LMFDB - Embedded newform 702.2.bc.a.557.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(305,702)] 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("702.305"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bc (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.8
Character	$\chi$	$=$	702.557
Dual form			702.2.bc.a.305.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.817032 - 3.04921i) q^{5} +(-2.08075 + 2.08075i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.73384 - 1.57838i) q^{10} +(0.842637 - 0.225784i) q^{11} +(-0.0715101 + 3.60484i) q^{13} +(-2.54838 - 1.47131i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.80087 + 3.11920i) q^{17} +(-4.90132 + 1.31331i) q^{19} +(2.23217 + 2.23217i) q^{20} +(0.436181 + 0.755487i) q^{22} -3.73515 q^{23} +(-4.29998 + 2.48260i) q^{25} +(-3.50052 + 0.863928i) q^{26} +(0.761606 - 2.84235i) q^{28} +(-7.44735 - 4.29973i) q^{29} +(-4.96612 + 1.33067i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-3.47902 - 0.932200i) q^{34} +(8.04466 + 4.64459i) q^{35} +(-5.77159 - 1.54649i) q^{37} +(-2.53711 - 4.39440i) q^{38} +(-1.57838 + 2.73384i) q^{40} +(7.72453 - 7.72453i) q^{41} +6.33580i q^{43} +(-0.616853 + 0.616853i) q^{44} +(-0.966728 - 3.60788i) q^{46} +(-1.63674 + 6.10838i) q^{47} -1.65902i q^{49} +(-3.51092 - 3.51092i) q^{50} +(-1.74049 - 3.15764i) q^{52} +6.73100i q^{53} +(-1.37692 - 2.38490i) q^{55} +2.94262 q^{56} +(2.22570 - 8.30644i) q^{58} +(-1.42714 + 5.32616i) q^{59} +6.36898 q^{61} +(-2.57066 - 4.45251i) q^{62} +1.00000i q^{64} +(11.0503 - 2.72722i) q^{65} +(5.85124 + 5.85124i) q^{67} -3.60175i q^{68} +(-2.40422 + 8.97266i) q^{70} +(-1.65986 - 6.19468i) q^{71} +(10.6419 - 10.6419i) q^{73} -5.97519i q^{74} +(3.58802 - 3.58802i) q^{76} +(-1.28351 + 2.22311i) q^{77} +(-1.30671 - 2.26329i) q^{79} +(-3.04921 - 0.817032i) q^{80} +(9.46058 + 5.46207i) q^{82} +(-11.0800 - 2.96889i) q^{83} +(10.9825 + 2.94274i) q^{85} +(-6.11991 + 1.63983i) q^{86} +(-0.755487 - 0.436181i) q^{88} +(2.10194 - 7.84455i) q^{89} +(-7.35197 - 7.64956i) q^{91} +(3.23474 - 1.86758i) q^{92} -6.32386 q^{94} +(8.00907 + 13.8721i) q^{95} +(-11.9612 - 11.9612i) q^{97} +(1.60249 - 0.429386i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) $ 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.817032	−	3.04921i	−0.365388	−	1.36365i	−0.866894	−	0.498492i	$-0.833887\pi$
$5$	−0.817032	−	3.04921i	−0.365388	−	1.36365i	0.501506	−	0.865154i	$-0.332779\pi$
$6$		0			0
$7$	−2.08075	+	2.08075i	−0.786449	+	0.786449i	−0.980910	−	0.194462i	$-0.937704\pi$
$7$	−2.08075	+	2.08075i	−0.786449	+	0.786449i	0.194462	+	0.980910i	$0.437704\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	2.73384	−	1.57838i	0.864517	−	0.499129i
$11$	0.842637	−	0.225784i	0.254064	−	0.0680764i	−0.129539	−	0.991574i	$-0.541350\pi$
$11$	0.842637	−	0.225784i	0.254064	−	0.0680764i	0.383603	+	0.923498i	$0.374683\pi$
$12$		0			0
$13$	−0.0715101	+	3.60484i	−0.0198333	+	0.999803i
$13$	−0.0715101	+	3.60484i	−0.0198333	+	0.999803i
$14$	−2.54838	−	1.47131i	−0.681084	−	0.393224i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.80087	+	3.11920i	−0.436776	+	0.756518i	−0.997439	−	0.0715262i	$-0.977213\pi$
$17$	−1.80087	+	3.11920i	−0.436776	+	0.756518i	0.560663	+	0.828044i	$0.310546\pi$
$18$		0			0
$19$	−4.90132	+	1.31331i	−1.12444	+	0.301293i	−0.772679	−	0.634797i	$-0.781084\pi$
$19$	−4.90132	+	1.31331i	−1.12444	+	0.301293i	−0.351761	+	0.936090i	$0.614417\pi$
$20$	2.23217	+	2.23217i	0.499129	+	0.499129i
$21$		0			0
$22$	0.436181	+	0.755487i	0.0929941	+	0.161070i
$23$	−3.73515			−0.778833			−0.389416	−	0.921062i	$-0.627323\pi$
$23$	−3.73515			−0.778833			−0.389416	+	0.921062i	$0.627323\pi$
$24$		0			0
$25$	−4.29998	+	2.48260i	−0.859997	+	0.496519i
$26$	−3.50052	+	0.863928i	−0.686508	+	0.169430i
$27$		0			0
$28$	0.761606	−	2.84235i	0.143930	−	0.537154i
$29$	−7.44735	−	4.29973i	−1.38294	−	0.798439i	−0.390431	−	0.920632i	$-0.627674\pi$
$29$	−7.44735	−	4.29973i	−1.38294	−	0.798439i	−0.992506	+	0.122193i	$0.961007\pi$
$30$		0			0
$31$	−4.96612	+	1.33067i	−0.891942	+	0.238995i	−0.675553	−	0.737312i	$-0.736095\pi$
$31$	−4.96612	+	1.33067i	−0.891942	+	0.238995i	−0.216390	+	0.976307i	$0.569428\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$		0			0
$34$	−3.47902	−	0.932200i	−0.596647	−	0.159871i
$35$	8.04466	+	4.64459i	1.35980	+	0.785079i
$36$		0			0
$37$	−5.77159	−	1.54649i	−0.948844	−	0.254242i	−0.248972	−	0.968511i	$-0.580093\pi$
$37$	−5.77159	−	1.54649i	−0.948844	−	0.254242i	−0.699872	+	0.714269i	$0.746760\pi$
$38$	−2.53711	−	4.39440i	−0.411574	−	0.712867i
$39$		0			0
$40$	−1.57838	+	2.73384i	−0.249565	+	0.432258i
$41$	7.72453	−	7.72453i	1.20637	−	1.20637i	0.234175	−	0.972194i	$-0.424761\pi$
$41$	7.72453	−	7.72453i	1.20637	−	1.20637i	0.972194	−	0.234175i	$-0.0752389\pi$
$42$		0			0
$43$			6.33580i			0.966200i	0.875565	+	0.483100i	$0.160489\pi$
$43$			6.33580i			0.966200i	−0.875565	+	0.483100i	$0.839511\pi$
$44$	−0.616853	+	0.616853i	−0.0929941	+	0.0929941i
$45$		0			0
$46$	−0.966728	−	3.60788i	−0.142536	−	0.531953i
$47$	−1.63674	+	6.10838i	−0.238742	+	0.890999i	0.737684	+	0.675146i	$0.235920\pi$
$47$	−1.63674	+	6.10838i	−0.238742	+	0.890999i	−0.976426	+	0.215852i	$0.930747\pi$
$48$		0			0
$49$		−	1.65902i		−	0.237003i
$50$	−3.51092	−	3.51092i	−0.496519	−	0.496519i
$51$		0			0
$52$	−1.74049	−	3.15764i	−0.241363	−	0.437886i
$53$			6.73100i			0.924574i	0.886730	+	0.462287i	$0.152971\pi$
$53$			6.73100i			0.924574i	−0.886730	+	0.462287i	$0.847029\pi$
$54$		0			0
$55$	−1.37692	−	2.38490i	−0.185664	−	0.321580i
$56$	2.94262			0.393224
$57$		0			0
$58$	2.22570	−	8.30644i	0.292249	−	1.09069i
$59$	−1.42714	+	5.32616i	−0.185798	+	0.693407i	0.808660	+	0.588276i	$0.200193\pi$
$59$	−1.42714	+	5.32616i	−0.185798	+	0.693407i	−0.994458	+	0.105131i	$0.966474\pi$
$60$		0			0
$61$	6.36898			0.815464			0.407732	−	0.913102i	$-0.366320\pi$
$61$	6.36898			0.815464			0.407732	+	0.913102i	$0.366320\pi$
$62$	−2.57066	−	4.45251i	−0.326474	−	0.565469i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	11.0503	−	2.72722i	1.37062	−	0.338270i
$66$		0			0
$67$	5.85124	+	5.85124i	0.714842	+	0.714842i	0.967544	−	0.252702i	$-0.0813192\pi$
$67$	5.85124	+	5.85124i	0.714842	+	0.714842i	−0.252702	+	0.967544i	$0.581319\pi$
$68$		−	3.60175i		−	0.436776i
$69$		0			0
$70$	−2.40422	+	8.97266i	−0.287359	+	1.07244i
$71$	−1.65986	−	6.19468i	−0.196989	−	0.735174i	−0.991743	−	0.128242i	$-0.959067\pi$
$71$	−1.65986	−	6.19468i	−0.196989	−	0.735174i	0.794754	−	0.606932i	$-0.207600\pi$
$72$		0			0
$73$	10.6419	−	10.6419i	1.24555	−	1.24555i	0.287878	−	0.957667i	$-0.407050\pi$
$73$	10.6419	−	10.6419i	1.24555	−	1.24555i	0.957667	−	0.287878i	$-0.0929498\pi$
$74$		−	5.97519i		−	0.694602i
$75$		0			0
$76$	3.58802	−	3.58802i	0.411574	−	0.411574i
$77$	−1.28351	+	2.22311i	−0.146270	+	0.253347i
$78$		0			0
$79$	−1.30671	−	2.26329i	−0.147016	−	0.254640i	0.783107	−	0.621887i	$-0.213634\pi$
$79$	−1.30671	−	2.26329i	−0.147016	−	0.254640i	−0.930123	+	0.367247i	$0.880300\pi$
$80$	−3.04921	−	0.817032i	−0.340912	−	0.0913470i
$81$		0			0
$82$	9.46058	+	5.46207i	1.04475	+	0.603185i
$83$	−11.0800	−	2.96889i	−1.21619	−	0.325878i	−0.407004	−	0.913426i	$-0.633427\pi$
$83$	−11.0800	−	2.96889i	−1.21619	−	0.325878i	−0.809189	+	0.587548i	$0.800093\pi$
$84$		0			0
