LMFDB - Embedded newform 676.2.e.b.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(529,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("676.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.39788717664$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	676.529
Dual form			676.2.e.b.653.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{11} +(-3.00000 - 5.19615i) q^{17} +(-3.00000 - 5.19615i) q^{19} +(-4.00000 + 6.92820i) q^{23} -1.00000 q^{25} +(-1.00000 + 1.73205i) q^{29} -10.0000 q^{31} +(2.00000 + 3.46410i) q^{35} +(-3.00000 + 5.19615i) q^{37} +(-3.00000 + 5.19615i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(-3.00000 - 5.19615i) q^{45} +2.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +6.00000 q^{53} +(2.00000 - 3.46410i) q^{55} +(-5.00000 - 8.66025i) q^{59} +(1.00000 + 1.73205i) q^{61} +(3.00000 - 5.19615i) q^{63} +(5.00000 - 8.66025i) q^{67} +(5.00000 + 8.66025i) q^{71} -2.00000 q^{73} +4.00000 q^{77} -4.00000 q^{79} +(-4.50000 + 7.79423i) q^{81} +6.00000 q^{83} +(6.00000 + 10.3923i) q^{85} +(-3.00000 + 5.19615i) q^{89} +(6.00000 + 10.3923i) q^{95} +(1.00000 + 1.73205i) q^{97} -6.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{5} - 2 q^{7} + 3 q^{9} - 2 q^{11} - 6 q^{17} - 6 q^{19} - 8 q^{23} - 2 q^{25} - 2 q^{29} - 20 q^{31} + 4 q^{35} - 6 q^{37} - 6 q^{41} - 4 q^{43} - 6 q^{45} + 4 q^{47} + 3 q^{49} + 12 q^{53} + 4 q^{55}+ \cdots - 12 q^{99}+O(q^{100}) $ 2 * q - 4 * q^5 - 2 * q^7 + 3 * q^9 - 2 * q^11 - 6 * q^17 - 6 * q^19 - 8 * q^23 - 2 * q^25 - 2 * q^29 - 20 * q^31 + 4 * q^35 - 6 * q^37 - 6 * q^41 - 4 * q^43 - 6 * q^45 + 4 * q^47 + 3 * q^49 + 12 * q^53 + 4 * q^55 - 10 * q^59 + 2 * q^61 + 6 * q^63 + 10 * q^67 + 10 * q^71 - 4 * q^73 + 8 * q^77 - 8 * q^79 - 9 * q^81 + 12 * q^83 + 12 * q^85 - 6 * q^89 + 12 * q^95 + 2 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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		−0.866025	−	0.500000i	$-0.833333\pi$
$3$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$4$		0			0
$5$	−2.00000			−0.894427			−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$		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
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	0.0607377	+	0.998154i	$0.480655\pi$
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	−0.894795	+	0.446476i	$0.852679\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	−0.943811	−	0.330487i	$-0.892787\pi$
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	0.758115	+	0.652121i	$0.226120\pi$
$30$		0			0
$31$	−10.0000			−1.79605			−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000			−1.79605			−0.898027	+	0.439941i	$0.854999\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.00000	+	3.46410i	0.338062	+	0.585540i
$36$		0			0
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	−0.999969	−	0.00783774i	$-0.997505\pi$
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	0.506772	+	0.862080i	$0.330838\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$		0			0
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	0.672264	−	0.740312i	$-0.265322\pi$
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	−0.977261	+	0.212041i	$0.931989\pi$
$44$		0			0
$45$	−3.00000	−	5.19615i	−0.447214	−	0.774597i
$46$		0			0
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		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
$55$	2.00000	−	3.46410i	0.269680	−	0.467099i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	−0.982894	−	0.184172i	$-0.941040\pi$
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	0.331949	−	0.943297i	$-0.392294\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$		0			0
$63$	3.00000	−	5.19615i	0.377964	−	0.654654i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	−0.380251	−	0.924883i	$-0.624162\pi$
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	0.991098	−	0.133135i	$-0.0425044\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.00000	+	8.66025i	0.593391	+	1.02778i	0.993772	+	0.111434i	$0.0355445\pi$
$71$	5.00000	+	8.66025i	0.593391	+	1.02778i	−0.400381	+	0.916349i	$0.631122\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.00000			0.455842
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$	6.00000	+	10.3923i	0.650791	+	1.12720i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	6.00000	+	10.3923i	0.615587	+	1.06623i
$96$		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
$99$	−6.00000			−0.603023
$100$		0			0
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	−0.811976	−	0.583691i	$-0.801608\pi$
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	0.911479	+	0.411346i	$0.134941\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.00000	−	13.8564i	0.773389	−	1.33955i	−0.162306	−	0.986740i	$-0.551893\pi$
$107$	8.00000	−	13.8564i	0.773389	−	1.33955i	0.935695	−	0.352809i	$-0.114773\pi$
$108$		0			0
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	−0.981003	−	0.193993i	$-0.937856\pi$
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	0.322498	−	0.946570i	$-0.395477\pi$
$114$		0			0
