LMFDB - Embedded newform 2592.2.r.g.433.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2592,2,Mod(433,2592)] 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("2592.433"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2592, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2592 = 2^{5} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2592.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,-4,0,0,0,0,0,0,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$20.6972242039$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			433.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2592.433
Dual form			2592.2.r.g.2161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 - 1.00000i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(-3.46410 - 2.00000i) q^{13} +2.00000 q^{17} +4.00000i q^{19} +(-2.00000 + 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-5.19615 + 3.00000i) q^{29} +(1.00000 - 1.73205i) q^{31} +4.00000i q^{35} -8.00000i q^{37} +(1.00000 - 1.73205i) q^{41} +(-3.46410 + 2.00000i) q^{43} +(6.00000 + 10.3923i) q^{47} +(1.50000 - 2.59808i) q^{49} +6.00000i q^{53} +(3.46410 + 2.00000i) q^{59} +(4.00000 + 6.92820i) q^{65} +(10.3923 + 6.00000i) q^{67} +12.0000 q^{71} -6.00000 q^{73} +(5.00000 + 8.66025i) q^{79} +(-13.8564 + 8.00000i) q^{83} +(-3.46410 - 2.00000i) q^{85} +10.0000 q^{89} +8.00000i q^{91} +(4.00000 - 6.92820i) q^{95} +(1.00000 + 1.73205i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{7} + 8 q^{17} - 8 q^{23} - 2 q^{25} + 4 q^{31} + 4 q^{41} + 24 q^{47} + 6 q^{49} + 16 q^{65} + 48 q^{71} - 24 q^{73} + 20 q^{79} + 40 q^{89} + 16 q^{95} + 4 q^{97}+O(q^{100}) $ 4 * q - 4 * q^7 + 8 * q^17 - 8 * q^23 - 2 * q^25 + 4 * q^31 + 4 * q^41 + 24 * q^47 + 6 * q^49 + 16 * q^65 + 48 * q^71 - 24 * q^73 + 20 * q^79 + 40 * q^89 + 16 * q^95 + 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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
$5$	−1.73205	−	1.00000i	−0.774597	−	0.447214i	0.0599153	−	0.998203i	$-0.480917\pi$
$5$	−1.73205	−	1.00000i	−0.774597	−	0.447214i	−0.834512	+	0.550990i	$0.814250\pi$
$6$		0			0
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$		0			0
$13$	−3.46410	−	2.00000i	−0.960769	−	0.554700i	−0.0643593	−	0.997927i	$-0.520500\pi$
$13$	−3.46410	−	2.00000i	−0.960769	−	0.554700i	−0.896410	+	0.443227i	$0.853834\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.19615	+	3.00000i	−0.964901	+	0.557086i	−0.897678	−	0.440652i	$-0.854747\pi$
$29$	−5.19615	+	3.00000i	−0.964901	+	0.557086i	−0.0672232	+	0.997738i	$0.521414\pi$
$30$		0			0
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			4.00000i			0.676123i
$36$		0			0
$37$		−	8.00000i		−	1.31519i	−0.753371	−	0.657596i	$-0.771573\pi$
$37$		−	8.00000i		−	1.31519i	0.753371	−	0.657596i	$-0.228427\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	−0.777312	−	0.629115i	$-0.783417\pi$
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	0.933486	+	0.358614i	$0.116751\pi$
$42$		0			0
$43$	−3.46410	+	2.00000i	−0.528271	+	0.304997i	−0.740312	−	0.672264i	$-0.765322\pi$
$43$	−3.46410	+	2.00000i	−0.528271	+	0.304997i	0.212041	+	0.977261i	$0.431989\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.856560	+	0.516047i	$0.172597\pi$
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.0186297	+	0.999826i	$0.494070\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.46410	+	2.00000i	0.450988	+	0.260378i	0.708247	−	0.705965i	$-0.249486\pi$
$59$	3.46410	+	2.00000i	0.450988	+	0.260378i	−0.257260	+	0.966342i	$0.582820\pi$
$60$		0			0
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.00000	+	6.92820i	0.496139	+	0.859338i
$66$		0			0
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.974916	−	0.222571i	$-0.0714450\pi$
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.294706	+	0.955588i	$0.404778\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−13.8564	+	8.00000i	−1.52094	+	0.878114i	−0.521243	+	0.853408i	$0.674532\pi$
$83$	−13.8564	+	8.00000i	−1.52094	+	0.878114i	−0.999695	+	0.0247060i	$0.992135\pi$
$84$		0			0
$85$	−3.46410	−	2.00000i	−0.375735	−	0.216930i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$		0			0
$91$			8.00000i			0.838628i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.00000	−	6.92820i	0.410391	−	0.710819i
$96$		0			0
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.66025	+	5.00000i	−0.861727	+	0.497519i	−0.864590	−	0.502477i	$-0.832422\pi$
$101$	−8.66025	+	5.00000i	−0.861727	+	0.497519i	0.00286291	+	0.999996i	$0.499089\pi$
$102$		0			0
$103$	−3.00000	+	5.19615i	−0.295599	+	0.511992i	−0.975124	−	0.221660i	$-0.928852\pi$
$103$	−3.00000	+	5.19615i	−0.295599	+	0.511992i	0.679525	+	0.733652i	$0.262186\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			12.0000i			1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$			12.0000i			1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$		0			0
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$		0			0
$115$	6.92820	−	4.00000i	0.646058	−	0.373002i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.00000	−	3.46410i	−0.183340	−	0.317554i
$120$		0			0
