LMFDB - Embedded newform 676.2.h.c.485.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(361,676)]

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, 5]))

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

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

chi := DirichletCharacter("676.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.h (of order $6$, 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:	$0$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			485.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	676.485
Dual form			676.2.h.c.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{5} +(-1.73205 + 1.00000i) q^{7} +(1.50000 + 2.59808i) q^{9} +(1.73205 + 1.00000i) q^{11} +(3.00000 + 5.19615i) q^{17} +(5.19615 - 3.00000i) q^{19} +(4.00000 - 6.92820i) q^{23} +1.00000 q^{25} +(-1.00000 + 1.73205i) q^{29} -10.0000i q^{31} +(2.00000 + 3.46410i) q^{35} +(5.19615 + 3.00000i) q^{37} +(-5.19615 - 3.00000i) q^{41} +(2.00000 + 3.46410i) q^{43} +(5.19615 - 3.00000i) q^{45} -2.00000i q^{47} +(-1.50000 + 2.59808i) q^{49} +6.00000 q^{53} +(2.00000 - 3.46410i) q^{55} +(-8.66025 + 5.00000i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-5.19615 - 3.00000i) q^{63} +(8.66025 + 5.00000i) q^{67} +(-8.66025 + 5.00000i) q^{71} +2.00000i q^{73} -4.00000 q^{77} -4.00000 q^{79} +(-4.50000 + 7.79423i) q^{81} +6.00000i q^{83} +(10.3923 - 6.00000i) q^{85} +(5.19615 + 3.00000i) q^{89} +(-6.00000 - 10.3923i) q^{95} +(-1.73205 + 1.00000i) q^{97} +6.00000i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{9} + 12 q^{17} + 16 q^{23} + 4 q^{25} - 4 q^{29} + 8 q^{35} + 8 q^{43} - 6 q^{49} + 24 q^{53} + 8 q^{55} + 4 q^{61} - 16 q^{77} - 16 q^{79} - 18 q^{81} - 24 q^{95}+O(q^{100}) $ 4 * q + 6 * q^9 + 12 * q^17 + 16 * q^23 + 4 * q^25 - 4 * q^29 + 8 * q^35 + 8 * q^43 - 6 * q^49 + 24 * q^53 + 8 * q^55 + 4 * q^61 - 16 * q^77 - 16 * q^79 - 18 * q^81 - 24 * q^95

Character values

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

$n$	$339$	$509$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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
$5$		−	2.00000i		−	0.894427i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$		−	2.00000i		−	0.894427i	0.894427	−	0.447214i	$-0.147584\pi$
$6$		0			0
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	−0.790237	−	0.612801i	$-0.790043\pi$
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	0.135583	+	0.990766i	$0.456709\pi$
$8$		0			0
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	1.73205	+	1.00000i	0.522233	+	0.301511i	0.737848	−	0.674967i	$-0.235842\pi$
$11$	1.73205	+	1.00000i	0.522233	+	0.301511i	−0.215615	+	0.976478i	$0.569176\pi$
$12$		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	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$		0			0
$19$	5.19615	−	3.00000i	1.19208	−	0.688247i	0.233301	−	0.972404i	$-0.425047\pi$
$19$	5.19615	−	3.00000i	1.19208	−	0.688247i	0.958778	+	0.284157i	$0.0917138\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	−0.0607377	−	0.998154i	$-0.519345\pi$
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	0.894795	−	0.446476i	$-0.147321\pi$
$24$		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
$31$		−	10.0000i		−	1.79605i	−0.439941	−	0.898027i	$-0.645001\pi$
$31$		−	10.0000i		−	1.79605i	0.439941	−	0.898027i	$-0.354999\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.00000	+	3.46410i	0.338062	+	0.585540i
$36$		0			0
$37$	5.19615	+	3.00000i	0.854242	+	0.493197i	0.862080	−	0.506772i	$-0.169162\pi$
$37$	5.19615	+	3.00000i	0.854242	+	0.493197i	−0.00783774	+	0.999969i	$0.502495\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.19615	−	3.00000i	−0.811503	−	0.468521i	0.0359748	−	0.999353i	$-0.488546\pi$
$41$	−5.19615	−	3.00000i	−0.811503	−	0.468521i	−0.847477	+	0.530831i	$0.821880\pi$
$42$		0			0
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$		0			0
$45$	5.19615	−	3.00000i	0.774597	−	0.447214i
$46$		0			0
$47$		−	2.00000i		−	0.291730i	−0.989305	−	0.145865i	$-0.953403\pi$
$47$		−	2.00000i		−	0.291730i	0.989305	−	0.145865i	$-0.0465965\pi$
$48$		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
$59$	−8.66025	+	5.00000i	−1.12747	+	0.650945i	−0.943297	−	0.331949i	$-0.892294\pi$
$59$	−8.66025	+	5.00000i	−1.12747	+	0.650945i	−0.184172	+	0.982894i	$0.558960\pi$
$60$		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
$63$	−5.19615	−	3.00000i	−0.654654	−	0.377964i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	8.66025	+	5.00000i	1.05802	+	0.610847i	0.924883	−	0.380251i	$-0.124162\pi$
