LMFDB - Embedded newform 392.2.m.f.19.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(19,392)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("392.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,0,0,0,0,0,16,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.3
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	392.19
Dual form			392.2.m.f.227.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 - 0.366025i) q^{2} +(-2.12132 + 1.22474i) q^{3} +(1.73205 - 1.00000i) q^{4} +(1.22474 - 2.12132i) q^{5} +(-2.44949 + 2.44949i) q^{6} +(2.00000 - 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +(0.896575 - 3.34607i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-2.44949 + 4.24264i) q^{12} +2.44949 q^{13} +6.00000i q^{15} +(2.00000 - 3.46410i) q^{16} +(4.24264 - 2.44949i) q^{17} +(1.09808 - 4.09808i) q^{18} +(-2.12132 - 1.22474i) q^{19} -4.89898i q^{20} +(-2.00000 - 2.00000i) q^{22} +(3.46410 + 2.00000i) q^{23} +(-1.79315 + 6.69213i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.34607 - 0.896575i) q^{26} +4.00000i q^{29} +(2.19615 + 8.19615i) q^{30} +(2.44949 + 4.24264i) q^{31} +(1.46410 - 5.46410i) q^{32} +(4.24264 + 2.44949i) q^{33} +(4.89898 - 4.89898i) q^{34} -6.00000i q^{36} +(-6.92820 - 4.00000i) q^{37} +(-3.34607 - 0.896575i) q^{38} +(-5.19615 + 3.00000i) q^{39} +(-1.79315 - 6.69213i) q^{40} -6.00000 q^{43} +(-3.46410 - 2.00000i) q^{44} +(-3.67423 - 6.36396i) q^{45} +(5.46410 + 1.46410i) q^{46} +(-2.44949 + 4.24264i) q^{47} +9.79796i q^{48} +(-1.00000 - 1.00000i) q^{50} +(-6.00000 + 10.3923i) q^{51} +(4.24264 - 2.44949i) q^{52} +(-3.46410 + 2.00000i) q^{53} -4.89898 q^{55} +6.00000 q^{57} +(1.46410 + 5.46410i) q^{58} +(2.12132 - 1.22474i) q^{59} +(6.00000 + 10.3923i) q^{60} +(-3.67423 + 6.36396i) q^{61} +(4.89898 + 4.89898i) q^{62} -8.00000i q^{64} +(3.00000 - 5.19615i) q^{65} +(6.69213 + 1.79315i) q^{66} +(1.00000 + 1.73205i) q^{67} +(4.89898 - 8.48528i) q^{68} -9.79796 q^{69} +10.0000i q^{71} +(-2.19615 - 8.19615i) q^{72} +(-12.7279 + 7.34847i) q^{73} +(-10.9282 - 2.92820i) q^{74} +(2.12132 + 1.22474i) q^{75} -4.89898 q^{76} +(-6.00000 + 6.00000i) q^{78} +(5.19615 + 3.00000i) q^{79} +(-4.89898 - 8.48528i) q^{80} +(4.50000 + 7.79423i) q^{81} -2.44949i q^{83} -12.0000i q^{85} +(-8.19615 + 2.19615i) q^{86} +(-4.89898 - 8.48528i) q^{87} +(-5.46410 - 1.46410i) q^{88} +(-12.7279 - 7.34847i) q^{89} +(-7.34847 - 7.34847i) q^{90} +8.00000 q^{92} +(-10.3923 - 6.00000i) q^{93} +(-1.79315 + 6.69213i) q^{94} +(-5.19615 + 3.00000i) q^{95} +(3.58630 + 13.3843i) q^{96} +4.89898i q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 16 q^{8} + 12 q^{9} - 8 q^{11} + 16 q^{16} - 12 q^{18} - 16 q^{22} - 4 q^{25} - 24 q^{30} - 16 q^{32} - 48 q^{43} + 16 q^{46} - 8 q^{50} - 48 q^{51} + 48 q^{57} - 16 q^{58} + 48 q^{60} + 24 q^{65}+ \cdots - 48 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 16 * q^8 + 12 * q^9 - 8 * q^11 + 16 * q^16 - 12 * q^18 - 16 * q^22 - 4 * q^25 - 24 * q^30 - 16 * q^32 - 48 * q^43 + 16 * q^46 - 8 * q^50 - 48 * q^51 + 48 * q^57 - 16 * q^58 + 48 * q^60 + 24 * q^65 + 8 * q^67 + 24 * q^72 - 32 * q^74 - 48 * q^78 + 36 * q^81 - 24 * q^86 - 16 * q^88 + 64 * q^92 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.36603	−	0.366025i	0.965926	−	0.258819i
$2$	1.36603	−	0.366025i	0.965926	−	0.258819i
$3$	−2.12132	+	1.22474i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$3$	−2.12132	+	1.22474i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$	1.22474	−	2.12132i	0.547723	−	0.948683i	−0.450708	−	0.892672i	$-0.648828\pi$
$5$	1.22474	−	2.12132i	0.547723	−	0.948683i	0.998430	−	0.0560116i	$-0.0178384\pi$
$6$	−2.44949	+	2.44949i	−1.00000	+	1.00000i
$7$		0			0
$7$		0			0
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	0.896575	−	3.34607i	0.283522	−	1.05812i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	−2.44949	+	4.24264i	−0.707107	+	1.22474i
$13$	2.44949			0.679366			0.339683	−	0.940540i	$-0.389680\pi$
$13$	2.44949			0.679366			0.339683	+	0.940540i	$0.389680\pi$
$14$		0			0
$15$			6.00000i			1.54919i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	4.24264	−	2.44949i	1.02899	−	0.594089i	0.112296	−	0.993675i	$-0.464180\pi$
$17$	4.24264	−	2.44949i	1.02899	−	0.594089i	0.916696	+	0.399586i	$0.130846\pi$
$18$	1.09808	−	4.09808i	0.258819	−	0.965926i
$19$	−2.12132	−	1.22474i	−0.486664	−	0.280976i	0.236525	−	0.971625i	$-0.423991\pi$
$19$	−2.12132	−	1.22474i	−0.486664	−	0.280976i	−0.723190	+	0.690650i	$0.757325\pi$
$20$		−	4.89898i		−	1.09545i
$21$		0			0
$22$	−2.00000	−	2.00000i	−0.426401	−	0.426401i
$23$	3.46410	+	2.00000i	0.722315	+	0.417029i	0.815604	−	0.578610i	$-0.196405\pi$
$23$	3.46410	+	2.00000i	0.722315	+	0.417029i	−0.0932891	+	0.995639i	$0.529738\pi$
$24$	−1.79315	+	6.69213i	−0.366025	+	1.36603i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	3.34607	−	0.896575i	0.656217	−	0.175833i
$27$		0			0
$28$		0			0
$29$			4.00000i			0.742781i	0.928477	+	0.371391i	$0.121119\pi$
$29$			4.00000i			0.742781i	−0.928477	+	0.371391i	$0.878881\pi$
$30$	2.19615	+	8.19615i	0.400961	+	1.49641i
$31$	2.44949	+	4.24264i	0.439941	+	0.762001i	0.997684	−	0.0680129i	$-0.0216659\pi$
$31$	2.44949	+	4.24264i	0.439941	+	0.762001i	−0.557743	+	0.830014i	$0.688333\pi$
$32$	1.46410	−	5.46410i	0.258819	−	0.965926i
$33$	4.24264	+	2.44949i	0.738549	+	0.426401i
$34$	4.89898	−	4.89898i	0.840168	−	0.840168i
$35$		0			0
$36$		−	6.00000i		−	1.00000i
$37$	−6.92820	−	4.00000i	−1.13899	−	0.657596i	−0.192809	−	0.981236i	$-0.561760\pi$
$37$	−6.92820	−	4.00000i	−1.13899	−	0.657596i	−0.946180	+	0.323640i	$0.895093\pi$
$38$	−3.34607	−	0.896575i	−0.542803	−	0.145444i
$39$	−5.19615	+	3.00000i	−0.832050	+	0.480384i
$40$	−1.79315	−	6.69213i	−0.283522	−	1.05812i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$	−3.46410	−	2.00000i	−0.522233	−	0.301511i
$45$	−3.67423	−	6.36396i	−0.547723	−	0.948683i
$46$	5.46410	+	1.46410i	0.805638	+	0.215870i
$47$	−2.44949	+	4.24264i	−0.357295	+	0.618853i	−0.987508	−	0.157569i	$-0.949634\pi$
$47$	−2.44949	+	4.24264i	−0.357295	+	0.618853i	0.630213	+	0.776422i	$0.282968\pi$
$48$			9.79796i			1.41421i
$49$		0			0
$50$	−1.00000	−	1.00000i	−0.141421	−	0.141421i
$51$	−6.00000	+	10.3923i	−0.840168	+	1.45521i
$52$	4.24264	−	2.44949i	0.588348	−	0.339683i
$53$	−3.46410	+	2.00000i	−0.475831	+	0.274721i	−0.718677	−	0.695344i	$-0.755252\pi$
$53$	−3.46410	+	2.00000i	−0.475831	+	0.274721i	0.242846	+	0.970065i	$0.421919\pi$
$54$		0			0
$55$	−4.89898			−0.660578
$56$		0			0
$57$	6.00000			0.794719
$58$	1.46410	+	5.46410i	0.192246	+	0.717472i
$59$	2.12132	−	1.22474i	0.276172	−	0.159448i	−0.355517	−	0.934670i	$-0.615695\pi$
$59$	2.12132	−	1.22474i	0.276172	−	0.159448i	0.631689	+	0.775222i	$0.282362\pi$
$60$	6.00000	+	10.3923i	0.774597	+	1.34164i
$61$	−3.67423	+	6.36396i	−0.470438	+	0.814822i	−0.999428	−	0.0338058i	$-0.989237\pi$
$61$	−3.67423	+	6.36396i	−0.470438	+	0.814822i	0.528991	+	0.848628i	$0.322571\pi$
$62$	4.89898	+	4.89898i	0.622171	+	0.622171i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	3.00000	−	5.19615i	0.372104	−	0.644503i
$66$	6.69213	+	1.79315i	0.823744	+	0.220722i
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	4.89898	−	8.48528i	0.594089	−	1.02899i
$69$	−9.79796			−1.17954
$70$		0			0
$71$			10.0000i			1.18678i	0.804914	+	0.593391i	$0.202211\pi$
$71$			10.0000i			1.18678i	−0.804914	+	0.593391i	$0.797789\pi$
$72$	−2.19615	−	8.19615i	−0.258819	−	0.965926i
$73$	−12.7279	+	7.34847i	−1.48969	+	0.860073i	−0.999931	−	0.0117840i	$-0.996249\pi$
$73$	−12.7279	+	7.34847i	−1.48969	+	0.860073i	−0.489760	+	0.871857i	$0.662916\pi$
$74$	−10.9282	−	2.92820i	−1.27038	−	0.340397i
$75$	2.12132	+	1.22474i	0.244949	+	0.141421i
$76$	−4.89898			−0.561951
$77$		0			0
$78$	−6.00000	+	6.00000i	−0.679366	+	0.679366i
$79$	5.19615	+	3.00000i	0.584613	+	0.337526i	0.762964	−	0.646440i	$-0.223743\pi$
$79$	5.19615	+	3.00000i	0.584613	+	0.337526i	−0.178352	+	0.983967i	$0.557076\pi$
$80$	−4.89898	−	8.48528i	−0.547723	−	0.948683i
