LMFDB - Embedded newform 273.2.cg.a.262.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			262.7
Character	$\chi$	$=$	273.262
Dual form			273.2.cg.a.124.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.255728 + 0.954388i) q^{2} -1.00000i q^{3} +(0.886590 - 0.511873i) q^{4} +(-0.244406 + 0.912136i) q^{5} +(0.954388 - 0.255728i) q^{6} +(2.46785 - 0.953787i) q^{7} +(2.11257 + 2.11257i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.255728 + 0.954388i) q^{2} -1.00000i q^{3} +(0.886590 - 0.511873i) q^{4} +(-0.244406 + 0.912136i) q^{5} +(0.954388 - 0.255728i) q^{6} +(2.46785 - 0.953787i) q^{7} +(2.11257 + 2.11257i) q^{8} -1.00000 q^{9} -0.933034 q^{10} +(-4.64956 - 4.64956i) q^{11} +(-0.511873 - 0.886590i) q^{12} +(3.43957 + 1.08136i) q^{13} +(1.54138 + 2.11138i) q^{14} +(0.912136 + 0.244406i) q^{15} +(-0.452226 + 0.783279i) q^{16} +(1.86677 + 3.23334i) q^{17} +(-0.255728 - 0.954388i) q^{18} +(0.889632 + 0.889632i) q^{19} +(0.250210 + 0.933796i) q^{20} +(-0.953787 - 2.46785i) q^{21} +(3.24847 - 5.62651i) q^{22} +(0.202140 + 0.116706i) q^{23} +(2.11257 - 2.11257i) q^{24} +(3.55787 + 2.05414i) q^{25} +(-0.152440 + 3.55922i) q^{26} +1.00000i q^{27} +(1.69975 - 2.10884i) q^{28} +(-2.32457 - 4.02628i) q^{29} +0.933034i q^{30} +(-7.35090 + 1.96967i) q^{31} +(4.90846 + 1.31522i) q^{32} +(-4.64956 + 4.64956i) q^{33} +(-2.60848 + 2.60848i) q^{34} +(0.266825 + 2.48413i) q^{35} +(-0.886590 + 0.511873i) q^{36} +(-4.85874 + 1.30189i) q^{37} +(-0.621551 + 1.07656i) q^{38} +(1.08136 - 3.43957i) q^{39} +(-2.44328 + 1.41063i) q^{40} +(-2.49056 + 9.29490i) q^{41} +(2.11138 - 1.54138i) q^{42} +(-10.4062 - 6.00801i) q^{43} +(-6.50224 - 1.74227i) q^{44} +(0.244406 - 0.912136i) q^{45} +(-0.0596897 + 0.222765i) q^{46} +(-2.10393 - 0.563747i) q^{47} +(0.783279 + 0.452226i) q^{48} +(5.18058 - 4.70761i) q^{49} +(-1.05060 + 3.92089i) q^{50} +(3.23334 - 1.86677i) q^{51} +(3.60301 - 0.801905i) q^{52} +(2.04084 - 3.53484i) q^{53} +(-0.954388 + 0.255728i) q^{54} +(5.37742 - 3.10465i) q^{55} +(7.22846 + 3.19857i) q^{56} +(0.889632 - 0.889632i) q^{57} +(3.24817 - 3.24817i) q^{58} +(-7.20872 - 1.93157i) q^{59} +(0.933796 - 0.250210i) q^{60} +2.45527i q^{61} +(-3.75966 - 6.51191i) q^{62} +(-2.46785 + 0.953787i) q^{63} +6.82982i q^{64} +(-1.82700 + 2.87307i) q^{65} +(-5.62651 - 3.24847i) q^{66} +(-7.19137 + 7.19137i) q^{67} +(3.31012 + 1.91110i) q^{68} +(0.116706 - 0.202140i) q^{69} +(-2.30259 + 0.889915i) q^{70} +(0.433350 + 1.61728i) q^{71} +(-2.11257 - 2.11257i) q^{72} +(-2.10388 - 7.85180i) q^{73} +(-2.48503 - 4.30419i) q^{74} +(2.05414 - 3.55787i) q^{75} +(1.24412 + 0.333360i) q^{76} +(-15.9091 - 7.03974i) q^{77} +(3.55922 + 0.152440i) q^{78} +(-0.942160 - 1.63187i) q^{79} +(-0.603930 - 0.603930i) q^{80} +1.00000 q^{81} -9.50785 q^{82} +(9.95023 + 9.95023i) q^{83} +(-2.10884 - 1.69975i) q^{84} +(-3.40550 + 0.912500i) q^{85} +(3.07283 - 11.4680i) q^{86} +(-4.02628 + 2.32457i) q^{87} -19.6451i q^{88} +(1.05604 + 3.94121i) q^{89} +0.933034 q^{90} +(9.51974 - 0.611992i) q^{91} +0.238954 q^{92} +(1.96967 + 7.35090i) q^{93} -2.15213i q^{94} +(-1.02890 + 0.594034i) q^{95} +(1.31522 - 4.90846i) q^{96} +(-2.41702 + 0.647638i) q^{97} +(5.81770 + 3.74042i) q^{98} +(4.64956 + 4.64956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 - 36 * q^9	$ 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.255728	+	0.954388i	0.180827	+	0.674855i	0.995485	+	0.0949139i	$0.0302576\pi$
$2$	0.255728	+	0.954388i	0.180827	+	0.674855i	−0.814659	+	0.579941i	$0.803076\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.886590	−	0.511873i	0.443295	−	0.255936i
$5$	−0.244406	+	0.912136i	−0.109302	+	0.407920i	−0.998798	−	0.0490235i	$-0.984389\pi$
$5$	−0.244406	+	0.912136i	−0.109302	+	0.407920i	0.889496	+	0.456943i	$0.151056\pi$
$6$	0.954388	−	0.255728i	0.389627	−	0.104400i
$7$	2.46785	−	0.953787i	0.932760	−	0.360497i
$7$	2.46785	−	0.953787i	0.932760	−	0.360497i
$8$	2.11257	+	2.11257i	0.746907	+	0.746907i
$9$	−1.00000			−0.333333
$10$	−0.933034			−0.295051
$11$	−4.64956	−	4.64956i	−1.40190	−	1.40190i	−0.794071	−	0.607824i	$-0.792042\pi$
$11$	−4.64956	−	4.64956i	−1.40190	−	1.40190i	−0.607824	−	0.794071i	$-0.707958\pi$
$12$	−0.511873	−	0.886590i	−0.147765	−	0.255936i
$13$	3.43957	+	1.08136i	0.953966	+	0.299914i
$13$	3.43957	+	1.08136i	0.953966	+	0.299914i
$14$	1.54138	+	2.11138i	0.411951	+	0.564290i
$15$	0.912136	+	0.244406i	0.235513	+	0.0631054i
$16$	−0.452226	+	0.783279i	−0.113057	+	0.195820i
$17$	1.86677	+	3.23334i	0.452758	+	0.784200i	0.998556	−	0.0537166i	$-0.0171068\pi$
$17$	1.86677	+	3.23334i	0.452758	+	0.784200i	−0.545798	+	0.837917i	$0.683773\pi$
$18$	−0.255728	−	0.954388i	−0.0602756	−	0.224952i
$19$	0.889632	+	0.889632i	0.204095	+	0.204095i	0.801752	−	0.597657i	$-0.203901\pi$
$19$	0.889632	+	0.889632i	0.204095	+	0.204095i	−0.597657	+	0.801752i	$0.703901\pi$
$20$	0.250210	+	0.933796i	0.0559486	+	0.208803i
$21$	−0.953787	−	2.46785i	−0.208133	−	0.538529i
$22$	3.24847	−	5.62651i	0.692576	−	1.19958i
$23$	0.202140	+	0.116706i	0.0421491	+	0.0243348i	0.520927	−	0.853602i	$-0.325587\pi$
$23$	0.202140	+	0.116706i	0.0421491	+	0.0243348i	−0.478777	+	0.877936i	$0.658920\pi$
$24$	2.11257	−	2.11257i	0.431227	−	0.431227i
$25$	3.55787	+	2.05414i	0.711574	+	0.410827i
$26$	−0.152440	+	3.55922i	−0.0298960	+	0.698021i
$27$			1.00000i			0.192450i
