LMFDB - Embedded newform 294.2.m.b.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(25,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("294.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.m (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			151.1
Character	$\chi$	$=$	294.151
Dual form			294.2.m.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.826239 + 0.563320i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.365341 + 0.930874i) q^{4} +(-3.12319 + 0.963376i) q^{5} +(-0.222521 - 0.974928i) q^{6} +(-2.56883 - 0.633346i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.0747301 + 0.997204i) q^{9} +O(q^{10})$	\(q+(0.826239 + 0.563320i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.365341 + 0.930874i) q^{4} +(-3.12319 + 0.963376i) q^{5} +(-0.222521 - 0.974928i) q^{6} +(-2.56883 - 0.633346i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.0747301 + 0.997204i) q^{9} +(-3.12319 - 0.963376i) q^{10} +(-0.402312 + 5.36848i) q^{11} +(0.365341 - 0.930874i) q^{12} +(-4.97235 + 2.39456i) q^{13} +(-1.76569 - 1.97037i) q^{14} +(2.94472 + 1.41810i) q^{15} +(-0.733052 + 0.680173i) q^{16} +(7.74318 - 1.16710i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.78794 - 4.82885i) q^{19} +(-2.03781 - 2.55533i) q^{20} +(1.45230 + 2.21152i) q^{21} +(-3.35658 + 4.20902i) q^{22} +(-1.63260 - 0.246074i) q^{23} +(0.826239 - 0.563320i) q^{24} +(4.69503 - 3.20101i) q^{25} +(-5.45725 - 0.822549i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-0.348932 - 2.62264i) q^{28} +(-1.04749 - 1.31351i) q^{29} +(1.63420 + 2.83051i) q^{30} +(-0.881015 + 1.52596i) q^{31} +(-0.988831 + 0.149042i) q^{32} +(3.94641 - 3.66173i) q^{33} +(7.05516 + 3.39759i) q^{34} +(8.63308 - 0.496687i) q^{35} +(-0.900969 + 0.433884i) q^{36} +(-0.104426 + 0.266074i) q^{37} +(0.416685 - 5.56028i) q^{38} +(5.27371 + 1.62672i) q^{39} +(-0.244247 - 3.25926i) q^{40} +(-1.60682 + 7.03994i) q^{41} +(-0.0458492 + 2.64535i) q^{42} +(-0.367365 - 1.60953i) q^{43} +(-5.14436 + 1.58682i) q^{44} +(-1.19408 - 3.04246i) q^{45} +(-1.21030 - 1.12299i) q^{46} +(0.818587 + 0.558103i) q^{47} +1.00000 q^{48} +(6.19774 + 3.25391i) q^{49} +5.68241 q^{50} +(-6.46998 - 4.41116i) q^{51} +(-4.04564 - 3.75380i) q^{52} +(2.62684 + 6.69307i) q^{53} +(0.955573 - 0.294755i) q^{54} +(-3.91537 - 17.1544i) q^{55} +(1.18908 - 2.36349i) q^{56} +(-1.24075 + 5.43607i) q^{57} +(-0.125550 - 1.67535i) q^{58} +(-5.68241 - 1.75279i) q^{59} +(-0.244247 + 3.25926i) q^{60} +(-4.56195 + 11.6237i) q^{61} +(-1.58753 + 0.764516i) q^{62} +(0.439607 - 2.60897i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(13.2227 - 12.2689i) q^{65} +(5.32341 - 0.802374i) q^{66} +(3.25130 - 5.63141i) q^{67} +(3.91532 + 6.78153i) q^{68} +(1.02941 + 1.29083i) q^{69} +(7.41278 + 4.45281i) q^{70} +(-1.76171 + 2.20912i) q^{71} +(-0.988831 - 0.149042i) q^{72} +(5.78254 - 3.94247i) q^{73} +(-0.236166 + 0.161015i) q^{74} +(-5.61894 - 0.846919i) q^{75} +(3.47650 - 4.35939i) q^{76} +(4.43358 - 13.5359i) q^{77} +(3.44097 + 4.31485i) q^{78} +(2.69706 + 4.67145i) q^{79} +(1.63420 - 2.83051i) q^{80} +(-0.988831 + 0.149042i) q^{81} +(-5.29336 + 4.91152i) q^{82} +(-1.29112 - 0.621772i) q^{83} +(-1.52806 + 2.15987i) q^{84} +(-23.0591 + 11.1047i) q^{85} +(0.603149 - 1.53680i) q^{86} +(-0.125550 + 1.67535i) q^{87} +(-5.14436 - 1.58682i) q^{88} +(0.926649 + 12.3653i) q^{89} +(0.727286 - 3.18645i) q^{90} +(14.2897 - 3.00199i) q^{91} +(-0.367390 - 1.60964i) q^{92} +(1.68375 - 0.519367i) q^{93} +(0.361958 + 0.922253i) q^{94} +(13.3592 + 12.3956i) q^{95} +(0.826239 + 0.563320i) q^{96} -18.6334 q^{97} +(3.28782 + 6.17982i) q^{98} -5.38353 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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 $

$2$	0.826239	+	0.563320i	0.584239	+	0.398327i
$2$	0.826239	+	0.563320i	0.584239	+	0.398327i
$3$	−0.733052	−	0.680173i	−0.423228	−	0.392698i
$3$	−0.733052	−	0.680173i	−0.423228	−	0.392698i
$4$	0.365341	+	0.930874i	0.182671	+	0.465437i
$5$	−3.12319	+	0.963376i	−1.39673	+	0.430835i	−0.899553	−	0.436812i	$-0.856107\pi$
$5$	−3.12319	+	0.963376i	−1.39673	+	0.430835i	−0.497180	+	0.867647i	$0.665631\pi$
$6$	−0.222521	−	0.974928i	−0.0908438	−	0.398013i
$7$	−2.56883	−	0.633346i	−0.970925	−	0.239382i
$7$	−2.56883	−	0.633346i	−0.970925	−	0.239382i
$8$	−0.222521	+	0.974928i	−0.0786730	+	0.344689i
$9$	0.0747301	+	0.997204i	0.0249100	+	0.332401i
$10$	−3.12319	−	0.963376i	−0.987639	−	0.304646i
$11$	−0.402312	+	5.36848i	−0.121302	+	1.61866i	0.521931	+	0.852988i	$0.325212\pi$
$11$	−0.402312	+	5.36848i	−0.121302	+	1.61866i	−0.643233	+	0.765671i	$0.722407\pi$
$12$	0.365341	−	0.930874i	0.105465	−	0.268720i
$13$	−4.97235	+	2.39456i	−1.37908	+	0.664131i	−0.968804	−	0.247829i	$-0.920283\pi$
$13$	−4.97235	+	2.39456i	−1.37908	+	0.664131i	−0.410279	+	0.911960i	$0.634569\pi$
$14$	−1.76569	−	1.97037i	−0.471900	−	0.526603i
$15$	2.94472	+	1.41810i	0.760324	+	0.366153i
$16$	−0.733052	+	0.680173i	−0.183263	+	0.170043i
$17$	7.74318	−	1.16710i	1.87800	−	0.283062i	0.892281	−	0.451480i	$-0.149104\pi$
$17$	7.74318	−	1.16710i	1.87800	−	0.283062i	0.985716	+	0.168418i	$0.0538658\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−2.78794	−	4.82885i	−0.639596	−	1.10781i	−0.985521	−	0.169551i	$-0.945768\pi$
$19$	−2.78794	−	4.82885i	−0.639596	−	1.10781i	0.345925	−	0.938262i	$-0.387565\pi$
$20$	−2.03781	−	2.55533i	−0.455668	−	0.571390i
$21$	1.45230	+	2.21152i	0.316918	+	0.482594i
$22$	−3.35658	+	4.20902i	−0.715625	+	0.897365i
$23$	−1.63260	−	0.246074i	−0.340420	−	0.0513101i	−0.0233924	−	0.999726i	$-0.507447\pi$
$23$	−1.63260	−	0.246074i	−0.340420	−	0.0513101i	−0.317028	+	0.948416i	$0.602685\pi$
$24$	0.826239	−	0.563320i	0.168655	−	0.114987i
$25$	4.69503	−	3.20101i	0.939005	−	0.640203i
$26$	−5.45725	−	0.822549i	−1.07026	−	0.161315i
$27$	0.623490	−	0.781831i	0.119991	−	0.150464i
$28$	−0.348932	−	2.62264i	−0.0659420	−	0.495633i
$29$	−1.04749	−	1.31351i	−0.194515	−	0.243914i	0.675004	−	0.737814i	$-0.264142\pi$
$29$	−1.04749	−	1.31351i	−0.194515	−	0.243914i	−0.869518	+	0.493901i	$0.835571\pi$
$30$	1.63420	+	2.83051i	0.298362	+	0.516779i
$31$	−0.881015	+	1.52596i	−0.158235	+	0.274071i	−0.934232	−	0.356665i	$-0.883914\pi$
$31$	−0.881015	+	1.52596i	−0.158235	+	0.274071i	0.775997	+	0.630736i	$0.217247\pi$
$32$	−0.988831	+	0.149042i	−0.174802	+	0.0263472i
$33$	3.94641	−	3.66173i	0.686982	−	0.637426i
$34$	7.05516	+	3.39759i	1.20995	+	0.582681i
$35$	8.63308	−	0.496687i	1.45926	−	0.0839554i
$36$	−0.900969	+	0.433884i	−0.150161	+	0.0723140i
$37$	−0.104426	+	0.266074i	−0.0171676	+	0.0437423i	−0.939201	−	0.343369i	$-0.888432\pi$
$37$	−0.104426	+	0.266074i	−0.0171676	+	0.0437423i	0.922033	+	0.387111i	$0.126527\pi$
$38$	0.416685	−	5.56028i	0.0675953	−	0.901997i
$39$	5.27371	+	1.62672i	0.844469	+	0.260484i
$40$	−0.244247	−	3.25926i	−0.0386189	−	0.515334i
$41$	−1.60682	+	7.03994i	−0.250943	+	1.09945i	0.679690	+	0.733500i	$0.262115\pi$
$41$	−1.60682	+	7.03994i	−0.250943	+	1.09945i	−0.930633	+	0.365954i	$0.880743\pi$
$42$	−0.0458492	+	2.64535i	−0.00707468	+	0.408187i
$43$	−0.367365	−	1.60953i	−0.0560226	−	0.245451i	0.939161	−	0.343476i	$-0.111605\pi$
$43$	−0.367365	−	1.60953i	−0.0560226	−	0.245451i	−0.995184	+	0.0980254i	$0.968747\pi$
$44$	−5.14436	+	1.58682i	−0.775541	+	0.239223i
$45$	−1.19408	−	3.04246i	−0.178003	−	0.453544i
$46$	−1.21030	−	1.12299i	−0.178448	−	0.165576i
$47$	0.818587	+	0.558103i	0.119403	+	0.0814077i	0.621549	−	0.783375i	$-0.286504\pi$
$47$	0.818587	+	0.558103i	0.119403	+	0.0814077i	−0.502146	+	0.864783i	$0.667456\pi$
$48$	1.00000			0.144338
$49$	6.19774	+	3.25391i	0.885392	+	0.464845i
$50$	5.68241			0.803614
$51$	−6.46998	−	4.41116i	−0.905978	−	0.617686i
$52$	−4.04564	−	3.75380i	−0.561029	−	0.520559i
$53$	2.62684	+	6.69307i	0.360824	+	0.919364i	0.989868	+	0.141994i	$0.0453514\pi$
$53$	2.62684	+	6.69307i	0.360824	+	0.919364i	−0.629044	+	0.777370i	$0.716553\pi$
$54$	0.955573	−	0.294755i	0.130037	−	0.0401111i
$55$	−3.91537	−	17.1544i	−0.527949	−	2.31309i
$56$	1.18908	−	2.36349i	0.158898	−	0.315834i
$57$	−1.24075	+	5.43607i	−0.164341	+	0.720025i
$58$	−0.125550	−	1.67535i	−0.0164855	−	0.219984i
$59$	−5.68241	−	1.75279i	−0.739786	−	0.228194i	−0.0981166	−	0.995175i	$-0.531282\pi$
$59$	−5.68241	−	1.75279i	−0.739786	−	0.228194i	−0.641670	+	0.766981i	$0.721758\pi$
$60$	−0.244247	+	3.25926i	−0.0315322	+	0.420768i
$61$	−4.56195	+	11.6237i	−0.584098	+	1.48826i	0.267235	+	0.963631i	$0.413890\pi$
$61$	−4.56195	+	11.6237i	−0.584098	+	1.48826i	−0.851333	+	0.524626i	$0.824205\pi$
$62$	−1.58753	+	0.764516i	−0.201617	+	0.0970936i
$63$	0.439607	−	2.60897i	0.0553852	−	0.328700i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	13.2227	−	12.2689i	1.64008	−	1.52177i
$66$	5.32341	−	0.802374i	0.655266	−	0.0987654i
$67$	3.25130	−	5.63141i	0.397209	−	0.687987i	−0.596171	−	0.802857i	$-0.703312\pi$
$67$	3.25130	−	5.63141i	0.397209	−	0.687987i	0.993380	+	0.114871i	$0.0366454\pi$
$68$	3.91532	+	6.78153i	0.474802	+	0.822382i
$69$	1.02941	+	1.29083i	0.123926	+	0.155398i
$70$	7.41278	+	4.45281i	0.885997	+	0.532212i
$71$	−1.76171	+	2.20912i	−0.209077	+	0.262174i	−0.875302	−	0.483576i	$-0.839338\pi$
$71$	−1.76171	+	2.20912i	−0.209077	+	0.262174i	0.666225	+	0.745751i	$0.267909\pi$
$72$	−0.988831	−	0.149042i	−0.116535	−	0.0175648i
$73$	5.78254	−	3.94247i	0.676795	−	0.461431i	−0.175509	−	0.984478i	$-0.556157\pi$
