LMFDB - Embedded newform 2352.2.q.x.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2352,2,Mod(961,2352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2352, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("2352.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2352 = 2^{4} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2352.q (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:	$18.7808145554$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2352.961
Dual form			2352.2.q.x.1537.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(0.500000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{11} -2.00000 q^{13} +2.00000 q^{15} +(3.00000 + 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{19} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -2.00000 q^{29} +(-2.00000 + 3.46410i) q^{33} +(-3.00000 + 5.19615i) q^{37} +(-1.00000 - 1.73205i) q^{39} +2.00000 q^{41} +4.00000 q^{43} +(1.00000 + 1.73205i) q^{45} +(-3.00000 + 5.19615i) q^{51} +(-3.00000 - 5.19615i) q^{53} +8.00000 q^{55} +4.00000 q^{57} +(6.00000 + 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +(-2.00000 + 3.46410i) q^{65} +(2.00000 + 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(-8.00000 + 13.8564i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +12.0000 q^{85} +(-1.00000 - 1.73205i) q^{87} +(7.00000 - 12.1244i) q^{89} +(-4.00000 - 6.92820i) q^{95} +18.0000 q^{97} -4.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + 2 q^{5} - q^{9}+O(q^{10}) $ 2 * q + q^3 + 2 * q^5 - q^9	$ 2 q + q^{3} + 2 q^{5} - q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{15} + 6 q^{17} + 4 q^{19} + q^{25} - 2 q^{27} - 4 q^{29} - 4 q^{33} - 6 q^{37} - 2 q^{39} + 4 q^{41} + 8 q^{43} + 2 q^{45} - 6 q^{51} - 6 q^{53} + 16 q^{55} + 8 q^{57} + 12 q^{59} + 2 q^{61} - 4 q^{65} + 4 q^{67} + 6 q^{73} - q^{75} - 16 q^{79} - q^{81} + 24 q^{83} + 24 q^{85} - 2 q^{87} + 14 q^{89} - 8 q^{95} + 36 q^{97} - 8 q^{99}+O(q^{100}) $ 2 * q + q^3 + 2 * q^5 - q^9 + 4 * q^11 - 4 * q^13 + 4 * q^15 + 6 * q^17 + 4 * q^19 + q^25 - 2 * q^27 - 4 * q^29 - 4 * q^33 - 6 * q^37 - 2 * q^39 + 4 * q^41 + 8 * q^43 + 2 * q^45 - 6 * q^51 - 6 * q^53 + 16 * q^55 + 8 * q^57 + 12 * q^59 + 2 * q^61 - 4 * q^65 + 4 * q^67 + 6 * q^73 - q^75 - 16 * q^79 - q^81 + 24 * q^83 + 24 * q^85 - 2 * q^87 + 14 * q^89 - 8 * q^95 + 36 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times$.

$n$	$785$	$1471$	$1765$	$2257$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	0.992361	+	0.123371i	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$		0			0
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$		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
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$		0			0
$33$	−2.00000	+	3.46410i	−0.348155	+	0.603023i
$34$		0			0
$35$		0			0
$36$		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
$39$	−1.00000	−	1.73205i	−0.160128	−	0.277350i
$40$		0			0
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$		0			0
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$	8.00000			1.07872
$56$		0			0
$57$	4.00000			0.529813
$58$		0			0
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	0.986447	−	0.164083i	$-0.0524664\pi$
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	−0.635323	+	0.772246i	$0.719133\pi$
$74$		0			0
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−8.00000	+	13.8564i	−0.900070	+	1.55897i	−0.0726692	+	0.997356i	$0.523152\pi$
$79$	−8.00000	+	13.8564i	−0.900070	+	1.55897i	−0.827401	+	0.561611i	$0.810182\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	12.0000			1.30158
$86$		0			0
$87$	−1.00000	−	1.73205i	−0.107211	−	0.185695i
$88$		0			0
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	−0.209585	−	0.977790i	$-0.567211\pi$
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	0.951584	−	0.307389i	$-0.0994552\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.00000	−	6.92820i	−0.410391	−	0.710819i
$96$		0			0
$97$	18.0000			1.82762			0.913812	−	0.406138i	$-0.133125\pi$
$97$	18.0000			1.82762			0.913812	+	0.406138i	$0.133125\pi$
$98$		0			0
$99$	−4.00000			−0.402015
$100$		0			0
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	−0.969664	−	0.244443i	$-0.921395\pi$
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	0.273138	−	0.961975i	$-0.411939\pi$
$102$		0			0
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	−0.753010	−	0.658009i	$-0.771399\pi$
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	0.946357	+	0.323122i	$0.104732\pi$
$108$		0			0
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	0.869953	+	0.493135i	$0.164149\pi$
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	−0.00790932	+	0.999969i	$0.502518\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$		0			0