$28$	1.69975	−	2.10884i	0.321223	−	0.398534i
$29$	−2.32457	−	4.02628i	−0.431662	−	0.747661i	0.565354	−	0.824848i	$-0.308739\pi$
$29$	−2.32457	−	4.02628i	−0.431662	−	0.747661i	−0.997017	+	0.0771873i	$0.975406\pi$
$30$			0.933034i			0.170348i
$31$	−7.35090	+	1.96967i	−1.32026	+	0.353763i	−0.849075	−	0.528272i	$-0.822840\pi$
$31$	−7.35090	+	1.96967i	−1.32026	+	0.353763i	−0.471185	+	0.882034i	$0.656174\pi$
$32$	4.90846	+	1.31522i	0.867701	+	0.232500i
$33$	−4.64956	+	4.64956i	−0.809385	+	0.809385i
$34$	−2.60848	+	2.60848i	−0.447350	+	0.447350i
$35$	0.266825	+	2.48413i	0.0451017	+	0.419894i
$36$	−0.886590	+	0.511873i	−0.147765	+	0.0853122i
$37$	−4.85874	+	1.30189i	−0.798771	+	0.214030i	−0.635045	−	0.772476i	$-0.719018\pi$
$37$	−4.85874	+	1.30189i	−0.798771	+	0.214030i	−0.163727	+	0.986506i	$0.552352\pi$
$38$	−0.621551	+	1.07656i	−0.100829	+	0.174641i
$39$	1.08136	−	3.43957i	0.173156	−	0.550773i
$40$	−2.44328	+	1.41063i	−0.386317	+	0.223040i
$41$	−2.49056	+	9.29490i	−0.388960	+	1.45162i	0.442868	+	0.896587i	$0.353961\pi$
$41$	−2.49056	+	9.29490i	−0.388960	+	1.45162i	−0.831828	+	0.555033i	$0.812706\pi$
$42$	2.11138	−	1.54138i	0.325793	−	0.237840i
$43$	−10.4062	−	6.00801i	−1.58693	−	0.916213i	−0.993809	−	0.111099i	$-0.964563\pi$
$43$	−10.4062	−	6.00801i	−1.58693	−	0.916213i	−0.593119	−	0.805115i	$-0.702104\pi$
$44$	−6.50224	−	1.74227i	−0.980250	−	0.262657i
$45$	0.244406	−	0.912136i	0.0364339	−	0.135973i
$46$	−0.0596897	+	0.222765i	−0.00880077	+	0.0328449i
$47$	−2.10393	−	0.563747i	−0.306890	−	0.0822309i	0.102087	−	0.994775i	$-0.467448\pi$
$47$	−2.10393	−	0.563747i	−0.306890	−	0.0822309i	−0.408977	+	0.912545i	$0.634115\pi$
$48$	0.783279	+	0.452226i	0.113057	+	0.0652732i
$49$	5.18058	−	4.70761i	0.740083	−	0.672515i
$50$	−1.05060	+	3.92089i	−0.148577	+	0.554497i
$51$	3.23334	−	1.86677i	0.452758	−	0.261400i
$52$	3.60301	−	0.801905i	0.499647	−	0.111204i
$53$	2.04084	−	3.53484i	0.280331	−	0.485548i	−0.691135	−	0.722726i	$-0.742889\pi$
$53$	2.04084	−	3.53484i	0.280331	−	0.485548i	0.971466	+	0.237178i	$0.0762224\pi$
$54$	−0.954388	+	0.255728i	−0.129876	+	0.0348001i
$55$	5.37742	−	3.10465i	0.725091	−	0.418631i
$56$	7.22846	+	3.19857i	0.965944	+	0.427427i
$57$	0.889632	−	0.889632i	0.117835	−	0.117835i
$58$	3.24817	−	3.24817i	0.426506	−	0.426506i
$59$	−7.20872	−	1.93157i	−0.938495	−	0.251469i	−0.243022	−	0.970021i	$-0.578139\pi$
$59$	−7.20872	−	1.93157i	−0.938495	−	0.251469i	−0.695473	+	0.718552i	$0.744805\pi$
$60$	0.933796	−	0.250210i	0.120553	−	0.0323020i
$61$			2.45527i			0.314365i	0.987570	+	0.157183i	$0.0502412\pi$
$61$			2.45527i			0.314365i	−0.987570	+	0.157183i	$0.949759\pi$
$62$	−3.75966	−	6.51191i	−0.477477	−	0.827014i
$63$	−2.46785	+	0.953787i	−0.310920	+	0.120166i
$64$			6.82982i			0.853727i
$65$	−1.82700	+	2.87307i	−0.226611	+	0.356361i
$66$	−5.62651	−	3.24847i	−0.692576	−	0.399859i
$67$	−7.19137	+	7.19137i	−0.878566	+	0.878566i	−0.993386	−	0.114820i	$-0.963371\pi$
$67$	−7.19137	+	7.19137i	−0.878566	+	0.878566i	0.114820	+	0.993386i	$0.463371\pi$
$68$	3.31012	+	1.91110i	0.401411	+	0.231755i
$69$	0.116706	−	0.202140i	0.0140497	−	0.0243348i
$70$	−2.30259	+	0.889915i	−0.275212	+	0.106365i
$71$	0.433350	+	1.61728i	0.0514292	+	0.191936i	0.986861	−	0.161570i	$-0.0516559\pi$
$71$	0.433350	+	1.61728i	0.0514292	+	0.191936i	−0.935432	+	0.353507i	$0.884989\pi$
$72$	−2.11257	−	2.11257i	−0.248969	−	0.248969i
$73$	−2.10388	−	7.85180i	−0.246241	−	0.918984i	−0.972756	−	0.231833i	$-0.925528\pi$
$73$	−2.10388	−	7.85180i	−0.246241	−	0.918984i	0.726515	−	0.687151i	$-0.241139\pi$
$74$	−2.48503	−	4.30419i	−0.288878	−	0.500352i
$75$	2.05414	−	3.55787i	0.237191	−	0.410827i
$76$	1.24412	+	0.333360i	0.142710	+	0.0382390i
$77$	−15.9091	−	7.03974i	−1.81301	−	0.802253i
$78$	3.55922	+	0.152440i	0.403003	+	0.0172605i
$79$	−0.942160	−	1.63187i	−0.106001	−	0.183600i	0.808146	−	0.588983i	$-0.200471\pi$
$79$	−0.942160	−	1.63187i	−0.106001	−	0.183600i	−0.914147	+	0.405383i	$0.867138\pi$
$80$	−0.603930	−	0.603930i	−0.0675214	−	0.0675214i
$81$	1.00000			0.111111
$82$	−9.50785			−1.04997
$83$	9.95023	+	9.95023i	1.09218	+	1.09218i	0.995296	+	0.0968835i	$0.0308874\pi$
$83$	9.95023	+	9.95023i	1.09218	+	1.09218i	0.0968835	+	0.995296i	$0.469113\pi$
$84$	−2.10884	−	1.69975i	−0.230094	−	0.185458i
$85$	−3.40550	+	0.912500i	−0.369378	+	0.0989745i
$86$	3.07283	−	11.4680i	0.331352	−	1.23662i
$87$	−4.02628	+	2.32457i	−0.431662	+	0.249220i
$88$		−	19.6451i		−	2.09417i
$89$	1.05604	+	3.94121i	0.111940	+	0.417767i	0.999040	−	0.0438111i	$-0.0139500\pi$
$89$	1.05604	+	3.94121i	0.111940	+	0.417767i	−0.887099	+	0.461578i	$0.847283\pi$
$90$	0.933034			0.0983504
$91$	9.51974	−	0.611992i	0.997940	−	0.0641542i
$92$	0.238954			0.0249127
$93$	1.96967	+	7.35090i	0.204245	+	0.762253i
$94$		−	2.15213i		−	0.221976i
$95$	−1.02890	+	0.594034i	−0.105563	+	0.0609466i
$96$	1.31522	−	4.90846i	0.134234	−	0.500967i
$97$	−2.41702	+	0.647638i	−0.245411	+	0.0657576i	−0.379428	−	0.925221i	$-0.623879\pi$
$97$	−2.41702	+	0.647638i	−0.245411	+	0.0657576i	0.134017	+	0.990979i	$0.457212\pi$
$98$	5.81770	+	3.74042i	0.587677	+	0.377840i
$99$	4.64956	+	4.64956i	0.467299	+	0.467299i
$100$	4.20583			0.420583
$101$	2.40441			0.239248			0.119624	−	0.992819i	$-0.461831\pi$
$101$	2.40441			0.239248			0.119624	+	0.992819i	$0.461831\pi$
$102$	2.60848	+	2.60848i	0.258278	+	0.258278i