$85$	10.9825	+	2.94274i	1.19122	+	0.319185i
$86$	−6.11991	+	1.63983i	−0.659927	+	0.176827i
$87$		0			0
$88$	−0.755487	−	0.436181i	−0.0805352	−	0.0464970i
$89$	2.10194	−	7.84455i	0.222805	−	0.831521i	−0.760467	−	0.649377i	$-0.775030\pi$
$89$	2.10194	−	7.84455i	0.222805	−	0.831521i	0.983272	−	0.182144i	$-0.0583036\pi$
$90$		0			0
$91$	−7.35197	−	7.64956i	−0.770696	−	0.801892i
$92$	3.23474	−	1.86758i	0.337244	−	0.194708i
$93$		0			0
$94$	−6.32386			−0.652256
$95$	8.00907	+	13.8721i	0.821714	+	1.42325i
$96$		0			0
$97$	−11.9612	−	11.9612i	−1.21448	−	1.21448i	−0.969538	−	0.244941i	$-0.921231\pi$
$97$	−11.9612	−	11.9612i	−1.21448	−	1.21448i	−0.244941	−	0.969538i	$-0.578769\pi$
$98$	1.60249	−	0.429386i	0.161876	−	0.0433745i
$99$		0			0
$100$	2.48260	−	4.29998i	0.248260	−	0.429998i
$101$	−2.58133	+	4.47099i	−0.256851	+	0.444880i	−0.965397	−	0.260786i	$-0.916018\pi$
$101$	−2.58133	+	4.47099i	−0.256851	+	0.444880i	0.708545	+	0.705665i	$0.249352\pi$
$102$		0			0
$103$	7.99184	+	4.61409i	0.787459	+	0.454640i	0.839067	−	0.544028i	$-0.183101\pi$
$103$	7.99184	+	4.61409i	0.787459	+	0.454640i	−0.0516081	+	0.998667i	$0.516435\pi$
$104$	2.59957	−	2.49844i	0.254909	−	0.244992i
$105$		0			0
$106$	−6.50165	+	1.74211i	−0.631496	+	0.169209i
$107$	0.210437	−	0.121496i	0.0203437	−	0.0117454i	−0.489794	−	0.871838i	$-0.662928\pi$
$107$	0.210437	−	0.121496i	0.0203437	−	0.0117454i	0.510137	+	0.860093i	$0.329595\pi$
$108$		0			0
$109$	2.87971	+	2.87971i	0.275827	+	0.275827i	0.831440	−	0.555614i	$-0.187517\pi$
$109$	2.87971	+	2.87971i	0.275827	+	0.275827i	−0.555614	+	0.831440i	$0.687517\pi$
$110$	1.94726	−	1.94726i	0.185664	−	0.185664i
$111$		0			0
$112$	0.761606	+	2.84235i	0.0719650	+	0.268577i
$113$	−2.64736	+	1.52846i	−0.249043	+	0.143785i	−0.619326	−	0.785134i	$-0.712594\pi$
$113$	−2.64736	+	1.52846i	−0.249043	+	0.143785i	0.370283	+	0.928919i	$0.379261\pi$
$114$		0			0
$115$	3.05174	+	11.3892i	0.284576	+	1.06205i
$116$	8.59946			0.798439
$117$		0			0
$118$	−5.51405			−0.507609
$119$	−2.74311	−	10.2374i	−0.251461	−	0.938464i
$120$		0			0
$121$	−8.86722	+	5.11949i	−0.806111	+	0.465408i
$122$	1.64841	+	6.15196i	0.149240	+	0.556972i
$123$		0			0
$124$	3.63546	−	3.63546i	0.326474	−	0.326474i
$125$	−0.0776933	−	0.0776933i	−0.00694910	−	0.00694910i
$126$		0			0
$127$	16.5577	−	9.55958i	1.46926	−	0.848276i	0.469851	−	0.882746i	$-0.344308\pi$
$127$	16.5577	−	9.55958i	1.46926	−	0.848276i	0.999406	+	0.0344705i	$0.0109745\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$		0			0
$130$	5.49433	+	9.96794i	0.481885	+	0.874246i
$131$	10.6970	+	6.17593i	0.934603	+	0.539593i	0.888264	−	0.459332i	$-0.151911\pi$
$131$	10.6970	+	6.17593i	0.934603	+	0.539593i	0.0463386	+	0.998926i	$0.485245\pi$
$132$		0			0
$133$	7.46576	−	12.9311i	0.647363	−	1.12127i
$134$	−4.13745	+	7.16627i	−0.357421	+	0.619072i
$135$		0			0
$136$	3.47902	−	0.932200i	0.298323	−	0.0799355i
$137$	4.91649	+	4.91649i	0.420044	+	0.420044i	0.885219	−	0.465175i	$-0.154009\pi$
$137$	4.91649	+	4.91649i	0.420044	+	0.420044i	−0.465175	+	0.885219i	$0.654009\pi$
$138$		0			0
$139$	2.84060	+	4.92006i	0.240937	+	0.417314i	0.960981	−	0.276613i	$-0.0892121\pi$
$139$	2.84060	+	4.92006i	0.240937	+	0.417314i	−0.720045	+	0.693928i	$0.755879\pi$
$140$	−9.28918			−0.785079
$141$		0			0
$142$	5.55400	−	3.20660i	0.466081	−	0.269092i
$143$	0.753658	+	3.05372i	0.0630240	+	0.255365i
$144$		0			0
$145$	−7.02603	+	26.2215i	−0.583480	+	2.17758i
$146$	13.0337	+	7.52499i	1.07867	+	0.622773i
$147$		0			0
$148$	5.77159	−	1.54649i	0.474422	−	0.127121i
$149$	−20.0748	−	5.37903i	−1.64459	−	0.440668i	−0.686502	−	0.727128i	$-0.740855\pi$
$149$	−20.0748	−	5.37903i	−1.64459	−	0.440668i	−0.958092	+	0.286461i	$0.907521\pi$
$150$		0			0
$151$	7.11970	+	1.90772i	0.579393	+	0.155248i	0.536601	−	0.843836i	$-0.319708\pi$
$151$	7.11970	+	1.90772i	0.579393	+	0.155248i	0.0427921	+	0.999084i	$0.486375\pi$
$152$	4.39440	+	2.53711i	0.356433	+	0.205787i
$153$		0			0
$154$	−2.47956	−	0.664396i	−0.199809	−	0.0535386i
$155$	8.11497	+	14.0555i	0.651810	+	1.12897i
$156$		0			0
$157$	−5.21020	+	9.02434i	−0.415819	+	0.720220i	−0.995514	−	0.0946134i	$-0.969838\pi$
$157$	−5.21020	+	9.02434i	−0.415819	+	0.720220i	0.579695	+	0.814834i	$0.303172\pi$
$158$	1.84797	−	1.84797i	0.147016	−	0.147016i
$159$		0			0
$160$		−	3.15677i		−	0.249565i
$161$	7.77191	−	7.77191i	0.612512	−	0.612512i
$162$		0			0
$163$	1.76529	+	6.58816i	0.138268	+	0.516025i	0.999963	+	0.00859756i	$0.00273672\pi$
$163$	1.76529	+	6.58816i	0.138268	+	0.516025i	−0.861695	+	0.507427i	$0.830597\pi$
$164$	−2.82738	+	10.5519i	−0.220781	+	0.823966i
$165$		0			0
$166$		−	11.4709i		−	0.890315i
$167$	9.73117	+	9.73117i	0.753021	+	0.753021i	0.975042	−	0.222021i	$-0.0712654\pi$
$167$	9.73117	+	9.73117i	0.753021	+	0.753021i	−0.222021	+	0.975042i	$0.571265\pi$
$168$		0			0
$169$	−12.9898	−	0.515565i	−0.999213	−	0.0396588i
$170$			11.3699i			0.872030i
$171$		0			0
$172$	−3.16790	−	5.48696i	−0.241550	−	0.418377i
$173$	−4.06007			−0.308682			−0.154341	−	0.988018i	$-0.549325\pi$
$173$	−4.06007			−0.308682			−0.154341	+	0.988018i	$0.549325\pi$
$174$		0			0
$175$	3.78152	−	14.1128i	0.285856	−	1.06683i
$176$	0.225784	−	0.842637i	0.0170191	−	0.0635161i
$177$		0			0
$178$	8.12128			0.608715
$179$	−9.70640	−	16.8120i	−0.725490	−	1.25659i	−0.958772	−	0.284177i	$-0.908280\pi$
$179$	−9.70640	−	16.8120i	−0.725490	−	1.25659i	0.233282	−	0.972409i	$-0.425054\pi$
$180$		0			0
$181$		−	0.0982851i		−	0.00730547i	−0.999993	−	0.00365274i	$-0.998837\pi$
$181$		−	0.0982851i		−	0.00730547i	0.999993	−	0.00365274i	$-0.00116270\pi$
$182$	5.48608	−	9.08131i	0.406655	−	0.673152i
$183$		0			0
$184$	2.64115	+	2.64115i	0.194708	+	0.194708i
$185$			18.8623i			1.38678i
$186$		0			0
$187$	−0.813216	+	3.03496i	−0.0594682	+	0.221938i
$188$	−1.63674	−	6.10838i	−0.119371	−	0.445499i
$189$		0			0
$190$	−11.3265	+	11.3265i	−0.821714	+	0.821714i
$191$			12.6972i			0.918735i	0.888246	+	0.459367i	$0.151924\pi$
$191$			12.6972i			0.918735i	−0.888246	+	0.459367i	$0.848076\pi$
$192$		0			0
$193$	16.7784	−	16.7784i	1.20774	−	1.20774i	0.235981	−	0.971758i	$-0.424170\pi$
$193$	16.7784	−	16.7784i	1.20774	−	1.20774i	0.971758	−	0.235981i	$-0.0758303\pi$
$194$	8.45787	−	14.6495i	0.607240	−	1.05177i
$195$		0			0
$196$	0.829510	+	1.43675i	0.0592507	+	0.102625i
$197$	−5.16169	−	1.38307i	−0.367755	−	0.0985397i	0.0702085	−	0.997532i	$-0.477634\pi$
$197$	−5.16169	−	1.38307i	−0.367755	−	0.0985397i	−0.437964	+	0.898993i	$0.644300\pi$
$198$		0			0
$199$	−7.44445	−	4.29806i	−0.527723	−	0.304681i	0.212366	−	0.977190i	$-0.431883\pi$
$199$	−7.44445	−	4.29806i	−0.527723	−	0.304681i	−0.740089	+	0.672509i	$0.765217\pi$
$200$	4.79601	+	1.28509i	0.339129	+	0.0908694i
$201$		0			0
$202$	−4.98674	−	1.33619i	−0.350866	−	0.0940142i
$203$	24.4427	−	6.54940i	1.71554	−	0.459678i
$204$		0			0
$205$	−29.8649	−	17.2425i	−2.08585	−	1.20427i
$206$	−2.38843	+	8.91374i	−0.166410	+	0.621050i
$207$		0			0
$208$	3.08613	+	1.86435i	0.213985	+	0.129269i
$209$	−3.83351	+	2.21328i	−0.265169	+	0.153096i
$210$		0			0
$211$	−9.74147			−0.670630			−0.335315	−	0.942106i	$-0.608843\pi$
$211$	−9.74147			−0.670630			−0.335315	+	0.942106i	$0.608843\pi$
$212$	−3.36550	−	5.82922i	−0.231144	−	0.400352i
$213$		0			0
$214$	0.171821	+	0.171821i	0.0117454	+	0.0117454i