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.00000	−	1.73205i	0.0924500	−	0.160128i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$		0			0
$123$	1.00000	+	1.73205i	0.0901670	+	0.156174i
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		0			0
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$		0			0
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.00000	+	1.73205i	−0.0860663	+	0.149071i
$136$		0			0
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$		0			0
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.00000	−	6.92820i	−0.334497	−	0.579365i
$144$		0			0
$145$	−2.00000	+	3.46410i	−0.166091	+	0.287678i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	0.903167	−	0.429289i	$-0.141236\pi$
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	−0.823359	+	0.567521i	$0.807902\pi$
$158$		0			0
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$		0			0
$165$	4.00000	+	6.92820i	0.311400	+	0.539360i
$166$		0			0
$167$	8.00000			0.619059			0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000			0.619059			0.309529	+	0.950890i	$0.399829\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$		0			0
$173$	5.00000	−	8.66025i	0.380143	−	0.658427i	−0.610939	−	0.791677i	$-0.709208\pi$
$173$	5.00000	−	8.66025i	0.380143	−	0.658427i	0.991082	+	0.133250i	$0.0425415\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−6.00000	+	10.3923i	−0.450988	+	0.781133i
$178$		0			0
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	0.781551	−	0.623841i	$-0.214429\pi$
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	−0.931038	+	0.364922i	$0.881096\pi$
$180$		0			0
$181$	−26.0000			−1.93256			−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−26.0000			−1.93256			−0.966282	+	0.257485i	$0.917106\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$		0			0
$185$	6.00000	+	10.3923i	0.441129	+	0.764057i
$186$		0			0
$187$	−12.0000	+	20.7846i	−0.877527	+	1.51992i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$		0			0
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$		0			0
$195$	−4.00000			−0.286446
$196$		0			0
$197$	22.0000			1.56744			0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000			1.56744			0.783718	+	0.621117i	$0.213321\pi$
$198$		0			0
$199$	12.0000	+	20.7846i	0.850657	+	1.47338i	0.880616	+	0.473831i	$0.157129\pi$
$199$	12.0000	+	20.7846i	0.850657	+	1.47338i	−0.0299585	+	0.999551i	$0.509538\pi$
$200$		0			0
$201$	−2.00000	+	3.46410i	−0.141069	+	0.244339i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.00000	−	3.46410i	0.139686	−	0.241943i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	16.0000			1.10674
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.00000	−	6.92820i	0.272798	−	0.472500i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.00000	+	5.19615i	−0.202721	+	0.351123i
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$		0			0
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$		0			0
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−16.0000			−1.03931
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	0.832019	−	0.554747i	$-0.187185\pi$
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	−0.896435	+	0.443176i	$0.853852\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.00000	+	6.92820i	−0.254514	+	0.440831i
$248$		0			0
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$		0			0
$251$	20.0000			1.26239			0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000			1.26239			0.631194	+	0.775625i	$0.282565\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	6.00000	+	10.3923i	0.375735	+	0.650791i
$256$		0			0
$257$	−13.0000	+	22.5167i	−0.810918	+	1.40455i	0.101305	+	0.994855i	$0.467698\pi$
$257$	−13.0000	+	22.5167i	−0.810918	+	1.40455i	−0.912222	+	0.409695i	$0.865635\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.00000	−	1.73205i	0.0618984	−	0.107211i
$262$		0			0
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	0.999970	−	0.00771799i	$-0.00245674\pi$
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	−0.506669	+	0.862141i	$0.669123\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$	14.0000			0.856786
$268$		0			0
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$		0			0
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−22.0000			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$282$		0			0
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	−0.993626	−	0.112728i	$-0.964041\pi$
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	0.399188	−	0.916869i	$-0.369292\pi$
$284$		0			0
$285$	4.00000	−	6.92820i	0.236940	−	0.410391i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	9.00000	+	15.5885i	0.527589	+	0.913812i