$115$	8.00000	−	13.8564i	0.746004	−	1.29212i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.00000	+	10.3923i	−0.550019	+	0.952661i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	−0.632166	−	0.774833i	$-0.717834\pi$
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	0.987108	+	0.160055i	$0.0511671\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−16.0000			−1.39793			−0.698963	−	0.715158i	$-0.746355\pi$
$131$	−16.0000			−1.39793			−0.698963	+	0.715158i	$0.746355\pi$
$132$		0			0
$133$	−6.00000	+	10.3923i	−0.520266	+	0.901127i
$134$		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
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	0.296866	−	0.954919i	$-0.404058\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$	2.00000	−	3.46410i	0.166091	−	0.287678i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$	−6.00000			−0.488273			−0.244137	−	0.969741i	$-0.578505\pi$
$151$	−6.00000			−0.488273			−0.244137	+	0.969741i	$0.578505\pi$
$152$		0			0
$153$	9.00000	−	15.5885i	0.727607	−	1.26025i
$154$		0			0
$155$	20.0000			1.60644
$156$		0			0
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	16.0000			1.26098
$162$		0			0
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	0.601035	−	0.799223i	$-0.294755\pi$
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	−0.992665	+	0.120900i	$0.961422\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	−0.726293	−	0.687386i	$-0.758758\pi$
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	0.958440	+	0.285295i	$0.0920916\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	9.00000	−	15.5885i	0.688247	−	1.19208i
$172$		0			0
$173$	5.00000	+	8.66025i	0.380143	+	0.658427i	0.991082	−	0.133250i	$-0.0425415\pi$
$173$	5.00000	+	8.66025i	0.380143	+	0.658427i	−0.610939	+	0.791677i	$0.709208\pi$
$174$		0			0
$175$	1.00000	+	1.73205i	0.0755929	+	0.130931i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$		0			0
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.00000	−	10.3923i	0.441129	−	0.764057i
$186$		0			0
$187$	12.0000			0.877527
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$		0			0
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	0.899770	+	0.436365i	$0.143734\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.00000	+	5.19615i	−0.213741	+	0.370211i	−0.952882	−	0.303340i	$-0.901898\pi$
$197$	−3.00000	+	5.19615i	−0.213741	+	0.370211i	0.739141	+	0.673550i	$0.235232\pi$
$198$		0			0
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.00000			0.280745
$204$		0			0
$205$	6.00000	−	10.3923i	0.419058	−	0.725830i
$206$		0			0
$207$	−24.0000			−1.66812
$208$		0			0
$209$	12.0000			0.830057
$210$		0			0
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	−0.970229	−	0.242190i	$-0.922134\pi$
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	0.694857	+	0.719148i	$0.255467\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.00000	+	6.92820i	0.272798	+	0.472500i
$216$		0			0
$217$	10.0000	+	17.3205i	0.678844	+	1.17579i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−3.00000	+	5.19615i	−0.200895	+	0.347960i	−0.948817	−	0.315826i	$-0.897718\pi$
$223$	−3.00000	+	5.19615i	−0.200895	+	0.347960i	0.747922	+	0.663786i	$0.231052\pi$
$224$		0			0
$225$	−1.50000	−	2.59808i	−0.100000	−	0.173205i
$226$		0			0
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	0.993210	+	0.116331i	$0.0371134\pi$
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	−0.395860	+	0.918311i	$0.629553\pi$
$228$		0			0
$229$	−18.0000			−1.18947			−0.594737	−	0.803921i	$-0.702744\pi$
$229$	−18.0000			−1.18947			−0.594737	+	0.803921i	$0.702744\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$		0			0
$235$	−4.00000			−0.260931
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−18.0000			−1.16432			−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000			−1.16432			−0.582162	+	0.813073i	$0.697793\pi$
$240$		0			0
$241$	−3.00000	−	5.19615i	−0.193247	−	0.334714i	0.753077	−	0.657932i	$-0.228569\pi$
$241$	−3.00000	−	5.19615i	−0.193247	−	0.334714i	−0.946324	+	0.323218i	$0.895235\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.00000	+	5.19615i	−0.191663	+	0.331970i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	0.612159	−	0.790735i	$-0.290301\pi$
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	−0.990876	+	0.134778i	$0.956968\pi$
$252$		0			0
$253$	−8.00000	−	13.8564i	−0.502956	−	0.871145i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$		0			0
$259$	12.0000			0.745644
$260$		0			0
$261$	−6.00000			−0.371391
$262$		0			0
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	−0.619586	−	0.784929i	$-0.712699\pi$
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	0.989561	+	0.144112i	$0.0460326\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$		0			0
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	−0.894799	−	0.446469i	$-0.852681\pi$
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	0.834053	+	0.551684i	$0.186015\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$		0			0
$277$	−15.0000	−	25.9808i	−0.901263	−	1.56103i	−0.825857	−	0.563880i	$-0.809308\pi$
$277$	−15.0000	−	25.9808i	−0.901263	−	1.56103i	−0.0754058	−	0.997153i	$-0.524025\pi$
