LMFDB - Embedded newform 1274.2.m.e.491.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(491,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.491"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,0,0,0,0,0] 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:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 103x^{12} - 396x^{10} + 1089x^{8} - 1584x^{6} + 1648x^{4} - 768x^{2} + 256 $ x^16 - 12x^14 + 103x^12 - 396x^10 + 1089x^8 - 1584x^6 + 1648x^4 - 768*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.3
Root			$-0.646642 - 0.373339i$ of defining polynomial
Character	$\chi$	$=$	1274.491
Dual form			1274.2.m.e.589.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.373339 + 0.646642i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.93185i q^{5} +(-0.646642 - 0.373339i) q^{6} +1.00000i q^{8} +(1.22124 - 2.11524i) q^{9} +(-0.965926 - 1.67303i) q^{10} +(3.31599 - 1.91449i) q^{11} +0.746678 q^{12} +(-1.19966 + 3.40012i) q^{13} +(-1.24922 + 0.721236i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.129815 - 0.224846i) q^{17} +2.44247i q^{18} +(2.92286 + 1.68752i) q^{19} +(1.67303 + 0.965926i) q^{20} +(-1.91449 + 3.31599i) q^{22} +(-2.72124 - 4.71332i) q^{23} +(-0.646642 + 0.373339i) q^{24} +1.26795 q^{25} +(-0.661126 - 3.54442i) q^{26} +4.06378 q^{27} +(5.31931 + 9.21332i) q^{29} +(0.721236 - 1.24922i) q^{30} -6.85042i q^{31} +(0.866025 + 0.500000i) q^{32} +(2.47598 + 1.42951i) q^{33} +0.259630i q^{34} +(-1.22124 - 2.11524i) q^{36} +(6.27477 - 3.62274i) q^{37} -3.37503 q^{38} +(-2.64654 + 0.493649i) q^{39} -1.93185 q^{40} +(0.957850 - 0.553015i) q^{41} +(-1.00000 + 1.73205i) q^{43} -3.82898i q^{44} +(4.08633 + 2.35925i) q^{45} +(4.71332 + 2.72124i) q^{46} +6.36175i q^{47} +(0.373339 - 0.646642i) q^{48} +(-1.09808 + 0.633975i) q^{50} +0.193860 q^{51} +(2.34476 + 2.73899i) q^{52} -9.04447 q^{53} +(-3.51933 + 2.03189i) q^{54} +(3.69851 + 6.40601i) q^{55} +2.52006i q^{57} +(-9.21332 - 5.31931i) q^{58} +(3.12262 + 1.80285i) q^{59} +1.44247i q^{60} +(-2.21495 + 3.83640i) q^{61} +(3.42521 + 5.93263i) q^{62} -1.00000 q^{64} +(-6.56853 - 2.31756i) q^{65} -2.85902 q^{66} +(1.13356 - 0.654458i) q^{67} +(-0.129815 - 0.224846i) q^{68} +(2.03189 - 3.51933i) q^{69} +(5.88434 + 3.39732i) q^{71} +(2.11524 + 1.22124i) q^{72} +2.97832i q^{73} +(-3.62274 + 6.27477i) q^{74} +(0.473375 + 0.819910i) q^{75} +(2.92286 - 1.68752i) q^{76} +(2.04515 - 1.75078i) q^{78} -8.80301 q^{79} +(1.67303 - 0.965926i) q^{80} +(-2.14654 - 3.71792i) q^{81} +(-0.553015 + 0.957850i) q^{82} +14.8826i q^{83} +(0.434369 + 0.250783i) q^{85} -2.00000i q^{86} +(-3.97181 + 6.87938i) q^{87} +(1.91449 + 3.31599i) q^{88} +(13.4263 - 7.75168i) q^{89} -4.71849 q^{90} -5.44247 q^{92} +(4.42977 - 2.55753i) q^{93} +(-3.18087 - 5.50943i) q^{94} +(-3.26003 + 5.64654i) q^{95} +0.746678i q^{96} +(-9.65704 - 5.57550i) q^{97} -9.35218i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 12 q^{11} + 12 q^{15} - 8 q^{16} - 4 q^{22} - 24 q^{23} + 48 q^{25} + 24 q^{29} - 8 q^{30} + 12 q^{37} + 12 q^{39} - 16 q^{43} - 12 q^{46} + 24 q^{50} - 48 q^{51} - 24 q^{53} - 60 q^{58}+ \cdots - 12 q^{95}+O(q^{100}) $ 16 * q + 8 * q^4 - 12 * q^11 + 12 * q^15 - 8 * q^16 - 4 * q^22 - 24 * q^23 + 48 * q^25 + 24 * q^29 - 8 * q^30 + 12 * q^37 + 12 * q^39 - 16 * q^43 - 12 * q^46 + 24 * q^50 - 48 * q^51 - 24 * q^53 - 60 * q^58 - 16 * q^64 - 12 * q^65 - 48 * q^67 + 60 * q^71 - 12 * q^72 + 16 * q^78 - 64 * q^79 + 20 * q^81 + 24 * q^85 + 4 * q^88 - 48 * q^92 + 24 * q^93 - 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.373339	+	0.646642i	0.215547	+	0.373339i	0.953442	−	0.301577i	$-0.0975131\pi$
$3$	0.373339	+	0.646642i	0.215547	+	0.373339i	−0.737894	+	0.674916i	$0.764180\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			1.93185i			0.863950i	0.901886	+	0.431975i	$0.142183\pi$
$5$			1.93185i			0.863950i	−0.901886	+	0.431975i	$0.857817\pi$
$6$	−0.646642	−	0.373339i	−0.263991	−	0.152415i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.22124	−	2.11524i	0.407079	−	0.705081i
$10$	−0.965926	−	1.67303i	−0.305453	−	0.529059i
$11$	3.31599	−	1.91449i	0.999810	−	0.577241i	0.0916179	−	0.995794i	$-0.470796\pi$
$11$	3.31599	−	1.91449i	0.999810	−	0.577241i	0.908192	+	0.418554i	$0.137463\pi$
$12$	0.746678			0.215547
$13$	−1.19966	+	3.40012i	−0.332725	+	0.943024i
$13$	−1.19966	+	3.40012i	−0.332725	+	0.943024i
$14$		0			0
$15$	−1.24922	+	0.721236i	−0.322546	+	0.186222i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.129815	−	0.224846i	0.0314847	−	0.0545331i	−0.849854	−	0.527019i	$-0.823310\pi$
$17$	0.129815	−	0.224846i	0.0314847	−	0.0545331i	0.881338	+	0.472486i	$0.156643\pi$
$18$			2.44247i			0.575696i
$19$	2.92286	+	1.68752i	0.670551	+	0.387143i	0.796285	−	0.604921i	$-0.206795\pi$
$19$	2.92286	+	1.68752i	0.670551	+	0.387143i	−0.125734	+	0.992064i	$0.540129\pi$
$20$	1.67303	+	0.965926i	0.374101	+	0.215988i
$21$		0			0
$22$	−1.91449	+	3.31599i	−0.408171	+	0.706972i
$23$	−2.72124	−	4.71332i	−0.567417	−	0.982795i	−0.996820	−	0.0796821i	$-0.974609\pi$
$23$	−2.72124	−	4.71332i	−0.567417	−	0.982795i	0.429403	−	0.903113i	$-0.358724\pi$
$24$	−0.646642	+	0.373339i	−0.131995	+	0.0762075i
$25$	1.26795			0.253590
$26$	−0.661126	−	3.54442i	−0.129658	−	0.695118i
$27$	4.06378			0.782074
$28$		0			0
$29$	5.31931	+	9.21332i	0.987771	+	1.71087i	0.628907	+	0.777481i	$0.283503\pi$
$29$	5.31931	+	9.21332i	0.987771	+	1.71087i	0.358865	+	0.933390i	$0.383164\pi$
$30$	0.721236	−	1.24922i	0.131679	−	0.228075i
$31$		−	6.85042i		−	1.23037i	−0.788382	−	0.615186i	$-0.789081\pi$
$31$		−	6.85042i		−	1.23037i	0.788382	−	0.615186i	$-0.210919\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	2.47598	+	1.42951i	0.431013	+	0.248845i
$34$			0.259630i			0.0445261i
$35$		0			0
$36$	−1.22124	−	2.11524i	−0.203539	−	0.352540i
$37$	6.27477	−	3.62274i	1.03157	−	0.595575i	0.114133	−	0.993465i	$-0.463591\pi$
$37$	6.27477	−	3.62274i	1.03157	−	0.595575i	0.917433	+	0.397891i	$0.130258\pi$
$38$	−3.37503			−0.547503
$39$	−2.64654	+	0.493649i	−0.423786	+	0.0790471i
$40$	−1.93185			−0.305453
$41$	0.957850	−	0.553015i	0.149591	−	0.0863665i	−0.423336	−	0.905973i	$-0.639141\pi$
$41$	0.957850	−	0.553015i	0.149591	−	0.0863665i	0.572927	+	0.819606i	$0.305808\pi$
$42$		0			0
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	−0.932145	−	0.362084i	$-0.882065\pi$
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	0.779647	+	0.626219i	$0.215399\pi$
$44$		−	3.82898i		−	0.577241i
$45$	4.08633	+	2.35925i	0.609155	+	0.351696i
$46$	4.71332	+	2.72124i	0.694941	+	0.401224i
$47$			6.36175i			0.927956i	0.885847	+	0.463978i	$0.153578\pi$
$47$			6.36175i			0.927956i	−0.885847	+	0.463978i	$0.846422\pi$
$48$	0.373339	−	0.646642i	0.0538869	−	0.0933348i
$49$		0			0
$50$	−1.09808	+	0.633975i	−0.155291	+	0.0896575i
$51$	0.193860			0.0271458
$52$	2.34476	+	2.73899i	0.325160	+	0.379830i
$53$	−9.04447			−1.24235			−0.621177	−	0.783670i	$-0.713345\pi$
$53$	−9.04447			−1.24235			−0.621177	+	0.783670i	$0.713345\pi$
$54$	−3.51933	+	2.03189i	−0.478920	+	0.276505i
$55$	3.69851	+	6.40601i	0.498707	+	0.863786i
$56$		0			0
$57$			2.52006i			0.333791i
$58$	−9.21332	−	5.31931i	−1.20977	−	0.698460i
$59$	3.12262	+	1.80285i	0.406531	+	0.234711i	0.689298	−	0.724478i	$-0.257919\pi$
$59$	3.12262	+	1.80285i	0.406531	+	0.234711i	−0.282767	+	0.959189i	$0.591252\pi$
$60$			1.44247i			0.186222i
$61$	−2.21495	+	3.83640i	−0.283595	+	0.491201i	−0.972267	−	0.233872i	$-0.924860\pi$
$61$	−2.21495	+	3.83640i	−0.283595	+	0.491201i	0.688673	+	0.725073i	$0.258194\pi$
$62$	3.42521	+	5.93263i	0.435002	+	0.753445i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−6.56853	−	2.31756i	−0.814726	−	0.287458i
$66$	−2.85902			−0.351921
$67$	1.13356	−	0.654458i	0.138486	−	0.0799548i	−0.429156	−	0.903230i	$-0.641189\pi$
$67$	1.13356	−	0.654458i	0.138486	−	0.0799548i	0.567642	+	0.823275i	$0.307856\pi$
$68$	−0.129815	−	0.224846i	−0.0157424	−	0.0272666i
$69$	2.03189	−	3.51933i	0.244611	−	0.423678i
$70$		0			0
$71$	5.88434	+	3.39732i	0.698342	+	0.403188i	0.806730	−	0.590921i	$-0.201235\pi$