$67$	8.66025	+	5.00000i	1.05802	+	0.610847i	0.133135	+	0.991098i	$0.457496\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.66025	+	5.00000i	−1.02778	+	0.593391i	−0.916349	−	0.400381i	$-0.868878\pi$
$71$	−8.66025	+	5.00000i	−1.02778	+	0.593391i	−0.111434	+	0.993772i	$0.535544\pi$
$72$		0			0
$73$			2.00000i			0.234082i	0.993127	+	0.117041i	$0.0373409\pi$
$73$			2.00000i			0.234082i	−0.993127	+	0.117041i	$0.962659\pi$
$74$		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
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$		0			0
$85$	10.3923	−	6.00000i	1.12720	−	0.650791i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.19615	+	3.00000i	0.550791	+	0.317999i	0.749441	−	0.662071i	$-0.230322\pi$
$89$	5.19615	+	3.00000i	0.550791	+	0.317999i	−0.198650	+	0.980071i	$0.563656\pi$
$90$		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
$97$	−1.73205	+	1.00000i	−0.175863	+	0.101535i	−0.585348	−	0.810782i	$-0.699042\pi$
$97$	−1.73205	+	1.00000i	−0.175863	+	0.101535i	0.409484	+	0.912317i	$0.365709\pi$
$98$		0			0
$99$			6.00000i			0.603023i
$100$		0			0
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$		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
$109$			14.0000i			1.34096i	0.741929	+	0.670478i	$0.233911\pi$
$109$			14.0000i			1.34096i	−0.741929	+	0.670478i	$0.766089\pi$
$110$		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
$115$	−13.8564	−	8.00000i	−1.29212	−	0.746004i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−10.3923	−	6.00000i	−0.952661	−	0.550019i
$120$		0			0
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	12.0000i		−	1.07331i
$126$		0			0
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	−0.987108	−	0.160055i	$-0.948833\pi$
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	0.632166	+	0.774833i	$0.282166\pi$
$128$		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
$137$	15.5885	−	9.00000i	1.33181	−	0.768922i	0.346235	−	0.938148i	$-0.387460\pi$
$137$	15.5885	−	9.00000i	1.33181	−	0.768922i	0.985577	+	0.169226i	$0.0541268\pi$
$138$		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
$145$	3.46410	+	2.00000i	0.287678	+	0.166091i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−15.5885	+	9.00000i	−1.27706	+	0.737309i	−0.976306	−	0.216394i	$-0.930570\pi$
$149$	−15.5885	+	9.00000i	−1.27706	+	0.737309i	−0.300750	+	0.953703i	$0.597237\pi$
$150$		0			0
$151$			6.00000i			0.488273i	0.969741	+	0.244137i	$0.0785045\pi$
$151$			6.00000i			0.488273i	−0.969741	+	0.244137i	$0.921495\pi$
$152$		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
$161$			16.0000i			1.26098i
$162$		0			0
$163$	−8.66025	+	5.00000i	−0.678323	+	0.391630i	−0.799223	−	0.601035i	$-0.794755\pi$
$163$	−8.66025	+	5.00000i	−0.678323	+	0.391630i	0.120900	+	0.992665i	$0.461422\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.19615	−	3.00000i	−0.402090	−	0.232147i	0.285295	−	0.958440i	$-0.407908\pi$
$167$	−5.19615	−	3.00000i	−0.402090	−	0.232147i	−0.687386	+	0.726293i	$0.741242\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	15.5885	+	9.00000i	1.19208	+	0.688247i
$172$		0			0
$173$	−5.00000	−	8.66025i	−0.380143	−	0.658427i	0.610939	−	0.791677i	$-0.290792\pi$
$173$	−5.00000	−	8.66025i	−0.380143	−	0.658427i	−0.991082	+	0.133250i	$0.957459\pi$
$174$		0			0
$175$	−1.73205	+	1.00000i	−0.130931	+	0.0755929i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.00000	−	10.3923i	0.441129	−	0.764057i
$186$		0			0
$187$			12.0000i			0.877527i
$188$		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
$193$	−1.73205	−	1.00000i	−0.124676	−	0.0719816i	0.436365	−	0.899770i	$-0.356266\pi$
$193$	−1.73205	−	1.00000i	−0.124676	−	0.0719816i	−0.561041	+	0.827788i	$0.689599\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.19615	−	3.00000i	−0.370211	−	0.213741i	0.303340	−	0.952882i	$-0.401898\pi$
$197$	−5.19615	−	3.00000i	−0.370211	−	0.213741i	−0.673550	+	0.739141i	$0.735232\pi$
$198$		0			0
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	4.00000i		−	0.280745i
$204$		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
$215$	6.92820	−	4.00000i	0.472500	−	0.272798i
$216$		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
$223$	−5.19615	−	3.00000i	−0.347960	−	0.200895i	0.315826	−	0.948817i	$-0.397718\pi$
$223$	−5.19615	−	3.00000i	−0.347960	−	0.200895i	−0.663786	+	0.747922i	$0.731052\pi$
$224$		0			0
$225$	1.50000	+	2.59808i	0.100000	+	0.173205i
$226$		0			0
$227$	−15.5885	+	9.00000i	−1.03464	+	0.597351i	−0.918311	−	0.395860i	$-0.870447\pi$
$227$	−15.5885	+	9.00000i	−1.03464	+	0.597351i	−0.116331	+	0.993210i	$0.537113\pi$
$228$		0			0
$229$			18.0000i			1.18947i	0.803921	+	0.594737i	$0.202744\pi$