$278$		0			0
$279$	−15.0000	−	25.9808i	−0.898027	−	1.55543i
$280$		0			0
$281$	14.0000			0.835170			0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000			0.835170			0.417585	+	0.908638i	$0.362877\pi$
$282$		0			0
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.0000			0.708338
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.00000	−	12.1244i	−0.408944	−	0.708312i	0.585827	−	0.810436i	$-0.300770\pi$
$293$	−7.00000	−	12.1244i	−0.408944	−	0.708312i	−0.994772	+	0.102123i	$0.967436\pi$
$294$		0			0
$295$	10.0000	+	17.3205i	0.582223	+	1.00844i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−4.00000	+	6.92820i	−0.230556	+	0.399335i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.00000	−	3.46410i	−0.114520	−	0.198354i
$306$		0			0
$307$	34.0000			1.94048			0.970241	−	0.242140i	$-0.0778494\pi$
$307$	34.0000			1.94048			0.970241	+	0.242140i	$0.0778494\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$		0			0
$315$	−6.00000	+	10.3923i	−0.338062	+	0.585540i
$316$		0			0
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$		0			0
$319$	−2.00000	−	3.46410i	−0.111979	−	0.193952i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−18.0000	+	31.1769i	−1.00155	+	1.73473i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.00000	−	3.46410i	−0.110264	−	0.190982i
$330$		0			0
$331$	−11.0000	−	19.0526i	−0.604615	−	1.04722i	−0.992112	−	0.125353i	$-0.959994\pi$
$331$	−11.0000	−	19.0526i	−0.604615	−	1.04722i	0.387498	−	0.921871i	$-0.373340\pi$
$332$		0			0
$333$	−18.0000			−0.986394
$334$		0			0
$335$	−10.0000	+	17.3205i	−0.546358	+	0.946320i
$336$		0			0
$337$	−10.0000			−0.544735			−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000			−0.544735			−0.272367	+	0.962193i	$0.587807\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	10.0000	−	17.3205i	0.541530	−	0.937958i
$342$		0			0
$343$	−20.0000			−1.07990
$344$		0			0
$345$		0			0
$346$		0			0
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	0.984487	+	0.175457i	$0.0561403\pi$
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	−0.340293	+	0.940319i	$0.610526\pi$
$348$		0			0
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	−0.700609	−	0.713545i	$-0.747088\pi$
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	0.968253	+	0.249973i	$0.0804216\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	−0.989960	−	0.141344i	$-0.954858\pi$
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	0.617388	+	0.786659i	$0.288191\pi$
$354$		0			0
$355$	−10.0000	−	17.3205i	−0.530745	−	0.919277i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−30.0000			−1.58334			−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000			−1.58334			−0.791670	+	0.610949i	$0.790788\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.00000			0.209370
$366$		0			0
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	−0.809093	−	0.587680i	$-0.800041\pi$
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	0.913493	+	0.406855i	$0.133375\pi$
$368$		0			0
$369$	−18.0000			−0.937043
$370$		0			0
$371$	−6.00000	−	10.3923i	−0.311504	−	0.539542i
$372$		0			0
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	0.996610	+	0.0822766i	$0.0262191\pi$
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	−0.427051	+	0.904227i	$0.640448\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	5.00000	−	8.66025i	0.256833	−	0.444847i	−0.708559	−	0.705652i	$-0.750654\pi$
$379$	5.00000	−	8.66025i	0.256833	−	0.444847i	0.965392	+	0.260804i	$0.0839877\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	0.998954	−	0.0457244i	$-0.0145596\pi$
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	−0.539076	+	0.842257i	$0.681226\pi$
$384$		0			0
$385$	−8.00000			−0.407718
$386$		0			0
$387$	6.00000	−	10.3923i	0.304997	−	0.528271i
$388$		0			0
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$	48.0000			2.42746
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.00000			0.402524
$396$		0			0
$397$	1.00000	+	1.73205i	0.0501886	+	0.0869291i	0.890028	−	0.455905i	$-0.150684\pi$
$397$	1.00000	+	1.73205i	0.0501886	+	0.0869291i	−0.839840	+	0.542834i	$0.817351\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	−0.931158	−	0.364615i	$-0.881200\pi$
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	0.781345	+	0.624099i	$0.214534\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	9.00000	−	15.5885i	0.447214	−	0.774597i
$406$		0			0
$407$	−6.00000	−	10.3923i	−0.297409	−	0.515127i
$408$		0			0
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.0000	+	17.3205i	−0.492068	+	0.852286i
$414$		0			0
$415$	−12.0000			−0.589057
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−12.0000	+	20.7846i	−0.586238	+	1.01539i	0.408481	+	0.912767i	$0.366058\pi$
$419$	−12.0000	+	20.7846i	−0.586238	+	1.01539i	−0.994720	+	0.102628i	$0.967275\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$		0			0
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$		0			0
$425$	3.00000	+	5.19615i	0.145521	+	0.252050i
$426$		0			0
$427$	2.00000	−	3.46410i	0.0967868	−	0.167640i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$		0			0