$73$	5.78254	−	3.94247i	0.676795	−	0.461431i	0.852304	+	0.523047i	$0.175205\pi$
$74$	−0.236166	+	0.161015i	−0.0274537	+	0.0187176i
$75$	−5.61894	−	0.846919i	−0.648819	−	0.0977938i
$76$	3.47650	−	4.35939i	0.398782	−	0.500057i
$77$	4.43358	−	13.5359i	0.505253	−	1.54256i
$78$	3.44097	+	4.31485i	0.389614	+	0.488560i
$79$	2.69706	+	4.67145i	0.303443	+	0.525579i	0.976914	−	0.213635i	$-0.0685303\pi$
$79$	2.69706	+	4.67145i	0.303443	+	0.525579i	−0.673470	+	0.739214i	$0.735197\pi$
$80$	1.63420	−	2.83051i	0.182709	−	0.316461i
$81$	−0.988831	+	0.149042i	−0.109870	+	0.0165603i
$82$	−5.29336	+	4.91152i	−0.584554	+	0.542387i
$83$	−1.29112	−	0.621772i	−0.141719	−	0.0682483i	0.361680	−	0.932302i	$-0.382203\pi$
$83$	−1.29112	−	0.621772i	−0.141719	−	0.0682483i	−0.503399	+	0.864054i	$0.667918\pi$
$84$	−1.52806	+	2.15987i	−0.166725	+	0.235661i
$85$	−23.0591	+	11.1047i	−2.50111	+	1.20447i
$86$	0.603149	−	1.53680i	0.0650393	−	0.165717i
$87$	−0.125550	+	1.67535i	−0.0134604	+	0.179616i
$88$	−5.14436	−	1.58682i	−0.548391	−	0.169156i
$89$	0.926649	+	12.3653i	0.0982246	+	1.31072i	0.800725	+	0.599032i	$0.204448\pi$
$89$	0.926649	+	12.3653i	0.0982246	+	1.31072i	−0.702500	+	0.711683i	$0.747933\pi$
$90$	0.727286	−	3.18645i	0.0766627	−	0.335881i
$91$	14.2897	−	3.00199i	1.49797	−	0.314694i
$92$	−0.367390	−	1.60964i	−0.0383031	−	0.167817i
$93$	1.68375	−	0.519367i	0.174596	−	0.0538559i
$94$	0.361958	+	0.922253i	0.0373331	+	0.0951231i
$95$	13.3592	+	12.3956i	1.37063	+	1.27176i
$96$	0.826239	+	0.563320i	0.0843276	+	0.0574936i
$97$	−18.6334			−1.89193			−0.945966	−	0.324266i	$-0.894883\pi$
$97$	−18.6334			−1.89193			−0.945966	+	0.324266i	$0.894883\pi$
$98$	3.28782	+	6.17982i	0.332120	+	0.624257i
$99$	−5.38353			−0.541066
$100$	4.69503	+	3.20101i	0.469503	+	0.320101i
$101$	8.63085	+	8.00826i	0.858802	+	0.796852i	0.980665	−	0.195695i	$-0.0626964\pi$
$101$	8.63085	+	8.00826i	0.858802	+	0.796852i	−0.121863	+	0.992547i	$0.538887\pi$
$102$	−2.86085	−	7.28934i	−0.283267	−	0.721752i
$103$	4.40695	−	1.35936i	0.434230	−	0.133942i	−0.0699312	−	0.997552i	$-0.522278\pi$
$103$	4.40695	−	1.35936i	0.434230	−	0.133942i	0.504161	+	0.863610i	$0.331802\pi$
$104$	−1.22807	−	5.38052i	−0.120422	−	0.527604i
$105$	−6.66633	−	5.50789i	−0.650567	−	0.537515i
$106$	−1.59995	+	7.00982i	−0.155401	+	0.680854i
$107$	−0.137284	−	1.83193i	−0.0132718	−	0.177100i	−0.999900	−	0.0141150i	$-0.995507\pi$
$107$	−0.137284	−	1.83193i	−0.0132718	−	0.177100i	0.986629	−	0.162985i	$-0.0521121\pi$
$108$	0.955573	+	0.294755i	0.0919500	+	0.0283628i
$109$	−0.346118	+	4.61862i	−0.0331521	+	0.442384i	0.955787	+	0.294060i	$0.0950067\pi$
$109$	−0.346118	+	4.61862i	−0.0331521	+	0.442384i	−0.988939	+	0.148323i	$0.952612\pi$
$110$	6.42837	−	16.3792i	0.612921	−	1.56170i
$111$	0.257526	−	0.124018i	0.0244433	−	0.0117713i
$112$	2.31387	−	1.28297i	0.218640	−	0.121229i
$113$	12.3366	+	5.94098i	1.16053	+	0.558880i	0.912179	−	0.409791i	$-0.134398\pi$
$113$	12.3366	+	5.94098i	1.16053	+	0.558880i	0.248347	+	0.968671i	$0.420113\pi$
$114$	−4.08740	+	3.79256i	−0.382820	+	0.355205i
$115$	5.33597	−	0.804268i	0.497582	−	0.0749984i
$116$	0.840024	−	1.45496i	0.0779943	−	0.135090i
$117$	−2.75945	−	4.77950i	−0.255111	−	0.441865i
$118$	−3.70764	−	4.64924i	−0.341316	−	0.427997i
$119$	−20.6301	−	1.90604i	−1.89115	−	0.174727i
$120$	−2.03781	+	2.55533i	−0.186026	+	0.233269i
$121$	−17.7816	−	2.68014i	−1.61651	−	0.243650i
$122$	−10.3171	+	7.03408i	−0.934067	+	0.636836i
$123$	5.96626	−	4.06773i	0.537960	−	0.366775i
$124$	−1.74235	−	0.262617i	−0.156468	−	0.0235837i
$125$	−1.39062	+	1.74378i	−0.124381	+	0.155968i
$126$	1.83291	−	1.90800i	0.163288	−	0.169978i
$127$	−5.35799	−	6.71871i	−0.475445	−	0.596189i	0.485050	−	0.874486i	$-0.338801\pi$
$127$	−5.35799	−	6.71871i	−0.475445	−	0.596189i	−0.960495	+	0.278297i	$0.910230\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.825461	+	1.42974i	−0.0726778	+	0.125882i
$130$	17.8365	−	2.68841i	1.56436	−	0.235789i
$131$	−14.0621	+	13.0478i	−1.22862	+	1.13999i	−0.243172	+	0.969983i	$0.578188\pi$
$131$	−14.0621	+	13.0478i	−1.22862	+	1.13999i	−0.985443	+	0.170005i	$0.945622\pi$
$132$	4.85040	+	2.33583i	0.422173	+	0.203308i
$133$	4.10339	+	14.1702i	0.355809	+	1.22871i
$134$	5.85864	−	2.82137i	0.506109	−	0.243729i
$135$	−1.19408	+	3.04246i	−0.102770	+	0.261854i
$136$	−0.585184	+	7.80874i	−0.0501792	+	0.669594i
$137$	−14.9874	−	4.62300i	−1.28046	−	0.394969i	−0.421414	−	0.906869i	$-0.638466\pi$
$137$	−14.9874	−	4.62300i	−1.28046	−	0.394969i	−0.859046	+	0.511899i	$0.828942\pi$
$138$	0.123382	+	1.64642i	0.0105030	+	0.140153i
$139$	1.30655	−	5.72437i	0.110820	−	0.485535i	−0.888808	−	0.458279i	$-0.848466\pi$
$139$	1.30655	−	5.72437i	0.110820	−	0.485535i	0.999628	−	0.0272556i	$-0.00867679\pi$
$140$	3.61637	+	7.85485i	0.305639	+	0.663856i
$141$	−0.220460	−	0.965899i	−0.0185661	−	0.0813434i
$142$	−2.70004	+	0.832851i	−0.226582	+	0.0698913i
$143$	−10.8547	−	27.6573i	−0.907716	−	2.31282i
$144$	−0.733052	−	0.680173i	−0.0610877	−	0.0566811i
$145$	4.53693	+	3.09323i	0.376771	+	0.256878i
$146$	6.99863			0.579211
$147$	−2.33004	−	6.60083i	−0.192179	−	0.544427i
$148$	−0.285832			−0.0234953
$149$	−14.8601	−	10.1314i	−1.21739	−	0.830001i	−0.227768	−	0.973715i	$-0.573143\pi$
$149$	−14.8601	−	10.1314i	−1.21739	−	0.830001i	−0.989619	+	0.143715i	$0.954095\pi$
$150$	−4.16550	−	3.86502i	−0.340112	−	0.315577i
$151$	−3.65029	−	9.30079i	−0.297057	−	0.756888i	−0.999002	−	0.0446574i	$-0.985780\pi$
$151$	−3.65029	−	9.30079i	−0.297057	−	0.756888i	0.701946	−	0.712230i	$-0.252315\pi$
$152$	5.32815	−	1.64352i	0.432170	−	0.133307i
$153$	1.74248	+	7.63431i	0.140871	+	0.617197i
$154$	11.2882	−	8.68636i	0.909632	−	0.699967i
$155$	1.28150	−	5.61462i	0.102933	−	0.450977i
$156$	0.412427	+	5.50346i	0.0330206	+	0.440630i
$157$	7.87316	+	2.42855i	0.628347	+	0.193819i	0.592542	−	0.805540i	$-0.298124\pi$
$157$	7.87316	+	2.42855i	0.628347	+	0.193819i	0.0358046	+	0.999359i	$0.488601\pi$
$158$	−0.403104	+	5.37904i	−0.0320692	+	0.427934i
$159$	2.62684	−	6.69307i	0.208322	−	0.530795i
$160$	2.94472	−	1.41810i	0.232801	−	0.112111i
$161$	4.03801	+	1.66612i	0.318240	+	0.131309i
$162$	−0.900969	−	0.433884i	−0.0707868	−	0.0340891i
$163$	6.01307	−	5.57931i	0.470980	−	0.437006i	−0.408631	−	0.912700i	$-0.633994\pi$
$163$	6.01307	−	5.57931i	0.470980	−	0.437006i	0.879611	+	0.475694i	$0.157803\pi$
$164$	−7.14033	+	1.07623i	−0.557566	+	0.0840396i
$165$	−8.79776	+	15.2382i	−0.684905	+	1.18629i
$166$	−0.716519	−	1.24105i	−0.0556127	−	0.0963240i
$167$	0.293383	+	0.367890i	0.0227026	+	0.0284682i	0.793053	−	0.609152i	$-0.208490\pi$
$167$	0.293383	+	0.367890i	0.0227026	+	0.0284682i	−0.770351	+	0.637621i	$0.779919\pi$
$168$	−2.47924	+	0.923777i	−0.191278	+	0.0712709i
$169$	10.8850	−	13.6494i	0.837308	−	1.04995i
$170$	−25.3078	−	3.81453i	−1.94102	−	0.292561i
$171$	4.60700	−	3.14100i	0.352306	−	0.240198i
$172$	1.36406	−	0.929997i	0.104008	−	0.0709116i
$173$	−3.29836	−	0.497147i	−0.250769	−	0.0377974i	0.0224545	−	0.999748i	$-0.492852\pi$
$173$	−3.29836	−	0.497147i	−0.250769	−	0.0377974i	−0.273224	+	0.961950i	$0.588090\pi$
$174$	−1.04749	+	1.31351i	−0.0794102	+	0.0995773i
$175$	−14.0881	+	5.24927i	−1.06496	+	0.396808i
$176$	−3.35658	−	4.20902i	−0.253012	−	0.317267i
$177$	2.97330	+	5.14990i	0.223487	+	0.387091i
$178$	−6.19997	+	10.7387i	−0.464707	+	0.804897i
$179$	4.44723	−	0.670312i	0.332401	−	0.0501015i	0.0192788	−	0.999814i	$-0.493863\pi$
$179$	4.44723	−	0.670312i	0.332401	−	0.0501015i	0.313123	+	0.949713i	$0.398625\pi$
$180$	2.39590	−	2.22307i	0.178580	−	0.165698i
$181$	10.4773	+	5.04560i	0.778771	+	0.375036i	0.780655	−	0.624962i	$-0.214885\pi$
$181$	10.4773	+	5.04560i	0.778771	+	0.375036i	−0.00188420	+	0.999998i	$0.500600\pi$
$182$	13.4978	+	5.56932i	1.00052	+	0.412825i
$183$	11.2502	−	5.41783i	0.831642	−	0.400498i
$184$	0.603192	−	1.53691i	0.0444679	−	0.113302i
$185$	0.0698139	−	0.931601i	0.00513282	−	0.0684927i
$186$	1.68375	+	0.519367i	0.123458	+	0.0380819i
$187$	3.15036	+	42.0386i	0.230377	+	3.07417i
$188$	−0.220460	+	0.965899i	−0.0160787	+	0.0704454i
$189$	−2.09681	+	1.61350i	−0.152520	+	0.117365i
$190$	4.05526	+	17.7672i	0.294199	+	1.28897i
$191$	−16.0842	+	4.96132i	−1.16381	+	0.358988i	−0.815706	−	0.578467i	$-0.803651\pi$
$191$	−16.0842	+	4.96132i	−1.16381	+	0.358988i	−0.348106	+	0.937455i	$0.613175\pi$
$192$	0.365341	+	0.930874i	0.0263662	+	0.0671800i
$193$	13.5107	+	12.5361i	0.972521	+	0.902368i	0.995248	−	0.0973739i	$-0.0310443\pi$
$193$	13.5107	+	12.5361i	0.972521	+	0.902368i	−0.0227267	+	0.999742i	$0.507235\pi$
$194$	−15.3956	−	10.4965i	−1.10534	−	0.753608i
$195$	−18.0379			−1.29172
$196$	−0.764693	+	6.95811i	−0.0546209	+	0.497008i
$197$	−3.77694			−0.269096			−0.134548	−	0.990907i	$-0.542958\pi$
$197$	−3.77694			−0.269096			−0.134548	+	0.990907i	$0.542958\pi$
$198$	−4.44809	−	3.03265i	−0.316112	−	0.215521i
$199$	−6.93366	−	6.43349i	−0.491514	−	0.456058i	0.395053	−	0.918658i	$-0.370726\pi$
$199$	−6.93366	−	6.43349i	−0.491514	−	0.456058i	−0.886567	+	0.462600i	$0.846917\pi$
$200$	2.07602	+	5.28960i	0.146797	+	0.374031i
$201$	−6.21370	+	1.91667i	−0.438281	+	0.135192i
$202$	2.61993	+	11.4787i	0.184338	+	0.807636i
$203$	1.85892	+	4.03762i	0.130471	+	0.283385i
$204$	1.74248	−	7.63431i	0.121998	−	0.534509i
$205$	−1.76371	−	23.5350i	−0.123183	−	1.64376i
$206$	4.40695	+	1.35936i	0.307047	+	0.0947114i