$71$	5.88434	+	3.39732i	0.698342	+	0.403188i	−0.108387	+	0.994109i	$0.534569\pi$
$72$	2.11524	+	1.22124i	0.249284	+	0.143924i
$73$			2.97832i			0.348586i	0.984694	+	0.174293i	$0.0557641\pi$
$73$			2.97832i			0.348586i	−0.984694	+	0.174293i	$0.944236\pi$
$74$	−3.62274	+	6.27477i	−0.421135	+	0.729427i
$75$	0.473375	+	0.819910i	0.0546606	+	0.0946750i
$76$	2.92286	−	1.68752i	0.335276	−	0.193571i
$77$		0			0
$78$	2.04515	−	1.75078i	0.231567	−	0.198237i
$79$	−8.80301			−0.990416			−0.495208	−	0.868774i	$-0.664908\pi$
$79$	−8.80301			−0.990416			−0.495208	+	0.868774i	$0.664908\pi$
$80$	1.67303	−	0.965926i	0.187051	−	0.107994i
$81$	−2.14654	−	3.71792i	−0.238505	−	0.413102i
$82$	−0.553015	+	0.957850i	−0.0610703	+	0.105777i
$83$			14.8826i			1.63357i	0.576939	+	0.816787i	$0.304247\pi$
$83$			14.8826i			1.63357i	−0.576939	+	0.816787i	$0.695753\pi$
$84$		0			0
$85$	0.434369	+	0.250783i	0.0471139	+	0.0272012i
$86$		−	2.00000i		−	0.215666i
$87$	−3.97181	+	6.87938i	−0.425823	+	0.737547i
$88$	1.91449	+	3.31599i	0.204085	+	0.353486i
$89$	13.4263	−	7.75168i	1.42319	−	0.821677i	0.426616	−	0.904433i	$-0.359706\pi$
$89$	13.4263	−	7.75168i	1.42319	−	0.821677i	0.996570	+	0.0827560i	$0.0263722\pi$
$90$	−4.71849			−0.497373
$91$		0			0
$92$	−5.44247			−0.567417
$93$	4.42977	−	2.55753i	0.459346	−	0.265203i
$94$	−3.18087	−	5.50943i	−0.328082	−	0.568255i
$95$	−3.26003	+	5.64654i	−0.334472	+	0.579323i
$96$			0.746678i			0.0762075i
$97$	−9.65704	−	5.57550i	−0.980524	−	0.566106i	−0.0780959	−	0.996946i	$-0.524884\pi$
$97$	−9.65704	−	5.57550i	−0.980524	−	0.566106i	−0.902428	+	0.430840i	$0.858217\pi$
$98$		0			0
$99$		−	9.35218i		−	0.939929i
$100$	0.633975	−	1.09808i	0.0633975	−	0.109808i
$101$	5.53114	+	9.58021i	0.550369	+	0.953267i	0.998248	+	0.0591725i	$0.0188462\pi$
$101$	5.53114	+	9.58021i	0.550369	+	0.953267i	−0.447879	+	0.894094i	$0.647820\pi$
$102$	−0.167887	+	0.0969299i	−0.0166233	+	0.00959749i
$103$	−0.946750			−0.0932861			−0.0466430	−	0.998912i	$-0.514852\pi$
$103$	−0.946750			−0.0932861			−0.0466430	+	0.998912i	$0.514852\pi$
$104$	−3.40012	−	1.19966i	−0.333409	−	0.117636i
$105$		0			0
$106$	7.83274	−	4.52224i	0.760783	−	0.439238i
$107$	0.245037	+	0.424416i	0.0236886	+	0.0410299i	0.877627	−	0.479345i	$-0.159126\pi$
$107$	0.245037	+	0.424416i	0.0236886	+	0.0410299i	−0.853938	+	0.520375i	$0.825792\pi$
$108$	2.03189	−	3.51933i	0.195518	−	0.338648i
$109$			7.97090i			0.763473i	0.924271	+	0.381737i	$0.124674\pi$
$109$			7.97090i			0.763473i	−0.924271	+	0.381737i	$0.875326\pi$
$110$	−6.40601	−	3.69851i	−0.610789	−	0.352639i
$111$	4.68523	+	2.70502i	0.444703	+	0.256749i
$112$		0			0
$113$	−1.53723	+	2.66256i	−0.144610	+	0.250473i	−0.929228	−	0.369508i	$-0.879526\pi$
$113$	−1.53723	+	2.66256i	−0.144610	+	0.250473i	0.784617	+	0.619981i	$0.212860\pi$
$114$	−1.26003	−	2.18244i	−0.118013	−	0.204404i
$115$	9.10543	−	5.25702i	0.849086	−	0.490220i
$116$	10.6386			0.987771
$117$	5.72702	+	6.68992i	0.529463	+	0.618483i
$118$	−3.60569			−0.331931
$119$		0			0
$120$	−0.721236	−	1.24922i	−0.0658395	−	0.114037i
$121$	1.83055	−	3.17060i	0.166413	−	0.288236i
$122$		−	4.42989i		−	0.401064i
$123$	0.715206	+	0.412924i	0.0644880	+	0.0372321i
$124$	−5.93263	−	3.42521i	−0.532766	−	0.307593i
$125$			12.1087i			1.08304i
$126$		0			0
$127$	−1.99582	−	3.45686i	−0.177100	−	0.306747i	0.763786	−	0.645470i	$-0.223338\pi$
$127$	−1.99582	−	3.45686i	−0.177100	−	0.306747i	−0.940886	+	0.338723i	$0.890005\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−1.49336			−0.131483
$130$	6.84729	−	1.27720i	0.600547	−	0.112018i
$131$	19.5815			1.71084			0.855421	−	0.517933i	$-0.173299\pi$
$131$	19.5815			1.71084			0.855421	+	0.517933i	$0.173299\pi$
$132$	2.47598	−	1.42951i	0.215506	−	0.124423i
$133$		0			0
$134$	−0.654458	+	1.13356i	−0.0565366	+	0.0979242i
$135$			7.85061i			0.675673i
$136$	0.224846	+	0.129815i	0.0192804	+	0.0111315i
$137$	−2.61786	−	1.51142i	−0.223659	−	0.129129i	0.383985	−	0.923340i	$-0.374552\pi$
$137$	−2.61786	−	1.51142i	−0.223659	−	0.129129i	−0.607643	+	0.794210i	$0.707885\pi$
$138$			4.06378i			0.345932i
$139$	1.83741	−	3.18249i	0.155847	−	0.269936i	−0.777520	−	0.628858i	$-0.783523\pi$
$139$	1.83741	−	3.18249i	0.155847	−	0.269936i	0.933367	+	0.358923i	$0.116856\pi$
$140$		0			0
$141$	−4.11377	+	2.37509i	−0.346442	+	0.200019i
$142$	−6.79465			−0.570194
$143$	2.53144	+	13.5715i	0.211690	+	1.13491i
$144$	−2.44247			−0.203539
$145$	−17.7988	+	10.2761i	−1.47811	+	0.853385i
$146$	−1.48916	−	2.57930i	−0.123244	−	0.213465i
$147$		0			0
$148$		−	7.24548i		−	0.595575i
$149$	6.77213	+	3.90989i	0.554794	+	0.320311i	0.751053	−	0.660241i	$-0.229546\pi$
$149$	6.77213	+	3.90989i	0.554794	+	0.320311i	−0.196259	+	0.980552i	$0.562879\pi$
$150$	−0.819910	−	0.473375i	−0.0669453	−	0.0386509i
$151$		−	21.2398i		−	1.72847i	−0.503089	−	0.864235i	$-0.667803\pi$
$151$		−	21.2398i		−	1.72847i	0.503089	−	0.864235i	$-0.332197\pi$
$152$	−1.68752	+	2.92286i	−0.136876	+	0.237076i
$153$	−0.317069	−	0.549180i	−0.0256335	−	0.0443985i
$154$		0			0
$155$	13.2340			1.06298
$156$	−0.895758	+	2.53880i	−0.0717181	+	0.203266i
$157$	−19.7800			−1.57862			−0.789309	−	0.613996i	$-0.789561\pi$
$157$	−19.7800			−1.57862			−0.789309	+	0.613996i	$0.789561\pi$
$158$	7.62363	−	4.40150i	0.606503	−	0.350165i
$159$	−3.37665	−	5.84854i	−0.267786	−	0.463819i
$160$	−0.965926	+	1.67303i	−0.0763631	+	0.132265i
$161$		0			0
$162$	3.71792	+	2.14654i	0.292107	+	0.168648i
$163$	11.8793	+	6.85853i	0.930460	+	0.537201i	0.886957	−	0.461852i	$-0.152815\pi$
$163$	11.8793	+	6.85853i	0.930460	+	0.537201i	0.0435030	+	0.999053i	$0.486148\pi$
$164$		−	1.10603i		−	0.0863665i
$165$	−2.76160	+	4.78323i	−0.214990	+	0.372374i
$166$	−7.44129	−	12.8887i	−0.577556	−	1.00036i
$167$	−2.52616	+	1.45848i	−0.195480	+	0.112860i	−0.594545	−	0.804062i	$-0.702668\pi$
$167$	−2.52616	+	1.45848i	−0.195480	+	0.112860i	0.399066	+	0.916922i	$0.369335\pi$
$168$		0			0
$169$	−10.1216	−	8.15796i	−0.778588	−	0.627535i
$170$	−0.501566			−0.0384683
$171$	7.13901	−	4.12171i	0.545934	−	0.315195i
$172$	1.00000	+	1.73205i	0.0762493	+	0.132068i
$173$	−8.90477	+	15.4235i	−0.677017	+	1.17263i	0.298858	+	0.954298i	$0.403394\pi$
$173$	−8.90477	+	15.4235i	−0.677017	+	1.17263i	−0.975875	+	0.218330i	$0.929939\pi$
$174$		−	7.94363i		−	0.602205i
$175$		0			0
$176$	−3.31599	−	1.91449i	−0.249952	−	0.144310i
$177$			2.69229i			0.202365i
$178$	−7.75168	+	13.4263i	−0.581013	+	1.00634i
$179$	−0.910987	−	1.57788i	−0.0680904	−	0.117936i	0.829970	−	0.557808i	$-0.188357\pi$
$179$	−0.910987	−	1.57788i	−0.0680904	−	0.117936i	−0.898061	+	0.439872i	$0.855024\pi$
$180$	4.08633	−	2.35925i	0.304577	−	0.175848i
$181$	−18.7124			−1.39088			−0.695439	−	0.718585i	$-0.744790\pi$
$181$	−18.7124			−1.39088			−0.695439	+	0.718585i	$0.744790\pi$
$182$		0			0
$183$	−3.30771			−0.244513
$184$	4.71332	−	2.72124i	0.347470	−	0.200612i
$185$	6.99860	+	12.1219i	0.514547	+	0.891222i
$186$	−2.55753	+	4.42977i	−0.187527	+	0.324806i
$187$		−	0.994117i		−	0.0726970i
$188$	5.50943	+	3.18087i	0.401817	+	0.231989i
$189$		0			0
$190$		−	6.52006i		−	0.473015i
$191$	−11.6453	+	20.1702i	−0.842621	+	1.45946i	0.0450496	+	0.998985i	$0.485655\pi$
$191$	−11.6453	+	20.1702i	−0.842621	+	1.45946i	−0.887671	+	0.460478i	$0.847678\pi$
$192$	−0.373339	−	0.646642i	−0.0269434	−	0.0466674i
$193$	7.82749	−	4.51920i	0.563435	−	0.325299i	−0.191088	−	0.981573i	$-0.561202\pi$
$193$	7.82749	−	4.51920i	0.563435	−	0.325299i	0.754523	+	0.656274i	$0.227868\pi$
$194$	11.1510			0.800595
$195$	−0.953656	−	5.11272i	−0.0682927	−	0.366130i
$196$		0			0
$197$	1.22442	−	0.706918i	0.0872361	−	0.0503658i	−0.455747	−	0.890109i	$-0.650628\pi$
$197$	1.22442	−	0.706918i	0.0872361	−	0.0503658i	0.542983	+	0.839743i	$0.317295\pi$
$198$	4.67609	+	8.09922i	0.332315	+	0.575587i
$199$	3.95223	−	6.84546i	0.280166	−	0.485262i	−0.691259	−	0.722607i	$-0.742944\pi$
$199$	3.95223	−	6.84546i	0.280166	−	0.485262i	0.971425	+	0.237345i	$0.0762771\pi$
$200$			1.26795i			0.0896575i
$201$	0.846401	+	0.488670i	0.0597005	+	0.0344681i
$202$	−9.58021	−	5.53114i	−0.674061	−	0.389169i
