LMFDB - Embedded newform 294.2.m.b.37.1

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			37.1
Character	$\chi$	$=$	294.37
Dual form			294.2.m.b.151.1

$q$-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 $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

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	−0.497180	−	0.867647i	$-0.665631\pi$
$5$	−3.12319	−	0.963376i	−1.39673	−	0.430835i	−0.899553	+	0.436812i	$0.856107\pi$
$6$	−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	−0.643233	−	0.765671i	$-0.722407\pi$
$11$	−0.402312	−	5.36848i	−0.121302	−	1.61866i	0.521931	−	0.852988i	$-0.325212\pi$
$12$	0.365341	+	0.930874i	0.105465	+	0.268720i
$13$	−4.97235	−	2.39456i	−1.37908	−	0.664131i	−0.410279	−	0.911960i	$-0.634569\pi$
$13$	−4.97235	−	2.39456i	−1.37908	−	0.664131i	−0.968804	+	0.247829i	$0.920283\pi$
$14$	−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	0.985716	−	0.168418i	$-0.0538658\pi$
$17$	7.74318	+	1.16710i	1.87800	+	0.283062i	0.892281	+	0.451480i	$0.149104\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−2.78794	+	4.82885i	−0.639596	+	1.10781i	0.345925	+	0.938262i	$0.387565\pi$
$19$	−2.78794	+	4.82885i	−0.639596	+	1.10781i	−0.985521	+	0.169551i	$0.945768\pi$
$20$	−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	−0.317028	−	0.948416i	$-0.602685\pi$
$23$	−1.63260	+	0.246074i	−0.340420	+	0.0513101i	−0.0233924	+	0.999726i	$0.507447\pi$
$24$	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	−0.869518	−	0.493901i	$-0.835571\pi$
$29$	−1.04749	+	1.31351i	−0.194515	+	0.243914i	0.675004	+	0.737814i	$0.264142\pi$
$30$	1.63420	−	2.83051i	0.298362	−	0.516779i
$31$	−0.881015	−	1.52596i	−0.158235	−	0.274071i	0.775997	−	0.630736i	$-0.217247\pi$
$31$	−0.881015	−	1.52596i	−0.158235	−	0.274071i	−0.934232	+	0.356665i	$0.883914\pi$
$32$	−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	0.922033	−	0.387111i	$-0.126527\pi$
$37$	−0.104426	−	0.266074i	−0.0171676	−	0.0437423i	−0.939201	+	0.343369i	$0.888432\pi$
$38$	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	−0.930633	−	0.365954i	$-0.880743\pi$
$41$	−1.60682	−	7.03994i	−0.250943	−	1.09945i	0.679690	−	0.733500i	$-0.262115\pi$
$42$	−0.0458492	−	2.64535i	−0.00707468	−	0.408187i
$43$	−0.367365	+	1.60953i	−0.0560226	+	0.245451i	−0.995184	−	0.0980254i	$-0.968747\pi$
$43$	−0.367365	+	1.60953i	−0.0560226	+	0.245451i	0.939161	+	0.343476i	$0.111605\pi$
$44$	−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	−0.502146	−	0.864783i	$-0.667456\pi$
$47$	0.818587	−	0.558103i	0.119403	−	0.0814077i	0.621549	+	0.783375i	$0.286504\pi$
$48$	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	−0.629044	−	0.777370i	$-0.716553\pi$
$53$	2.62684	−	6.69307i	0.360824	−	0.919364i	0.989868	−	0.141994i	$-0.0453514\pi$
$54$	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	−0.641670	−	0.766981i	$-0.721758\pi$
$59$	−5.68241	+	1.75279i	−0.739786	+	0.228194i	−0.0981166	+	0.995175i	$0.531282\pi$
$60$	−0.244247	−	3.25926i	−0.0315322	−	0.420768i
$61$	−4.56195	−	11.6237i	−0.584098	−	1.48826i	−0.851333	−	0.524626i	$-0.824205\pi$
$61$	−4.56195	−	11.6237i	−0.584098	−	1.48826i	0.267235	−	0.963631i	$-0.413890\pi$
$62$	−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	0.993380	−	0.114871i	$-0.0366454\pi$
$67$	3.25130	+	5.63141i	0.397209	+	0.687987i	−0.596171	+	0.802857i	$0.703312\pi$
$68$	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	0.666225	−	0.745751i	$-0.267909\pi$
$71$	−1.76171	−	2.20912i	−0.209077	−	0.262174i	−0.875302	+	0.483576i	$0.839338\pi$
$72$	−0.988831	+	0.149042i	−0.116535	+	0.0175648i
$73$	5.78254	+	3.94247i	0.676795	+	0.461431i	0.852304	−	0.523047i	$-0.175205\pi$
$73$	5.78254	+	3.94247i	0.676795	+	0.461431i	−0.175509	+	0.984478i	$0.556157\pi$
$74$	−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	−0.673470	−	0.739214i	$-0.735197\pi$