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$		0			0
$83$		−	2.44949i		−	0.268866i	−0.990923	−	0.134433i	$-0.957079\pi$
$83$		−	2.44949i		−	0.268866i	0.990923	−	0.134433i	$-0.0429214\pi$
$84$		0			0
$85$		−	12.0000i		−	1.30158i
$86$	−8.19615	+	2.19615i	−0.883814	+	0.236817i
$87$	−4.89898	−	8.48528i	−0.525226	−	0.909718i
$88$	−5.46410	−	1.46410i	−0.582475	−	0.156074i
$89$	−12.7279	−	7.34847i	−1.34916	−	0.778936i	−0.361027	−	0.932555i	$-0.617574\pi$
$89$	−12.7279	−	7.34847i	−1.34916	−	0.778936i	−0.988130	+	0.153619i	$0.950907\pi$
$90$	−7.34847	−	7.34847i	−0.774597	−	0.774597i
$91$		0			0
$92$	8.00000			0.834058
$93$	−10.3923	−	6.00000i	−1.07763	−	0.622171i
$94$	−1.79315	+	6.69213i	−0.184949	+	0.690241i
$95$	−5.19615	+	3.00000i	−0.533114	+	0.307794i
$96$	3.58630	+	13.3843i	0.366025	+	1.36603i
$97$			4.89898i			0.497416i	0.968579	+	0.248708i	$0.0800060\pi$
$97$			4.89898i			0.497416i	−0.968579	+	0.248708i	$0.919994\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$	−1.73205	−	1.00000i	−0.173205	−	0.100000i
$101$	8.57321	+	14.8492i	0.853067	+	1.47755i	0.878427	+	0.477876i	$0.158593\pi$
$101$	8.57321	+	14.8492i	0.853067	+	1.47755i	−0.0253604	+	0.999678i	$0.508073\pi$
$102$	−4.39230	+	16.3923i	−0.434903	+	1.62308i
$103$	4.89898	−	8.48528i	0.482711	−	0.836080i	−0.517092	−	0.855930i	$-0.672986\pi$
$103$	4.89898	−	8.48528i	0.482711	−	0.836080i	0.999803	+	0.0198501i	$0.00631890\pi$
$104$	4.89898	−	4.89898i	0.480384	−	0.480384i
$105$		0			0
$106$	−4.00000	+	4.00000i	−0.388514	+	0.388514i
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	−0.813632	−	0.581380i	$-0.802513\pi$
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	0.910306	+	0.413936i	$0.135846\pi$
$108$		0			0
$109$	3.46410	−	2.00000i	0.331801	−	0.191565i	−0.324840	−	0.945769i	$-0.605310\pi$
$109$	3.46410	−	2.00000i	0.331801	−	0.191565i	0.656640	+	0.754204i	$0.271977\pi$
$110$	−6.69213	+	1.79315i	−0.638070	+	0.170970i
$111$	19.5959			1.85996
$112$		0			0
$113$	4.00000			0.376288			0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000			0.376288			0.188144	+	0.982141i	$0.439753\pi$
$114$	8.19615	−	2.19615i	0.767640	−	0.205689i
$115$	8.48528	−	4.89898i	0.791257	−	0.456832i
$116$	4.00000	+	6.92820i	0.371391	+	0.643268i
$117$	3.67423	−	6.36396i	0.339683	−	0.588348i
$118$	2.44949	−	2.44949i	0.225494	−	0.225494i
$119$		0			0
$120$	12.0000	+	12.0000i	1.09545	+	1.09545i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−2.68973	+	10.0382i	−0.243516	+	0.908816i
$123$		0			0
$124$	8.48528	+	4.89898i	0.762001	+	0.439941i
$125$	9.79796			0.876356
$126$		0			0
$127$		−	12.0000i		−	1.06483i	−0.846484	−	0.532414i	$-0.821285\pi$
$127$		−	12.0000i		−	1.06483i	0.846484	−	0.532414i	$-0.178715\pi$
$128$	−2.92820	−	10.9282i	−0.258819	−	0.965926i
$129$	12.7279	−	7.34847i	1.12063	−	0.646997i
$130$	2.19615	−	8.19615i	0.192615	−	0.718850i
$131$	10.6066	+	6.12372i	0.926703	+	0.535032i	0.885767	−	0.464130i	$-0.153633\pi$
$131$	10.6066	+	6.12372i	0.926703	+	0.535032i	0.0409357	+	0.999162i	$0.486966\pi$
$132$	9.79796			0.852803
$133$		0			0
$134$	2.00000	+	2.00000i	0.172774	+	0.172774i
$135$		0			0
$136$	3.58630	−	13.3843i	0.307523	−	1.14769i
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$	−13.3843	+	3.58630i	−1.13934	+	0.305286i
$139$			2.44949i			0.207763i	0.994590	+	0.103882i	$0.0331263\pi$
$139$			2.44949i			0.207763i	−0.994590	+	0.103882i	$0.966874\pi$
$140$		0			0
$141$		−	12.0000i		−	1.01058i
$142$	3.66025	+	13.6603i	0.307162	+	1.14634i
$143$	−2.44949	−	4.24264i	−0.204837	−	0.354787i
$144$	−6.00000	−	10.3923i	−0.500000	−	0.866025i
$145$	8.48528	+	4.89898i	0.704664	+	0.406838i
$146$	−14.6969	+	14.6969i	−1.21633	+	1.21633i
$147$		0			0
$148$	−16.0000			−1.31519
$149$	13.8564	+	8.00000i	1.13516	+	0.655386i	0.945228	−	0.326411i	$-0.105840\pi$
$149$	13.8564	+	8.00000i	1.13516	+	0.655386i	0.189933	+	0.981797i	$0.439173\pi$
$150$	3.34607	+	0.896575i	0.273205	+	0.0732051i
$151$	17.3205	−	10.0000i	1.40952	−	0.813788i	0.414181	−	0.910195i	$-0.364068\pi$
$151$	17.3205	−	10.0000i	1.40952	−	0.813788i	0.995342	+	0.0964061i	$0.0307348\pi$
$152$	−6.69213	+	1.79315i	−0.542803	+	0.145444i
$153$		−	14.6969i		−	1.18818i
$154$		0			0
$155$	12.0000			0.963863
$156$	−6.00000	+	10.3923i	−0.480384	+	0.832050i
$157$	3.67423	+	6.36396i	0.293236	+	0.507899i	0.974573	−	0.224070i	$-0.0719345\pi$
$157$	3.67423	+	6.36396i	0.293236	+	0.507899i	−0.681337	+	0.731970i	$0.738601\pi$
$158$	8.19615	+	2.19615i	0.652051	+	0.174717i
$159$	4.89898	−	8.48528i	0.388514	−	0.672927i
$160$	−9.79796	−	9.79796i	−0.774597	−	0.774597i
$161$		0			0
$162$	9.00000	+	9.00000i	0.707107	+	0.707107i
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	0.450110	+	0.892973i	$0.351385\pi$
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	−0.998392	+	0.0566798i	$0.981949\pi$
$164$		0			0
$165$	10.3923	−	6.00000i	0.809040	−	0.467099i
$166$	−0.896575	−	3.34607i	−0.0695878	−	0.259705i
$167$	−19.5959			−1.51638			−0.758189	−	0.652035i	$-0.773915\pi$
$167$	−19.5959			−1.51638			−0.758189	+	0.652035i	$0.773915\pi$
$168$		0			0
$169$	−7.00000			−0.538462
$170$	−4.39230	−	16.3923i	−0.336874	−	1.25723i
$171$	−6.36396	+	3.67423i	−0.486664	+	0.280976i
$172$	−10.3923	+	6.00000i	−0.792406	+	0.457496i
$173$	−1.22474	+	2.12132i	−0.0931156	+	0.161281i	−0.908821	−	0.417187i	$-0.863016\pi$
$173$	−1.22474	+	2.12132i	−0.0931156	+	0.161281i	0.815705	+	0.578468i	$0.196349\pi$
$174$	−9.79796	−	9.79796i	−0.742781	−	0.742781i
$175$		0			0
$176$	−8.00000			−0.603023
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$	−20.0764	−	5.37945i	−1.50479	−	0.403207i
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	0.616417	−	0.787420i	$-0.288584\pi$
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	−0.990134	+	0.140122i	$0.955250\pi$
$180$	−12.7279	−	7.34847i	−0.948683	−	0.547723i
$181$	7.34847			0.546207			0.273104	−	0.961985i	$-0.411950\pi$
$181$	7.34847			0.546207			0.273104	+	0.961985i	$0.411950\pi$
$182$		0			0
$183$		−	18.0000i		−	1.33060i
$184$	10.9282	−	2.92820i	0.805638	−	0.215870i
$185$	−16.9706	+	9.79796i	−1.24770	+	0.720360i
$186$	−16.3923	−	4.39230i	−1.20194	−	0.322059i
$187$	−8.48528	−	4.89898i	−0.620505	−	0.358249i
$188$			9.79796i			0.714590i
$189$		0			0
$190$	−6.00000	+	6.00000i	−0.435286	+	0.435286i
$191$	8.66025	+	5.00000i	0.626634	+	0.361787i	0.779447	−	0.626468i	$-0.215500\pi$
$191$	8.66025	+	5.00000i	0.626634	+	0.361787i	−0.152813	+	0.988255i	$0.548833\pi$
$192$	9.79796	+	16.9706i	0.707107	+	1.22474i
$193$	−12.0000	−	20.7846i	−0.863779	−	1.49611i	−0.868255	−	0.496119i	$-0.834758\pi$
$193$	−12.0000	−	20.7846i	−0.863779	−	1.49611i	0.00447566	−	0.999990i	$-0.498575\pi$
$194$	1.79315	+	6.69213i	0.128741	+	0.480467i
$195$			14.6969i			1.05247i
$196$		0			0
$197$			8.00000i			0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$			8.00000i			0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$	−8.19615	+	2.19615i	−0.582475	+	0.156074i
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	−2.73205	−	0.732051i	−0.193185	−	0.0517638i
$201$	−4.24264	−	2.44949i	−0.299253	−	0.172774i
$202$	17.1464	+	17.1464i	1.20642	+	1.20642i
$203$		0			0
$204$			24.0000i			1.68034i
$205$		0			0
$206$	3.58630	−	13.3843i	0.249869	−	0.932526i
$207$	10.3923	−	6.00000i	0.722315	−	0.417029i
$208$	4.89898	−	8.48528i	0.339683	−	0.588348i
$209$			4.89898i			0.338869i
$210$		0			0
$211$	−18.0000			−1.23917			−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000			−1.23917			−0.619586	+	0.784929i	$0.712699\pi$
$212$	−4.00000	+	6.92820i	−0.274721	+	0.475831i
$213$	−12.2474	−	21.2132i	−0.839181	−	1.45350i
$214$	0.732051	−	2.73205i	0.0500420	−	0.186759i
$215$	−7.34847	+	12.7279i	−0.501161	+	0.868037i
$216$		0			0
$217$		0			0
$218$	4.00000	−	4.00000i	0.270914	−	0.270914i
$219$	18.0000	−	31.1769i	1.21633	−	2.10674i
$220$	−8.48528	+	4.89898i	−0.572078	+	0.330289i
$221$	10.3923	−	6.00000i	0.699062	−	0.403604i
$222$	26.7685	−	7.17260i	1.79659	−	0.481394i