$207$	0.123382	−	1.64642i	0.00857566	−	0.114434i
$208$	2.01628	−	5.13739i	0.139804	−	0.356214i
$209$	27.0452	−	13.0243i	1.87076	−	0.900908i
$210$	−2.40528	−	8.30611i	−0.165980	−	0.573176i
$211$	−0.645240	−	0.310731i	−0.0444201	−	0.0213916i	0.411542	−	0.911391i	$-0.364990\pi$
$211$	−0.645240	−	0.310731i	−0.0444201	−	0.0213916i	−0.455962	+	0.889999i	$0.650705\pi$
$212$	−5.27071	+	4.89051i	−0.361994	+	0.335881i
$213$	2.79401	−	0.421129i	0.191442	−	0.0288553i
$214$	0.918536	−	1.59095i	0.0627898	−	0.108755i
$215$	2.69793	+	4.67296i	0.183997	+	0.318693i
$216$	0.623490	+	0.781831i	0.0424231	+	0.0531969i
$217$	3.22964	−	3.36195i	0.219242	−	0.228224i
$218$	−2.88774	+	3.62111i	−0.195582	+	0.245252i
$219$	−6.92046	−	1.04309i	−0.467641	−	0.0704856i
$220$	14.5381	−	9.91191i	0.980159	−	0.668261i
$221$	−35.7071	+	24.3447i	−2.40192	+	1.63760i
$222$	0.282640	+	0.0426011i	0.0189696	+	0.00285920i
$223$	14.1756	−	17.7756i	0.949266	−	1.19034i	−0.0323506	−	0.999477i	$-0.510299\pi$
$223$	14.1756	−	17.7756i	0.949266	−	1.19034i	0.981616	−	0.190865i	$-0.0611292\pi$
$224$	2.63453	+	0.243409i	0.176027	+	0.0162634i
$225$	3.54292	+	4.44268i	0.236195	+	0.296179i
$226$	6.84628	+	11.8581i	0.455408	+	0.788789i
$227$	0.111114	−	0.192456i	0.00737491	−	0.0127737i	−0.862314	−	0.506373i	$-0.830986\pi$
$227$	0.111114	−	0.192456i	0.00737491	−	0.0127737i	0.869689	+	0.493600i	$0.164319\pi$
$228$	−5.51359	+	0.831041i	−0.365147	+	0.0550370i
$229$	8.88191	−	8.24121i	0.586933	−	0.544595i	−0.329822	−	0.944043i	$-0.606989\pi$
$229$	8.88191	−	8.24121i	0.586933	−	0.544595i	0.916756	+	0.399448i	$0.130798\pi$
$230$	4.86185	+	2.34134i	0.320581	+	0.154384i
$231$	−12.4568	+	6.90692i	−0.819597	+	0.454442i
$232$	1.51367	−	0.728946i	0.0993774	−	0.0478576i
$233$	−5.11119	+	13.0231i	−0.334845	+	0.853172i	0.659953	+	0.751307i	$0.270576\pi$
$233$	−5.11119	+	13.0231i	−0.334845	+	0.853172i	−0.994798	+	0.101865i	$0.967519\pi$
$234$	0.412427	−	5.50346i	0.0269612	−	0.359773i
$235$	−3.09427	−	0.954454i	−0.201848	−	0.0622617i
$236$	−0.444390	−	5.92997i	−0.0289273	−	0.386008i
$237$	1.20031	−	5.25889i	0.0779683	−	0.341601i
$238$	−15.9716	−	13.1962i	−1.03529	−	0.855381i
$239$	3.44025	+	15.0727i	0.222531	+	0.974973i	0.955565	+	0.294781i	$0.0952466\pi$
$239$	3.44025	+	15.0727i	0.222531	+	0.974973i	−0.733034	+	0.680192i	$0.761896\pi$
$240$	−3.12319	+	0.963376i	−0.201601	+	0.0621857i
$241$	2.75695	+	7.02458i	0.177591	+	0.452493i	0.991756	−	0.128139i	$-0.0409005\pi$
$241$	2.75695	+	7.02458i	0.177591	+	0.452493i	−0.814166	+	0.580633i	$0.802805\pi$
$242$	−13.1821	−	12.2312i	−0.847375	−	0.786249i
$243$	0.826239	+	0.563320i	0.0530032	+	0.0361370i
$244$	−12.4868			−0.799387
$245$	−22.4915	−	4.19183i	−1.43693	−	0.267806i
$246$	7.22099			0.460393
$247$	25.4256	+	17.3349i	1.61779	+	1.10299i
$248$	−1.29166	−	1.19848i	−0.0820204	−	0.0761038i
$249$	0.523548	+	1.33398i	0.0331785	+	0.0845374i
$250$	−2.13129	+	0.657415i	−0.134794	+	0.0415786i
$251$	3.37920	+	14.8052i	0.213293	+	0.934499i	0.962312	+	0.271949i	$0.0876684\pi$
$251$	3.37920	+	14.8052i	0.213293	+	0.934499i	−0.749018	+	0.662549i	$0.769475\pi$
$252$	2.58923	−	0.543947i	0.163106	−	0.0342654i
$253$	1.97786	−	8.66557i	0.124347	−	0.544800i
$254$	−0.642197	−	8.56952i	−0.0402950	−	0.537700i
$255$	24.4566	+	7.54385i	1.53153	+	0.472414i
$256$	0.0747301	−	0.997204i	0.00467063	−	0.0623252i
$257$	3.46081	−	8.81800i	0.215879	−	0.550052i	−0.781378	−	0.624058i	$-0.785483\pi$
$257$	3.46081	−	8.81800i	0.215879	−	0.550052i	0.997258	+	0.0740058i	$0.0235783\pi$
$258$	−1.48743	+	0.716308i	−0.0926033	+	0.0445954i
$259$	0.436770	−	0.617360i	0.0271396	−	0.0383609i
$260$	16.2516	+	7.82636i	1.00788	+	0.485370i
$261$	1.23156	−	1.14272i	0.0762318	−	0.0707328i
$262$	−18.9688	+	2.85908i	−1.17189	+	0.176635i
$263$	8.74672	−	15.1498i	0.539346	−	0.934175i	−0.459593	−	0.888129i	$-0.652005\pi$
$263$	8.74672	−	15.1498i	0.539346	−	0.934175i	0.998939	−	0.0460452i	$-0.0146618\pi$
$264$	2.69177	+	4.66228i	0.165667	+	0.286943i
$265$	−14.6521	−	18.3731i	−0.900069	−	1.12865i
$266$	−4.59198	+	14.0195i	−0.281552	+	0.859590i
$267$	7.73124	−	9.69466i	0.473144	−	0.593304i
$268$	6.42997	+	0.969162i	0.392773	+	0.0592010i
$269$	17.1380	−	11.6845i	1.04492	−	0.712416i	0.0860609	−	0.996290i	$-0.472572\pi$
$269$	17.1380	−	11.6845i	1.04492	−	0.712416i	0.958862	+	0.283874i	$0.0916196\pi$
$270$	−2.70047	+	1.84115i	−0.164346	+	0.112049i
$271$	−13.3859	−	2.01760i	−0.813135	−	0.122560i	−0.270706	−	0.962662i	$-0.587257\pi$
$271$	−13.3859	−	2.01760i	−0.813135	−	0.122560i	−0.542429	+	0.840102i	$0.682495\pi$
$272$	−4.88232	+	6.12224i	−0.296034	+	0.371215i
$273$	−12.5170	−	7.51885i	−0.757561	−	0.455062i
$274$	−9.77894	−	12.2624i	−0.590767	−	0.740799i
$275$	15.2957	+	26.4930i	0.922367	+	1.59759i
$276$	−0.825519	+	1.42984i	−0.0496904	+	0.0860663i
$277$	16.2368	−	2.44730i	0.975573	−	0.147044i	0.358140	−	0.933668i	$-0.383411\pi$
$277$	16.2368	−	2.44730i	0.975573	−	0.147044i	0.617433	+	0.786624i	$0.288173\pi$
$278$	4.30417	−	3.99369i	0.258147	−	0.239526i
$279$	−1.58753	−	0.764516i	−0.0950432	−	0.0457704i
$280$	−1.43681	+	8.52716i	−0.0858657	+	0.509595i
$281$	13.8273	−	6.65890i	0.824870	−	0.397236i	0.0266813	−	0.999644i	$-0.491506\pi$
$281$	13.8273	−	6.65890i	0.824870	−	0.397236i	0.798189	+	0.602408i	$0.205792\pi$
$282$	0.361958	−	0.922253i	0.0215543	−	0.0549194i
$283$	−2.40929	+	32.1498i	−0.143218	+	1.91111i	0.213580	+	0.976926i	$0.431488\pi$
$283$	−2.40929	+	32.1498i	−0.143218	+	1.91111i	−0.356798	+	0.934182i	$0.616132\pi$
$284$	−2.70004	−	0.832851i	−0.160218	−	0.0494206i
$285$	−1.36189	−	18.1732i	−0.0806716	−	1.07649i
$286$	6.61136	−	28.9662i	0.390938	−	1.71281i
$287$	8.58637	−	17.0667i	0.506837	−	1.00742i
$288$	−0.222521	−	0.974928i	−0.0131122	−	0.0574482i
$289$	42.3500	−	13.0632i	2.49117	−	0.768426i
$290$	2.00611	+	5.11149i	0.117803	+	0.300157i
$291$	13.6592	+	12.6739i	0.800718	+	0.742958i
$292$	5.78254	+	3.94247i	0.338398	+	0.230716i
$293$	8.43424			0.492733			0.246367	−	0.969177i	$-0.420763\pi$
$293$	8.43424			0.492733			0.246367	+	0.969177i	$0.420763\pi$
$294$	1.79320	−	6.76642i	0.104582	−	0.394626i
$295$	19.4358			1.13160
$296$	−0.236166	−	0.161015i	−0.0137269	−	0.00935882i
$297$	3.94641	+	3.66173i	0.228994	+	0.212475i
$298$	−6.57075	−	16.7420i	−0.380633	−	0.969837i
$299$	8.70709	−	2.68578i	0.503544	−	0.155323i
$300$	−1.26445	−	5.53994i	−0.0730033	−	0.319848i
$301$	−0.0756934	+	4.36727i	−0.00436289	+	0.251725i
$302$	2.22331	−	9.74096i	0.127937	−	0.560529i
$303$	−0.879862	−	11.7409i	−0.0505467	−	0.674499i
$304$	5.32815	+	1.64352i	0.305590	+	0.0942622i
$305$	3.04988	−	40.6978i	0.174635	−	2.33035i
$306$	−2.86085	+	7.28934i	−0.163544	+	0.416704i
$307$	−20.1699	+	9.71330i	−1.15116	+	0.554367i	−0.909381	−	0.415965i	$-0.863444\pi$
$307$	−20.1699	+	9.71330i	−1.15116	+	0.554367i	−0.241775	+	0.970332i	$0.577730\pi$
$308$	14.2200	−	0.818117i	0.810259	−	0.0466166i
$309$	−4.15513	−	2.00100i	−0.236377	−	0.113833i
$310$	4.22165	−	3.91712i	0.239774	−	0.222477i
$311$	32.1409	−	4.84445i	1.82254	−	0.274704i	0.853408	−	0.521244i	$-0.174532\pi$
$311$	32.1409	−	4.84445i	1.82254	−	0.274704i	0.969133	+	0.246540i	$0.0792937\pi$
$312$	−2.75945	+	4.77950i	−0.156223	+	0.270586i
$313$	0.720694	+	1.24828i	0.0407360	+	0.0705569i	0.885675	−	0.464307i	$-0.153696\pi$
$313$	0.720694	+	1.24828i	0.0407360	+	0.0705569i	−0.844939	+	0.534863i	$0.820363\pi$
$314$	5.13706	+	6.44167i	0.289901	+	0.363524i
$315$	1.14045	+	8.57183i	0.0642570	+	0.482968i
$316$	−3.36318	+	4.21730i	−0.189194	+	0.237242i
$317$	9.71819	+	1.46478i	0.545828	+	0.0822704i	0.416167	−	0.909288i	$-0.363373\pi$
$317$	9.71819	+	1.46478i	0.545828	+	0.0822704i	0.129661	+	0.991558i	$0.458611\pi$
$318$	5.94074	−	4.05032i	0.333140	−	0.227131i
$319$	7.47300	−	5.09500i	0.418408	−	0.285265i
$320$	3.23189	+	0.487129i	0.180668	+	0.0272313i
$321$	−1.14540	+	1.43628i	−0.0639297	+	0.0801653i
$322$	2.39780	+	3.65131i	0.133624	+	0.203479i
$323$	−27.2232	−	34.1368i	−1.51474	−	1.89942i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−15.6803	+	27.1591i	−0.869787	+	1.50651i
$326$	8.11117	−	1.22256i	0.449236	−	0.0677115i
$327$	3.39518	−	3.15027i	0.187754	−	0.174210i
$328$	−6.50588	−	3.13307i	−0.359227	−	0.172995i
$329$	−1.74934	−	1.95212i	−0.0964440	−	0.107624i
$330$	−15.8530	+	7.63441i	−0.872680	+	0.420260i
$331$	−1.33895	+	3.41158i	−0.0735951	+	0.187517i	−0.962938	−	0.269724i	$-0.913067\pi$
$331$	−1.33895	+	3.41158i	−0.0735951	+	0.187517i	0.889342	+	0.457242i	$0.151163\pi$
$332$	0.107091	−	1.42903i	0.00587739	−	0.0784283i
$333$	−0.273134	−	0.0842506i	−0.0149676	−	0.00461690i
$334$	0.0351642	+	0.469234i	0.00192410	+	0.0256753i
$335$	−4.72925	+	20.7202i	−0.258386	+	1.13207i
$336$	−2.56883	−	0.633346i	−0.140141	−	0.0345519i
$337$	−3.00793	−	13.1786i	−0.163853	−	0.717885i	−0.988372	−	0.152052i	$-0.951412\pi$
$337$	−3.00793	−	13.1786i	−0.163853	−	0.717885i	0.824520	−	0.565833i	$-0.191445\pi$
$338$	16.6826	−	5.14589i	0.907413	−	0.279900i
$339$	−5.00245	−	12.7460i	−0.271696	−	0.692270i
$340$	−18.7615	−	17.4081i	−1.01748	−	0.944086i
$341$	−7.83766	−	5.34362i	−0.424433	−	0.289373i
$342$	5.57587			0.301509
$343$	−13.8601	−	12.2841i	−0.748374	−	0.663277i
$344$	1.65092			0.0890117
$345$	−4.45859	−	3.03981i	−0.240042	−	0.163658i
$346$	−2.44518	−	2.26879i	−0.131454	−	0.121971i
$347$	2.71844	+	6.92647i	0.145934	+	0.371833i	0.985086	−	0.172064i	$-0.0550436\pi$