$292$		0			0
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$		0			0
$295$	24.0000			1.39733
$296$		0			0
$297$	−2.00000	−	3.46410i	−0.116052	−	0.201008i
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$	7.00000	−	12.1244i	0.402139	−	0.696526i
$304$		0			0
$305$	−2.00000	−	3.46410i	−0.114520	−	0.198354i
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	−13.0000	+	22.5167i	−0.734803	+	1.27272i	0.220006	+	0.975499i	$0.429392\pi$
$313$	−13.0000	+	22.5167i	−0.734803	+	1.27272i	−0.954810	+	0.297218i	$0.903941\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$		0			0
$321$	4.00000			0.223258
$322$		0			0
$323$	24.0000			1.33540
$324$		0			0
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$		0			0
$327$	−9.00000	+	15.5885i	−0.497701	+	0.862044i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	−0.915742	−	0.401768i	$-0.868396\pi$
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	0.805812	+	0.592172i	$0.201729\pi$
$332$		0			0
$333$	−3.00000	−	5.19615i	−0.164399	−	0.284747i
$334$		0			0
$335$	8.00000			0.437087
$336$		0			0
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$		0			0
$339$	−7.00000	−	12.1244i	−0.380188	−	0.658505i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−14.0000	−	24.2487i	−0.751559	−	1.30174i	−0.947067	−	0.321037i	$-0.895969\pi$
$347$	−14.0000	−	24.2487i	−0.751559	−	1.30174i	0.195507	−	0.980702i	$-0.437365\pi$
$348$		0			0
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	2.00000			0.106752
$352$		0			0
$353$	−5.00000	−	8.66025i	−0.266123	−	0.460939i	0.701734	−	0.712439i	$-0.252409\pi$
$353$	−5.00000	−	8.66025i	−0.266123	−	0.460939i	−0.967857	+	0.251500i	$0.919076\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	16.0000	−	27.7128i	0.844448	−	1.46263i	−0.0416523	−	0.999132i	$-0.513262\pi$
$359$	16.0000	−	27.7128i	0.844448	−	1.46263i	0.886100	−	0.463494i	$-0.153404\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$		0			0
$363$	−5.00000			−0.262432
$364$		0			0
$365$	12.0000			0.628109
$366$		0			0
$367$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$367$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$368$		0			0
$369$	−1.00000	+	1.73205i	−0.0520579	+	0.0901670i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$		0			0
$375$	6.00000	+	10.3923i	0.309839	+	0.536656i
$376$		0			0
$377$	4.00000			0.206010
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.00000	+	3.46410i	−0.101666	+	0.176090i
$388$		0			0
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	0.779895	−	0.625910i	$-0.215272\pi$
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	−0.932002	+	0.362454i	$0.881939\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	4.00000			0.201773
$394$		0			0
$395$	16.0000	+	27.7128i	0.805047	+	1.39438i
$396$		0			0
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	−0.546795	−	0.837267i	$-0.684152\pi$
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	0.998492	+	0.0549046i	$0.0174855\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	−0.199207	−	0.979957i	$-0.563837\pi$
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	0.948272	−	0.317460i	$-0.102830\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−2.00000			−0.0993808
$406$		0			0
$407$	−24.0000			−1.18964
$408$		0			0
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	−0.454759	+	0.890614i	$0.650275\pi$
$410$		0			0
$411$	−3.00000	+	5.19615i	−0.147979	+	0.256307i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	12.0000	−	20.7846i	0.589057	−	1.02028i
$416$		0			0
$417$	−6.00000	−	10.3923i	−0.293821	−	0.508913i
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	38.0000			1.85201			0.926003	−	0.377515i	$-0.123221\pi$
$421$	38.0000			1.85201			0.926003	+	0.377515i	$0.123221\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	4.00000	−	6.92820i	0.193122	−	0.334497i
$430$		0			0
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	−0.995706	−	0.0925683i	$-0.970492\pi$
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	0.417687	−	0.908591i	$-0.362841\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$	−4.00000			−0.191785
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	0.423556	+	0.905870i	$0.360782\pi$
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	−0.996284	+	0.0861252i	$0.972552\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$		0			0
$445$	−14.0000	−	24.2487i	−0.663664	−	1.14950i
$446$		0			0
$447$	−6.00000			−0.283790
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	4.00000	+	6.92820i	0.188353	+	0.326236i
$452$		0			0
$453$	−4.00000	+	6.92820i	−0.187936	+	0.325515i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	0.725059	+	0.688686i	$0.241812\pi$