$433$	7.00000	+	12.1244i	0.336399	+	0.582659i	0.983752	−	0.179530i	$-0.0574578\pi$
$433$	7.00000	+	12.1244i	0.336399	+	0.582659i	−0.647354	+	0.762190i	$0.724124\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	48.0000			2.29615
$438$		0			0
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	−0.609503	−	0.792784i	$-0.708631\pi$
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	0.991322	+	0.131453i	$0.0419644\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$		0			0
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$		0			0
$445$	6.00000	−	10.3923i	0.284427	−	0.492642i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−19.0000	−	32.9090i	−0.896665	−	1.55307i	−0.831730	−	0.555181i	$-0.812649\pi$
$449$	−19.0000	−	32.9090i	−0.896665	−	1.55307i	−0.0649356	−	0.997889i	$-0.520684\pi$
$450$		0			0
$451$	−6.00000	−	10.3923i	−0.282529	−	0.489355i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.0000	−	29.4449i	0.795226	−	1.37737i	−0.127469	−	0.991843i	$-0.540685\pi$
$457$	17.0000	−	29.4449i	0.795226	−	1.37737i	0.922695	−	0.385530i	$-0.125981\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	0.787668	−	0.616100i	$-0.211288\pi$
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	−0.927392	+	0.374091i	$0.877955\pi$
$462$		0			0
$463$	−22.0000			−1.02243			−0.511213	−	0.859454i	$-0.670804\pi$
$463$	−22.0000			−1.02243			−0.511213	+	0.859454i	$0.670804\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	20.0000			0.925490			0.462745	−	0.886492i	$-0.346865\pi$
$467$	20.0000			0.925490			0.462745	+	0.886492i	$0.346865\pi$
$468$		0			0
$469$	−20.0000			−0.923514
$470$		0			0
$471$		0			0
$472$		0			0
$473$	8.00000			0.367840
$474$		0			0
$475$	3.00000	+	5.19615i	0.137649	+	0.238416i
$476$		0			0
$477$	9.00000	+	15.5885i	0.412082	+	0.713746i
$478$		0			0
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.00000	−	3.46410i	−0.0908153	−	0.157297i
$486$		0			0
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	0.887793	−	0.460243i	$-0.152238\pi$
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	−0.842479	+	0.538730i	$0.818904\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	10.0000	−	17.3205i	0.451294	−	0.781664i	−0.547173	−	0.837020i	$-0.684296\pi$
$491$	10.0000	−	17.3205i	0.451294	−	0.781664i	0.998467	+	0.0553560i	$0.0176294\pi$
$492$		0			0
$493$	12.0000			0.540453
$494$		0			0
$495$	12.0000			0.539360
$496$		0			0
$497$	10.0000	−	17.3205i	0.448561	−	0.776931i
$498$		0			0
$499$	14.0000			0.626726			0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000			0.626726			0.313363	+	0.949633i	$0.398544\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−14.0000	−	24.2487i	−0.624229	−	1.08120i	−0.988689	−	0.149978i	$-0.952080\pi$
$503$	−14.0000	−	24.2487i	−0.624229	−	1.08120i	0.364460	−	0.931219i	$-0.381254\pi$
$504$		0			0
$505$	−2.00000	+	3.46410i	−0.0889988	+	0.154150i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.00000	+	12.1244i	−0.310270	+	0.537403i	−0.978421	−	0.206623i	$-0.933753\pi$
$509$	−7.00000	+	12.1244i	−0.310270	+	0.537403i	0.668151	+	0.744026i	$0.267086\pi$
$510$		0			0
$511$	2.00000	+	3.46410i	0.0884748	+	0.153243i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	16.0000			0.705044
$516$		0			0
$517$	−2.00000	+	3.46410i	−0.0879599	+	0.152351i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$		0			0
$523$	−12.0000	+	20.7846i	−0.524723	+	0.908848i	0.474862	+	0.880060i	$0.342498\pi$
$523$	−12.0000	+	20.7846i	−0.524723	+	0.908848i	−0.999586	+	0.0287874i	$0.990835\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	30.0000	+	51.9615i	1.30682	+	2.26348i
$528$		0			0
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$		0			0
$531$	15.0000	−	25.9808i	0.650945	−	1.12747i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−16.0000	+	27.7128i	−0.691740	+	1.19813i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.00000	+	5.19615i	0.129219	+	0.223814i
$540$		0			0
$541$	−26.0000			−1.11783			−0.558914	−	0.829226i	$-0.688782\pi$
$541$	−26.0000			−1.11783			−0.558914	+	0.829226i	$0.688782\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−28.0000			−1.19939
$546$		0			0
$547$	−32.0000			−1.36822			−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000			−1.36822			−0.684111	+	0.729378i	$0.739809\pi$
$548$		0			0
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$		0			0
$551$	12.0000			0.511217
$552$		0			0
$553$	4.00000	+	6.92820i	0.170097	+	0.294617i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	21.0000	−	36.3731i	0.889799	−	1.54118i	0.0496855	−	0.998765i	$-0.484178\pi$
$557$	21.0000	−	36.3731i	0.889799	−	1.54118i	0.840113	−	0.542411i	$-0.182489\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	0.905088	−	0.425223i	$-0.139804\pi$
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	−0.820798	+	0.571218i	$0.806471\pi$
$564$		0			0
$565$	14.0000	+	24.2487i	0.588984	+	1.02015i
$566$		0			0
$567$	18.0000			0.755929
$568$		0			0
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	−0.951592	−	0.307364i	$-0.900553\pi$
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	0.741981	+	0.670421i	$0.233886\pi$
$570$		0			0