$347$	2.71844	+	6.92647i	0.145934	+	0.371833i	−0.839152	+	0.543897i	$0.816948\pi$
$348$	−1.60541	+	0.495203i	−0.0860589	+	0.0265457i
$349$	4.37108	+	19.1510i	0.233979	+	1.02513i	0.946304	+	0.323278i	$0.104785\pi$
$349$	4.37108	+	19.1510i	0.233979	+	1.02513i	−0.712325	+	0.701849i	$0.752358\pi$
$350$	−14.5971	−	3.59893i	−0.780249	−	0.192371i
$351$	−1.22807	+	5.38052i	−0.0655495	+	0.287191i
$352$	−0.402312	−	5.36848i	−0.0214433	−	0.286141i
$353$	−18.1022	−	5.58380i	−0.963485	−	0.297196i	−0.227185	−	0.973852i	$-0.572952\pi$
$353$	−18.1022	−	5.58380i	−0.963485	−	0.297196i	−0.736299	+	0.676656i	$0.763428\pi$
$354$	−0.444390	+	5.92997i	−0.0236191	+	0.315174i
$355$	3.37395	−	8.59669i	0.179071	−	0.456265i
$356$	−11.1720	+	5.38013i	−0.592113	+	0.285146i
$357$	13.8265	+	15.4292i	0.731774	+	0.816602i
$358$	4.05207	+	1.95138i	0.214159	+	0.103133i
$359$	−13.6200	+	12.6375i	−0.718837	+	0.666983i	−0.952224	−	0.305401i	$-0.901209\pi$
$359$	−13.6200	+	12.6375i	−0.718837	+	0.666983i	0.233387	+	0.972384i	$0.425019\pi$
$360$	3.23189	−	0.487129i	0.170336	−	0.0256740i
$361$	−6.04517	+	10.4705i	−0.318167	+	0.551082i
$362$	5.81446	+	10.0709i	0.305601	+	0.529317i
$363$	11.2119	+	14.0592i	0.588471	+	0.737919i
$364$	8.01508	+	12.2052i	0.420104	+	0.639724i
$365$	−14.2619	+	17.8838i	−0.746501	+	0.936083i
$366$	12.3474	+	1.86107i	0.645407	+	0.0972795i
$367$	−12.4526	+	8.49001i	−0.650018	+	0.443175i	−0.842917	−	0.538044i	$-0.819163\pi$
$367$	−12.4526	+	8.49001i	−0.650018	+	0.443175i	0.192899	+	0.981219i	$0.438211\pi$
$368$	1.36415	−	0.930063i	0.0711113	−	0.0484829i
$369$	−7.14033	−	1.07623i	−0.371711	−	0.0560264i
$370$	0.582473	−	0.730398i	0.0302813	−	0.0379716i
$371$	−2.50886	−	18.8570i	−0.130253	−	0.979009i
$372$	1.09861	+	1.37761i	0.0569601	+	0.0714258i
$373$	−5.01263	−	8.68213i	−0.259544	−	0.449544i	0.706576	−	0.707638i	$-0.250239\pi$
$373$	−5.01263	−	8.68213i	−0.259544	−	0.449544i	−0.966120	+	0.258094i	$0.916906\pi$
$374$	−21.0783	+	36.5086i	−1.08993	+	1.88782i
$375$	2.20547	−	0.332420i	0.113890	−	0.0171661i
$376$	−0.726263	+	0.673874i	−0.0374542	+	0.0347524i
$377$	8.35379	+	4.02297i	0.430242	+	0.207194i
$378$	−2.64138	+	0.151967i	−0.135858	+	0.00781632i
$379$	−7.54617	+	3.63405i	−0.387621	+	0.186668i	−0.617537	−	0.786542i	$-0.711869\pi$
$379$	−7.54617	+	3.63405i	−0.387621	+	0.186668i	0.229916	+	0.973211i	$0.426155\pi$
$380$	−6.65803	+	16.9644i	−0.341550	+	0.870255i
$381$	−0.642197	+	8.56952i	−0.0329008	+	0.439030i
$382$	−16.0842	−	4.96132i	−0.822939	−	0.253843i
$383$	−0.00680038	−	0.0907447i	−0.000347483	−	0.00463684i	0.997027	−	0.0770483i	$-0.0245496\pi$
$383$	−0.00680038	−	0.0907447i	−0.000347483	−	0.00463684i	−0.997375	+	0.0724115i	$0.976931\pi$
$384$	−0.222521	+	0.974928i	−0.0113555	+	0.0497516i
$385$	−0.806740	+	46.5464i	−0.0411153	+	2.37222i
$386$	4.10123	+	17.9687i	0.208747	+	0.914580i
$387$	1.57758	−	0.486618i	0.0801927	−	0.0247362i
$388$	−6.80753	−	17.3453i	−0.345600	−	0.880575i
$389$	−13.0705	−	12.1276i	−0.662700	−	0.614895i	0.275372	−	0.961338i	$-0.411199\pi$
$389$	−13.0705	−	12.1276i	−0.662700	−	0.614895i	−0.938071	+	0.346443i	$0.887390\pi$
$390$	−14.9036	−	10.1611i	−0.754675	−	0.514529i
$391$	−12.9287			−0.653832
$392$	−4.55146	+	5.31829i	−0.229883	+	0.268614i
$393$	19.1830			0.967655
$394$	−3.12065	−	2.12763i	−0.157216	−	0.107188i
$395$	−12.9238	−	11.9915i	−0.650267	−	0.603360i
$396$	−1.96683	−	5.01139i	−0.0988367	−	0.251832i
$397$	−4.34742	+	1.34100i	−0.218191	+	0.0673029i	−0.401923	−	0.915673i	$-0.631658\pi$
$397$	−4.34742	+	1.34100i	−0.218191	+	0.0673029i	0.183733	+	0.982976i	$0.441182\pi$
$398$	−2.10474	−	9.22147i	−0.105501	−	0.462230i
$399$	6.63018	−	13.1785i	0.331924	−	0.659751i
$400$	−1.26445	+	5.53994i	−0.0632227	+	0.276997i
$401$	−1.27619	−	17.0296i	−0.0637300	−	0.850418i	−0.933870	−	0.357613i	$-0.883591\pi$
$401$	−1.27619	−	17.0296i	−0.0637300	−	0.850418i	0.870140	−	0.492805i	$-0.164028\pi$
$402$	−6.21370	−	1.91667i	−0.309911	−	0.0955950i
$403$	0.726709	−	9.69726i	0.0362000	−	0.483055i
$404$	−4.30147	+	10.9600i	−0.214006	+	0.545279i
$405$	2.94472	−	1.41810i	0.146324	−	0.0704661i
$406$	−0.738560	+	4.38320i	−0.0366541	+	0.217535i
$407$	−1.38640	−	0.667656i	−0.0687213	−	0.0330945i
$408$	5.74027	−	5.32619i	0.284185	−	0.263686i
$409$	−0.226503	+	0.0341399i	−0.0111999	+	0.00168811i	−0.154640	−	0.987971i	$-0.549422\pi$
$409$	−0.226503	+	0.0341399i	−0.0111999	+	0.00168811i	0.143440	+	0.989659i	$0.454184\pi$
$410$	11.8005	−	20.4391i	0.582786	−	1.00942i
$411$	7.84210	+	13.5829i	0.386822	+	0.669996i
$412$	2.87544	+	3.60568i	0.141663	+	0.177639i
$413$	13.4870	+	8.10155i	0.663652	+	0.398651i
$414$	1.02941	−	1.29083i	0.0505925	−	0.0634410i
$415$	4.63142	+	0.698074i	0.227348	+	0.0342671i
$416$	4.55992	−	3.10890i	0.223569	−	0.152427i
$417$	−4.85133	+	3.30758i	−0.237571	+	0.161973i
$418$	29.6826	+	4.47394i	1.45182	+	0.218827i
$419$	−11.5495	+	14.4826i	−0.564231	+	0.707524i	−0.979334	−	0.202251i	$-0.935174\pi$
$419$	−11.5495	+	14.4826i	−0.564231	+	0.707524i	0.415102	+	0.909775i	$0.363746\pi$
$420$	2.69167	−	8.21777i	0.131340	−	0.400986i
$421$	−9.29008	−	11.6494i	−0.452771	−	0.567757i	0.502088	−	0.864817i	$-0.332565\pi$
$421$	−9.29008	−	11.6494i	−0.452771	−	0.567757i	−0.954859	+	0.297060i	$0.903994\pi$
$422$	−0.358081	−	0.620215i	−0.0174311	−	0.0301916i
$423$	−0.495369	+	0.858005i	−0.0240857	+	0.0417176i
$424$	−7.10979	+	1.07163i	−0.345282	+	0.0520429i
$425$	32.6185	−	30.2656i	1.58223	−	1.46810i
$426$	2.54575	+	1.22597i	0.123342	+	0.0593984i
$427$	19.0807	−	26.9699i	0.923378	−	1.30516i
$428$	1.65514	−	0.797075i	0.0800044	−	0.0385281i
$429$	−10.8547	+	27.6573i	−0.524070	+	1.33531i
$430$	−0.403233	+	5.38078i	−0.0194456	+	0.259484i
$431$	−8.96766	−	2.76616i	−0.431957	−	0.133241i	0.0711492	−	0.997466i	$-0.477333\pi$
$431$	−8.96766	−	2.76616i	−0.431957	−	0.133241i	−0.503106	+	0.864225i	$0.667810\pi$
$432$	0.0747301	+	0.997204i	0.00359545	+	0.0479780i
$433$	−5.87772	+	25.7520i	−0.282465	+	1.23756i	0.612156	+	0.790737i	$0.290302\pi$
$433$	−5.87772	+	25.7520i	−0.282465	+	1.23756i	−0.894622	+	0.446825i	$0.852555\pi$
$434$	4.56230	−	0.958451i	0.218998	−	0.0460071i
$435$	−1.22188	−	5.35339i	−0.0585845	−	0.256675i
$436$	−4.42580	+	1.36518i	−0.211958	+	0.0653803i
$437$	3.36332	+	8.56960i	0.160889	+	0.409940i
$438$	−5.13036	−	4.76028i	−0.245138	−	0.227455i
$439$	12.2368	+	8.34291i	0.584031	+	0.398185i	0.818980	−	0.573822i	$-0.194540\pi$
$439$	12.2368	+	8.34291i	0.584031	+	0.398185i	−0.234949	+	0.972008i	$0.575492\pi$
$440$	17.5955			0.838833
$441$	−2.78166	+	6.42358i	−0.132460	+	0.305885i
$442$	−43.2165			−2.05560
$443$	3.13578	+	2.13794i	0.148986	+	0.101577i	0.635519	−	0.772085i	$-0.280786\pi$
$443$	3.13578	+	2.13794i	0.148986	+	0.101577i	−0.486533	+	0.873662i	$0.661739\pi$
$444$	0.209530	+	0.194415i	0.00994386	+	0.00922655i
$445$	−14.8065	−	37.7264i	−0.701896	−	1.78840i
$446$	21.7257	−	6.70150i	1.02874	−	0.317325i
$447$	4.00209	+	17.5343i	0.189292	+	0.829345i
$448$	2.03963	+	1.68520i	0.0963637	+	0.0796181i
$449$	−5.39920	+	23.6554i	−0.254804	+	1.11637i	0.671919	+	0.740624i	$0.265470\pi$
$449$	−5.39920	+	23.6554i	−0.254804	+	1.11637i	−0.926723	+	0.375745i	$0.877387\pi$
$450$	0.424647	+	5.66652i	0.0200180	+	0.267122i
$451$	−37.1474	−	11.4584i	−1.74920	−	0.539557i
$452$	−1.02325	+	13.6543i	−0.0481294	+	0.642243i
$453$	−3.65029	+	9.30079i	−0.171506	+	0.436989i
$454$	0.200221	−	0.0964213i	0.00939684	−	0.00452528i
$455$	−41.7374	+	23.1421i	−1.95668	+	1.08492i
$456$	−5.02369	−	2.41928i	−0.235256	−	0.113293i
$457$	5.19433	−	4.81964i	0.242981	−	0.225453i	−0.549276	−	0.835641i	$-0.685096\pi$
$457$	5.19433	−	4.81964i	0.242981	−	0.225453i	0.792257	+	0.610188i	$0.208906\pi$
$458$	11.9810	−	1.80585i	0.559836	−	0.0843817i
$459$	3.91532	−	6.78153i	0.182751	−	0.316535i
$460$	2.69812	+	4.67328i	0.125801	+	0.217893i
$461$	−4.77618	−	5.98914i	−0.222449	−	0.278942i	0.658066	−	0.752960i	$-0.271375\pi$
$461$	−4.77618	−	5.98914i	−0.222449	−	0.278942i	−0.880515	+	0.474018i	$0.842803\pi$
$462$	−14.1831	−	1.31040i	−0.659857	−	0.0609652i
$463$	−6.68706	+	8.38531i	−0.310774	+	0.389698i	−0.912549	−	0.408967i	$-0.865889\pi$
$463$	−6.68706	+	8.38531i	−0.310774	+	0.389698i	0.601775	+	0.798666i	$0.294460\pi$
$464$	1.66128	+	0.250398i	0.0771232	+	0.0116244i
$465$	−4.75832	+	3.24416i	−0.220662	+	0.150445i
$466$	−11.5592	+	7.88096i	−0.535472	+	0.365078i
$467$	−1.79960	−	0.271247i	−0.0832757	−	0.0125518i	0.107272	−	0.994230i	$-0.465788\pi$
$467$	−1.79960	−	0.271247i	−0.0832757	−	0.0125518i	−0.190548	+	0.981678i	$0.561026\pi$
$468$	3.44097	−	4.31485i	0.159059	−	0.199454i
$469$	−11.9187	+	12.4069i	−0.550352	+	0.572899i
$470$	−2.01894	−	2.53167i	−0.0931267	−	0.116777i
$471$	−4.11960	−	7.13536i	−0.189821	−	0.328780i
$472$	2.97330	−	5.14990i	0.136857	−	0.237044i
$473$	8.78852	−	1.32466i	0.404097	−	0.0609078i
$474$	3.95418	−	3.66894i	0.181621	−	0.168520i
$475$	−28.5466	−	13.7473i	−1.30981	−	0.630771i
$476$	−5.76272	−	19.9003i	−0.264134	−	0.912131i
$477$	−6.47805	+	3.11967i	−0.296610	+	0.142840i
$478$	−5.64830	+	14.3916i	−0.258347	+	0.658258i
$479$	−2.24428	+	29.9478i	−0.102544	+	1.36835i	0.674206	+	0.738543i	$0.264486\pi$
$479$	−2.24428	+	29.9478i	−0.102544	+	1.36835i	−0.776750	+	0.629809i	$0.783133\pi$
$480$	−3.12319	−	0.963376i	−0.142553	−	0.0439719i
$481$	−0.117885	−	1.57307i	−0.00537510	−	0.0717257i