$103$	−1.45067	−	2.51263i	−0.142938	−	0.247577i	0.785663	−	0.618654i	$-0.212322\pi$
$103$	−1.45067	−	2.51263i	−0.142938	−	0.247577i	−0.928602	+	0.371077i	$0.878988\pi$
$104$	4.98191	+	9.55080i	0.488516	+	0.936533i
$105$	2.48413	−	0.266825i	0.242426	−	0.0260395i
$106$	3.89551	+	1.04380i	0.378366	+	0.101383i
$107$	5.54205	−	9.59911i	0.535770	−	0.927981i	−0.463356	−	0.886172i	$-0.653355\pi$
$107$	5.54205	−	9.59911i	0.535770	−	0.927981i	0.999126	−	0.0418082i	$-0.0133119\pi$
$108$	0.511873	+	0.886590i	0.0492550	+	0.0853122i
$109$	−1.87996	−	7.01612i	−0.180068	−	0.672023i	−0.995633	−	0.0933569i	$-0.970240\pi$
$109$	−1.87996	−	7.01612i	−0.180068	−	0.672023i	0.815565	−	0.578666i	$-0.196426\pi$
$110$	4.33820	+	4.33820i	0.413631	+	0.413631i
$111$	1.30189	+	4.85874i	0.123570	+	0.461171i
$112$	−0.368946	+	2.36434i	−0.0348621	+	0.223409i
$113$	−0.604359	+	1.04678i	−0.0568533	+	0.0984728i	−0.893051	−	0.449955i	$-0.851440\pi$
$113$	−0.604359	+	1.04678i	−0.0568533	+	0.0984728i	0.836198	+	0.548428i	$0.184773\pi$
$114$	1.07656	+	0.621551i	0.100829	+	0.0582136i
$115$	−0.155856	+	0.155856i	−0.0145336	+	0.0145336i
$116$	−4.12188	−	2.37977i	−0.382707	−	0.220956i
$117$	−3.43957	−	1.08136i	−0.317989	−	0.0999715i
$118$		−	7.37387i		−	0.678820i
$119$	7.69083	+	6.19890i	0.705017	+	0.568253i
$120$	1.41063	+	2.44328i	0.128772	+	0.223040i
$121$			32.2369i			2.93062i
$122$	−2.34328	+	0.627881i	−0.212151	+	0.0568457i
$123$	9.29490	+	2.49056i	0.838093	+	0.224566i
$124$	−5.50901	+	5.50901i	−0.494724	+	0.494724i
$125$	−6.08187	+	6.08187i	−0.543979	+	0.543979i
$126$	−1.54138	−	2.11138i	−0.137317	−	0.188097i
$127$	−8.44594	+	4.87627i	−0.749456	+	0.432699i	−0.825497	−	0.564406i	$-0.809105\pi$
$127$	−8.44594	+	4.87627i	−0.749456	+	0.432699i	0.0760413	+	0.997105i	$0.475772\pi$
$128$	3.29862	−	0.883862i	0.291559	−	0.0781231i
$129$	−6.00801	+	10.4062i	−0.528976	+	0.916213i
$130$	−3.20924	−	1.00894i	−0.281469	−	0.0884901i
$131$	14.7264	−	8.50232i	1.28666	−	0.742851i	0.308599	−	0.951192i	$-0.400140\pi$
$131$	14.7264	−	8.50232i	1.28666	−	0.742851i	0.978056	+	0.208341i	$0.0668065\pi$
$132$	−1.74227	+	6.50224i	−0.151645	+	0.565947i
$133$	3.04400	+	1.34696i	0.263948	+	0.116796i
$134$	−8.70239	−	5.02433i	−0.751772	−	0.434036i
$135$	−0.912136	−	0.244406i	−0.0785042	−	0.0210351i
$136$	−2.88698	+	10.7744i	−0.247556	+	0.923893i
$137$	−1.24138	+	4.63290i	−0.106058	+	0.395816i	−0.998463	−	0.0554205i	$-0.982350\pi$
$137$	−1.24138	+	4.63290i	−0.106058	+	0.395816i	0.892405	+	0.451236i	$0.149017\pi$
$138$	0.222765	+	0.0596897i	0.0189630	+	0.00508113i
$139$	6.97771	+	4.02859i	0.591842	+	0.341700i	0.765826	−	0.643048i	$-0.222331\pi$
$139$	6.97771	+	4.02859i	0.591842	+	0.341700i	−0.173984	+	0.984749i	$0.555664\pi$
$140$	1.50812	+	2.06582i	0.127460	+	0.174594i
$141$	−0.563747	+	2.10393i	−0.0474760	+	0.177183i
$142$	−1.43270	+	0.827168i	−0.120229	+	0.0694144i
$143$	−10.9647	−	21.0203i	−0.916912	−	1.75781i
$144$	0.452226	−	0.783279i	0.0376855	−	0.0652732i
$145$	4.24065	−	1.13628i	0.352167	−	0.0943629i
$146$	6.95565	−	4.01584i	0.575653	−	0.332354i
$147$	−4.70761	−	5.18058i	−0.388277	−	0.427287i
$148$	−3.64130	+	3.64130i	−0.299313	+	0.299313i
$149$	10.8793	−	10.8793i	0.891265	−	0.891265i	−0.103378	−	0.994642i	$-0.532965\pi$
$149$	10.8793	−	10.8793i	0.891265	−	0.891265i	0.994642	+	0.103378i	$0.0329650\pi$
$150$	3.92089	+	1.05060i	0.320139	+	0.0857810i
$151$	23.6057	−	6.32512i	1.92100	−	0.514731i	0.933111	−	0.359589i	$-0.117083\pi$
$151$	23.6057	−	6.32512i	1.92100	−	0.514731i	0.987892	−	0.155142i	$-0.0495836\pi$
$152$			3.75882i			0.304881i
$153$	−1.86677	−	3.23334i	−0.150919	−	0.261400i
$154$	2.65024	−	16.9837i	0.213563	−	1.36859i
$155$		−	7.18642i		−	0.577227i
$156$	−0.801905	−	3.60301i	−0.0642038	−	0.288472i
$157$	8.18219	+	4.72399i	0.653010	+	0.377015i	0.789608	−	0.613611i	$-0.210284\pi$
$157$	8.18219	+	4.72399i	0.653010	+	0.377015i	−0.136599	+	0.990626i	$0.543617\pi$
$158$	1.31650	−	1.31650i	0.104735	−	0.104735i
$159$	−3.53484	−	2.04084i	−0.280331	−	0.161849i
$160$	−2.39932	+	4.15574i	−0.189683	+	0.328540i
$161$	0.610164	+	0.0952137i	0.0480877	+	0.00750389i
$162$	0.255728	+	0.954388i	0.0200919	+	0.0749838i
$163$	13.3170	+	13.3170i	1.04306	+	1.04306i	0.999030	+	0.0440343i	$0.0140211\pi$
$163$	13.3170	+	13.3170i	1.04306	+	1.04306i	0.0440343	+	0.999030i	$0.485979\pi$
$164$	2.54970	+	9.51562i	0.199098	+	0.743045i
$165$	−3.10465	−	5.37742i	−0.241697	−	0.418631i
$166$	−6.95183	+	12.0409i	−0.539567	+	0.934557i
$167$	−22.1608	−	5.93797i	−1.71486	−	0.459494i	−0.738249	−	0.674528i	$-0.764347\pi$
$167$	−22.1608	−	5.93797i	−1.71486	−	0.459494i	−0.976606	+	0.215034i	$0.931014\pi$
$168$	3.19857	−	7.22846i	0.246775	−	0.557688i
$169$	10.6613	+	7.43881i	0.820103	+	0.572216i
$170$	−1.74176	−	3.01682i	−0.133587	−	0.231379i
$171$	−0.889632	−	0.889632i	−0.0680318	−	0.0680318i
$172$	−12.3014			−0.937970
$173$	8.58805			0.652937			0.326469	−	0.945208i	$-0.394141\pi$
$173$	8.58805			0.652937			0.326469	+	0.945208i	$0.394141\pi$
$174$	−3.24817	−	3.24817i	−0.246243	−	0.246243i
$175$	10.7395	+	1.67586i	0.811830	+	0.126683i
$176$	5.74456	−	1.53925i	0.433012	−	0.116025i
$177$	−1.93157	+	7.20872i	−0.145186	+	0.541840i
$178$	−3.49138	+	2.01575i	−0.261690	+	0.151087i
$179$		−	13.6367i		−	1.01926i	−0.860394	−	0.509629i	$-0.829783\pi$