$79$	2.69706	−	4.67145i	0.303443	−	0.525579i	0.976914	+	0.213635i	$0.0685303\pi$
$80$	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	−0.503399	−	0.864054i	$-0.667918\pi$
$83$	−1.29112	+	0.621772i	−0.141719	+	0.0682483i	0.361680	+	0.932302i	$0.382203\pi$
$84$	−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	−0.702500	−	0.711683i	$-0.747933\pi$
$89$	0.926649	−	12.3653i	0.0982246	−	1.31072i	0.800725	−	0.599032i	$-0.204448\pi$
$90$	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	−0.121863	−	0.992547i	$-0.538887\pi$
$101$	8.63085	−	8.00826i	0.858802	−	0.796852i	0.980665	+	0.195695i	$0.0626964\pi$
$102$	−2.86085	+	7.28934i	−0.283267	+	0.721752i
$103$	4.40695	+	1.35936i	0.434230	+	0.133942i	0.504161	−	0.863610i	$-0.331802\pi$
$103$	4.40695	+	1.35936i	0.434230	+	0.133942i	−0.0699312	+	0.997552i	$0.522278\pi$
$104$	−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	0.986629	+	0.162985i	$0.0521121\pi$
$107$	−0.137284	+	1.83193i	−0.0132718	+	0.177100i	−0.999900	+	0.0141150i	$0.995507\pi$
$108$	0.955573	−	0.294755i	0.0919500	−	0.0283628i
$109$	−0.346118	−	4.61862i	−0.0331521	−	0.442384i	−0.988939	−	0.148323i	$-0.952612\pi$
$109$	−0.346118	−	4.61862i	−0.0331521	−	0.442384i	0.955787	−	0.294060i	$-0.0950067\pi$
$110$	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	0.248347	−	0.968671i	$-0.420113\pi$
$113$	12.3366	−	5.94098i	1.16053	−	0.558880i	0.912179	+	0.409791i	$0.134398\pi$
$114$	−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	−0.960495	−	0.278297i	$-0.910230\pi$
$127$	−5.35799	+	6.71871i	−0.475445	+	0.596189i	0.485050	+	0.874486i	$0.338801\pi$
$128$	−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	−0.985443	−	0.170005i	$-0.945622\pi$
$131$	−14.0621	−	13.0478i	−1.22862	−	1.13999i	−0.243172	−	0.969983i	$-0.578188\pi$
$132$	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	−0.859046	−	0.511899i	$-0.828942\pi$
$137$	−14.9874	+	4.62300i	−1.28046	+	0.394969i	−0.421414	+	0.906869i	$0.638466\pi$
$138$	0.123382	−	1.64642i	0.0105030	−	0.140153i
$139$	1.30655	+	5.72437i	0.110820	+	0.485535i	0.999628	+	0.0272556i	$0.00867679\pi$
$139$	1.30655	+	5.72437i	0.110820	+	0.485535i	−0.888808	+	0.458279i	$0.848466\pi$
$140$	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	−0.989619	−	0.143715i	$-0.954095\pi$
$149$	−14.8601	+	10.1314i	−1.21739	+	0.830001i	−0.227768	+	0.973715i	$0.573143\pi$
$150$	−4.16550	+	3.86502i	−0.340112	+	0.315577i
$151$	−3.65029	+	9.30079i	−0.297057	+	0.756888i	0.701946	+	0.712230i	$0.252315\pi$
$151$	−3.65029	+	9.30079i	−0.297057	+	0.756888i	−0.999002	+	0.0446574i	$0.985780\pi$
$152$	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	0.0358046	−	0.999359i	$-0.488601\pi$
$157$	7.87316	−	2.42855i	0.628347	−	0.193819i	0.592542	+	0.805540i	$0.298124\pi$
$158$	−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	0.879611	−	0.475694i	$-0.157803\pi$
$163$	6.01307	+	5.57931i	0.470980	+	0.437006i	−0.408631	+	0.912700i	$0.633994\pi$
$164$	−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	−0.770351	−	0.637621i	$-0.779919\pi$
$167$	0.293383	−	0.367890i	0.0227026	−	0.0284682i	0.793053	+	0.609152i	$0.208490\pi$
$168$	−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	−0.273224	−	0.961950i	$-0.588090\pi$
$173$	−3.29836	+	0.497147i	−0.250769	+	0.0377974i	0.0224545	+	0.999748i	$0.492852\pi$
$174$	−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	0.313123	−	0.949713i	$-0.398625\pi$
$179$	4.44723	+	0.670312i	0.332401	+	0.0501015i	0.0192788	+	0.999814i	$0.493863\pi$
$180$	2.39590	+	2.22307i	0.178580	+	0.165698i
$181$	10.4773	−	5.04560i	0.778771	−	0.375036i	−0.00188420	−	0.999998i	$-0.500600\pi$
$181$	10.4773	−	5.04560i	0.778771	−	0.375036i	0.780655	+	0.624962i	$0.214885\pi$
$182$	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	−0.348106	−	0.937455i	$-0.613175\pi$