$458$		0			0
$459$	−3.00000	−	5.19615i	−0.140028	−	0.242536i
$460$		0			0
$461$	−10.0000			−0.465746			−0.232873	−	0.972507i	$-0.574813\pi$
$461$	−10.0000			−0.465746			−0.232873	+	0.972507i	$0.574813\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	−0.0627555	−	0.998029i	$-0.519989\pi$
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	0.895696	−	0.444667i	$-0.146678\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.00000	+	1.73205i	−0.0460776	+	0.0798087i
$472$		0			0
$473$	8.00000	+	13.8564i	0.367840	+	0.637118i
$474$		0			0
$475$	4.00000			0.183533
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	0.623332	−	0.781958i	$-0.285779\pi$
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	−0.988861	+	0.148842i	$0.952445\pi$
$480$		0			0
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	18.0000	−	31.1769i	0.817338	−	1.41567i
$486$		0			0
$487$	−4.00000	−	6.92820i	−0.181257	−	0.313947i	0.761052	−	0.648691i	$-0.224683\pi$
$487$	−4.00000	−	6.92820i	−0.181257	−	0.313947i	−0.942309	+	0.334744i	$0.891350\pi$
$488$		0			0
$489$	4.00000			0.180886
$490$		0			0
$491$	−20.0000			−0.902587			−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000			−0.902587			−0.451294	+	0.892375i	$0.649037\pi$
$492$		0			0
$493$	−6.00000	−	10.3923i	−0.270226	−	0.468046i
$494$		0			0
$495$	−4.00000	+	6.92820i	−0.179787	+	0.311400i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$		0			0
$501$	4.00000	+	6.92820i	0.178707	+	0.309529i
$502$		0			0
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	−28.0000			−1.24598
$506$		0			0
$507$	−4.50000	−	7.79423i	−0.199852	−	0.346154i
$508$		0			0
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	−0.733679	−	0.679496i	$-0.762199\pi$
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	0.955300	+	0.295637i	$0.0955319\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.00000	+	3.46410i	−0.0883022	+	0.152944i
$514$		0			0
$515$	−8.00000	−	13.8564i	−0.352522	−	0.610586i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	10.0000			0.438951
$520$		0			0
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$		0			0
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	−0.997478	−	0.0709788i	$-0.977388\pi$
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	0.560208	+	0.828352i	$0.310721\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$	−12.0000			−0.520756
$532$		0			0
$533$	−4.00000			−0.173259
$534$		0			0
$535$	−4.00000	−	6.92820i	−0.172935	−	0.299532i
$536$		0			0
$537$	2.00000	−	3.46410i	0.0863064	−	0.149487i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	−0.225617	−	0.974216i	$-0.572440\pi$
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	0.956504	−	0.291718i	$-0.0942267\pi$
$542$		0			0
$543$	−13.0000	−	22.5167i	−0.557883	−	0.966282i
$544$		0			0
$545$	36.0000			1.54207
$546$		0			0
$547$	−4.00000			−0.171028			−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000			−0.171028			−0.0855138	+	0.996337i	$0.527253\pi$
$548$		0			0
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$		0			0
$551$	−4.00000	+	6.92820i	−0.170406	+	0.295151i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−6.00000	+	10.3923i	−0.254686	+	0.441129i
$556$		0			0
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	0.886433	−	0.462856i	$-0.153175\pi$
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	−0.844062	+	0.536246i	$0.819842\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$		0			0
$561$	−24.0000			−1.01328
$562$		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
$567$		0			0
$568$		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
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$		0			0
$573$	−8.00000			−0.334205
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−17.0000	−	29.4449i	−0.707719	−	1.22581i	−0.965701	−	0.259656i	$-0.916391\pi$
$577$	−17.0000	−	29.4449i	−0.707719	−	1.22581i	0.257982	−	0.966150i	$-0.416942\pi$
$578$		0			0
$579$	1.00000	−	1.73205i	0.0415586	−	0.0719816i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$		0			0
$585$	−2.00000	−	3.46410i	−0.0826898	−	0.143223i
$586$		0			0
$587$	−28.0000			−1.15568			−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000			−1.15568			−0.577842	+	0.816149i	$0.696105\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	11.0000	+	19.0526i	0.452480	+	0.783718i
$592$		0			0
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.0000	+	20.7846i	−0.491127	+	0.850657i
$598$		0			0
$599$	24.0000	+	41.5692i	0.980613	+	1.69847i	0.660006	+	0.751260i	$0.270554\pi$
$599$	24.0000	+	41.5692i	0.980613	+	1.69847i	0.320607	+	0.947212i	$0.396113\pi$
$600$		0			0