$482$	−1.67919	+	7.35703i	−0.0764852	+	0.335103i
$483$	−1.82682	−	3.96790i	−0.0831232	−	0.180546i
$484$	−4.00147	−	17.5316i	−0.181885	−	0.796890i
$485$	58.1955	−	17.9509i	2.64252	−	0.815110i
$486$	0.365341	+	0.930874i	0.0165722	+	0.0422253i
$487$	28.5677	+	26.5070i	1.29453	+	1.20115i	0.966555	+	0.256458i	$0.0825557\pi$
$487$	28.5677	+	26.5070i	1.29453	+	1.20115i	0.327972	+	0.944687i	$0.393635\pi$
$488$	−10.3171	−	7.03408i	−0.467033	−	0.318418i
$489$	−8.20279			−0.370943
$490$	−16.2220	−	16.1334i	−0.732835	−	0.728831i
$491$	33.5030			1.51197			0.755984	−	0.654590i	$-0.227159\pi$
$491$	33.5030			1.51197			0.755984	+	0.654590i	$0.227159\pi$
$492$	5.96626	+	4.06773i	0.268980	+	0.183387i
$493$	−9.64392	−	8.94825i	−0.434341	−	0.403009i
$494$	11.2425	+	28.6455i	0.505824	+	1.28882i
$495$	16.8138	−	5.18637i	0.755724	−	0.233110i
$496$	−0.392088	−	1.71785i	−0.0176053	−	0.0771338i
$497$	5.92468	−	4.55907i	0.265758	−	0.204502i
$498$	−0.318881	+	1.39711i	−0.0142894	+	0.0626059i
$499$	−1.44946	−	19.3417i	−0.0648868	−	0.865854i	−0.930769	−	0.365607i	$-0.880861\pi$
$499$	−1.44946	−	19.3417i	−0.0648868	−	0.865854i	0.865883	−	0.500247i	$-0.166758\pi$
$500$	−2.13129	−	0.657415i	−0.0953141	−	0.0294005i
$501$	0.0351642	−	0.469234i	0.00157102	−	0.0209638i
$502$	−5.54806	+	14.1362i	−0.247622	+	0.630931i
$503$	11.7326	−	5.65012i	0.523130	−	0.251926i	−0.153632	−	0.988128i	$-0.549097\pi$
$503$	11.7326	−	5.65012i	0.523130	−	0.251926i	0.676762	+	0.736202i	$0.263383\pi$
$504$	2.44574	+	1.00914i	0.108942	+	0.0449505i
$505$	−34.6708	−	16.6966i	−1.54283	−	0.742987i
$506$	6.51567	−	6.04566i	0.289657	−	0.268762i
$507$	−17.2632	+	2.60201i	−0.766686	+	0.115559i
$508$	4.29678	−	7.44224i	0.190639	−	0.330196i
$509$	−6.45926	−	11.1878i	−0.286302	−	0.495889i	0.686622	−	0.727014i	$-0.259093\pi$
$509$	−6.45926	−	11.1878i	−0.286302	−	0.495889i	−0.972924	+	0.231125i	$0.925759\pi$
$510$	15.9574	+	20.0099i	0.706604	+	0.886053i
$511$	−17.3513	+	6.46517i	−0.767576	+	0.286002i
$512$	0.623490	−	0.781831i	0.0275546	−	0.0345524i
$513$	−5.51359	−	0.831041i	−0.243431	−	0.0366913i
$514$	7.82681	−	5.33623i	0.345226	−	0.235371i
$515$	−12.4542	+	8.49111i	−0.548796	+	0.374163i
$516$	−1.63248	−	0.246057i	−0.0718660	−	0.0108321i
$517$	−3.32549	+	4.17004i	−0.146255	+	0.183398i
$518$	0.708648	−	0.264045i	0.0311362	−	0.0116015i
$519$	2.07972	+	2.60789i	0.0912896	+	0.114474i
$520$	9.01896	+	15.6213i	0.395508	+	0.685040i
$521$	−10.1565	+	17.5915i	−0.444964	+	0.770700i	−0.998050	−	0.0624245i	$-0.980117\pi$
$521$	−10.1565	+	17.5915i	−0.444964	+	0.770700i	0.553086	+	0.833124i	$0.313450\pi$
$522$	1.66128	−	0.250398i	0.0727124	−	0.0109596i
$523$	25.2349	−	23.4145i	1.10344	−	1.02385i	0.103872	−	0.994591i	$-0.466877\pi$
$523$	25.2349	−	23.4145i	1.10344	−	1.02385i	0.999572	−	0.0292558i	$-0.00931375\pi$
$524$	−17.2833	−	8.32320i	−0.755024	−	0.363601i
$525$	13.8977	+	5.73432i	0.606545	+	0.250266i
$526$	15.7610	−	7.59012i	0.687214	−	0.330945i
$527$	−5.04091	+	12.8440i	−0.219585	+	0.559495i
$528$	−0.402312	+	5.36848i	−0.0175084	+	0.233633i
$529$	−19.3734	−	5.97589i	−0.842320	−	0.259821i
$530$	−1.75616	−	23.4344i	−0.0762828	−	1.01792i
$531$	1.32324	−	5.79750i	0.0574238	−	0.251590i
$532$	−11.6915	+	8.99670i	−0.506892	+	0.390056i
$533$	−8.86787	−	38.8527i	−0.384110	−	1.68290i
$534$	11.8490	−	3.65495i	0.512758	−	0.158165i
$535$	2.19361	+	5.58922i	0.0948379	+	0.241643i
$536$	4.76674	+	4.42289i	0.205892	+	0.191040i
$537$	−3.71598	−	2.53351i	−0.160356	−	0.109329i
$538$	20.7422			0.894259
$539$	−19.9620	+	31.9634i	−0.859824	+	1.37676i
$540$	−3.26840			−0.140649
$541$	15.5456	+	10.5988i	0.668360	+	0.455680i	0.849368	−	0.527802i	$-0.176984\pi$
$541$	15.5456	+	10.5988i	0.668360	+	0.455680i	−0.181008	+	0.983482i	$0.557936\pi$
$542$	−9.92339	−	9.20756i	−0.426246	−	0.395499i
$543$	−4.24852	−	10.8251i	−0.182321	−	0.464548i
$544$	−7.48275	+	2.30812i	−0.320820	+	0.0989599i
$545$	−3.36848	−	14.7583i	−0.144290	−	0.632175i
$546$	−6.10648	−	13.2634i	−0.261333	−	0.567622i
$547$	2.26994	−	9.94527i	0.0970557	−	0.425229i	−0.902934	−	0.429779i	$-0.858591\pi$
$547$	2.26994	−	9.94527i	0.0970557	−	0.425229i	0.999990	+	0.00455049i	$0.00144847\pi$
$548$	−1.17208	−	15.6403i	−0.0500688	−	0.668122i
$549$	−11.9321	−	3.68056i	−0.509249	−	0.157082i
$550$	−2.28610	+	30.5059i	−0.0974797	+	1.30078i
$551$	−3.42242	+	8.72018i	−0.145800	+	0.371492i
$552$	−1.48753	+	0.716358i	−0.0633136	+	0.0304902i
$553$	−3.96964	−	13.7083i	−0.168806	−	0.582937i
$554$	14.7941	+	7.12445i	0.628540	+	0.302689i
$555$	−0.684827	+	0.635427i	−0.0290693	+	0.0269724i
$556$	5.80600	−	0.875114i	0.246229	−	0.0371131i
$557$	−12.8171	+	22.1998i	−0.543076	+	0.940636i	0.455649	+	0.890160i	$0.349407\pi$
$557$	−12.8171	+	22.1998i	−0.543076	+	0.940636i	−0.998725	+	0.0504763i	$0.983926\pi$
$558$	−0.881015	−	1.52596i	−0.0372963	−	0.0645991i
$559$	5.68078	+	7.12347i	0.240271	+	0.301291i
$560$	−5.99067	+	6.23609i	−0.253152	+	0.263523i
$561$	26.2842	−	32.9593i	1.10972	−	1.39154i
$562$	15.1758	+	2.28738i	0.640151	+	0.0964873i
$563$	3.69489	−	2.51913i	0.155721	−	0.106169i	−0.482953	−	0.875646i	$-0.660436\pi$
$563$	3.69489	−	2.51913i	0.155721	−	0.106169i	0.638674	+	0.769478i	$0.279483\pi$
$564$	0.818587	−	0.558103i	0.0344687	−	0.0235004i
$565$	−44.2528	−	6.67004i	−1.86173	−	0.280611i
$566$	−20.1013	+	25.2062i	−0.844920	+	1.05950i
$567$	2.63453	+	0.243409i	0.110640	+	0.0102222i
$568$	−1.76171	−	2.20912i	−0.0739199	−	0.0926926i
$569$	−4.47096	−	7.74393i	−0.187432	−	0.324642i	0.756961	−	0.653460i	$-0.226683\pi$
$569$	−4.47096	−	7.74393i	−0.187432	−	0.324642i	−0.944393	+	0.328818i	$0.893350\pi$
$570$	9.11208	−	15.7826i	0.381663	−	0.661060i
$571$	−38.5925	+	5.81689i	−1.61505	+	0.243429i	−0.893542	−	0.448980i	$-0.851787\pi$
$571$	−38.5925	+	5.81689i	−1.61505	+	0.243429i	−0.721505	+	0.692409i	$0.756549\pi$
$572$	21.7798	−	20.2087i	0.910660	−	0.844969i
$573$	15.1651	+	7.30313i	0.633531	+	0.305093i
$574$	16.7084	−	9.26431i	0.697396	−	0.386685i
$575$	−8.45277	+	4.07064i	−0.352505	+	0.169757i
$576$	0.365341	−	0.930874i	0.0152225	−	0.0387864i
$577$	2.11186	−	28.1808i	0.0879178	−	1.17318i	−0.762469	−	0.647024i	$-0.776013\pi$
$577$	2.11186	−	28.1808i	0.0879178	−	1.17318i	0.850387	−	0.526158i	$-0.176368\pi$
$578$	42.3500	+	13.0632i	1.76153	+	0.543359i
$579$	−1.37733	−	18.3792i	−0.0572400	−	0.763814i
$580$	−1.22188	+	5.35339i	−0.0507357	+	0.222287i
$581$	2.92287	+	2.41495i	0.121261	+	0.100189i
$582$	4.14631	+	18.1662i	0.171870	+	0.753013i
$583$	−36.9884	+	11.4094i	−1.53190	+	0.472530i
$584$	2.55689	+	6.51484i	0.105805	+	0.269586i
$585$	13.2227	+	12.2689i	0.546693	+	0.507257i
$586$	6.96869	+	4.75118i	0.287874	+	0.196269i
$587$	38.1346			1.57398			0.786992	−	0.616963i	$-0.211637\pi$
$587$	38.1346			1.57398			0.786992	+	0.616963i	$0.211637\pi$
$588$	5.29327	−	4.58053i	0.218291	−	0.188898i
$589$	9.82485			0.404826
$590$	16.0586	+	10.9486i	0.661124	+	0.450746i
$591$	2.76869	+	2.56897i	0.113889	+	0.105673i
$592$	−0.104426	−	0.266074i	−0.00429190	−	0.0109356i
$593$	−22.0053	+	6.78774i	−0.903650	+	0.278739i	−0.711549	−	0.702636i	$-0.752006\pi$
$593$	−22.0053	+	6.78774i	−0.903650	+	0.278739i	−0.192101	+	0.981375i	$0.561530\pi$
$594$	1.19795	+	5.24856i	0.0491525	+	0.215351i
$595$	66.2678	−	13.9216i	2.71672	−	0.570729i
$596$	4.00209	−	17.5343i	0.163932	−	0.718234i
$597$	0.706843	+	9.43217i	0.0289292	+	0.386033i
$598$	8.70709	+	2.68578i	0.356059	+	0.109830i
$599$	−2.50924	+	33.4834i	−0.102525	+	1.36810i	0.674337	+	0.738424i	$0.264430\pi$
$599$	−2.50924	+	33.4834i	−0.102525	+	1.36810i	−0.776861	+	0.629672i	$0.783189\pi$
$600$	2.07602	−	5.28960i	0.0847530	−	0.215947i
$601$	28.6246	−	13.7849i	1.16762	−	0.562297i	0.253340	−	0.967377i	$-0.418471\pi$
$601$	28.6246	−	13.7849i	1.16762	−	0.562297i	0.914281	+	0.405081i	$0.132757\pi$
$602$	−2.52271	+	3.56577i	−0.102818	+	0.145330i
$603$	5.85864	+	2.82137i	0.238582	+	0.114895i
$604$	7.32426	−	6.79592i	0.298020	−	0.276522i
$605$	58.1173	−	8.75977i	2.36280	−	0.356135i
$606$	5.88693	−	10.1965i	0.239140	−	0.414203i
$607$	−9.35539	−	16.2040i	−0.379723	−	0.657700i	0.611298	−	0.791400i	$-0.290647\pi$
$607$	−9.35539	−	16.2040i	−0.379723	−	0.657700i	−0.991022	+	0.133700i	$0.957314\pi$
$608$	3.47650	+	4.35939i	0.140991	+	0.176797i
$609$	1.38359	−	4.22417i	0.0560661	−	0.171172i
$610$	25.4458	−	31.9080i	1.03027	−	1.29192i
$611$	−5.40671	−	0.814931i	−0.218732	−	0.0329686i
$612$	−6.46998	+	4.41116i	−0.261533	+	0.178310i
$613$	40.6103	−	27.6876i	1.64023	−	1.11829i	0.751667	−	0.659542i	$-0.229250\pi$
$613$	40.6103	−	27.6876i	1.64023	−	1.11829i	0.888566	−	0.458750i	$-0.151703\pi$
$614$	−22.1368	−	3.33659i	−0.893370	−	0.134654i
$615$	−14.7150	+	18.4520i	−0.593366	+	0.744058i
$616$	12.2100	+	7.33444i	0.491953	+	0.295513i
$617$	−1.54430	−	1.93649i	−0.0621711	−	0.0779601i	0.749774	−	0.661694i	$-0.230162\pi$
$617$	−1.54430	−	1.93649i	−0.0621711	−	0.0779601i	−0.811945	+	0.583734i	$0.801591\pi$
$618$	−2.30592	−	3.99397i	−0.0927578	−	0.160661i
$619$	−6.10363	+	10.5718i	−0.245326	+	0.424916i	−0.962223	−	0.272262i	$-0.912228\pi$
$619$	−6.10363	+	10.5718i	−0.245326	+	0.424916i	0.716897	+	0.697179i	$0.245562\pi$
$620$	5.69469	−	0.858336i	0.228704	−	0.0344716i
$621$	−1.21030	+	1.12299i	−0.0485675	+	0.0450641i
$622$	29.2850	+	14.1029i	1.17422	+	0.565475i
$623$	5.45110	−	32.3511i	0.218394	−	1.29612i
$624$	−4.97235	+	2.39456i	−0.199053	+	0.0958591i