$191$	−16.0842	−	4.96132i	−1.16381	−	0.358988i	−0.815706	+	0.578467i	$0.803651\pi$
$192$	0.365341	−	0.930874i	0.0263662	−	0.0671800i
$193$	13.5107	−	12.5361i	0.972521	−	0.902368i	−0.0227267	−	0.999742i	$-0.507235\pi$
$193$	13.5107	−	12.5361i	0.972521	−	0.902368i	0.995248	+	0.0973739i	$0.0310443\pi$
$194$	−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	−0.886567	−	0.462600i	$-0.846917\pi$
$199$	−6.93366	+	6.43349i	−0.491514	+	0.456058i	0.395053	+	0.918658i	$0.370726\pi$
$200$	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	−0.455962	−	0.889999i	$-0.650705\pi$
$211$	−0.645240	+	0.310731i	−0.0444201	+	0.0213916i	0.411542	+	0.911391i	$0.364990\pi$
$212$	−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	0.981616	+	0.190865i	$0.0611292\pi$
$223$	14.1756	+	17.7756i	0.949266	+	1.19034i	−0.0323506	+	0.999477i	$0.510299\pi$
$224$	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	0.869689	−	0.493600i	$-0.164319\pi$
$227$	0.111114	+	0.192456i	0.00737491	+	0.0127737i	−0.862314	+	0.506373i	$0.830986\pi$
$228$	−5.51359	−	0.831041i	−0.365147	−	0.0550370i
$229$	8.88191	+	8.24121i	0.586933	+	0.544595i	0.916756	−	0.399448i	$-0.130798\pi$
$229$	8.88191	+	8.24121i	0.586933	+	0.544595i	−0.329822	+	0.944043i	$0.606989\pi$
$230$	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	−0.994798	−	0.101865i	$-0.967519\pi$
$233$	−5.11119	−	13.0231i	−0.334845	−	0.853172i	0.659953	−	0.751307i	$-0.270576\pi$
$234$	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	−0.733034	−	0.680192i	$-0.761896\pi$
$239$	3.44025	−	15.0727i	0.222531	−	0.974973i	0.955565	−	0.294781i	$-0.0952466\pi$
$240$	−3.12319	−	0.963376i	−0.201601	−	0.0621857i
$241$	2.75695	−	7.02458i	0.177591	−	0.452493i	−0.814166	−	0.580633i	$-0.802805\pi$
$241$	2.75695	−	7.02458i	0.177591	−	0.452493i	0.991756	+	0.128139i	$0.0409005\pi$
$242$	−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	−0.749018	−	0.662549i	$-0.769475\pi$
$251$	3.37920	−	14.8052i	0.213293	−	0.934499i	0.962312	−	0.271949i	$-0.0876684\pi$
$252$	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	0.997258	−	0.0740058i	$-0.0235783\pi$
$257$	3.46081	+	8.81800i	0.215879	+	0.550052i	−0.781378	+	0.624058i	$0.785483\pi$
$258$	−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	0.998939	+	0.0460452i	$0.0146618\pi$
$263$	8.74672	+	15.1498i	0.539346	+	0.934175i	−0.459593	+	0.888129i	$0.652005\pi$
$264$	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	0.958862	−	0.283874i	$-0.0916196\pi$
$269$	17.1380	+	11.6845i	1.04492	+	0.712416i	0.0860609	+	0.996290i	$0.472572\pi$
$270$	−2.70047	−	1.84115i	−0.164346	−	0.112049i
$271$	−13.3859	+	2.01760i	−0.813135	+	0.122560i	−0.542429	−	0.840102i	$-0.682495\pi$
$271$	−13.3859	+	2.01760i	−0.813135	+	0.122560i	−0.270706	+	0.962662i	$0.587257\pi$
$272$	−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	0.617433	−	0.786624i	$-0.288173\pi$
$277$	16.2368	+	2.44730i	0.975573	+	0.147044i	0.358140	+	0.933668i	$0.383411\pi$
$278$	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	0.798189	−	0.602408i	$-0.205792\pi$
$281$	13.8273	+	6.65890i	0.824870	+	0.397236i	0.0266813	+	0.999644i	$0.491506\pi$
$282$	0.361958	+	0.922253i	0.0215543	+	0.0549194i
$283$	−2.40929	−	32.1498i	−0.143218	−	1.91111i	−0.356798	−	0.934182i	$-0.616132\pi$
$283$	−2.40929	−	32.1498i	−0.143218	−	1.91111i	0.213580	−	0.976926i	$-0.431488\pi$
$284$	−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	−0.241775	−	0.970332i	$-0.577730\pi$
$307$	−20.1699	−	9.71330i	−1.15116	−	0.554367i	−0.909381	+	0.415965i	$0.863444\pi$
$308$	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	0.969133	−	0.246540i	$-0.0792937\pi$
$311$	32.1409	+	4.84445i	1.82254	+	0.274704i	0.853408	+	0.521244i	$0.174532\pi$
$312$	−2.75945	−	4.77950i	−0.156223	−	0.270586i
$313$	0.720694	−	1.24828i	0.0407360	−	0.0705569i	−0.844939	−	0.534863i	$-0.820363\pi$