$215$	19.3191	−	5.17655i	1.31755	−	0.353038i
$216$		0			0
$217$	7.56446	−	13.1020i	0.513509	−	0.889424i
$218$	−2.03627	+	3.52692i	−0.137913	+	0.238873i
$219$		0			0
$220$	2.38490	+	1.37692i	0.160790	+	0.0928321i
$221$	−11.1155	−	6.71492i	−0.747706	−	0.451694i
$222$		0			0
$223$	−18.3352	+	4.91290i	−1.22782	+	0.328992i	−0.813729	−	0.581245i	$-0.802566\pi$
$223$	−18.3352	+	4.91290i	−1.22782	+	0.328992i	−0.414087	+	0.910237i	$0.635899\pi$
$224$	−2.54838	+	1.47131i	−0.170271	+	0.0983061i
$225$		0			0
$226$	−2.16156	−	2.16156i	−0.143785	−	0.143785i
$227$	10.9382	−	10.9382i	0.725991	−	0.725991i	−0.243827	−	0.969819i	$-0.578403\pi$
$227$	10.9382	−	10.9382i	0.725991	−	0.725991i	0.969819	+	0.243827i	$0.0784030\pi$
$228$		0			0
$229$	3.92348	+	14.6426i	0.259271	+	0.967612i	0.965664	+	0.259792i	$0.0836542\pi$
$229$	3.92348	+	14.6426i	0.259271	+	0.967612i	−0.706394	+	0.707819i	$0.749679\pi$
$230$	−10.2113	+	5.89551i	−0.673314	+	0.388738i
$231$		0			0
$232$	2.22570	+	8.30644i	0.146125	+	0.545344i
$233$	−11.5129			−0.754237			−0.377118	−	0.926165i	$-0.623085\pi$
$233$	−11.5129			−0.754237			−0.377118	+	0.926165i	$0.623085\pi$
$234$		0			0
$235$	19.9630			1.30224
$236$	−1.42714	−	5.32616i	−0.0928989	−	0.346704i
$237$		0			0
$238$	9.17863	−	5.29929i	0.594963	−	0.343502i
$239$	−1.04280	−	3.89177i	−0.0674528	−	0.251737i	0.923963	−	0.382481i	$-0.124930\pi$
$239$	−1.04280	−	3.89177i	−0.0674528	−	0.251737i	−0.991416	+	0.130743i	$0.958264\pi$
$240$		0			0
$241$	10.4725	−	10.4725i	0.674591	−	0.674591i	−0.284180	−	0.958771i	$-0.591721\pi$
$241$	10.4725	−	10.4725i	0.674591	−	0.674591i	0.958771	+	0.284180i	$0.0917212\pi$
$242$	−7.24006	−	7.24006i	−0.465408	−	0.465408i
$243$		0			0
$244$	−5.51569	+	3.18449i	−0.353106	+	0.203866i
$245$	−5.05869	+	1.35547i	−0.323188	+	0.0865980i
$246$		0			0
$247$	−4.38376	−	17.7624i	−0.278932	−	1.13019i
$248$	4.45251	+	2.57066i	0.282734	+	0.163237i
$249$		0			0
$250$	0.0549375	−	0.0951545i	0.00347455	−	0.00601810i
$251$	1.98281	−	3.43432i	0.125154	−	0.216772i	−0.796639	−	0.604455i	$-0.793391\pi$
$251$	1.98281	−	3.43432i	0.125154	−	0.216772i	0.921793	+	0.387682i	$0.126724\pi$
$252$		0			0
$253$	−3.14737	+	0.843337i	−0.197874	+	0.0530201i
$254$	13.5193	+	13.5193i	0.848276	+	0.848276i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.8559			0.864307			0.432153	−	0.901800i	$-0.357754\pi$
$257$	13.8559			0.864307			0.432153	+	0.901800i	$0.357754\pi$
$258$		0			0
$259$	15.2271	−	8.79137i	0.946165	−	0.546269i
$260$	−8.20625	+	7.88701i	−0.508930	+	0.489132i
$261$		0			0
$262$	−3.19690	+	11.9310i	−0.197505	+	0.737098i
$263$	−13.8744	−	8.01036i	−0.855529	−	0.493940i	0.00698346	−	0.999976i	$-0.497777\pi$
$263$	−13.8744	−	8.01036i	−0.855529	−	0.493940i	−0.862513	+	0.506036i	$0.831110\pi$
$264$		0			0
$265$	20.5242	−	5.49945i	1.26079	−	0.337828i
$266$	14.4227	+	3.86456i	0.884314	+	0.236951i
$267$		0			0
$268$	−7.99294	−	2.14170i	−0.488246	−	0.130825i
$269$	1.90561	+	1.10021i	0.116187	+	0.0670808i	0.556967	−	0.830534i	$-0.311965\pi$
$269$	1.90561	+	1.10021i	0.116187	+	0.0670808i	−0.440780	+	0.897615i	$0.645298\pi$
$270$		0			0
$271$	−5.96826	−	1.59919i	−0.362546	−	0.0971439i	0.0729474	−	0.997336i	$-0.476759\pi$
$271$	−5.96826	−	1.59919i	−0.362546	−	0.0971439i	−0.435494	+	0.900192i	$0.643426\pi$
$272$	1.80087	+	3.11920i	0.109194	+	0.189129i
$273$		0			0
$274$	−3.47648	+	6.02145i	−0.210022	+	0.363769i
$275$	−3.06279	+	3.06279i	−0.184693	+	0.184693i
$276$		0			0
$277$			20.4207i			1.22696i	0.789711	+	0.613479i	$0.210231\pi$
$277$			20.4207i			1.22696i	−0.789711	+	0.613479i	$0.789769\pi$
$278$	−4.01721	+	4.01721i	−0.240937	+	0.240937i
$279$		0			0
$280$	−2.40422	−	8.97266i	−0.143679	−	0.536219i
$281$	−5.37665	+	20.0659i	−0.320744	+	1.19703i	0.597777	+	0.801662i	$0.296051\pi$
$281$	−5.37665	+	20.0659i	−0.320744	+	1.19703i	−0.918521	+	0.395372i	$0.870616\pi$
$282$		0			0
$283$			24.1047i			1.43287i	0.697652	+	0.716436i	$0.254228\pi$
$283$			24.1047i			1.43287i	−0.697652	+	0.716436i	$0.745772\pi$
$284$	4.53482	+	4.53482i	0.269092	+	0.269092i
$285$		0			0
$286$	−2.75460	+	1.51834i	−0.162883	+	0.0897812i
$287$			32.1456i			1.89750i
$288$		0			0
$289$	2.01371	+	3.48785i	0.118454	+	0.205168i
$290$	−27.1465			−1.59410
$291$		0			0
$292$	−3.89522	+	14.5372i	−0.227951	+	0.850723i
$293$	0.671035	−	2.50434i	0.0392023	−	0.146305i	−0.943551	−	0.331228i	$-0.892537\pi$
$293$	0.671035	−	2.50434i	0.0392023	−	0.146305i	0.982753	+	0.184923i	$0.0592037\pi$
$294$		0			0
$295$	17.4066			1.01345
$296$	2.98760	+	5.17467i	0.173651	+	0.300772i
$297$		0			0
$298$		−	20.7830i		−	1.20393i
$299$	0.267101	−	13.4646i	0.0154468	−	0.778680i
$300$		0			0
$301$	−13.1832	−	13.1832i	−0.759867	−	0.759867i
$302$			7.37086i			0.424145i
$303$		0			0
$304$	−1.31331	+	4.90132i	−0.0753232	+	0.281110i
$305$	−5.20366	−	19.4203i	−0.297961	−	1.11200i
$306$		0			0
$307$	0.409589	−	0.409589i	0.0233765	−	0.0233765i	−0.695322	−	0.718698i	$-0.744738\pi$
$307$	0.409589	−	0.409589i	0.0233765	−	0.0233765i	0.718698	+	0.695322i	$0.244738\pi$
$308$		−	2.56703i		−	0.146270i
$309$		0			0
$310$	−11.4763	+	11.4763i	−0.651810	+	0.651810i
$311$	8.67641	−	15.0280i	0.491994	−	0.852159i	−0.507963	−	0.861379i	$-0.669602\pi$
$311$	8.67641	−	15.0280i	0.491994	−	0.852159i	0.999957	+	0.00921998i	$0.00293485\pi$
$312$		0			0
$313$	12.3328	+	21.3610i	0.697089	+	1.20739i	0.969471	+	0.245205i	$0.0788552\pi$
$313$	12.3328	+	21.3610i	0.697089	+	1.20739i	−0.272382	+	0.962189i	$0.587812\pi$
$314$	−10.0653	−	2.69700i	−0.568020	−	0.152200i
$315$		0			0
$316$	2.26329	+	1.30671i	0.127320	+	0.0735082i
$317$	−24.1300	−	6.46561i	−1.35528	−	0.363145i	−0.493196	−	0.869918i	$-0.664172\pi$
$317$	−24.1300	−	6.46561i	−1.35528	−	0.363145i	−0.862080	+	0.506773i	$0.830838\pi$
$318$		0			0
$319$	−7.24622	−	1.94162i	−0.405710	−	0.108710i
$320$	3.04921	−	0.817032i	0.170456	−	0.0456735i
$321$		0			0
$322$	9.51860	+	5.49557i	0.530451	+	0.306256i
$323$	4.73019	−	17.6533i	0.263195	−	0.982257i
$324$		0			0
$325$	−8.64188	−	15.6783i	−0.479365	−	0.869675i
$326$	−5.90679	+	3.41028i	−0.327147	+	0.188878i
$327$		0			0
$328$	−10.9241			−0.603185
$329$	−9.30436	−	16.1156i	−0.512966	−	0.888483i
$330$		0			0
$331$	22.7569	+	22.7569i	1.25083	+	1.25083i	0.955347	+	0.295486i	$0.0954817\pi$
$331$	22.7569	+	22.7569i	1.25083	+	1.25083i	0.295486	+	0.955347i	$0.404518\pi$
$332$	11.0800	−	2.96889i	0.608097	−	0.162939i
$333$		0			0
$334$	−6.88098	+	11.9182i	−0.376510	+	0.652135i
$335$	13.0610	−	22.6223i	0.713597	−	1.23599i
$336$		0			0
$337$	−25.7601	−	14.8726i	−1.40324	−	0.810161i	−0.408516	−	0.912751i	$-0.633954\pi$
$337$	−25.7601	−	14.8726i	−1.40324	−	0.810161i	−0.994724	+	0.102590i	$0.967287\pi$
$338$	−2.86400	−	12.6806i	−0.155781	−	0.689733i
$339$		0			0
$340$	−10.9825	+	2.94274i	−0.595608	+	0.159593i
$341$	−3.88419	+	2.24254i	−0.210341	+	0.121440i
$342$		0			0
$343$	−11.1132	−	11.1132i	−0.600058	−	0.600058i
$344$	4.48009	−	4.48009i	0.241550	−	0.241550i
$345$		0			0
$346$	−1.05082	−	3.92173i	−0.0564927	−	0.210833i
$347$	−29.4281	+	16.9903i	−1.57978	+	0.912088i	−0.584894	+	0.811110i	$0.698864\pi$
$347$	−29.4281	+	16.9903i	−1.57978	+	0.912088i	−0.994889	+	0.100978i	$0.967803\pi$
$348$		0			0
$349$	−2.12443	−	7.92850i	−0.113718	−	0.424403i	0.885469	−	0.464698i	$-0.153837\pi$