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			12.0000i			1.07331i
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−17.3205	−	10.0000i	−1.51330	−	0.873704i	−0.999879	−	0.0155672i	$-0.995045\pi$
$131$	−17.3205	−	10.0000i	−1.51330	−	0.873704i	−0.513421	−	0.858137i	$-0.671622\pi$
$132$		0			0
$133$	6.92820	−	4.00000i	0.600751	−	0.346844i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	0.938148	+	0.346235i	$0.112540\pi$
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	−0.169226	+	0.985577i	$0.554127\pi$
$138$		0			0
$139$	−3.46410	−	2.00000i	−0.293821	−	0.169638i	0.345843	−	0.938293i	$-0.387593\pi$
$139$	−3.46410	−	2.00000i	−0.293821	−	0.169638i	−0.639664	+	0.768655i	$0.720926\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$	12.0000			0.996546
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	0.697507	−	0.716578i	$-0.254293\pi$
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	−0.271821	+	0.962348i	$0.587626\pi$
$150$		0			0
$151$	−9.00000	−	15.5885i	−0.732410	−	1.26857i	−0.955851	−	0.293853i	$-0.905062\pi$
$151$	−9.00000	−	15.5885i	−0.732410	−	1.26857i	0.223441	−	0.974717i	$-0.428271\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.46410	+	2.00000i	−0.278243	+	0.160644i
$156$		0			0
$157$	6.92820	+	4.00000i	0.552931	+	0.319235i	0.750303	−	0.661094i	$-0.229907\pi$
$157$	6.92820	+	4.00000i	0.552931	+	0.319235i	−0.197372	+	0.980329i	$0.563241\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.00000			0.630488
$162$		0			0
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	−0.978259	−	0.207385i	$-0.933505\pi$
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	0.668730	+	0.743505i	$0.266838\pi$
$168$		0			0
$169$	1.50000	+	2.59808i	0.115385	+	0.199852i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.19615	−	3.00000i	0.395056	−	0.228086i	−0.289292	−	0.957241i	$-0.593420\pi$
$173$	5.19615	−	3.00000i	0.395056	−	0.228086i	0.684349	+	0.729155i	$0.260087\pi$
$174$		0			0
$175$	−1.00000	+	1.73205i	−0.0755929	+	0.130931i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	4.00000i		−	0.298974i	−0.988764	−	0.149487i	$-0.952238\pi$
$179$		−	4.00000i		−	0.298974i	0.988764	−	0.149487i	$-0.0477622\pi$
$180$		0			0
$181$			20.0000i			1.48659i	0.668965	+	0.743294i	$0.266738\pi$
$181$			20.0000i			1.48659i	−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−8.00000	+	13.8564i	−0.588172	+	1.01874i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$		0			0
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	−0.737620	−	0.675216i	$-0.764050\pi$
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	0.953564	+	0.301189i	$0.0973836\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$		0			0
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.3923	+	6.00000i	0.729397	+	0.421117i
$204$		0			0
$205$	−3.46410	+	2.00000i	−0.241943	+	0.139686i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−17.3205	−	10.0000i	−1.19239	−	0.688428i	−0.233544	−	0.972346i	$-0.575032\pi$
$211$	−17.3205	−	10.0000i	−1.19239	−	0.688428i	−0.958849	+	0.283918i	$0.908366\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.00000			0.545595
$216$		0			0
$217$	−4.00000			−0.271538
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−6.92820	−	4.00000i	−0.466041	−	0.269069i
$222$		0			0
$223$	7.00000	+	12.1244i	0.468755	+	0.811907i	0.999362	−	0.0357107i	$-0.0113695\pi$
$223$	7.00000	+	12.1244i	0.468755	+	0.811907i	−0.530607	+	0.847618i	$0.678036\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.92820	+	4.00000i	−0.459841	+	0.265489i	−0.711977	−	0.702202i	$-0.752200\pi$
$227$	−6.92820	+	4.00000i	−0.459841	+	0.265489i	0.252136	+	0.967692i	$0.418867\pi$
$228$		0			0
$229$	3.46410	+	2.00000i	0.228914	+	0.132164i	0.610071	−	0.792347i	$-0.291141\pi$
$229$	3.46410	+	2.00000i	0.228914	+	0.132164i	−0.381157	+	0.924510i	$0.624474\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.0000			−0.917170			−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000			−0.917170			−0.458585	+	0.888650i	$0.651644\pi$
$234$		0			0
$235$		−	24.0000i		−	1.56559i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	0.832019	−	0.554747i	$-0.187185\pi$
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	−0.896435	+	0.443176i	$0.853852\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.19615	+	3.00000i	−0.331970	+	0.191663i
$246$		0			0
$247$	8.00000	−	13.8564i	0.509028	−	0.881662i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$		0			0
$259$	−13.8564	+	8.00000i	−0.860995	+	0.497096i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	0.999970	−	0.00771799i	$-0.00245674\pi$
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	−0.506669	+	0.862141i	$0.669123\pi$
$264$		0			0
$265$	6.00000	−	10.3923i	0.368577	−	0.638394i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	6.00000i		−	0.365826i	−0.983129	−	0.182913i	$-0.941447\pi$
$269$		−	6.00000i		−	0.365826i	0.983129	−	0.182913i	$-0.0585527\pi$
$270$		0			0
$271$	18.0000			1.09342			0.546711	−	0.837321i	$-0.315880\pi$
$271$	18.0000			1.09342			0.546711	+	0.837321i	$0.315880\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−24.2487	+	14.0000i	−1.45696	+	0.841178i	−0.998861	−	0.0477206i	$-0.984804\pi$