$313$	0.720694	−	1.24828i	0.0407360	−	0.0705569i	0.885675	+	0.464307i	$0.153696\pi$
$314$	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	0.129661	−	0.991558i	$-0.458611\pi$
$317$	9.71819	−	1.46478i	0.545828	−	0.0822704i	0.416167	+	0.909288i	$0.363373\pi$
$318$	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	0.889342	−	0.457242i	$-0.151163\pi$
$331$	−1.33895	−	3.41158i	−0.0735951	−	0.187517i	−0.962938	+	0.269724i	$0.913067\pi$
$332$	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	0.824520	+	0.565833i	$0.191445\pi$
$337$	−3.00793	+	13.1786i	−0.163853	+	0.717885i	−0.988372	+	0.152052i	$0.951412\pi$
$338$	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	−0.839152	−	0.543897i	$-0.816948\pi$
$347$	2.71844	−	6.92647i	0.145934	−	0.371833i	0.985086	+	0.172064i	$0.0550436\pi$
$348$	−1.60541	−	0.495203i	−0.0860589	−	0.0265457i
$349$	4.37108	−	19.1510i	0.233979	−	1.02513i	−0.712325	−	0.701849i	$-0.752358\pi$
$349$	4.37108	−	19.1510i	0.233979	−	1.02513i	0.946304	−	0.323278i	$-0.104785\pi$
$350$	−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	−0.736299	−	0.676656i	$-0.763428\pi$
$353$	−18.1022	+	5.58380i	−0.963485	+	0.297196i	−0.227185	+	0.973852i	$0.572952\pi$
$354$	−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	0.233387	−	0.972384i	$-0.425019\pi$
$359$	−13.6200	−	12.6375i	−0.718837	−	0.666983i	−0.952224	+	0.305401i	$0.901209\pi$
$360$	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	0.192899	−	0.981219i	$-0.438211\pi$
$367$	−12.4526	−	8.49001i	−0.650018	−	0.443175i	−0.842917	+	0.538044i	$0.819163\pi$
$368$	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	−0.966120	−	0.258094i	$-0.916906\pi$
$373$	−5.01263	+	8.68213i	−0.259544	+	0.449544i	0.706576	+	0.707638i	$0.250239\pi$
$374$	−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	0.229916	−	0.973211i	$-0.426155\pi$
$379$	−7.54617	−	3.63405i	−0.387621	−	0.186668i	−0.617537	+	0.786542i	$0.711869\pi$
$380$	−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	−0.997375	−	0.0724115i	$-0.976931\pi$
$383$	−0.00680038	+	0.0907447i	−0.000347483	+	0.00463684i	0.997027	+	0.0770483i	$0.0245496\pi$
$384$	−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	−0.938071	−	0.346443i	$-0.887390\pi$
$389$	−13.0705	+	12.1276i	−0.662700	+	0.614895i	0.275372	+	0.961338i	$0.411199\pi$
$390$	−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	0.183733	−	0.982976i	$-0.441182\pi$
$397$	−4.34742	−	1.34100i	−0.218191	−	0.0673029i	−0.401923	+	0.915673i	$0.631658\pi$
$398$	−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	0.870140	+	0.492805i	$0.164028\pi$
$401$	−1.27619	+	17.0296i	−0.0637300	+	0.850418i	−0.933870	+	0.357613i	$0.883591\pi$
$402$	−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	0.143440	−	0.989659i	$-0.454184\pi$
$409$	−0.226503	−	0.0341399i	−0.0111999	−	0.00168811i	−0.154640	+	0.987971i	$0.549422\pi$
$410$	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	0.415102	−	0.909775i	$-0.363746\pi$
$419$	−11.5495	−	14.4826i	−0.564231	−	0.707524i	−0.979334	+	0.202251i	$0.935174\pi$
$420$	2.69167	+	8.21777i	0.131340	+	0.400986i
$421$	−9.29008	+	11.6494i	−0.452771	+	0.567757i	−0.954859	−	0.297060i	$-0.903994\pi$
$421$	−9.29008	+	11.6494i	−0.452771	+	0.567757i	0.502088	+	0.864817i	$0.332565\pi$
$422$	−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	−0.503106	−	0.864225i	$-0.667810\pi$
$431$	−8.96766	+	2.76616i	−0.431957	+	0.133241i	0.0711492	+	0.997466i	$0.477333\pi$
$432$	0.0747301	−	0.997204i	0.00359545	−	0.0479780i
$433$	−5.87772	−	25.7520i	−0.282465	−	1.23756i	−0.894622	−	0.446825i	$-0.852555\pi$
$433$	−5.87772	−	25.7520i	−0.282465	−	1.23756i	0.612156	−	0.790737i	$-0.290302\pi$
$434$	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	−0.234949	−	0.972008i	$-0.575492\pi$