$601$	−6.00000			−0.244745			−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000			−0.244745			−0.122373	+	0.992484i	$0.539050\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$		0			0
$605$	5.00000	+	8.66025i	0.203279	+	0.352089i
$606$		0			0
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	−0.981454	−	0.191700i	$-0.938600\pi$
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	0.656744	+	0.754114i	$0.271933\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	13.0000	+	22.5167i	0.525065	+	0.909439i	0.999574	+	0.0291886i	$0.00929235\pi$
$613$	13.0000	+	22.5167i	0.525065	+	0.909439i	−0.474509	+	0.880251i	$0.657374\pi$
$614$		0			0
$615$	4.00000			0.161296
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	0.592025	−	0.805919i	$-0.298329\pi$
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	−0.993959	+	0.109749i	$0.964995\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		0			0
$627$	8.00000	+	13.8564i	0.319489	+	0.553372i
$628$		0			0
$629$	−36.0000			−1.43541
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$		0			0
$633$	−2.00000	−	3.46410i	−0.0794929	−	0.137686i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	0.631721	−	0.775196i	$-0.282349\pi$
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	−0.987200	+	0.159489i	$0.949015\pi$
$642$		0			0
$643$	−20.0000			−0.788723			−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000			−0.788723			−0.394362	+	0.918955i	$0.629034\pi$
$644$		0			0
$645$	8.00000			0.315000
$646$		0			0
$647$	−20.0000	−	34.6410i	−0.786281	−	1.36188i	−0.928231	−	0.372005i	$-0.878670\pi$
$647$	−20.0000	−	34.6410i	−0.786281	−	1.36188i	0.141950	−	0.989874i	$-0.454663\pi$
$648$		0			0
$649$	−24.0000	+	41.5692i	−0.942082	+	1.63173i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	−0.634437	−	0.772975i	$-0.718768\pi$
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	0.986634	+	0.162951i	$0.0521013\pi$
$654$		0			0
$655$	−4.00000	−	6.92820i	−0.156293	−	0.270707i
$656$		0			0
$657$	−6.00000			−0.234082
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	0.568831	−	0.822454i	$-0.307396\pi$
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	−0.996682	+	0.0813955i	$0.974062\pi$
$662$		0			0
$663$	6.00000	−	10.3923i	0.233021	−	0.403604i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−8.00000	−	13.8564i	−0.309298	−	0.535720i
$670$		0			0
$671$	8.00000			0.308837
$672$		0			0
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$		0			0
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$		0			0
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	−0.639618	−	0.768693i	$-0.720908\pi$
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	0.985517	+	0.169580i	$0.0542410\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	6.00000	−	10.3923i	0.229920	−	0.398234i
$682$		0			0
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$		0			0
$687$	10.0000			0.381524
$688$		0			0
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	−0.610704	−	0.791859i	$-0.709113\pi$
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	0.991122	+	0.132956i	$0.0424468\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−12.0000	+	20.7846i	−0.455186	+	0.788405i
$696$		0			0
$697$	6.00000	+	10.3923i	0.227266	+	0.393637i
$698$		0			0
$699$	6.00000			0.226941
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$	12.0000	+	20.7846i	0.452589	+	0.783906i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	−0.916845	−	0.399244i	$-0.869273\pi$
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	0.804178	+	0.594389i	$0.202606\pi$
$710$		0			0
$711$	−8.00000	−	13.8564i	−0.300023	−	0.519656i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−16.0000			−0.598366
$716$		0			0
$717$	−12.0000	−	20.7846i	−0.448148	−	0.776215i
$718$		0			0
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.0613050	+	0.998119i	$0.519526\pi$
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.833744	+	0.552151i	$0.813807\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1.00000	−	1.73205i	0.0371904	−	0.0644157i
$724$		0			0
$725$	−1.00000	−	1.73205i	−0.0371391	−	0.0643268i
$726$		0			0
$727$	40.0000			1.48352			0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000			1.48352			0.741759	+	0.670667i	$0.233992\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$		0			0
$733$	9.00000	−	15.5885i	0.332423	−	0.575773i	−0.650564	−	0.759452i	$-0.725467\pi$
$733$	9.00000	−	15.5885i	0.332423	−	0.575773i	0.982986	+	0.183679i	$0.0588007\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.00000	+	13.8564i	−0.294684	+	0.510407i
$738$		0			0
$739$	18.0000	+	31.1769i	0.662141	+	1.14686i	0.980052	+	0.198741i	$0.0636852\pi$
$739$	18.0000	+	31.1769i	0.662141	+	1.14686i	−0.317911	+	0.948120i	$0.602981\pi$