$229$			18.0000i			1.18947i	−0.803921	+	0.594737i	$0.797256\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.0000			−0.655122			−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000			−0.655122			−0.327561	+	0.944830i	$0.606227\pi$
$234$		0			0
$235$	−4.00000			−0.260931
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	18.0000i		−	1.16432i	−0.813073	−	0.582162i	$-0.802207\pi$
$239$		−	18.0000i		−	1.16432i	0.813073	−	0.582162i	$-0.197793\pi$
$240$		0			0
$241$	−5.19615	+	3.00000i	−0.334714	+	0.193247i	−0.657932	−	0.753077i	$-0.728569\pi$
$241$	−5.19615	+	3.00000i	−0.334714	+	0.193247i	0.323218	+	0.946324i	$0.395235\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.19615	+	3.00000i	0.331970	+	0.191663i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	0.990876	−	0.134778i	$-0.0430322\pi$
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	−0.612159	+	0.790735i	$0.709699\pi$
$252$		0			0
$253$	13.8564	−	8.00000i	0.871145	−	0.502956i
$254$		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
$259$	−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
$265$		−	12.0000i		−	0.737154i
$266$		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
$271$	1.73205	+	1.00000i	0.105215	+	0.0607457i	0.551684	−	0.834053i	$-0.313985\pi$
$271$	1.73205	+	1.00000i	0.105215	+	0.0607457i	−0.446469	+	0.894799i	$0.647319\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.73205	+	1.00000i	0.104447	+	0.0603023i
$276$		0			0
$277$	15.0000	+	25.9808i	0.901263	+	1.56103i	0.825857	+	0.563880i	$0.190692\pi$
$277$	15.0000	+	25.9808i	0.901263	+	1.56103i	0.0754058	+	0.997153i	$0.475975\pi$
$278$		0			0
$279$	25.9808	−	15.0000i	1.55543	−	0.898027i
$280$		0			0
$281$		−	14.0000i		−	0.835170i	−0.908638	−	0.417585i	$-0.862877\pi$
$281$		−	14.0000i		−	0.835170i	0.908638	−	0.417585i	$-0.137123\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$		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
$293$	−12.1244	+	7.00000i	−0.708312	+	0.408944i	−0.810436	−	0.585827i	$-0.800770\pi$
$293$	−12.1244	+	7.00000i	−0.708312	+	0.408944i	0.102123	+	0.994772i	$0.467436\pi$
$294$		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
$301$	−6.92820	−	4.00000i	−0.399335	−	0.230556i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.46410	−	2.00000i	0.198354	−	0.114520i
$306$		0			0
$307$		−	34.0000i		−	1.94048i	−0.242140	−	0.970241i	$-0.577849\pi$
$307$		−	34.0000i		−	1.94048i	0.242140	−	0.970241i	$-0.422151\pi$
$308$		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
$317$		−	18.0000i		−	1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$		0			0
$319$	−3.46410	+	2.00000i	−0.193952	+	0.111979i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	31.1769	+	18.0000i	1.73473	+	1.00155i
$324$		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
$331$	19.0526	−	11.0000i	1.04722	−	0.604615i	0.125353	−	0.992112i	$-0.459994\pi$
$331$	19.0526	−	11.0000i	1.04722	−	0.604615i	0.921871	+	0.387498i	$0.126660\pi$
$332$		0			0
$333$			18.0000i			0.986394i
$334$		0			0
$335$	10.0000	−	17.3205i	0.546358	−	0.946320i
$336$		0			0
$337$	10.0000			0.544735			0.272367	−	0.962193i	$-0.412193\pi$
$337$	10.0000			0.544735			0.272367	+	0.962193i	$0.412193\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	10.0000	−	17.3205i	0.541530	−	0.937958i
$342$		0			0
$343$		−	20.0000i		−	1.07990i
$344$		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
$349$	−8.66025	−	5.00000i	−0.463573	−	0.267644i	0.249973	−	0.968253i	$-0.419578\pi$
$349$	−8.66025	−	5.00000i	−0.463573	−	0.267644i	−0.713545	+	0.700609i	$0.752912\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.1244	−	7.00000i	−0.645314	−	0.372572i	0.141344	−	0.989960i	$-0.454858\pi$
$353$	−12.1244	−	7.00000i	−0.645314	−	0.372572i	−0.786659	+	0.617388i	$0.788191\pi$
$354$		0			0
$355$	10.0000	+	17.3205i	0.530745	+	0.919277i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			30.0000i			1.58334i	0.610949	+	0.791670i	$0.290788\pi$
$359$			30.0000i			1.58334i	−0.610949	+	0.791670i	$0.709212\pi$
$360$		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
$369$		−	18.0000i		−	0.937043i
$370$		0			0
$371$	−10.3923	+	6.00000i	−0.539542	+	0.311504i
$372$		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
$379$	8.66025	+	5.00000i	0.444847	+	0.256833i	0.705652	−	0.708559i	$-0.250654\pi$
$379$	8.66025	+	5.00000i	0.444847	+	0.256833i	−0.260804	+	0.965392i	$0.583988\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−15.5885	+	9.00000i	−0.796533	+	0.459879i	−0.842257	−	0.539076i	$-0.818774\pi$
$383$	−15.5885	+	9.00000i	−0.796533	+	0.459879i	0.0457244	+	0.998954i	$0.485440\pi$
$384$		0			0