$277$	−24.2487	+	14.0000i	−1.45696	+	0.841178i	−0.458103	+	0.888899i	$0.651471\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.00000	−	15.5885i	−0.536895	−	0.929929i	−0.999069	−	0.0431402i	$-0.986264\pi$
$281$	−9.00000	−	15.5885i	−0.536895	−	0.929929i	0.462174	−	0.886789i	$-0.347070\pi$
$282$		0			0
$283$	3.46410	+	2.00000i	0.205919	+	0.118888i	0.599414	−	0.800439i	$-0.295400\pi$
$283$	3.46410	+	2.00000i	0.205919	+	0.118888i	−0.393494	+	0.919327i	$0.628734\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.00000			−0.236113
$288$		0			0
$289$	−13.0000			−0.764706
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.19615	−	3.00000i	−0.303562	−	0.175262i	0.340480	−	0.940252i	$-0.389411\pi$
$293$	−5.19615	−	3.00000i	−0.303562	−	0.175262i	−0.644042	+	0.764990i	$0.722744\pi$
$294$		0			0
$295$	−4.00000	−	6.92820i	−0.232889	−	0.403376i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	13.8564	−	8.00000i	0.801337	−	0.462652i
$300$		0			0
$301$	6.92820	+	4.00000i	0.399335	+	0.230556i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	12.0000i		−	0.684876i	−0.939540	−	0.342438i	$-0.888747\pi$
$307$		−	12.0000i		−	0.684876i	0.939540	−	0.342438i	$-0.111253\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	−0.730044	−	0.683400i	$-0.760501\pi$
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	0.956864	+	0.290537i	$0.0938340\pi$
$312$		0			0
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	0.597522	−	0.801852i	$-0.296152\pi$
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	−0.993186	+	0.116543i	$0.962819\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−19.0526	+	11.0000i	−1.07010	+	0.617822i	−0.928208	−	0.372061i	$-0.878651\pi$
$317$	−19.0526	+	11.0000i	−1.07010	+	0.617822i	−0.141890	+	0.989882i	$0.545318\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$			8.00000i			0.445132i
$324$		0			0
$325$			4.00000i			0.221880i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.0000	−	20.7846i	0.661581	−	1.14589i
$330$		0			0
$331$	17.3205	−	10.0000i	0.952021	−	0.549650i	0.0583130	−	0.998298i	$-0.481428\pi$
$331$	17.3205	−	10.0000i	0.952021	−	0.549650i	0.893708	+	0.448649i	$0.148095\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−12.0000	−	20.7846i	−0.655630	−	1.13558i
$336$		0			0
$337$	1.00000	−	1.73205i	0.0544735	−	0.0943508i	−0.837503	−	0.546433i	$-0.815985\pi$
$337$	1.00000	−	1.73205i	0.0544735	−	0.0943508i	0.891976	+	0.452082i	$0.149319\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−20.0000			−1.07990
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.92820	+	4.00000i	0.371925	+	0.214731i	0.674299	−	0.738458i	$-0.264446\pi$
$347$	6.92820	+	4.00000i	0.371925	+	0.214731i	−0.302374	+	0.953189i	$0.597779\pi$
$348$		0			0
$349$	13.8564	−	8.00000i	0.741716	−	0.428230i	−0.0809766	−	0.996716i	$-0.525804\pi$
$349$	13.8564	−	8.00000i	0.741716	−	0.428230i	0.822693	+	0.568486i	$0.192471\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$		0			0
$355$	−20.7846	−	12.0000i	−1.10313	−	0.636894i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−20.0000			−1.05556			−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000			−1.05556			−0.527780	+	0.849381i	$0.676975\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$		0			0
$363$		0			0
$364$		0			0
$365$	10.3923	+	6.00000i	0.543958	+	0.314054i
$366$		0			0
$367$	9.00000	+	15.5885i	0.469796	+	0.813711i	0.999404	−	0.0345320i	$-0.0109941\pi$
$367$	9.00000	+	15.5885i	0.469796	+	0.813711i	−0.529607	+	0.848243i	$0.677661\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	10.3923	−	6.00000i	0.539542	−	0.311504i
$372$		0			0
$373$	13.8564	+	8.00000i	0.717458	+	0.414224i	0.813816	−	0.581122i	$-0.197386\pi$
$373$	13.8564	+	8.00000i	0.717458	+	0.414224i	−0.0963587	+	0.995347i	$0.530720\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	24.0000			1.23606
$378$		0			0
$379$			4.00000i			0.205466i	0.994709	+	0.102733i	$0.0327588\pi$
$379$			4.00000i			0.205466i	−0.994709	+	0.102733i	$0.967241\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	0.377531	+	0.925997i	$0.376773\pi$
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	−0.990702	+	0.136047i	$0.956560\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	29.4449	−	17.0000i	1.49291	−	0.861934i	0.492947	−	0.870059i	$-0.335920\pi$
$389$	29.4449	−	17.0000i	1.49291	−	0.861934i	0.999967	+	0.00812520i	$0.00258636\pi$
$390$		0			0
$391$	−4.00000	+	6.92820i	−0.202289	+	0.350374i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	20.0000i		−	1.00631i
$396$		0			0
$397$			32.0000i			1.60603i	0.595956	+	0.803017i	$0.296773\pi$
$397$			32.0000i			1.60603i	−0.595956	+	0.803017i	$0.703227\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$		0			0
$403$	−6.92820	+	4.00000i	−0.345118	+	0.199254i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	8.00000i		−	0.393654i
$414$		0			0
$415$	32.0000			1.57082
$416$		0			0
$417$		0			0
$418$		0			0
$419$	20.7846	+	12.0000i	1.01539	+	0.586238i	0.912767	−	0.408481i	$-0.133942\pi$
$419$	20.7846	+	12.0000i	1.01539	+	0.586238i	0.102628	+	0.994720i	$0.467275\pi$
$420$		0			0