$203$		0			0
$204$	0.0969299	−	0.167887i	0.00678645	−	0.0117545i
$205$	1.06834	+	1.85043i	0.0746163	+	0.129239i
$206$	0.819910	−	0.473375i	0.0571258	−	0.0329816i
$207$	−13.2931			−0.923933
$208$	3.54442	−	0.661126i	0.245761	−	0.0458409i
$209$	12.9229			0.893898
$210$		0			0
$211$	11.3923	+	19.7321i	0.784279	+	1.35841i	0.929429	+	0.369001i	$0.120300\pi$
$211$	11.3923	+	19.7321i	0.784279	+	1.35841i	−0.145150	+	0.989410i	$0.546367\pi$
$212$	−4.52224	+	7.83274i	−0.310588	+	0.537955i
$213$			5.07342i			0.347625i
$214$	−0.424416	−	0.245037i	−0.0290125	−	0.0167504i
$215$	−3.34607	−	1.93185i	−0.228200	−	0.131751i
$216$			4.06378i			0.276505i
$217$		0			0
$218$	−3.98545	−	6.90300i	−0.269929	−	0.467530i
$219$	−1.92591	+	1.11192i	−0.130141	+	0.0751369i
$220$	7.39702			0.498707
$221$	0.608770	+	0.711124i	0.0409503	+	0.0478354i
$222$	−5.41004			−0.363098
$223$	20.6339	−	11.9130i	1.38175	−	0.797751i	0.389380	−	0.921077i	$-0.372689\pi$
$223$	20.6339	−	11.9130i	1.38175	−	0.797751i	0.992366	+	0.123326i	$0.0393561\pi$
$224$		0			0
$225$	1.54846	−	2.68202i	0.103231	−	0.178801i
$226$		−	3.07446i		−	0.204510i
$227$	−20.9972	−	12.1227i	−1.39363	−	0.804614i	−0.399917	−	0.916551i	$-0.630961\pi$
$227$	−20.9972	−	12.1227i	−1.39363	−	0.804614i	−0.993715	+	0.111937i	$0.964295\pi$
$228$	2.18244	+	1.26003i	0.144536	+	0.0834477i
$229$		−	20.1075i		−	1.32874i	−0.747403	−	0.664371i	$-0.768700\pi$
$229$		−	20.1075i		−	1.32874i	0.747403	−	0.664371i	$-0.231300\pi$
$230$	−5.25702	+	9.10543i	−0.346638	+	0.600394i
$231$		0			0
$232$	−9.21332	+	5.31931i	−0.604884	+	0.349230i
$233$	9.53156			0.624433			0.312217	−	0.950011i	$-0.398929\pi$
$233$	9.53156			0.624433			0.312217	+	0.950011i	$0.398929\pi$
$234$	−8.30470	−	2.93013i	−0.542895	−	0.191549i
$235$	−12.2900			−0.801708
$236$	3.12262	−	1.80285i	0.203265	−	0.117355i
$237$	−3.28651	−	5.69240i	−0.213482	−	0.369761i
$238$		0			0
$239$		−	24.2296i		−	1.56729i	−0.621212	−	0.783643i	$-0.713359\pi$
$239$		−	24.2296i		−	1.56729i	0.621212	−	0.783643i	$-0.286641\pi$
$240$	1.24922	+	0.721236i	0.0806366	+	0.0465556i
$241$	−10.4503	−	6.03348i	−0.673163	−	0.388651i	0.124111	−	0.992268i	$-0.460392\pi$
$241$	−10.4503	−	6.03348i	−0.673163	−	0.388651i	−0.797274	+	0.603618i	$0.793725\pi$
$242$			3.66109i			0.235344i
$243$	7.69844	−	13.3341i	0.493855	−	0.855382i
$244$	2.21495	+	3.83640i	0.141797	+	0.245600i
$245$		0			0
$246$	−0.825849			−0.0526542
$247$	−9.24420	+	7.91365i	−0.588194	+	0.503534i
$248$	6.85042			0.435002
$249$	−9.62370	+	5.55625i	−0.609877	+	0.352113i
$250$	−6.05437	−	10.4865i	−0.382912	−	0.663223i
$251$	15.3532	−	26.5924i	0.969083	−	1.67850i	0.270861	−	0.962618i	$-0.412692\pi$
$251$	15.3532	−	26.5924i	0.969083	−	1.67850i	0.698221	−	0.715882i	$-0.253975\pi$
$252$		0			0
$253$	−18.0472	−	10.4196i	−1.13462	−	0.655072i
$254$	3.45686	+	1.99582i	0.216903	+	0.125229i
$255$			0.374508i			0.0234526i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.62356	−	6.27619i	−0.226032	−	0.391498i	0.730597	−	0.682809i	$-0.239242\pi$
$257$	−3.62356	−	6.27619i	−0.226032	−	0.391498i	−0.956628	+	0.291311i	$0.905909\pi$
$258$	1.29328	−	0.746678i	0.0805164	−	0.0464862i
$259$		0			0
$260$	−5.29133	+	4.52973i	−0.328154	+	0.280922i
$261$	25.9845			1.60840
$262$	−16.9581	+	9.79074i	−1.04767	+	0.604874i
$263$	−1.29018	−	2.23467i	−0.0795562	−	0.137795i	0.823502	−	0.567313i	$-0.192017\pi$
$263$	−1.29018	−	2.23467i	−0.0795562	−	0.137795i	−0.903059	+	0.429518i	$0.858684\pi$
$264$	−1.42951	+	2.47598i	−0.0879802	+	0.152386i
$265$		−	17.4726i		−	1.07333i
$266$		0			0
$267$	10.0251	+	5.78801i	0.613528	+	0.354221i
$268$		−	1.30892i		−	0.0799548i
$269$	6.27231	−	10.8640i	0.382430	−	0.662388i	−0.608979	−	0.793186i	$-0.708421\pi$
$269$	6.27231	−	10.8640i	0.382430	−	0.662388i	0.991409	+	0.130798i	$0.0417541\pi$
$270$	−3.92531	−	6.79883i	−0.238886	−	0.413764i
$271$	−8.35249	+	4.82231i	−0.507378	+	0.292935i	−0.731755	−	0.681568i	$-0.761299\pi$
$271$	−8.35249	+	4.82231i	−0.507378	+	0.292935i	0.224377	+	0.974502i	$0.427965\pi$
$272$	−0.259630			−0.0157424
$273$		0			0
$274$	3.02284			0.182616
$275$	4.20451	−	2.42748i	0.253542	−	0.146382i
$276$	−2.03189	−	3.51933i	−0.122305	−	0.211839i
$277$	8.52931	−	14.7732i	0.512477	−	0.887636i	−0.487419	−	0.873168i	$-0.662061\pi$
$277$	8.52931	−	14.7732i	0.512477	−	0.887636i	0.999895	−	0.0144673i	$-0.00460526\pi$
$278$			3.67483i			0.220402i
$279$	−14.4903	−	8.36597i	−0.867511	−	0.500858i
$280$		0			0
$281$		−	14.5518i		−	0.868090i	−0.900891	−	0.434045i	$-0.857086\pi$
$281$		−	14.5518i		−	0.868090i	0.900891	−	0.434045i	$-0.142914\pi$
$282$	2.37509	−	4.11377i	0.141434	−	0.244972i
$283$	−10.3722	−	17.9652i	−0.616565	−	1.06792i	−0.990108	−	0.140309i	$-0.955190\pi$
$283$	−10.3722	−	17.9652i	−0.616565	−	1.06792i	0.373543	−	0.927613i	$-0.378143\pi$
$284$	5.88434	−	3.39732i	0.349171	−	0.201594i
$285$	−4.86839			−0.288379
$286$	−8.97805	−	10.4876i	−0.530883	−	0.620142i
$287$		0			0
$288$	2.11524	−	1.22124i	0.124642	−	0.0719620i
$289$	8.46630	+	14.6641i	0.498017	+	0.862591i
$290$	10.2761	−	17.7988i	0.603435	−	1.04518i
$291$		−	8.32620i		−	0.488091i
$292$	2.57930	+	1.48916i	0.150942	+	0.0871466i
$293$	−2.98843	−	1.72537i	−0.174586	−	0.100797i	0.410161	−	0.912013i	$-0.365473\pi$
$293$	−2.98843	−	1.72537i	−0.174586	−	0.100797i	−0.584746	+	0.811216i	$0.698806\pi$
$294$		0			0
$295$	−3.48283	+	6.03245i	−0.202778	+	0.351223i
$296$	3.62274	+	6.27477i	0.210567	+	0.364714i
$297$	13.4755	−	7.78006i	0.781925	−	0.451445i
$298$	−7.81978			−0.452988
$299$	19.2904	−	3.59816i	1.11559	−	0.208087i
$300$	0.946750			0.0546606
$301$		0			0
$302$	10.6199	+	18.3942i	0.611106	+	1.05847i
$303$	−4.12998	+	7.15334i	−0.237261	+	0.410948i
$304$		−	3.37503i		−	0.193571i
$305$	−7.41136	−	4.27895i	−0.424373	−	0.245012i
$306$	0.549180	+	0.317069i	0.0313945	+	0.0181256i
$307$		−	15.1001i		−	0.861807i	−0.902398	−	0.430904i	$-0.858195\pi$
$307$		−	15.1001i		−	0.861807i	0.902398	−	0.430904i	$-0.141805\pi$
$308$		0			0
$309$	−0.353459	−	0.612209i	−0.0201076	−	0.0348273i
$310$	−11.4610	+	6.61699i	−0.650939	+	0.375820i
$311$	14.5048			0.822493			0.411246	−	0.911524i	$-0.365094\pi$
$311$	14.5048			0.822493			0.411246	+	0.911524i	$0.365094\pi$
$312$	−0.493649	−	2.64654i	−0.0279474	−	0.149831i
$313$	−0.258110			−0.0145892			−0.00729462	−	0.999973i	$-0.502322\pi$
$313$	−0.258110			−0.0145892			−0.00729462	+	0.999973i	$0.502322\pi$
$314$	17.1300	−	9.89002i	0.966702	−	0.558126i
$315$		0			0
$316$	−4.40150	+	7.62363i	−0.247604	+	0.428863i
$317$		−	23.3984i		−	1.31418i	−0.753811	−	0.657092i	$-0.771786\pi$
$317$		−	23.3984i		−	1.31418i	0.753811	−	0.657092i	$-0.228214\pi$
$318$	5.84854	+	3.37665i	0.327970	+	0.189353i
$319$	35.2776	+	20.3675i	1.97517	+	1.14036i
$320$		−	1.93185i		−	0.107994i
$321$	−0.182964	+	0.316903i	−0.0102120	+	0.0176878i
$322$		0			0
$323$	0.758862	−	0.438129i	0.0422242	−	0.0243782i
$324$	−4.29308			−0.238505
$325$	−1.52110	+	4.31118i	−0.0843757	+	0.239141i
$326$	−13.7171			−0.759717
$327$	−5.15432	+	2.97585i	−0.285034	+	0.164565i
$328$	0.553015	+	0.957850i	0.0305352	+	0.0528884i
$329$		0			0
$330$		−	5.52320i		−	0.304042i
$331$	−3.52357	−	2.03433i	−0.193673	−	0.111817i	0.400028	−	0.916503i	$-0.369000\pi$
$331$	−3.52357	−	2.03433i	−0.193673	−	0.111817i	−0.593701	+	0.804686i	$0.702334\pi$
$332$	12.8887	+	7.44129i	0.707358	+	0.408394i
$333$		−	17.6969i		−	0.969783i
$334$	1.45848	−	2.52616i	0.0798043	−	0.138225i
$335$	1.26432	+	2.18986i	0.0690770	+	0.119645i
$336$		0			0
$337$	−19.2548			−1.04887			−0.524437	−	0.851449i	$-0.675724\pi$
$337$	−19.2548			−1.04887			−0.524437	+	0.851449i	$0.675724\pi$
$338$	12.8446	+	2.00418i	0.698653	+	0.109013i
$339$	−2.29563			−0.124682
$340$	0.434369	−	0.250783i	0.0235570	−	0.0136006i
$341$	−13.1151	−	22.7159i	−0.710220	−	1.23014i
$342$	−4.12171	+	7.13901i	−0.222877	+	0.386034i
$343$		0			0
$344$	−1.73205	−	1.00000i	−0.0933859	−	0.0539164i
$345$	6.79883	+	3.92531i	0.366037	+	0.211331i
$346$		−	17.8095i		−	0.957447i
$347$	5.70601	−	9.88309i	0.306314	−	0.530552i	−0.671239	−	0.741241i	$-0.734237\pi$