$223$	−9.79796			−0.656120			−0.328060	−	0.944657i	$-0.606395\pi$
$223$	−9.79796			−0.656120			−0.328060	+	0.944657i	$0.606395\pi$
$224$		0			0
$225$	−3.00000			−0.200000
$226$	5.46410	−	1.46410i	0.363467	−	0.0973906i
$227$	−6.36396	+	3.67423i	−0.422391	+	0.243868i	−0.696100	−	0.717945i	$-0.745083\pi$
$227$	−6.36396	+	3.67423i	−0.422391	+	0.243868i	0.273709	+	0.961813i	$0.411750\pi$
$228$	10.3923	−	6.00000i	0.688247	−	0.397360i
$229$	−6.12372	+	10.6066i	−0.404667	+	0.700904i	−0.994283	−	0.106780i	$-0.965946\pi$
$229$	−6.12372	+	10.6066i	−0.404667	+	0.700904i	0.589616	+	0.807684i	$0.299279\pi$
$230$	9.79796	−	9.79796i	0.646058	−	0.646058i
$231$		0			0
$232$	8.00000	+	8.00000i	0.525226	+	0.525226i
$233$	−7.00000	+	12.1244i	−0.458585	+	0.794293i	−0.998886	−	0.0471787i	$-0.984977\pi$
$233$	−7.00000	+	12.1244i	−0.458585	+	0.794293i	0.540301	+	0.841472i	$0.318310\pi$
$234$	2.68973	−	10.0382i	0.175833	−	0.656217i
$235$	6.00000	+	10.3923i	0.391397	+	0.677919i
$236$	2.44949	−	4.24264i	0.159448	−	0.276172i
$237$	−14.6969			−0.954669
$238$		0			0
$239$			4.00000i			0.258738i	0.991596	+	0.129369i	$0.0412952\pi$
$239$			4.00000i			0.258738i	−0.991596	+	0.129369i	$0.958705\pi$
$240$	20.7846	+	12.0000i	1.34164	+	0.774597i
$241$	21.2132	−	12.2474i	1.36646	−	0.788928i	0.375988	−	0.926624i	$-0.377303\pi$
$241$	21.2132	−	12.2474i	1.36646	−	0.788928i	0.990474	+	0.137697i	$0.0439700\pi$
$242$	2.56218	−	9.56218i	0.164703	−	0.614680i
$243$	−19.0919	−	11.0227i	−1.22474	−	0.707107i
$244$			14.6969i			0.940875i
$245$		0			0
$246$		0			0
$247$	−5.19615	−	3.00000i	−0.330623	−	0.190885i
$248$	13.3843	+	3.58630i	0.849901	+	0.227730i
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	13.3843	−	3.58630i	0.846495	−	0.226818i
$251$		−	12.2474i		−	0.773052i	−0.922278	−	0.386526i	$-0.873675\pi$
$251$		−	12.2474i		−	0.773052i	0.922278	−	0.386526i	$-0.126325\pi$
$252$		0			0
$253$		−	8.00000i		−	0.502956i
$254$	−4.39230	−	16.3923i	−0.275598	−	1.02854i
$255$	14.6969	+	25.4558i	0.920358	+	1.59411i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	16.9706	+	9.79796i	1.05859	+	0.611180i	0.925043	−	0.379862i	$-0.124029\pi$
$257$	16.9706	+	9.79796i	1.05859	+	0.611180i	0.133551	+	0.991042i	$0.457362\pi$
$258$	14.6969	−	14.6969i	0.914991	−	0.914991i
$259$		0			0
$260$		−	12.0000i		−	0.744208i
$261$	10.3923	+	6.00000i	0.643268	+	0.371391i
$262$	16.7303	+	4.48288i	1.03360	+	0.276953i
$263$	−12.1244	+	7.00000i	−0.747620	+	0.431638i	−0.824833	−	0.565376i	$-0.808731\pi$
$263$	−12.1244	+	7.00000i	−0.747620	+	0.431638i	0.0772134	+	0.997015i	$0.475398\pi$
$264$	13.3843	−	3.58630i	0.823744	−	0.220722i
$265$			9.79796i			0.601884i
$266$		0			0
$267$	36.0000			2.20316
$268$	3.46410	+	2.00000i	0.211604	+	0.122169i
$269$	−6.12372	−	10.6066i	−0.373370	−	0.646696i	0.616712	−	0.787189i	$-0.288464\pi$
$269$	−6.12372	−	10.6066i	−0.373370	−	0.646696i	−0.990082	+	0.140493i	$0.955131\pi$
$270$		0			0
$271$	−9.79796	+	16.9706i	−0.595184	+	1.03089i	0.398337	+	0.917239i	$0.369587\pi$
$271$	−9.79796	+	16.9706i	−0.595184	+	1.03089i	−0.993521	+	0.113649i	$0.963746\pi$
$272$		−	19.5959i		−	1.18818i
$273$		0			0
$274$	2.00000	+	2.00000i	0.120824	+	0.120824i
$275$	−1.00000	+	1.73205i	−0.0603023	+	0.104447i
$276$	−16.9706	+	9.79796i	−1.02151	+	0.589768i
$277$	−10.3923	+	6.00000i	−0.624413	+	0.360505i	−0.778585	−	0.627539i	$-0.784062\pi$
$277$	−10.3923	+	6.00000i	−0.624413	+	0.360505i	0.154172	+	0.988044i	$0.450729\pi$
$278$	0.896575	+	3.34607i	0.0537730	+	0.200684i
$279$	14.6969			0.879883
$280$		0			0
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	−4.39230	−	16.3923i	−0.261558	−	0.976148i
$283$	−2.12132	+	1.22474i	−0.126099	+	0.0728035i	−0.561723	−	0.827325i	$-0.689861\pi$
$283$	−2.12132	+	1.22474i	−0.126099	+	0.0728035i	0.435623	+	0.900129i	$0.356528\pi$
$284$	10.0000	+	17.3205i	0.593391	+	1.02778i
$285$	7.34847	−	12.7279i	0.435286	−	0.753937i
$286$	−4.89898	−	4.89898i	−0.289683	−	0.289683i
$287$		0			0
$288$	−12.0000	−	12.0000i	−0.707107	−	0.707107i
$289$	3.50000	−	6.06218i	0.205882	−	0.356599i
$290$	13.3843	+	3.58630i	0.785951	+	0.210595i
$291$	−6.00000	−	10.3923i	−0.351726	−	0.609208i
$292$	−14.6969	+	25.4558i	−0.860073	+	1.48969i
$293$	2.44949			0.143101			0.0715504	−	0.997437i	$-0.477205\pi$
$293$	2.44949			0.143101			0.0715504	+	0.997437i	$0.477205\pi$
$294$		0			0
$295$		−	6.00000i		−	0.349334i
$296$	−21.8564	+	5.85641i	−1.27038	+	0.340397i
$297$		0			0
$298$	21.8564	+	5.85641i	1.26611	+	0.339253i
$299$	8.48528	+	4.89898i	0.490716	+	0.283315i
$300$	4.89898			0.282843
$301$		0			0
$302$	20.0000	−	20.0000i	1.15087	−	1.15087i
$303$	−36.3731	−	21.0000i	−2.08958	−	1.20642i
$304$	−8.48528	+	4.89898i	−0.486664	+	0.280976i
$305$	9.00000	+	15.5885i	0.515339	+	0.892592i
$306$	−5.37945	−	20.0764i	−0.307523	−	1.14769i
$307$		−	31.8434i		−	1.81740i	−0.417453	−	0.908698i	$-0.637077\pi$
$307$		−	31.8434i		−	1.81740i	0.417453	−	0.908698i	$-0.362923\pi$
$308$		0			0
$309$			24.0000i			1.36531i
$310$	16.3923	−	4.39230i	0.931020	−	0.249466i
$311$	2.44949	+	4.24264i	0.138898	+	0.240578i	0.927080	−	0.374864i	$-0.122311\pi$
$311$	2.44949	+	4.24264i	0.138898	+	0.240578i	−0.788182	+	0.615442i	$0.788977\pi$
$312$	−4.39230	+	16.3923i	−0.248665	+	0.928032i
$313$	−8.48528	−	4.89898i	−0.479616	−	0.276907i	0.240640	−	0.970614i	$-0.422643\pi$
$313$	−8.48528	−	4.89898i	−0.479616	−	0.276907i	−0.720257	+	0.693708i	$0.755976\pi$
$314$	7.34847	+	7.34847i	0.414698	+	0.414698i
$315$		0			0
$316$	12.0000			0.675053
$317$	27.7128	+	16.0000i	1.55651	+	0.898650i	0.997587	+	0.0694277i	$0.0221173\pi$
$317$	27.7128	+	16.0000i	1.55651	+	0.898650i	0.558920	+	0.829222i	$0.311216\pi$
$318$	3.58630	−	13.3843i	0.201110	−	0.750552i
$319$	6.92820	−	4.00000i	0.387905	−	0.223957i
$320$	−16.9706	−	9.79796i	−0.948683	−	0.547723i
$321$			4.89898i			0.273434i
$322$		0			0
$323$	−12.0000			−0.667698
$324$	15.5885	+	9.00000i	0.866025	+	0.500000i
$325$	−1.22474	−	2.12132i	−0.0679366	−	0.117670i
$326$	−5.12436	+	19.1244i	−0.283812	+	1.05920i
$327$	−4.89898	+	8.48528i	−0.270914	+	0.469237i
$328$		0			0
$329$		0			0
$330$	12.0000	−	12.0000i	0.660578	−	0.660578i
$331$	9.00000	−	15.5885i	0.494685	−	0.856819i	−0.505296	−	0.862946i	$-0.668617\pi$
$331$	9.00000	−	15.5885i	0.494685	−	0.856819i	0.999981	+	0.00612670i	$0.00195020\pi$
$332$	−2.44949	−	4.24264i	−0.134433	−	0.232845i
$333$	−20.7846	+	12.0000i	−1.13899	+	0.657596i
$334$	−26.7685	+	7.17260i	−1.46471	+	0.392467i
$335$	4.89898			0.267660
$336$		0			0
$337$	−12.0000			−0.653682			−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000			−0.653682			−0.326841	+	0.945079i	$0.605984\pi$
$338$	−9.56218	+	2.56218i	−0.520114	+	0.139364i
$339$	−8.48528	+	4.89898i	−0.460857	+	0.266076i
$340$	−12.0000	−	20.7846i	−0.650791	−	1.12720i
$341$	4.89898	−	8.48528i	0.265295	−	0.459504i
$342$	−7.34847	+	7.34847i	−0.397360	+	0.397360i
$343$		0			0
$344$	−12.0000	+	12.0000i	−0.646997	+	0.646997i
$345$	−12.0000	+	20.7846i	−0.646058	+	1.11901i
$346$	−0.896575	+	3.34607i	−0.0482002	+	0.179886i
$347$	11.0000	+	19.0526i	0.590511	+	1.02279i	0.994164	+	0.107883i	$0.0344071\pi$
$347$	11.0000	+	19.0526i	0.590511	+	1.02279i	−0.403653	+	0.914912i	$0.632260\pi$
$348$	−16.9706	−	9.79796i	−0.909718	−	0.525226i
$349$	−12.2474			−0.655591			−0.327795	−	0.944749i	$-0.606306\pi$
$349$	−12.2474			−0.655591			−0.327795	+	0.944749i	$0.606306\pi$
$350$		0			0
$351$		0			0
$352$	−10.9282	+	2.92820i	−0.582475	+	0.156074i
$353$	8.48528	−	4.89898i	0.451626	−	0.260746i	−0.256891	−	0.966440i	$-0.582698\pi$
$353$	8.48528	−	4.89898i	0.451626	−	0.260746i	0.708517	+	0.705694i	$0.249365\pi$
$354$	−2.19615	+	8.19615i	−0.116724	+	0.435621i
$355$	21.2132	+	12.2474i	1.12588	+	0.650027i
$356$	−29.3939			−1.55787
$357$		0			0
$358$	−10.0000	−	10.0000i	−0.528516	−	0.528516i
$359$	−3.46410	−	2.00000i	−0.182828	−	0.105556i	0.405793	−	0.913965i	$-0.366996\pi$
$359$	−3.46410	−	2.00000i	−0.182828	−	0.105556i	−0.588621	+	0.808409i	$0.700329\pi$