$349$	−2.12443	−	7.92850i	−0.113718	−	0.424403i	−0.999188	+	0.0402949i	$0.987170\pi$
$350$	14.6107			0.780974
$351$		0			0
$352$	0.872362			0.0464970
$353$	−4.06187	−	15.1591i	−0.216192	−	0.806838i	−0.985744	−	0.168254i	$-0.946187\pi$
$353$	−4.06187	−	15.1591i	−0.216192	−	0.806838i	0.769552	−	0.638584i	$-0.220479\pi$
$354$		0			0
$355$	−17.5327	+	10.1225i	−0.930539	+	0.537247i
$356$	2.10194	+	7.84455i	0.111403	+	0.415760i
$357$		0			0
$358$	13.7269	−	13.7269i	0.725490	−	0.725490i
$359$	−12.5155	−	12.5155i	−0.660544	−	0.660544i	0.294964	−	0.955508i	$-0.404692\pi$
$359$	−12.5155	−	12.5155i	−0.660544	−	0.660544i	−0.955508	+	0.294964i	$0.904692\pi$
$360$		0			0
$361$	5.84370	−	3.37386i	0.307563	−	0.177572i
$362$	0.0949361	−	0.0254381i	0.00498973	−	0.00133699i
$363$		0			0
$364$	10.1918	+	2.94873i	0.534194	+	0.154555i
$365$	−41.1443	−	23.7547i	−2.15359	−	1.24338i
$366$		0			0
$367$	−13.2121	+	22.8840i	−0.689666	+	1.19454i	0.282280	+	0.959332i	$0.408909\pi$
$367$	−13.2121	+	22.8840i	−0.689666	+	1.19454i	−0.971946	+	0.235204i	$0.924424\pi$
$368$	−1.86758	+	3.23474i	−0.0973541	+	0.168622i
$369$		0			0
$370$	−18.2196	+	4.88192i	−0.947191	+	0.253799i
$371$	−14.0055	−	14.0055i	−0.727130	−	0.727130i
$372$		0			0
$373$	−11.3495	−	19.6580i	−0.587656	−	1.01785i	−0.994539	−	0.104370i	$-0.966718\pi$
$373$	−11.3495	−	19.6580i	−0.587656	−	1.01785i	0.406883	−	0.913480i	$-0.366616\pi$
$374$	−3.14202			−0.162470
$375$		0			0
$376$	5.47662	−	3.16193i	0.282435	−	0.163064i
$377$	16.0324	−	26.5390i	0.825711	−	1.36683i
$378$		0			0
$379$	−2.62959	+	9.81377i	−0.135073	+	0.504100i	0.864924	+	0.501902i	$0.167366\pi$
$379$	−2.62959	+	9.81377i	−0.135073	+	0.504100i	−0.999998	+	0.00219770i	$0.999300\pi$
$380$	−13.8721	−	8.00907i	−0.711625	−	0.410857i
$381$		0			0
$382$	−12.2645	+	3.28627i	−0.627508	+	0.168140i
$383$	18.0806	+	4.84467i	0.923874	+	0.247551i	0.689240	−	0.724533i	$-0.257944\pi$
$383$	18.0806	+	4.84467i	0.923874	+	0.247551i	0.234633	+	0.972084i	$0.424611\pi$
$384$		0			0
$385$	7.82740	+	2.09735i	0.398921	+	0.106891i
$386$	20.5493	+	11.8641i	1.04593	+	0.603869i
$387$		0			0
$388$	16.3393	+	4.37811i	0.829505	+	0.222265i
$389$	10.9802	+	19.0182i	0.556716	+	0.964261i	0.997768	+	0.0667792i	$0.0212723\pi$
$389$	10.9802	+	19.0182i	0.556716	+	0.964261i	−0.441051	+	0.897482i	$0.645394\pi$
$390$		0			0
$391$	6.72653	−	11.6507i	0.340175	−	0.589201i
$392$	−1.17310	+	1.17310i	−0.0592507	+	0.0592507i
$393$		0			0
$394$		−	5.34378i		−	0.269216i
$395$	−5.83361	+	5.83361i	−0.293521	+	0.293521i
$396$		0			0
$397$	0.908301	+	3.38983i	0.0455863	+	0.170130i	0.984966	−	0.172748i	$-0.0552647\pi$
$397$	0.908301	+	3.38983i	0.0455863	+	0.170130i	−0.939380	+	0.342879i	$0.888598\pi$
$398$	2.22484	−	8.30321i	0.111521	−	0.416202i
$399$		0			0
$400$			4.96519i			0.248260i
$401$	1.78155	+	1.78155i	0.0889663	+	0.0889663i	0.750189	−	0.661223i	$-0.229962\pi$
$401$	1.78155	+	1.78155i	0.0889663	+	0.0889663i	−0.661223	+	0.750189i	$0.729962\pi$
$402$		0			0
$403$	−4.44172	−	17.9972i	−0.221258	−	0.896507i
$404$		−	5.16265i		−	0.256851i
$405$		0			0
$406$	12.6525	+	21.9147i	0.627932	+	1.08761i
$407$	−5.21253			−0.258375
$408$		0			0
$409$	4.46385	−	16.6593i	0.220723	−	0.823751i	−0.763350	−	0.645986i	$-0.776447\pi$
$409$	4.46385	−	16.6593i	0.220723	−	0.823751i	0.984073	−	0.177765i	$-0.0568867\pi$
$410$	8.92537	−	33.3099i	0.440793	−	1.64506i
$411$		0			0
$412$	−9.22818			−0.454640
$413$	−8.11288	−	14.0519i	−0.399209	−	0.691450i
$414$		0			0
$415$			36.2110i			1.77753i
$416$	−1.00208	+	3.46350i	−0.0491308	+	0.169812i
$417$		0			0
$418$	−3.13005	−	3.13005i	−0.153096	−	0.153096i
$419$			18.7654i			0.916750i	0.888759	+	0.458375i	$0.151568\pi$
$419$			18.7654i			0.916750i	−0.888759	+	0.458375i	$0.848432\pi$
$420$		0			0
$421$	6.19861	−	23.1335i	0.302102	−	1.12746i	−0.633310	−	0.773898i	$-0.718304\pi$
$421$	6.19861	−	23.1335i	0.302102	−	1.12746i	0.935412	−	0.353560i	$-0.115029\pi$
$422$	−2.52128	−	9.40954i	−0.122734	−	0.458049i
$423$		0			0
$424$	4.75954	−	4.75954i	0.231144	−	0.231144i
$425$		−	17.8834i		−	0.867471i
$426$		0			0
$427$	−13.2522	+	13.2522i	−0.641320	+	0.641320i
$428$	−0.121496	+	0.210437i	−0.00587271	+	0.0101718i
$429$		0			0
$430$	10.0003	+	17.3211i	0.482259	+	0.835296i
$431$	−0.739992	−	0.198280i	−0.0356441	−	0.00955082i	0.240953	−	0.970537i	$-0.422540\pi$
$431$	−0.739992	−	0.198280i	−0.0356441	−	0.00955082i	−0.276597	+	0.960986i	$0.589207\pi$
$432$		0			0
$433$	12.3652	+	7.13904i	0.594233	+	0.343080i	0.766769	−	0.641923i	$-0.221863\pi$
$433$	12.3652	+	7.13904i	0.594233	+	0.343080i	−0.172537	+	0.985003i	$0.555196\pi$
$434$	14.6134	+	3.91565i	0.701467	+	0.187957i
$435$		0			0
$436$	−3.93376	−	1.05405i	−0.188393	−	0.0504798i
$437$	18.3072	−	4.90539i	0.875751	−	0.234657i
$438$		0			0
$439$	−10.9885	−	6.34419i	−0.524451	−	0.302792i	0.214303	−	0.976767i	$-0.431252\pi$
$439$	−10.9885	−	6.34419i	−0.524451	−	0.302792i	−0.738754	+	0.673975i	$0.764585\pi$
$440$	−0.712747	+	2.66001i	−0.0339789	+	0.126811i
$441$		0			0
$442$	3.60922	−	12.4747i	0.171673	−	0.593359i
$443$	−9.00475	+	5.19889i	−0.427828	+	0.247007i	−0.698421	−	0.715687i	$-0.746114\pi$
$443$	−9.00475	+	5.19889i	−0.427828	+	0.247007i	0.270593	+	0.962694i	$0.412780\pi$
$444$		0			0
$445$	−25.6370			−1.21531
$446$	−9.49100	−	16.4389i	−0.449412	−	0.778404i
$447$		0			0
$448$	−2.08075	−	2.08075i	−0.0983061	−	0.0983061i
$449$	−8.91529	+	2.38885i	−0.420739	+	0.112737i	−0.462976	−	0.886371i	$-0.653218\pi$
$449$	−8.91529	+	2.38885i	−0.420739	+	0.112737i	0.0422369	+	0.999108i	$0.486552\pi$
$450$		0			0
$451$	4.76490	−	8.25305i	0.224370	−	0.388621i
$452$	1.52846	−	2.64736i	0.0718925	−	0.124521i
$453$		0			0
$454$	13.3965	+	7.73445i	0.628727	+	0.362996i
$455$	−17.3183	+	28.6676i	−0.811894	+	1.34396i
$456$		0			0
$457$	8.40882	−	2.25314i	0.393348	−	0.105397i	−0.0567231	−	0.998390i	$-0.518065\pi$
$457$	8.40882	−	2.25314i	0.393348	−	0.105397i	0.450071	+	0.892993i	$0.351399\pi$
$458$	−13.1282	+	7.57958i	−0.613441	+	0.354170i
$459$		0			0
$460$	−8.33750	−	8.33750i	−0.388738	−	0.388738i
$461$	−7.38995	+	7.38995i	−0.344184	+	0.344184i	−0.857938	−	0.513753i	$-0.828255\pi$
$461$	−7.38995	+	7.38995i	−0.344184	+	0.344184i	0.513753	+	0.857938i	$0.328255\pi$
$462$		0			0
$463$	−1.45201	−	5.41897i	−0.0674806	−	0.251841i	0.923943	−	0.382531i	$-0.124947\pi$
$463$	−1.45201	−	5.41897i	−0.0674806	−	0.251841i	−0.991423	+	0.130690i	$0.958281\pi$
$464$	−7.44735	+	4.29973i	−0.345734	+	0.199610i
$465$		0			0
$466$	−2.97976	−	11.1206i	−0.138035	−	0.515153i
$467$	11.8737			0.549447			0.274724	−	0.961523i	$-0.411414\pi$
$467$	11.8737			0.549447			0.274724	+	0.961523i	$0.411414\pi$
$468$		0			0
$469$	−24.3499			−1.12437
$470$	5.16680	+	19.2827i	0.238327	+	0.889447i
$471$		0			0
$472$	4.77531	−	2.75702i	0.219801	−	0.126902i
$473$	1.43052	+	5.33877i	0.0657754	+	0.245477i
$474$		0			0
$475$	17.8152	−	17.8152i	0.817417	−	0.817417i
$476$	7.49432	+	7.49432i	0.343502	+	0.343502i
$477$		0			0
$478$	3.48926	−	2.01453i	0.159595	−	0.0921423i
$479$	−30.3482	+	8.13177i	−1.38664	+	0.371550i	−0.873530	−	0.486771i	$-0.838175\pi$
$479$	−30.3482	+	8.13177i	−1.38664	+	0.371550i	−0.513113	+	0.858321i	$0.671508\pi$
$480$		0			0
$481$	5.98759	−	20.6951i	0.273011	−	0.943615i
$482$	12.8261	+	7.40516i	0.584213	+	0.337296i
$483$		0			0
$484$	5.11949	−	8.86722i	0.232704	−	0.403056i