$179$		−	13.6367i		−	1.01926i	0.860394	−	0.509629i	$-0.170217\pi$
$180$	−0.250210	−	0.933796i	−0.0186495	−	0.0696010i
$181$	−11.2556			−0.836622			−0.418311	−	0.908304i	$-0.637378\pi$
$181$	−11.2556			−0.836622			−0.418311	+	0.908304i	$0.637378\pi$
$182$	3.01854	+	8.92903i	0.223749	+	0.661864i
$183$	2.45527			0.181499
$184$	0.180487	+	0.673585i	0.0133057	+	0.0496574i
$185$		−	4.75002i		−	0.349229i
$186$	−6.51191	+	3.75966i	−0.477477	+	0.275671i
$187$	6.35395	−	23.7133i	0.464647	−	1.73409i
$188$	−2.15389	+	0.577134i	−0.157089	+	0.0420918i
$189$	0.953787	+	2.46785i	0.0693778	+	0.179510i
$190$	−0.830056	−	0.830056i	−0.0602186	−	0.0602186i
$191$	11.3967			0.824637			0.412319	−	0.911040i	$-0.364719\pi$
$191$	11.3967			0.824637			0.412319	+	0.911040i	$0.364719\pi$
$192$	6.82982			0.492900
$193$	−1.75587	−	1.75587i	−0.126390	−	0.126390i	0.641082	−	0.767472i	$-0.278486\pi$
$193$	−1.75587	−	1.75587i	−0.126390	−	0.126390i	−0.767472	+	0.641082i	$0.778486\pi$
$194$	−1.23620	−	2.14115i	−0.0887537	−	0.153726i
$195$	2.87307	+	1.82700i	0.205745	+	0.130834i
$196$	2.18336	−	6.82552i	0.155954	−	0.487537i
$197$	−14.0826	−	3.77342i	−1.00334	−	0.268845i	−0.280498	−	0.959854i	$-0.590500\pi$
$197$	−14.0826	−	3.77342i	−1.00334	−	0.268845i	−0.722846	+	0.691009i	$0.757166\pi$
$198$	−3.24847	+	5.62651i	−0.230859	+	0.399859i
$199$	2.61480	+	4.52897i	0.185358	+	0.321050i	0.943697	−	0.330811i	$-0.107322\pi$
$199$	2.61480	+	4.52897i	0.185358	+	0.321050i	−0.758339	+	0.651860i	$0.773989\pi$
$200$	3.17674	+	11.8558i	0.224630	+	0.838330i
$201$	7.19137	+	7.19137i	0.507240	+	0.507240i
$202$	0.614874	+	2.29474i	0.0432624	+	0.161457i
$203$	−9.57691	−	7.71911i	−0.672167	−	0.541775i
$204$	1.91110	−	3.31012i	0.133804	−	0.231755i
$205$	−7.86951	−	4.54346i	−0.549630	−	0.317329i
$206$	2.02705	−	2.02705i	0.141231	−	0.141231i
$207$	−0.202140	−	0.116706i	−0.0140497	−	0.00811161i
$208$	−2.40247	+	2.20513i	−0.166581	+	0.152898i
$209$		−	8.27280i		−	0.572241i
$210$	0.889915	+	2.30259i	0.0614100	+	0.158894i
$211$	5.55565	+	9.62266i	0.382466	+	0.662451i	0.991414	−	0.130759i	$-0.0417414\pi$
$211$	5.55565	+	9.62266i	0.382466	+	0.662451i	−0.608948	+	0.793210i	$0.708408\pi$
$212$		−	4.17861i		−	0.286988i
$213$	1.61728	−	0.433350i	0.110814	−	0.0296926i
$214$	10.5785	+	2.83451i	0.723133	+	0.193763i
$215$	8.02346	−	8.02346i	0.547196	−	0.547196i
$216$	−2.11257	+	2.11257i	−0.143742	+	0.143742i
$217$	−16.2623	+	11.8720i	−1.10396	+	0.805926i
$218$	6.21535	−	3.58843i	0.420956	−	0.243039i
$219$	−7.85180	+	2.10388i	−0.530576	+	0.142167i
$220$	3.17838	−	5.50511i	0.214286	−	0.371154i
$221$	2.92450	+	13.1400i	0.196723	+	0.883889i
$222$	−4.30419	+	2.48503i	−0.288878	+	0.166784i
$223$	7.12168	−	26.5785i	0.476903	−	1.77983i	−0.137137	−	0.990552i	$-0.543790\pi$
$223$	7.12168	−	26.5785i	0.476903	−	1.77983i	0.614040	−	0.789275i	$-0.289543\pi$
$224$	13.3678	−	1.43586i	0.893173	−	0.0959374i
$225$	−3.55787	−	2.05414i	−0.237191	−	0.136942i
$226$	−1.15359	−	0.309102i	−0.0767354	−	0.0205612i
$227$	3.03858	−	11.3401i	0.201677	−	0.752670i	−0.788759	−	0.614702i	$-0.789276\pi$
$227$	3.03858	−	11.3401i	0.201677	−	0.752670i	0.990437	−	0.137968i	$-0.0440571\pi$
$228$	0.333360	−	1.24412i	0.0220773	−	0.0823937i
$229$	−13.5399	−	3.62802i	−0.894745	−	0.239746i	−0.217987	−	0.975952i	$-0.569949\pi$
$229$	−13.5399	−	3.62802i	−0.894745	−	0.239746i	−0.676758	+	0.736206i	$0.736616\pi$
$230$	−0.188604	−	0.108890i	−0.0124362	−	0.00718002i
$231$	−7.03974	+	15.9091i	−0.463181	+	1.04674i
$232$	3.59498	−	13.4166i	0.236022	−	0.880845i
$233$	5.26788	−	3.04141i	0.345110	−	0.199249i	−0.317419	−	0.948285i	$-0.602816\pi$
$233$	5.26788	−	3.04141i	0.345110	−	0.199249i	0.662529	+	0.749036i	$0.269483\pi$
$234$	0.152440	−	3.55922i	0.00996534	−	0.232674i
$235$	1.02843	−	1.78129i	0.0670872	−	0.116199i
$236$	−7.37989	+	1.97744i	−0.480390	+	0.128720i
$237$	−1.63187	+	0.942160i	−0.106001	+	0.0611999i
$238$	−3.94940	+	8.92527i	−0.256002	+	0.578539i
$239$	−3.72605	+	3.72605i	−0.241018	+	0.241018i	−0.817271	−	0.576253i	$-0.804514\pi$
$239$	−3.72605	+	3.72605i	−0.241018	+	0.241018i	0.576253	+	0.817271i	$0.304514\pi$
$240$	−0.603930	+	0.603930i	−0.0389835	+	0.0389835i
$241$	−25.9354	−	6.94938i	−1.67065	−	0.447649i	−0.705363	−	0.708846i	$-0.749216\pi$
$241$	−25.9354	−	6.94938i	−1.67065	−	0.447649i	−0.965285	+	0.261197i	$0.915883\pi$
$242$	−30.7665	+	8.24386i	−1.97775	+	0.529935i
$243$		−	1.00000i		−	0.0641500i
$244$	1.25679	+	2.17682i	0.0804576	+	0.139357i
$245$	3.02781	+	5.87597i	0.193440	+	0.375402i
$246$			9.50785i			0.606198i
$247$	2.09794	+	4.02196i	0.133489	+	0.255911i
$248$	−19.6904	−	11.3682i	−1.25034	−	0.721884i
$249$	9.95023	−	9.95023i	0.630570	−	0.630570i
$250$	−7.35977	−	4.24916i	−0.465473	−	0.268741i
$251$	6.48321	−	11.2292i	0.409217	−	0.708784i	−0.585586	−	0.810611i	$-0.699135\pi$
$251$	6.48321	−	11.2292i	0.409217	−	0.708784i	0.994802	+	0.101827i	$0.0324687\pi$
$252$	−1.69975	+	2.10884i	−0.107074	+	0.132845i
$253$	−0.397233	−	1.48249i	−0.0249738	−	0.0932036i
$254$	−6.81371	−	6.81371i	−0.427530	−	0.427530i
$255$	0.912500	+	3.40550i	0.0571430	+	0.213261i
$256$	8.51691	+	14.7517i	0.532307	+	0.921983i
$257$	9.28663	−	16.0849i	0.579284	−	1.00335i	−0.416278	−	0.909238i	$-0.636666\pi$
$257$	9.28663	−	16.0849i	0.579284	−	1.00335i	0.995562	−	0.0941119i	$-0.0300011\pi$
$258$	−11.4680	−	3.07283i	−0.713964	−	0.191306i