$421$	17.3205	−	10.0000i	0.844150	−	0.487370i	−0.0145228	−	0.999895i	$-0.504623\pi$
$421$	17.3205	−	10.0000i	0.844150	−	0.487370i	0.858673	+	0.512524i	$0.171290\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−13.8564	−	8.00000i	−0.662842	−	0.382692i
$438$		0			0
$439$	−15.0000	−	25.9808i	−0.715911	−	1.23999i	−0.962607	−	0.270901i	$-0.912678\pi$
$439$	−15.0000	−	25.9808i	−0.715911	−	1.23999i	0.246696	−	0.969093i	$-0.420655\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	20.7846	−	12.0000i	0.987507	−	0.570137i	0.0829786	−	0.996551i	$-0.473557\pi$
$443$	20.7846	−	12.0000i	0.987507	−	0.570137i	0.904528	+	0.426414i	$0.140223\pi$
$444$		0			0
$445$	−17.3205	−	10.0000i	−0.821071	−	0.474045i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$	8.00000	−	13.8564i	0.375046	−	0.649598i
$456$		0			0
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	0.999857	+	0.0168929i	$0.00537742\pi$
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	−0.485299	+	0.874348i	$0.661289\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	25.9808	−	15.0000i	1.21004	−	0.698620i	0.247276	−	0.968945i	$-0.420465\pi$
$461$	25.9808	−	15.0000i	1.21004	−	0.698620i	0.962769	+	0.270326i	$0.0871313\pi$
$462$		0			0
$463$	−13.0000	+	22.5167i	−0.604161	+	1.04644i	0.388022	+	0.921650i	$0.373158\pi$
$463$	−13.0000	+	22.5167i	−0.604161	+	1.04644i	−0.992183	+	0.124788i	$0.960175\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	8.00000i		−	0.370196i	−0.982720	−	0.185098i	$-0.940740\pi$
$467$		−	8.00000i		−	0.370196i	0.982720	−	0.185098i	$-0.0592602\pi$
$468$		0			0
$469$		−	24.0000i		−	1.10822i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	3.46410	−	2.00000i	0.158944	−	0.0917663i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−10.0000	−	17.3205i	−0.456912	−	0.791394i	0.541884	−	0.840453i	$-0.317711\pi$
$479$	−10.0000	−	17.3205i	−0.456912	−	0.791394i	−0.998796	+	0.0490589i	$0.984378\pi$
$480$		0			0
$481$	−16.0000	+	27.7128i	−0.729537	+	1.26360i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	4.00000i		−	0.181631i
$486$		0			0
$487$	−38.0000			−1.72194			−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000			−1.72194			−0.860972	+	0.508652i	$0.830144\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.3205	−	10.0000i	−0.781664	−	0.451294i	0.0553560	−	0.998467i	$-0.482371\pi$
$491$	−17.3205	−	10.0000i	−0.781664	−	0.451294i	−0.837020	+	0.547173i	$0.815704\pi$
$492$		0			0
$493$	−10.3923	+	6.00000i	−0.468046	+	0.270226i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.0000	−	20.7846i	−0.538274	−	0.932317i
$498$		0			0
$499$	31.1769	+	18.0000i	1.39567	+	0.805791i	0.993935	−	0.109965i	$-0.0350740\pi$
$499$	31.1769	+	18.0000i	1.39567	+	0.805791i	0.401735	+	0.915756i	$0.368407\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−36.0000			−1.60516			−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000			−1.60516			−0.802580	+	0.596544i	$0.796540\pi$
$504$		0			0
$505$	20.0000			0.889988
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.19615	+	3.00000i	0.230315	+	0.132973i	0.610718	−	0.791849i	$-0.290881\pi$
$509$	5.19615	+	3.00000i	0.230315	+	0.132973i	−0.380402	+	0.924821i	$0.624214\pi$
$510$		0			0
$511$	6.00000	+	10.3923i	0.265424	+	0.459728i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	10.3923	−	6.00000i	0.457940	−	0.264392i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−42.0000			−1.84005			−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000			−1.84005			−0.920027	+	0.391856i	$0.871833\pi$
$522$		0			0
$523$			36.0000i			1.57417i	0.616844	+	0.787085i	$0.288411\pi$
$523$			36.0000i			1.57417i	−0.616844	+	0.787085i	$0.711589\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.00000	−	3.46410i	0.0871214	−	0.150899i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−6.92820	+	4.00000i	−0.300094	+	0.173259i
$534$		0			0
$535$	12.0000	−	20.7846i	0.518805	−	0.898597i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$		−	20.0000i		−	0.859867i	−0.902861	−	0.429934i	$-0.858537\pi$
$541$		−	20.0000i		−	0.859867i	0.902861	−	0.429934i	$-0.141463\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−4.00000	+	6.92820i	−0.171341	+	0.296772i
$546$		0			0
$547$	24.2487	−	14.0000i	1.03680	−	0.598597i	0.117875	−	0.993028i	$-0.462392\pi$
$547$	24.2487	−	14.0000i	1.03680	−	0.598597i	0.918925	+	0.394432i	$0.129059\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−12.0000	−	20.7846i	−0.511217	−	0.885454i
$552$		0			0
$553$	10.0000	−	17.3205i	0.425243	−	0.736543i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	42.0000i		−	1.77960i	−0.456354	−	0.889799i	$-0.650845\pi$
$557$		−	42.0000i		−	1.77960i	0.456354	−	0.889799i	$-0.349155\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−20.7846	−	12.0000i	−0.875967	−	0.505740i	−0.00664037	−	0.999978i	$-0.502114\pi$
$563$	−20.7846	−	12.0000i	−0.875967	−	0.505740i	−0.869326	+	0.494238i	$0.835447\pi$
$564$		0			0
$565$	10.3923	−	6.00000i	0.437208	−	0.252422i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	−0.987786	−	0.155815i	$-0.950200\pi$
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	0.358954	−	0.933355i	$-0.383134\pi$
$570$		0			0