$385$			8.00000i			0.407718i
$386$		0			0
$387$	−6.00000	+	10.3923i	−0.304997	+	0.528271i
$388$		0			0
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$		0			0
$391$	48.0000			2.42746
$392$		0			0
$393$		0			0
$394$		0			0
$395$			8.00000i			0.402524i
$396$		0			0
$397$	1.73205	−	1.00000i	0.0869291	−	0.0501886i	−0.455905	−	0.890028i	$-0.650684\pi$
$397$	1.73205	−	1.00000i	0.0869291	−	0.0501886i	0.542834	+	0.839840i	$0.317351\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.19615	+	3.00000i	0.259483	+	0.149813i	0.624099	−	0.781345i	$-0.285466\pi$
$401$	5.19615	+	3.00000i	0.259483	+	0.149813i	−0.364615	+	0.931158i	$0.618800\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	15.5885	+	9.00000i	0.774597	+	0.447214i
$406$		0			0
$407$	6.00000	+	10.3923i	0.297409	+	0.515127i
$408$		0			0
$409$	12.1244	−	7.00000i	0.599511	−	0.346128i	−0.169338	−	0.985558i	$-0.554163\pi$
$409$	12.1244	−	7.00000i	0.599511	−	0.346128i	0.768849	+	0.639430i	$0.220830\pi$
$410$		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
$421$		−	10.0000i		−	0.487370i	−0.969854	−	0.243685i	$-0.921644\pi$
$421$		−	10.0000i		−	0.487370i	0.969854	−	0.243685i	$-0.0783563\pi$
$422$		0			0
$423$	5.19615	−	3.00000i	0.252646	−	0.145865i
$424$		0			0
$425$	3.00000	+	5.19615i	0.145521	+	0.252050i
$426$		0			0
$427$	−3.46410	−	2.00000i	−0.167640	−	0.0967868i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−25.9808	−	15.0000i	−1.25145	−	0.722525i	−0.280052	−	0.959985i	$-0.590352\pi$
$431$	−25.9808	−	15.0000i	−1.25145	−	0.722525i	−0.971397	+	0.237460i	$0.923685\pi$
$432$		0			0
$433$	−7.00000	−	12.1244i	−0.336399	−	0.582659i	0.647354	−	0.762190i	$-0.275876\pi$
$433$	−7.00000	−	12.1244i	−0.336399	−	0.582659i	−0.983752	+	0.179530i	$0.942542\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	48.0000i		−	2.29615i
$438$		0			0
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	−0.991322	−	0.131453i	$-0.958036\pi$
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	0.609503	+	0.792784i	$0.291369\pi$
$440$		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
$449$	−32.9090	+	19.0000i	−1.55307	+	0.896665i	−0.555181	+	0.831730i	$0.687351\pi$
$449$	−32.9090	+	19.0000i	−1.55307	+	0.896665i	−0.997889	+	0.0649356i	$0.979316\pi$
$450$		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
$457$	29.4449	+	17.0000i	1.37737	+	0.795226i	0.991843	−	0.127469i	$-0.0406853\pi$
$457$	29.4449	+	17.0000i	1.37737	+	0.795226i	0.385530	+	0.922695i	$0.374019\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.19615	−	3.00000i	0.242009	−	0.139724i	−0.374091	−	0.927392i	$-0.622045\pi$
$461$	5.19615	−	3.00000i	0.242009	−	0.139724i	0.616100	+	0.787668i	$0.288712\pi$
$462$		0			0
$463$			22.0000i			1.02243i	0.859454	+	0.511213i	$0.170804\pi$
$463$			22.0000i			1.02243i	−0.859454	+	0.511213i	$0.829196\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−20.0000			−0.925490			−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000			−0.925490			−0.462745	+	0.886492i	$0.653135\pi$
$468$		0			0
$469$	−20.0000			−0.923514
$470$		0			0
$471$		0			0
$472$		0			0
$473$			8.00000i			0.367840i
$474$		0			0
$475$	5.19615	−	3.00000i	0.238416	−	0.137649i
$476$		0			0
$477$	9.00000	+	15.5885i	0.412082	+	0.713746i
$478$		0			0
$479$	15.5885	+	9.00000i	0.712255	+	0.411220i	0.811895	−	0.583803i	$-0.198436\pi$
$479$	15.5885	+	9.00000i	0.712255	+	0.411220i	−0.0996406	+	0.995023i	$0.531769\pi$
$480$		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
$487$	−1.73205	+	1.00000i	−0.0784867	+	0.0453143i	−0.538730	−	0.842479i	$-0.681096\pi$
$487$	−1.73205	+	1.00000i	−0.0784867	+	0.0453143i	0.460243	+	0.887793i	$0.347762\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	−0.998467	−	0.0553560i	$-0.982371\pi$
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	0.547173	+	0.837020i	$0.315704\pi$
$492$		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
$499$			14.0000i			0.626726i	0.949633	+	0.313363i	$0.101456\pi$
$499$			14.0000i			0.626726i	−0.949633	+	0.313363i	$0.898544\pi$
$500$		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
$505$	3.46410	+	2.00000i	0.154150	+	0.0889988i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.1244	−	7.00000i	−0.537403	−	0.310270i	0.206623	−	0.978421i	$-0.433753\pi$
$509$	−12.1244	−	7.00000i	−0.537403	−	0.310270i	−0.744026	+	0.668151i	$0.767086\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	16.0000i		−	0.705044i
$516$		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
$527$	51.9615	−	30.0000i	2.26348	−	1.30682i
$528$		0			0
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$		0			0