$360$	−20.0764	−	5.37945i	−1.05812	−	0.283522i
$361$	−6.50000	−	11.2583i	−0.342105	−	0.592544i
$362$	10.0382	−	2.68973i	0.527596	−	0.141369i
$363$			17.1464i			0.899954i
$364$		0			0
$365$			36.0000i			1.88433i
$366$	−6.58846	−	24.5885i	−0.344384	−	1.28526i
$367$	−14.6969	−	25.4558i	−0.767174	−	1.32878i	−0.939090	−	0.343673i	$-0.888329\pi$
$367$	−14.6969	−	25.4558i	−0.767174	−	1.32878i	0.171916	−	0.985112i	$-0.445004\pi$
$368$	13.8564	−	8.00000i	0.722315	−	0.417029i
$369$		0			0
$370$	−19.5959	+	19.5959i	−1.01874	+	1.01874i
$371$		0			0
$372$	−24.0000			−1.24434
$373$	−31.1769	−	18.0000i	−1.61428	−	0.932005i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−31.1769	−	18.0000i	−1.61428	−	0.932005i	−0.625917	−	0.779890i	$-0.715275\pi$
$374$	−13.3843	−	3.58630i	−0.692084	−	0.185443i
$375$	−20.7846	+	12.0000i	−1.07331	+	0.619677i
$376$	3.58630	+	13.3843i	0.184949	+	0.690241i
$377$			9.79796i			0.504621i
$378$		0			0
$379$	30.0000			1.54100			0.770498	−	0.637442i	$-0.220007\pi$
$379$	30.0000			1.54100			0.770498	+	0.637442i	$0.220007\pi$
$380$	−6.00000	+	10.3923i	−0.307794	+	0.533114i
$381$	14.6969	+	25.4558i	0.752947	+	1.30414i
$382$	13.6603	+	3.66025i	0.698919	+	0.187275i
$383$	17.1464	−	29.6985i	0.876142	−	1.51752i	0.0205998	−	0.999788i	$-0.493442\pi$
$383$	17.1464	−	29.6985i	0.876142	−	1.51752i	0.855542	−	0.517734i	$-0.173224\pi$
$384$	19.5959	+	19.5959i	1.00000	+	1.00000i
$385$		0			0
$386$	−24.0000	−	24.0000i	−1.22157	−	1.22157i
$387$	−9.00000	+	15.5885i	−0.457496	+	0.792406i
$388$	4.89898	+	8.48528i	0.248708	+	0.430775i
$389$	−13.8564	+	8.00000i	−0.702548	+	0.405616i	−0.808296	−	0.588777i	$-0.799610\pi$
$389$	−13.8564	+	8.00000i	−0.702548	+	0.405616i	0.105748	+	0.994393i	$0.466276\pi$
$390$	5.37945	+	20.0764i	0.272399	+	1.01661i
$391$	19.5959			0.991008
$392$		0			0
$393$	−30.0000			−1.51330
$394$	2.92820	+	10.9282i	0.147521	+	0.550555i
$395$	12.7279	−	7.34847i	0.640411	−	0.369742i
$396$	−10.3923	+	6.00000i	−0.522233	+	0.301511i
$397$	15.9217	−	27.5772i	0.799086	−	1.38406i	−0.121125	−	0.992637i	$-0.538650\pi$
$397$	15.9217	−	27.5772i	0.799086	−	1.38406i	0.920212	−	0.391421i	$-0.128016\pi$
$398$		0			0
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−16.0000	+	27.7128i	−0.799002	+	1.38391i	0.121265	+	0.992620i	$0.461305\pi$
$401$	−16.0000	+	27.7128i	−0.799002	+	1.38391i	−0.920267	+	0.391292i	$0.872028\pi$
$402$	−6.69213	−	1.79315i	−0.333773	−	0.0894342i
$403$	6.00000	+	10.3923i	0.298881	+	0.517678i
$404$	29.6985	+	17.1464i	1.47755	+	0.853067i
$405$	22.0454			1.09545
$406$		0			0
$407$			16.0000i			0.793091i
$408$	8.78461	+	32.7846i	0.434903	+	1.62308i
$409$	−8.48528	+	4.89898i	−0.419570	+	0.242239i	−0.694893	−	0.719113i	$-0.744548\pi$
$409$	−8.48528	+	4.89898i	−0.419570	+	0.242239i	0.275323	+	0.961352i	$0.411215\pi$
$410$		0			0
$411$	−4.24264	−	2.44949i	−0.209274	−	0.120824i
$412$		−	19.5959i		−	0.965422i
$413$		0			0
$414$	12.0000	−	12.0000i	0.589768	−	0.589768i
$415$	−5.19615	−	3.00000i	−0.255069	−	0.147264i
$416$	3.58630	−	13.3843i	0.175833	−	0.656217i
$417$	−3.00000	−	5.19615i	−0.146911	−	0.254457i
$418$	1.79315	+	6.69213i	0.0877059	+	0.327323i
$419$			26.9444i			1.31632i	0.752878	+	0.658160i	$0.228665\pi$
$419$			26.9444i			1.31632i	−0.752878	+	0.658160i	$0.771335\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	−24.5885	+	6.58846i	−1.19695	+	0.320721i
$423$	7.34847	+	12.7279i	0.357295	+	0.618853i
$424$	−2.92820	+	10.9282i	−0.142206	+	0.530720i
$425$	−4.24264	−	2.44949i	−0.205798	−	0.118818i
$426$	−24.4949	−	24.4949i	−1.18678	−	1.18678i
$427$		0			0
$428$		−	4.00000i		−	0.193347i
$429$	10.3923	+	6.00000i	0.501745	+	0.289683i
$430$	−5.37945	+	20.0764i	−0.259420	+	0.968170i
$431$	−17.3205	+	10.0000i	−0.834300	+	0.481683i	−0.855323	−	0.518096i	$-0.826641\pi$
$431$	−17.3205	+	10.0000i	−0.834300	+	0.481683i	0.0210230	+	0.999779i	$0.493308\pi$
$432$		0			0
$433$		−	14.6969i		−	0.706290i	−0.935569	−	0.353145i	$-0.885112\pi$
$433$		−	14.6969i		−	0.706290i	0.935569	−	0.353145i	$-0.114888\pi$
$434$		0			0
$435$	−24.0000			−1.15071
$436$	4.00000	−	6.92820i	0.191565	−	0.331801i
$437$	−4.89898	−	8.48528i	−0.234350	−	0.405906i
$438$	13.1769	−	49.1769i	0.629617	−	2.34976i
$439$	12.2474	−	21.2132i	0.584539	−	1.01245i	−0.410394	−	0.911908i	$-0.634609\pi$
$439$	12.2474	−	21.2132i	0.584539	−	1.01245i	0.994933	−	0.100543i	$-0.0320579\pi$
$440$	−9.79796	+	9.79796i	−0.467099	+	0.467099i
$441$		0			0
$442$	12.0000	−	12.0000i	0.570782	−	0.570782i
$443$	13.0000	−	22.5167i	0.617649	−	1.06980i	−0.372265	−	0.928126i	$-0.621419\pi$
$443$	13.0000	−	22.5167i	0.617649	−	1.06980i	0.989914	−	0.141672i	$-0.0452479\pi$
$444$	33.9411	−	19.5959i	1.61077	−	0.929981i
$445$	−31.1769	+	18.0000i	−1.47793	+	0.853282i
$446$	−13.3843	+	3.58630i	−0.633763	+	0.169816i
$447$	−39.1918			−1.85371
$448$		0			0
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$	−4.09808	+	1.09808i	−0.193185	+	0.0517638i
$451$		0			0
$452$	6.92820	−	4.00000i	0.325875	−	0.188144i
$453$	−24.4949	+	42.4264i	−1.15087	+	1.99337i
$454$	−7.34847	+	7.34847i	−0.344881	+	0.344881i
$455$		0			0
$456$	12.0000	−	12.0000i	0.561951	−	0.561951i
$457$	6.00000	−	10.3923i	0.280668	−	0.486132i	−0.690881	−	0.722968i	$-0.742777\pi$
$457$	6.00000	−	10.3923i	0.280668	−	0.486132i	0.971549	+	0.236837i	$0.0761106\pi$
$458$	−4.48288	+	16.7303i	−0.209471	+	0.781757i
$459$		0			0
$460$	9.79796	−	16.9706i	0.456832	−	0.791257i
$461$	7.34847			0.342252			0.171126	−	0.985249i	$-0.445259\pi$
$461$	7.34847			0.342252			0.171126	+	0.985249i	$0.445259\pi$
$462$		0			0
$463$			6.00000i			0.278844i	0.990233	+	0.139422i	$0.0445244\pi$
$463$			6.00000i			0.278844i	−0.990233	+	0.139422i	$0.955476\pi$
$464$	13.8564	+	8.00000i	0.643268	+	0.371391i
$465$	−25.4558	+	14.6969i	−1.18049	+	0.681554i
$466$	−5.12436	+	19.1244i	−0.237381	+	0.885919i
$467$	−36.0624	−	20.8207i	−1.66877	−	0.963465i	−0.968302	−	0.249783i	$-0.919641\pi$
$467$	−36.0624	−	20.8207i	−1.66877	−	0.963465i	−0.700469	−	0.713683i	$-0.747026\pi$
$468$		−	14.6969i		−	0.679366i
$469$		0			0
$470$	12.0000	+	12.0000i	0.553519	+	0.553519i
$471$	−15.5885	−	9.00000i	−0.718278	−	0.414698i
$472$	1.79315	−	6.69213i	0.0825365	−	0.308030i
$473$	6.00000	+	10.3923i	0.275880	+	0.477839i
$474$	−20.0764	+	5.37945i	−0.922139	+	0.247086i
$475$			2.44949i			0.112390i
$476$		0			0
$477$			12.0000i			0.549442i
$478$	1.46410	+	5.46410i	0.0669664	+	0.249922i
$479$	−12.2474	−	21.2132i	−0.559600	−	0.969256i	−0.997530	−	0.0702467i	$-0.977621\pi$
$479$	−12.2474	−	21.2132i	−0.559600	−	0.969256i	0.437929	−	0.899009i	$-0.355712\pi$
$480$	32.7846	+	8.78461i	1.49641	+	0.400961i
$481$	−16.9706	−	9.79796i	−0.773791	−	0.446748i
$482$	24.4949	−	24.4949i	1.11571	−	1.11571i
$483$		0			0
$484$		−	14.0000i		−	0.636364i
$485$	10.3923	+	6.00000i	0.471890	+	0.272446i
$486$	−30.1146	−	8.06918i	−1.36603	−	0.366025i
$487$	24.2487	−	14.0000i	1.09881	−	0.634401i	0.162905	−	0.986642i	$-0.447914\pi$
$487$	24.2487	−	14.0000i	1.09881	−	0.634401i	0.935909	+	0.352241i	$0.114580\pi$
$488$	5.37945	+	20.0764i	0.243516	+	0.908816i
$489$		−	34.2929i		−	1.55078i
$490$		0			0
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$		0			0
$493$	9.79796	+	16.9706i	0.441278	+	0.764316i
$494$	−8.19615	−	2.19615i	−0.368762	−	0.0988096i
$495$	−7.34847	+	12.7279i	−0.330289	+	0.572078i
$496$	19.5959			0.879883
$497$		0			0
$498$	6.00000	+	6.00000i	0.268866	+	0.268866i
$499$	−15.0000	+	25.9808i	−0.671492	+	1.16306i	0.305989	+	0.952035i	$0.401013\pi$
$499$	−15.0000	+	25.9808i	−0.671492	+	1.16306i	−0.977481	+	0.211024i	$0.932320\pi$
$500$	16.9706	−	9.79796i	0.758947	−	0.438178i
$501$	41.5692	−	24.0000i	1.85718	−	1.07224i
$502$	−4.48288	−	16.7303i	−0.200081	−	0.746711i
$503$	14.6969			0.655304			0.327652	−	0.944798i	$-0.393743\pi$
$503$	14.6969			0.655304			0.327652	+	0.944798i	$0.393743\pi$
$504$		0			0
$505$	42.0000			1.86898
$506$	−2.92820	−	10.9282i	−0.130175	−	0.485818i
$507$	14.8492	−	8.57321i	0.659478	−	0.380750i
$508$	−12.0000	−	20.7846i	−0.532414	−	0.922168i