$571$	−12.0000			−0.502184			−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000			−0.502184			−0.251092	+	0.967963i	$0.580790\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.00000	−	6.92820i	0.166812	−	0.288926i
$576$		0			0
$577$	6.00000			0.249783			0.124892	−	0.992170i	$-0.460142\pi$
$577$	6.00000			0.249783			0.124892	+	0.992170i	$0.460142\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−6.00000	−	10.3923i	−0.248922	−	0.431145i
$582$		0			0
$583$	−6.00000	+	10.3923i	−0.248495	+	0.430405i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.0000	−	22.5167i	0.536567	−	0.929362i	−0.462518	−	0.886610i	$-0.653054\pi$
$587$	13.0000	−	22.5167i	0.536567	−	0.929362i	0.999086	−	0.0427523i	$-0.0136126\pi$
$588$		0			0
$589$	30.0000	+	51.9615i	1.23613	+	2.14104i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−26.0000			−1.06769			−0.533846	−	0.845582i	$-0.679254\pi$
$593$	−26.0000			−1.06769			−0.533846	+	0.845582i	$0.679254\pi$
$594$		0			0
$595$	12.0000	−	20.7846i	0.491952	−	0.852086i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	4.00000			0.163436			0.0817178	−	0.996656i	$-0.473959\pi$
$599$	4.00000			0.163436			0.0817178	+	0.996656i	$0.473959\pi$
$600$		0			0
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	−0.469095	−	0.883148i	$-0.655420\pi$
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	0.999376	−	0.0353259i	$-0.0112469\pi$
$602$		0			0
$603$	30.0000			1.22169
$604$		0			0
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	6.00000	+	10.3923i	0.243532	+	0.421811i	0.961718	−	0.274041i	$-0.0883604\pi$
$607$	6.00000	+	10.3923i	0.243532	+	0.421811i	−0.718186	+	0.695852i	$0.755027\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	13.0000	−	22.5167i	0.525065	−	0.909439i	−0.474509	−	0.880251i	$-0.657374\pi$
$613$	13.0000	−	22.5167i	0.525065	−	0.909439i	0.999574	−	0.0291886i	$-0.00929235\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	17.0000	+	29.4449i	0.684394	+	1.18541i	0.973627	+	0.228147i	$0.0732666\pi$
$617$	17.0000	+	29.4449i	0.684394	+	1.18541i	−0.289233	+	0.957259i	$0.593400\pi$
$618$		0			0
$619$	2.00000			0.0803868			0.0401934	−	0.999192i	$-0.487203\pi$
$619$	2.00000			0.0803868			0.0401934	+	0.999192i	$0.487203\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	12.0000			0.480770
$624$		0			0
$625$	−19.0000			−0.760000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	36.0000			1.43541
$630$		0			0
$631$	11.0000	+	19.0526i	0.437903	+	0.758470i	0.997528	−	0.0702759i	$-0.0223880\pi$
$631$	11.0000	+	19.0526i	0.437903	+	0.758470i	−0.559625	+	0.828746i	$0.689055\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.00000	+	13.8564i	−0.317470	+	0.549875i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−15.0000	+	25.9808i	−0.593391	+	1.02778i
$640$		0			0
$641$	13.0000	+	22.5167i	0.513469	+	0.889355i	0.999878	+	0.0156233i	$0.00497325\pi$
$641$	13.0000	+	22.5167i	0.513469	+	0.889355i	−0.486409	+	0.873731i	$0.661693\pi$
$642$		0			0
$643$	1.00000	+	1.73205i	0.0394362	+	0.0683054i	0.885070	−	0.465458i	$-0.154110\pi$
$643$	1.00000	+	1.73205i	0.0394362	+	0.0683054i	−0.845634	+	0.533764i	$0.820777\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.0000	−	27.7128i	0.629025	−	1.08950i	−0.358723	−	0.933444i	$-0.616788\pi$
$647$	16.0000	−	27.7128i	0.629025	−	1.08950i	0.987748	−	0.156059i	$-0.0498790\pi$
$648$		0			0
$649$	20.0000			0.785069
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$		0			0
$655$	32.0000			1.25034
$656$		0			0
$657$	−3.00000	−	5.19615i	−0.117041	−	0.202721i
$658$		0			0
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$	1.00000	−	1.73205i	0.0388955	−	0.0673690i	−0.845922	−	0.533306i	$-0.820949\pi$
$661$	1.00000	−	1.73205i	0.0388955	−	0.0673690i	0.884818	+	0.465937i	$0.154283\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	12.0000	−	20.7846i	0.465340	−	0.805993i
$666$		0			0
$667$	−8.00000	−	13.8564i	−0.309761	−	0.536522i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.00000			−0.154418
$672$		0			0
$673$	13.0000	−	22.5167i	0.501113	−	0.867953i	−0.498886	−	0.866668i	$-0.666257\pi$
$673$	13.0000	−	22.5167i	0.501113	−	0.867953i	0.999999	−	0.00128586i	$-0.000409302\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$		0			0
$679$	2.00000	−	3.46410i	0.0767530	−	0.132940i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.00000	−	1.73205i	−0.0382639	−	0.0662751i	0.846259	−	0.532771i	$-0.178849\pi$
$683$	−1.00000	−	1.73205i	−0.0382639	−	0.0662751i	−0.884523	+	0.466496i	$0.845516\pi$
$684$		0			0
$685$	−18.0000	−	31.1769i	−0.687745	−	1.19121i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	17.0000	−	29.4449i	0.646710	−	1.12014i	−0.337193	−	0.941435i	$-0.609478\pi$
$691$	17.0000	−	29.4449i	0.646710	−	1.12014i	0.983904	−	0.178700i	$-0.0571891\pi$
$692$		0			0
$693$	6.00000	+	10.3923i	0.227921	+	0.394771i
$694$		0			0
$695$	16.0000	+	27.7128i	0.606915	+	1.05121i
$696$		0			0
$697$	36.0000			1.36360
$698$		0			0
$699$		0			0
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	36.0000			1.35777
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.00000			−0.150435
$708$		0			0