$531$	−25.9808	−	15.0000i	−1.12747	−	0.650945i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−27.7128	−	16.0000i	−1.19813	−	0.691740i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5.19615	+	3.00000i	−0.223814	+	0.129219i
$540$		0			0
$541$			26.0000i			1.11783i	0.829226	+	0.558914i	$0.188782\pi$
$541$			26.0000i			1.11783i	−0.829226	+	0.558914i	$0.811218\pi$
$542$		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
$551$			12.0000i			0.511217i
$552$		0			0
$553$	6.92820	−	4.00000i	0.294617	−	0.170097i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−36.3731	−	21.0000i	−1.54118	−	0.889799i	−0.998765	−	0.0496855i	$-0.984178\pi$
$557$	−36.3731	−	21.0000i	−1.54118	−	0.889799i	−0.542411	−	0.840113i	$-0.682489\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	0.820798	−	0.571218i	$-0.193529\pi$
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	−0.905088	+	0.425223i	$0.860196\pi$
$564$		0			0
$565$	−24.2487	+	14.0000i	−1.02015	+	0.588984i
$566$		0			0
$567$		−	18.0000i		−	0.755929i
$568$		0			0
$569$	5.00000	−	8.66025i	0.209611	−	0.363057i	−0.741981	−	0.670421i	$-0.766114\pi$
$569$	5.00000	−	8.66025i	0.209611	−	0.363057i	0.951592	+	0.307364i	$0.0994469\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.00000	−	6.92820i	0.166812	−	0.288926i
$576$		0			0
$577$			6.00000i			0.249783i	0.992170	+	0.124892i	$0.0398583\pi$
$577$			6.00000i			0.249783i	−0.992170	+	0.124892i	$0.960142\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−6.00000	−	10.3923i	−0.248922	−	0.431145i
$582$		0			0
$583$	10.3923	+	6.00000i	0.430405	+	0.248495i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	22.5167	+	13.0000i	0.929362	+	0.536567i	0.886610	−	0.462518i	$-0.153054\pi$
$587$	22.5167	+	13.0000i	0.929362	+	0.536567i	0.0427523	+	0.999086i	$0.486387\pi$
$588$		0			0
$589$	−30.0000	−	51.9615i	−1.23613	−	2.14104i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			26.0000i			1.06769i	0.845582	+	0.533846i	$0.179254\pi$
$593$			26.0000i			1.06769i	−0.845582	+	0.533846i	$0.820746\pi$
$594$		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
$603$			30.0000i			1.22169i
$604$		0			0
$605$	−12.1244	+	7.00000i	−0.492925	+	0.284590i
$606$		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
$613$	22.5167	+	13.0000i	0.909439	+	0.525065i	0.880251	−	0.474509i	$-0.157374\pi$
$613$	22.5167	+	13.0000i	0.909439	+	0.525065i	0.0291886	+	0.999574i	$0.490708\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−29.4449	+	17.0000i	−1.18541	+	0.684394i	−0.957259	−	0.289233i	$-0.906600\pi$
$617$	−29.4449	+	17.0000i	−1.18541	+	0.684394i	−0.228147	+	0.973627i	$0.573267\pi$
$618$		0			0
$619$		−	2.00000i		−	0.0803868i	−0.999192	−	0.0401934i	$-0.987203\pi$
$619$		−	2.00000i		−	0.0803868i	0.999192	−	0.0401934i	$-0.0127974\pi$
$620$		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
$629$			36.0000i			1.43541i
$630$		0			0
$631$	19.0526	−	11.0000i	0.758470	−	0.437903i	−0.0702759	−	0.997528i	$-0.522388\pi$
$631$	19.0526	−	11.0000i	0.758470	−	0.437903i	0.828746	+	0.559625i	$0.189055\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	13.8564	+	8.00000i	0.549875	+	0.317470i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−25.9808	−	15.0000i	−1.02778	−	0.593391i
$640$		0			0
$641$	−13.0000	−	22.5167i	−0.513469	−	0.889355i	−0.999878	−	0.0156233i	$-0.995027\pi$
$641$	−13.0000	−	22.5167i	−0.513469	−	0.889355i	0.486409	−	0.873731i	$-0.338307\pi$
$642$		0			0
$643$	−1.73205	+	1.00000i	−0.0683054	+	0.0394362i	−0.533764	−	0.845634i	$-0.679223\pi$
$643$	−1.73205	+	1.00000i	−0.0683054	+	0.0394362i	0.465458	+	0.885070i	$0.345890\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−16.0000	+	27.7128i	−0.629025	+	1.08950i	0.358723	+	0.933444i	$0.383212\pi$
$647$	−16.0000	+	27.7128i	−0.629025	+	1.08950i	−0.987748	+	0.156059i	$0.950121\pi$
$648$		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
$655$			32.0000i			1.25034i
$656$		0			0
$657$	−5.19615	+	3.00000i	−0.202721	+	0.117041i
$658$		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
$661$	−1.73205	−	1.00000i	−0.0673690	−	0.0388955i	0.465937	−	0.884818i	$-0.345717\pi$
$661$	−1.73205	−	1.00000i	−0.0673690	−	0.0388955i	−0.533306	+	0.845922i	$0.679051\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	20.7846	+	12.0000i	0.805993	+	0.465340i
$666$		0			0
$667$	8.00000	+	13.8564i	0.309761	+	0.536522i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			4.00000i			0.154418i
$672$		0			0
$673$	−13.0000	+	22.5167i	−0.501113	+	0.867953i	0.498886	+	0.866668i	$0.333743\pi$
$673$	−13.0000	+	22.5167i	−0.501113	+	0.867953i	−0.999999	+	0.00128586i	$0.999591\pi$