$509$	−18.3712	+	31.8198i	−0.814288	+	1.41039i	0.0955502	+	0.995425i	$0.469539\pi$
$509$	−18.3712	+	31.8198i	−0.814288	+	1.41039i	−0.909838	+	0.414963i	$0.863794\pi$
$510$	29.3939	+	29.3939i	1.30158	+	1.30158i
$511$		0			0
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	26.7685	+	7.17260i	1.18071	+	0.316370i
$515$	−12.0000	−	20.7846i	−0.528783	−	0.915879i
$516$	14.6969	−	25.4558i	0.646997	−	1.12063i
$517$	9.79796			0.430914
$518$		0			0
$519$		−	6.00000i		−	0.263371i
$520$	−4.39230	−	16.3923i	−0.192615	−	0.718850i
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$	16.3923	+	4.39230i	0.717472	+	0.192246i
$523$	23.3345	+	13.4722i	1.02035	+	0.589098i	0.914205	−	0.405253i	$-0.132817\pi$
$523$	23.3345	+	13.4722i	1.02035	+	0.589098i	0.106143	+	0.994351i	$0.466150\pi$
$524$	24.4949			1.07006
$525$		0			0
$526$	−14.0000	+	14.0000i	−0.610429	+	0.610429i
$527$	20.7846	+	12.0000i	0.905392	+	0.522728i
$528$	16.9706	−	9.79796i	0.738549	−	0.426401i
$529$	−3.50000	−	6.06218i	−0.152174	−	0.263573i
$530$	3.58630	+	13.3843i	0.155779	+	0.581375i
$531$		−	7.34847i		−	0.318896i
$532$		0			0
$533$		0			0
$534$	49.1769	−	13.1769i	2.12809	−	0.570221i
$535$	−2.44949	−	4.24264i	−0.105901	−	0.183425i
$536$	5.46410	+	1.46410i	0.236013	+	0.0632396i
$537$	21.2132	+	12.2474i	0.915417	+	0.528516i
$538$	−12.2474	−	12.2474i	−0.528025	−	0.528025i
$539$		0			0
$540$		0			0
$541$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$541$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$542$	−7.17260	+	26.7685i	−0.308090	+	1.14981i
$543$	−15.5885	+	9.00000i	−0.668965	+	0.386227i
$544$	−7.17260	−	26.7685i	−0.307523	−	1.14769i
$545$		−	9.79796i		−	0.419698i
$546$		0			0
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$	3.46410	+	2.00000i	0.147979	+	0.0854358i
$549$	11.0227	+	19.0919i	0.470438	+	0.814822i
$550$	−0.732051	+	2.73205i	−0.0312148	+	0.116495i
$551$	4.89898	−	8.48528i	0.208704	−	0.361485i
$552$	−19.5959	+	19.5959i	−0.834058	+	0.834058i
$553$		0			0
$554$	−12.0000	+	12.0000i	−0.509831	+	0.509831i
$555$	24.0000	−	41.5692i	1.01874	−	1.76452i
$556$	2.44949	+	4.24264i	0.103882	+	0.179928i
$557$	24.2487	−	14.0000i	1.02745	−	0.593199i	0.111198	−	0.993798i	$-0.464531\pi$
$557$	24.2487	−	14.0000i	1.02745	−	0.593199i	0.916253	+	0.400599i	$0.131198\pi$
$558$	20.0764	−	5.37945i	0.849901	−	0.227730i
$559$	−14.6969			−0.621614
$560$		0			0
$561$	24.0000			1.01328
$562$	2.73205	−	0.732051i	0.115245	−	0.0308797i
$563$	19.0919	−	11.0227i	0.804627	−	0.464552i	−0.0404596	−	0.999181i	$-0.512882\pi$
$563$	19.0919	−	11.0227i	0.804627	−	0.464552i	0.845087	+	0.534630i	$0.179549\pi$
$564$	−12.0000	−	20.7846i	−0.505291	−	0.875190i
$565$	4.89898	−	8.48528i	0.206102	−	0.356978i
$566$	−2.44949	+	2.44949i	−0.102960	+	0.102960i
$567$		0			0
$568$	20.0000	+	20.0000i	0.839181	+	0.839181i
$569$	10.0000	−	17.3205i	0.419222	−	0.726113i	−0.576640	−	0.816999i	$-0.695636\pi$
$569$	10.0000	−	17.3205i	0.419222	−	0.726113i	0.995861	+	0.0908852i	$0.0289696\pi$
$570$	5.37945	−	20.0764i	0.225320	−	0.840907i
$571$	−1.00000	−	1.73205i	−0.0418487	−	0.0724841i	0.844342	−	0.535804i	$-0.179991\pi$
$571$	−1.00000	−	1.73205i	−0.0418487	−	0.0724841i	−0.886191	+	0.463320i	$0.846658\pi$
$572$	−8.48528	−	4.89898i	−0.354787	−	0.204837i
$573$	−24.4949			−1.02329
$574$		0			0
$575$		−	4.00000i		−	0.166812i
$576$	−20.7846	−	12.0000i	−0.866025	−	0.500000i
$577$	−16.9706	+	9.79796i	−0.706494	+	0.407894i	−0.809761	−	0.586759i	$-0.800404\pi$
$577$	−16.9706	+	9.79796i	−0.706494	+	0.407894i	0.103268	+	0.994654i	$0.467070\pi$
$578$	2.56218	−	9.56218i	0.106573	−	0.397734i
$579$	50.9117	+	29.3939i	2.11582	+	1.22157i
$580$	19.5959			0.813676
$581$		0			0
$582$	−12.0000	−	12.0000i	−0.497416	−	0.497416i
$583$	6.92820	+	4.00000i	0.286937	+	0.165663i
$584$	−10.7589	+	40.1528i	−0.445207	+	1.66153i
$585$	−9.00000	−	15.5885i	−0.372104	−	0.644503i
$586$	3.34607	−	0.896575i	0.138225	−	0.0370372i
$587$		−	7.34847i		−	0.303304i	−0.988434	−	0.151652i	$-0.951541\pi$
$587$		−	7.34847i		−	0.303304i	0.988434	−	0.151652i	$-0.0484593\pi$
$588$		0			0
$589$		−	12.0000i		−	0.494451i
$590$	−2.19615	−	8.19615i	−0.0904142	−	0.337430i
$591$	−9.79796	−	16.9706i	−0.403034	−	0.698076i
$592$	−27.7128	+	16.0000i	−1.13899	+	0.657596i
$593$	−8.48528	−	4.89898i	−0.348449	−	0.201177i	0.315553	−	0.948908i	$-0.397810\pi$
$593$	−8.48528	−	4.89898i	−0.348449	−	0.201177i	−0.664002	+	0.747731i	$0.731143\pi$
$594$		0			0
$595$		0			0
$596$	32.0000			1.31077
$597$		0			0
$598$	13.3843	+	3.58630i	0.547323	+	0.146655i
$599$	12.1244	−	7.00000i	0.495388	−	0.286012i	−0.231419	−	0.972854i	$-0.574337\pi$
$599$	12.1244	−	7.00000i	0.495388	−	0.286012i	0.726807	+	0.686842i	$0.241004\pi$
$600$	6.69213	−	1.79315i	0.273205	−	0.0732051i
$601$			24.4949i			0.999168i	0.866266	+	0.499584i	$0.166514\pi$
$601$			24.4949i			0.999168i	−0.866266	+	0.499584i	$0.833486\pi$
$602$		0			0
$603$	6.00000			0.244339
$604$	20.0000	−	34.6410i	0.813788	−	1.40952i
$605$	−8.57321	−	14.8492i	−0.348551	−	0.603708i
$606$	−57.3731	−	15.3731i	−2.33062	−	0.624488i
$607$	−14.6969	+	25.4558i	−0.596530	+	1.03322i	0.396799	+	0.917906i	$0.370121\pi$
$607$	−14.6969	+	25.4558i	−0.596530	+	1.03322i	−0.993329	+	0.115315i	$0.963212\pi$
$608$	−9.79796	+	9.79796i	−0.397360	+	0.397360i
$609$		0			0
$610$	18.0000	+	18.0000i	0.728799	+	0.728799i
$611$	−6.00000	+	10.3923i	−0.242734	+	0.420428i
$612$	−14.6969	−	25.4558i	−0.594089	−	1.02899i
$613$	−20.7846	+	12.0000i	−0.839482	+	0.484675i	−0.857088	−	0.515170i	$-0.827729\pi$
$613$	−20.7846	+	12.0000i	−0.839482	+	0.484675i	0.0176058	+	0.999845i	$0.494396\pi$
$614$	−11.6555	−	43.4988i	−0.470377	−	1.75547i
$615$		0			0
$616$		0			0
$617$	−32.0000			−1.28827			−0.644136	−	0.764911i	$-0.722783\pi$
$617$	−32.0000			−1.28827			−0.644136	+	0.764911i	$0.722783\pi$
$618$	8.78461	+	32.7846i	0.353369	+	1.31879i
$619$	−19.0919	+	11.0227i	−0.767368	+	0.443040i	−0.831935	−	0.554873i	$-0.812767\pi$
$619$	−19.0919	+	11.0227i	−0.767368	+	0.443040i	0.0645672	+	0.997913i	$0.479433\pi$
$620$	20.7846	−	12.0000i	0.834730	−	0.481932i
$621$		0			0
$622$	4.89898	+	4.89898i	0.196431	+	0.196431i
$623$		0			0
$624$			24.0000i			0.960769i
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	−13.3843	−	3.58630i	−0.534943	−	0.143337i
$627$	−6.00000	−	10.3923i	−0.239617	−	0.415029i
$628$	12.7279	+	7.34847i	0.507899	+	0.293236i
$629$	−39.1918			−1.56268
$630$		0			0
$631$			30.0000i			1.19428i	0.802137	+	0.597141i	$0.203697\pi$
$631$			30.0000i			1.19428i	−0.802137	+	0.597141i	$0.796303\pi$
$632$	16.3923	−	4.39230i	0.652051	−	0.174717i
$633$	38.1838	−	22.0454i	1.51767	−	0.876226i
$634$	43.7128	+	11.7128i	1.73606	+	0.465175i
$635$	−25.4558	−	14.6969i	−1.01018	−	0.583230i
$636$		−	19.5959i		−	0.777029i
$637$		0			0
$638$	8.00000	−	8.00000i	0.316723	−	0.316723i
$639$	25.9808	+	15.0000i	1.02778	+	0.593391i
$640$	−26.7685	−	7.17260i	−1.05812	−	0.283522i
$641$	4.00000	+	6.92820i	0.157991	+	0.273648i	0.934144	−	0.356897i	$-0.116165\pi$
$641$	4.00000	+	6.92820i	0.157991	+	0.273648i	−0.776153	+	0.630544i	$0.782832\pi$
$642$	1.79315	+	6.69213i	0.0707700	+	0.264117i
$643$			22.0454i			0.869386i	0.900579	+	0.434693i	$0.143143\pi$
$643$			22.0454i			0.869386i	−0.900579	+	0.434693i	$0.856857\pi$
$644$		0			0
$645$		−	36.0000i		−	1.41750i
$646$	−16.3923	+	4.39230i	−0.644947	+	0.172813i
$647$	9.79796	+	16.9706i	0.385198	+	0.667182i	0.991797	−	0.127826i	$-0.0408000\pi$
$647$	9.79796	+	16.9706i	0.385198	+	0.667182i	−0.606599	+	0.795008i	$0.707467\pi$
$648$	24.5885	+	6.58846i	0.965926	+	0.258819i
$649$	−4.24264	−	2.44949i	−0.166538	−	0.0961509i
$650$	−2.44949	−	2.44949i	−0.0960769	−	0.0960769i
$651$		0			0
$652$			28.0000i			1.09656i
$653$	−13.8564	−	8.00000i	−0.542243	−	0.313064i	0.203744	−	0.979024i	$-0.434689\pi$
$653$	−13.8564	−	8.00000i	−0.542243	−	0.313064i	−0.745988	+	0.665960i	$0.768022\pi$
$654$	−3.58630	+	13.3843i	−0.140236	+	0.523366i
$655$	25.9808	−	15.0000i	1.01515	−	0.586098i
$656$		0			0