$259$	−10.7489	+	7.84708i	−0.667905	+	0.487594i
$260$	−0.149151	+	3.48243i	−0.00924996	+	0.215971i
$261$	2.32457	+	4.02628i	0.143887	+	0.249220i
$262$	11.8805	+	11.8805i	0.733978	+	0.733978i
$263$	−8.66221			−0.534135			−0.267067	−	0.963678i	$-0.586055\pi$
$263$	−8.66221			−0.534135			−0.267067	+	0.963678i	$0.586055\pi$
$264$	−19.6451			−1.20907
$265$	2.72546	+	2.72546i	0.167424	+	0.167424i
$266$	−0.507089	+	3.24961i	−0.0310916	+	0.199246i
$267$	3.94121	−	1.05604i	0.241198	−	0.0646288i
$268$	−2.69473	+	10.0569i	−0.164607	+	0.614321i
$269$	−6.31308	+	3.64486i	−0.384915	+	0.222231i	−0.679955	−	0.733254i	$-0.738001\pi$
$269$	−6.31308	+	3.64486i	−0.384915	+	0.222231i	0.295039	+	0.955485i	$0.404667\pi$
$270$		−	0.933034i		−	0.0567826i
$271$	6.08174	+	22.6974i	0.369440	+	1.37877i	0.861301	+	0.508094i	$0.169650\pi$
$271$	6.08174	+	22.6974i	0.369440	+	1.37877i	−0.491862	+	0.870673i	$0.663683\pi$
$272$	−3.37681			−0.204749
$273$	−0.611992	−	9.51974i	−0.0370394	−	0.576161i
$274$	−4.73904			−0.286296
$275$	−6.99170	−	26.0934i	−0.421615	−	1.57349i
$276$		−	0.238954i		−	0.0143833i
$277$	−2.12311	+	1.22578i	−0.127565	+	0.0736499i	−0.562425	−	0.826848i	$-0.690131\pi$
$277$	−2.12311	+	1.22578i	−0.127565	+	0.0736499i	0.434859	+	0.900498i	$0.356798\pi$
$278$	−2.06044	+	7.68967i	−0.123577	+	0.461196i
$279$	7.35090	−	1.96967i	0.440087	−	0.117921i
$280$	−4.68422	+	5.81159i	−0.279935	+	0.347309i
$281$	−9.26224	−	9.26224i	−0.552539	−	0.552539i	0.374634	−	0.927173i	$-0.377768\pi$
$281$	−9.26224	−	9.26224i	−0.552539	−	0.552539i	−0.927173	+	0.374634i	$0.877768\pi$
$282$	−2.15213			−0.128158
$283$	0.575760			0.0342254			0.0171127	−	0.999854i	$-0.494553\pi$
$283$	0.575760			0.0342254			0.0171127	+	0.999854i	$0.494553\pi$
$284$	1.21205	+	1.21205i	0.0719218	+	0.0719218i
$285$	0.594034	+	1.02890i	0.0351875	+	0.0609466i
$286$	17.2576	−	15.8400i	1.02046	−	0.936642i
$287$	2.71902	+	25.3139i	0.160498	+	1.49423i
$288$	−4.90846	−	1.31522i	−0.289234	−	0.0774999i
$289$	1.53034	−	2.65063i	0.0900201	−	0.155919i
$290$	2.16890	+	3.75665i	0.127362	+	0.220598i
$291$	0.647638	+	2.41702i	0.0379652	+	0.141688i
$292$	−5.88441	−	5.88441i	−0.344359	−	0.344359i
$293$	4.53613	+	16.9291i	0.265004	+	0.989007i	0.962248	+	0.272174i	$0.0877425\pi$
$293$	4.53613	+	16.9291i	0.265004	+	0.989007i	−0.697245	+	0.716833i	$0.745591\pi$
$294$	3.74042	−	5.81770i	0.218146	−	0.339295i
$295$	3.52371	−	6.10324i	0.205158	−	0.355345i
$296$	−13.0148	−	7.51409i	−0.756469	−	0.436748i
$297$	4.64956	−	4.64956i	0.269795	−	0.269795i
$298$	13.1652	+	7.60092i	0.762638	+	0.440310i
$299$	0.569076	+	0.620004i	0.0329105	+	0.0358557i
$300$		−	4.20583i		−	0.242824i
$301$	−31.4113	−	4.90161i	−1.81052	−	0.282524i
$302$	12.0732	+	20.9115i	0.694737	+	1.20332i
$303$		−	2.40441i		−	0.138130i
$304$	−1.09914	+	0.294515i	−0.0630402	+	0.0168916i
$305$	−2.23954	−	0.600084i	−0.128236	−	0.0343607i
$306$	2.60848	−	2.60848i	0.149117	−	0.149117i
$307$	10.3888	−	10.3888i	0.592923	−	0.592923i	−0.345497	−	0.938420i	$-0.612290\pi$
$307$	10.3888	−	10.3888i	0.592923	−	0.592923i	0.938420	+	0.345497i	$0.112290\pi$
$308$	−17.7083	+	1.90209i	−1.00903	+	0.108381i
$309$	−2.51263	+	1.45067i	−0.142938	+	0.0825256i
$310$	6.85864	−	1.83777i	0.389544	−	0.104378i
$311$	−6.38744	+	11.0634i	−0.362199	+	0.627346i	−0.988322	−	0.152377i	$-0.951307\pi$
$311$	−6.38744	+	11.0634i	−0.362199	+	0.627346i	0.626124	+	0.779724i	$0.284640\pi$
$312$	9.55080	−	4.98191i	0.540707	−	0.282045i
$313$	12.3070	−	7.10546i	0.695633	−	0.401624i	−0.110086	−	0.993922i	$-0.535112\pi$
$313$	12.3070	−	7.10546i	0.695633	−	0.401624i	0.805719	+	0.592298i	$0.201779\pi$
$314$	−2.41611	+	9.01704i	−0.136349	+	0.508861i
$315$	−0.266825	−	2.48413i	−0.0150339	−	0.139965i
$316$	−1.67062	−	0.964532i	−0.0939797	−	0.0542592i
$317$	18.0701	+	4.84186i	1.01492	+	0.271946i	0.727682	−	0.685914i	$-0.240598\pi$
$317$	18.0701	+	4.84186i	1.01492	+	0.271946i	0.287234	+	0.957860i	$0.407264\pi$
$318$	1.04380	−	3.89551i	0.0585333	−	0.218449i
$319$	−7.91218	+	29.5287i	−0.442997	+	1.65329i
$320$	−6.22973	−	1.66925i	−0.348252	−	0.0933139i
$321$	−9.59911	−	5.54205i	−0.535770	−	0.309327i
$322$	0.0651650	+	0.606683i	0.00363150	+	0.0338091i
$323$	−1.21574	+	4.53722i	−0.0676458	+	0.252458i
$324$	0.886590	−	0.511873i	0.0492550	−	0.0284374i
$325$	10.0163	+	10.9127i	0.555604	+	0.605326i
$326$	−9.30403	+	16.1151i	−0.515303	+	0.892531i
$327$	−7.01612	+	1.87996i	−0.387992	+	0.103962i
$328$	−24.8976	+	14.3747i	−1.37474	+	0.793708i
$329$	−5.72989	+	0.615458i	−0.315899	+	0.0339313i
$330$	4.33820	−	4.33820i	0.238810	−	0.238810i
$331$	−2.79186	+	2.79186i	−0.153454	+	0.153454i	−0.779659	−	0.626204i	$-0.784608\pi$
$331$	−2.79186	+	2.79186i	−0.153454	+	0.153454i	0.626204	+	0.779659i	$0.284608\pi$
$332$	13.9150	+	3.72852i	0.763686	+	0.204629i
$333$	4.85874	−	1.30189i	0.266257	−	0.0713434i
$334$		−	22.6685i		−	1.24037i
$335$	−4.80190	−	8.31713i	−0.262356	−	0.454413i
$336$	2.36434	+	0.368946i	0.128985	+	0.0201277i
$337$		−	15.1443i		−	0.824962i	−0.910966	−	0.412481i	$-0.864662\pi$
$337$		−	15.1443i		−	0.824962i	0.910966	−	0.412481i	$-0.135338\pi$
$338$	−4.37312	+	12.0774i	−0.237866	+	0.656922i
$339$	1.04678	+	0.604359i	0.0568533	+	0.0328243i
$340$	−2.55220	+	2.55220i	−0.138412	+	0.138412i
$341$	43.3366	+	25.0204i	2.34681	+	1.35493i
$342$	0.621551	−	1.07656i	0.0336096	−	0.0582136i