$709$	−11.0000	−	19.0526i	−0.413114	−	0.715534i	0.582115	−	0.813107i	$-0.302225\pi$
$709$	−11.0000	−	19.0526i	−0.413114	−	0.715534i	−0.995228	+	0.0975728i	$0.968892\pi$
$710$		0			0
$711$	−6.00000	−	10.3923i	−0.225018	−	0.389742i
$712$		0			0
$713$	40.0000	−	69.2820i	1.49801	−	2.59463i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	20.0000	+	34.6410i	0.745874	+	1.29189i	0.949785	+	0.312903i	$0.101301\pi$
$719$	20.0000	+	34.6410i	0.745874	+	1.29189i	−0.203911	+	0.978989i	$0.565365\pi$
$720$		0			0
$721$	8.00000	+	13.8564i	0.297936	+	0.516040i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.00000	−	1.73205i	0.0371391	−	0.0643268i
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−12.0000	+	20.7846i	−0.443836	+	0.768747i
$732$		0			0
$733$	−26.0000			−0.960332			−0.480166	−	0.877178i	$-0.659424\pi$
$733$	−26.0000			−0.960332			−0.480166	+	0.877178i	$0.659424\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.0000	+	17.3205i	0.368355	+	0.638009i
$738$		0			0
$739$	3.00000	−	5.19615i	0.110357	−	0.191144i	−0.805557	−	0.592518i	$-0.798134\pi$
$739$	3.00000	−	5.19615i	0.110357	−	0.191144i	0.915914	+	0.401374i	$0.131467\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−7.00000	+	12.1244i	−0.256805	+	0.444799i	−0.965384	−	0.260832i	$-0.916003\pi$
$743$	−7.00000	+	12.1244i	−0.256805	+	0.444799i	0.708579	+	0.705631i	$0.249337\pi$
$744$		0			0
$745$	−18.0000	−	31.1769i	−0.659469	−	1.14223i
$746$		0			0
$747$	9.00000	+	15.5885i	0.329293	+	0.570352i
$748$		0			0
$749$	−32.0000			−1.16925
$750$		0			0
$751$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$751$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	12.0000			0.436725
$756$		0			0
$757$	21.0000	−	36.3731i	0.763258	−	1.32200i	−0.177905	−	0.984048i	$-0.556932\pi$
$757$	21.0000	−	36.3731i	0.763258	−	1.32200i	0.941163	−	0.337954i	$-0.109735\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	0.981764	−	0.190101i	$-0.0608816\pi$
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	−0.655515	+	0.755182i	$0.727548\pi$
$762$		0			0
$763$	−14.0000	−	24.2487i	−0.506834	−	0.877862i
$764$		0			0
$765$	−18.0000	+	31.1769i	−0.650791	+	1.12720i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−27.0000	+	46.7654i	−0.973645	+	1.68640i	−0.289309	+	0.957236i	$0.593425\pi$
$769$	−27.0000	+	46.7654i	−0.973645	+	1.68640i	−0.684336	+	0.729167i	$0.739908\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−23.0000	−	39.8372i	−0.827253	−	1.43284i	−0.900186	−	0.435507i	$-0.856569\pi$
$773$	−23.0000	−	39.8372i	−0.827253	−	1.43284i	0.0729331	−	0.997337i	$-0.476764\pi$
$774$		0			0
$775$	10.0000			0.359211
$776$		0			0
$777$		0			0
$778$		0			0
$779$	36.0000			1.28983
$780$		0			0
$781$	−20.0000			−0.715656
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.00000			−0.142766
$786$		0			0
$787$	19.0000	+	32.9090i	0.677277	+	1.17308i	0.975798	+	0.218675i	$0.0701734\pi$
$787$	19.0000	+	32.9090i	0.677277	+	1.17308i	−0.298521	+	0.954403i	$0.596493\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−14.0000	+	24.2487i	−0.497783	+	0.862185i
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	0.661441	−	0.749997i	$-0.269945\pi$
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	−0.980237	+	0.197826i	$0.936612\pi$
$798$		0			0
$799$	−6.00000	−	10.3923i	−0.212265	−	0.367653i
$800$		0			0
$801$	−18.0000			−0.635999
$802$		0			0
$803$	2.00000	−	3.46410i	0.0705785	−	0.122245i
$804$		0			0
$805$	−32.0000			−1.12785
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	−0.913932	−	0.405868i	$-0.866969\pi$
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	0.808458	+	0.588555i	$0.200303\pi$
$810$		0			0
$811$	22.0000			0.772524			0.386262	−	0.922389i	$-0.373766\pi$
$811$	22.0000			0.772524			0.386262	+	0.922389i	$0.373766\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	10.0000	+	17.3205i	0.350285	+	0.606711i
$816$		0			0
$817$	−12.0000	+	20.7846i	−0.419827	+	0.727161i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.00000	−	1.73205i	0.0349002	−	0.0604490i	−0.848048	−	0.529920i	$-0.822222\pi$
$821$	1.00000	−	1.73205i	0.0349002	−	0.0604490i	0.882948	+	0.469471i	$0.155555\pi$
$822$		0			0
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	0.995768	−	0.0919029i	$-0.0292950\pi$
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	−0.577474	+	0.816409i	$0.695962\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$		0			0
$829$	−11.0000	+	19.0526i	−0.382046	+	0.661723i	−0.991355	−	0.131210i	$-0.958114\pi$
$829$	−11.0000	+	19.0526i	−0.382046	+	0.661723i	0.609309	+	0.792933i	$0.291447\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−18.0000			−0.623663
$834$		0			0
$835$	−6.00000	+	10.3923i	−0.207639	+	0.359641i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−5.00000	−	8.66025i	−0.172619	−	0.298985i	0.766716	−	0.641987i	$-0.221890\pi$
$839$	−5.00000	−	8.66025i	−0.172619	−	0.298985i	−0.939335	+	0.343002i	$0.888556\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$		0			0
$847$	7.00000	−	12.1244i	0.240523	−	0.416598i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−24.0000	−	41.5692i	−0.822709	−	1.42497i