$571$	17.3205	+	10.0000i	0.724841	+	0.418487i	0.816532	−	0.577301i	$-0.195894\pi$
$571$	17.3205	+	10.0000i	0.724841	+	0.418487i	−0.0916910	+	0.995788i	$0.529227\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.00000			0.166812
$576$		0			0
$577$	−42.0000			−1.74848			−0.874241	−	0.485491i	$-0.838641\pi$
$577$	−42.0000			−1.74848			−0.874241	+	0.485491i	$0.838641\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	27.7128	+	16.0000i	1.14972	+	0.663792i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−24.2487	+	14.0000i	−1.00085	+	0.577842i	−0.908500	−	0.417885i	$-0.862772\pi$
$587$	−24.2487	+	14.0000i	−1.00085	+	0.577842i	−0.0923513	+	0.995726i	$0.529438\pi$
$588$		0			0
$589$	6.92820	+	4.00000i	0.285472	+	0.164817i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$			8.00000i			0.327968i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10.0000	−	17.3205i	0.408589	−	0.707697i	−0.586143	−	0.810208i	$-0.699354\pi$
$599$	10.0000	−	17.3205i	0.408589	−	0.707697i	0.994732	+	0.102511i	$0.0326876\pi$
$600$		0			0
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	0.844909	−	0.534910i	$-0.179654\pi$
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	−0.885700	+	0.464258i	$0.846321\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	19.0526	−	11.0000i	0.774597	−	0.447214i
$606$		0			0
$607$	−1.00000	+	1.73205i	−0.0405887	+	0.0703018i	−0.885606	−	0.464437i	$-0.846257\pi$
$607$	−1.00000	+	1.73205i	−0.0405887	+	0.0703018i	0.845017	+	0.534739i	$0.179590\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	48.0000i		−	1.94187i
$612$		0			0
$613$		−	16.0000i		−	0.646234i	−0.946359	−	0.323117i	$-0.895269\pi$
$613$		−	16.0000i		−	0.646234i	0.946359	−	0.323117i	$-0.104731\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.00000	+	1.73205i	−0.0402585	+	0.0697297i	−0.885453	−	0.464730i	$-0.846151\pi$
$617$	−1.00000	+	1.73205i	−0.0402585	+	0.0697297i	0.845194	+	0.534460i	$0.179485\pi$
$618$		0			0
$619$	−31.1769	+	18.0000i	−1.25311	+	0.723481i	−0.971725	−	0.236115i	$-0.924126\pi$
$619$	−31.1769	+	18.0000i	−1.25311	+	0.723481i	−0.281381	+	0.959596i	$0.590792\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−10.0000	−	17.3205i	−0.400642	−	0.693932i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	16.0000i		−	0.637962i
$630$		0			0
$631$	−22.0000			−0.875806			−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000			−0.875806			−0.437903	+	0.899022i	$0.644279\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.46410	−	2.00000i	−0.137469	−	0.0793676i
$636$		0			0
$637$	−10.3923	+	6.00000i	−0.411758	+	0.237729i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	11.0000	+	19.0526i	0.434474	+	0.752531i	0.997253	−	0.0740768i	$-0.0236010\pi$
$641$	11.0000	+	19.0526i	0.434474	+	0.752531i	−0.562779	+	0.826608i	$0.690268\pi$
$642$		0			0
$643$	3.46410	+	2.00000i	0.136611	+	0.0788723i	0.566748	−	0.823891i	$-0.308201\pi$
$643$	3.46410	+	2.00000i	0.136611	+	0.0788723i	−0.430137	+	0.902764i	$0.641535\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.19615	−	3.00000i	−0.203341	−	0.117399i	0.394872	−	0.918736i	$-0.370789\pi$
$653$	−5.19615	−	3.00000i	−0.203341	−	0.117399i	−0.598213	+	0.801337i	$0.704122\pi$
$654$		0			0
$655$	20.0000	+	34.6410i	0.781465	+	1.35354i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	31.1769	−	18.0000i	1.21448	−	0.701180i	0.250748	−	0.968052i	$-0.419323\pi$
$659$	31.1769	−	18.0000i	1.21448	−	0.701180i	0.963732	+	0.266872i	$0.0859901\pi$
$660$		0			0
$661$	−34.6410	−	20.0000i	−1.34738	−	0.777910i	−0.359502	−	0.933144i	$-0.617053\pi$
$661$	−34.6410	−	20.0000i	−1.34738	−	0.777910i	−0.987878	+	0.155235i	$0.950387\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−16.0000			−0.620453
$666$		0			0
$667$		−	24.0000i		−	0.929284i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	0.698988	−	0.715134i	$-0.253634\pi$
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	−0.968818	+	0.247774i	$0.920301\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.5885	−	9.00000i	0.599113	−	0.345898i	−0.169580	−	0.985517i	$-0.554241\pi$
$677$	15.5885	−	9.00000i	0.599113	−	0.345898i	0.768693	+	0.639618i	$0.220908\pi$
$678$		0			0
$679$	2.00000	−	3.46410i	0.0767530	−	0.132940i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	16.0000i		−	0.612223i	−0.951996	−	0.306111i	$-0.900972\pi$
$683$		−	16.0000i		−	0.612223i	0.951996	−	0.306111i	$-0.0990280\pi$
$684$		0			0
$685$		−	36.0000i		−	1.37549i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$		0			0
$691$	−17.3205	+	10.0000i	−0.658903	+	0.380418i	−0.791859	−	0.610704i	$-0.790887\pi$
$691$	−17.3205	+	10.0000i	−0.658903	+	0.380418i	0.132956	+	0.991122i	$0.457553\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.00000	+	6.92820i	0.151729	+	0.262802i
$696$		0			0
$697$	2.00000	−	3.46410i	0.0757554	−	0.131212i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			50.0000i			1.88847i	0.329267	+	0.944237i	$0.393198\pi$
$701$			50.0000i			1.88847i	−0.329267	+	0.944237i	$0.606802\pi$
$702$		0			0
$703$	32.0000			1.20690
$704$		0			0
$705$		0			0
$706$		0			0
$707$	17.3205	+	10.0000i	0.651405	+	0.376089i
