	+	0.110481i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−42.0000			−1.77960			−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000			−1.77960			−0.889799	+	0.456354i	$0.849155\pi$
$558$		0			0
$559$	45.0000			1.90330
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.50000	−	7.79423i	−0.189652	−	0.328488i	0.755482	−	0.655169i	$-0.227403\pi$
$563$	−4.50000	−	7.79423i	−0.189652	−	0.328488i	−0.945134	+	0.326682i	$0.894069\pi$
$564$		0			0
$565$	−22.5000	−	12.9904i	−0.946582	−	0.546509i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	19.5000	−	33.7750i	0.817483	−	1.41592i	−0.0900490	−	0.995937i	$-0.528702\pi$
$569$	19.5000	−	33.7750i	0.817483	−	1.41592i	0.907532	−	0.419984i	$-0.137964\pi$
$570$		0			0
$571$	−16.5000	+	9.52628i	−0.690504	+	0.398662i	−0.803801	−	0.594899i	$-0.797192\pi$
$571$	−16.5000	+	9.52628i	−0.690504	+	0.398662i	0.113297	+	0.993561i	$0.463859\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			10.3923i			0.433389i
$576$		0			0
$577$			34.6410i			1.44212i	0.692870	+	0.721062i	$0.256346\pi$
$577$			34.6410i			1.44212i	−0.692870	+	0.721062i	$0.743654\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.50000	+	23.3827i	0.186691	+	0.970077i
$582$		0			0
$583$	9.00000	+	5.19615i	0.372742	+	0.215203i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.50000	−	7.79423i	0.185735	−	0.321702i	−0.758089	−	0.652151i	$-0.773867\pi$
$587$	4.50000	−	7.79423i	0.185735	−	0.321702i	0.943824	+	0.330449i	$0.107200\pi$
$588$		0			0
$589$	14.0000	+	24.2487i	0.576860	+	0.999151i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	34.6410i		−	1.42254i	−0.702921	−	0.711268i	$-0.748121\pi$
$593$		−	34.6410i		−	1.42254i	0.702921	−	0.711268i	$-0.251879\pi$
$594$		0			0
$595$	−30.0000	−	10.3923i	−1.22988	−	0.426043i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.50000	+	0.866025i	−0.0612883	+	0.0353848i	−0.530331	−	0.847791i	$-0.677932\pi$
$599$	−1.50000	+	0.866025i	−0.0612883	+	0.0353848i	0.469043	+	0.883175i	$0.344599\pi$
$600$		0			0
$601$	−28.5000	−	16.4545i	−1.16254	−	0.671192i	−0.210628	−	0.977566i	$-0.567551\pi$
$601$	−28.5000	−	16.4545i	−1.16254	−	0.671192i	−0.951911	+	0.306374i	$0.900884\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	12.0000	+	6.92820i	0.487869	+	0.281672i
$606$		0			0
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	0.967256	−	0.253804i	$-0.0816819\pi$
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	−0.703429	+	0.710766i	$0.748349\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	15.5885i		−	0.630641i
$612$		0			0
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	0.894639	−	0.446790i	$-0.147433\pi$
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	−0.834251	+	0.551385i	$0.814100\pi$
$618$		0			0
$619$	17.5000	−	30.3109i	0.703384	−	1.21830i	−0.263887	−	0.964554i	$-0.585005\pi$
$619$	17.5000	−	30.3109i	0.703384	−	1.21830i	0.967271	−	0.253744i	$-0.0816620\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	12.0000	+	13.8564i	0.480770	+	0.555145i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	69.2820i		−	2.76246i
$630$		0			0
$631$			38.1051i			1.51694i	0.651707	+	0.758470i	$0.274053\pi$
$631$			38.1051i			1.51694i	−0.651707	+	0.758470i	$0.725947\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	15.0000	+	25.9808i	0.595257	+	1.03102i
$636$		0			0