$485$	−26.6995	+	46.2450i	−1.21236	+	2.09988i
$486$		0			0
$487$	−25.9413	+	6.95096i	−1.17551	+	0.314978i	−0.793145	−	0.609032i	$-0.791558\pi$
$487$	−25.9413	+	6.95096i	−1.17551	+	0.314978i	−0.382368	+	0.924010i	$0.624891\pi$
$488$	−4.50355	−	4.50355i	−0.203866	−	0.203866i
$489$		0			0
$490$	−2.61857	−	4.53550i	−0.118295	−	0.204893i
$491$	−2.67459			−0.120702			−0.0603512	−	0.998177i	$-0.519222\pi$
$491$	−2.67459			−0.120702			−0.0603512	+	0.998177i	$0.519222\pi$
$492$		0			0
$493$	26.8235	−	15.4865i	1.20807	−	0.697478i
$494$	16.0226	−	8.83164i	0.720889	−	0.397354i
$495$		0			0
$496$	−1.33067	+	4.96612i	−0.0597488	+	0.222986i
$497$	16.3433	+	9.43582i	0.733098	+	0.423254i
$498$		0			0
$499$	4.32098	−	1.15780i	0.193434	−	0.0518304i	−0.160802	−	0.986987i	$-0.551408\pi$
$499$	4.32098	−	1.15780i	0.193434	−	0.0518304i	0.354235	+	0.935156i	$0.384741\pi$
$500$	0.106131	+	0.0284377i	0.00474633	+	0.00127177i
$501$		0			0
$502$	3.83049	+	1.02638i	0.170963	+	0.0458094i
$503$	35.5709	+	20.5369i	1.58603	+	0.915694i	0.993952	+	0.109812i	$0.0350249\pi$
$503$	35.5709	+	20.5369i	1.58603	+	0.915694i	0.592076	+	0.805882i	$0.298308\pi$
$504$		0			0
$505$	15.7420	+	4.21805i	0.700509	+	0.187701i
$506$	−1.62920	−	2.82186i	−0.0724268	−	0.125447i
$507$		0			0
$508$	−9.55958	+	16.5577i	−0.424138	+	0.734628i
$509$	−6.73502	+	6.73502i	−0.298525	+	0.298525i	−0.840436	−	0.541911i	$-0.817701\pi$
$509$	−6.73502	+	6.73502i	−0.298525	+	0.298525i	0.541911	+	0.840436i	$0.317701\pi$
$510$		0			0
$511$			44.2864i			1.95911i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	3.58617	+	13.3838i	0.158179	+	0.590333i
$515$	7.53972	−	28.1386i	0.332240	−	1.23994i
$516$		0			0
$517$			5.51669i			0.242624i
$518$	12.4329	+	12.4329i	0.546269	+	0.546269i
$519$		0			0
$520$	−9.74220	−	5.88533i	−0.427224	−	0.258089i
$521$			8.13120i			0.356234i	0.984009	+	0.178117i	$0.0570006\pi$
$521$			8.13120i			0.356234i	−0.984009	+	0.178117i	$0.942999\pi$
$522$		0			0
$523$	18.9364	+	32.7988i	0.828031	+	1.43419i	0.899580	+	0.436755i	$0.143872\pi$
$523$	18.9364	+	32.7988i	0.828031	+	1.43419i	−0.0715491	+	0.997437i	$0.522794\pi$
$524$	−12.3519			−0.539593
$525$		0			0
$526$	4.14647	−	15.4748i	0.180795	−	0.674735i
$527$	4.79273	−	17.8867i	0.208775	−	0.779158i
$528$		0			0
$529$	−9.04865			−0.393419
$530$	10.6241	+	18.4015i	0.461482	+	0.799310i
$531$		0			0
$532$			14.9315i			0.647363i
$533$	27.2933	+	28.3981i	1.18221	+	1.23006i
$534$		0			0
$535$	−0.542398	−	0.542398i	−0.0234499	−	0.0234499i
$536$		−	8.27490i		−	0.357421i
$537$		0			0
$538$	−0.569509	+	2.12544i	−0.0245533	+	0.0916341i
$539$	−0.374580	−	1.39795i	−0.0161343	−	0.0602140i
$540$		0			0
$541$	−9.80824	+	9.80824i	−0.421689	+	0.421689i	−0.885785	−	0.464096i	$-0.846379\pi$
$541$	−9.80824	+	9.80824i	−0.421689	+	0.421689i	0.464096	+	0.885785i	$0.346379\pi$
$542$		−	6.17880i		−	0.265402i
$543$		0			0
$544$	−2.54682	+	2.54682i	−0.109194	+	0.109194i
$545$	6.42802	−	11.1337i	0.275346	−	0.476914i
$546$		0			0
$547$	−18.8226	−	32.6018i	−0.804798	−	1.39395i	−0.916427	−	0.400201i	$-0.868940\pi$
$547$	−18.8226	−	32.6018i	−0.804798	−	1.39395i	0.111629	−	0.993750i	$-0.464393\pi$
$548$	−6.71605	−	1.79956i	−0.286895	−	0.0768734i
$549$		0			0
$550$	−3.75114	−	2.16572i	−0.159949	−	0.0923467i
$551$	42.1487	+	11.2937i	1.79559	+	0.481128i
$552$		0			0
$553$	7.42827	+	1.99040i	0.315882	+	0.0846404i
$554$	−19.7248	+	5.28525i	−0.838028	+	0.224549i
$555$		0			0
$556$	−4.92006	−	2.84060i	−0.208657	−	0.120468i
$557$	−8.83844	+	32.9855i	−0.374497	+	1.39764i	0.479582	+	0.877497i	$0.340788\pi$
$557$	−8.83844	+	32.9855i	−0.374497	+	1.39764i	−0.854079	+	0.520143i	$0.825878\pi$
$558$		0			0
$559$	−22.8396	−	0.453073i	−0.966010	−	0.0191630i
$560$	8.04466	−	4.64459i	0.339949	−	0.196270i
$561$		0			0
$562$	−20.7738			−0.876290
$563$	14.7518	+	25.5508i	0.621713	+	1.07684i	0.989167	+	0.146796i	$0.0468962\pi$
$563$	14.7518	+	25.5508i	0.621713	+	1.07684i	−0.367454	+	0.930042i	$0.619770\pi$
$564$		0			0
$565$	6.82355	+	6.82355i	0.287069	+	0.287069i
$566$	−23.2833	+	6.23874i	−0.978670	+	0.262234i
$567$		0			0
$568$	−3.20660	+	5.55400i	−0.134546	+	0.233041i
$569$	−7.35978	+	12.7475i	−0.308538	+	0.534404i	−0.978043	−	0.208404i	$-0.933173\pi$
$569$	−7.35978	+	12.7475i	−0.308538	+	0.534404i	0.669505	+	0.742808i	$0.266506\pi$
$570$		0			0
$571$	−16.5923	−	9.57956i	−0.694365	−	0.400892i	0.110880	−	0.993834i	$-0.464633\pi$
$571$	−16.5923	−	9.57956i	−0.694365	−	0.400892i	−0.805245	+	0.592942i	$0.797966\pi$
$572$	−2.17955	−	2.26777i	−0.0911314	−	0.0948201i
$573$		0			0
$574$	−31.0503	+	8.31990i	−1.29601	+	0.347266i
$575$	16.0611	−	9.27287i	0.669794	−	0.386706i
$576$		0			0
$577$	0.887796	+	0.887796i	0.0369594	+	0.0369594i	0.725345	−	0.688386i	$-0.241680\pi$
$577$	0.887796	+	0.887796i	0.0369594	+	0.0369594i	−0.688386	+	0.725345i	$0.741680\pi$
$578$	−2.84782	+	2.84782i	−0.118454	+	0.118454i
$579$		0			0
$580$	−7.02603	−	26.2215i	−0.291740	−	1.08879i
$581$	29.2323	−	16.8773i	1.21276	−	0.700187i
$582$		0			0
$583$	1.51975	+	5.67179i	0.0629417	+	0.234902i
$584$	−15.0500			−0.622773
$585$		0			0
$586$	2.59268			0.107103
$587$	−2.59294	−	9.67698i	−0.107022	−	0.399412i	0.891545	−	0.452933i	$-0.149622\pi$
$587$	−2.59294	−	9.67698i	−0.107022	−	0.399412i	−0.998567	+	0.0535210i	$0.982956\pi$
$588$		0			0
$589$	22.5930	−	13.0441i	0.930928	−	0.537472i
$590$	4.50515	+	16.8135i	0.185474	+	0.692199i
$591$		0			0
$592$	−4.22510	+	4.22510i	−0.173651	+	0.173651i
$593$	26.1095	+	26.1095i	1.07219	+	1.07219i	0.997183	+	0.0750069i	$0.0238979\pi$
$593$	26.1095	+	26.1095i	1.07219	+	1.07219i	0.0750069	+	0.997183i	$0.476102\pi$
$594$		0			0
$595$	−28.9748	+	16.7286i	−1.18785	+	0.685807i
$596$	20.0748	−	5.37903i	0.822297	−	0.220334i
$597$		0			0
$598$	13.0750	−	3.22690i	0.534675	−	0.131958i
$599$	−6.17074	−	3.56268i	−0.252130	−	0.145567i	0.368609	−	0.929584i	$-0.379834\pi$
$599$	−6.17074	−	3.56268i	−0.252130	−	0.145567i	−0.620739	+	0.784017i	$0.713167\pi$
$600$		0			0
$601$	1.60598	−	2.78164i	0.0655092	−	0.113465i	−0.831411	−	0.555659i	$-0.812466\pi$
$601$	1.60598	−	2.78164i	0.0655092	−	0.113465i	0.896920	+	0.442193i	$0.145799\pi$
$602$	9.32193	−	16.1461i	0.379933	−	0.658064i
$603$		0			0
$604$	−7.11970	+	1.90772i	−0.289697	+	0.0776240i
$605$	22.8552	+	22.8552i	0.929196	+	0.929196i
$606$		0			0
$607$	20.6661	+	35.7948i	0.838812	+	1.45286i	0.890889	+	0.454222i	$0.150083\pi$
$607$	20.6661	+	35.7948i	0.838812	+	1.45286i	−0.0520768	+	0.998643i	$0.516584\pi$
$608$	−5.07422			−0.205787
$609$		0			0
$610$	17.4118	−	10.0527i	0.704982	−	0.407022i
$611$	−21.9027	−	6.33698i	−0.886088	−	0.256367i
$612$		0			0
$613$	5.73651	−	21.4090i	0.231695	−	0.864699i	−0.747915	−	0.663794i	$-0.768945\pi$
$613$	5.73651	−	21.4090i	0.231695	−	0.864699i	0.979611	−	0.200905i	$-0.0643883\pi$
$614$	0.501642	+	0.289623i	0.0202446	+	0.0116882i
$615$		0			0
$616$	2.47956	−	0.664396i	0.0999043	−	0.0267693i
$617$	21.5609	+	5.77723i	0.868010	+	0.232583i	0.665227	−	0.746641i	$-0.268335\pi$
$617$	21.5609	+	5.77723i	0.868010	+	0.232583i	0.202783	+	0.979224i	$0.435001\pi$
$618$		0			0
$619$	16.0700	+	4.30594i	0.645907	+	0.173070i	0.566878	−	0.823802i	$-0.308151\pi$
$619$	16.0700	+	4.30594i	0.645907	+	0.173070i	0.0790293	+	0.996872i	$0.474818\pi$
$620$	−14.0555	−	8.11497i	−0.564484	−	0.325905i