$708$		0			0
$709$	−3.46410	+	2.00000i	−0.130097	+	0.0751116i	−0.563636	−	0.826023i	$-0.690598\pi$
$709$	−3.46410	+	2.00000i	−0.130097	+	0.0751116i	0.433539	+	0.901135i	$0.357265\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.00000	+	6.92820i	0.149801	+	0.259463i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−20.0000			−0.745874			−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000			−0.745874			−0.372937	+	0.927857i	$0.621649\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$		0			0
$723$		0			0
$724$		0			0
$725$	5.19615	+	3.00000i	0.192980	+	0.111417i
$726$		0			0
$727$	−21.0000	−	36.3731i	−0.778847	−	1.34900i	−0.932607	−	0.360894i	$-0.882472\pi$
$727$	−21.0000	−	36.3731i	−0.778847	−	1.34900i	0.153760	−	0.988108i	$-0.450862\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.92820	+	4.00000i	−0.256249	+	0.147945i
$732$		0			0
$733$	−3.46410	−	2.00000i	−0.127950	−	0.0738717i	0.434659	−	0.900595i	$-0.356869\pi$
$733$	−3.46410	−	2.00000i	−0.127950	−	0.0738717i	−0.562609	+	0.826723i	$0.690202\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$			44.0000i			1.61857i	0.587419	+	0.809283i	$0.300144\pi$
$739$			44.0000i			1.61857i	−0.587419	+	0.809283i	$0.699856\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	8.00000	−	13.8564i	0.293492	−	0.508342i	−0.681141	−	0.732152i	$-0.738516\pi$
$743$	8.00000	−	13.8564i	0.293492	−	0.508342i	0.974633	+	0.223810i	$0.0718494\pi$
$744$		0			0
$745$	−6.00000	−	10.3923i	−0.219823	−	0.380745i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	20.7846	−	12.0000i	0.759453	−	0.438470i
$750$		0			0
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	−0.847203	−	0.531269i	$-0.821715\pi$
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	0.883694	+	0.468065i	$0.155049\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			36.0000i			1.31017i
$756$		0			0
$757$			12.0000i			0.436147i	0.975932	+	0.218074i	$0.0699773\pi$
$757$			12.0000i			0.436147i	−0.975932	+	0.218074i	$0.930023\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−19.0000	+	32.9090i	−0.688749	+	1.19295i	0.283493	+	0.958974i	$0.408507\pi$
$761$	−19.0000	+	32.9090i	−0.688749	+	1.19295i	−0.972243	+	0.233975i	$0.924827\pi$
$762$		0			0
$763$	−6.92820	+	4.00000i	−0.250818	+	0.144810i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.00000	−	13.8564i	−0.288863	−	0.500326i
$768$		0			0
$769$	−5.00000	+	8.66025i	−0.180305	+	0.312297i	−0.941984	−	0.335657i	$-0.891042\pi$
$769$	−5.00000	+	8.66025i	−0.180305	+	0.312297i	0.761680	+	0.647954i	$0.224375\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	34.0000i		−	1.22290i	−0.791285	−	0.611448i	$-0.790588\pi$
$773$		−	34.0000i		−	1.22290i	0.791285	−	0.611448i	$-0.209412\pi$
$774$		0			0
$775$	−2.00000			−0.0718421
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.92820	+	4.00000i	0.248229	+	0.143315i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−8.00000	−	13.8564i	−0.285532	−	0.494556i
$786$		0			0
$787$	10.3923	+	6.00000i	0.370446	+	0.213877i	0.673653	−	0.739048i	$-0.264724\pi$
$787$	10.3923	+	6.00000i	0.370446	+	0.213877i	−0.303207	+	0.952925i	$0.598058\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	12.0000			0.426671
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.73205	+	1.00000i	0.0613524	+	0.0354218i	0.530362	−	0.847771i	$-0.322056\pi$
$797$	1.73205	+	1.00000i	0.0613524	+	0.0354218i	−0.469010	+	0.883193i	$0.655389\pi$
$798$		0			0
$799$	12.0000	+	20.7846i	0.424529	+	0.735307i
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−13.8564	−	8.00000i	−0.488374	−	0.281963i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	30.0000			1.05474			0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$		0			0
$811$			20.0000i			0.702295i	0.936320	+	0.351147i	$0.114208\pi$
$811$			20.0000i			0.702295i	−0.936320	+	0.351147i	$0.885792\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4.00000	+	6.92820i	−0.140114	+	0.242684i
$816$		0			0
$817$	−8.00000	−	13.8564i	−0.279885	−	0.484774i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.66025	+	5.00000i	−0.302245	+	0.174501i	−0.643451	−	0.765487i	$-0.722498\pi$
$821$	−8.66025	+	5.00000i	−0.302245	+	0.174501i	0.341206	+	0.939989i	$0.389165\pi$
$822$		0			0
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	−0.717847	−	0.696201i	$-0.754872\pi$
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	0.961851	+	0.273573i	$0.0882054\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$		0			0
$829$		−	4.00000i		−	0.138926i	−0.997585	−	0.0694629i	$-0.977871\pi$
$829$		−	4.00000i		−	0.138926i	0.997585	−	0.0694629i	$-0.0221285\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.00000	−	5.19615i	0.103944	−	0.180036i
$834$		0			0
$835$	13.8564	−	8.00000i	0.479521	−	0.276851i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−10.0000	−	17.3205i	−0.345238	−	0.597970i	0.640159	−	0.768243i	$-0.278869\pi$
$839$	−10.0000	−	17.3205i	−0.345238	−	0.597970i	−0.985397	+	0.170272i	$0.945535\pi$
$840$		0			0
$841$	3.50000	−	6.06218i	0.120690	−	0.209041i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	6.00000i		−	0.206406i
$846$		0			0
$847$	22.0000			0.755929