$347$	5.70601	−	9.88309i	0.306314	−	0.530552i	0.977553	+	0.210689i	$0.0675708\pi$
$348$	3.97181	+	6.87938i	0.212912	+	0.368774i
$349$	−21.2148	+	12.2484i	−1.13560	+	0.655639i	−0.945337	−	0.326094i	$-0.894268\pi$
$349$	−21.2148	+	12.2484i	−1.13560	+	0.655639i	−0.190263	+	0.981733i	$0.560934\pi$
$350$		0			0
$351$	−4.87514	+	13.8173i	−0.260216	+	0.737514i
$352$	3.82898			0.204085
$353$	3.93089	−	2.26950i	0.209220	−	0.120793i	−0.391729	−	0.920081i	$-0.628123\pi$
$353$	3.93089	−	2.26950i	0.209220	−	0.120793i	0.600949	+	0.799287i	$0.294790\pi$
$354$	−1.34615	−	2.33159i	−0.0715469	−	0.123923i
$355$	−6.56313	+	11.3677i	−0.348335	+	0.603333i
$356$		−	15.5034i		−	0.821677i
$357$		0			0
$358$	1.57788	+	0.910987i	0.0833933	+	0.0481472i
$359$		−	8.35652i		−	0.441040i	−0.975382	−	0.220520i	$-0.929225\pi$
$359$		−	8.35652i		−	0.441040i	0.975382	−	0.220520i	$-0.0707755\pi$
$360$	−2.35925	+	4.08633i	−0.124343	+	0.215369i
$361$	−3.80457	−	6.58972i	−0.200241	−	0.346827i
$362$	16.2054	−	9.35618i	0.851735	−	0.491750i
$363$	2.73366			0.143480
$364$		0			0
$365$	−5.75368			−0.301161
$366$	2.86456	−	1.65385i	0.149733	−	0.0864483i
$367$	12.4612	+	21.5834i	0.650469	+	1.12665i	0.983009	+	0.183556i	$0.0587610\pi$
$367$	12.4612	+	21.5834i	0.650469	+	1.12665i	−0.332540	+	0.943089i	$0.607906\pi$
$368$	−2.72124	+	4.71332i	−0.141854	+	0.245699i
$369$		−	2.70145i		−	0.140632i
$370$	−12.1219	−	6.99860i	−0.630189	−	0.363840i
$371$		0			0
$372$		−	5.11506i		−	0.265203i
$373$	−10.2477	+	17.7495i	−0.530603	+	0.919032i	0.468759	+	0.883326i	$0.344701\pi$
$373$	−10.2477	+	17.7495i	−0.530603	+	0.919032i	−0.999362	+	0.0357058i	$0.988632\pi$
$374$	0.497058	+	0.860930i	0.0257023	+	0.0445177i
$375$	−7.83003	+	4.52067i	−0.404341	+	0.233446i
$376$	−6.36175			−0.328082
$377$	−37.7077	+	7.03348i	−1.94205	+	0.362242i
$378$		0			0
$379$	2.28701	−	1.32041i	0.117476	−	0.0678248i	−0.440111	−	0.897944i	$-0.645061\pi$
$379$	2.28701	−	1.32041i	0.117476	−	0.0678248i	0.557587	+	0.830119i	$0.311727\pi$
$380$	3.26003	+	5.64654i	0.167236	+	0.289661i
$381$	1.49024	−	2.58116i	0.0763471	−	0.132237i
$382$		−	23.2905i		−	1.19165i
$383$	13.7442	+	7.93524i	0.702298	+	0.405472i	0.808203	−	0.588904i	$-0.200441\pi$
$383$	13.7442	+	7.93524i	0.702298	+	0.405472i	−0.105905	+	0.994376i	$0.533774\pi$
$384$	0.646642	+	0.373339i	0.0329988	+	0.0190519i
$385$		0			0
$386$	−4.51920	+	7.82749i	−0.230021	+	0.398409i
$387$	2.44247	+	4.23048i	0.124158	+	0.215048i
$388$	−9.65704	+	5.57550i	−0.490262	+	0.283053i
$389$	−22.7875			−1.15537			−0.577687	−	0.816258i	$-0.696045\pi$
$389$	−22.7875			−1.15537			−0.577687	+	0.816258i	$0.696045\pi$
$390$	3.38225	+	3.95092i	0.171267	+	0.200063i
$391$	−1.41303			−0.0714598
$392$		0			0
$393$	7.31053	+	12.6622i	0.368768	+	0.638724i
$394$	−0.706918	+	1.22442i	−0.0356140	+	0.0616853i
$395$		−	17.0061i		−	0.855670i
$396$	−8.09922	−	4.67609i	−0.407001	−	0.234982i
$397$	−20.4984	−	11.8347i	−1.02878	−	0.593968i	−0.112147	−	0.993692i	$-0.535773\pi$
$397$	−20.4984	−	11.8347i	−1.02878	−	0.593968i	−0.916636	+	0.399724i	$0.869106\pi$
$398$			7.90446i			0.396215i
$399$		0			0
$400$	−0.633975	−	1.09808i	−0.0316987	−	0.0549038i
$401$	7.23425	−	4.17669i	0.361261	−	0.208574i	−0.308373	−	0.951266i	$-0.599784\pi$
$401$	7.23425	−	4.17669i	0.361261	−	0.208574i	0.669634	+	0.742691i	$0.266451\pi$
$402$	−0.977340			−0.0487453
$403$	23.2922	+	8.21815i	1.16027	+	0.409375i
$404$	11.0623			0.550369
$405$	7.18247	−	4.14680i	0.356900	−	0.206056i
$406$		0			0
$407$	13.8714	−	24.0260i	0.687580	−	1.19092i
$408$			0.193860i			0.00959749i
$409$	−16.3786	−	9.45621i	−0.809872	−	0.467580i	0.0370397	−	0.999314i	$-0.488207\pi$
$409$	−16.3786	−	9.45621i	−0.809872	−	0.467580i	−0.846911	+	0.531734i	$0.821541\pi$
$410$	−1.85043	−	1.06834i	−0.0913860	−	0.0527617i
$411$		−	2.25709i		−	0.111334i
$412$	−0.473375	+	0.819910i	−0.0233215	+	0.0403940i
$413$		0			0
$414$	11.5121	−	6.64654i	0.565791	−	0.326660i
$415$	−28.7509			−1.41133
$416$	−2.73899	+	2.34476i	−0.134290	+	0.114961i
$417$	2.74391			0.134370
$418$	−11.1916	+	6.46147i	−0.547399	+	0.316041i
$419$	−3.22104	−	5.57900i	−0.157358	−	0.272552i	0.776557	−	0.630047i	$-0.216964\pi$
$419$	−3.22104	−	5.57900i	−0.157358	−	0.272552i	−0.933915	+	0.357495i	$0.883631\pi$
$420$		0			0
$421$			4.13898i			0.201722i	0.994901	+	0.100861i	$0.0321597\pi$
$421$			4.13898i			0.201722i	−0.994901	+	0.100861i	$0.967840\pi$
$422$	−19.7321	−	11.3923i	−0.960541	−	0.554569i
$423$	13.4566	+	7.76919i	0.654284	+	0.377751i
$424$		−	9.04447i		−	0.439238i
$425$	0.164599	−	0.285093i	0.00798420	−	0.0138290i
$426$	−2.53671	−	4.39371i	−0.122904	−	0.212876i
$427$		0			0
$428$	0.490074			0.0236886
$429$	−7.83083	+	6.70371i	−0.378076	+	0.323658i
$430$	3.86370			0.186324
$431$	2.51939	−	1.45457i	0.121355	−	0.0700641i	−0.438094	−	0.898929i	$-0.644346\pi$
$431$	2.51939	−	1.45457i	0.121355	−	0.0700641i	0.559449	+	0.828865i	$0.311013\pi$
$432$	−2.03189	−	3.51933i	−0.0977592	−	0.169324i
$433$	−2.97439	+	5.15180i	−0.142940	+	0.247580i	−0.928603	−	0.371076i	$-0.878989\pi$
$433$	−2.97439	+	5.15180i	−0.142940	+	0.247580i	0.785662	+	0.618655i	$0.212322\pi$
$434$		0			0
$435$	−13.2900	−	7.67296i	−0.637204	−	0.367890i
$436$	6.90300	+	3.98545i	0.330594	+	0.190868i
$437$		−	18.3685i		−	0.878686i
$438$	1.11192	−	1.92591i	0.0531298	−	0.0920236i
$439$	−16.3940	−	28.3953i	−0.782444	−	1.35523i	−0.930514	−	0.366256i	$-0.880639\pi$
$439$	−16.3940	−	28.3953i	−0.782444	−	1.35523i	0.148070	−	0.988977i	$-0.452694\pi$
$440$	−6.40601	+	3.69851i	−0.305395	+	0.176320i
$441$		0			0
$442$	−0.882772	−	0.311467i	−0.0419892	−	0.0148150i
$443$	−28.7255			−1.36479			−0.682395	−	0.730983i	$-0.739062\pi$
$443$	−28.7255			−1.36479			−0.682395	+	0.730983i	$0.739062\pi$
$444$	4.68523	−	2.70502i	0.222351	−	0.128375i
$445$	14.9751	+	25.9376i	0.709888	+	1.22956i
$446$	−11.9130	+	20.6339i	−0.564095	+	0.977042i
$447$			5.83886i			0.276169i
$448$		0			0
$449$	22.7208	+	13.1179i	1.07226	+	0.619071i	0.928799	−	0.370584i	$-0.120843\pi$
$449$	22.7208	+	13.1179i	1.07226	+	0.619071i	0.143464	+	0.989656i	$0.454176\pi$
$450$			3.09693i			0.145991i
$451$	2.11748	−	3.66759i	0.0997085	−	0.172700i
$452$	1.53723	+	2.66256i	0.0723052	+	0.125236i
$453$	13.7345	−	7.92964i	0.645305	−	0.372567i
$454$	24.2455			1.13790
$455$		0			0
$456$	−2.52006			−0.118013
$457$	13.8319	−	7.98587i	0.647030	−	0.373563i	−0.140287	−	0.990111i	$-0.544803\pi$
$457$	13.8319	−	7.98587i	0.647030	−	0.373563i	0.787318	+	0.616548i	$0.211469\pi$
$458$	10.0538	+	17.4136i	0.469781	+	0.813685i
$459$	0.527538	−	0.913723i	0.0246234	−	0.0426489i
$460$		−	10.5140i		−	0.490220i
$461$	16.8887	+	9.75067i	0.786583	+	0.454134i	0.838758	−	0.544504i	$-0.183282\pi$
$461$	16.8887	+	9.75067i	0.786583	+	0.454134i	−0.0521751	+	0.998638i	$0.516615\pi$
$462$		0			0
$463$		−	39.7898i		−	1.84919i	−0.380951	−	0.924595i	$-0.624403\pi$
$463$		−	39.7898i		−	1.84919i	0.380951	−	0.924595i	$-0.375597\pi$
$464$	5.31931	−	9.21332i	0.246943	−	0.427718i
$465$	4.94077	+	8.55766i	0.229123	+	0.396852i
$466$	−8.25457	+	4.76578i	−0.382386	+	0.220770i
$467$	3.60569			0.166852			0.0834258	−	0.996514i	$-0.473414\pi$
$467$	3.60569			0.166852			0.0834258	+	0.996514i	$0.473414\pi$
$468$	8.65714	−	1.61478i	0.400177	−	0.0746434i
$469$		0			0
$470$	10.6434	−	6.14498i	0.490944	−	0.283447i
$471$	−7.38466	−	12.7906i	−0.340267	−	0.589360i
$472$	−1.80285	+	3.12262i	−0.0829828	+	0.143730i
$473$			7.65796i			0.352113i
$474$	5.69240	+	3.28651i	0.261460	+	0.150954i
$475$	3.70604	+	2.13969i	0.170045	+	0.0981755i
$476$		0			0
$477$	−11.0454	+	19.1312i	−0.505736	+	0.875960i
$478$	12.1148	+	20.9835i	0.554119	+	0.959762i
$479$	−23.0597	+	13.3135i	−1.05362	+	0.608310i	−0.923662	−	0.383209i	$-0.874819\pi$
$479$	−23.0597	+	13.3135i	−1.05362	+	0.608310i	−0.129962	+	0.991519i	$0.541485\pi$
$480$	−1.44247			−0.0658395
$481$	4.79018	+	25.6810i	0.218413	+	1.17095i
$482$	12.0670			0.549635
$483$		0			0
$484$	−1.83055	−	3.17060i	−0.0832067	−	0.144118i
$485$	10.7710	−	18.6560i	0.489087	−	0.847124i
$486$			15.3969i			0.698417i