$621$		0			0
$622$	16.7615	+	4.49124i	0.672076	+	0.180082i
$623$	11.9489	+	20.6961i	0.478723	+	0.829173i
$624$		0			0
$625$	−12.5864	+	21.8003i	−0.503456	+	0.872012i
$626$	−17.4412	+	17.4412i	−0.697089	+	0.697089i
$627$		0			0
$628$		−	10.4204i		−	0.415819i
$629$	15.2177	−	15.2177i	0.606771	−	0.606771i
$630$		0			0
$631$	−3.53536	−	13.1942i	−0.140741	−	0.525251i	−0.999908	−	0.0135565i	$-0.995685\pi$
$631$	−3.53536	−	13.1942i	−0.140741	−	0.525251i	0.859168	−	0.511694i	$-0.170982\pi$
$632$	−0.676403	+	2.52437i	−0.0269059	+	0.100414i
$633$		0			0
$634$		−	24.9812i		−	0.992131i
$635$	−42.6773	−	42.6773i	−1.69360	−	1.69360i
$636$		0			0
$637$	5.98051	+	0.118637i	0.236956	+	0.00470055i
$638$		−	7.50184i		−	0.297000i
$639$		0			0
$640$	1.57838	+	2.73384i	0.0623911	+	0.108065i
$641$	22.1785			0.876000			0.438000	−	0.898975i	$-0.355687\pi$
$641$	22.1785			0.876000			0.438000	+	0.898975i	$0.355687\pi$
$642$		0			0
$643$	2.39351	−	8.93270i	0.0943908	−	0.352271i	−0.902536	−	0.430615i	$-0.858297\pi$
$643$	2.39351	−	8.93270i	0.0943908	−	0.352271i	0.996926	+	0.0783440i	$0.0249632\pi$
$644$	−2.84471	+	10.6166i	−0.112097	+	0.418353i
$645$		0			0
$646$	18.2761			0.719062
$647$	−8.23841	−	14.2694i	−0.323886	−	0.560986i	0.657401	−	0.753541i	$-0.271656\pi$
$647$	−8.23841	−	14.2694i	−0.323886	−	0.560986i	−0.981286	+	0.192555i	$0.938323\pi$
$648$		0			0
$649$			4.81024i			0.188819i
$650$	12.9074	−	12.4053i	0.506269	−	0.486574i
$651$		0			0
$652$	−4.82287	−	4.82287i	−0.188878	−	0.188878i
$653$		−	33.8732i		−	1.32556i	−0.748813	−	0.662781i	$-0.769376\pi$
$653$		−	33.8732i		−	1.32556i	0.748813	−	0.662781i	$-0.230624\pi$
$654$		0			0
$655$	10.0919	−	37.6633i	0.394322	−	1.47163i
$656$	−2.82738	−	10.5519i	−0.110390	−	0.411983i
$657$		0			0
$658$	13.1584	−	13.1584i	0.512966	−	0.512966i
$659$			9.62356i			0.374881i	0.982276	+	0.187440i	$0.0600191\pi$
$659$			9.62356i			0.374881i	−0.982276	+	0.187440i	$0.939981\pi$
$660$		0			0
$661$	18.6266	−	18.6266i	0.724492	−	0.724492i	−0.245025	−	0.969517i	$-0.578796\pi$
$661$	18.6266	−	18.6266i	0.724492	−	0.724492i	0.969517	+	0.245025i	$0.0787961\pi$
$662$	−16.0916	+	27.8714i	−0.625417	+	1.08325i
$663$		0			0
$664$	5.73546	+	9.93410i	0.222579	+	0.385518i
$665$	−45.5292	−	12.1995i	−1.76555	−	0.473077i
$666$		0			0
$667$	27.8170	+	16.0601i	1.07708	+	0.621851i
$668$	−13.2930	−	3.56186i	−0.514323	−	0.137812i
$669$		0			0
$670$	25.2319	+	6.76086i	0.974792	+	0.261195i
$671$	5.36673	−	1.43801i	0.207180	−	0.0555138i
$672$		0			0
$673$	4.64587	+	2.68230i	0.179085	+	0.103395i	0.586863	−	0.809686i	$-0.300363\pi$
$673$	4.64587	+	2.68230i	0.179085	+	0.103395i	−0.407778	+	0.913081i	$0.633696\pi$
$674$	7.69861	−	28.7316i	0.296539	−	1.10670i
$675$		0			0
$676$	11.5073	−	6.04839i	0.442587	−	0.232631i
$677$	6.42329	−	3.70849i	0.246867	−	0.142529i	−0.371462	−	0.928448i	$-0.621143\pi$
$677$	6.42329	−	3.70849i	0.246867	−	0.142529i	0.618329	+	0.785919i	$0.287810\pi$
$678$		0			0
$679$	49.7766			1.91025
$680$	−5.68494	−	9.84661i	−0.218008	−	0.377600i
$681$		0			0
$682$	−3.17143	−	3.17143i	−0.121440	−	0.121440i
$683$	17.3967	−	4.66144i	0.665668	−	0.178365i	0.0898653	−	0.995954i	$-0.471356\pi$
$683$	17.3967	−	4.66144i	0.665668	−	0.178365i	0.575803	+	0.817589i	$0.304690\pi$
$684$		0			0
$685$	10.9745	−	19.0083i	0.419312	−	0.726270i
$686$	7.85824	−	13.6109i	0.300029	−	0.519665i
$687$		0			0
$688$	5.48696	+	3.16790i	0.209188	+	0.120775i
$689$	−24.2642	−	0.481334i	−0.924393	−	0.0183374i
$690$		0			0
$691$	−15.3897	+	4.12366i	−0.585452	+	0.156871i	−0.539374	−	0.842066i	$-0.681339\pi$
$691$	−15.3897	+	4.12366i	−0.585452	+	0.156871i	−0.0460781	+	0.998938i	$0.514672\pi$
$692$	3.51613	−	2.03004i	0.133663	−	0.0771704i
$693$		0			0
$694$	−24.0279	−	24.0279i	−0.912088	−	0.912088i
$695$	12.6814	−	12.6814i	0.481034	−	0.481034i
$696$		0			0
$697$	10.1835	+	38.0053i	0.385727	+	1.43955i
$698$	7.10849	−	4.10409i	0.269060	−	0.155342i
$699$		0			0
$700$	3.78152	+	14.1128i	0.142928	+	0.533415i
$701$	−10.3675			−0.391576			−0.195788	−	0.980646i	$-0.562726\pi$
$701$	−10.3675			−0.391576			−0.195788	+	0.980646i	$0.562726\pi$
$702$		0			0
$703$	30.3195			1.14352
$704$	0.225784	+	0.842637i	0.00850955	+	0.0317581i
$705$		0			0
$706$	13.5913	−	7.84693i	0.511515	−	0.295323i
$707$	−3.93191	−	14.6741i	−0.147875	−	0.551876i
$708$		0			0
$709$	−16.2379	+	16.2379i	−0.609826	+	0.609826i	−0.942901	−	0.333074i	$-0.891914\pi$
$709$	−16.2379	+	16.2379i	−0.609826	+	0.609826i	0.333074	+	0.942901i	$0.391914\pi$
$710$	−14.3154	−	14.3154i	−0.537247	−	0.537247i
$711$		0			0
$712$	−7.03323	+	4.06064i	−0.263582	+	0.152179i
$713$	18.5492	−	4.97025i	0.694674	−	0.186137i
$714$		0			0
$715$	8.69565	−	4.79304i	0.325199	−	0.179250i
$716$	16.8120	+	9.70640i	0.628293	+	0.362745i
$717$		0			0
$718$	8.84981	−	15.3283i	0.330272	−	0.572048i
$719$	−25.3323	+	43.8768i	−0.944735	+	1.63633i	−0.188454	+	0.982082i	$0.560348\pi$
$719$	−25.3323	+	43.8768i	−0.944735	+	1.63633i	−0.756281	+	0.654247i	$0.772986\pi$
$720$		0			0
$721$	−26.2298	+	7.02824i	−0.976847	+	0.261745i
$722$	4.77136	+	4.77136i	0.177572	+	0.177572i
$723$		0			0
$724$	0.0491425	+	0.0851174i	0.00182637	+	0.00316336i
$725$	42.6980			1.58576
$726$		0			0
$727$	26.9809	−	15.5774i	1.00067	−	0.577734i	0.0922201	−	0.995739i	$-0.470604\pi$
$727$	26.9809	−	15.5774i	1.00067	−	0.577734i	0.908445	+	0.418004i	$0.137270\pi$
$728$	−0.210427	+	10.6077i	−0.00779894	+	0.393147i
$729$		0			0
$730$	12.2963	−	45.8905i	0.455107	−	1.69848i
$731$	−19.7626	−	11.4100i	−0.730948	−	0.422013i
$732$		0			0
$733$	−7.44254	+	1.99422i	−0.274896	+	0.0736583i	−0.393634	−	0.919267i	$-0.628782\pi$
$733$	−7.44254	+	1.99422i	−0.274896	+	0.0736583i	0.118737	+	0.992926i	$0.462115\pi$
$734$	−25.5238	−	6.83908i	−0.942101	−	0.252435i
$735$		0			0
$736$	−3.60788	−	0.966728i	−0.132988	−	0.0356341i
$737$	6.25158	+	3.60935i	0.230280	+	0.132952i
$738$		0			0
$739$	9.13725	+	2.44832i	0.336119	+	0.0900629i	0.422931	−	0.906162i	$-0.361001\pi$
$739$	9.13725	+	2.44832i	0.336119	+	0.0900629i	−0.0868119	+	0.996225i	$0.527668\pi$
$740$	−9.43115	−	16.3352i	−0.346696	−	0.600495i
$741$		0			0
$742$	9.90340	−	17.1532i	0.363565	−	0.629713i
$743$	−3.73934	+	3.73934i	−0.137183	+	0.137183i	−0.772364	−	0.635181i	$-0.780926\pi$
$743$	−3.73934	+	3.73934i	−0.137183	+	0.137183i	0.635181	+	0.772364i	$0.280926\pi$
$744$		0			0
$745$			65.6071i			2.40366i
$746$	16.0506	−	16.0506i	0.587656	−	0.587656i
$747$		0			0
$748$	−0.813216	−	3.03496i	−0.0297341	−	0.110969i
$749$	−0.185064	+	0.690667i	−0.00676208	+	0.0252364i
$750$		0			0
$751$			15.6205i			0.569999i	0.958528	+	0.284999i	$0.0919934\pi$
$751$			15.6205i			0.569999i	−0.958528	+	0.284999i	$0.908007\pi$
$752$	4.47164	+	4.47164i	0.163064	+	0.163064i
$753$		0			0
$754$	29.7842	+	8.61730i	1.08468	+	0.313824i
$755$		−	23.2681i		−	0.846813i
$756$		0			0
$757$	−2.81998	−	4.88435i	−0.102494	−	0.177525i	0.810218	−	0.586129i	$-0.199349\pi$
$757$	−2.81998	−	4.88435i	−0.102494	−	0.177525i	−0.912712	+	0.408604i	$0.866016\pi$
$758$	−10.1600			−0.369027
$759$		0			0
$760$	4.14580	−	15.4723i	0.150384	−	0.561241i
$761$	−4.74969	+	17.7261i	−0.172176	+	0.642571i	0.824839	+	0.565367i	$0.191266\pi$
$761$	−4.74969	+	17.7261i	−0.172176	+	0.642571i	−0.997015	+	0.0772030i	$0.975401\pi$
$762$		0			0
$763$	−11.9839			−0.433847