$674$		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
$683$	−1.73205	+	1.00000i	−0.0662751	+	0.0382639i	−0.532771	−	0.846259i	$-0.678849\pi$
$683$	−1.73205	+	1.00000i	−0.0662751	+	0.0382639i	0.466496	+	0.884523i	$0.345516\pi$
$684$		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
$691$	29.4449	+	17.0000i	1.12014	+	0.646710i	0.941435	−	0.337193i	$-0.109478\pi$
$691$	29.4449	+	17.0000i	1.12014	+	0.646710i	0.178700	+	0.983904i	$0.442811\pi$
$692$		0			0
$693$	−6.00000	−	10.3923i	−0.227921	−	0.394771i
$694$		0			0
$695$	−27.7128	+	16.0000i	−1.05121	+	0.606915i
$696$		0			0
$697$		−	36.0000i		−	1.36360i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$	36.0000			1.35777
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	4.00000i		−	0.150435i
$708$		0			0
$709$	−19.0526	+	11.0000i	−0.715534	+	0.413114i	−0.813107	−	0.582115i	$-0.802225\pi$
$709$	−19.0526	+	11.0000i	−0.715534	+	0.413114i	0.0975728	+	0.995228i	$0.468892\pi$
$710$		0			0
$711$	−6.00000	−	10.3923i	−0.225018	−	0.389742i
$712$		0			0
$713$	−69.2820	−	40.0000i	−2.59463	−	1.49801i
$714$		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	$-0.898699\pi$
$719$	−20.0000	−	34.6410i	−0.745874	−	1.29189i	0.203911	−	0.978989i	$-0.434635\pi$
$720$		0			0
$721$	−13.8564	+	8.00000i	−0.516040	+	0.297936i
$722$		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	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−12.0000	+	20.7846i	−0.443836	+	0.768747i
$732$		0			0
$733$		−	26.0000i		−	0.960332i	−0.877178	−	0.480166i	$-0.840576\pi$
$733$		−	26.0000i		−	0.960332i	0.877178	−	0.480166i	$-0.159424\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.0000	+	17.3205i	0.368355	+	0.638009i
$738$		0			0
$739$	−5.19615	−	3.00000i	−0.191144	−	0.110357i	0.401374	−	0.915914i	$-0.368533\pi$
$739$	−5.19615	−	3.00000i	−0.191144	−	0.110357i	−0.592518	+	0.805557i	$0.701866\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−12.1244	−	7.00000i	−0.444799	−	0.256805i	0.260832	−	0.965384i	$-0.416003\pi$
$743$	−12.1244	−	7.00000i	−0.444799	−	0.256805i	−0.705631	+	0.708579i	$0.749337\pi$
$744$		0			0
$745$	18.0000	+	31.1769i	0.659469	+	1.14223i
$746$		0			0
$747$	−15.5885	+	9.00000i	−0.570352	+	0.329293i
$748$		0			0
$749$			32.0000i			1.16925i
$750$		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
$761$	15.5885	−	9.00000i	0.565081	−	0.326250i	−0.190101	−	0.981764i	$-0.560882\pi$
$761$	15.5885	−	9.00000i	0.565081	−	0.326250i	0.755182	+	0.655515i	$0.227548\pi$
$762$		0			0
$763$	−14.0000	−	24.2487i	−0.506834	−	0.877862i
$764$		0			0
$765$	31.1769	+	18.0000i	1.12720	+	0.650791i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−46.7654	−	27.0000i	−1.68640	−	0.973645i	−0.957236	−	0.289309i	$-0.906575\pi$
$769$	−46.7654	−	27.0000i	−1.68640	−	0.973645i	−0.729167	−	0.684336i	$-0.760092\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	39.8372	−	23.0000i	1.43284	−	0.827253i	0.435507	−	0.900186i	$-0.356569\pi$
$773$	39.8372	−	23.0000i	1.43284	−	0.827253i	0.997337	+	0.0729331i	$0.0232359\pi$
$774$		0			0
$775$		−	10.0000i		−	0.359211i
$776$		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
$785$		−	4.00000i		−	0.142766i
$786$		0			0
$787$	32.9090	−	19.0000i	1.17308	−	0.677277i	0.218675	−	0.975798i	$-0.429827\pi$
$787$	32.9090	−	19.0000i	1.17308	−	0.677277i	0.954403	+	0.298521i	$0.0964933\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	24.2487	+	14.0000i	0.862185	+	0.497783i
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.00000	+	15.5885i	0.318796	+	0.552171i	0.980237	−	0.197826i	$-0.0633881\pi$
$797$	9.00000	+	15.5885i	0.318796	+	0.552171i	−0.661441	+	0.749997i	$0.730055\pi$
$798$		0			0
$799$	10.3923	−	6.00000i	0.367653	−	0.212265i
$800$		0			0
$801$			18.0000i			0.635999i
$802$		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
$811$			22.0000i			0.772524i	0.922389	+	0.386262i	$0.126234\pi$
$811$			22.0000i			0.772524i	−0.922389	+	0.386262i	$0.873766\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	10.0000	+	17.3205i	0.350285	+	0.606711i
$816$		0			0
$817$	20.7846	+	12.0000i	0.727161	+	0.419827i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.73205	+	1.00000i	0.0604490	+	0.0349002i	0.529920	−	0.848048i	$-0.322222\pi$
$821$	1.73205	+	1.00000i	0.0604490	+	0.0349002i	−0.469471	+	0.882948i	$0.655555\pi$
$822$		0			0
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	0.577474	−	0.816409i	$-0.304038\pi$
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	−0.995768	+	0.0919029i	$0.970705\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			6.00000i			0.208640i	0.994544	+	0.104320i	$0.0332667\pi$