$487$	34.6506	+	20.0056i	1.57017	+	0.906539i	0.996147	+	0.0877000i	$0.0279517\pi$
$487$	34.6506	+	20.0056i	1.57017	+	0.906539i	0.574024	+	0.818839i	$0.305382\pi$
$488$	−3.83640	−	2.21495i	−0.173666	−	0.100266i
$489$			10.2422i			0.463170i
$490$		0			0
$491$	20.8281	+	36.0754i	0.939961	+	1.62806i	0.765540	+	0.643389i	$0.222472\pi$
$491$	20.8281	+	36.0754i	0.939961	+	1.62806i	0.174421	+	0.984671i	$0.444195\pi$
$492$	0.715206	−	0.412924i	0.0322440	−	0.0186161i
$493$	2.76210			0.124399
$494$	4.04888	−	11.4755i	0.182168	−	0.516308i
$495$	18.0670			0.812052
$496$	−5.93263	+	3.42521i	−0.266383	+	0.153796i
$497$		0			0
$498$	5.55625	−	9.62370i	0.248981	−	0.431248i
$499$			3.95418i			0.177013i	0.996076	+	0.0885066i	$0.0282094\pi$
$499$			3.95418i			0.177013i	−0.996076	+	0.0885066i	$0.971791\pi$
$500$	10.4865	+	6.05437i	0.468970	+	0.270760i
$501$	−1.88623	−	1.08901i	−0.0842703	−	0.0486535i
$502$			30.7063i			1.37049i
$503$	−1.21662	+	2.10725i	−0.0542464	+	0.0939574i	−0.891873	−	0.452285i	$-0.850609\pi$
$503$	−1.21662	+	2.10725i	−0.0542464	+	0.0939574i	0.837627	+	0.546243i	$0.183942\pi$
$504$		0			0
$505$	−18.5075	+	10.6853i	−0.823575	+	0.475491i
$506$	20.8391			0.926412
$507$	1.49648	−	9.59077i	0.0664609	−	0.425941i
$508$	−3.99164			−0.177100
$509$	−29.7196	+	17.1586i	−1.31730	+	0.760543i	−0.983293	−	0.182028i	$-0.941734\pi$
$509$	−29.7196	+	17.1586i	−1.31730	+	0.760543i	−0.334005	+	0.942571i	$0.608400\pi$
$510$	−0.187254	−	0.324334i	−0.00829175	−	0.0143617i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	11.8779	+	6.85769i	0.524421	+	0.302774i
$514$	6.27619	+	3.62356i	0.276831	+	0.159829i
$515$		−	1.82898i		−	0.0805945i
$516$	−0.746678	+	1.29328i	−0.0328707	+	0.0569337i
$517$	12.1795	+	21.0955i	0.535654	+	0.927780i
$518$		0			0
$519$	−13.2980			−0.583717
$520$	2.31756	−	6.56853i	0.101632	−	0.288049i
$521$	−34.1422			−1.49580			−0.747898	−	0.663814i	$-0.768937\pi$
$521$	−34.1422			−1.49580			−0.747898	+	0.663814i	$0.768937\pi$
$522$	−22.5033	+	12.9923i	−0.984941	+	0.568656i
$523$	−17.5069	−	30.3229i	−0.765525	−	1.32593i	−0.939968	−	0.341262i	$-0.889146\pi$
$523$	−17.5069	−	30.3229i	−0.765525	−	1.32593i	0.174443	−	0.984667i	$-0.444188\pi$
$524$	9.79074	−	16.9581i	0.427710	−	0.740816i
$525$		0			0
$526$	2.23467	+	1.29018i	0.0974360	+	0.0562547i
$527$	−1.54029	−	0.889285i	−0.0670960	−	0.0387379i
$528$		−	2.85902i		−	0.124423i
$529$	−3.31025	+	5.73352i	−0.143924	+	0.249283i
$530$	8.73629	+	15.1317i	0.379480	+	0.657279i
$531$	7.62692	−	4.40340i	0.330980	−	0.191091i
$532$		0			0
$533$	0.731226	+	3.92024i	0.0316729	+	0.169804i
$534$	−11.5760			−0.500944
$535$	−0.819910	+	0.473375i	−0.0354478	+	0.0204658i
$536$	0.654458	+	1.13356i	0.0282683	+	0.0489621i
$537$	0.680214	−	1.17817i	0.0293534	−	0.0508416i
$538$			12.5446i			0.540837i
$539$		0			0
$540$	6.79883	+	3.92531i	0.292575	+	0.168918i
$541$		−	36.2358i		−	1.55790i	−0.627086	−	0.778950i	$-0.715753\pi$
$541$		−	36.2358i		−	1.55790i	0.627086	−	0.778950i	$-0.284247\pi$
$542$	4.82231	−	8.35249i	0.207136	−	0.358770i
$543$	−6.98605	−	12.1002i	−0.299800	−	0.519269i
$544$	0.224846	−	0.129815i	0.00964019	−	0.00556576i
$545$	−15.3986			−0.659603
$546$		0			0
$547$	−30.8075			−1.31723			−0.658616	−	0.752479i	$-0.728858\pi$
$547$	−30.8075			−1.31723			−0.658616	+	0.752479i	$0.728858\pi$
$548$	−2.61786	+	1.51142i	−0.111829	+	0.0645647i
$549$	5.40995	+	9.37030i	0.230891	+	0.399915i
$550$	−2.42748	+	4.20451i	−0.103508	+	0.179281i
$551$			35.9057i			1.52963i
$552$	3.51933	+	2.03189i	0.149793	+	0.0864829i
$553$		0			0
$554$			17.0586i			0.724752i
$555$	−5.22570	+	9.05118i	−0.221819	+	0.384201i
$556$	−1.83741	−	3.18249i	−0.0779237	−	0.134968i
$557$	−13.3209	+	7.69083i	−0.564425	+	0.325871i	−0.754920	−	0.655817i	$-0.772324\pi$
$557$	−13.3209	+	7.69083i	−0.564425	+	0.325871i	0.190495	+	0.981688i	$0.438991\pi$
$558$	16.7319			0.708320
$559$	−4.68952	−	5.47799i	−0.198346	−	0.231694i
$560$		0			0
$561$	0.642838	−	0.371143i	0.0271406	−	0.0156697i
$562$	7.27592	+	12.6023i	0.306916	+	0.531594i
$563$	−20.8529	+	36.1183i	−0.878845	+	1.52220i	−0.0262347	+	0.999656i	$0.508352\pi$
$563$	−20.8529	+	36.1183i	−0.878845	+	1.52220i	−0.852610	+	0.522548i	$0.824982\pi$
$564$			4.75018i			0.200019i
$565$	−5.14367	−	2.96970i	−0.216396	−	0.124936i
$566$	17.9652	+	10.3722i	0.755135	+	0.435977i
$567$		0			0
$568$	−3.39732	+	5.88434i	−0.142549	+	0.246901i
$569$	−15.8548	−	27.4613i	−0.664667	−	1.15124i	−0.979375	−	0.202049i	$-0.935240\pi$
$569$	−15.8548	−	27.4613i	−0.664667	−	1.15124i	0.314708	−	0.949189i	$-0.398093\pi$
$570$	4.21615	−	2.43420i	0.176595	−	0.101957i
$571$	45.7815			1.91590			0.957948	−	0.286943i	$-0.0926391\pi$
$571$	45.7815			1.91590			0.957948	+	0.286943i	$0.0926391\pi$
$572$	13.0190	+	4.59347i	0.544352	+	0.192062i
$573$	−17.3905			−0.726500
$574$		0			0
$575$	−3.45039	−	5.97625i	−0.143891	−	0.249227i
$576$	−1.22124	+	2.11524i	−0.0508848	+	0.0881351i
$577$		−	12.9508i		−	0.539150i	−0.962979	−	0.269575i	$-0.913117\pi$
$577$		−	12.9508i		−	0.539150i	0.962979	−	0.269575i	$-0.0868832\pi$
$578$	−14.6641	−	8.46630i	−0.609944	−	0.352151i
$579$	5.84461	+	3.37439i	0.242894	+	0.140235i
$580$			20.5522i			0.853385i
$581$		0			0
$582$	4.16310	+	7.21070i	0.172566	+	0.298893i
$583$	−29.9914	+	17.3156i	−1.24212	+	0.717137i
$584$	−2.97832			−0.123244
$585$	−12.9239	+	11.0637i	−0.534339	+	0.457430i
$586$	3.45074			0.142549
$587$	18.4964	−	10.6789i	0.763430	−	0.440766i	−0.0670960	−	0.997747i	$-0.521373\pi$
$587$	18.4964	−	10.6789i	0.763430	−	0.440766i	0.830526	+	0.556980i	$0.188040\pi$
$588$		0			0
$589$	11.5602	−	20.0228i	0.476329	−	0.825027i
$590$		−	6.96567i		−	0.286772i
$591$	0.914246	+	0.527840i	0.0376070	+	0.0217124i
$592$	−6.27477	−	3.62274i	−0.257891	−	0.148894i
$593$			29.5910i			1.21516i	0.794260	+	0.607578i	$0.207859\pi$
$593$			29.5910i			1.21516i	−0.794260	+	0.607578i	$0.792141\pi$
$594$	−7.78006	+	13.4755i	−0.319220	+	0.552905i
$595$		0			0
$596$	6.77213	−	3.90989i	0.277397	−	0.160155i
$597$	5.90209			0.241556
$598$	−14.9069	+	12.7613i	−0.609588	+	0.521848i
$599$	−15.0581			−0.615256			−0.307628	−	0.951507i	$-0.599535\pi$
$599$	−15.0581			−0.615256			−0.307628	+	0.951507i	$0.599535\pi$
$600$	−0.819910	+	0.473375i	−0.0334727	+	0.0193255i
$601$	21.6117	+	37.4326i	0.881560	+	1.52691i	0.849607	+	0.527417i	$0.176839\pi$
$601$	21.6117	+	37.4326i	0.881560	+	1.52691i	0.0319529	+	0.999489i	$0.489827\pi$
$602$		0			0
$603$		−	3.19699i		−	0.130192i
$604$	−18.3942	−	10.6199i	−0.748449	−	0.432117i
$605$	6.12513	+	3.53634i	0.249022	+	0.143773i
$606$		−	8.25996i		−	0.335538i
$607$	14.6731	−	25.4146i	0.595563	−	1.03155i	−0.397904	−	0.917427i	$-0.630262\pi$
$607$	14.6731	−	25.4146i	0.595563	−	1.03155i	0.993467	−	0.114119i	$-0.0364045\pi$
$608$	1.68752	+	2.92286i	0.0684378	+	0.118538i
$609$		0			0
$610$	8.55790			0.346499
$611$	−21.6307	−	7.63192i	−0.875085	−	0.308754i
$612$	−0.634138			−0.0256335
$613$	3.29378	−	1.90167i	0.133035	−	0.0768076i	−0.432006	−	0.901871i	$-0.642194\pi$
$613$	3.29378	−	1.90167i	0.133035	−	0.0768076i	0.565040	+	0.825063i	$0.308861\pi$
$614$	7.55004	+	13.0771i	0.304695	+	0.527747i
$615$	−0.797709	+	1.38167i	−0.0321667	+	0.0557144i
$616$		0			0
$617$	−13.3461	−	7.70535i	−0.537292	−	0.310206i	0.206689	−	0.978407i	$-0.433731\pi$
$617$	−13.3461	−	7.70535i	−0.537292	−	0.310206i	−0.743981	+	0.668201i	$0.767065\pi$
$618$	0.612209	+	0.353459i	0.0246266	+	0.0142182i
$619$			5.88560i			0.236562i	0.992980	+	0.118281i	$0.0377384\pi$
$619$			5.88560i			0.236562i	−0.992980	+	0.118281i	$0.962262\pi$
$620$	6.61699	−	11.4610i	0.265745	−	0.460284i
$621$	−11.0585	−	19.1539i	−0.443762	−	0.768618i
$622$	−12.5615	+	7.25241i	−0.503672	+	0.290795i
$623$		0			0
$624$	1.75078	+	2.04515i	0.0700874	+	0.0818714i
$625$	−17.0526			−0.682102
$626$	0.223530	−	0.129055i	0.00893405	−	0.00515807i
$627$	4.82464	+	8.35652i	0.192677	+	0.333727i
$628$	−9.89002	+	17.1300i	−0.394655	+	0.683562i
$629$		−	1.88114i		−	0.0750060i
$630$		0			0
$631$	37.6719	+	21.7499i	1.49969	+	0.865849i	1.00000		0.000353231i	$-0.000112437\pi$