$764$	−6.34858	−	10.9961i	−0.229684	−	0.397824i
$765$		0			0
$766$			18.7184i			0.676323i
$767$	−19.0979	−	5.52549i	−0.689586	−	0.199514i
$768$		0			0
$769$	14.2488	+	14.2488i	0.513824	+	0.513824i	0.915696	−	0.401872i	$-0.131640\pi$
$769$	14.2488	+	14.2488i	0.513824	+	0.513824i	−0.401872	+	0.915696i	$0.631640\pi$
$770$			8.10352i			0.292031i
$771$		0			0
$772$	−6.14134	+	22.9198i	−0.221031	+	0.824901i
$773$	5.89523	+	22.0013i	0.212037	+	0.791331i	0.987189	+	0.159557i	$0.0510065\pi$
$773$	5.89523	+	22.0013i	0.212037	+	0.791331i	−0.775152	+	0.631774i	$0.782327\pi$
$774$		0			0
$775$	18.0507	−	18.0507i	0.648402	−	0.648402i
$776$			16.9157i			0.607240i
$777$		0			0
$778$	−15.5283	+	15.5283i	−0.556716	+	0.556716i
$779$	−27.7158	+	48.0051i	−0.993020	+	1.71996i
$780$		0			0
$781$	−2.79732	−	4.84510i	−0.100096	−	0.173371i
$782$	12.9947	+	3.48191i	0.464688	+	0.124513i
$783$		0			0
$784$	−1.43675	−	0.829510i	−0.0513126	−	0.0296254i
$785$	31.7740	+	8.51380i	1.13406	+	0.303871i
$786$		0			0
$787$	−53.7496	−	14.4022i	−1.91597	−	0.513382i	−0.991106	−	0.133078i	$-0.957514\pi$
$787$	−53.7496	−	14.4022i	−1.91597	−	0.513382i	−0.924862	−	0.380304i	$-0.875819\pi$
$788$	5.16169	−	1.38307i	0.183878	−	0.0492699i
$789$		0			0
$790$	−7.14468	−	4.12498i	−0.254196	−	0.146760i
$791$	2.32816	−	8.68882i	0.0827799	−	0.308939i
$792$		0			0
$793$	−0.455446	+	22.9592i	−0.0161734	+	0.815303i
$794$	−3.03923	+	1.75470i	−0.107858	+	0.0622721i
$795$		0			0
$796$	8.59611			0.304681
$797$	6.64298	+	11.5060i	0.235306	+	0.407562i	0.959362	−	0.282179i	$-0.0910573\pi$
$797$	6.64298	+	11.5060i	0.235306	+	0.407562i	−0.724055	+	0.689742i	$0.757724\pi$
$798$		0			0
$799$	−16.1057	−	16.1057i	−0.569780	−	0.569780i
$800$	−4.79601	+	1.28509i	−0.169565	+	0.0454347i
$801$		0			0
$802$	−1.25974	+	2.18194i	−0.0444831	+	0.0770470i
$803$	6.56451	−	11.3701i	0.231657	−	0.401241i
$804$		0			0
$805$	−30.0480	−	17.3482i	−1.05905	−	0.611445i
$806$	16.2344	−	8.94841i	0.571833	−	0.315194i
$807$		0			0
$808$	4.98674	−	1.33619i	0.175433	−	0.0470071i
$809$	27.6216	−	15.9473i	0.971122	−	0.560678i	0.0715440	−	0.997437i	$-0.477207\pi$
$809$	27.6216	−	15.9473i	0.971122	−	0.560678i	0.899578	+	0.436760i	$0.143874\pi$
$810$		0			0
$811$	−3.25912	−	3.25912i	−0.114443	−	0.114443i	0.647566	−	0.762009i	$-0.275787\pi$
$811$	−3.25912	−	3.25912i	−0.114443	−	0.114443i	−0.762009	+	0.647566i	$0.775787\pi$
$812$	−17.8933	+	17.8933i	−0.627932	+	0.627932i
$813$		0			0
$814$	−1.34910	−	5.03492i	−0.0472860	−	0.176474i
$815$	18.6464	−	10.7655i	0.653154	−	0.377098i
$816$		0			0
$817$	−8.32084	−	31.0538i	−0.291109	−	1.08643i
$818$	17.2470			0.603027
$819$		0			0
$820$	34.4850			1.20427
$821$	−11.9877	−	44.7389i	−0.418375	−	1.56140i	−0.777978	−	0.628292i	$-0.783754\pi$
$821$	−11.9877	−	44.7389i	−0.418375	−	1.56140i	0.359603	−	0.933106i	$-0.382912\pi$
$822$		0			0
$823$	8.59314	−	4.96125i	0.299538	−	0.172938i	−0.342697	−	0.939446i	$-0.611341\pi$
$823$	8.59314	−	4.96125i	0.299538	−	0.172938i	0.642235	+	0.766508i	$0.278007\pi$
$824$	−2.38843	−	8.91374i	−0.0832049	−	0.310525i
$825$		0			0
$826$	11.4733	−	11.4733i	0.399209	−	0.399209i
$827$	16.5758	+	16.5758i	0.576398	+	0.576398i	0.933909	−	0.357511i	$-0.116375\pi$
$827$	16.5758	+	16.5758i	0.576398	+	0.576398i	−0.357511	+	0.933909i	$0.616375\pi$
$828$		0			0
$829$	−29.4031	+	16.9759i	−1.02121	+	0.589598i	−0.914455	−	0.404687i	$-0.867380\pi$
$829$	−29.4031	+	16.9759i	−1.02121	+	0.589598i	−0.106758	+	0.994285i	$0.534047\pi$
$830$	−34.9772	+	9.37210i	−1.21408	+	0.325310i
$831$		0			0
$832$	−3.60484	−	0.0715101i	−0.124975	−	0.00247917i
$833$	5.17482	+	2.98768i	0.179297	+	0.103517i
$834$		0			0
$835$	21.7217	−	37.6230i	0.751709	−	1.30200i
$836$	2.21328	−	3.83351i	0.0765478	−	0.132585i
$837$		0			0
$838$	−18.1260	+	4.85685i	−0.626152	+	0.167777i
$839$	−1.52746	−	1.52746i	−0.0527338	−	0.0527338i	0.680248	−	0.732982i	$-0.261872\pi$
$839$	−1.52746	−	1.52746i	−0.0527338	−	0.0527338i	−0.732982	+	0.680248i	$0.761872\pi$
$840$		0			0
$841$	22.4753	+	38.9284i	0.775011	+	1.34236i
$842$	23.9496			0.825357
$843$		0			0
$844$	8.43636	−	4.87073i	0.290391	−	0.167658i
$845$	9.04100	+	40.0297i	0.311020	+	1.37706i
$846$		0			0
$847$	7.79808	−	29.1028i	0.267945	−	0.999985i
$848$	5.82922	+	3.36550i	0.200176	+	0.115572i
$849$		0			0
$850$	17.2740	−	4.62856i	0.592493	−	0.158758i
$851$	21.5578	+	5.77639i	0.738991	+	0.198012i
$852$		0			0
$853$	−37.4530	−	10.0355i	−1.28237	−	0.343609i	−0.447611	−	0.894229i	$-0.647725\pi$
$853$	−37.4530	−	10.0355i	−1.28237	−	0.343609i	−0.834756	+	0.550619i	$0.814392\pi$
$854$	−16.2306	−	9.37074i	−0.555400	−	0.320660i
$855$		0			0
$856$	−0.234711	−	0.0628908i	−0.00802227	−	0.00214956i
$857$	9.92497	+	17.1906i	0.339031	+	0.587218i	0.984251	−	0.176779i	$-0.0565677\pi$
$857$	9.92497	+	17.1906i	0.339031	+	0.587218i	−0.645220	+	0.763997i	$0.723234\pi$
$858$		0			0
$859$	−6.14228	+	10.6387i	−0.209572	+	0.362989i	−0.951580	−	0.307402i	$-0.900540\pi$
$859$	−6.14228	+	10.6387i	−0.209572	+	0.362989i	0.742008	+	0.670391i	$0.233874\pi$
$860$	−14.1426	+	14.1426i	−0.482259	+	0.482259i
$861$		0			0
$862$		−	0.766096i		−	0.0260933i
$863$	−30.8583	+	30.8583i	−1.05043	+	1.05043i	−0.0517694	+	0.998659i	$0.516486\pi$
$863$	−30.8583	+	30.8583i	−1.05043	+	1.05043i	−0.998659	+	0.0517694i	$0.983514\pi$
$864$		0			0
$865$	3.31721	+	12.3800i	0.112789	+	0.420932i
$866$	−3.69544	+	13.7916i	−0.125576	+	0.468656i
$867$		0			0
$868$			15.1289i			0.513509i
$869$	−1.61210	−	1.61210i	−0.0546866	−	0.0546866i
$870$		0			0
$871$	−21.5112	+	20.6744i	−0.728879	+	0.700524i
$872$		−	4.07253i		−	0.137913i
$873$		0			0
$874$	9.47649	+	16.4138i	0.320547	+	0.555204i
$875$	0.323320			0.0109302
$876$		0			0
$877$	8.30313	−	30.9877i	0.280377	−	1.04638i	−0.671775	−	0.740755i	$-0.734468\pi$
$877$	8.30313	−	30.9877i	0.280377	−	1.04638i	0.952152	−	0.305626i	$-0.0988656\pi$
$878$	3.28400	−	12.2560i	0.110830	−	0.413621i
$879$		0			0
$880$	−2.75384			−0.0928321
$881$	−7.71084	−	13.3556i	−0.259785	−	0.449960i	0.706399	−	0.707813i	$-0.250318\pi$
$881$	−7.71084	−	13.3556i	−0.259785	−	0.449960i	−0.966184	+	0.257853i	$0.916985\pi$
$882$		0			0
$883$		−	37.0096i		−	1.24547i	−0.782432	−	0.622736i	$-0.786021\pi$
$883$		−	37.0096i		−	1.24547i	0.782432	−	0.622736i	$-0.213979\pi$
$884$	12.9837	+	0.257561i	0.436690	+	0.00866272i
$885$		0			0
$886$	−7.35234	−	7.35234i	−0.247007	−	0.247007i
$887$			8.80501i			0.295643i	0.989014	+	0.147822i	$0.0472262\pi$
$887$			8.80501i			0.295643i	−0.989014	+	0.147822i	$0.952774\pi$
$888$		0			0
$889$	−14.5613	+	54.3434i	−0.488369	+	1.82262i
$890$	−6.63534	−	24.7634i	−0.222417	−	0.830072i
$891$		0			0
$892$	13.4223	−	13.4223i	0.449412	−	0.449412i
$893$		−	32.0887i		−	1.07381i
$894$		0			0
$895$	−43.3327	+	43.3327i	−1.44845	+	1.44845i
$896$	1.47131	−	2.54838i	0.0491530	−	0.0851356i
$897$		0			0
$898$	−4.61489	−	7.99323i	−0.154001	−	0.266738i
$899$	42.7060	+	11.4430i	1.42432	+	0.381646i
$900$		0			0
$901$	−20.9954	−	12.1217i	−0.699457	−	0.403832i
$902$	9.20508	+	2.46649i	0.306496	+	0.0821253i
$903$		0			0
$904$	2.95275	+	0.791187i	0.0982070	+	0.0263145i
$905$	−0.299691	+	0.0803021i	−0.00996208	+	0.00266933i
$906$		0			0
$907$	−30.5565	−	17.6418i	−1.01461	−	0.585787i	−0.102074	−	0.994777i	$-0.532548\pi$
$907$	−30.5565	−	17.6418i	−1.01461	−	0.585787i	−0.912539	+	0.408990i	$0.865881\pi$