$848$		0			0
$849$		0			0
$850$		0			0
$851$	27.7128	+	16.0000i	0.949983	+	0.548473i
$852$		0			0
$853$	20.7846	−	12.0000i	0.711651	−	0.410872i	−0.100021	−	0.994985i	$-0.531891\pi$
$853$	20.7846	−	12.0000i	0.711651	−	0.410872i	0.811672	+	0.584113i	$0.198558\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	0.977800	−	0.209539i	$-0.0671963\pi$
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	−0.670366	+	0.742030i	$0.733863\pi$
$858$		0			0
$859$	−38.1051	−	22.0000i	−1.30013	−	0.750630i	−0.319704	−	0.947518i	$-0.603583\pi$
$859$	−38.1051	−	22.0000i	−1.30013	−	0.750630i	−0.980426	+	0.196887i	$0.936917\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		0			0
$865$	−12.0000			−0.408012
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−24.0000	−	41.5692i	−0.813209	−	1.40852i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	20.7846	−	12.0000i	0.702648	−	0.405674i
$876$		0			0
$877$	−27.7128	−	16.0000i	−0.935795	−	0.540282i	−0.0471555	−	0.998888i	$-0.515016\pi$
$877$	−27.7128	−	16.0000i	−0.935795	−	0.540282i	−0.888640	+	0.458606i	$0.848349\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$		0			0
$883$		−	4.00000i		−	0.134611i	−0.997732	−	0.0673054i	$-0.978560\pi$
$883$		−	4.00000i		−	0.134611i	0.997732	−	0.0673054i	$-0.0214402\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	0.109881	+	0.993945i	$0.464953\pi$
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	−0.915722	+	0.401813i	$0.868380\pi$
$888$		0			0
$889$	−2.00000	−	3.46410i	−0.0670778	−	0.116182i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−41.5692	+	24.0000i	−1.39106	+	0.803129i
$894$		0			0
$895$	−4.00000	+	6.92820i	−0.133705	+	0.231584i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			12.0000i			0.400222i
$900$		0			0
$901$			12.0000i			0.399778i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	20.0000	−	34.6410i	0.664822	−	1.15151i
$906$		0			0
$907$	24.2487	−	14.0000i	0.805165	−	0.464862i	−0.0401089	−	0.999195i	$-0.512770\pi$
$907$	24.2487	−	14.0000i	0.805165	−	0.464862i	0.845274	+	0.534333i	$0.179437\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	24.0000	+	41.5692i	0.795155	+	1.37725i	0.922740	+	0.385422i	$0.125944\pi$
$911$	24.0000	+	41.5692i	0.795155	+	1.37725i	−0.127585	+	0.991828i	$0.540723\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$			40.0000i			1.32092i
$918$		0			0
$919$	−30.0000			−0.989609			−0.494804	−	0.869004i	$-0.664760\pi$
$919$	−30.0000			−0.989609			−0.494804	+	0.869004i	$0.664760\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−41.5692	−	24.0000i	−1.36827	−	0.789970i
$924$		0			0
$925$	−6.92820	+	4.00000i	−0.227798	+	0.131519i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−25.0000	−	43.3013i	−0.820223	−	1.42067i	−0.905516	−	0.424313i	$-0.860516\pi$
$929$	−25.0000	−	43.3013i	−0.820223	−	1.42067i	0.0852924	−	0.996356i	$-0.472818\pi$
$930$		0			0
$931$	10.3923	+	6.00000i	0.340594	+	0.196642i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−25.9808	−	15.0000i	−0.846949	−	0.488986i	0.0126715	−	0.999920i	$-0.495966\pi$
$941$	−25.9808	−	15.0000i	−0.846949	−	0.488986i	−0.859620	+	0.510934i	$0.829300\pi$
$942$		0			0
$943$	4.00000	+	6.92820i	0.130258	+	0.225613i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	−0.321552	−	0.946892i	$-0.604204\pi$
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	0.659256	+	0.751918i	$0.270871\pi$
$948$		0			0
$949$	20.7846	+	12.0000i	0.674697	+	0.389536i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$		−	16.0000i		−	0.517748i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	18.0000	−	31.1769i	0.581250	−	1.00676i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−10.3923	+	6.00000i	−0.334540	+	0.193147i
$966$		0			0
$967$	−11.0000	+	19.0526i	−0.353736	+	0.612689i	−0.986901	−	0.161328i	$-0.948422\pi$
$967$	−11.0000	+	19.0526i	−0.353736	+	0.612689i	0.633165	+	0.774017i	$0.281756\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$		0			0
$973$			8.00000i			0.256468i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	−0.881579	−	0.472037i	$-0.843519\pi$
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	0.849586	+	0.527451i	$0.176852\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$	8.00000	+	13.8564i	0.255160	+	0.441951i	0.964939	−	0.262474i	$-0.0845384\pi$
$983$	8.00000	+	13.8564i	0.255160	+	0.441951i	−0.709779	+	0.704425i	$0.751205\pi$
$984$		0			0
$985$	−2.00000	+	3.46410i	−0.0637253	+	0.110375i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	16.0000i		−	0.508770i
$990$		0			0
$991$	−2.00000			−0.0635321			−0.0317660	−	0.999495i	$-0.510113\pi$
$991$	−2.00000			−0.0635321			−0.0317660	+	0.999495i	$0.510113\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	17.3205	+	10.0000i	0.549097	+	0.317021i
$996$		0			0
$997$	−41.5692	+	24.0000i	−1.31651	+	0.760088i	−0.983165	−	0.182717i	$-0.941511\pi$
$997$	−41.5692	+	24.0000i	−1.31651	+	0.760088i	−0.333345	+	0.942805i	$0.608177\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.r.g.433.1		4
3.2	odd	2		2592.2.r.f.433.2		4
4.3	odd	2		648.2.n.c.109.1		4
8.3	odd	2		648.2.n.c.109.2		4
8.5	even	2	inner	2592.2.r.g.433.2		4