$625$	−7.71684	+	19.6622i	−0.308673	+	0.786487i
$626$	−0.107715	+	1.43736i	−0.00430516	+	0.0574484i
$627$	−28.6843	−	8.84793i	−1.14554	−	0.353352i
$628$	0.615717	+	8.21617i	0.0245698	+	0.327861i
$629$	−0.498058	+	2.18213i	−0.0198589	+	0.0870074i
$630$	−3.88640	+	7.72481i	−0.154838	+	0.307764i
$631$	5.03737	+	22.0701i	0.200534	+	0.878599i	0.970612	+	0.240649i	$0.0773602\pi$
$631$	5.03737	+	22.0701i	0.200534	+	0.878599i	−0.770078	+	0.637950i	$0.779783\pi$
$632$	−5.15448	+	1.58995i	−0.205034	+	0.0632447i
$633$	0.261643	+	0.666657i	0.0103994	+	0.0264972i
$634$	7.20441	+	6.68471i	0.286124	+	0.265484i
$635$	23.2067	+	15.8220i	0.920929	+	0.627879i
$636$	7.19009			0.285106
$637$	−38.6091	−	1.33874i	−1.52975	−	0.0530430i
$638$	9.04460			0.358079
$639$	−2.33460	−	1.59170i	−0.0923552	−	0.0629667i
$640$	2.39590	+	2.22307i	0.0947064	+	0.0878747i
$641$	−4.14920	−	10.5720i	−0.163883	−	0.417568i	0.825216	−	0.564817i	$-0.191053\pi$
$641$	−4.14920	−	10.5720i	−0.163883	−	0.417568i	−0.989099	+	0.147249i	$0.952958\pi$
$642$	−1.75546	+	0.541486i	−0.0692823	+	0.0213708i
$643$	9.57096	+	41.9331i	0.377442	+	1.65368i	0.705267	+	0.708942i	$0.250827\pi$
$643$	9.57096	+	41.9331i	0.377442	+	1.65368i	−0.327826	+	0.944738i	$0.606316\pi$
$644$	−0.0756987	+	4.36758i	−0.00298295	+	0.172107i
$645$	1.20069	−	5.26058i	0.0472772	−	0.207135i
$646$	−3.26291	−	43.5406i	−0.128378	−	1.71308i
$647$	8.98246	+	2.77072i	0.353137	+	0.108928i	0.466248	−	0.884654i	$-0.345605\pi$
$647$	8.98246	+	2.77072i	0.353137	+	0.108928i	−0.113111	+	0.993582i	$0.536082\pi$
$648$	0.0747301	−	0.997204i	0.00293568	−	0.0391739i
$649$	11.6959	−	29.8007i	0.459105	−	1.16978i
$650$	−28.2549	+	13.6069i	−1.10825	+	0.533705i
$651$	−4.65420	+	0.267770i	−0.182412	+	0.0104947i
$652$	7.39046	+	3.55906i	0.289433	+	0.139383i
$653$	−19.0821	+	17.7056i	−0.746739	+	0.692872i	−0.958704	−	0.284405i	$-0.908204\pi$
$653$	−19.0821	+	17.7056i	−0.746739	+	0.692872i	0.211966	+	0.977277i	$0.432014\pi$
$654$	4.57984	−	0.690300i	0.179086	−	0.0269929i
$655$	31.3488	−	54.2978i	1.22490	−	2.12159i
$656$	−3.61049	−	6.25356i	−0.140966	−	0.244160i
$657$	4.36357	+	5.47175i	0.170239	+	0.213473i
$658$	−0.345701	−	2.59835i	−0.0134768	−	0.101294i
$659$	4.06325	−	5.09515i	0.158282	−	0.198479i	−0.696367	−	0.717686i	$-0.745201\pi$
$659$	4.06325	−	5.09515i	0.158282	−	0.198479i	0.854648	+	0.519207i	$0.173773\pi$
$660$	−17.3990	−	2.62248i	−0.677255	−	0.102080i
$661$	−38.8549	+	26.4909i	−1.51128	+	1.03037i	−0.527800	+	0.849368i	$0.676983\pi$
$661$	−38.8549	+	26.4909i	−1.51128	+	1.03037i	−0.983482	+	0.181006i	$0.942065\pi$
$662$	−3.02810	+	2.06452i	−0.117690	+	0.0802400i
$663$	42.7338	+	6.44108i	1.65964	+	0.250151i
$664$	0.893485	−	1.12039i	0.0346739	−	0.0434797i
$665$	−26.4669	−	40.3031i	−1.02634	−	1.56289i
$666$	−0.178214	−	0.223473i	−0.00690564	−	0.00865940i
$667$	1.38691	+	2.40220i	0.0537014	+	0.0930136i
$668$	−0.235275	+	0.407508i	−0.00910306	+	0.0157670i
$669$	−22.4819	+	3.38860i	−0.869200	+	0.131011i
$670$	−15.5796	+	14.4557i	−0.601892	+	0.558474i
$671$	−60.5661	−	29.1671i	−2.33813	−	1.12598i
$672$	−1.76569	−	1.97037i	−0.0681129	−	0.0760086i
$673$	−35.3736	+	17.0350i	−1.36355	+	0.656651i	−0.965425	−	0.260680i	$-0.916053\pi$
$673$	−35.3736	+	17.0350i	−1.36355	+	0.656651i	−0.398125	+	0.917331i	$0.630339\pi$
$674$	4.93851	−	12.5831i	0.190224	−	0.484684i
$675$	0.424647	−	5.66652i	0.0163447	−	0.218104i
$676$	16.6826	+	5.14589i	0.641638	+	0.197919i
$677$	−1.74537	−	23.2904i	−0.0670801	−	0.895122i	−0.924665	−	0.380780i	$-0.875655\pi$
$677$	−1.74537	−	23.2904i	−0.0670801	−	0.895122i	0.857585	−	0.514342i	$-0.171964\pi$
$678$	3.04688	−	13.3493i	0.117015	−	0.512675i
$679$	47.8659	+	11.8014i	1.83692	+	0.452895i
$680$	−5.69512	−	24.9519i	−0.218398	−	0.956863i
$681$	−0.212356	+	0.0655030i	−0.00813748	+	0.00251008i
$682$	−3.46561	−	8.83022i	−0.132705	−	0.338127i
$683$	−8.85311	−	8.21449i	−0.338755	−	0.314319i	0.492390	−	0.870375i	$-0.336123\pi$
$683$	−8.85311	−	8.21449i	−0.338755	−	0.314319i	−0.831145	+	0.556056i	$0.812314\pi$
$684$	4.60700	+	3.14100i	0.176153	+	0.120099i
$685$	51.2621			1.95863
$686$	−4.53188	−	17.9572i	−0.173028	−	0.685610i
$687$	−12.1163			−0.462268
$688$	1.36406	+	0.929997i	0.0520041	+	0.0354558i
$689$	−29.0885	−	26.9902i	−1.10818	−	1.02824i
$690$	−1.97147	−	5.02322i	−0.0750526	−	0.191231i
$691$	20.4805	−	6.31739i	0.779114	−	0.240325i	0.120407	−	0.992725i	$-0.461580\pi$
$691$	20.4805	−	6.31739i	0.779114	−	0.240325i	0.658707	+	0.752400i	$0.271104\pi$
$692$	−0.742244	−	3.25198i	−0.0282159	−	0.123622i
$693$	13.8294	+	3.40964i	0.525334	+	0.129522i
$694$	−1.65574	+	7.25427i	−0.0628511	+	0.275368i
$695$	1.43412	+	19.1370i	0.0543992	+	0.725907i
$696$	−1.60541	−	0.495203i	−0.0608529	−	0.0187706i
$697$	−4.22561	+	56.3868i	−0.160056	+	2.13580i
$698$	−7.17656	+	18.2856i	−0.271637	+	0.692119i
$699$	12.6047	−	6.07012i	0.476755	−	0.229593i
$700$	−10.0334	−	11.1964i	−0.379225	−	0.423185i
$701$	−21.1138	−	10.1679i	−0.797458	−	0.384036i	−0.00964775	−	0.999953i	$-0.503071\pi$
$701$	−21.1138	−	10.1679i	−0.797458	−	0.384036i	−0.787810	+	0.615918i	$0.788785\pi$
$702$	−4.04564	+	3.75380i	−0.152693	+	0.141678i
$703$	1.57596	−	0.237538i	0.0594386	−	0.00895893i
$704$	2.69177	−	4.66228i	0.101450	−	0.175716i
$705$	1.61906	+	2.80430i	0.0609774	+	0.105616i
$706$	−11.8113	−	14.8109i	−0.444524	−	0.557416i
$707$	−17.0992	−	26.0382i	−0.643080	−	0.979265i
$708$	−3.70764	+	4.64924i	−0.139342	+	0.174729i
$709$	15.5749	+	2.34753i	0.584926	+	0.0881634i	0.434837	−	0.900509i	$-0.356806\pi$
$709$	15.5749	+	2.34753i	0.584926	+	0.0881634i	0.150089	+	0.988672i	$0.452044\pi$
$710$	7.63038	−	5.20231i	0.286363	−	0.195239i
$711$	−4.45684	+	3.03862i	−0.167144	+	0.113957i
$712$	−12.2614	−	1.84812i	−0.459517	−	0.0692610i
$713$	1.81384	−	2.27449i	0.0679289	−	0.0851802i
$714$	2.73236	+	20.5370i	0.102256	+	0.768576i
$715$	60.5457	+	75.9219i	2.26428	+	2.83932i
$716$	2.24873	+	3.89492i	0.0840390	+	0.145560i
$717$	7.73017	−	13.3891i	0.288689	−	0.500023i
$718$	−18.3723	+	2.76919i	−0.685650	+	0.103345i
$719$	−10.6427	+	9.87494i	−0.396904	+	0.368273i	−0.853226	−	0.521542i	$-0.825357\pi$
$719$	−10.6427	+	9.87494i	−0.396904	+	0.368273i	0.456322	+	0.889815i	$0.349167\pi$
$720$	2.94472	+	1.41810i	0.109743	+	0.0528496i
$721$	−12.1816	+	0.700846i	−0.453668	+	0.0261009i
$722$	−10.8930	+	5.24581i	−0.405397	+	0.195229i
$723$	2.75695	−	7.02458i	0.102532	−	0.261247i
$724$	−0.869030	+	11.5964i	−0.0322973	+	0.430977i
$725$	−9.12259	−	2.81395i	−0.338804	−	0.104507i
$726$	1.34383	+	17.9322i	0.0498742	+	0.665525i
$727$	5.95016	−	26.0693i	0.220679	−	0.966859i	−0.736289	−	0.676667i	$-0.763424\pi$
$727$	5.95016	−	26.0693i	0.220679	−	0.966859i	0.956969	−	0.290192i	$-0.0937191\pi$
$728$	−0.253037	+	14.5994i	−0.00937817	+	0.541091i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	−21.8581	+	6.74232i	−0.809003	+	0.249544i
$731$	−4.72305	−	12.0341i	−0.174688	−	0.445098i
$732$	9.15349	+	8.49320i	0.338323	+	0.313918i
$733$	−12.4435	−	8.48381i	−0.459610	−	0.313357i	0.311288	−	0.950316i	$-0.399240\pi$
$733$	−12.4435	−	8.48381i	−0.459610	−	0.313357i	−0.770898	+	0.636959i	$0.780192\pi$
$734$	−15.0714			−0.556295
$735$	13.6363	+	18.3709i	0.502981	+	0.677622i
$736$	1.65104			0.0608581
$737$	28.9241	+	19.7201i	1.06543	+	0.726400i
$738$	−5.29336	−	4.91152i	−0.194851	−	0.180796i
$739$	7.73574	+	19.7103i	0.284564	+	0.725057i	0.999661	+	0.0260318i	$0.00828713\pi$
$739$	7.73574	+	19.7103i	0.284564	+	0.725057i	−0.715097	+	0.699025i	$0.753618\pi$
$740$	0.892709	−	0.275364i	0.0328166	−	0.0101226i
$741$	−6.84756	−	30.0011i	−0.251551	−	1.10212i
$742$	8.54963	−	16.9937i	0.313867	−	0.623859i
$743$	−4.95134	+	21.6932i	−0.181647	+	0.795847i	0.799200	+	0.601066i	$0.205257\pi$
$743$	−4.95134	+	21.6932i	−0.181647	+	0.795847i	−0.980847	+	0.194782i	$0.937600\pi$
$744$	0.131677	+	1.75710i	0.00482750	+	0.0644185i
$745$	56.1713	+	17.3266i	2.05796	+	0.634796i
$746$	0.749189	−	9.99723i	0.0274298	−	0.366025i
$747$	0.523548	−	1.33398i	0.0191556	−	0.0488077i
$748$	−37.9817	+	18.2910i	−1.38875	+	0.668786i
$749$	−0.807589	+	4.79287i	−0.0295086	+	0.175128i
$750$	2.00950	+	0.967724i	0.0733766	+	0.0353363i
$751$	−27.5700	+	25.5813i	−1.00605	+	0.933474i	−0.997787	−	0.0664922i	$-0.978819\pi$
$751$	−27.5700	+	25.5813i	−1.00605	+	0.933474i	−0.00825846	+	0.999966i	$0.502629\pi$
$752$	−0.979673	+	0.147662i	−0.0357250	+	0.00538468i
$753$	7.59299	−	13.1515i	0.276704	−	0.479266i
$754$	4.63601	+	8.02980i	0.168833	+	0.292428i
$755$	20.3607	+	25.5315i	0.741002	+	0.929188i
$756$	−2.26802	−	1.36238i	−0.0824871	−	0.0495494i
$757$	2.75612	−	3.45606i	0.100173	−	0.125613i	−0.729218	−	0.684281i	$-0.760116\pi$
$757$	2.75612	−	3.45606i	0.100173	−	0.125613i	0.829391	+	0.558668i	$0.188688\pi$
$758$	−8.28207	−	1.24832i	−0.300818	−	0.0453411i
$759$	−7.34396	+	5.00702i	−0.266569	+	0.181743i
$760$	−15.0575	+	10.2660i	−0.546193	+	0.372388i
$761$	41.2312	+	6.21460i	1.49463	+	0.225279i	0.844915	−	0.534900i	$-0.179651\pi$
$761$	41.2312	+	6.21460i	1.49463	+	0.225279i	0.649713	+	0.760179i	$0.274889\pi$
$762$	−5.35799	+	6.71871i	−0.194100	+	0.243393i
$763$	3.81430	−	11.6452i	0.138087	−	0.421586i
$764$	−10.4946	−	13.1598i	−0.379681	−	0.476104i
$765$	−12.7968	−	22.1647i	−0.462670	−	0.801368i
$766$	0.0454996	−	0.0788076i	0.00164397	−	0.00284743i
$767$	32.4521	−	4.89137i	1.17178	−	0.176617i
$768$	−0.733052	+	0.680173i	−0.0264517	+	0.0245436i