$908$	−4.00365	+	14.9418i	−0.132866	+	0.495861i
$909$		0			0
$910$	−32.1731	−	9.30845i	−1.06653	−	0.308572i
$911$	−28.0830	+	16.2137i	−0.930431	+	0.537185i	−0.886948	−	0.461870i	$-0.847179\pi$
$911$	−28.0830	+	16.2137i	−0.930431	+	0.537185i	−0.0434832	+	0.999054i	$0.513845\pi$
$912$		0			0
$913$	−10.0068			−0.331176
$914$	4.35273	+	7.53915i	0.143975	+	0.249373i
$915$		0			0
$916$	−10.7191	−	10.7191i	−0.354170	−	0.354170i
$917$	−35.1083	+	9.40725i	−1.15938	+	0.310655i
$918$		0			0
$919$	−14.7996	+	25.6336i	−0.488193	+	0.845575i	−0.999908	−	0.0135801i	$-0.995677\pi$
$919$	−14.7996	+	25.6336i	−0.488193	+	0.845575i	0.511715	+	0.859155i	$0.329011\pi$
$920$	5.89551	−	10.2113i	0.194369	−	0.336657i
$921$		0			0
$922$	−9.05081	−	5.22549i	−0.298072	−	0.172092i
$923$	22.4495	−	5.54055i	0.738936	−	0.182369i
$924$		0			0
$925$	28.6571	−	7.67864i	0.942239	−	0.252472i
$926$	4.85852	−	2.80507i	0.159661	−	0.0921802i
$927$		0			0
$928$	−6.08073	−	6.08073i	−0.199610	−	0.199610i
$929$	−16.5152	+	16.5152i	−0.541847	+	0.541847i	−0.924070	−	0.382223i	$-0.875159\pi$
$929$	−16.5152	+	16.5152i	−0.541847	+	0.541847i	0.382223	+	0.924070i	$0.375159\pi$
$930$		0			0
$931$	2.17880	+	8.13139i	0.0714073	+	0.266496i
$932$	9.97049	−	5.75646i	0.326594	−	0.188559i
$933$		0			0
$934$	3.07313	+	11.4691i	0.100556	+	0.375280i
$935$	9.91865			0.324374
$936$		0			0
$937$	13.0003			0.424700			0.212350	−	0.977194i	$-0.431888\pi$
$937$	13.0003			0.424700			0.212350	+	0.977194i	$0.431888\pi$
$938$	−6.30221	−	23.5202i	−0.205775	−	0.767961i
$939$		0			0
$940$	−17.2884	+	9.98148i	−0.563887	+	0.325560i
$941$	−8.01337	−	29.9063i	−0.261229	−	0.974918i	−0.964519	−	0.264015i	$-0.914953\pi$
$941$	−8.01337	−	29.9063i	−0.261229	−	0.974918i	0.703290	−	0.710903i	$-0.251714\pi$
$942$		0			0
$943$	−28.8523	+	28.8523i	−0.939560	+	0.939560i
$944$	3.89902	+	3.89902i	0.126902	+	0.126902i
$945$		0			0
$946$	−4.78661	+	2.76355i	−0.155626	+	0.0898509i
$947$	−19.8309	+	5.31368i	−0.644419	+	0.172671i	−0.566204	−	0.824265i	$-0.691589\pi$
$947$	−19.8309	+	5.31368i	−0.644419	+	0.172671i	−0.0782146	+	0.996937i	$0.524922\pi$
$948$		0			0
$949$	37.6015	+	39.1235i	1.22060	+	1.27000i
$950$	21.8191	+	12.5972i	0.707904	+	0.408709i
$951$		0			0
$952$	−5.29929	+	9.17863i	−0.171751	+	0.297481i
$953$	17.8354	−	30.8919i	0.577747	−	1.00069i	−0.417990	−	0.908451i	$-0.637265\pi$
$953$	17.8354	−	30.8919i	0.577747	−	1.00069i	0.995737	−	0.0922353i	$-0.0294012\pi$
$954$		0			0
$955$	38.7163	−	10.3740i	1.25283	−	0.335695i
$956$	2.84897	+	2.84897i	0.0921423	+	0.0921423i
$957$		0			0
$958$	−15.7094	−	27.2094i	−0.507547	−	0.879096i
$959$	−20.4599			−0.660686
$960$		0			0
$961$	−3.95508	+	2.28347i	−0.127583	+	0.0736602i
$962$	21.5396	+	0.427286i	0.694466	+	0.0137763i
$963$		0			0
$964$	−3.83319	+	14.3057i	−0.123459	+	0.460754i
$965$	−64.8694	−	37.4524i	−2.08822	−	1.20563i
$966$		0			0
$967$	35.4997	−	9.51213i	1.14159	−	0.305889i	0.362003	−	0.932177i	$-0.382093\pi$
$967$	35.4997	−	9.51213i	1.14159	−	0.305889i	0.779592	+	0.626288i	$0.215426\pi$
$968$	9.89010	+	2.65004i	0.317880	+	0.0851757i
$969$		0			0
$970$	−51.5796	−	13.8207i	−1.65612	−	0.443756i
$971$	−2.23727	−	1.29169i	−0.0717976	−	0.0414523i	0.463671	−	0.886007i	$-0.346532\pi$
$971$	−2.23727	−	1.29169i	−0.0717976	−	0.0414523i	−0.535469	+	0.844555i	$0.679865\pi$
$972$		0			0
$973$	−16.1480	−	4.32684i	−0.517680	−	0.138712i
$974$	−13.4282	−	23.2584i	−0.430268	−	0.745246i
$975$		0			0
$976$	3.18449	−	5.51569i	0.101933	−	0.176553i
$977$	−22.2793	+	22.2793i	−0.712777	+	0.712777i	−0.967115	−	0.254339i	$-0.918142\pi$
$977$	−22.2793	+	22.2793i	−0.712777	+	0.712777i	0.254339	+	0.967115i	$0.418142\pi$
$978$		0			0
$979$		−	7.08469i		−	0.226428i
$980$	3.70322	−	3.70322i	0.118295	−	0.118295i
$981$		0			0
$982$	−0.692234	−	2.58345i	−0.0220901	−	0.0824413i
$983$	−6.89232	+	25.7225i	−0.219831	+	0.820420i	0.764579	+	0.644530i	$0.222947\pi$
$983$	−6.89232	+	25.7225i	−0.219831	+	0.820420i	−0.984410	+	0.175890i	$0.943720\pi$
$984$		0			0
$985$			16.8691i			0.537493i
$986$	21.9013	+	21.9013i	0.697478	+	0.697478i
$987$		0			0
$988$	12.6777	+	13.1908i	0.403330	+	0.419656i
$989$		−	23.6652i		−	0.752508i
$990$		0			0
$991$	−12.7440	−	22.0732i	−0.404826	−	0.701179i	0.589475	−	0.807787i	$-0.299335\pi$
$991$	−12.7440	−	22.0732i	−0.404826	−	0.701179i	−0.994301	+	0.106607i	$0.966001\pi$
$992$	−5.14131			−0.163237
$993$		0			0
$994$	−4.88434	+	18.2286i	−0.154922	+	0.578176i
$995$	−7.02330	+	26.2113i	−0.222654	+	0.830954i
$996$		0			0
$997$	6.42015			0.203328			0.101664	−	0.994819i	$-0.467583\pi$
$997$	6.42015			0.203328			0.101664	+	0.994819i	$0.467583\pi$
$998$	2.23670	+	3.87408i	0.0708016	+	0.122632i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bc.a.557.8		56
3.2	odd	2		234.2.z.a.167.2	yes	56
9.2	odd	6		702.2.bb.a.89.1		56
9.7	even	3		234.2.y.a.11.11	✓	56
13.6	odd	12		702.2.bb.a.71.1		56
39.32	even	12		234.2.y.a.149.11	yes	56
117.97	odd	12		234.2.z.a.227.2	yes	56
117.110	even	12	inner	702.2.bc.a.305.8		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.11	✓	56	9.7	even	3
234.2.y.a.149.11	yes	56	39.32	even	12
234.2.z.a.167.2	yes	56	3.2	odd	2
234.2.z.a.227.2	yes	56	117.97	odd	12
702.2.bb.a.71.1		56	13.6	odd	12
702.2.bb.a.89.1		56	9.2	odd	6
702.2.bc.a.305.8		56	117.110	even	12	inner
702.2.bc.a.557.8		56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.817032 - 3.04921i) q^{5} +(-2.08075 + 2.08075i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.73384 - 1.57838i) q^{10} +(0.842637 - 0.225784i) q^{11} +(-0.0715101 + 3.60484i) q^{13} +(-2.54838 - 1.47131i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.80087 + 3.11920i) q^{17} +(-4.90132 + 1.31331i) q^{19} +(2.23217 + 2.23217i) q^{20} +(0.436181 + 0.755487i) q^{22} -3.73515 q^{23} +(-4.29998 + 2.48260i) q^{25} +(-3.50052 + 0.863928i) q^{26} +(0.761606 - 2.84235i) q^{28} +(-7.44735 - 4.29973i) q^{29} +(-4.96612 + 1.33067i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-3.47902 - 0.932200i) q^{34} +(8.04466 + 4.64459i) q^{35} +(-5.77159 - 1.54649i) q^{37} +(-2.53711 - 4.39440i) q^{38} +(-1.57838 + 2.73384i) q^{40} +(7.72453 - 7.72453i) q^{41} +6.33580i q^{43} +(-0.616853 + 0.616853i) q^{44} +(-0.966728 - 3.60788i) q^{46} +(-1.63674 + 6.10838i) q^{47} -1.65902i q^{49} +(-3.51092 - 3.51092i) q^{50} +(-1.74049 - 3.15764i) q^{52} +6.73100i q^{53} +(-1.37692 - 2.38490i) q^{55} +2.94262 q^{56} +(2.22570 - 8.30644i) q^{58} +(-1.42714 + 5.32616i) q^{59} +6.36898 q^{61} +(-2.57066 - 4.45251i) q^{62} +1.00000i q^{64} +(11.0503 - 2.72722i) q^{65} +(5.85124 + 5.85124i) q^{67} -3.60175i q^{68} +(-2.40422 + 8.97266i) q^{70} +(-1.65986 - 6.19468i) q^{71} +(10.6419 - 10.6419i) q^{73} -5.97519i q^{74} +(3.58802 - 3.58802i) q^{76} +(-1.28351 + 2.22311i) q^{77} +(-1.30671 - 2.26329i) q^{79} +(-3.04921 - 0.817032i) q^{80} +(9.46058 + 5.46207i) q^{82} +(-11.0800 - 2.96889i) q^{83} +(10.9825 + 2.94274i) q^{85} +(-6.11991 + 1.63983i) q^{86} +(-0.755487 - 0.436181i) q^{88} +(2.10194 - 7.84455i) q^{89} +(-7.35197 - 7.64956i) q^{91} +(3.23474 - 1.86758i) q^{92} -6.32386 q^{94} +(8.00907 + 13.8721i) q^{95} +(-11.9612 - 11.9612i) q^{97} +(1.60249 - 0.429386i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) \) 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more