$637$	13.5000	+	33.7750i	0.534889	+	1.33821i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	−0.167247	−	0.985915i	$-0.553488\pi$
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	0.937451	−	0.348117i	$-0.113179\pi$
$642$		0			0
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	0.545086	−	0.838380i	$-0.316497\pi$
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	−0.998602	+	0.0528680i	$0.983164\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$		0			0
$649$			5.19615i			0.203967i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.50000	−	7.79423i	−0.176099	−	0.305012i	0.764442	−	0.644692i	$-0.223014\pi$
$653$	−4.50000	−	7.79423i	−0.176099	−	0.305012i	−0.940541	+	0.339680i	$0.889681\pi$
$654$		0			0
$655$	31.5000	+	18.1865i	1.23081	+	0.710607i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−22.5000	−	12.9904i	−0.876476	−	0.506033i	−0.00698084	−	0.999976i	$-0.502222\pi$
$659$	−22.5000	−	12.9904i	−0.876476	−	0.506033i	−0.869495	+	0.493942i	$0.835555\pi$
$660$		0			0
$661$	1.50000	−	0.866025i	0.0583432	−	0.0336845i	−0.470545	−	0.882376i	$-0.655943\pi$
$661$	1.50000	−	0.866025i	0.0583432	−	0.0336845i	0.528888	+	0.848692i	$0.322609\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.00000	+	17.3205i	−0.232670	+	0.671660i
$666$		0			0
$667$			46.7654i			1.81076i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.50000	+	2.59808i	0.0579069	+	0.100298i
$672$		0			0
$673$	−21.5000	+	37.2391i	−0.828764	+	1.43546i	0.0702442	+	0.997530i	$0.477622\pi$
$673$	−21.5000	+	37.2391i	−0.828764	+	1.43546i	−0.899008	+	0.437932i	$0.855711\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19.5000	−	11.2583i	−0.749446	−	0.432693i	0.0760478	−	0.997104i	$-0.475770\pi$
$677$	−19.5000	−	11.2583i	−0.749446	−	0.432693i	−0.825494	+	0.564411i	$0.809103\pi$
$678$		0			0
$679$	13.5000	−	2.59808i	0.518082	−	0.0997050i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			51.9615i			1.98825i	0.108227	+	0.994126i	$0.465483\pi$
$683$			51.9615i			1.98825i	−0.108227	+	0.994126i	$0.534517\pi$
$684$		0			0
$685$			5.19615i			0.198535i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−27.0000	+	15.5885i	−1.02862	+	0.593873i
$690$		0			0
$691$	11.5000	−	19.9186i	0.437481	−	0.757739i	−0.560014	−	0.828483i	$-0.689204\pi$
$691$	11.5000	−	19.9186i	0.437481	−	0.757739i	0.997494	+	0.0707446i	$0.0225375\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.50000	−	4.33013i	−0.284491	−	0.164251i
$696$		0			0
$697$	−18.0000	−	31.1769i	−0.681799	−	1.18091i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	−40.0000			−1.50863
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−49.5000	+	9.52628i	−1.86164	+	0.358273i
$708$		0			0
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	−0.950628	−	0.310334i	$-0.899559\pi$
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	0.744071	+	0.668101i	$0.232892\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−31.5000	−	18.1865i	−1.17968	−	0.681091i
$714$		0			0
$715$	13.5000	−	7.79423i	0.504871	−	0.291488i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−24.0000			−0.895049			−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$		0			0
$721$	−12.5000	−	4.33013i	−0.465524	−	0.161262i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−9.00000	−	15.5885i	−0.334252	−	0.578941i
$726$		0			0
$727$	−12.5000	+	21.6506i	−0.463599	+	0.802978i	−0.999137	−	0.0415337i	$-0.986776\pi$