$631$	37.6719	+	21.7499i	1.49969	+	0.865849i	0.499694	+	0.866202i	$0.333446\pi$
$632$		−	8.80301i		−	0.350165i
$633$	−8.50639	+	14.7335i	−0.338098	+	0.585604i
$634$	11.6992	+	20.2636i	0.464634	+	0.804770i
$635$	6.67814	−	3.85563i	0.265014	−	0.153006i
$636$	−6.75331			−0.267786
$637$		0			0
$638$	−40.7351			−1.61272
$639$	14.3723	−	8.29787i	0.568561	−	0.328259i
$640$	0.965926	+	1.67303i	0.0381816	+	0.0661324i
$641$	−9.86953	+	17.0945i	−0.389823	+	0.675193i	−0.992425	−	0.122848i	$-0.960797\pi$
$641$	−9.86953	+	17.0945i	−0.389823	+	0.675193i	0.602603	+	0.798041i	$0.294130\pi$
$642$		−	0.365928i		−	0.0144420i
$643$	27.0556	+	15.6205i	1.06697	+	0.616014i	0.927352	−	0.374191i	$-0.122080\pi$
$643$	27.0556	+	15.6205i	1.06697	+	0.616014i	0.139617	+	0.990206i	$0.455413\pi$
$644$		0			0
$645$		−	2.88494i		−	0.113595i
$646$	−0.438129	+	0.758862i	−0.0172380	+	0.0298570i
$647$	−0.463136	−	0.802175i	−0.0182078	−	0.0315368i	0.856778	−	0.515685i	$-0.172463\pi$
$647$	−0.463136	−	0.802175i	−0.0182078	−	0.0315368i	−0.874986	+	0.484149i	$0.839129\pi$
$648$	3.71792	−	2.14654i	0.146054	−	0.0843241i
$649$	13.8061			0.541938
$650$	−0.838275	−	4.49414i	−0.0328798	−	0.176275i
$651$		0			0
$652$	11.8793	−	6.85853i	0.465230	−	0.268601i
$653$	22.8647	+	39.6028i	0.894765	+	1.54978i	0.834096	+	0.551620i	$0.185990\pi$
$653$	22.8647	+	39.6028i	0.894765	+	1.54978i	0.0606690	+	0.998158i	$0.480677\pi$
$654$	2.97585	−	5.15432i	0.116365	−	0.201550i
$655$			37.8285i			1.47808i
$656$	−0.957850	−	0.553015i	−0.0373978	−	0.0215916i
$657$	6.29988	+	3.63724i	0.245782	+	0.141902i
$658$		0			0
$659$	1.19349	−	2.06718i	0.0464917	−	0.0805260i	−0.841843	−	0.539722i	$-0.818529\pi$
$659$	1.19349	−	2.06718i	0.0464917	−	0.0805260i	0.888335	+	0.459196i	$0.151863\pi$
$660$	2.76160	+	4.78323i	0.107495	+	0.186187i
$661$	−27.8930	+	16.1040i	−1.08491	+	0.626374i	−0.932217	−	0.361899i	$-0.882128\pi$
$661$	−27.8930	+	16.1040i	−1.08491	+	0.626374i	−0.152695	+	0.988273i	$0.548795\pi$
$662$	4.06866			0.158133
$663$	−0.232565	+	0.659147i	−0.00903209	+	0.0255991i
$664$	−14.8826			−0.577556
$665$		0			0
$666$	8.84844	+	15.3259i	0.342870	+	0.593868i
$667$	28.9502	−	50.1432i	1.12096	−	1.94155i
$668$			2.91695i			0.112860i
$669$	15.4069	+	8.89515i	0.595664	+	0.343906i
$670$	−2.18986	−	1.26432i	−0.0846017	−	0.0488448i
$671$			16.9620i			0.654810i
$672$		0			0
$673$	−22.4907	−	38.9550i	−0.866953	−	1.50161i	−0.865095	−	0.501608i	$-0.832742\pi$
$673$	−22.4907	−	38.9550i	−0.866953	−	1.50161i	−0.00185793	−	0.999998i	$-0.500591\pi$
$674$	16.6751	−	9.62739i	0.642302	−	0.370833i
$675$	5.15266			0.198326
$676$	−12.1258	+	4.68662i	−0.466378	+	0.180255i
$677$	17.4725			0.671522			0.335761	−	0.941947i	$-0.391007\pi$
$677$	17.4725			0.671522			0.335761	+	0.941947i	$0.391007\pi$
$678$	1.98808	−	1.14782i	0.0763516	−	0.0440816i
$679$		0			0
$680$	−0.250783	+	0.434369i	−0.00961709	+	0.0166573i
$681$		−	18.1036i		−	0.693730i
$682$	22.7159	+	13.1151i	0.869838	+	0.502201i
$683$	10.5640	+	6.09915i	0.404222	+	0.233378i	0.688304	−	0.725422i	$-0.258356\pi$
$683$	10.5640	+	6.09915i	0.404222	+	0.233378i	−0.284082	+	0.958800i	$0.591689\pi$
$684$		−	8.24342i		−	0.315195i
$685$	2.91984	−	5.05731i	0.111561	−	0.193230i
$686$		0			0
$687$	13.0024	−	7.50692i	0.496071	−	0.286407i
$688$	2.00000			0.0762493
$689$	10.8503	−	30.7523i	0.413362	−	1.17157i
$690$	−7.85061			−0.298868
$691$	−29.9974	+	17.3190i	−1.14116	+	0.658847i	−0.946717	−	0.322067i	$-0.895622\pi$
$691$	−29.9974	+	17.3190i	−1.14116	+	0.658847i	−0.194440	+	0.980914i	$0.562289\pi$
$692$	8.90477	+	15.4235i	0.338508	+	0.586314i
$693$		0			0
$694$			11.4120i			0.433194i
$695$	6.14811	+	3.54961i	0.233211	+	0.134644i
$696$	−6.87938	−	3.97181i	−0.260762	−	0.150551i
$697$		−	0.287158i		−	0.0108769i
$698$	12.2484	−	21.2148i	0.463607	−	0.802991i
$699$	3.55850	+	6.16351i	0.134595	+	0.233125i
$700$		0			0
$701$	33.1229			1.25104			0.625518	−	0.780210i	$-0.284888\pi$
$701$	33.1229			1.25104			0.625518	+	0.780210i	$0.284888\pi$
$702$	−2.68667	−	14.4037i	−0.101402	−	0.543634i
$703$	24.4537			0.922290
$704$	−3.31599	+	1.91449i	−0.124976	+	0.0721551i
$705$	−4.58832	−	7.94720i	−0.172806	−	0.299309i
$706$	−2.26950	+	3.93089i	−0.0854138	+	0.147941i
$707$		0			0
$708$	2.33159	+	1.34615i	0.0876267	+	0.0505913i
$709$	−26.3801	−	15.2305i	−0.990724	−	0.571995i	−0.0852333	−	0.996361i	$-0.527164\pi$
$709$	−26.3801	−	15.2305i	−0.990724	−	0.571995i	−0.905491	+	0.424366i	$0.860497\pi$
$710$		−	13.1263i		−	0.492619i
$711$	−10.7505	+	18.6205i	−0.403177	+	0.698323i
$712$	7.75168	+	13.4263i	0.290507	+	0.503172i
$713$	−32.2882	+	18.6416i	−1.20920	+	0.698133i
$714$		0			0
$715$	−26.2182	+	4.89037i	−0.980503	+	0.182889i
$716$	−1.82197			−0.0680904
$717$	15.6679	−	9.04587i	0.585129	−	0.337824i
$718$	4.17826	+	7.23696i	0.155931	+	0.270081i
$719$	0.576532	−	0.998583i	0.0215010	−	0.0372409i	−0.855075	−	0.518505i	$-0.826489\pi$
$719$	0.576532	−	0.998583i	0.0215010	−	0.0372409i	0.876576	+	0.481264i	$0.159822\pi$
$720$		−	4.71849i		−	0.175848i
$721$		0			0
$722$	6.58972	+	3.80457i	0.245244	+	0.141592i
$723$		−	9.01014i		−	0.335091i
$724$	−9.35618	+	16.2054i	−0.347720	+	0.602268i
$725$	6.74462	+	11.6820i	0.250489	+	0.433859i
$726$	−2.36742	+	1.36683i	−0.0878631	+	0.0507278i
$727$	−12.1545			−0.450785			−0.225393	−	0.974268i	$-0.572366\pi$
$727$	−12.1545			−0.450785			−0.225393	+	0.974268i	$0.572366\pi$
$728$		0			0
$729$	−1.38273			−0.0512124
$730$	4.98283	−	2.87684i	0.184423	−	0.106477i
$731$	0.259630	+	0.449692i	0.00960275	+	0.0166324i
$732$	−1.65385	+	2.86456i	−0.0611282	+	0.105877i
$733$			50.4631i			1.86390i	0.362588	+	0.931949i	$0.381893\pi$
$733$			50.4631i			1.86390i	−0.362588	+	0.931949i	$0.618107\pi$
$734$	−21.5834	−	12.4612i	−0.796659	−	0.459951i
$735$		0			0
$736$		−	5.44247i		−	0.200612i
$737$	2.50591	−	4.34036i	0.0923063	−	0.159879i
$738$	1.35072	+	2.33952i	0.0497208	+	0.0861190i
$739$	−6.87096	+	3.96695i	−0.252752	+	0.145927i	−0.621024	−	0.783792i	$-0.713283\pi$
$739$	−6.87096	+	3.96695i	−0.252752	+	0.145927i	0.368272	+	0.929718i	$0.379950\pi$
$740$	13.9972			0.514547
$741$	−8.56852	−	3.02321i	−0.314773	−	0.111061i
$742$		0			0
$743$	42.5950	−	24.5922i	1.56266	−	0.902201i	0.565672	−	0.824630i	$-0.308617\pi$
$743$	42.5950	−	24.5922i	1.56266	−	0.902201i	0.996987	−	0.0775712i	$-0.0247165\pi$
$744$	2.55753	+	4.42977i	0.0937635	+	0.162403i
$745$	−7.55333	+	13.0827i	−0.276733	+	0.479315i
$746$		−	20.4953i		−	0.750386i
$747$	31.4802	+	18.1751i	1.15180	+	0.664993i
$748$	−0.860930	−	0.497058i	−0.0314787	−	0.0181743i
$749$		0			0
$750$	4.52067	−	7.83003i	0.165072	−	0.285912i
$751$	−10.8332	−	18.7636i	−0.395308	−	0.684693i	0.597833	−	0.801621i	$-0.296029\pi$
$751$	−10.8332	−	18.7636i	−0.395308	−	0.684693i	−0.993140	+	0.116928i	$0.962695\pi$
$752$	5.50943	−	3.18087i	0.200908	−	0.115995i
$753$	22.9277			0.835533
$754$	29.1391	−	24.9450i	1.06118	−	0.908445i
$755$	41.0321			1.49331
$756$		0			0
$757$	16.8793	+	29.2358i	0.613489	+	1.06259i	0.990648	+	0.136446i	$0.0435679\pi$
$757$	16.8793	+	29.2358i	0.613489	+	1.06259i	−0.377158	+	0.926149i	$0.623099\pi$
$758$	−1.32041	+	2.28701i	−0.0479594	+	0.0830681i
$759$		−	15.5601i		−	0.564796i
$760$	−5.64654	−	3.26003i	−0.204822	−	0.118254i
$761$	−30.5727	−	17.6512i	−1.10826	−	0.639855i	−0.169882	−	0.985464i	$-0.554339\pi$
$761$	−30.5727	−	17.6512i	−1.10826	−	0.639855i	−0.938378	+	0.345610i	$0.887672\pi$
$762$			2.98047i			0.107971i
$763$		0			0
$764$	11.6453	+	20.1702i	0.421311	+	0.729732i
$765$	1.06093	−	0.612530i	0.0383581	−	0.0221461i
$766$	−15.8705			−0.573424
$767$	−9.87598	+	8.45450i	−0.356601	+	0.305274i
$768$	−0.746678			−0.0269434
$769$	−18.0964	+	10.4480i	−0.652574	+	0.376764i	−0.789442	−	0.613825i	$-0.789630\pi$
$769$	−18.0964	+	10.4480i	−0.652574	+	0.376764i	0.136867	+	0.990589i	$0.456297\pi$
$770$		0			0
$771$	2.70564	−	4.68630i	0.0974411	−	0.168773i
$772$		−	9.03840i		−	0.325299i
$773$	8.96397	+	5.17535i	0.322412	+	0.186145i	0.652467	−	0.757817i	$-0.273734\pi$
$773$	8.96397	+	5.17535i	0.322412	+	0.186145i	−0.330055	+	0.943962i	$0.607067\pi$
$774$	−4.23048	−	2.44247i	−0.152062	−	0.0877928i