$769$	33.8661	+	16.3090i	1.22124	+	0.588119i	0.929657	−	0.368426i	$-0.120103\pi$
$769$	33.8661	+	16.3090i	1.22124	+	0.588119i	0.291585	+	0.956545i	$0.405817\pi$
$770$	−26.8871	+	38.0040i	−0.968943	+	1.36957i
$771$	−8.53472	+	4.11010i	−0.307370	+	0.148022i
$772$	−6.73351	+	17.1567i	−0.242344	+	0.617483i
$773$	−0.540375	+	7.21080i	−0.0194359	+	0.259354i	0.979018	+	0.203773i	$0.0653204\pi$
$773$	−0.540375	+	7.21080i	−0.0194359	+	0.259354i	−0.998454	+	0.0555816i	$0.982299\pi$
$774$	1.57758	+	0.486618i	0.0567048	+	0.0174911i
$775$	0.748240	+	9.98457i	0.0268776	+	0.358656i
$776$	4.14631	−	18.1662i	0.148844	−	0.652128i
$777$	−0.740087	+	0.155478i	−0.0265505	+	0.00557773i
$778$	−3.96760	−	17.3832i	−0.142245	−	0.623217i
$779$	38.4745	−	11.8678i	1.37849	−	0.425209i
$780$	−6.59000	−	16.7910i	−0.235960	−	0.601215i
$781$	−11.1509	−	10.3465i	−0.399009	−	0.370226i
$782$	−10.6822	−	7.28299i	−0.381994	−	0.260439i
$783$	−1.68005			−0.0600400
$784$	−6.75649	+	1.83025i	−0.241303	+	0.0653660i
$785$	−26.9290			−0.961136
$786$	15.8497	+	10.8062i	0.565342	+	0.385443i
$787$	−36.3977	−	33.7722i	−1.29744	−	1.20385i	−0.965457	−	0.260562i	$-0.916092\pi$
$787$	−36.3977	−	33.7722i	−1.29744	−	1.20385i	−0.331982	−	0.943286i	$-0.607717\pi$
$788$	−1.37987	−	3.51585i	−0.0491559	−	0.125247i
$789$	−16.7163	+	5.15628i	−0.595115	+	0.183569i
$790$	−3.92308	−	17.1881i	−0.139577	−	0.611526i
$791$	−27.9278	−	23.0747i	−0.992998	−	0.820440i
$792$	1.19795	−	5.24856i	0.0425673	−	0.186499i
$793$	−5.14991	−	68.7208i	−0.182879	−	2.44035i
$794$	−4.34742	−	1.34100i	−0.154284	−	0.0475904i
$795$	−1.75616	+	23.4344i	−0.0622847	+	0.831131i
$796$	3.45562	−	8.80478i	0.122481	−	0.312077i
$797$	13.1884	−	6.35119i	0.467157	−	0.224971i	−0.185471	−	0.982650i	$-0.559381\pi$
$797$	13.1884	−	6.35119i	0.467157	−	0.224971i	0.652627	+	0.757679i	$0.273667\pi$
$798$	12.9018	−	7.15368i	0.456720	−	0.253237i
$799$	6.98982	+	3.36612i	0.247282	+	0.119085i
$800$	−4.16550	+	3.86502i	−0.147273	+	0.136649i
$801$	−12.2614	+	1.84812i	−0.433237	+	0.0652999i
$802$	8.53868	−	14.7894i	0.301511	−	0.522233i
$803$	18.8387	+	32.6296i	0.664803	+	1.15147i
$804$	−4.05430	−	5.08393i	−0.142984	−	0.179297i
$805$	−14.2166	−	1.31349i	−0.501068	−	0.0462945i
$806$	6.06310	−	7.60288i	0.213564	−	0.267800i
$807$	−20.5105	−	3.09146i	−0.722005	−	0.108825i
$808$	−9.72802	+	6.63245i	−0.342231	+	0.233329i
$809$	−9.66379	+	6.58866i	−0.339761	+	0.231645i	−0.721165	−	0.692763i	$-0.756393\pi$
$809$	−9.66379	+	6.58866i	−0.339761	+	0.231645i	0.381404	+	0.924408i	$0.375441\pi$
$810$	3.23189	+	0.487129i	0.113557	+	0.0171160i
$811$	−1.19916	+	1.50370i	−0.0421082	+	0.0528021i	−0.802440	−	0.596733i	$-0.796465\pi$
$811$	−1.19916	+	1.50370i	−0.0421082	+	0.0528021i	0.760331	+	0.649535i	$0.225037\pi$
$812$	−3.07937	+	3.20553i	−0.108065	+	0.112492i
$813$	8.44024	+	10.5837i	0.296012	+	0.371187i
$814$	−0.769395	−	1.33263i	−0.0269673	−	0.0467087i
$815$	−13.4050	+	23.2181i	−0.469556	+	0.813295i
$816$	7.74318	−	1.16710i	0.271065	−	0.0408565i
$817$	−6.74798	+	6.26121i	−0.236082	+	0.219052i
$818$	−0.206378	−	0.0993862i	−0.00721582	−	0.00347496i
$819$	4.06146	+	14.0254i	0.141919	+	0.490087i
$820$	21.2638	−	10.2401i	0.742564	−	0.357600i
$821$	−15.9455	+	40.6284i	−0.556501	+	1.41794i	0.324980	+	0.945721i	$0.394643\pi$
$821$	−15.9455	+	40.6284i	−0.556501	+	1.41794i	−0.881481	+	0.472220i	$0.843453\pi$
$822$	−1.17208	+	15.6403i	−0.0408810	+	0.545519i
$823$	−37.2952	−	11.5041i	−1.30003	−	0.401006i	−0.433961	−	0.900932i	$-0.642885\pi$
$823$	−37.2952	−	11.5041i	−1.30003	−	0.401006i	−0.866068	+	0.499925i	$0.833361\pi$
$824$	0.344643	+	4.59895i	0.0120062	+	0.160212i
$825$	6.80724	−	29.8244i	0.236998	−	1.03835i
$826$	6.57972	+	14.2913i	0.228938	+	0.497258i
$827$	4.74770	+	20.8010i	0.165094	+	0.723323i	0.987912	+	0.155018i	$0.0495435\pi$
$827$	4.74770	+	20.8010i	0.165094	+	0.723323i	−0.822818	+	0.568305i	$0.807599\pi$
$828$	1.57769	−	0.486652i	0.0548284	−	0.0169123i
$829$	−7.15030	−	18.2187i	−0.248340	−	0.632761i	0.751289	−	0.659973i	$-0.229432\pi$
$829$	−7.15030	−	18.2187i	−0.248340	−	0.632761i	−0.999630	+	0.0272122i	$0.991337\pi$
$830$	3.43342	+	3.18575i	0.119176	+	0.110579i
$831$	−13.5670	−	9.24981i	−0.470633	−	0.320872i
$832$	5.51889			0.191333
$833$	51.7879	+	17.9623i	1.79434	+	0.622356i
$834$	−5.87158			−0.203316
$835$	−1.27071	−	0.866354i	−0.0439746	−	0.0299814i
$836$	22.0047	+	20.4174i	0.761048	+	0.706149i
$837$	0.643742	+	1.64023i	0.0222510	+	0.0566945i
$838$	−17.7010	+	5.46005i	−0.611472	+	0.188614i
$839$	−8.28201	−	36.2858i	−0.285927	−	1.25273i	−0.890060	−	0.455843i	$-0.849338\pi$
$839$	−8.28201	−	36.2858i	−0.285927	−	1.25273i	0.604134	−	0.796883i	$-0.293519\pi$
$840$	6.85320	−	5.27357i	0.236458	−	0.181956i
$841$	5.82503	−	25.5211i	0.200863	−	0.880038i
$842$	−1.11349	−	14.8585i	−0.0383733	−	0.512057i
$843$	−14.6654	−	4.52366i	−0.505102	−	0.155803i
$844$	0.0535189	−	0.714160i	0.00184220	−	0.0245824i
$845$	−20.8465	+	53.1159i	−0.717140	+	1.82724i
$846$	−0.892625	+	0.429865i	−0.0306891	+	0.0147791i
$847$	43.9804	+	18.1467i	1.51118	+	0.623529i
$848$	−6.47805	−	3.11967i	−0.222457	−	0.107130i
$849$	23.6336	−	21.9287i	0.811101	−	0.752592i
$850$	43.9999	−	6.63192i	1.50918	−	0.227473i
$851$	0.235960	−	0.408695i	0.00808861	−	0.0140099i
$852$	1.41279	+	2.44702i	0.0484012	+	0.0838334i
$853$	−13.4256	−	16.8352i	−0.459684	−	0.576426i	0.496927	−	0.867792i	$-0.334462\pi$
$853$	−13.4256	−	16.8352i	−0.459684	−	0.576426i	−0.956612	+	0.291366i	$0.905890\pi$
$854$	30.9579	−	11.5350i	1.05936	−	0.394721i
$855$	−11.3626	+	14.2482i	−0.388592	+	0.487279i
$856$	1.81655	+	0.273801i	0.0620885	+	0.00935833i
$857$	3.73284	−	2.54500i	0.127511	−	0.0869357i	−0.497885	−	0.867243i	$-0.665890\pi$
$857$	3.73284	−	2.54500i	0.127511	−	0.0869357i	0.625396	+	0.780307i	$0.284937\pi$
$858$	−24.5485	+	16.7369i	−0.838072	+	0.571388i
$859$	−2.57028	−	0.387407i	−0.0876968	−	0.0132182i	0.105047	−	0.994467i	$-0.466501\pi$
$859$	−2.57028	−	0.387407i	−0.0876968	−	0.0132182i	−0.192744	+	0.981249i	$0.561739\pi$
$860$	−3.36427	+	4.21866i	−0.114721	+	0.143855i
$861$	−17.9026	+	6.67058i	−0.610118	+	0.227333i
$862$	−5.85120	−	7.33717i	−0.199293	−	0.249905i
$863$	18.5589	+	32.1449i	0.631751	+	1.09423i	0.987194	+	0.159527i	$0.0509969\pi$
$863$	18.5589	+	32.1449i	0.631751	+	1.09423i	−0.355442	+	0.934698i	$0.615670\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	10.7803	−	1.62487i	0.366542	−	0.0552474i
$866$	−19.3630	+	17.9663i	−0.657982	+	0.610518i
$867$	−39.9300	−	19.2293i	−1.35609	−	0.653060i
$868$	4.30947	+	1.77813i	0.146273	+	0.0603536i
$869$	−26.1637	+	12.5998i	−0.887541	+	0.427417i
$870$	2.00611	−	5.11149i	0.0680135	−	0.173296i
$871$	−2.68185	+	35.7868i	−0.0908710	+	1.21259i
$872$	−4.42580	−	1.36518i	−0.149877	−	0.0462308i
$873$	−1.39247	−	18.5813i	−0.0471281	−	0.628880i
$874$	−2.04852	+	8.97516i	−0.0692923	+	0.303589i
$875$	4.67667	−	3.59872i	0.158100	−	0.121659i
$876$	−1.55734	−	6.82316i	−0.0526177	−	0.230533i
$877$	9.40115	−	2.89987i	0.317454	−	0.0979217i	−0.131933	−	0.991259i	$-0.542118\pi$
$877$	9.40115	−	2.89987i	0.317454	−	0.0979217i	0.449388	+	0.893337i	$0.351642\pi$
$878$	5.41079	+	13.7865i	0.182605	+	0.465271i
$879$	−6.18273	−	5.73674i	−0.208538	−	0.193495i
$880$	14.5381	+	9.91191i	0.490079	+	0.334130i
$881$	19.3747			0.652751			0.326376	−	0.945240i	$-0.394173\pi$
$881$	19.3747			0.652751			0.326376	+	0.945240i	$0.394173\pi$
$882$	−5.91684	+	3.74045i	−0.199231	+	0.125947i
$883$	−15.4182			−0.518865			−0.259432	−	0.965761i	$-0.583535\pi$
$883$	−15.4182			−0.518865			−0.259432	+	0.965761i	$0.583535\pi$
$884$	−35.7071	−	24.3447i	−1.20096	−	0.818801i
$885$	−14.2475	−	13.2197i	−0.478924	−	0.444376i
$886$	1.38656	+	3.53290i	0.0465824	+	0.118690i
$887$	−51.1335	+	15.7726i	−1.71689	+	0.529592i	−0.987922	−	0.154951i	$-0.950478\pi$
$887$	−51.1335	+	15.7726i	−1.71689	+	0.529592i	−0.728973	+	0.684543i	$0.760002\pi$
$888$	0.0636037	+	0.278666i	0.00213440	+	0.00935142i
$889$	9.50849	+	20.6527i	0.318904	+	0.692668i
$890$	9.01831	−	39.5118i	0.302294	−	1.32444i
$891$	−0.402312	−	5.36848i	−0.0134780	−	0.179851i
$892$	21.7257	+	6.70150i	0.727432	+	0.224383i
$893$	0.412826	−	5.50879i	0.0138147	−	0.184344i
$894$	−6.57075	+	16.7420i	−0.219759	+	0.559936i
$895$	−13.2438	+	6.37787i	−0.442691	+	0.213189i
$896$	0.735920	+	2.54134i	0.0245853	+	0.0849003i
$897$	−8.20954	−	3.95351i	−0.274109	−	0.132004i
$898$	−17.7866	+	16.5036i	−0.593547	+	0.550731i
$899$	2.92723	−	0.441209i	0.0976286	−	0.0147151i
$900$	−2.84120	+	4.92111i	−0.0947068	+	0.164037i
$901$	28.1515	+	48.7599i	0.937863	+	1.62443i
$902$	−24.2378	−	30.3933i	−0.807031	−	1.01198i
$903$	3.02599	−	3.14995i	0.100699	−	0.104824i
$904$	−8.53717	+	10.7053i	−0.283942	+	0.356052i
$905$	−37.5834	−	5.66478i	−1.24931	−	0.188304i
$906$	−8.25534	+	5.62839i	−0.274265	+	0.186991i
$907$	−23.1555	+	15.7872i	−0.768866	+	0.524204i	−0.883063	−	0.469254i	$-0.844523\pi$
$907$	−23.1555	+	15.7872i	−0.768866	+	0.524204i	0.114197	+	0.993458i	$0.463570\pi$
$908$	0.219746	+	0.0331214i	0.00729254	+	0.00109917i
$909$	−7.34088	+	9.20518i	−0.243482	+	0.305316i
$910$	−47.5215	−	4.39059i	−1.57532	−	0.145546i
$911$	31.8222	+	39.9038i	1.05432	+	1.32207i	0.944641	+	0.328105i	$0.106410\pi$
$911$	31.8222	+	39.9038i	1.05432	+	1.32207i	0.109676	+	0.993967i	$0.465019\pi$
$912$	−2.78794	−	4.82885i	−0.0923178	−	0.159899i