$727$	−12.5000	+	21.6506i	−0.463599	+	0.802978i	0.535538	+	0.844511i	$0.320109\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−30.0000	+	51.9615i	−1.10959	+	1.92187i
$732$		0			0
$733$	19.5000	−	11.2583i	0.720249	−	0.415836i	−0.0945954	−	0.995516i	$-0.530156\pi$
$733$	19.5000	−	11.2583i	0.720249	−	0.415836i	0.814844	+	0.579680i	$0.196822\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	15.0000			0.552532
$738$		0			0
$739$			24.2487i			0.892003i	0.895032	+	0.446002i	$0.147152\pi$
$739$			24.2487i			0.892003i	−0.895032	+	0.446002i	$0.852848\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−37.5000	+	21.6506i	−1.37574	+	0.794285i	−0.991644	−	0.129008i	$-0.958821\pi$
$743$	−37.5000	+	21.6506i	−1.37574	+	0.794285i	−0.384098	+	0.923292i	$0.625488\pi$
$744$		0			0
$745$	−4.50000	−	2.59808i	−0.164867	−	0.0951861i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	30.0000	+	34.6410i	1.09618	+	1.26576i
$750$		0			0
$751$	−10.5000	+	6.06218i	−0.383150	+	0.221212i	−0.679188	−	0.733964i	$-0.737668\pi$
$751$	−10.5000	+	6.06218i	−0.383150	+	0.221212i	0.296038	+	0.955176i	$0.404335\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	39.0000			1.41936
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.50000	+	4.33013i	−0.271875	+	0.156967i	−0.629739	−	0.776807i	$-0.716838\pi$
$761$	−7.50000	+	4.33013i	−0.271875	+	0.156967i	0.357865	+	0.933774i	$0.383505\pi$
$762$		0			0
$763$	−4.00000	+	3.46410i	−0.144810	+	0.125409i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.5000	−	7.79423i	−0.487457	−	0.281433i
$768$		0			0
$769$	−22.5000	+	12.9904i	−0.811371	+	0.468445i	−0.847432	−	0.530904i	$-0.821852\pi$
$769$	−22.5000	+	12.9904i	−0.811371	+	0.468445i	0.0360609	+	0.999350i	$0.488519\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			41.5692i			1.49514i	0.664183	+	0.747570i	$0.268780\pi$
$773$			41.5692i			1.49514i	−0.664183	+	0.747570i	$0.731220\pi$
$774$		0			0
$775$	14.0000			0.502895
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−18.0000	+	10.3923i	−0.644917	+	0.372343i
$780$		0			0
$781$	3.00000	−	5.19615i	0.107348	−	0.185933i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.50000	+	2.59808i	−0.0535373	+	0.0927293i
$786$		0			0
$787$	2.50000	+	4.33013i	0.0891154	+	0.154352i	0.907137	−	0.420834i	$-0.138263\pi$
$787$	2.50000	+	4.33013i	0.0891154	+	0.154352i	−0.818022	+	0.575187i	$0.804929\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−37.5000	−	12.9904i	−1.33335	−	0.461885i
$792$		0			0
$793$	−9.00000			−0.319599
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.50000	−	2.59808i	0.159398	−	0.0920286i	−0.418179	−	0.908365i	$-0.637332\pi$
$797$	4.50000	−	2.59808i	0.159398	−	0.0920286i	0.577577	+	0.816336i	$0.303998\pi$
$798$		0			0
$799$	18.0000	+	10.3923i	0.636794	+	0.367653i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.00000	+	10.3923i	−0.211735	+	0.366736i
$804$		0			0
$805$	−4.50000	−	23.3827i	−0.158604	−	0.824131i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−6.00000			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$810$		0			0
$811$	52.0000			1.82597			0.912983	−	0.407997i	$-0.133772\pi$
$811$	52.0000			1.82597			0.912983	+	0.407997i	$0.133772\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3.00000	−	5.19615i	−0.105085	−	0.182013i
$816$		0			0