$657$			44.0908i			1.72015i
$658$		0			0
$659$	10.0000			0.389545			0.194772	−	0.980848i	$-0.437603\pi$
$659$	10.0000			0.389545			0.194772	+	0.980848i	$0.437603\pi$
$660$	12.0000	−	20.7846i	0.467099	−	0.809040i
$661$	−15.9217	−	27.5772i	−0.619282	−	1.07263i	−0.989617	−	0.143729i	$-0.954091\pi$
$661$	−15.9217	−	27.5772i	−0.619282	−	1.07263i	0.370335	−	0.928898i	$-0.379243\pi$
$662$	6.58846	−	24.5885i	0.256068	−	0.955658i
$663$	−14.6969	+	25.4558i	−0.570782	+	0.988623i
$664$	−4.89898	−	4.89898i	−0.190117	−	0.190117i
$665$		0			0
$666$	−24.0000	+	24.0000i	−0.929981	+	0.929981i
$667$	−8.00000	+	13.8564i	−0.309761	+	0.536522i
$668$	−33.9411	+	19.5959i	−1.31322	+	0.758189i
$669$	20.7846	−	12.0000i	0.803579	−	0.463947i
$670$	6.69213	−	1.79315i	0.258540	−	0.0692755i
$671$	14.6969			0.567369
$672$		0			0
$673$	−6.00000			−0.231283			−0.115642	−	0.993291i	$-0.536892\pi$
$673$	−6.00000			−0.231283			−0.115642	+	0.993291i	$0.536892\pi$
$674$	−16.3923	+	4.39230i	−0.631408	+	0.169185i
$675$		0			0
$676$	−12.1244	+	7.00000i	−0.466321	+	0.269231i
$677$	15.9217	−	27.5772i	0.611920	−	1.05988i	−0.378997	−	0.925398i	$-0.623731\pi$
$677$	15.9217	−	27.5772i	0.611920	−	1.05988i	0.990917	−	0.134478i	$-0.0429359\pi$
$678$	−9.79796	+	9.79796i	−0.376288	+	0.376288i
$679$		0			0
$680$	−24.0000	−	24.0000i	−0.920358	−	0.920358i
$681$	9.00000	−	15.5885i	0.344881	−	0.597351i
$682$	3.58630	−	13.3843i	0.137327	−	0.512510i
$683$	−7.00000	−	12.1244i	−0.267848	−	0.463926i	0.700458	−	0.713693i	$-0.252979\pi$
$683$	−7.00000	−	12.1244i	−0.267848	−	0.463926i	−0.968306	+	0.249768i	$0.919646\pi$
$684$	−7.34847	+	12.7279i	−0.280976	+	0.486664i
$685$	4.89898			0.187180
$686$		0			0
$687$		−	30.0000i		−	1.14457i
$688$	−12.0000	+	20.7846i	−0.457496	+	0.792406i
$689$	−8.48528	+	4.89898i	−0.323263	+	0.186636i
$690$	−8.78461	+	32.7846i	−0.334424	+	1.24809i
$691$	−31.8198	−	18.3712i	−1.21048	−	0.698872i	−0.247618	−	0.968858i	$-0.579648\pi$
$691$	−31.8198	−	18.3712i	−1.21048	−	0.698872i	−0.962864	+	0.269985i	$0.912981\pi$
$692$			4.89898i			0.186231i
$693$		0			0
$694$	22.0000	+	22.0000i	0.835109	+	0.835109i
$695$	5.19615	+	3.00000i	0.197101	+	0.113796i
$696$	−26.7685	−	7.17260i	−1.01466	−	0.271877i
$697$		0			0
$698$	−16.7303	+	4.48288i	−0.633252	+	0.169679i
$699$		−	34.2929i		−	1.29707i
$700$		0			0
$701$		−	40.0000i		−	1.51078i	−0.655276	−	0.755390i	$-0.727448\pi$
$701$		−	40.0000i		−	1.51078i	0.655276	−	0.755390i	$-0.272552\pi$
$702$		0			0
$703$	9.79796	+	16.9706i	0.369537	+	0.640057i
$704$	−13.8564	+	8.00000i	−0.522233	+	0.301511i
$705$	−25.4558	−	14.6969i	−0.958723	−	0.553519i
$706$	9.79796	−	9.79796i	0.368751	−	0.368751i
$707$		0			0
$708$			12.0000i			0.450988i
$709$	−3.46410	−	2.00000i	−0.130097	−	0.0751116i	0.433539	−	0.901135i	$-0.357265\pi$
$709$	−3.46410	−	2.00000i	−0.130097	−	0.0751116i	−0.563636	+	0.826023i	$0.690598\pi$
$710$	33.4607	+	8.96575i	1.25576	+	0.336479i
$711$	15.5885	−	9.00000i	0.584613	−	0.337526i
$712$	−40.1528	+	10.7589i	−1.50479	+	0.403207i
$713$			19.5959i			0.733873i
$714$		0			0
$715$	−12.0000			−0.448775
$716$	−17.3205	−	10.0000i	−0.647298	−	0.373718i
$717$	−4.89898	−	8.48528i	−0.182956	−	0.316889i
$718$	−5.46410	−	1.46410i	−0.203918	−	0.0546398i
$719$	12.2474	−	21.2132i	0.456753	−	0.791119i	−0.542034	−	0.840356i	$-0.682346\pi$
$719$	12.2474	−	21.2132i	0.456753	−	0.791119i	0.998787	+	0.0492373i	$0.0156791\pi$
$720$	−29.3939			−1.09545
$721$		0			0
$722$	−13.0000	−	13.0000i	−0.483810	−	0.483810i
$723$	−30.0000	+	51.9615i	−1.11571	+	1.93247i
$724$	12.7279	−	7.34847i	0.473029	−	0.273104i
$725$	3.46410	−	2.00000i	0.128654	−	0.0742781i
$726$	6.27603	+	23.4225i	0.232925	+	0.869289i
$727$	29.3939			1.09016			0.545079	−	0.838385i	$-0.316500\pi$
$727$	29.3939			1.09016			0.545079	+	0.838385i	$0.316500\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	13.1769	+	49.1769i	0.487699	+	1.82012i
$731$	−25.4558	+	14.6969i	−0.941518	+	0.543586i
$732$	−18.0000	−	31.1769i	−0.665299	−	1.15233i
$733$	11.0227	−	19.0919i	0.407133	−	0.705175i	−0.587434	−	0.809272i	$-0.699862\pi$
$733$	11.0227	−	19.0919i	0.407133	−	0.705175i	0.994567	+	0.104097i	$0.0331953\pi$
$734$	−29.3939	−	29.3939i	−1.08495	−	1.08495i
$735$		0			0
$736$	16.0000	−	16.0000i	0.589768	−	0.589768i
$737$	2.00000	−	3.46410i	0.0736709	−	0.127602i
$738$		0			0
$739$	25.0000	+	43.3013i	0.919640	+	1.59286i	0.799962	+	0.600050i	$0.204853\pi$
$739$	25.0000	+	43.3013i	0.919640	+	1.59286i	0.119677	+	0.992813i	$0.461814\pi$
$740$	−19.5959	+	33.9411i	−0.720360	+	1.24770i
$741$	14.6969			0.539906
$742$		0			0
$743$		−	44.0000i		−	1.61420i	−0.590412	−	0.807102i	$-0.701035\pi$
$743$		−	44.0000i		−	1.61420i	0.590412	−	0.807102i	$-0.298965\pi$
$744$	−32.7846	+	8.78461i	−1.20194	+	0.322059i
$745$	33.9411	−	19.5959i	1.24351	−	0.717939i
$746$	−49.1769	−	13.1769i	−1.80049	−	0.482441i
$747$	−6.36396	−	3.67423i	−0.232845	−	0.134433i
$748$	−19.5959			−0.716498
$749$		0			0
$750$	−24.0000	+	24.0000i	−0.876356	+	0.876356i
$751$	17.3205	+	10.0000i	0.632034	+	0.364905i	0.781540	−	0.623856i	$-0.214435\pi$
$751$	17.3205	+	10.0000i	0.632034	+	0.364905i	−0.149505	+	0.988761i	$0.547768\pi$
$752$	9.79796	+	16.9706i	0.357295	+	0.618853i
$753$	15.0000	+	25.9808i	0.546630	+	0.946792i
$754$	3.58630	+	13.3843i	0.130605	+	0.487426i
$755$		−	48.9898i		−	1.78292i
$756$		0			0
$757$			8.00000i			0.290765i	0.989376	+	0.145382i	$0.0464413\pi$
$757$			8.00000i			0.290765i	−0.989376	+	0.145382i	$0.953559\pi$
$758$	40.9808	−	10.9808i	1.48849	−	0.398839i
$759$	9.79796	+	16.9706i	0.355643	+	0.615992i
$760$	−4.39230	+	16.3923i	−0.159326	+	0.594611i
$761$	42.4264	+	24.4949i	1.53796	+	0.887939i	0.998958	+	0.0456321i	$0.0145302\pi$
$761$	42.4264	+	24.4949i	1.53796	+	0.887939i	0.538998	+	0.842307i	$0.318803\pi$
$762$	29.3939	+	29.3939i	1.06483	+	1.06483i
$763$		0			0
$764$	20.0000			0.723575
$765$	−31.1769	−	18.0000i	−1.12720	−	0.650791i
$766$	12.5521	−	46.8449i	0.453524	−	1.69258i
$767$	5.19615	−	3.00000i	0.187622	−	0.108324i
$768$	33.9411	+	19.5959i	1.22474	+	0.707107i
$769$		−	34.2929i		−	1.23663i	−0.785930	−	0.618316i	$-0.787815\pi$
$769$		−	34.2929i		−	1.23663i	0.785930	−	0.618316i	$-0.212185\pi$
$770$		0			0
$771$	−48.0000			−1.72868
$772$	−41.5692	−	24.0000i	−1.49611	−	0.863779i
$773$	11.0227	+	19.0919i	0.396459	+	0.686687i	0.993286	−	0.115683i	$-0.0369055\pi$
$773$	11.0227	+	19.0919i	0.396459	+	0.686687i	−0.596827	+	0.802370i	$0.703572\pi$
$774$	−6.58846	+	24.5885i	−0.236817	+	0.883814i
$775$	2.44949	−	4.24264i	0.0879883	−	0.152400i
$776$	9.79796	+	9.79796i	0.351726	+	0.351726i
$777$		0			0
$778$	−16.0000	+	16.0000i	−0.573628	+	0.573628i
$779$		0			0
$780$	14.6969	+	25.4558i	0.526235	+	0.911465i
$781$	17.3205	−	10.0000i	0.619777	−	0.357828i
$782$	26.7685	−	7.17260i	0.957240	−	0.256492i
$783$		0			0
$784$		0			0
$785$	18.0000			0.642448
$786$	−40.9808	+	10.9808i	−1.46174	+	0.391671i
$787$	−6.36396	+	3.67423i	−0.226851	+	0.130972i	−0.609118	−	0.793079i	$-0.708477\pi$
$787$	−6.36396	+	3.67423i	−0.226851	+	0.130972i	0.382268	+	0.924052i	$0.375143\pi$
$788$	8.00000	+	13.8564i	0.284988	+	0.493614i
$789$	17.1464	−	29.6985i	0.610429	−	1.05729i
$790$	14.6969	−	14.6969i	0.522894	−	0.522894i
$791$		0			0
$792$	−12.0000	+	12.0000i	−0.426401	+	0.426401i
$793$	−9.00000	+	15.5885i	−0.319599	+	0.553562i
$794$	11.6555	−	43.4988i	0.413638	−	1.54372i
$795$	−12.0000	−	20.7846i	−0.425596	−	0.737154i
$796$		0			0
$797$	41.6413			1.47501			0.737506	−	0.675341i	$-0.236003\pi$
$797$	41.6413			1.47501			0.737506	+	0.675341i	$0.236003\pi$
$798$		0			0
$799$			24.0000i			0.849059i
$800$	−5.46410	+	1.46410i	−0.193185	+	0.0517638i
$801$	−38.1838	+	22.0454i	−1.34916	+	0.778936i
$802$	−11.7128	+	43.7128i	−0.413594	+	1.54355i
$803$	25.4558	+	14.6969i	0.898317	+	0.518644i
$804$	−9.79796			−0.345547
$805$		0			0
$806$	12.0000	+	12.0000i	0.422682	+	0.422682i
$807$	25.9808	+	15.0000i	0.914566	+	0.528025i
$808$	46.8449	+	12.5521i	1.64800	+	0.441580i