$827$			6.00000i			0.208640i	−0.994544	+	0.104320i	$0.966733\pi$
$828$		0			0
$829$	11.0000	−	19.0526i	0.382046	−	0.661723i	−0.609309	−	0.792933i	$-0.708553\pi$
$829$	11.0000	−	19.0526i	0.382046	−	0.661723i	0.991355	+	0.131210i	$0.0418863\pi$
$830$		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
$839$	−8.66025	+	5.00000i	−0.298985	+	0.172619i	−0.641987	−	0.766716i	$-0.721890\pi$
$839$	−8.66025	+	5.00000i	−0.298985	+	0.172619i	0.343002	+	0.939335i	$0.388556\pi$
$840$		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
$847$	12.1244	+	7.00000i	0.416598	+	0.240523i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	41.5692	−	24.0000i	1.42497	−	0.822709i
$852$		0			0
$853$		−	38.0000i		−	1.30110i	−0.759465	−	0.650548i	$-0.774539\pi$
$853$		−	38.0000i		−	1.30110i	0.759465	−	0.650548i	$-0.225461\pi$
$854$		0			0
$855$	18.0000	−	31.1769i	0.615587	−	1.06623i
$856$		0			0
$857$	38.0000			1.29806			0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000			1.29806			0.649028	+	0.760765i	$0.275176\pi$
$858$		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
$863$		−	34.0000i		−	1.15737i	−0.815550	−	0.578687i	$-0.803565\pi$
$863$		−	34.0000i		−	1.15737i	0.815550	−	0.578687i	$-0.196435\pi$
$864$		0			0
$865$	−17.3205	+	10.0000i	−0.588915	+	0.340010i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6.92820	−	4.00000i	−0.235023	−	0.135691i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−5.19615	−	3.00000i	−0.175863	−	0.101535i
$874$		0			0
$875$	12.0000	+	20.7846i	0.405674	+	0.702648i
$876$		0			0
$877$	−15.5885	+	9.00000i	−0.526385	+	0.303908i	−0.739543	−	0.673109i	$-0.764958\pi$
$877$	−15.5885	+	9.00000i	−0.526385	+	0.303908i	0.213158	+	0.977018i	$0.431625\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	9.00000	−	15.5885i	0.303218	−	0.525188i	−0.673645	−	0.739055i	$-0.735272\pi$
$881$	9.00000	−	15.5885i	0.303218	−	0.525188i	0.976863	+	0.213866i	$0.0686057\pi$
$882$		0			0
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$		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
$889$		−	16.0000i		−	0.536623i
$890$		0			0
$891$	−15.5885	+	9.00000i	−0.522233	+	0.301511i
$892$		0			0
$893$	−6.00000	−	10.3923i	−0.200782	−	0.347765i
$894$		0			0
$895$	−20.7846	−	12.0000i	−0.694753	−	0.401116i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	17.3205	+	10.0000i	0.577671	+	0.333519i
$900$		0			0
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	12.0000i		−	0.398893i
$906$		0			0
$907$	18.0000	−	31.1769i	0.597680	−	1.03521i	−0.395482	−	0.918474i	$-0.629423\pi$
$907$	18.0000	−	31.1769i	0.597680	−	1.03521i	0.993163	−	0.116739i	$-0.0372441\pi$
$908$		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
$917$	27.7128	−	16.0000i	0.915158	−	0.528367i
$918$		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
$925$	5.19615	+	3.00000i	0.170848	+	0.0986394i
$926$		0			0
$927$	12.0000	+	20.7846i	0.394132	+	0.682656i
$928$		0			0
$929$	46.7654	−	27.0000i	1.53432	−	0.885841i	0.535167	−	0.844746i	$-0.320249\pi$
$929$	46.7654	−	27.0000i	1.53432	−	0.885841i	0.999155	−	0.0410949i	$-0.0130846\pi$
$930$		0			0
$931$			18.0000i			0.589926i
$932$		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
$941$		−	10.0000i		−	0.325991i	−0.986627	−	0.162995i	$-0.947884\pi$
$941$		−	10.0000i		−	0.325991i	0.986627	−	0.162995i	$-0.0521156\pi$
$942$		0			0
$943$	−41.5692	+	24.0000i	−1.35368	+	0.781548i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	36.3731	+	21.0000i	1.18197	+	0.682408i	0.956469	−	0.291835i	$-0.0942660\pi$
$947$	36.3731	+	21.0000i	1.18197	+	0.682408i	0.225497	+	0.974244i	$0.427599\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	13.0000	+	22.5167i	0.421111	+	0.729386i	0.996048	−	0.0888114i	$-0.0283068\pi$
$953$	13.0000	+	22.5167i	0.421111	+	0.729386i	−0.574937	+	0.818198i	$0.694974\pi$
$954$		0			0
$955$	−6.92820	+	4.00000i	−0.224191	+	0.129437i
$956$		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
$967$		−	50.0000i		−	1.60789i	−0.594703	−	0.803946i	$-0.702730\pi$
$967$		−	50.0000i		−	1.60789i	0.594703	−	0.803946i	$-0.297270\pi$
$968$		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
$973$	27.7128	+	16.0000i	0.888432	+	0.512936i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.5885	+	9.00000i	0.498719	+	0.287936i	0.728184	−	0.685381i	$-0.240364\pi$
$977$	15.5885	+	9.00000i	0.498719	+	0.287936i	−0.229465	+	0.973317i	$0.573698\pi$
$978$		0			0
$979$	6.00000	+	10.3923i	0.191761	+	0.332140i
$980$		0			0
$981$	−36.3731	+	21.0000i	−1.16130	+	0.670478i
$982$		0			0
$983$			14.0000i			0.446531i	0.974758	+	0.223265i	$0.0716716\pi$