$343$	8.29486	−	16.5588i	0.447880	−	0.894094i
$344$	−9.29146	−	34.6762i	−0.500962	−	1.86961i
$345$	0.155856	+	0.155856i	0.00839100	+	0.00839100i
$346$	2.19620	+	8.19633i	0.118069	+	0.440638i
$347$	−3.39724	−	5.88420i	−0.182374	−	0.315880i	0.760315	−	0.649555i	$-0.225045\pi$
$347$	−3.39724	−	5.88420i	−0.182374	−	0.315880i	−0.942688	+	0.333675i	$0.891711\pi$
$348$	−2.37977	+	4.12188i	−0.127569	+	0.220956i
$349$	−0.378000	−	0.101285i	−0.0202339	−	0.00542165i	0.248688	−	0.968584i	$-0.420001\pi$
$349$	−0.378000	−	0.101285i	−0.0202339	−	0.00542165i	−0.268922	+	0.963162i	$0.586667\pi$
$350$	1.14697	+	10.6782i	0.0613081	+	0.570775i
$351$	−1.08136	+	3.43957i	−0.0577185	+	0.183591i
$352$	−16.7070	−	28.9374i	−0.890486	−	1.54237i
$353$	14.1200	+	14.1200i	0.751534	+	0.751534i	0.974765	−	0.223232i	$-0.0716606\pi$
$353$	14.1200	+	14.1200i	0.751534	+	0.751534i	−0.223232	+	0.974765i	$0.571661\pi$
$354$	−7.37387			−0.391917
$355$	−1.58110			−0.0839159
$356$	2.95368	+	2.95368i	0.156545	+	0.156545i
$357$	6.19890	−	7.69083i	0.328081	−	0.407042i
$358$	13.0147	−	3.48729i	0.687851	−	0.184309i
$359$	−7.17397	+	26.7736i	−0.378628	+	1.41306i	0.469344	+	0.883016i	$0.344491\pi$
$359$	−7.17397	+	26.7736i	−0.378628	+	1.41306i	−0.847971	+	0.530042i	$0.822176\pi$
$360$	2.44328	−	1.41063i	0.128772	−	0.0743467i
$361$		−	17.4171i		−	0.916690i
$362$	−2.87837	−	10.7422i	−0.151284	−	0.564598i
$363$	32.2369			1.69200
$364$	8.12685	−	5.41548i	0.425962	−	0.283848i
$365$	7.67612			0.401786
$366$	0.627881	+	2.34328i	0.0328199	+	0.122485i
$367$		−	6.67905i		−	0.348644i	−0.984689	−	0.174322i	$-0.944227\pi$
$367$		−	6.67905i		−	0.348644i	0.984689	−	0.174322i	$-0.0557733\pi$
$368$	−0.182826	+	0.105555i	−0.00953047	+	0.00550242i
$369$	2.49056	−	9.29490i	0.129653	−	0.483873i
$370$	4.53337	−	1.21471i	0.235678	−	0.0631499i
$371$	1.66501	−	10.6700i	0.0864430	−	0.553958i
$372$	5.50901	+	5.50901i	0.285629	+	0.285629i
$373$	1.00610			0.0520939			0.0260469	−	0.999661i	$-0.491708\pi$
$373$	1.00610			0.0520939			0.0260469	+	0.999661i	$0.491708\pi$
$374$	24.2566			1.25428
$375$	6.08187	+	6.08187i	0.314066	+	0.314066i
$376$	−3.25375	−	5.63567i	−0.167800	−	0.290637i
$377$	−3.64170	−	16.3624i	−0.187557	−	0.842705i
$378$	−2.11138	+	1.54138i	−0.108598	+	0.0792801i
$379$	−20.6414	−	5.53086i	−1.06028	−	0.284101i	−0.313786	−	0.949494i	$-0.601597\pi$
$379$	−20.6414	−	5.53086i	−1.06028	−	0.284101i	−0.746493	+	0.665393i	$0.768264\pi$
$380$	−0.608140	+	1.05333i	−0.0311969	+	0.0540346i
$381$	4.87627	+	8.44594i	0.249819	+	0.432699i
$382$	2.91445	+	10.8769i	0.149116	+	0.556510i
$383$	16.1566	+	16.1566i	0.825562	+	0.825562i	0.986899	−	0.161338i	$-0.0515808\pi$
$383$	16.1566	+	16.1566i	0.825562	+	0.825562i	−0.161338	+	0.986899i	$0.551581\pi$
$384$	−0.883862	−	3.29862i	−0.0451044	−	0.168332i
$385$	10.3095	−	12.7907i	0.525420	−	0.651876i
$386$	1.22676	−	2.12480i	0.0624402	−	0.108150i
$387$	10.4062	+	6.00801i	0.528976	+	0.305404i
$388$	−1.81139	+	1.81139i	−0.0919596	+	0.0919596i
$389$	−17.3058	−	9.99148i	−0.877437	−	0.506588i	−0.00762436	−	0.999971i	$-0.502427\pi$
$389$	−17.3058	−	9.99148i	−0.877437	−	0.506588i	−0.869812	+	0.493383i	$0.835760\pi$
$390$	−1.00894	+	3.20924i	−0.0510898	+	0.162506i
$391$			0.871451i			0.0440712i
$392$	20.8895	+	0.999194i	1.05508	+	0.0504669i
$393$	−8.50232	−	14.7264i	−0.428885	−	0.742851i
$394$		−	14.4052i		−	0.725726i
$395$	1.71876	−	0.460539i	0.0864800	−	0.0231723i
$396$	6.50224	+	1.74227i	0.326750	+	0.0875524i
$397$	17.6864	−	17.6864i	0.887654	−	0.887654i	−0.106643	−	0.994297i	$-0.534010\pi$
$397$	17.6864	−	17.6864i	0.887654	−	0.887654i	0.994297	+	0.106643i	$0.0340103\pi$
$398$	−3.65372	+	3.65372i	−0.183144	+	0.183144i
$399$	1.34696	−	3.04400i	0.0674323	−	0.152390i
$400$	−3.21792	+	1.85787i	−0.160896	+	0.0928934i
$401$	−1.35838	+	0.363977i	−0.0678343	+	0.0181761i	−0.292577	−	0.956242i	$-0.594513\pi$
$401$	−1.35838	+	0.363977i	−0.0678343	+	0.0181761i	0.224742	+	0.974418i	$0.427846\pi$
$402$	−5.02433	+	8.70239i	−0.250591	+	0.434036i
$403$	−27.4139	−	1.17413i	−1.36558	−	0.0584874i
$404$	2.13173	−	1.23075i	0.106057	−	0.0612322i
$405$	−0.244406	+	0.912136i	−0.0121446	+	0.0453244i
$406$	4.91795	−	11.1141i	0.244074	−	0.551582i
$407$	28.6442	+	16.5378i	1.41984	+	0.819746i
$408$	10.7744	+	2.88698i	0.533410	+	0.142927i
$409$	−0.717754	+	2.67870i	−0.0354907	+	0.132453i	−0.981398	−	0.191984i	$-0.938508\pi$
$409$	−0.717754	+	2.67870i	−0.0354907	+	0.132453i	0.945907	+	0.324436i	$0.105175\pi$
$410$	2.32378	−	8.67246i	0.114763	−	0.428302i
$411$	4.63290	+	1.24138i	0.228524	+	0.0612329i
$412$	−2.57229	−	1.48511i	−0.126728	−	0.0731663i
$413$	−19.6323	+	2.10875i	−0.966044	+	0.103765i
$414$	0.0596897	−	0.222765i	0.00293359	−	0.0109483i
$415$	−11.5079	+	6.64407i	−0.564899	+	0.326144i
$416$	15.4608	+	9.83158i	0.758027	+	0.482033i
$417$	4.02859	−	6.97771i	0.197281	−	0.341700i
$418$	7.89546	−	2.11558i	0.386180	−	0.103477i
$419$	−16.7456	+	9.66807i	−0.818075	+	0.472316i	−0.849752	−	0.527182i	$-0.823249\pi$
$419$	−16.7456	+	9.66807i	−0.818075	+	0.472316i	0.0316770	+	0.999498i	$0.489915\pi$
$420$	2.06582	−	1.50812i	0.100802	−	0.0735889i
$421$	2.40433	−	2.40433i	0.117180	−	0.117180i	−0.646085	−	0.763265i	$-0.723595\pi$
$421$	2.40433	−	2.40433i	0.117180	−	0.117180i	0.763265	+	0.646085i	$0.223595\pi$
$422$	−7.76303	+	7.76303i	−0.377898	+	0.377898i