$809$	−10.0000	−	17.3205i	−0.351581	−	0.608957i	0.634945	−	0.772557i	$-0.281023\pi$
$809$	−10.0000	−	17.3205i	−0.351581	−	0.608957i	−0.986527	+	0.163600i	$0.947689\pi$
$810$	30.1146	−	8.06918i	1.05812	−	0.283522i
$811$			36.7423i			1.29020i	0.764099	+	0.645099i	$0.223184\pi$
$811$			36.7423i			1.29020i	−0.764099	+	0.645099i	$0.776816\pi$
$812$		0			0
$813$		−	48.0000i		−	1.68343i
$814$	5.85641	+	21.8564i	0.205267	+	0.766067i
$815$	17.1464	+	29.6985i	0.600613	+	1.04029i
$816$	24.0000	+	41.5692i	0.840168	+	1.45521i
$817$	12.7279	+	7.34847i	0.445294	+	0.257090i
$818$	−9.79796	+	9.79796i	−0.342578	+	0.342578i
$819$		0			0
$820$		0			0
$821$	17.3205	+	10.0000i	0.604490	+	0.349002i	0.770806	−	0.637070i	$-0.219854\pi$
$821$	17.3205	+	10.0000i	0.604490	+	0.349002i	−0.166316	+	0.986073i	$0.553187\pi$
$822$	−6.69213	−	1.79315i	−0.233415	−	0.0625433i
$823$	−46.7654	+	27.0000i	−1.63014	+	0.941161i	−0.646090	+	0.763261i	$0.723597\pi$
$823$	−46.7654	+	27.0000i	−1.63014	+	0.941161i	−0.984049	+	0.177899i	$0.943070\pi$
$824$	−7.17260	−	26.7685i	−0.249869	−	0.932526i
$825$		−	4.89898i		−	0.170561i
$826$		0			0
$827$	−22.0000			−0.765015			−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000			−0.765015			−0.382507	+	0.923952i	$0.624939\pi$
$828$	12.0000	−	20.7846i	0.417029	−	0.722315i
$829$	−18.3712	−	31.8198i	−0.638057	−	1.10515i	−0.985859	−	0.167579i	$-0.946405\pi$
$829$	−18.3712	−	31.8198i	−0.638057	−	1.10515i	0.347801	−	0.937568i	$-0.386928\pi$
$830$	−8.19615	−	2.19615i	−0.284493	−	0.0762296i
$831$	14.6969	−	25.4558i	0.509831	−	0.883053i
$832$		−	19.5959i		−	0.679366i
$833$		0			0
$834$	−6.00000	−	6.00000i	−0.207763	−	0.207763i
$835$	−24.0000	+	41.5692i	−0.830554	+	1.43856i
$836$	4.89898	+	8.48528i	0.169435	+	0.293470i
$837$		0			0
$838$	9.86233	+	36.8067i	0.340689	+	1.27147i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	13.0000			0.448276
$842$		0			0
$843$	−4.24264	+	2.44949i	−0.146124	+	0.0843649i
$844$	−31.1769	+	18.0000i	−1.07315	+	0.619586i
$845$	−8.57321	+	14.8492i	−0.294928	+	0.510829i
$846$	14.6969	+	14.6969i	0.505291	+	0.505291i
$847$		0			0
$848$			16.0000i			0.549442i
$849$	3.00000	−	5.19615i	0.102960	−	0.178331i
$850$	−6.69213	−	1.79315i	−0.229538	−	0.0615046i
$851$	−16.0000	−	27.7128i	−0.548473	−	0.949983i
$852$	−42.4264	−	24.4949i	−1.45350	−	0.839181i
$853$	2.44949			0.0838689			0.0419345	−	0.999120i	$-0.486648\pi$
$853$	2.44949			0.0838689			0.0419345	+	0.999120i	$0.486648\pi$
$854$		0			0
$855$			18.0000i			0.615587i
$856$	−1.46410	−	5.46410i	−0.0500420	−	0.186759i
$857$	25.4558	−	14.6969i	0.869555	−	0.502038i	0.00235471	−	0.999997i	$-0.499250\pi$
$857$	25.4558	−	14.6969i	0.869555	−	0.502038i	0.867200	+	0.497959i	$0.165917\pi$
$858$	16.3923	+	4.39230i	0.559624	+	0.149951i
$859$	−23.3345	−	13.4722i	−0.796164	−	0.459665i	0.0459643	−	0.998943i	$-0.485364\pi$
$859$	−23.3345	−	13.4722i	−0.796164	−	0.459665i	−0.842128	+	0.539278i	$0.818697\pi$
$860$			29.3939i			1.00232i
$861$		0			0
$862$	−20.0000	+	20.0000i	−0.681203	+	0.681203i
$863$	−39.8372	−	23.0000i	−1.35607	−	0.782929i	−0.366981	−	0.930228i	$-0.619609\pi$
$863$	−39.8372	−	23.0000i	−1.35607	−	0.782929i	−0.989092	+	0.147299i	$0.952942\pi$
$864$		0			0
$865$	3.00000	+	5.19615i	0.102003	+	0.176674i
$866$	−5.37945	−	20.0764i	−0.182801	−	0.682224i
$867$			17.1464i			0.582323i
$868$		0			0
$869$		−	12.0000i		−	0.407072i
$870$	−32.7846	+	8.78461i	−1.11150	+	0.297826i
$871$	2.44949	+	4.24264i	0.0829978	+	0.143756i
$872$	2.92820	−	10.9282i	0.0991615	−	0.370076i
$873$	12.7279	+	7.34847i	0.430775	+	0.248708i
$874$	−9.79796	−	9.79796i	−0.331421	−	0.331421i
$875$		0			0
$876$		−	72.0000i		−	2.43265i
$877$	−41.5692	−	24.0000i	−1.40369	−	0.810422i	−0.408923	−	0.912569i	$-0.634096\pi$
$877$	−41.5692	−	24.0000i	−1.40369	−	0.810422i	−0.994769	+	0.102146i	$0.967429\pi$
$878$	8.96575	−	33.4607i	0.302580	−	1.12924i
$879$	−5.19615	+	3.00000i	−0.175262	+	0.101187i
$880$	−9.79796	+	16.9706i	−0.330289	+	0.572078i
$881$		−	48.9898i		−	1.65051i	−0.564762	−	0.825254i	$-0.691032\pi$
$881$		−	48.9898i		−	1.65051i	0.564762	−	0.825254i	$-0.308968\pi$
$882$		0			0
$883$	−6.00000			−0.201916			−0.100958	−	0.994891i	$-0.532191\pi$
$883$	−6.00000			−0.201916			−0.100958	+	0.994891i	$0.532191\pi$
$884$	12.0000	−	20.7846i	0.403604	−	0.699062i
$885$	7.34847	+	12.7279i	0.247016	+	0.427844i
$886$	9.51666	−	35.5167i	0.319718	−	1.19321i
$887$	−14.6969	+	25.4558i	−0.493475	+	0.854724i	−0.999972	−	0.00751822i	$-0.997607\pi$
$887$	−14.6969	+	25.4558i	−0.493475	+	0.854724i	0.506497	+	0.862242i	$0.330940\pi$
$888$	39.1918	−	39.1918i	1.31519	−	1.31519i
$889$		0			0
$890$	−36.0000	+	36.0000i	−1.20672	+	1.20672i
$891$	9.00000	−	15.5885i	0.301511	−	0.522233i
$892$	−16.9706	+	9.79796i	−0.568216	+	0.328060i
$893$	10.3923	−	6.00000i	0.347765	−	0.200782i
$894$	−53.5370	+	14.3452i	−1.79055	+	0.479776i
$895$	−24.4949			−0.818774
$896$		0			0
$897$	−24.0000			−0.801337
$898$	−13.6603	+	3.66025i	−0.455849	+	0.122144i
$899$	−16.9706	+	9.79796i	−0.566000	+	0.326780i
$900$	−5.19615	+	3.00000i	−0.173205	+	0.100000i
$901$	−9.79796	+	16.9706i	−0.326417	+	0.565371i
$902$		0			0
$903$		0			0
$904$	8.00000	−	8.00000i	0.266076	−	0.266076i
$905$	9.00000	−	15.5885i	0.299170	−	0.518178i
$906$	−17.9315	+	66.9213i	−0.595734	+	2.22331i
$907$	21.0000	+	36.3731i	0.697294	+	1.20775i	0.969401	+	0.245481i	$0.0789459\pi$
$907$	21.0000	+	36.3731i	0.697294	+	1.20775i	−0.272108	+	0.962267i	$0.587721\pi$
$908$	−7.34847	+	12.7279i	−0.243868	+	0.422391i
$909$	51.4393			1.70613
$910$		0			0
$911$			20.0000i			0.662630i	0.943520	+	0.331315i	$0.107492\pi$
$911$			20.0000i			0.662630i	−0.943520	+	0.331315i	$0.892508\pi$
$912$	12.0000	−	20.7846i	0.397360	−	0.688247i
$913$	−4.24264	+	2.44949i	−0.140411	+	0.0810663i
$914$	4.39230	−	16.3923i	0.145285	−	0.542209i
$915$	−38.1838	−	22.0454i	−1.26232	−	0.728799i
$916$			24.4949i			0.809334i
$917$		0			0
$918$		0			0
$919$	39.8372	+	23.0000i	1.31411	+	0.758700i	0.982774	−	0.184814i	$-0.0591682\pi$
$919$	39.8372	+	23.0000i	1.31411	+	0.758700i	0.331333	+	0.943514i	$0.392502\pi$
$920$	7.17260	−	26.7685i	0.236474	−	0.882532i
$921$	39.0000	+	67.5500i	1.28509	+	2.22585i
$922$	10.0382	−	2.68973i	0.330590	−	0.0885814i
$923$			24.4949i			0.806259i
$924$		0			0
$925$			8.00000i			0.263038i
$926$	2.19615	+	8.19615i	0.0721700	+	0.269342i
$927$	−14.6969	−	25.4558i	−0.482711	−	0.836080i
$928$	21.8564	+	5.85641i	0.717472	+	0.192246i
$929$	−12.7279	−	7.34847i	−0.417590	−	0.241095i	0.276456	−	0.961027i	$-0.410840\pi$
$929$	−12.7279	−	7.34847i	−0.417590	−	0.241095i	−0.694045	+	0.719931i	$0.744173\pi$
$930$	−29.3939	+	29.3939i	−0.963863	+	0.963863i
$931$		0			0
$932$			28.0000i			0.917170i
$933$	−10.3923	−	6.00000i	−0.340229	−	0.196431i
$934$	−56.8831	−	15.2418i	−1.86127	−	0.498726i
$935$	−20.7846	+	12.0000i	−0.679729	+	0.392442i
$936$	−5.37945	−	20.0764i	−0.175833	−	0.656217i
$937$			4.89898i			0.160043i	0.996793	+	0.0800213i	$0.0254988\pi$
$937$			4.89898i			0.160043i	−0.996793	+	0.0800213i	$0.974501\pi$
$938$		0			0
$939$	24.0000			0.783210
$940$	20.7846	+	12.0000i	0.677919	+	0.391397i
$941$	−15.9217	−	27.5772i	−0.519032	−	0.898990i	−0.999755	−	0.0221175i	$-0.992959\pi$
$941$	−15.9217	−	27.5772i	−0.519032	−	0.898990i	0.480723	−	0.876872i	$-0.340374\pi$
$942$	−24.5885	−	6.58846i	−0.801135	−	0.214664i
$943$		0			0
$944$		−	9.79796i		−	0.318896i
$945$		0			0
$946$	12.0000	+	12.0000i	0.390154	+	0.390154i
$947$	11.0000	−	19.0526i	0.357452	−	0.619125i	−0.630082	−	0.776528i	$-0.716979\pi$
$947$	11.0000	−	19.0526i	0.357452	−	0.619125i	0.987534	+	0.157403i	$0.0503122\pi$
$948$	−25.4558	+	14.6969i	−0.826767	+	0.477334i
$949$	−31.1769	+	18.0000i	−1.01205	+	0.584305i
$950$	0.896575	+	3.34607i	0.0290887	+	0.108561i
$951$	−78.3837			−2.54176
$952$		0			0
$953$	34.0000			1.10137			0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000			1.10137			0.550684	+	0.834714i	$0.314367\pi$
$954$	4.39230	+	16.3923i	0.142206	+	0.530720i
$955$	21.2132	−	12.2474i	0.686443	−	0.396318i