$439$	12.2368	−	8.34291i	0.584031	−	0.398185i	0.818980	+	0.573822i	$0.194540\pi$
$440$	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	−0.486533	−	0.873662i	$-0.661739\pi$
$443$	3.13578	−	2.13794i	0.148986	−	0.101577i	0.635519	+	0.772085i	$0.280786\pi$
$444$	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	−0.926723	−	0.375745i	$-0.877387\pi$
$449$	−5.39920	−	23.6554i	−0.254804	−	1.11637i	0.671919	−	0.740624i	$-0.265470\pi$
$450$	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	0.792257	−	0.610188i	$-0.208906\pi$
$457$	5.19433	+	4.81964i	0.242981	+	0.225453i	−0.549276	+	0.835641i	$0.685096\pi$
$458$	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	−0.880515	−	0.474018i	$-0.842803\pi$
$461$	−4.77618	+	5.98914i	−0.222449	+	0.278942i	0.658066	+	0.752960i	$0.271375\pi$
$462$	−14.1831	+	1.31040i	−0.659857	+	0.0609652i
$463$	−6.68706	−	8.38531i	−0.310774	−	0.389698i	0.601775	−	0.798666i	$-0.294460\pi$
$463$	−6.68706	−	8.38531i	−0.310774	−	0.389698i	−0.912549	+	0.408967i	$0.865889\pi$
$464$	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	−0.190548	−	0.981678i	$-0.561026\pi$
$467$	−1.79960	+	0.271247i	−0.0832757	+	0.0125518i	0.107272	+	0.994230i	$0.465788\pi$
$468$	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	−0.776750	−	0.629809i	$-0.783133\pi$
$479$	−2.24428	−	29.9478i	−0.102544	−	1.36835i	0.674206	−	0.738543i	$-0.264486\pi$
$480$	−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	0.327972	−	0.944687i	$-0.393635\pi$
$487$	28.5677	−	26.5070i	1.29453	−	1.20115i	0.966555	−	0.256458i	$-0.0825557\pi$
$488$	−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	0.865883	+	0.500247i	$0.166758\pi$
$499$	−1.44946	+	19.3417i	−0.0648868	+	0.865854i	−0.930769	+	0.365607i	$0.880861\pi$
$500$	−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	0.676762	−	0.736202i	$-0.263383\pi$
$503$	11.7326	+	5.65012i	0.523130	+	0.251926i	−0.153632	+	0.988128i	$0.549097\pi$
$504$	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	−0.972924	−	0.231125i	$-0.925759\pi$
$509$	−6.45926	+	11.1878i	−0.286302	+	0.495889i	0.686622	+	0.727014i	$0.259093\pi$
$510$	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	0.553086	−	0.833124i	$-0.313450\pi$
$521$	−10.1565	−	17.5915i	−0.444964	−	0.770700i	−0.998050	+	0.0624245i	$0.980117\pi$
$522$	1.66128	+	0.250398i	0.0727124	+	0.0109596i
$523$	25.2349	+	23.4145i	1.10344	+	1.02385i	0.999572	+	0.0292558i	$0.00931375\pi$
$523$	25.2349	+	23.4145i	1.10344	+	1.02385i	0.103872	+	0.994591i	$0.466877\pi$
$524$	−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	−0.181008	−	0.983482i	$-0.557936\pi$
$541$	15.5456	−	10.5988i	0.668360	−	0.455680i	0.849368	+	0.527802i	$0.176984\pi$
$542$	−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	0.999990	−	0.00455049i	$-0.00144847\pi$
$547$	2.26994	+	9.94527i	0.0970557	+	0.425229i	−0.902934	+	0.429779i	$0.858591\pi$
$548$	−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	−0.998725	−	0.0504763i	$-0.983926\pi$
$557$	−12.8171	−	22.1998i	−0.543076	−	0.940636i	0.455649	−	0.890160i	$-0.349407\pi$
$558$	−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	0.638674	−	0.769478i	$-0.279483\pi$
$563$	3.69489	+	2.51913i	0.155721	+	0.106169i	−0.482953	+	0.875646i	$0.660436\pi$
$564$	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	−0.944393	−	0.328818i	$-0.893350\pi$
$569$	−4.47096	+	7.74393i	−0.187432	+	0.324642i	0.756961	+	0.653460i	$0.226683\pi$
$570$	9.11208	+	15.7826i	0.381663	+	0.661060i
$571$	−38.5925	−	5.81689i	−1.61505	−	0.243429i	−0.721505	−	0.692409i	$-0.756549\pi$
$571$	−38.5925	−	5.81689i	−1.61505	−	0.243429i	−0.893542	+	0.448980i	$0.851787\pi$
$572$	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	0.850387	+	0.526158i	$0.176368\pi$
$577$	2.11186	+	28.1808i	0.0879178	+	1.17318i	−0.762469	+	0.647024i	$0.776013\pi$