$423$	2.10393	+	0.563747i	0.102297	+	0.0274103i
$424$	11.7790	−	3.15618i	0.572041	−	0.153278i
$425$			15.3384i			0.744022i
$426$	0.827168	+	1.43270i	0.0400764	+	0.0694144i
$427$	2.34181	+	6.05925i	0.113328	+	0.293228i
$428$		−	11.3473i		−	0.548492i
$429$	−21.0203	+	10.9647i	−1.01487	+	0.529380i
$430$	9.70932	+	5.60568i	0.468225	+	0.270330i
$431$	−0.490482	+	0.490482i	−0.0236257	+	0.0236257i	−0.718821	−	0.695195i	$-0.755318\pi$
$431$	−0.490482	+	0.490482i	−0.0236257	+	0.0236257i	0.695195	+	0.718821i	$0.255318\pi$
$432$	−0.783279	−	0.452226i	−0.0376855	−	0.0217577i
$433$	−10.5144	+	18.2115i	−0.505290	+	0.875188i	0.494691	+	0.869069i	$0.335281\pi$
$433$	−10.5144	+	18.2115i	−0.505290	+	0.875188i	−0.999981	+	0.00611893i	$0.998052\pi$
$434$	−15.4892	−	12.4845i	−0.743508	−	0.599277i
$435$	−1.13628	−	4.24065i	−0.0544804	−	0.203324i
$436$	−5.25812	−	5.25812i	−0.251818	−	0.251818i
$437$	0.0760052	+	0.283655i	0.00363582	+	0.0135691i
$438$	−4.01584	−	6.95565i	−0.191884	−	0.332354i
$439$	−11.4119	+	19.7659i	−0.544659	+	0.943376i	0.453970	+	0.891017i	$0.350007\pi$
$439$	−11.4119	+	19.7659i	−0.544659	+	0.943376i	−0.998628	+	0.0523593i	$0.983326\pi$
$440$	17.9190	+	4.80138i	0.854255	+	0.228897i
$441$	−5.18058	+	4.70761i	−0.246694	+	0.224172i
$442$	−11.7927	+	6.15136i	−0.560924	+	0.292590i
$443$	−8.38733	−	14.5273i	−0.398494	−	0.690212i	0.595046	−	0.803691i	$-0.297134\pi$
$443$	−8.38733	−	14.5273i	−0.398494	−	0.690212i	−0.993540	+	0.113480i	$0.963800\pi$
$444$	3.64130	+	3.64130i	0.172809	+	0.172809i
$445$	−3.85302			−0.182651
$446$	27.1874			1.28736
$447$	−10.8793	−	10.8793i	−0.514572	−	0.514572i
$448$	6.51419	+	16.8550i	0.307766	+	0.796323i
$449$	14.8030	−	3.96646i	0.698599	−	0.187189i	0.107996	−	0.994151i	$-0.465557\pi$
$449$	14.8030	−	3.96646i	0.698599	−	0.187189i	0.590603	+	0.806962i	$0.298890\pi$
$450$	1.05060	−	3.92089i	0.0495257	−	0.184832i
$451$	54.7972	−	31.6372i	2.58030	−	1.48974i
$452$			1.23742i			0.0582033i
$453$	−6.32512	−	23.6057i	−0.297180	−	1.10909i
$454$	11.5999			0.544412
$455$	−1.76846	+	8.83288i	−0.0829069	+	0.414092i
$456$	3.75882			0.176023
$457$	−3.60447	−	13.4521i	−0.168610	−	0.629261i	−0.997552	−	0.0699267i	$-0.977723\pi$
$457$	−3.60447	−	13.4521i	−0.168610	−	0.629261i	0.828942	−	0.559334i	$-0.188943\pi$
$458$		−	13.8501i		−	0.647175i
$459$	−3.23334	+	1.86677i	−0.150919	+	0.0871333i
$460$	−0.0584018	+	0.217959i	−0.00272300	+	0.0101624i
$461$	−15.2937	+	4.09793i	−0.712298	+	0.190860i	−0.596733	−	0.802440i	$-0.703535\pi$
$461$	−15.2937	+	4.09793i	−0.712298	+	0.190860i	−0.115565	+	0.993300i	$0.536868\pi$
$462$	−16.9837	−	2.65024i	−0.790155	−	0.123301i
$463$	26.2699	+	26.2699i	1.22086	+	1.22086i	0.967325	+	0.253538i	$0.0815943\pi$
$463$	26.2699	+	26.2699i	1.22086	+	1.22086i	0.253538	+	0.967325i	$0.418406\pi$
$464$	4.20493			0.195209
$465$	−7.18642			−0.333262
$466$	4.24983	+	4.24983i	0.196869	+	0.196869i
$467$	−16.6813	−	28.8928i	−0.771917	−	1.33700i	−0.936511	−	0.350637i	$-0.885965\pi$
$467$	−16.6813	−	28.8928i	−0.771917	−	1.33700i	0.164595	−	0.986361i	$-0.447368\pi$
$468$	−3.60301	+	0.801905i	−0.166549	+	0.0370681i
$469$	−10.8882	+	24.6063i	−0.502771	+	1.13621i
$470$	1.96304	+	0.525995i	0.0905483	+	0.0242623i
$471$	4.72399	−	8.18219i	0.217670	−	0.377015i
$472$	−11.1484	−	19.3095i	−0.513145	−	0.888793i
$473$	20.4496	+	76.3188i	0.940272	+	3.50914i
$474$	−1.31650	−	1.31650i	−0.0604689	−	0.0604689i
$475$	1.33777	+	4.99262i	0.0613810	+	0.229077i
$476$	9.99166	+	1.55916i	0.457967	+	0.0714639i
$477$	−2.04084	+	3.53484i	−0.0934437	+	0.161849i
$478$	−4.50896	−	2.60325i	−0.206235	−	0.119070i
$479$	3.75854	−	3.75854i	0.171732	−	0.171732i	−0.616008	−	0.787740i	$-0.711251\pi$
$479$	3.75854	−	3.75854i	0.171732	−	0.171732i	0.787740	+	0.616008i	$0.211251\pi$
$480$	4.15574	+	2.39932i	0.189683	+	0.109513i
$481$	−18.1198	−	0.776065i	−0.826192	−	0.0353855i
$482$		−	26.5296i		−	1.20839i
$483$	0.0952137	−	0.610164i	0.00433237	−	0.0277634i
$484$	16.5012	+	28.5809i	0.750054	+	1.29913i
$485$		−	2.36294i		−	0.107295i
$486$	0.954388	−	0.255728i	0.0432919	−	0.0116000i
$487$	−13.4339	−	3.59961i	−0.608749	−	0.163114i	−0.0587410	−	0.998273i	$-0.518709\pi$
$487$	−13.4339	−	3.59961i	−0.608749	−	0.163114i	−0.550008	+	0.835160i	$0.685375\pi$
$488$	−5.18694	+	5.18694i	−0.234802	+	0.234802i
$489$	13.3170	−	13.3170i	0.602213	−	0.602213i
$490$	−4.83366	+	4.39236i	−0.218362	+	0.198426i
$491$	−6.73956	+	3.89109i	−0.304152	+	0.175602i	−0.644307	−	0.764767i	$-0.722854\pi$
$491$	−6.73956	+	3.89109i	−0.304152	+	0.175602i	0.340155	+	0.940370i	$0.389521\pi$
$492$	9.51562	−	2.54970i	0.428997	−	0.114949i
$493$	8.67888	−	15.0323i	0.390877	−	0.677019i
$494$	−3.30201	+	3.03078i	−0.148565	+	0.136361i
$495$	−5.37742	+	3.10465i	−0.241697	+	0.139544i
$496$	1.78147	−	6.64854i	0.0799904	−	0.298528i
$497$	2.61199	+	3.57789i	0.117164	+	0.160490i
$498$	12.0409	+	6.95183i	0.539567	+	0.311519i
$499$	12.4657	+	3.34017i	0.558041	+	0.149527i	0.526806	−	0.849985i	$-0.323389\pi$
$499$	12.4657	+	3.34017i	0.558041	+	0.149527i	0.0312347	+	0.999512i	$0.490056\pi$
$500$	−2.27898	+	8.50527i	−0.101919	+	0.380367i
$501$	−5.93797	+	22.1608i	−0.265289	+	0.990072i
$502$	12.3750	+	3.31587i	0.552323	+	0.147995i
$503$	0.631010	+	0.364314i	0.0281354	+	0.0162440i	0.514002	−	0.857789i	$-0.328162\pi$
$503$	0.631010	+	0.364314i	0.0281354	+	0.0162440i	−0.485866	+	0.874033i	$0.661496\pi$