$956$	4.00000	+	6.92820i	0.129369	+	0.224074i
$957$	−9.79796	+	16.9706i	−0.316723	+	0.548580i
$958$	−24.4949	−	24.4949i	−0.791394	−	0.791394i
$959$		0			0
$960$	48.0000			1.54919
$961$	3.50000	−	6.06218i	0.112903	−	0.195554i
$962$	−26.7685	−	7.17260i	−0.863052	−	0.231254i
$963$	−3.00000	−	5.19615i	−0.0966736	−	0.167444i
$964$	24.4949	−	42.4264i	0.788928	−	1.36646i
$965$	−58.7878			−1.89244
$966$		0			0
$967$		−	12.0000i		−	0.385894i	−0.981209	−	0.192947i	$-0.938195\pi$
$967$		−	12.0000i		−	0.385894i	0.981209	−	0.192947i	$-0.0618045\pi$
$968$	−5.12436	−	19.1244i	−0.164703	−	0.614680i
$969$	25.4558	−	14.6969i	0.817760	−	0.472134i
$970$	16.3923	+	4.39230i	0.526325	+	0.141028i
$971$	31.8198	+	18.3712i	1.02115	+	0.589559i	0.914436	−	0.404731i	$-0.132635\pi$
$971$	31.8198	+	18.3712i	1.02115	+	0.589559i	0.106710	+	0.994290i	$0.465968\pi$
$972$	−44.0908			−1.41421
$973$		0			0
$974$	28.0000	−	28.0000i	0.897178	−	0.897178i
$975$	5.19615	+	3.00000i	0.166410	+	0.0960769i
$976$	14.6969	+	25.4558i	0.470438	+	0.814822i
$977$	−19.0000	−	32.9090i	−0.607864	−	1.05285i	−0.991592	−	0.129405i	$-0.958693\pi$
$977$	−19.0000	−	32.9090i	−0.607864	−	1.05285i	0.383728	−	0.923446i	$-0.374640\pi$
$978$	−12.5521	−	46.8449i	−0.401371	−	1.49794i
$979$			29.3939i			0.939432i
$980$		0			0
$981$		−	12.0000i		−	0.383131i
$982$	2.73205	−	0.732051i	0.0871832	−	0.0233607i
$983$	−19.5959	−	33.9411i	−0.625013	−	1.08255i	−0.988538	−	0.150970i	$-0.951760\pi$
$983$	−19.5959	−	33.9411i	−0.625013	−	1.08255i	0.363526	−	0.931584i	$-0.381573\pi$
$984$		0			0
$985$	16.9706	+	9.79796i	0.540727	+	0.312189i
$986$	19.5959	+	19.5959i	0.624061	+	0.624061i
$987$		0			0
$988$	−12.0000			−0.381771
$989$	−20.7846	−	12.0000i	−0.660912	−	0.381578i
$990$	−5.37945	+	20.0764i	−0.170970	+	0.638070i
$991$	8.66025	−	5.00000i	0.275102	−	0.158830i	−0.356102	−	0.934447i	$-0.615894\pi$
$991$	8.66025	−	5.00000i	0.275102	−	0.158830i	0.631204	+	0.775617i	$0.282561\pi$
$992$	26.7685	−	7.17260i	0.849901	−	0.227730i
$993$			44.0908i			1.39918i
$994$		0			0
$995$		0			0
$996$	10.3923	+	6.00000i	0.329293	+	0.190117i
$997$	15.9217	+	27.5772i	0.504245	+	0.873378i	0.999988	+	0.00490839i	$0.00156240\pi$
$997$	15.9217	+	27.5772i	0.504245	+	0.873378i	−0.495743	+	0.868469i	$0.665104\pi$
$998$	−10.9808	+	40.9808i	−0.347590	+	1.29722i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.m.f.19.3		8
4.3	odd	2		1568.2.q.e.1391.4		8
7.2	even	3		56.2.e.b.27.1	✓	4
7.3	odd	6	inner	392.2.m.f.227.1		8
7.4	even	3	inner	392.2.m.f.227.2		8
7.5	odd	6		56.2.e.b.27.2	yes	4
7.6	odd	2	inner	392.2.m.f.19.4		8
8.3	odd	2	inner	392.2.m.f.19.1		8
8.5	even	2		1568.2.q.e.1391.3		8
21.2	odd	6		504.2.p.f.307.4		4
21.5	even	6		504.2.p.f.307.3		4
28.3	even	6		1568.2.q.e.815.3		8
28.11	odd	6		1568.2.q.e.815.2		8
28.19	even	6		224.2.e.b.111.2		4
28.23	odd	6		224.2.e.b.111.3		4
28.27	even	2		1568.2.q.e.1391.1		8
56.3	even	6	inner	392.2.m.f.227.3		8
56.5	odd	6		224.2.e.b.111.1		4
56.11	odd	6	inner	392.2.m.f.227.4		8
56.13	odd	2		1568.2.q.e.1391.2		8
56.19	even	6		56.2.e.b.27.4	yes	4
56.27	even	2	inner	392.2.m.f.19.2		8
56.37	even	6		224.2.e.b.111.4		4
56.45	odd	6		1568.2.q.e.815.4		8
56.51	odd	6		56.2.e.b.27.3	yes	4
56.53	even	6		1568.2.q.e.815.1		8
84.23	even	6		2016.2.p.e.559.4		4
84.47	odd	6		2016.2.p.e.559.2		4
112.5	odd	12		1792.2.f.f.1791.4		4
112.19	even	12		1792.2.f.e.1791.3		4
112.37	even	12		1792.2.f.f.1791.1		4
112.51	odd	12		1792.2.f.e.1791.2		4
112.61	odd	12		1792.2.f.e.1791.1		4
112.75	even	12		1792.2.f.f.1791.2		4
112.93	even	12		1792.2.f.e.1791.4		4
112.107	odd	12		1792.2.f.f.1791.3		4
168.5	even	6		2016.2.p.e.559.3		4
168.107	even	6		504.2.p.f.307.1		4
168.131	odd	6		504.2.p.f.307.2		4
168.149	odd	6		2016.2.p.e.559.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.e.b.27.1	✓	4	7.2	even	3
56.2.e.b.27.2	yes	4	7.5	odd	6
56.2.e.b.27.3	yes	4	56.51	odd	6
56.2.e.b.27.4	yes	4	56.19	even	6
224.2.e.b.111.1		4	56.5	odd	6
224.2.e.b.111.2		4	28.19	even	6
224.2.e.b.111.3		4	28.23	odd	6
224.2.e.b.111.4		4	56.37	even	6
392.2.m.f.19.1		8	8.3	odd	2	inner
392.2.m.f.19.2		8	56.27	even	2	inner
392.2.m.f.19.3		8	1.1	even	1	trivial
392.2.m.f.19.4		8	7.6	odd	2	inner
392.2.m.f.227.1		8	7.3	odd	6	inner
392.2.m.f.227.2		8	7.4	even	3	inner
392.2.m.f.227.3		8	56.3	even	6	inner
392.2.m.f.227.4		8	56.11	odd	6	inner
504.2.p.f.307.1		4	168.107	even	6
504.2.p.f.307.2		4	168.131	odd	6
504.2.p.f.307.3		4	21.5	even	6
504.2.p.f.307.4		4	21.2	odd	6
1568.2.q.e.815.1		8	56.53	even	6
1568.2.q.e.815.2		8	28.11	odd	6
1568.2.q.e.815.3		8	28.3	even	6
1568.2.q.e.815.4		8	56.45	odd	6
1568.2.q.e.1391.1		8	28.27	even	2
1568.2.q.e.1391.2		8	56.13	odd	2
1568.2.q.e.1391.3		8	8.5	even	2
1568.2.q.e.1391.4		8	4.3	odd	2
1792.2.f.e.1791.1		4	112.61	odd	12
1792.2.f.e.1791.2		4	112.51	odd	12
1792.2.f.e.1791.3		4	112.19	even	12
1792.2.f.e.1791.4		4	112.93	even	12
1792.2.f.f.1791.1		4	112.37	even	12
1792.2.f.f.1791.2		4	112.75	even	12
1792.2.f.f.1791.3		4	112.107	odd	12
1792.2.f.f.1791.4		4	112.5	odd	12
2016.2.p.e.559.1		4	168.149	odd	6
2016.2.p.e.559.2		4	84.47	odd	6
2016.2.p.e.559.3		4	168.5	even	6
2016.2.p.e.559.4		4	84.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(-2.12132 + 1.22474i) q^{3} +(1.73205 - 1.00000i) q^{4} +(1.22474 - 2.12132i) q^{5} +(-2.44949 + 2.44949i) q^{6} +(2.00000 - 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +(0.896575 - 3.34607i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-2.44949 + 4.24264i) q^{12} +2.44949 q^{13} +6.00000i q^{15} +(2.00000 - 3.46410i) q^{16} +(4.24264 - 2.44949i) q^{17} +(1.09808 - 4.09808i) q^{18} +(-2.12132 - 1.22474i) q^{19} -4.89898i q^{20} +(-2.00000 - 2.00000i) q^{22} +(3.46410 + 2.00000i) q^{23} +(-1.79315 + 6.69213i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.34607 - 0.896575i) q^{26} +4.00000i q^{29} +(2.19615 + 8.19615i) q^{30} +(2.44949 + 4.24264i) q^{31} +(1.46410 - 5.46410i) q^{32} +(4.24264 + 2.44949i) q^{33} +(4.89898 - 4.89898i) q^{34} -6.00000i q^{36} +(-6.92820 - 4.00000i) q^{37} +(-3.34607 - 0.896575i) q^{38} +(-5.19615 + 3.00000i) q^{39} +(-1.79315 - 6.69213i) q^{40} -6.00000 q^{43} +(-3.46410 - 2.00000i) q^{44} +(-3.67423 - 6.36396i) q^{45} +(5.46410 + 1.46410i) q^{46} +(-2.44949 + 4.24264i) q^{47} +9.79796i q^{48} +(-1.00000 - 1.00000i) q^{50} +(-6.00000 + 10.3923i) q^{51} +(4.24264 - 2.44949i) q^{52} +(-3.46410 + 2.00000i) q^{53} -4.89898 q^{55} +6.00000 q^{57} +(1.46410 + 5.46410i) q^{58} +(2.12132 - 1.22474i) q^{59} +(6.00000 + 10.3923i) q^{60} +(-3.67423 + 6.36396i) q^{61} +(4.89898 + 4.89898i) q^{62} -8.00000i q^{64} +(3.00000 - 5.19615i) q^{65} +(6.69213 + 1.79315i) q^{66} +(1.00000 + 1.73205i) q^{67} +(4.89898 - 8.48528i) q^{68} -9.79796 q^{69} +10.0000i q^{71} +(-2.19615 - 8.19615i) q^{72} +(-12.7279 + 7.34847i) q^{73} +(-10.9282 - 2.92820i) q^{74} +(2.12132 + 1.22474i) q^{75} -4.89898 q^{76} +(-6.00000 + 6.00000i) q^{78} +(5.19615 + 3.00000i) q^{79} +(-4.89898 - 8.48528i) q^{80} +(4.50000 + 7.79423i) q^{81} -2.44949i q^{83} -12.0000i q^{85} +(-8.19615 + 2.19615i) q^{86} +(-4.89898 - 8.48528i) q^{87} +(-5.46410 - 1.46410i) q^{88} +(-12.7279 - 7.34847i) q^{89} +(-7.34847 - 7.34847i) q^{90} +8.00000 q^{92} +(-10.3923 - 6.00000i) q^{93} +(-1.79315 + 6.69213i) q^{94} +(-5.19615 + 3.00000i) q^{95} +(3.58630 + 13.3843i) q^{96} +4.89898i q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 16 q^{8} + 12 q^{9} - 8 q^{11} + 16 q^{16} - 12 q^{18} - 16 q^{22} - 4 q^{25} - 24 q^{30} - 16 q^{32} - 48 q^{43} + 16 q^{46} - 8 q^{50} - 48 q^{51} + 48 q^{57} - 16 q^{58} + 48 q^{60} + 24 q^{65}+ \cdots - 48 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 16 * q^8 + 12 * q^9 - 8 * q^11 + 16 * q^16 - 12 * q^18 - 16 * q^22 - 4 * q^25 - 24 * q^30 - 16 * q^32 - 48 * q^43 + 16 * q^46 - 8 * q^50 - 48 * q^51 + 48 * q^57 - 16 * q^58 + 48 * q^60 + 24 * q^65 + 8 * q^67 + 24 * q^72 - 32 * q^74 - 48 * q^78 + 36 * q^81 - 24 * q^86 - 16 * q^88 + 64 * q^92 - 48 * q^99

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