$775$		−	8.68598i		−	0.312010i
$776$	5.57550	−	9.65704i	0.200149	−	0.346668i
$777$		0			0
$778$	19.7346	−	11.3938i	0.707519	−	0.408487i
$779$	3.73289			0.133745
$780$	−4.90458	−	1.73047i	−0.175612	−	0.0619608i
$781$	26.0166			0.930946
$782$	1.22372	−	0.706513i	0.0437600	−	0.0252649i
$783$	21.6165	+	37.4409i	0.772510	+	1.33803i
$784$		0			0
$785$		−	38.2121i		−	1.36385i
$786$	−12.6622	−	7.31053i	−0.451646	−	0.260758i
$787$	−5.30505	−	3.06287i	−0.189105	−	0.109180i	0.402459	−	0.915438i	$-0.368156\pi$
$787$	−5.30505	−	3.06287i	−0.189105	−	0.109180i	−0.591563	+	0.806259i	$0.701489\pi$
$788$		−	1.41384i		−	0.0503658i
$789$	0.963353	−	1.66858i	0.0342963	−	0.0594029i
$790$	8.50305	+	14.7277i	0.302525	+	0.523989i
$791$		0			0
$792$	9.35218			0.332315
$793$	−10.3871	−	12.1335i	−0.368855	−	0.430872i
$794$	23.6695			0.839998
$795$	11.2985	−	6.52320i	0.400717	−	0.231354i
$796$	−3.95223	−	6.84546i	−0.140083	−	0.242631i
$797$	2.97989	−	5.16133i	0.105553	−	0.182824i	−0.808411	−	0.588619i	$-0.799672\pi$
$797$	2.97989	−	5.16133i	0.105553	−	0.182824i	0.913964	+	0.405795i	$0.133005\pi$
$798$		0			0
$799$	1.43041	+	0.825849i	0.0506043	+	0.0292164i
$800$	1.09808	+	0.633975i	0.0388229	+	0.0224144i
$801$		−	37.8665i		−	1.33795i
$802$	−4.17669	+	7.23425i	−0.147484	+	0.255450i
$803$	5.70197	+	9.87611i	0.201218	+	0.348520i
$804$	0.846401	−	0.488670i	0.0298503	−	0.0172341i
$805$		0			0
$806$	−24.2808	+	4.52899i	−0.855253	+	0.159527i
$807$	9.36680			0.329727
$808$	−9.58021	+	5.53114i	−0.337031	+	0.194585i
$809$	10.1525	+	17.5846i	0.356943	+	0.618243i	0.987448	−	0.157942i	$-0.0504858\pi$
$809$	10.1525	+	17.5846i	0.356943	+	0.618243i	−0.630506	+	0.776185i	$0.717152\pi$
$810$	−4.14680	+	7.18247i	−0.145704	+	0.252366i
$811$		−	17.2012i		−	0.604017i	−0.953305	−	0.302008i	$-0.902343\pi$
$811$		−	17.2012i		−	0.604017i	0.953305	−	0.302008i	$-0.0976570\pi$
$812$		0			0
$813$	−6.23662	−	3.60072i	−0.218728	−	0.126283i
$814$			27.7428i			0.972385i
$815$	−13.2497	+	22.9491i	−0.464115	+	0.803871i
$816$	−0.0969299	−	0.167887i	−0.00339322	−	0.00587724i
$817$	−5.84573	+	3.37503i	−0.204516	+	0.118077i
$818$	18.9124			0.661257
$819$		0			0
$820$	2.13669			0.0746163
$821$	−24.3160	+	14.0388i	−0.848634	+	0.489959i	−0.860190	−	0.509974i	$-0.829655\pi$
$821$	−24.3160	+	14.0388i	−0.848634	+	0.489959i	0.0115557	+	0.999933i	$0.496322\pi$
$822$	1.12854	+	1.95470i	0.0393625	+	0.0681779i
$823$	16.2766	−	28.1920i	0.567368	−	0.982710i	−0.429457	−	0.903087i	$-0.641295\pi$
$823$	16.2766	−	28.1920i	0.567368	−	0.982710i	0.996825	−	0.0796230i	$-0.0253717\pi$
$824$		−	0.946750i		−	0.0329816i
$825$	3.13942	+	1.81254i	0.109301	+	0.0631047i
$826$		0			0
$827$			51.9965i			1.80810i	0.427432	+	0.904048i	$0.359419\pi$
$827$			51.9965i			1.80810i	−0.427432	+	0.904048i	$0.640581\pi$
$828$	−6.64654	+	11.5121i	−0.230983	+	0.400075i
$829$	−0.941056	−	1.62996i	−0.0326842	−	0.0566107i	0.849221	−	0.528038i	$-0.177072\pi$
$829$	−0.941056	−	1.62996i	−0.0326842	−	0.0566107i	−0.881905	+	0.471428i	$0.843739\pi$
$830$	24.8990	−	14.3755i	0.864258	−	0.498980i
$831$	12.7373			0.441852
$832$	1.19966	−	3.40012i	0.0415906	−	0.117878i
$833$		0			0
$834$	−2.37630	+	1.37196i	−0.0822845	+	0.0475070i
$835$	−2.81756	−	4.88016i	−0.0975057	−	0.168885i
$836$	6.46147	−	11.1916i	0.223475	−	0.387069i
$837$		−	27.8386i		−	0.962241i
$838$	5.57900	+	3.22104i	0.192723	+	0.111269i
$839$	−6.73034	−	3.88577i	−0.232357	−	0.134152i	0.379302	−	0.925273i	$-0.376164\pi$
$839$	−6.73034	−	3.88577i	−0.232357	−	0.134152i	−0.611659	+	0.791121i	$0.709498\pi$
$840$		0			0
$841$	−42.0902	+	72.9023i	−1.45138	+	2.51387i
$842$	−2.06949	−	3.58446i	−0.0713193	−	0.123529i
$843$	9.40983	−	5.43277i	0.324092	−	0.187114i
$844$	22.7846			0.784279
$845$	15.7600	−	19.5535i	0.542159	−	0.672661i
$846$	−15.5384			−0.534221
$847$		0			0
$848$	4.52224	+	7.83274i	0.155294	+	0.268977i
$849$	7.74472	−	13.4142i	0.265798	−	0.460376i
$850$			0.329197i			0.0112914i
$851$	−34.1503	−	19.7167i	−1.17066	−	0.675878i
$852$	4.39371	+	2.53671i	0.150526	+	0.0869062i
$853$		−	42.8107i		−	1.46581i	−0.680330	−	0.732906i	$-0.738164\pi$
$853$		−	42.8107i		−	1.46581i	0.680330	−	0.732906i	$-0.261836\pi$
$854$		0			0
$855$	7.96254	+	13.7915i	0.272313	+	0.471660i
$856$	−0.424416	+	0.245037i	−0.0145063	+	0.00837519i
$857$	−32.1321			−1.09761			−0.548805	−	0.835950i	$-0.684917\pi$
$857$	−32.1321			−1.09761			−0.548805	+	0.835950i	$0.684917\pi$
$858$	3.42984	−	9.72100i	0.117093	−	0.331870i
$859$	−41.4827			−1.41537			−0.707686	−	0.706527i	$-0.750261\pi$
$859$	−41.4827			−1.41537			−0.707686	+	0.706527i	$0.750261\pi$
$860$	−3.34607	+	1.93185i	−0.114100	+	0.0658756i
$861$		0			0
$862$	−1.45457	+	2.51939i	−0.0495428	+	0.0858107i
$863$			26.9806i			0.918429i	0.888325	+	0.459215i	$0.151869\pi$
$863$			26.9806i			0.918429i	−0.888325	+	0.459215i	$0.848131\pi$
$864$	3.51933	+	2.03189i	0.119730	+	0.0691262i
$865$	−29.7959	−	17.2027i	−1.01309	−	0.584909i
$866$		−	5.94879i		−	0.202148i
$867$	−6.32160	+	10.9493i	−0.214693	+	0.371859i
$868$		0			0
$869$	−29.1907	+	16.8533i	−0.990228	+	0.571708i
$870$	15.3459			0.520275
$871$	0.865359	+	4.63935i	0.0293216	+	0.157198i
$872$	−7.97090			−0.269929
$873$	−23.5871	+	13.6180i	−0.798301	+	0.460899i
$874$	9.18426	+	15.9076i	0.310662	+	0.538083i
$875$		0			0
$876$			2.22385i			0.0751369i
$877$	27.1342	+	15.6659i	0.916256	+	0.529001i	0.882439	−	0.470427i	$-0.155900\pi$
$877$	27.1342	+	15.6659i	0.916256	+	0.529001i	0.0338175	+	0.999428i	$0.489234\pi$
$878$	28.3953	+	16.3940i	0.958295	+	0.553272i
$879$		−	2.57659i		−	0.0869064i
$880$	3.69851	−	6.40601i	0.124677	−	0.215947i
$881$	−16.6444	−	28.8289i	−0.560763	−	0.971270i	−0.997430	−	0.0716470i	$-0.977174\pi$
$881$	−16.6444	−	28.8289i	−0.560763	−	0.971270i	0.436667	−	0.899623i	$-0.356159\pi$
$882$		0			0
$883$	−30.3862			−1.02258			−0.511288	−	0.859409i	$-0.670832\pi$
$883$	−30.3862			−1.02258			−0.511288	+	0.859409i	$0.670832\pi$
$884$	0.920236	−	0.171648i	0.0309509	−	0.00577315i
$885$	−5.20111			−0.174833
$886$	24.8770	−	14.3628i	0.835760	−	0.482526i
$887$	−5.10315	−	8.83891i	−0.171347	−	0.296782i	0.767544	−	0.640996i	$-0.221479\pi$
$887$	−5.10315	−	8.83891i	−0.171347	−	0.296782i	−0.938891	+	0.344215i	$0.888145\pi$
$888$	−2.70502	+	4.68523i	−0.0907746	+	0.157226i
$889$		0			0
$890$	−25.9376	−	14.9751i	−0.869432	−	0.501967i
$891$	−14.2358	−	8.21906i	−0.476919	−	0.275349i
$892$		−	23.8259i		−	0.797751i
$893$	−10.7356	+	18.5945i	−0.359252	+	0.622242i
$894$	−2.91943	−	5.05660i	−0.0976404	−	0.169118i
$895$	3.04822	−	1.75989i	0.101891	−	0.0588267i
$896$		0			0
$897$	9.52859	+	11.1307i	0.318150	+	0.371642i
$898$	−26.2358			−0.875499
$899$	63.1151	−	36.4395i	2.10501	−	1.21533i
$900$	−1.54846	−	2.68202i	−0.0516155	−	0.0894007i
$901$	−1.17411	+	2.03361i	−0.0391151	+	0.0677494i
$902$			4.23497i			0.141009i
$903$		0			0
$904$	−2.66256	−	1.53723i	−0.0885555	−	0.0511275i
$905$		−	36.1495i		−	1.20165i
$906$	−7.92964	+	13.7345i	−0.263445	+	0.456300i
$907$	−18.1221	−	31.3883i	−0.601733	−	1.04223i	−0.992559	−	0.121768i	$-0.961144\pi$
$907$	−18.1221	−	31.3883i	−0.601733	−	1.04223i	0.390825	−	0.920465i	$-0.372190\pi$
$908$	−20.9972	+	12.1227i	−0.696816	+	0.402307i
$909$	27.0193			0.896173
$910$		0			0
$911$	−0.198769			−0.00658552			−0.00329276	−	0.999995i	$-0.501048\pi$
$911$	−0.198769			−0.00658552			−0.00329276	+	0.999995i	$0.501048\pi$
$912$	2.18244	−	1.26003i	0.0722678	−	0.0417238i
$913$	28.4925	+	49.3505i	0.942965	+	1.63326i
$914$	−7.98587	+	13.8319i	−0.264149	+	0.457520i
$915$		−	6.39000i		−	0.211247i
$916$	−17.4136	−	10.0538i	−0.575362	−	0.332185i
$917$		0			0
$918$			1.05508i			0.0348227i
$919$	7.63839	−	13.2301i	0.251967	−	0.436420i	−0.712100	−	0.702078i	$-0.752256\pi$
$919$	7.63839	−	13.2301i	0.251967	−	0.436420i	0.964067	+	0.265658i	$0.0855891\pi$
$920$	5.25702	+	9.10543i	0.173319	+	0.300197i
$921$	9.76435	−	5.63745i	0.321746	−	0.185760i
$922$	−19.5013			−0.642242
$923$	−18.6105	+	15.9318i	−0.612572	+	0.524403i
$924$		0			0
$925$	7.95609	−	4.59345i	0.261595	−	0.151032i