$578$	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	−0.192101	−	0.981375i	$-0.561530\pi$
$593$	−22.0053	−	6.78774i	−0.903650	−	0.278739i	−0.711549	+	0.702636i	$0.752006\pi$
$594$	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	−0.776861	−	0.629672i	$-0.783189\pi$
$599$	−2.50924	−	33.4834i	−0.102525	−	1.36810i	0.674337	−	0.738424i	$-0.264430\pi$
$600$	2.07602	+	5.28960i	0.0847530	+	0.215947i
$601$	28.6246	+	13.7849i	1.16762	+	0.562297i	0.914281	−	0.405081i	$-0.132757\pi$
$601$	28.6246	+	13.7849i	1.16762	+	0.562297i	0.253340	+	0.967377i	$0.418471\pi$
$602$	−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	−0.991022	−	0.133700i	$-0.957314\pi$
$607$	−9.35539	+	16.2040i	−0.379723	+	0.657700i	0.611298	+	0.791400i	$0.290647\pi$
$608$	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	0.888566	+	0.458750i	$0.151703\pi$
$613$	40.6103	+	27.6876i	1.64023	+	1.11829i	0.751667	+	0.659542i	$0.229250\pi$
$614$	−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	−0.811945	−	0.583734i	$-0.801591\pi$
$617$	−1.54430	+	1.93649i	−0.0621711	+	0.0779601i	0.749774	+	0.661694i	$0.230162\pi$
$618$	−2.30592	+	3.99397i	−0.0927578	+	0.160661i
$619$	−6.10363	−	10.5718i	−0.245326	−	0.424916i	0.716897	−	0.697179i	$-0.245562\pi$
$619$	−6.10363	−	10.5718i	−0.245326	−	0.424916i	−0.962223	+	0.272262i	$0.912228\pi$
$620$	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	−0.770078	−	0.637950i	$-0.779783\pi$
$631$	5.03737	−	22.0701i	0.200534	−	0.878599i	0.970612	−	0.240649i	$-0.0773602\pi$
$632$	−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	−0.989099	−	0.147249i	$-0.952958\pi$
$641$	−4.14920	+	10.5720i	−0.163883	+	0.417568i	0.825216	+	0.564817i	$0.191053\pi$
$642$	−1.75546	−	0.541486i	−0.0692823	−	0.0213708i
$643$	9.57096	−	41.9331i	0.377442	−	1.65368i	−0.327826	−	0.944738i	$-0.606316\pi$
$643$	9.57096	−	41.9331i	0.377442	−	1.65368i	0.705267	−	0.708942i	$-0.250827\pi$
$644$	−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	−0.113111	−	0.993582i	$-0.536082\pi$
$647$	8.98246	−	2.77072i	0.353137	−	0.108928i	0.466248	+	0.884654i	$0.345605\pi$
$648$	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	0.211966	−	0.977277i	$-0.432014\pi$
$653$	−19.0821	−	17.7056i	−0.746739	−	0.692872i	−0.958704	+	0.284405i	$0.908204\pi$
$654$	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	0.854648	−	0.519207i	$-0.173773\pi$
$659$	4.06325	+	5.09515i	0.158282	+	0.198479i	−0.696367	+	0.717686i	$0.745201\pi$
$660$	−17.3990	+	2.62248i	−0.677255	+	0.102080i
$661$	−38.8549	−	26.4909i	−1.51128	−	1.03037i	−0.983482	−	0.181006i	$-0.942065\pi$
$661$	−38.8549	−	26.4909i	−1.51128	−	1.03037i	−0.527800	−	0.849368i	$-0.676983\pi$
$662$	−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	−0.398125	−	0.917331i	$-0.630339\pi$
$673$	−35.3736	−	17.0350i	−1.36355	−	0.656651i	−0.965425	+	0.260680i	$0.916053\pi$
$674$	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	0.857585	+	0.514342i	$0.171964\pi$
$677$	−1.74537	+	23.2904i	−0.0670801	+	0.895122i	−0.924665	+	0.380780i	$0.875655\pi$
$678$	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	−0.831145	−	0.556056i	$-0.812314\pi$
$683$	−8.85311	+	8.21449i	−0.338755	+	0.314319i	0.492390	+	0.870375i	$0.336123\pi$
$684$	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	0.658707	−	0.752400i	$-0.271104\pi$
$691$	20.4805	+	6.31739i	0.779114	+	0.240325i	0.120407	+	0.992725i	$0.461580\pi$
$692$	−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	−0.787810	−	0.615918i	$-0.788785\pi$
$701$	−21.1138	+	10.1679i	−0.797458	+	0.384036i	−0.00964775	+	0.999953i	$0.503071\pi$
$702$	−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	0.150089	−	0.988672i	$-0.452044\pi$
$709$	15.5749	−	2.34753i	0.584926	−	0.0881634i	0.434837	+	0.900509i	$0.356806\pi$
$710$	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	0.456322	−	0.889815i	$-0.349167\pi$