$740$		0			0
$741$	−8.00000			−0.293887
$742$		0			0
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$		0			0
$745$	6.00000	+	10.3923i	0.219823	+	0.380745i
$746$		0			0
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$		0			0
$753$	10.0000	+	17.3205i	0.364420	+	0.631194i
$754$		0			0
$755$	16.0000			0.582300
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−6.00000	+	10.3923i	−0.216930	+	0.375735i
$766$		0			0
$767$	−12.0000	−	20.7846i	−0.433295	−	0.750489i
$768$		0			0
$769$	2.00000			0.0721218			0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000			0.0721218			0.0360609	+	0.999350i	$0.488519\pi$
$770$		0			0
$771$	−26.0000			−0.936367
$772$		0			0
$773$	−7.00000	−	12.1244i	−0.251773	−	0.436083i	0.712241	−	0.701935i	$-0.247680\pi$
$773$	−7.00000	−	12.1244i	−0.251773	−	0.436083i	−0.964014	+	0.265852i	$0.914347\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.00000	−	6.92820i	0.143315	−	0.248229i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	2.00000			0.0714742
$784$		0			0
$785$	4.00000			0.142766
$786$		0			0
$787$	−22.0000	−	38.1051i	−0.784215	−	1.35830i	−0.929467	−	0.368906i	$-0.879732\pi$
$787$	−22.0000	−	38.1051i	−0.784215	−	1.35830i	0.145251	−	0.989395i	$-0.453601\pi$
$788$		0			0
$789$	−8.00000	+	13.8564i	−0.284808	+	0.493301i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2.00000	+	3.46410i	−0.0710221	+	0.123014i
$794$		0			0
$795$	−6.00000	−	10.3923i	−0.212798	−	0.368577i
$796$		0			0
$797$	−26.0000			−0.920967			−0.460484	−	0.887668i	$-0.652324\pi$
$797$	−26.0000			−0.920967			−0.460484	+	0.887668i	$0.652324\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	7.00000	+	12.1244i	0.247333	+	0.428393i
$802$		0			0
$803$	−12.0000	+	20.7846i	−0.423471	+	0.733473i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.00000	−	5.19615i	0.105605	−	0.182913i
$808$		0			0
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	−0.953251	−	0.302180i	$-0.902286\pi$
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	0.214930	−	0.976629i	$-0.431048\pi$
$810$		0			0
$811$	−44.0000			−1.54505			−0.772524	−	0.634985i	$-0.781006\pi$
$811$	−44.0000			−1.54505			−0.772524	+	0.634985i	$0.781006\pi$
$812$		0			0
$813$	16.0000			0.561144
$814$		0			0
$815$	−4.00000	−	6.92820i	−0.140114	−	0.242684i
$816$		0			0
$817$	8.00000	−	13.8564i	0.279885	−	0.484774i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−19.0000	+	32.9090i	−0.663105	+	1.14853i	0.316691	+	0.948529i	$0.397428\pi$
$821$	−19.0000	+	32.9090i	−0.663105	+	1.14853i	−0.979795	+	0.200002i	$0.935905\pi$
$822$		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
$825$	−4.00000			−0.139262
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	0.718481	−	0.695546i	$-0.244838\pi$
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	−0.961601	+	0.274450i	$0.911504\pi$
$830$		0			0
$831$	11.0000	−	19.0526i	0.381586	−	0.660926i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	8.00000	−	13.8564i	0.276851	−	0.479521i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.00000			0.276191			0.138095	−	0.990419i	$-0.455902\pi$
$839$	8.00000			0.276191			0.138095	+	0.990419i	$0.455902\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$	−11.0000	−	19.0526i	−0.378860	−	0.656205i
$844$		0			0
$845$	−9.00000	+	15.5885i	−0.309609	+	0.536259i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	10.0000	−	17.3205i	0.343199	−	0.594438i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−10.0000			−0.342393			−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$		0			0
$855$	8.00000			0.273594
$856$		0			0
$857$	7.00000	+	12.1244i	0.239115	+	0.414160i	0.960461	−	0.278416i	$-0.0898092\pi$
$857$	7.00000	+	12.1244i	0.239115	+	0.414160i	−0.721345	+	0.692576i	$0.756476\pi$
$858$		0			0
$859$	22.0000	−	38.1051i	0.750630	−	1.30013i	−0.196887	−	0.980426i	$-0.563083\pi$
$859$	22.0000	−	38.1051i	0.750630	−	1.30013i	0.947518	−	0.319704i	$-0.103583\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	−0.994720	−	0.102624i	$-0.967276\pi$
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	0.586235	+	0.810141i	$0.300609\pi$
$864$		0			0
$865$	−10.0000	−	17.3205i	−0.340010	−	0.588915i
$866$		0			0
$867$	−19.0000			−0.645274
$868$		0			0
$869$	−64.0000			−2.17105
$870$		0			0
$871$	−4.00000	−	6.92820i	−0.135535	−	0.234753i
$872$		0			0
$873$	−9.00000	+	15.5885i	−0.304604	+	0.527589i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−23.0000	+	39.8372i	−0.776655	+	1.34521i	0.157205	+	0.987566i	$0.449752\pi$
$877$	−23.0000	+	39.8372i	−0.776655	+	1.34521i	−0.933860	+	0.357640i	$0.883582\pi$
$878$		0			0
$879$	7.00000	+	12.1244i	0.236104	+	0.408944i
$880$		0			0