$817$	30.0000	+	17.3205i	1.04957	+	0.605968i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.50000	+	7.79423i	−0.157051	+	0.272020i	−0.933804	−	0.357785i	$-0.883532\pi$
$821$	−4.50000	+	7.79423i	−0.157051	+	0.272020i	0.776753	+	0.629805i	$0.216865\pi$
$822$		0			0
$823$	31.5000	−	18.1865i	1.09802	−	0.633943i	0.162320	−	0.986738i	$-0.448102\pi$
$823$	31.5000	−	18.1865i	1.09802	−	0.633943i	0.935700	+	0.352795i	$0.114769\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	45.0333i		−	1.56596i	−0.622046	−	0.782981i	$-0.713698\pi$
$827$		−	45.0333i		−	1.56596i	0.622046	−	0.782981i	$-0.286302\pi$
$828$		0			0
$829$		−	41.5692i		−	1.44376i	−0.692019	−	0.721879i	$-0.743279\pi$
$829$		−	41.5692i		−	1.44376i	0.692019	−	0.721879i	$-0.256721\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−48.0000	−	6.92820i	−1.66310	−	0.240048i
$834$		0			0
$835$	−4.50000	−	2.59808i	−0.155729	−	0.0899101i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	22.5000	−	38.9711i	0.776786	−	1.34543i	−0.156999	−	0.987599i	$-0.550182\pi$
$839$	22.5000	−	38.9711i	0.776786	−	1.34543i	0.933785	−	0.357834i	$-0.116485\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			24.2487i			0.834181i
$846$		0			0
$847$	20.0000	+	6.92820i	0.687208	+	0.238056i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	45.0000	−	25.9808i	1.54258	−	0.890609i
$852$		0			0
$853$	−46.5000	−	26.8468i	−1.59213	−	0.919216i	−0.992941	−	0.118609i	$-0.962157\pi$
$853$	−46.5000	−	26.8468i	−1.59213	−	0.919216i	−0.599189	−	0.800608i	$-0.704510\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.50000	+	2.59808i	0.153717	+	0.0887486i	0.574886	−	0.818234i	$-0.305047\pi$
$857$	4.50000	+	2.59808i	0.153717	+	0.0887486i	−0.421168	+	0.906982i	$0.638380\pi$
$858$		0			0
$859$	−11.5000	−	19.9186i	−0.392375	−	0.679613i	0.600387	−	0.799709i	$-0.295013\pi$
$859$	−11.5000	−	19.9186i	−0.392375	−	0.679613i	−0.992762	+	0.120096i	$0.961680\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			31.1769i			1.06127i	0.847599	+	0.530637i	$0.178047\pi$
$863$			31.1769i			1.06127i	−0.847599	+	0.530637i	$0.821953\pi$
$864$		0			0
$865$	−9.00000			−0.306009
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.50000	+	7.79423i	0.152652	+	0.264401i
$870$		0			0
$871$	−22.5000	+	38.9711i	−0.762383	+	1.32049i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	21.0000	+	24.2487i	0.709930	+	0.819756i
$876$		0			0
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	0.954652	−	0.297724i	$-0.0962275\pi$
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	−0.735163	+	0.677891i	$0.762894\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			6.92820i			0.233417i	0.993166	+	0.116709i	$0.0372343\pi$
$881$			6.92820i			0.233417i	−0.993166	+	0.116709i	$0.962766\pi$
$882$		0			0
$883$			31.1769i			1.04919i	0.851353	+	0.524593i	$0.175783\pi$
$883$			31.1769i			1.04919i	−0.851353	+	0.524593i	$0.824217\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.50000	+	12.9904i	0.251825	+	0.436174i	0.964028	−	0.265799i	$-0.0856358\pi$
$887$	7.50000	+	12.9904i	0.251825	+	0.436174i	−0.712203	+	0.701974i	$0.752302\pi$
$888$		0			0
$889$	30.0000	+	34.6410i	1.00617	+	1.16182i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.00000	−	10.3923i	0.200782	−	0.347765i
$894$		0			0
$895$	3.00000	+	5.19615i	0.100279	+	0.173688i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	63.0000			2.10117
$900$		0			0