$719$	−10.6427	−	9.87494i	−0.396904	−	0.368273i	−0.853226	+	0.521542i	$0.825357\pi$
$720$	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	0.956969	+	0.290192i	$0.0937191\pi$
$727$	5.95016	+	26.0693i	0.220679	+	0.966859i	−0.736289	+	0.676667i	$0.763424\pi$
$728$	−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	−0.770898	−	0.636959i	$-0.780192\pi$
$733$	−12.4435	+	8.48381i	−0.459610	+	0.313357i	0.311288	+	0.950316i	$0.399240\pi$
$734$	−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	−0.715097	−	0.699025i	$-0.753618\pi$
$739$	7.73574	−	19.7103i	0.284564	−	0.725057i	0.999661	−	0.0260318i	$-0.00828713\pi$
$740$	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	−0.980847	−	0.194782i	$-0.937600\pi$
$743$	−4.95134	−	21.6932i	−0.181647	−	0.795847i	0.799200	−	0.601066i	$-0.205257\pi$
$744$	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	−0.00825846	−	0.999966i	$-0.502629\pi$
$751$	−27.5700	−	25.5813i	−1.00605	−	0.933474i	−0.997787	+	0.0664922i	$0.978819\pi$
$752$	−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	0.829391	−	0.558668i	$-0.188688\pi$
$757$	2.75612	+	3.45606i	0.100173	+	0.125613i	−0.729218	+	0.684281i	$0.760116\pi$
$758$	−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	0.649713	−	0.760179i	$-0.274889\pi$
$761$	41.2312	−	6.21460i	1.49463	−	0.225279i	0.844915	+	0.534900i	$0.179651\pi$
$762$	−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	0.291585	−	0.956545i	$-0.405817\pi$
$769$	33.8661	−	16.3090i	1.22124	−	0.588119i	0.929657	+	0.368426i	$0.120103\pi$
$770$	−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	−0.998454	−	0.0555816i	$-0.982299\pi$
$773$	−0.540375	−	7.21080i	−0.0194359	−	0.259354i	0.979018	−	0.203773i	$-0.0653204\pi$
$774$	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	−0.331982	+	0.943286i	$0.607717\pi$
$787$	−36.3977	+	33.7722i	−1.29744	+	1.20385i	−0.965457	+	0.260562i	$0.916092\pi$
$788$	−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	0.652627	−	0.757679i	$-0.273667\pi$
$797$	13.1884	+	6.35119i	0.467157	+	0.224971i	−0.185471	+	0.982650i	$0.559381\pi$
$798$	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	0.381404	−	0.924408i	$-0.375441\pi$
$809$	−9.66379	−	6.58866i	−0.339761	−	0.231645i	−0.721165	+	0.692763i	$0.756393\pi$
$810$	3.23189	−	0.487129i	0.113557	−	0.0171160i
$811$	−1.19916	−	1.50370i	−0.0421082	−	0.0528021i	0.760331	−	0.649535i	$-0.225037\pi$
$811$	−1.19916	−	1.50370i	−0.0421082	−	0.0528021i	−0.802440	+	0.596733i	$0.796465\pi$
$812$	−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	−0.881481	−	0.472220i	$-0.843453\pi$
$821$	−15.9455	−	40.6284i	−0.556501	−	1.41794i	0.324980	−	0.945721i	$-0.394643\pi$
$822$	−1.17208	−	15.6403i	−0.0408810	−	0.545519i
$823$	−37.2952	+	11.5041i	−1.30003	+	0.401006i	−0.866068	−	0.499925i	$-0.833361\pi$
$823$	−37.2952	+	11.5041i	−1.30003	+	0.401006i	−0.433961	+	0.900932i	$0.642885\pi$
$824$	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	−0.822818	−	0.568305i	$-0.807599\pi$
$827$	4.74770	−	20.8010i	0.165094	−	0.723323i	0.987912	−	0.155018i	$-0.0495435\pi$
$828$	1.57769	+	0.486652i	0.0548284	+	0.0169123i
$829$	−7.15030	+	18.2187i	−0.248340	+	0.632761i	−0.999630	−	0.0272122i	$-0.991337\pi$
$829$	−7.15030	+	18.2187i	−0.248340	+	0.632761i	0.751289	+	0.659973i	$0.229432\pi$
$830$	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	0.604134	+	0.796883i	$0.293519\pi$
$839$	−8.28201	+	36.2858i	−0.285927	+	1.25273i	−0.890060	+	0.455843i	$0.849338\pi$
$840$	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	−0.956612	−	0.291366i	$-0.905890\pi$
$853$	−13.4256	+	16.8352i	−0.459684	+	0.576426i	0.496927	+	0.867792i	$0.334462\pi$
$854$	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	0.625396	−	0.780307i	$-0.284937\pi$
$857$	3.73284	+	2.54500i	0.127511	+	0.0869357i	−0.497885	+	0.867243i	$0.665890\pi$