$983$			14.0000i			0.446531i	−0.974758	+	0.223265i	$0.928328\pi$
$984$		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
$995$	−27.7128	+	16.0000i	−0.878555	+	0.507234i
$996$		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.h.c.485.1		4
13.2	odd	12		676.2.e.b.653.1		2
13.3	even	3	inner	676.2.h.c.361.1		4
13.4	even	6		676.2.d.c.337.2		2
13.5	odd	4		676.2.e.b.529.1		2
13.6	odd	12		676.2.a.c.1.1		1
13.7	odd	12		52.2.a.a.1.1	✓	1
13.8	odd	4		676.2.e.c.529.1		2
13.9	even	3		676.2.d.c.337.1		2
13.10	even	6	inner	676.2.h.c.361.2		4
13.11	odd	12		676.2.e.c.653.1		2
13.12	even	2	inner	676.2.h.c.485.2		4
39.17	odd	6		6084.2.b.m.4393.1		2
39.20	even	12		468.2.a.b.1.1		1
39.32	even	12		6084.2.a.m.1.1		1
39.35	odd	6		6084.2.b.m.4393.2		2
52.7	even	12		208.2.a.c.1.1		1
52.19	even	12		2704.2.a.g.1.1		1
52.35	odd	6		2704.2.f.f.337.1		2
52.43	odd	6		2704.2.f.f.337.2		2
65.7	even	12		1300.2.c.c.1249.1		2
65.33	even	12		1300.2.c.c.1249.2		2
65.59	odd	12		1300.2.a.d.1.1		1
91.20	even	12		2548.2.a.e.1.1		1
91.33	even	12		2548.2.j.f.1145.1		2
91.46	odd	12		2548.2.j.e.1353.1		2
91.59	even	12		2548.2.j.f.1353.1		2
91.72	odd	12		2548.2.j.e.1145.1		2
104.59	even	12		832.2.a.f.1.1		1
104.85	odd	12		832.2.a.e.1.1		1
117.7	odd	12		4212.2.i.d.1405.1		2
117.20	even	12		4212.2.i.i.1405.1		2
117.59	even	12		4212.2.i.i.2809.1		2
117.85	odd	12		4212.2.i.d.2809.1		2
143.98	even	12		6292.2.a.g.1.1		1
156.59	odd	12		1872.2.a.f.1.1		1
208.59	even	12		3328.2.b.e.1665.2		2
208.85	odd	12		3328.2.b.q.1665.2		2
208.163	even	12		3328.2.b.e.1665.1		2
208.189	odd	12		3328.2.b.q.1665.1		2
260.59	even	12		5200.2.a.q.1.1		1
312.59	odd	12		7488.2.a.bw.1.1		1
312.293	even	12		7488.2.a.bn.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.a.a.1.1	✓	1	13.7	odd	12
208.2.a.c.1.1		1	52.7	even	12
468.2.a.b.1.1		1	39.20	even	12
676.2.a.c.1.1		1	13.6	odd	12
676.2.d.c.337.1		2	13.9	even	3
676.2.d.c.337.2		2	13.4	even	6
676.2.e.b.529.1		2	13.5	odd	4
676.2.e.b.653.1		2	13.2	odd	12
676.2.e.c.529.1		2	13.8	odd	4
676.2.e.c.653.1		2	13.11	odd	12
676.2.h.c.361.1		4	13.3	even	3	inner
676.2.h.c.361.2		4	13.10	even	6	inner
676.2.h.c.485.1		4	1.1	even	1	trivial
676.2.h.c.485.2		4	13.12	even	2	inner
832.2.a.e.1.1		1	104.85	odd	12
832.2.a.f.1.1		1	104.59	even	12
1300.2.a.d.1.1		1	65.59	odd	12
1300.2.c.c.1249.1		2	65.7	even	12
1300.2.c.c.1249.2		2	65.33	even	12
1872.2.a.f.1.1		1	156.59	odd	12
2548.2.a.e.1.1		1	91.20	even	12
2548.2.j.e.1145.1		2	91.72	odd	12
2548.2.j.e.1353.1		2	91.46	odd	12
2548.2.j.f.1145.1		2	91.33	even	12
2548.2.j.f.1353.1		2	91.59	even	12
2704.2.a.g.1.1		1	52.19	even	12
2704.2.f.f.337.1		2	52.35	odd	6
2704.2.f.f.337.2		2	52.43	odd	6
3328.2.b.e.1665.1		2	208.163	even	12
3328.2.b.e.1665.2		2	208.59	even	12
3328.2.b.q.1665.1		2	208.189	odd	12
3328.2.b.q.1665.2		2	208.85	odd	12
4212.2.i.d.1405.1		2	117.7	odd	12
4212.2.i.d.2809.1		2	117.85	odd	12
4212.2.i.i.1405.1		2	117.20	even	12
4212.2.i.i.2809.1		2	117.59	even	12
5200.2.a.q.1.1		1	260.59	even	12
6084.2.a.m.1.1		1	39.32	even	12
6084.2.b.m.4393.1		2	39.17	odd	6
6084.2.b.m.4393.2		2	39.35	odd	6
6292.2.a.g.1.1		1	143.98	even	12
7488.2.a.bn.1.1		1	312.293	even	12
7488.2.a.bw.1.1		1	312.59	odd	12

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.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{5} +(-1.73205 + 1.00000i) q^{7} +(1.50000 + 2.59808i) q^{9} +(1.73205 + 1.00000i) q^{11} +(3.00000 + 5.19615i) q^{17} +(5.19615 - 3.00000i) q^{19} +(4.00000 - 6.92820i) q^{23} +1.00000 q^{25} +(-1.00000 + 1.73205i) q^{29} -10.0000i q^{31} +(2.00000 + 3.46410i) q^{35} +(5.19615 + 3.00000i) q^{37} +(-5.19615 - 3.00000i) q^{41} +(2.00000 + 3.46410i) q^{43} +(5.19615 - 3.00000i) q^{45} -2.00000i q^{47} +(-1.50000 + 2.59808i) q^{49} +6.00000 q^{53} +(2.00000 - 3.46410i) q^{55} +(-8.66025 + 5.00000i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-5.19615 - 3.00000i) q^{63} +(8.66025 + 5.00000i) q^{67} +(-8.66025 + 5.00000i) q^{71} +2.00000i q^{73} -4.00000 q^{77} -4.00000 q^{79} +(-4.50000 + 7.79423i) q^{81} +6.00000i q^{83} +(10.3923 - 6.00000i) q^{85} +(5.19615 + 3.00000i) q^{89} +(-6.00000 - 10.3923i) q^{95} +(-1.73205 + 1.00000i) q^{97} +6.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{9} + 12 q^{17} + 16 q^{23} + 4 q^{25} - 4 q^{29} + 8 q^{35} + 8 q^{43} - 6 q^{49} + 24 q^{53} + 8 q^{55} + 4 q^{61} - 16 q^{77} - 16 q^{79} - 18 q^{81} - 24 q^{95}+O(q^{100}) \) 4 * q + 6 * q^9 + 12 * q^17 + 16 * q^23 + 4 * q^25 - 4 * q^29 + 8 * q^35 + 8 * q^43 - 6 * q^49 + 24 * q^53 + 8 * q^55 + 4 * q^61 - 16 * q^77 - 16 * q^79 - 18 * q^81 - 24 * q^95

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