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		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
$885$	12.0000	+	20.7846i	0.403376	+	0.698667i
$886$		0			0
$887$	4.00000	−	6.92820i	0.134307	−	0.232626i	−0.791026	−	0.611783i	$-0.790453\pi$
$887$	4.00000	−	6.92820i	0.134307	−	0.232626i	0.925332	+	0.379157i	$0.123786\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.00000	−	3.46410i	0.0670025	−	0.116052i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−8.00000			−0.267411
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	18.0000	−	31.1769i	0.599667	−	1.03865i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−26.0000	+	45.0333i	−0.864269	+	1.49696i
$906$		0			0
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	0.830909	−	0.556408i	$-0.187821\pi$
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	−0.897318	+	0.441384i	$0.854488\pi$
$908$		0			0
$909$	14.0000			0.464351
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$		0			0
$913$	24.0000	+	41.5692i	0.794284	+	1.37574i
$914$		0			0
$915$	2.00000	−	3.46410i	0.0661180	−	0.114520i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	4.00000	−	6.92820i	0.131948	−	0.228540i	−0.792480	−	0.609898i	$-0.791210\pi$
$919$	4.00000	−	6.92820i	0.131948	−	0.228540i	0.924427	+	0.381358i	$0.124544\pi$
$920$		0			0
$921$	−2.00000	−	3.46410i	−0.0659022	−	0.114146i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−6.00000			−0.197279
$926$		0			0
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$		0			0
$929$	−13.0000	+	22.5167i	−0.426516	+	0.738748i	−0.996561	−	0.0828661i	$-0.973593\pi$
$929$	−13.0000	+	22.5167i	−0.426516	+	0.738748i	0.570045	+	0.821614i	$0.306926\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	12.0000	−	20.7846i	0.392862	−	0.680458i
$934$		0			0
$935$	24.0000	+	41.5692i	0.784884	+	1.35946i
$936$		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
$939$	−26.0000			−0.848478
$940$		0			0
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	−0.989599	−	0.143856i	$-0.954050\pi$
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	0.370216	−	0.928946i	$-0.379284\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	22.0000	−	38.1051i	0.714904	−	1.23825i	−0.248093	−	0.968736i	$-0.579804\pi$
$947$	22.0000	−	38.1051i	0.714904	−	1.23825i	0.962997	−	0.269514i	$-0.0868629\pi$
$948$		0			0
$949$	−6.00000	−	10.3923i	−0.194768	−	0.337348i
$950$		0			0
$951$	18.0000			0.583690
$952$		0			0
$953$	26.0000			0.842223			0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000			0.842223			0.421111	+	0.907009i	$0.361640\pi$
$954$		0			0
$955$	8.00000	+	13.8564i	0.258874	+	0.448383i
$956$		0			0
$957$	4.00000	−	6.92820i	0.129302	−	0.223957i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$		0			0
$963$	2.00000	+	3.46410i	0.0644491	+	0.111629i
$964$		0			0
$965$	−4.00000			−0.128765
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$		0			0
$969$	12.0000	+	20.7846i	0.385496	+	0.667698i
$970$		0			0
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	−0.753545	−	0.657396i	$-0.771658\pi$
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	0.946094	+	0.323891i	$0.104991\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1.00000	−	1.73205i	0.0320256	−	0.0554700i
$976$		0			0
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	0.999734	−	0.0230645i	$-0.00734232\pi$
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	−0.519841	+	0.854263i	$0.674009\pi$
$978$		0			0
$979$	56.0000			1.78977
$980$		0			0
$981$	−18.0000			−0.574696
$982$		0			0
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	0.991453	−	0.130465i	$-0.0416470\pi$
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	−0.608712	+	0.793391i	$0.708314\pi$
$984$		0			0
$985$	22.0000	−	38.1051i	0.700978	−	1.21413i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−8.00000	−	13.8564i	−0.254128	−	0.440163i	0.710530	−	0.703667i	$-0.248455\pi$
$991$	−8.00000	−	13.8564i	−0.254128	−	0.440163i	−0.964658	+	0.263504i	$0.915122\pi$
$992$		0			0
$993$	−4.00000			−0.126936
$994$		0			0
$995$	48.0000			1.52170
$996$		0			0
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	0.995077	−	0.0991016i	$-0.0315969\pi$
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	−0.583363	+	0.812211i	$0.698264\pi$
$998$		0			0
$999$	3.00000	−	5.19615i	0.0949158	−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2352.2.q.x.961.1		2
4.3	odd	2		147.2.e.b.79.1		2
7.2	even	3		336.2.a.a.1.1		1
7.3	odd	6		2352.2.q.e.1537.1		2
7.4	even	3	inner	2352.2.q.x.1537.1		2
7.5	odd	6		2352.2.a.v.1.1		1
7.6	odd	2		2352.2.q.e.961.1		2
12.11	even	2		441.2.e.a.226.1		2
21.2	odd	6		1008.2.a.l.1.1		1
21.5	even	6		7056.2.a.p.1.1		1
28.3	even	6		147.2.e.c.67.1		2