$913$	3.85740	−	6.68122i	0.127661	−	0.221116i
$914$	7.00676	−	1.05610i	0.231763	−	0.0349326i
$915$	−29.9172	+	27.7591i	−0.989033	+	0.917689i
$916$	10.9165	+	5.25709i	0.360690	+	0.173699i
$917$	44.3870	−	24.6112i	1.46579	−	0.812735i
$918$	7.05516	−	3.39759i	0.232855	−	0.112137i
$919$	11.9911	−	30.5529i	0.395551	−	1.00785i	−0.584903	−	0.811103i	$-0.698867\pi$
$919$	11.9911	−	30.5529i	0.395551	−	1.00785i	0.980455	−	0.196746i	$-0.0630373\pi$
$920$	−0.403262	+	5.38115i	−0.0132951	+	0.177411i
$921$	21.3923	+	6.59864i	0.704900	+	0.217433i
$922$	−0.572463	−	7.63898i	−0.0188531	−	0.251577i
$923$	3.47000	−	15.2030i	0.114216	−	0.500414i
$924$	−10.9804	−	9.07232i	−0.361230	−	0.298457i
$925$	0.361422	+	1.58349i	0.0118835	+	0.0520650i
$926$	−10.2487	+	3.16131i	−0.336794	+	0.103887i
$927$	1.68490	+	4.29304i	0.0553392	+	0.141002i
$928$	1.23156	+	1.14272i	0.0404280	+	0.0375117i
$929$	−5.74042	−	3.91375i	−0.188337	−	0.128406i	0.465481	−	0.885058i	$-0.345881\pi$
$929$	−5.74042	−	3.91375i	−0.188337	−	0.128406i	−0.653818	+	0.756652i	$0.726834\pi$
$930$	−5.75901			−0.188845
$931$	−1.56626	−	38.9997i	−0.0513322	−	1.27816i
$932$	−13.9902			−0.458264
$933$	−26.8560	−	18.3101i	−0.879225	−	0.599446i
$934$	−1.33410	−	1.23787i	−0.0436532	−	0.0405043i
$935$	−50.3382	−	128.260i	−1.64624	−	4.19454i
$936$	5.27371	−	1.62672i	0.172376	−	0.0531711i
$937$	−0.549275	−	2.40653i	−0.0179440	−	0.0786179i	0.965163	−	0.261649i	$-0.0842663\pi$
$937$	−0.549275	−	2.40653i	−0.0179440	−	0.0786179i	−0.983107	+	0.183031i	$0.941409\pi$
$938$	−16.8367	+	3.53707i	−0.549739	+	0.115489i
$939$	0.320739	−	1.40525i	0.0104669	−	0.0458586i
$940$	−0.241985	−	3.22907i	−0.00789270	−	0.105321i
$941$	25.2452	+	7.78711i	0.822969	+	0.253852i	0.677512	−	0.735512i	$-0.263058\pi$
$941$	25.2452	+	7.78711i	0.822969	+	0.253852i	0.145458	+	0.989364i	$0.453535\pi$
$942$	0.615717	−	8.21617i	0.0200611	−	0.267697i
$943$	4.35564	−	11.0980i	0.141839	−	0.361400i
$944$	5.35770	−	2.58013i	0.174378	−	0.0839761i
$945$	4.99431	−	7.05930i	0.162465	−	0.229639i
$946$	8.00763	+	3.85627i	0.260350	+	0.125378i
$947$	20.1338	−	18.6815i	0.654262	−	0.607066i	−0.281558	−	0.959544i	$-0.590851\pi$
$947$	20.1338	−	18.6815i	0.654262	−	0.607066i	0.935820	+	0.352478i	$0.114661\pi$
$948$	5.33388	−	0.803953i	0.173236	−	0.0261112i
$949$	−19.3124	+	33.4500i	−0.626905	+	1.08583i
$950$	−15.8422	−	27.4395i	−0.513988	−	0.890254i
$951$	−6.12764	−	7.68381i	−0.198702	−	0.249165i
$952$	6.44888	−	19.6887i	0.209009	−	0.638114i
$953$	−2.74785	+	3.44570i	−0.0890117	+	0.111617i	−0.824343	−	0.566091i	$-0.808455\pi$
$953$	−2.74785	+	3.44570i	−0.0890117	+	0.111617i	0.735331	+	0.677708i	$0.237027\pi$
$954$	−7.10979	−	1.07163i	−0.230188	−	0.0346952i
$955$	45.4544	−	30.9903i	1.47087	−	1.00282i
$956$	−12.7739	+	8.70912i	−0.413139	+	0.281673i
$957$	−8.94358	−	1.34803i	−0.289105	−	0.0435755i
$958$	−18.7245	+	23.4798i	−0.604962	+	0.758599i
$959$	35.5721	+	21.3679i	1.14868	+	0.690005i
$960$	−2.03781	−	2.55533i	−0.0657701	−	0.0824731i
$961$	13.9476	+	24.1580i	0.449923	+	0.779290i
$962$	0.788740	−	1.36614i	0.0254300	−	0.0440460i
$963$	1.81655	−	0.273801i	0.0585376	−	0.00882312i
$964$	−5.53178	+	5.13274i	−0.178166	+	0.165314i
$965$	−54.2734	−	26.1367i	−1.74712	−	0.841371i
$966$	0.725807	−	4.30751i	0.0233525	−	0.138592i
$967$	34.6968	−	16.7091i	1.11577	−	0.537328i	0.217189	−	0.976130i	$-0.430311\pi$
$967$	34.6968	−	16.7091i	1.11577	−	0.537328i	0.898584	+	0.438802i	$0.144597\pi$
$968$	6.56973	−	16.7394i	0.211159	−	0.538024i
$969$	−3.26291	+	43.5406i	−0.104820	+	1.39872i
$970$	58.1955	+	17.9509i	1.86855	+	0.576370i
$971$	−0.137096	−	1.82942i	−0.00439962	−	0.0587088i	0.994572	−	0.104052i	$-0.0331809\pi$
$971$	−0.137096	−	1.82942i	−0.00439962	−	0.0587088i	−0.998971	+	0.0453433i	$0.985562\pi$
$972$	−0.222521	+	0.974928i	−0.00713736	+	0.0312708i
$973$	−6.98181	+	13.8774i	−0.223826	+	0.444889i
$974$	8.67185	+	37.9939i	0.277864	+	1.21740i
$975$	29.9673	−	9.24370i	0.959723	−	0.296035i
$976$	−4.56195	−	11.6237i	−0.146025	−	0.372064i
$977$	25.2450	+	23.4240i	0.807660	+	0.749399i	0.971488	−	0.237090i	$-0.0761937\pi$
$977$	25.2450	+	23.4240i	0.807660	+	0.749399i	−0.163828	+	0.986489i	$0.552384\pi$
$978$	−6.77746	−	4.62080i	−0.216719	−	0.147757i
$979$	−66.7555			−2.13352
$980$	−4.31499	−	22.4682i	−0.137837	−	0.717719i
$981$	−4.63157			−0.147875
$982$	27.6814	+	18.8729i	0.883350	+	0.602258i
$983$	−15.5969	−	14.4718i	−0.497464	−	0.461580i	0.391089	−	0.920353i	$-0.372099\pi$
$983$	−15.5969	−	14.4718i	−0.497464	−	0.461580i	−0.888553	+	0.458773i	$0.848289\pi$
$984$	2.63812	+	6.72183i	0.0841003	+	0.214284i
$985$	11.7961	−	3.63862i	0.375855	−	0.115936i
$986$	−2.92745	−	12.8260i	−0.0932291	−	0.408463i
$987$	−0.0454246	+	2.62085i	−0.00144588	+	0.0834227i
$988$	−6.84756	+	30.0011i	−0.217850	+	0.954463i
$989$	0.203694	+	2.71811i	0.00647710	+	0.0864309i
$990$	16.8138	+	5.18637i	0.534378	+	0.164834i
$991$	3.60373	−	48.0884i	0.114476	−	1.52758i	−0.583888	−	0.811835i	$-0.698469\pi$
$991$	3.60373	−	48.0884i	0.114476	−	1.52758i	0.698364	−	0.715743i	$-0.253912\pi$
$992$	0.643742	−	1.64023i	0.0204388	−	0.0520773i
$993$	3.30198	−	1.59015i	0.104785	−	0.0504619i
$994$	7.46341	−	0.429392i	0.236725	−	0.0136195i
$995$	27.8530	+	13.4133i	0.882999	+	0.425230i
$996$	−1.05049	+	0.974713i	−0.0332861	+	0.0308850i
$997$	14.4006	−	2.17054i	0.456071	−	0.0687416i	0.0830104	−	0.996549i	$-0.473547\pi$
$997$	14.4006	−	2.17054i	0.456071	−	0.0687416i	0.373060	+	0.927807i	$0.378308\pi$
$998$	9.69798	−	16.7974i	0.306984	−	0.531712i
$999$	0.142916	+	0.247538i	0.00452167	+	0.00783176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.m.b.151.1	yes	24
3.2	odd	2		882.2.z.a.739.2		24
49.37	even	21	inner	294.2.m.b.37.1	✓	24
147.86	odd	42		882.2.z.a.37.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.b.37.1	✓	24	49.37	even	21	inner
294.2.m.b.151.1	yes	24	1.1	even	1	trivial
882.2.z.a.37.2		24	147.86	odd	42
882.2.z.a.739.2		24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.826239 + 0.563320i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.365341 + 0.930874i) q^{4} +(-3.12319 + 0.963376i) q^{5} +(-0.222521 - 0.974928i) q^{6} +(-2.56883 - 0.633346i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.0747301 + 0.997204i) q^{9} +O(q^{10})\)	\(q+(0.826239 + 0.563320i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.365341 + 0.930874i) q^{4} +(-3.12319 + 0.963376i) q^{5} +(-0.222521 - 0.974928i) q^{6} +(-2.56883 - 0.633346i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.0747301 + 0.997204i) q^{9} +(-3.12319 - 0.963376i) q^{10} +(-0.402312 + 5.36848i) q^{11} +(0.365341 - 0.930874i) q^{12} +(-4.97235 + 2.39456i) q^{13} +(-1.76569 - 1.97037i) q^{14} +(2.94472 + 1.41810i) q^{15} +(-0.733052 + 0.680173i) q^{16} +(7.74318 - 1.16710i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.78794 - 4.82885i) q^{19} +(-2.03781 - 2.55533i) q^{20} +(1.45230 + 2.21152i) q^{21} +(-3.35658 + 4.20902i) q^{22} +(-1.63260 - 0.246074i) q^{23} +(0.826239 - 0.563320i) q^{24} +(4.69503 - 3.20101i) q^{25} +(-5.45725 - 0.822549i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-0.348932 - 2.62264i) q^{28} +(-1.04749 - 1.31351i) q^{29} +(1.63420 + 2.83051i) q^{30} +(-0.881015 + 1.52596i) q^{31} +(-0.988831 + 0.149042i) q^{32} +(3.94641 - 3.66173i) q^{33} +(7.05516 + 3.39759i) q^{34} +(8.63308 - 0.496687i) q^{35} +(-0.900969 + 0.433884i) q^{36} +(-0.104426 + 0.266074i) q^{37} +(0.416685 - 5.56028i) q^{38} +(5.27371 + 1.62672i) q^{39} +(-0.244247 - 3.25926i) q^{40} +(-1.60682 + 7.03994i) q^{41} +(-0.0458492 + 2.64535i) q^{42} +(-0.367365 - 1.60953i) q^{43} +(-5.14436 + 1.58682i) q^{44} +(-1.19408 - 3.04246i) q^{45} +(-1.21030 - 1.12299i) q^{46} +(0.818587 + 0.558103i) q^{47} +1.00000 q^{48} +(6.19774 + 3.25391i) q^{49} +5.68241 q^{50} +(-6.46998 - 4.41116i) q^{51} +(-4.04564 - 3.75380i) q^{52} +(2.62684 + 6.69307i) q^{53} +(0.955573 - 0.294755i) q^{54} +(-3.91537 - 17.1544i) q^{55} +(1.18908 - 2.36349i) q^{56} +(-1.24075 + 5.43607i) q^{57} +(-0.125550 - 1.67535i) q^{58} +(-5.68241 - 1.75279i) q^{59} +(-0.244247 + 3.25926i) q^{60} +(-4.56195 + 11.6237i) q^{61} +(-1.58753 + 0.764516i) q^{62} +(0.439607 - 2.60897i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(13.2227 - 12.2689i) q^{65} +(5.32341 - 0.802374i) q^{66} +(3.25130 - 5.63141i) q^{67} +(3.91532 + 6.78153i) q^{68} +(1.02941 + 1.29083i) q^{69} +(7.41278 + 4.45281i) q^{70} +(-1.76171 + 2.20912i) q^{71} +(-0.988831 - 0.149042i) q^{72} +(5.78254 - 3.94247i) q^{73} +(-0.236166 + 0.161015i) q^{74} +(-5.61894 - 0.846919i) q^{75} +(3.47650 - 4.35939i) q^{76} +(4.43358 - 13.5359i) q^{77} +(3.44097 + 4.31485i) q^{78} +(2.69706 + 4.67145i) q^{79} +(1.63420 - 2.83051i) q^{80} +(-0.988831 + 0.149042i) q^{81} +(-5.29336 + 4.91152i) q^{82} +(-1.29112 - 0.621772i) q^{83} +(-1.52806 + 2.15987i) q^{84} +(-23.0591 + 11.1047i) q^{85} +(0.603149 - 1.53680i) q^{86} +(-0.125550 + 1.67535i) q^{87} +(-5.14436 - 1.58682i) q^{88} +(0.926649 + 12.3653i) q^{89} +(0.727286 - 3.18645i) q^{90} +(14.2897 - 3.00199i) q^{91} +(-0.367390 - 1.60964i) q^{92} +(1.68375 - 0.519367i) q^{93} +(0.361958 + 0.922253i) q^{94} +(13.3592 + 12.3956i) q^{95} +(0.826239 + 0.563320i) q^{96} -18.6334 q^{97} +(3.28782 + 6.17982i) q^{98} -5.38353 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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