$858$	−24.5485	−	16.7369i	−0.838072	−	0.571388i
$859$	−2.57028	+	0.387407i	−0.0876968	+	0.0132182i	−0.192744	−	0.981249i	$-0.561739\pi$
$859$	−2.57028	+	0.387407i	−0.0876968	+	0.0132182i	0.105047	+	0.994467i	$0.466501\pi$
$860$	−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	−0.355442	−	0.934698i	$-0.615670\pi$
$863$	18.5589	−	32.1449i	0.631751	−	1.09423i	0.987194	−	0.159527i	$-0.0509969\pi$
$864$	−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	0.449388	−	0.893337i	$-0.351642\pi$
$877$	9.40115	+	2.89987i	0.317454	+	0.0979217i	−0.131933	+	0.991259i	$0.542118\pi$
$878$	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	−0.728973	−	0.684543i	$-0.760002\pi$
$887$	−51.1335	−	15.7726i	−1.71689	−	0.529592i	−0.987922	+	0.154951i	$0.950478\pi$
$888$	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	0.114197	−	0.993458i	$-0.463570\pi$
$907$	−23.1555	−	15.7872i	−0.768866	−	0.524204i	−0.883063	+	0.469254i	$0.844523\pi$
$908$	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	0.109676	−	0.993967i	$-0.465019\pi$
$911$	31.8222	−	39.9038i	1.05432	−	1.32207i	0.944641	−	0.328105i	$-0.106410\pi$
$912$	−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	0.980455	+	0.196746i	$0.0630373\pi$
$919$	11.9911	+	30.5529i	0.395551	+	1.00785i	−0.584903	+	0.811103i	$0.698867\pi$
$920$	−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	−0.653818	−	0.756652i	$-0.726834\pi$
$929$	−5.74042	+	3.91375i	−0.188337	+	0.128406i	0.465481	+	0.885058i	$0.345881\pi$
$930$	−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	−0.983107	−	0.183031i	$-0.941409\pi$
$937$	−0.549275	+	2.40653i	−0.0179440	+	0.0786179i	0.965163	+	0.261649i	$0.0842663\pi$
$938$	−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	0.145458	−	0.989364i	$-0.453535\pi$
$941$	25.2452	−	7.78711i	0.822969	−	0.253852i	0.677512	+	0.735512i	$0.263058\pi$
$942$	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	0.935820	−	0.352478i	$-0.114661\pi$
$947$	20.1338	+	18.6815i	0.654262	+	0.607066i	−0.281558	+	0.959544i	$0.590851\pi$
$948$	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	0.735331	−	0.677708i	$-0.237027\pi$
$953$	−2.74785	−	3.44570i	−0.0890117	−	0.111617i	−0.824343	+	0.566091i	$0.808455\pi$
$954$	−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	0.898584	−	0.438802i	$-0.144597\pi$
$967$	34.6968	+	16.7091i	1.11577	+	0.537328i	0.217189	+	0.976130i	$0.430311\pi$
$968$	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	−0.998971	−	0.0453433i	$-0.985562\pi$
$971$	−0.137096	+	1.82942i	−0.00439962	+	0.0587088i	0.994572	+	0.104052i	$0.0331809\pi$
$972$	−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	−0.163828	−	0.986489i	$-0.552384\pi$
$977$	25.2450	−	23.4240i	0.807660	−	0.749399i	0.971488	+	0.237090i	$0.0761937\pi$
$978$	−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	−0.888553	−	0.458773i	$-0.848289\pi$
$983$	−15.5969	+	14.4718i	−0.497464	+	0.461580i	0.391089	+	0.920353i	$0.372099\pi$
$984$	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	0.698364	+	0.715743i	$0.253912\pi$
$991$	3.60373	+	48.0884i	0.114476	+	1.52758i	−0.583888	+	0.811835i	$0.698469\pi$
$992$	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	0.373060	−	0.927807i	$-0.378308\pi$
$997$	14.4006	+	2.17054i	0.456071	+	0.0687416i	0.0830104	+	0.996549i	$0.473547\pi$
$998$	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.37.1	✓	24
3.2	odd	2		882.2.z.a.37.2		24
49.4	even	21	inner	294.2.m.b.151.1	yes	24
147.53	odd	42		882.2.z.a.739.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.b.37.1	✓	24	1.1	even	1	trivial
294.2.m.b.151.1	yes	24	49.4	even	21	inner
882.2.z.a.37.2		24	3.2	odd	2
882.2.z.a.739.2		24	147.53	odd	42

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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