28.11	odd	6		147.2.e.b.67.1		2
28.19	even	6		147.2.a.a.1.1		1
28.23	odd	6		21.2.a.a.1.1	✓	1
28.27	even	2		147.2.e.c.79.1		2
35.9	even	6		8400.2.a.bn.1.1		1
56.5	odd	6		9408.2.a.m.1.1		1
56.19	even	6		9408.2.a.bv.1.1		1
56.37	even	6		1344.2.a.s.1.1		1
56.51	odd	6		1344.2.a.g.1.1		1
84.11	even	6		441.2.e.a.361.1		2
84.23	even	6		63.2.a.a.1.1		1
84.47	odd	6		441.2.a.f.1.1		1
84.59	odd	6		441.2.e.b.361.1		2
84.83	odd	2		441.2.e.b.226.1		2
112.37	even	12		5376.2.c.l.2689.2		2
112.51	odd	12		5376.2.c.r.2689.2		2
112.93	even	12		5376.2.c.l.2689.1		2
112.107	odd	12		5376.2.c.r.2689.1		2
140.19	even	6		3675.2.a.n.1.1		1
140.23	even	12		525.2.d.a.274.2		2
140.79	odd	6		525.2.a.d.1.1		1
140.107	even	12		525.2.d.a.274.1		2
168.107	even	6		4032.2.a.h.1.1		1
168.149	odd	6		4032.2.a.k.1.1		1
252.23	even	6		567.2.f.b.379.1		2
252.79	odd	6		567.2.f.g.190.1		2
252.191	even	6		567.2.f.b.190.1		2
252.247	odd	6		567.2.f.g.379.1		2
308.219	even	6		2541.2.a.j.1.1		1
364.51	odd	6		3549.2.a.c.1.1		1
420.23	odd	12		1575.2.d.a.1324.1		2
420.107	odd	12		1575.2.d.a.1324.2		2
420.359	even	6		1575.2.a.c.1.1		1
476.135	odd	6		6069.2.a.b.1.1		1
532.303	even	6		7581.2.a.d.1.1		1
924.527	odd	6		7623.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.2.a.a.1.1	✓	1	28.23	odd	6
63.2.a.a.1.1		1	84.23	even	6
147.2.a.a.1.1		1	28.19	even	6
147.2.e.b.67.1		2	28.11	odd	6
147.2.e.b.79.1		2	4.3	odd	2
147.2.e.c.67.1		2	28.3	even	6
147.2.e.c.79.1		2	28.27	even	2
336.2.a.a.1.1		1	7.2	even	3
441.2.a.f.1.1		1	84.47	odd	6
441.2.e.a.226.1		2	12.11	even	2
441.2.e.a.361.1		2	84.11	even	6
441.2.e.b.226.1		2	84.83	odd	2
441.2.e.b.361.1		2	84.59	odd	6
525.2.a.d.1.1		1	140.79	odd	6
525.2.d.a.274.1		2	140.107	even	12
525.2.d.a.274.2		2	140.23	even	12
567.2.f.b.190.1		2	252.191	even	6
567.2.f.b.379.1		2	252.23	even	6
567.2.f.g.190.1		2	252.79	odd	6
567.2.f.g.379.1		2	252.247	odd	6
1008.2.a.l.1.1		1	21.2	odd	6
1344.2.a.g.1.1		1	56.51	odd	6
1344.2.a.s.1.1		1	56.37	even	6
1575.2.a.c.1.1		1	420.359	even	6
1575.2.d.a.1324.1		2	420.23	odd	12
1575.2.d.a.1324.2		2	420.107	odd	12
2352.2.a.v.1.1		1	7.5	odd	6
2352.2.q.e.961.1		2	7.6	odd	2
2352.2.q.e.1537.1		2	7.3	odd	6
2352.2.q.x.961.1		2	1.1	even	1	trivial
2352.2.q.x.1537.1		2	7.4	even	3	inner
2541.2.a.j.1.1		1	308.219	even	6
3549.2.a.c.1.1		1	364.51	odd	6
3675.2.a.n.1.1		1	140.19	even	6
4032.2.a.h.1.1		1	168.107	even	6
4032.2.a.k.1.1		1	168.149	odd	6
5376.2.c.l.2689.1		2	112.93	even	12
5376.2.c.l.2689.2		2	112.37	even	12
5376.2.c.r.2689.1		2	112.107	odd	12
5376.2.c.r.2689.2		2	112.51	odd	12
6069.2.a.b.1.1		1	476.135	odd	6
7056.2.a.p.1.1		1	21.5	even	6
7581.2.a.d.1.1		1	532.303	even	6
7623.2.a.g.1.1		1	924.527	odd	6
8400.2.a.bn.1.1		1	35.9	even	6
9408.2.a.m.1.1		1	56.5	odd	6
9408.2.a.bv.1.1		1	56.19	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:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2352.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{11} -2.00000 q^{13} +2.00000 q^{15} +(3.00000 + 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{19} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -2.00000 q^{29} +(-2.00000 + 3.46410i) q^{33} +(-3.00000 + 5.19615i) q^{37} +(-1.00000 - 1.73205i) q^{39} +2.00000 q^{41} +4.00000 q^{43} +(1.00000 + 1.73205i) q^{45} +(-3.00000 + 5.19615i) q^{51} +(-3.00000 - 5.19615i) q^{53} +8.00000 q^{55} +4.00000 q^{57} +(6.00000 + 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +(-2.00000 + 3.46410i) q^{65} +(2.00000 + 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(-8.00000 + 13.8564i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +12.0000 q^{85} +(-1.00000 - 1.73205i) q^{87} +(7.00000 - 12.1244i) q^{89} +(-4.00000 - 6.92820i) q^{95} +18.0000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + 2 q^{5} - q^{9}+O(q^{10}) \) 2 * q + q^3 + 2 * q^5 - q^9	\( 2 q + q^{3} + 2 q^{5} - q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{15} + 6 q^{17} + 4 q^{19} + q^{25} - 2 q^{27} - 4 q^{29} - 4 q^{33} - 6 q^{37} - 2 q^{39} + 4 q^{41} + 8 q^{43} + 2 q^{45} - 6 q^{51} - 6 q^{53} + 16 q^{55} + 8 q^{57} + 12 q^{59} + 2 q^{61} - 4 q^{65} + 4 q^{67} + 6 q^{73} - q^{75} - 16 q^{79} - q^{81} + 24 q^{83} + 24 q^{85} - 2 q^{87} + 14 q^{89} - 8 q^{95} + 36 q^{97} - 8 q^{99}+O(q^{100}) \) 2 * q + q^3 + 2 * q^5 - q^9 + 4 * q^11 - 4 * q^13 + 4 * q^15 + 6 * q^17 + 4 * q^19 + q^25 - 2 * q^27 - 4 * q^29 - 4 * q^33 - 6 * q^37 - 2 * q^39 + 4 * q^41 + 8 * q^43 + 2 * q^45 - 6 * q^51 - 6 * q^53 + 16 * q^55 + 8 * q^57 + 12 * q^59 + 2 * q^61 - 4 * q^65 + 4 * q^67 + 6 * q^73 - q^75 - 16 * q^79 - q^81 + 24 * q^83 + 24 * q^85 - 2 * q^87 + 14 * q^89 - 8 * q^95 + 36 * q^97 - 8 * q^99

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