$901$		−	41.5692i		−	1.38487i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	12.0000	+	20.7846i	0.398893	+	0.690904i
$906$		0			0
$907$	−31.5000	−	18.1865i	−1.04594	−	0.603874i	−0.124430	−	0.992228i	$-0.539710\pi$
$907$	−31.5000	−	18.1865i	−1.04594	−	0.603874i	−0.921510	+	0.388354i	$0.873044\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.50000	−	2.59808i	−0.149092	−	0.0860781i	0.423598	−	0.905850i	$-0.360767\pi$
$911$	−4.50000	−	2.59808i	−0.149092	−	0.0860781i	−0.572690	+	0.819772i	$0.694100\pi$
$912$		0			0
$913$	13.5000	−	7.79423i	0.446785	−	0.257951i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	52.5000	+	18.1865i	1.73370	+	0.600572i
$918$		0			0
$919$		−	31.1769i		−	1.02843i	−0.857661	−	0.514216i	$-0.828083\pi$
$919$		−	31.1769i		−	1.02843i	0.857661	−	0.514216i	$-0.171917\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	9.00000	+	15.5885i	0.296239	+	0.513100i
$924$		0			0
$925$	−10.0000	+	17.3205i	−0.328798	+	0.569495i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	16.5000	+	9.52628i	0.541347	+	0.312547i	0.745625	−	0.666366i	$-0.232151\pi$
$929$	16.5000	+	9.52628i	0.541347	+	0.312547i	−0.204277	+	0.978913i	$0.565484\pi$
$930$		0			0
$931$	−4.00000	+	27.7128i	−0.131095	+	0.908251i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			20.7846i			0.679729i
$936$		0			0
$937$		−	34.6410i		−	1.13167i	−0.824518	−	0.565836i	$-0.808553\pi$
$937$		−	34.6410i		−	1.13167i	0.824518	−	0.565836i	$-0.191447\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.5000	−	6.06218i	0.342290	−	0.197621i	−0.318994	−	0.947757i	$-0.603345\pi$
$941$	10.5000	−	6.06218i	0.342290	−	0.197621i	0.661284	+	0.750135i	$0.270012\pi$
$942$		0			0
$943$	13.5000	−	23.3827i	0.439620	−	0.761445i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	37.5000	+	21.6506i	1.21859	+	0.703551i	0.964615	−	0.263661i	$-0.0849300\pi$
$947$	37.5000	+	21.6506i	1.21859	+	0.703551i	0.253971	+	0.967212i	$0.418263\pi$
$948$		0			0
$949$	−18.0000	−	31.1769i	−0.584305	−	1.01205i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	42.0000			1.36051			0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000			1.36051			0.680257	+	0.732974i	$0.261868\pi$
$954$		0			0
$955$	21.0000			0.679544
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.50000	+	7.79423i	0.0484375	+	0.251689i
$960$		0			0
$961$	−9.00000	+	15.5885i	−0.290323	+	0.502853i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−7.50000	−	4.33013i	−0.241434	−	0.139392i
$966$		0			0
$967$	−28.5000	+	16.4545i	−0.916498	+	0.529140i	−0.882516	−	0.470282i	$-0.844152\pi$
$967$	−28.5000	+	16.4545i	−0.916498	+	0.529140i	−0.0339820	+	0.999422i	$0.510819\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−48.0000			−1.54039			−0.770197	−	0.637806i	$-0.779842\pi$
$971$	−48.0000			−1.54039			−0.770197	+	0.637806i	$0.779842\pi$
$972$		0			0
$973$	−12.5000	−	4.33013i	−0.400732	−	0.138817i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−16.5000	−	28.5788i	−0.527882	−	0.914318i	−0.999472	−	0.0325001i	$-0.989653\pi$
$977$	−16.5000	−	28.5788i	−0.527882	−	0.914318i	0.471590	−	0.881818i	$-0.343680\pi$
$978$		0			0
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−7.50000	+	12.9904i	−0.239213	+	0.414329i	−0.960489	−	0.278319i	$-0.910223\pi$
$983$	−7.50000	+	12.9904i	−0.239213	+	0.414329i	0.721276	+	0.692648i	$0.243556\pi$
$984$		0			0