9.2	odd	6		2592.2.r.f.2161.1		4
9.4	even	3		288.2.d.b.145.2		2
9.5	odd	6		96.2.d.a.49.1		2
9.7	even	3	inner	2592.2.r.g.2161.2		4
12.11	even	2		648.2.n.k.109.2		4
24.5	odd	2		2592.2.r.f.433.1		4
24.11	even	2		648.2.n.k.109.1		4
36.7	odd	6		648.2.n.c.541.2		4
36.11	even	6		648.2.n.k.541.1		4
36.23	even	6		24.2.d.a.13.2	yes	2
36.31	odd	6		72.2.d.b.37.1		2
45.4	even	6		7200.2.k.d.3601.1		2
45.13	odd	12		7200.2.d.d.2449.1		2
45.14	odd	6		2400.2.k.a.1201.2		2
45.22	odd	12		7200.2.d.g.2449.2		2
45.23	even	12		2400.2.d.c.49.1		2
45.32	even	12		2400.2.d.b.49.2		2
63.41	even	6		4704.2.c.a.2353.2		2
72.5	odd	6		96.2.d.a.49.2		2
72.11	even	6		648.2.n.k.541.2		4
72.13	even	6		288.2.d.b.145.1		2
72.29	odd	6		2592.2.r.f.2161.2		4
72.43	odd	6		648.2.n.c.541.1		4
72.59	even	6		24.2.d.a.13.1	✓	2
72.61	even	6	inner	2592.2.r.g.2161.1		4
72.67	odd	6		72.2.d.b.37.2		2
144.5	odd	12		768.2.a.d.1.1		1
144.13	even	12		2304.2.a.l.1.1		1
144.59	even	12		768.2.a.h.1.1		1
144.67	odd	12		2304.2.a.o.1.1		1
144.77	odd	12		768.2.a.e.1.1		1
144.85	even	12		2304.2.a.b.1.1		1
144.131	even	12		768.2.a.a.1.1		1
144.139	odd	12		2304.2.a.e.1.1		1
180.23	odd	12		600.2.d.c.349.2		2
180.59	even	6		600.2.k.b.301.1		2
180.67	even	12		1800.2.d.i.1549.2		2
180.103	even	12		1800.2.d.b.1549.1		2
180.139	odd	6		1800.2.k.a.901.2		2
180.167	odd	12		600.2.d.b.349.1		2
252.167	odd	6		1176.2.c.a.589.2		2
360.13	odd	12		7200.2.d.g.2449.1		2
360.59	even	6		600.2.k.b.301.2		2
360.67	even	12		1800.2.d.b.1549.2		2
360.77	even	12		2400.2.d.c.49.2		2
360.139	odd	6		1800.2.k.a.901.1		2
360.149	odd	6		2400.2.k.a.1201.1		2
360.157	odd	12		7200.2.d.d.2449.2		2
360.203	odd	12		600.2.d.b.349.2		2
360.229	even	6		7200.2.k.d.3601.2		2
360.283	even	12		1800.2.d.i.1549.1		2
360.293	even	12		2400.2.d.b.49.1		2
360.347	odd	12		600.2.d.c.349.1		2
504.293	even	6		4704.2.c.a.2353.1		2
504.419	odd	6		1176.2.c.a.589.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.2.d.a.13.1	✓	2	72.59	even	6
24.2.d.a.13.2	yes	2	36.23	even	6
72.2.d.b.37.1		2	36.31	odd	6
72.2.d.b.37.2		2	72.67	odd	6
96.2.d.a.49.1		2	9.5	odd	6
96.2.d.a.49.2		2	72.5	odd	6
288.2.d.b.145.1		2	72.13	even	6
288.2.d.b.145.2		2	9.4	even	3
600.2.d.b.349.1		2	180.167	odd	12
600.2.d.b.349.2		2	360.203	odd	12
600.2.d.c.349.1		2	360.347	odd	12
600.2.d.c.349.2		2	180.23	odd	12
600.2.k.b.301.1		2	180.59	even	6
600.2.k.b.301.2		2	360.59	even	6
648.2.n.c.109.1		4	4.3	odd	2
648.2.n.c.109.2		4	8.3	odd	2
648.2.n.c.541.1		4	72.43	odd	6
648.2.n.c.541.2		4	36.7	odd	6
648.2.n.k.109.1		4	24.11	even	2
648.2.n.k.109.2		4	12.11	even	2
648.2.n.k.541.1		4	36.11	even	6
648.2.n.k.541.2		4	72.11	even	6
768.2.a.a.1.1		1	144.131	even	12
768.2.a.d.1.1		1	144.5	odd	12
768.2.a.e.1.1		1	144.77	odd	12
768.2.a.h.1.1		1	144.59	even	12
1176.2.c.a.589.1		2	504.419	odd	6
1176.2.c.a.589.2		2	252.167	odd	6
1800.2.d.b.1549.1		2	180.103	even	12
1800.2.d.b.1549.2		2	360.67	even	12
1800.2.d.i.1549.1		2	360.283	even	12
1800.2.d.i.1549.2		2	180.67	even	12
1800.2.k.a.901.1		2	360.139	odd	6
1800.2.k.a.901.2		2	180.139	odd	6
2304.2.a.b.1.1		1	144.85	even	12
2304.2.a.e.1.1		1	144.139	odd	12
2304.2.a.l.1.1		1	144.13	even	12
2304.2.a.o.1.1		1	144.67	odd	12
2400.2.d.b.49.1		2	360.293	even	12
2400.2.d.b.49.2		2	45.32	even	12
2400.2.d.c.49.1		2	45.23	even	12
2400.2.d.c.49.2		2	360.77	even	12
2400.2.k.a.1201.1		2	360.149	odd	6
2400.2.k.a.1201.2		2	45.14	odd	6
2592.2.r.f.433.1		4	24.5	odd	2
2592.2.r.f.433.2		4	3.2	odd	2
2592.2.r.f.2161.1		4	9.2	odd	6
2592.2.r.f.2161.2		4	72.29	odd	6
2592.2.r.g.433.1		4	1.1	even	1	trivial
2592.2.r.g.433.2		4	8.5	even	2	inner
2592.2.r.g.2161.1		4	72.61	even	6	inner
2592.2.r.g.2161.2		4	9.7	even	3	inner
4704.2.c.a.2353.1		2	504.293	even	6
4704.2.c.a.2353.2		2	63.41	even	6
7200.2.d.d.2449.1		2	45.13	odd	12
7200.2.d.d.2449.2		2	360.157	odd	12
7200.2.d.g.2449.1		2	360.13	odd	12
7200.2.d.g.2449.2		2	45.22	odd	12
7200.2.k.d.3601.1		2	45.4	even	6
7200.2.k.d.3601.2		2	360.229	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(-3.46410 - 2.00000i) q^{13} +2.00000 q^{17} +4.00000i q^{19} +(-2.00000 + 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-5.19615 + 3.00000i) q^{29} +(1.00000 - 1.73205i) q^{31} +4.00000i q^{35} -8.00000i q^{37} +(1.00000 - 1.73205i) q^{41} +(-3.46410 + 2.00000i) q^{43} +(6.00000 + 10.3923i) q^{47} +(1.50000 - 2.59808i) q^{49} +6.00000i q^{53} +(3.46410 + 2.00000i) q^{59} +(4.00000 + 6.92820i) q^{65} +(10.3923 + 6.00000i) q^{67} +12.0000 q^{71} -6.00000 q^{73} +(5.00000 + 8.66025i) q^{79} +(-13.8564 + 8.00000i) q^{83} +(-3.46410 - 2.00000i) q^{85} +10.0000 q^{89} +8.00000i q^{91} +(4.00000 - 6.92820i) q^{95} +(1.00000 + 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{7} + 8 q^{17} - 8 q^{23} - 2 q^{25} + 4 q^{31} + 4 q^{41} + 24 q^{47} + 6 q^{49} + 16 q^{65} + 48 q^{71} - 24 q^{73} + 20 q^{79} + 40 q^{89} + 16 q^{95} + 4 q^{97}+O(q^{100}) \) 4 * q - 4 * q^7 + 8 * q^17 - 8 * q^23 - 2 * q^25 + 4 * q^31 + 4 * q^41 + 24 * q^47 + 6 * q^49 + 16 * q^65 + 48 * q^71 - 24 * q^73 + 20 * q^79 + 40 * q^89 + 16 * q^95 + 4 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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