$852$		0			0
$853$	38.0000			1.30110			0.650548	−	0.759465i	$-0.274539\pi$
$853$	38.0000			1.30110			0.650548	+	0.759465i	$0.274539\pi$
$854$		0			0
$855$	−18.0000	+	31.1769i	−0.615587	+	1.06623i
$856$		0			0
$857$	−38.0000			−1.29806			−0.649028	−	0.760765i	$-0.724824\pi$
$857$	−38.0000			−1.29806			−0.649028	+	0.760765i	$0.724824\pi$
$858$		0			0
$859$	8.00000			0.272956			0.136478	−	0.990643i	$-0.456422\pi$
$859$	8.00000			0.272956			0.136478	+	0.990643i	$0.456422\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−34.0000			−1.15737			−0.578687	−	0.815550i	$-0.696435\pi$
$863$	−34.0000			−1.15737			−0.578687	+	0.815550i	$0.696435\pi$
$864$		0			0
$865$	−10.0000	−	17.3205i	−0.340010	−	0.588915i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.00000	−	6.92820i	0.135691	−	0.235023i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−3.00000	+	5.19615i	−0.101535	+	0.175863i
$874$		0			0
$875$	−12.0000	−	20.7846i	−0.405674	−	0.702648i
$876$		0			0
$877$	9.00000	+	15.5885i	0.303908	+	0.526385i	0.977018	−	0.213158i	$-0.0683750\pi$
$877$	9.00000	+	15.5885i	0.303908	+	0.526385i	−0.673109	+	0.739543i	$0.735042\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−9.00000	+	15.5885i	−0.303218	+	0.525188i	−0.976863	−	0.213866i	$-0.931394\pi$
$881$	−9.00000	+	15.5885i	−0.303218	+	0.525188i	0.673645	+	0.739055i	$0.264728\pi$
$882$		0			0
$883$	28.0000			0.942275			0.471138	−	0.882060i	$-0.343844\pi$
$883$	28.0000			0.942275			0.471138	+	0.882060i	$0.343844\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.00000	+	3.46410i	−0.0671534	+	0.116313i	−0.897647	−	0.440715i	$-0.854725\pi$
$887$	−2.00000	+	3.46410i	−0.0671534	+	0.116313i	0.830494	+	0.557028i	$0.188058\pi$
$888$		0			0
$889$	−16.0000			−0.536623
$890$		0			0
$891$	−9.00000	−	15.5885i	−0.301511	−	0.522233i
$892$		0			0
$893$	−6.00000	−	10.3923i	−0.200782	−	0.347765i
$894$		0			0
$895$	12.0000	−	20.7846i	0.401116	−	0.694753i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	10.0000	−	17.3205i	0.333519	−	0.577671i
$900$		0			0
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	12.0000			0.398893
$906$		0			0
$907$	−18.0000	+	31.1769i	−0.597680	+	1.03521i	0.395482	+	0.918474i	$0.370577\pi$
$907$	−18.0000	+	31.1769i	−0.597680	+	1.03521i	−0.993163	+	0.116739i	$0.962756\pi$
$908$		0			0
$909$	6.00000			0.199007
$910$		0			0
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$		0			0
$913$	−6.00000	+	10.3923i	−0.198571	+	0.343935i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	16.0000	+	27.7128i	0.528367	+	0.915158i
$918$		0			0
$919$	6.00000	+	10.3923i	0.197922	+	0.342811i	0.947854	−	0.318704i	$-0.103247\pi$
$919$	6.00000	+	10.3923i	0.197922	+	0.342811i	−0.749933	+	0.661514i	$0.769914\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	3.00000	−	5.19615i	0.0986394	−	0.170848i
$926$		0			0
$927$	−12.0000	−	20.7846i	−0.394132	−	0.682656i
$928$		0			0
$929$	−27.0000	−	46.7654i	−0.885841	−	1.53432i	−0.844746	−	0.535167i	$-0.820249\pi$
$929$	−27.0000	−	46.7654i	−0.885841	−	1.53432i	−0.0410949	−	0.999155i	$-0.513085\pi$
$930$		0			0
$931$	−18.0000			−0.589926
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−24.0000			−0.784884
$936$		0			0
$937$	42.0000			1.37208			0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000			1.37208			0.686040	+	0.727564i	$0.259347\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−10.0000			−0.325991			−0.162995	−	0.986627i	$-0.552116\pi$
$941$	−10.0000			−0.325991			−0.162995	+	0.986627i	$0.552116\pi$
$942$		0			0
$943$	−24.0000	−	41.5692i	−0.781548	−	1.35368i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−21.0000	+	36.3731i	−0.682408	+	1.18197i	0.291835	+	0.956469i	$0.405734\pi$
$947$	−21.0000	+	36.3731i	−0.682408	+	1.18197i	−0.974244	+	0.225497i	$0.927599\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−13.0000	−	22.5167i	−0.421111	−	0.729386i	0.574937	−	0.818198i	$-0.305026\pi$
$953$	−13.0000	−	22.5167i	−0.421111	−	0.729386i	−0.996048	+	0.0888114i	$0.971693\pi$
$954$		0			0
$955$	4.00000	+	6.92820i	0.129437	+	0.224191i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	18.0000	−	31.1769i	0.581250	−	1.00676i
$960$		0			0
$961$	69.0000			2.22581
$962$		0			0
$963$	48.0000			1.54678
$964$		0			0
$965$	−2.00000	+	3.46410i	−0.0643823	+	0.111513i
$966$		0			0
$967$	−50.0000			−1.60789			−0.803946	−	0.594703i	$-0.797270\pi$
$967$	−50.0000			−1.60789			−0.803946	+	0.594703i	$0.797270\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	24.0000	+	41.5692i	0.770197	+	1.33402i	0.937455	+	0.348107i	$0.113175\pi$
$971$	24.0000	+	41.5692i	0.770197	+	1.33402i	−0.167258	+	0.985913i	$0.553491\pi$
$972$		0			0
$973$	−16.0000	+	27.7128i	−0.512936	+	0.888432i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	−0.685381	−	0.728184i	$-0.740364\pi$
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	0.973317	+	0.229465i	$0.0736978\pi$
$978$		0			0
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$		0			0
$981$	21.0000	+	36.3731i	0.670478	+	1.16130i
$982$		0			0
$983$	−14.0000			−0.446531			−0.223265	−	0.974758i	$-0.571672\pi$
$983$	−14.0000			−0.446531			−0.223265	+	0.974758i	$0.571672\pi$