$926$	19.8949	+	34.4590i	0.653788	+	1.13239i
$927$	−1.15621	+	2.00261i	−0.0379748	+	0.0657742i
$928$			10.6386i			0.349230i
$929$	15.4387	+	8.91353i	0.506527	+	0.292444i	0.731405	−	0.681943i	$-0.238865\pi$
$929$	15.4387	+	8.91353i	0.506527	+	0.292444i	−0.224878	+	0.974387i	$0.572198\pi$
$930$	−8.55766	−	4.94077i	−0.280617	−	0.162014i
$931$		0			0
$932$	4.76578	−	8.25457i	0.156108	−	0.270387i
$933$	5.41522	+	9.37943i	0.177286	+	0.307069i
$934$	−3.12262	+	1.80285i	−0.102175	+	0.0589910i
$935$	1.92049			0.0628066
$936$	−6.68992	+	5.72702i	−0.218667	+	0.187193i
$937$	−20.0868			−0.656206			−0.328103	−	0.944642i	$-0.606409\pi$
$937$	−20.0868			−0.656206			−0.328103	+	0.944642i	$0.606409\pi$
$938$		0			0
$939$	−0.0963625	−	0.166905i	−0.00314467	−	0.00544673i
$940$	−6.14498	+	10.6434i	−0.200427	+	0.347150i
$941$		−	37.5519i		−	1.22416i	−0.790797	−	0.612079i	$-0.790334\pi$
$941$		−	37.5519i		−	1.22416i	0.790797	−	0.612079i	$-0.209666\pi$
$942$	12.7906	+	7.38466i	0.416740	+	0.240605i
$943$	−5.21307	−	3.00977i	−0.169761	−	0.0980116i
$944$		−	3.60569i		−	0.117355i
$945$		0			0
$946$	−3.82898	−	6.63199i	−0.124491	−	0.215625i
$947$	−26.4181	+	15.2525i	−0.858472	+	0.495639i	−0.863500	−	0.504348i	$-0.831733\pi$
$947$	−26.4181	+	15.2525i	−0.858472	+	0.495639i	0.00502811	+	0.999987i	$0.498399\pi$
$948$	−6.57301			−0.213482
$949$	−10.1267	−	3.57297i	−0.328725	−	0.115983i
$950$	−4.27937			−0.138841
$951$	15.1304	−	8.73553i	0.490636	−	0.283269i
$952$		0			0
$953$	0.723085	−	1.25242i	0.0234230	−	0.0405699i	−0.854076	−	0.520148i	$-0.825877\pi$
$953$	0.723085	−	1.25242i	0.0234230	−	0.0405699i	0.877499	+	0.479578i	$0.159210\pi$
$954$		−	22.0909i		−	0.715218i
$955$	−38.9658	−	22.4969i	−1.26090	−	0.727983i
$956$	−20.9835	−	12.1148i	−0.678655	−	0.391821i
$957$			30.4160i			0.983210i
$958$	13.3135	−	23.0597i	0.430140	−	0.745024i
$959$		0			0
$960$	1.24922	−	0.721236i	0.0403183	−	0.0232778i
$961$	−15.9282			−0.513813
$962$	−16.9889	−	19.8453i	−0.547745	−	0.639839i
$963$	1.19699			0.0385725
$964$	−10.4503	+	6.03348i	−0.336581	+	0.194325i
$965$	8.73043	+	15.1215i	0.281042	+	0.486780i
$966$		0			0
$967$		−	15.7699i		−	0.507125i	−0.967319	−	0.253563i	$-0.918398\pi$
$967$		−	15.7699i		−	0.507125i	0.967319	−	0.253563i	$-0.0816024\pi$
$968$	3.17060	+	1.83055i	0.101907	+	0.0588360i
$969$	0.566626	+	0.327142i	0.0182026	+	0.0105093i
$970$			21.5421i			0.691674i
$971$	10.5050	−	18.1952i	0.337122	−	0.583912i	−0.646768	−	0.762687i	$-0.723880\pi$
$971$	10.5050	−	18.1952i	0.337122	−	0.583912i	0.983890	+	0.178774i	$0.0572132\pi$
$972$	−7.69844	−	13.3341i	−0.246928	−	0.427691i
$973$		0			0
$974$	−40.0111			−1.28204
$975$	−3.35568	+	0.625922i	−0.107468	+	0.0200455i
$976$	4.42989			0.141797
$977$	−19.0301	+	10.9870i	−0.608826	+	0.351506i	−0.772506	−	0.635008i	$-0.780997\pi$
$977$	−19.0301	+	10.9870i	−0.608826	+	0.351506i	0.163680	+	0.986513i	$0.447664\pi$
$978$	−5.12111	−	8.87003i	−0.163755	−	0.283632i
$979$	29.6810	−	51.4091i	0.948610	−	1.64304i
$980$		0			0
$981$	16.8604	+	9.73434i	0.538310	+	0.310794i
$982$	−36.0754	−	20.8281i	−1.15121	−	0.664653i
$983$			55.7317i			1.77756i	0.458330	+	0.888782i	$0.348448\pi$
$983$			55.7317i			1.77756i	−0.458330	+	0.888782i	$0.651552\pi$
$984$	−0.412924	+	0.715206i	−0.0131636	+	0.0227999i
$985$	1.36566	+	2.36539i	0.0435135	+	0.0753677i
$986$	−2.39205	+	1.38105i	−0.0761784	+	0.0439816i
$987$		0			0
$988$	2.23132	+	11.9625i	0.0709879	+	0.380579i
$989$	10.8849			0.346121
$990$	−15.6465	+	9.03351i	−0.497278	+	0.287104i
$991$	−15.9210	−	27.5759i	−0.505746	−	0.875978i	−0.999978	−	0.00664774i	$-0.997884\pi$
$991$	−15.9210	−	27.5759i	−0.505746	−	0.875978i	0.494232	−	0.869330i	$-0.335449\pi$
$992$	3.42521	−	5.93263i	0.108750	−	0.188361i
$993$		−	3.03798i		−	0.0964075i
$994$		0			0
$995$	13.2244	+	7.63512i	0.419242	+	0.242050i
$996$			11.1125i			0.352113i
$997$	11.1418	−	19.2982i	0.352864	−	0.611179i	−0.633886	−	0.773427i	$-0.718541\pi$
$997$	11.1418	−	19.2982i	0.352864	−	0.611179i	0.986750	+	0.162248i	$0.0518744\pi$
$998$	−1.97709	−	3.42442i	−0.0625836	−	0.108398i
$999$	25.4993	−	14.7220i	0.806761	−	0.465783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.m.e.491.3	yes	16
7.2	even	3		1274.2.v.f.361.6		16
7.3	odd	6		1274.2.o.g.569.2		16
7.4	even	3		1274.2.o.g.569.3		16
7.5	odd	6		1274.2.v.f.361.7		16
7.6	odd	2	inner	1274.2.m.e.491.2	✓	16
13.4	even	6	inner	1274.2.m.e.589.3	yes	16
91.4	even	6		1274.2.v.f.667.6		16
91.17	odd	6		1274.2.v.f.667.7		16
91.30	even	6		1274.2.o.g.459.7		16
91.69	odd	6	inner	1274.2.m.e.589.2	yes	16
91.82	odd	6		1274.2.o.g.459.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1274.2.m.e.491.2	✓	16	7.6	odd	2	inner
1274.2.m.e.491.3	yes	16	1.1	even	1	trivial
1274.2.m.e.589.2	yes	16	91.69	odd	6	inner
1274.2.m.e.589.3	yes	16	13.4	even	6	inner
1274.2.o.g.459.6		16	91.82	odd	6
1274.2.o.g.459.7		16	91.30	even	6
1274.2.o.g.569.2		16	7.3	odd	6
1274.2.o.g.569.3		16	7.4	even	3
1274.2.v.f.361.6		16	7.2	even	3
1274.2.v.f.361.7		16	7.5	odd	6
1274.2.v.f.667.6		16	91.4	even	6
1274.2.v.f.667.7		16	91.17	odd	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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.373339 + 0.646642i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.93185i q^{5} +(-0.646642 - 0.373339i) q^{6} +1.00000i q^{8} +(1.22124 - 2.11524i) q^{9} +(-0.965926 - 1.67303i) q^{10} +(3.31599 - 1.91449i) q^{11} +0.746678 q^{12} +(-1.19966 + 3.40012i) q^{13} +(-1.24922 + 0.721236i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.129815 - 0.224846i) q^{17} +2.44247i q^{18} +(2.92286 + 1.68752i) q^{19} +(1.67303 + 0.965926i) q^{20} +(-1.91449 + 3.31599i) q^{22} +(-2.72124 - 4.71332i) q^{23} +(-0.646642 + 0.373339i) q^{24} +1.26795 q^{25} +(-0.661126 - 3.54442i) q^{26} +4.06378 q^{27} +(5.31931 + 9.21332i) q^{29} +(0.721236 - 1.24922i) q^{30} -6.85042i q^{31} +(0.866025 + 0.500000i) q^{32} +(2.47598 + 1.42951i) q^{33} +0.259630i q^{34} +(-1.22124 - 2.11524i) q^{36} +(6.27477 - 3.62274i) q^{37} -3.37503 q^{38} +(-2.64654 + 0.493649i) q^{39} -1.93185 q^{40} +(0.957850 - 0.553015i) q^{41} +(-1.00000 + 1.73205i) q^{43} -3.82898i q^{44} +(4.08633 + 2.35925i) q^{45} +(4.71332 + 2.72124i) q^{46} +6.36175i q^{47} +(0.373339 - 0.646642i) q^{48} +(-1.09808 + 0.633975i) q^{50} +0.193860 q^{51} +(2.34476 + 2.73899i) q^{52} -9.04447 q^{53} +(-3.51933 + 2.03189i) q^{54} +(3.69851 + 6.40601i) q^{55} +2.52006i q^{57} +(-9.21332 - 5.31931i) q^{58} +(3.12262 + 1.80285i) q^{59} +1.44247i q^{60} +(-2.21495 + 3.83640i) q^{61} +(3.42521 + 5.93263i) q^{62} -1.00000 q^{64} +(-6.56853 - 2.31756i) q^{65} -2.85902 q^{66} +(1.13356 - 0.654458i) q^{67} +(-0.129815 - 0.224846i) q^{68} +(2.03189 - 3.51933i) q^{69} +(5.88434 + 3.39732i) q^{71} +(2.11524 + 1.22124i) q^{72} +2.97832i q^{73} +(-3.62274 + 6.27477i) q^{74} +(0.473375 + 0.819910i) q^{75} +(2.92286 - 1.68752i) q^{76} +(2.04515 - 1.75078i) q^{78} -8.80301 q^{79} +(1.67303 - 0.965926i) q^{80} +(-2.14654 - 3.71792i) q^{81} +(-0.553015 + 0.957850i) q^{82} +14.8826i q^{83} +(0.434369 + 0.250783i) q^{85} -2.00000i q^{86} +(-3.97181 + 6.87938i) q^{87} +(1.91449 + 3.31599i) q^{88} +(13.4263 - 7.75168i) q^{89} -4.71849 q^{90} -5.44247 q^{92} +(4.42977 - 2.55753i) q^{93} +(-3.18087 - 5.50943i) q^{94} +(-3.26003 + 5.64654i) q^{95} +0.746678i q^{96} +(-9.65704 - 5.57550i) q^{97} -9.35218i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{11} + 12 q^{15} - 8 q^{16} - 4 q^{22} - 24 q^{23} + 48 q^{25} + 24 q^{29} - 8 q^{30} + 12 q^{37} + 12 q^{39} - 16 q^{43} - 12 q^{46} + 24 q^{50} - 48 q^{51} - 24 q^{53} - 60 q^{58}+ \cdots - 12 q^{95}+O(q^{100}) \) 16 * q + 8 * q^4 - 12 * q^11 + 12 * q^15 - 8 * q^16 - 4 * q^22 - 24 * q^23 + 48 * q^25 + 24 * q^29 - 8 * q^30 + 12 * q^37 + 12 * q^39 - 16 * q^43 - 12 * q^46 + 24 * q^50 - 48 * q^51 - 24 * q^53 - 60 * q^58 - 16 * q^64 - 12 * q^65 - 48 * q^67 + 60 * q^71 - 12 * q^72 + 16 * q^78 - 64 * q^79 + 20 * q^81 + 24 * q^85 + 4 * q^88 - 48 * q^92 + 24 * q^93 - 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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