$985$	9.00000	−	5.19615i	0.286764	−	0.165563i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−45.0000			−1.43092
$990$		0			0
$991$		−	17.3205i		−	0.550204i	−0.961415	−	0.275102i	$-0.911288\pi$
$991$		−	17.3205i		−	0.550204i	0.961415	−	0.275102i	$-0.0887116\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	6.00000	−	3.46410i	0.190213	−	0.109819i
$996$		0			0
$997$	31.5000	+	18.1865i	0.997615	+	0.575973i	0.907542	−	0.419962i	$-0.137957\pi$
$997$	31.5000	+	18.1865i	0.997615	+	0.575973i	0.0900732	+	0.995935i	$0.471290\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cx.b.559.1		2
3.2	odd	2		1008.2.cx.f.223.1	yes	2
4.3	odd	2		3024.2.cx.c.559.1		2
7.6	odd	2		3024.2.cx.h.559.1		2
9.4	even	3		3024.2.cx.e.2575.1		2
9.5	odd	6		1008.2.cx.b.895.1	yes	2
12.11	even	2		1008.2.cx.g.223.1	yes	2
21.20	even	2		1008.2.cx.c.223.1	yes	2
28.27	even	2		3024.2.cx.e.559.1		2
36.23	even	6		1008.2.cx.c.895.1	yes	2
36.31	odd	6		3024.2.cx.h.2575.1		2
63.13	odd	6		3024.2.cx.c.2575.1		2
63.41	even	6		1008.2.cx.g.895.1	yes	2
84.83	odd	2		1008.2.cx.b.223.1	✓	2
252.139	even	6	inner	3024.2.cx.b.2575.1		2
252.167	odd	6		1008.2.cx.f.895.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.cx.b.223.1	✓	2	84.83	odd	2
1008.2.cx.b.895.1	yes	2	9.5	odd	6
1008.2.cx.c.223.1	yes	2	21.20	even	2
1008.2.cx.c.895.1	yes	2	36.23	even	6
1008.2.cx.f.223.1	yes	2	3.2	odd	2
1008.2.cx.f.895.1	yes	2	252.167	odd	6
1008.2.cx.g.223.1	yes	2	12.11	even	2
1008.2.cx.g.895.1	yes	2	63.41	even	6
3024.2.cx.b.559.1		2	1.1	even	1	trivial
3024.2.cx.b.2575.1		2	252.139	even	6	inner
3024.2.cx.c.559.1		2	4.3	odd	2
3024.2.cx.c.2575.1		2	63.13	odd	6
3024.2.cx.e.559.1		2	28.27	even	2
3024.2.cx.e.2575.1		2	9.4	even	3
3024.2.cx.h.559.1		2	7.6	odd	2
3024.2.cx.h.2575.1		2	36.31	odd	6

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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cx (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.50000 + 0.866025i) q^{11} +(-4.50000 + 2.59808i) q^{13} -6.92820i q^{17} -4.00000 q^{19} +(4.50000 - 2.59808i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(-4.50000 + 7.79423i) q^{29} +(-3.50000 - 6.06218i) q^{31} +(1.50000 - 4.33013i) q^{35} +10.0000 q^{37} +(4.50000 - 2.59808i) q^{41} +(-7.50000 - 4.33013i) q^{43} +(-1.50000 + 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} +6.00000 q^{53} -3.00000 q^{55} +(1.50000 + 2.59808i) q^{59} +(1.50000 + 0.866025i) q^{61} +(4.50000 - 7.79423i) q^{65} +(7.50000 - 4.33013i) q^{67} -3.46410i q^{71} +6.92820i q^{73} +(-4.50000 + 0.866025i) q^{77} +(4.50000 + 2.59808i) q^{79} +(4.50000 - 7.79423i) q^{83} +(6.00000 + 10.3923i) q^{85} -6.92820i q^{89} +(4.50000 - 12.9904i) q^{91} +(6.00000 - 3.46410i) q^{95} +(-4.50000 - 2.59808i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{5} - 4 q^{7} + 3 q^{11} - 9 q^{13} - 8 q^{19} + 9 q^{23} - 2 q^{25} - 9 q^{29} - 7 q^{31} + 3 q^{35} + 20 q^{37} + 9 q^{41} - 15 q^{43} - 3 q^{47} + 2 q^{49} + 12 q^{53} - 6 q^{55} + 3 q^{59}+ \cdots - 9 q^{97}+O(q^{100}) \) 2 * q - 3 * q^5 - 4 * q^7 + 3 * q^11 - 9 * q^13 - 8 * q^19 + 9 * q^23 - 2 * q^25 - 9 * q^29 - 7 * q^31 + 3 * q^35 + 20 * q^37 + 9 * q^41 - 15 * q^43 - 3 * q^47 + 2 * q^49 + 12 * q^53 - 6 * q^55 + 3 * q^59 + 3 * q^61 + 9 * q^65 + 15 * q^67 - 9 * q^77 + 9 * q^79 + 9 * q^83 + 12 * q^85 + 9 * q^91 + 12 * q^95 - 9 * q^97

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