$984$		0			0
$985$	6.00000	−	10.3923i	0.191176	−	0.331126i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	32.0000			1.01754
$990$		0			0
$991$	−6.00000	+	10.3923i	−0.190596	+	0.330122i	−0.945448	−	0.325773i	$-0.894375\pi$
$991$	−6.00000	+	10.3923i	−0.190596	+	0.330122i	0.754852	+	0.655895i	$0.227709\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−16.0000	−	27.7128i	−0.507234	−	0.878555i
$996$		0			0
$997$	29.0000	+	50.2295i	0.918439	+	1.59078i	0.801786	+	0.597611i	$0.203883\pi$
$997$	29.0000	+	50.2295i	0.918439	+	1.59078i	0.116653	+	0.993173i	$0.462784\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.e.b.529.1		2
13.2	odd	12		676.2.h.c.361.2		4
13.3	even	3	inner	676.2.e.b.653.1		2
13.4	even	6		52.2.a.a.1.1	✓	1
13.5	odd	4		676.2.h.c.485.2		4
13.6	odd	12		676.2.d.c.337.2		2
13.7	odd	12		676.2.d.c.337.1		2
13.8	odd	4		676.2.h.c.485.1		4
13.9	even	3		676.2.a.c.1.1		1
13.10	even	6		676.2.e.c.653.1		2
13.11	odd	12		676.2.h.c.361.1		4
13.12	even	2		676.2.e.c.529.1		2
39.17	odd	6		468.2.a.b.1.1		1
39.20	even	12		6084.2.b.m.4393.2		2
39.32	even	12		6084.2.b.m.4393.1		2
39.35	odd	6		6084.2.a.m.1.1		1
52.7	even	12		2704.2.f.f.337.1		2
52.19	even	12		2704.2.f.f.337.2		2
52.35	odd	6		2704.2.a.g.1.1		1
52.43	odd	6		208.2.a.c.1.1		1
65.4	even	6		1300.2.a.d.1.1		1
65.17	odd	12		1300.2.c.c.1249.1		2
65.43	odd	12		1300.2.c.c.1249.2		2
91.4	even	6		2548.2.j.e.1353.1		2
91.17	odd	6		2548.2.j.f.1353.1		2
91.30	even	6		2548.2.j.e.1145.1		2
91.69	odd	6		2548.2.a.e.1.1		1
91.82	odd	6		2548.2.j.f.1145.1		2
104.43	odd	6		832.2.a.f.1.1		1
104.69	even	6		832.2.a.e.1.1		1
117.4	even	6		4212.2.i.d.2809.1		2
117.43	even	6		4212.2.i.d.1405.1		2
117.56	odd	6		4212.2.i.i.1405.1		2
117.95	odd	6		4212.2.i.i.2809.1		2
143.43	odd	6		6292.2.a.g.1.1		1
156.95	even	6		1872.2.a.f.1.1		1
208.43	odd	12		3328.2.b.e.1665.2		2
208.69	even	12		3328.2.b.q.1665.2		2
208.147	odd	12		3328.2.b.e.1665.1		2
208.173	even	12		3328.2.b.q.1665.1		2
260.199	odd	6		5200.2.a.q.1.1		1
312.173	odd	6		7488.2.a.bn.1.1		1
312.251	even	6		7488.2.a.bw.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.a.a.1.1	✓	1	13.4	even	6
208.2.a.c.1.1		1	52.43	odd	6
468.2.a.b.1.1		1	39.17	odd	6
676.2.a.c.1.1		1	13.9	even	3
676.2.d.c.337.1		2	13.7	odd	12
676.2.d.c.337.2		2	13.6	odd	12
676.2.e.b.529.1		2	1.1	even	1	trivial
676.2.e.b.653.1		2	13.3	even	3	inner
676.2.e.c.529.1		2	13.12	even	2
676.2.e.c.653.1		2	13.10	even	6
676.2.h.c.361.1		4	13.11	odd	12
676.2.h.c.361.2		4	13.2	odd	12
676.2.h.c.485.1		4	13.8	odd	4
676.2.h.c.485.2		4	13.5	odd	4
832.2.a.e.1.1		1	104.69	even	6
832.2.a.f.1.1		1	104.43	odd	6
1300.2.a.d.1.1		1	65.4	even	6
1300.2.c.c.1249.1		2	65.17	odd	12
1300.2.c.c.1249.2		2	65.43	odd	12
1872.2.a.f.1.1		1	156.95	even	6
2548.2.a.e.1.1		1	91.69	odd	6
2548.2.j.e.1145.1		2	91.30	even	6
2548.2.j.e.1353.1		2	91.4	even	6
2548.2.j.f.1145.1		2	91.82	odd	6
2548.2.j.f.1353.1		2	91.17	odd	6
2704.2.a.g.1.1		1	52.35	odd	6
2704.2.f.f.337.1		2	52.7	even	12
2704.2.f.f.337.2		2	52.19	even	12
3328.2.b.e.1665.1		2	208.147	odd	12
3328.2.b.e.1665.2		2	208.43	odd	12
3328.2.b.q.1665.1		2	208.173	even	12
3328.2.b.q.1665.2		2	208.69	even	12
4212.2.i.d.1405.1		2	117.43	even	6
4212.2.i.d.2809.1		2	117.4	even	6
4212.2.i.i.1405.1		2	117.56	odd	6
4212.2.i.i.2809.1		2	117.95	odd	6
5200.2.a.q.1.1		1	260.199	odd	6
6084.2.a.m.1.1		1	39.35	odd	6
6084.2.b.m.4393.1		2	39.32	even	12
6084.2.b.m.4393.2		2	39.20	even	12
6292.2.a.g.1.1		1	143.43	odd	6
7488.2.a.bn.1.1		1	312.173	odd	6
7488.2.a.bw.1.1		1	312.251	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{11} +(-3.00000 - 5.19615i) q^{17} +(-3.00000 - 5.19615i) q^{19} +(-4.00000 + 6.92820i) q^{23} -1.00000 q^{25} +(-1.00000 + 1.73205i) q^{29} -10.0000 q^{31} +(2.00000 + 3.46410i) q^{35} +(-3.00000 + 5.19615i) q^{37} +(-3.00000 + 5.19615i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(-3.00000 - 5.19615i) q^{45} +2.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +6.00000 q^{53} +(2.00000 - 3.46410i) q^{55} +(-5.00000 - 8.66025i) q^{59} +(1.00000 + 1.73205i) q^{61} +(3.00000 - 5.19615i) q^{63} +(5.00000 - 8.66025i) q^{67} +(5.00000 + 8.66025i) q^{71} -2.00000 q^{73} +4.00000 q^{77} -4.00000 q^{79} +(-4.50000 + 7.79423i) q^{81} +6.00000 q^{83} +(6.00000 + 10.3923i) q^{85} +(-3.00000 + 5.19615i) q^{89} +(6.00000 + 10.3923i) q^{95} +(1.00000 + 1.73205i) q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{5} - 2 q^{7} + 3 q^{9} - 2 q^{11} - 6 q^{17} - 6 q^{19} - 8 q^{23} - 2 q^{25} - 2 q^{29} - 20 q^{31} + 4 q^{35} - 6 q^{37} - 6 q^{41} - 4 q^{43} - 6 q^{45} + 4 q^{47} + 3 q^{49} + 12 q^{53} + 4 q^{55}+ \cdots - 12 q^{99}+O(q^{100}) \) 2 * q - 4 * q^5 - 2 * q^7 + 3 * q^9 - 2 * q^11 - 6 * q^17 - 6 * q^19 - 8 * q^23 - 2 * q^25 - 2 * q^29 - 20 * q^31 + 4 * q^35 - 6 * q^37 - 6 * q^41 - 4 * q^43 - 6 * q^45 + 4 * q^47 + 3 * q^49 + 12 * q^53 + 4 * q^55 - 10 * q^59 + 2 * q^61 + 6 * q^63 + 10 * q^67 + 10 * q^71 - 4 * q^73 + 8 * q^77 - 8 * q^79 - 9 * q^81 + 12 * q^83 + 12 * q^85 - 6 * q^89 + 12 * q^95 + 2 * q^97 - 12 * q^99

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