$504$	−7.22846	−	3.19857i	−0.321981	−	0.142476i
$505$	−0.587653	+	2.19315i	−0.0261502	+	0.0975939i
$506$	1.31329	−	0.758229i	0.0583829	−	0.0337074i
$507$	7.43881	−	10.6613i	0.330369	−	0.473487i
$508$	−4.99206	+	8.64650i	−0.221487	+	0.383626i
$509$	−14.4291	+	3.86626i	−0.639557	+	0.171369i	−0.564003	−	0.825773i	$-0.690739\pi$
$509$	−14.4291	+	3.86626i	−0.639557	+	0.171369i	−0.0755542	+	0.997142i	$0.524073\pi$
$510$	−3.01682	+	1.74176i	−0.133587	+	0.0771264i
$511$	−12.6810	−	17.3704i	−0.560975	−	0.768422i
$512$	−7.07136	+	7.07136i	−0.312513	+	0.312513i
$513$	−0.889632	+	0.889632i	−0.0392782	+	0.0392782i
$514$	17.7261	+	4.74970i	0.781865	+	0.209500i
$515$	2.64641	−	0.709104i	0.116615	−	0.0312469i
$516$			12.3014i			0.541537i
$517$	7.16119	+	12.4035i	0.314949	+	0.545507i
$518$	−10.2380	−	8.25192i	−0.449830	−	0.362569i
$519$		−	8.58805i		−	0.376973i
$520$	−9.92924	+	2.20990i	−0.435426	+	0.0969107i
$521$	26.7816	+	15.4624i	1.17332	+	0.677419i	0.954461	−	0.298336i	$-0.0964317\pi$
$521$	26.7816	+	15.4624i	1.17332	+	0.677419i	0.218864	+	0.975755i	$0.429765\pi$
$522$	−3.24817	+	3.24817i	−0.142169	+	0.142169i
$523$	−17.2017	−	9.93138i	−0.752176	−	0.434269i	0.0743038	−	0.997236i	$-0.476327\pi$
$523$	−17.2017	−	9.93138i	−0.752176	−	0.434269i	−0.826479	+	0.562967i	$0.809660\pi$
$524$	8.70421	−	15.0761i	0.380245	−	0.658604i
$525$	1.67586	−	10.7395i	0.0731404	−	0.468710i
$526$	−2.21517	−	8.26711i	−0.0965858	−	0.360463i
$527$	−20.0910	−	20.0910i	−0.875179	−	0.875179i
$528$	−1.53925	−	5.74456i	−0.0669872	−	0.250000i
$529$	−11.4728	−	19.8714i	−0.498816	−	0.863974i
$530$	−1.90417	+	3.29813i	−0.0827120	+	0.143261i
$531$	7.20872	+	1.93157i	0.312832	+	0.0838230i
$532$	3.38825	−	0.363939i	0.146899	−	0.0157787i
$533$	−18.6176	+	29.2773i	−0.806417	+	1.26814i
$534$	2.01575	+	3.49138i	0.0872301	+	0.151087i
$535$	7.40118	+	7.40118i	0.319981	+	0.319981i
$536$	−30.3846			−1.31241
$537$	−13.6367			−0.588469
$538$	−5.09304	−	5.09304i	−0.219577	−	0.219577i
$539$	−45.9758	−	2.19913i	−1.98032	−	0.0947231i
$540$	−0.933796	+	0.250210i	−0.0401842	+	0.0107673i
$541$	−2.57018	+	9.59205i	−0.110501	+	0.412395i	−0.998911	−	0.0466559i	$-0.985144\pi$
$541$	−2.57018	+	9.59205i	−0.110501	+	0.412395i	0.888410	+	0.459050i	$0.151810\pi$
$542$	−20.1068	+	11.6087i	−0.863663	+	0.498636i
$543$			11.2556i			0.483024i
$544$	4.91042	+	18.3259i	0.210532	+	0.785717i
$545$	6.85914			0.293813
$546$	8.92903	−	3.01854i	0.382127	−	0.129182i
$547$	−5.37266			−0.229718			−0.114859	−	0.993382i	$-0.536642\pi$
$547$	−5.37266			−0.229718			−0.114859	+	0.993382i	$0.536642\pi$
$548$	1.27086	+	4.74291i	0.0542885	+	0.202607i
$549$		−	2.45527i		−	0.104788i
$550$	23.1152	−	13.3456i	0.985637	−	0.569058i
$551$	1.51389	−	5.64992i	0.0644939	−	0.240694i
$552$	0.673585	−	0.180487i	0.0286697	−	0.00768202i
$553$	−3.88157	−	3.12859i	−0.165061	−	0.133041i
$554$	−1.71281	−	1.71281i	−0.0727702	−	0.0727702i
$555$	−4.75002			−0.201627
$556$	8.24850			0.349814
$557$	9.08545	+	9.08545i	0.384963	+	0.384963i	0.872886	−	0.487923i	$-0.162245\pi$
$557$	9.08545	+	9.08545i	0.384963	+	0.384963i	−0.487923	+	0.872886i	$0.662245\pi$
$558$	3.75966	+	6.51191i	0.159159	+	0.275671i
$559$	−29.2960	−	31.9178i	−1.23909	−	1.34998i
$560$	−2.06643	−	0.914389i	−0.0873226	−	0.0386400i
$561$	−23.7133	−	6.35395i	−1.00118	−	0.268264i
$562$	6.47117	−	11.2084i	0.272970	−	0.472797i
$563$	3.15942	+	5.47228i	0.133154	+	0.230629i	0.924891	−	0.380233i	$-0.124156\pi$
$563$	3.15942	+	5.47228i	0.133154	+	0.230629i	−0.791737	+	0.610862i	$0.790823\pi$
$564$	0.577134	+	2.15389i	0.0243017	+	0.0906952i
$565$	−0.807097	−	0.807097i	−0.0339548	−	0.0339548i
$566$	0.147238	+	0.549498i	0.00618886	+	0.0230971i
$567$	2.46785	−	0.953787i	0.103640	−	0.0400553i
$568$	−2.50115	+	4.33211i	−0.104946	+	0.181771i
$569$	4.42917	+	2.55718i	0.185680	+	0.107203i	0.589959	−	0.807433i	$-0.299144\pi$
$569$	4.42917	+	2.55718i	0.185680	+	0.107203i	−0.404278	+	0.914636i	$0.632477\pi$
$570$	−0.830056	+	0.830056i	−0.0347672	+	0.0347672i
$571$	24.2776	+	14.0167i	1.01599	+	0.586580i	0.912939	−	0.408097i	$-0.133807\pi$
$571$	24.2776	+	14.0167i	1.01599	+	0.586580i	0.103047	+	0.994676i	$0.467141\pi$
$572$	−20.4809	−	13.0239i	−0.856350	−	0.544557i
$573$		−	11.3967i		−	0.476105i
$574$	−23.4640	+	9.06846i	−0.979367	+	0.378510i
$575$	0.479459	+	0.830447i	0.0199948	+	0.0346320i
$576$		−	6.82982i		−	0.284576i
$577$	−19.3359	+	5.18104i	−0.804964	+	0.215689i	−0.637762	−	0.770233i	$-0.720140\pi$
$577$	−19.3359	+	5.18104i	−0.804964	+	0.215689i	−0.167202	+	0.985923i	$0.553473\pi$
$578$	2.92108	+	0.782701i	0.121501	+	0.0325561i
$579$	−1.75587	+	1.75587i	−0.0729713	+	0.0729713i
$580$	3.17809	−	3.17809i	0.131963	−	0.131963i
$581$	34.0461	+	15.0653i	1.41247	+	0.625014i
$582$	−2.14115	+	1.23620i	−0.0887537	+	0.0512420i
$583$	−25.9245	+	6.94644i	−1.07368	+	0.287692i
$584$	12.1429	−	21.0321i	0.502477	−	0.870315i
$585$	1.82700	−	2.87307i	0.0755371	−	0.118787i
$586$	−14.9969	+	8.65846i	−0.619516	+	0.357678i
$587$	−1.06109	+	3.96003i	−0.0437957	+	0.163448i	−0.984360	−	0.176167i	$-0.943630\pi$
$587$	−1.06109	+	3.96003i	−0.0437957	+	0.163448i	0.940565	+	0.339615i	$0.110297\pi$
$588$	−6.82552	−	2.18336i	−0.281480	−	0.0900401i
$589$	−8.29187	−	4.78731i	−0.341661	−	0.197258i
$590$	6.72598	+	1.80222i	0.276904	+	0.0741962i
$591$	−3.77342	+	14.0826i	−0.155218	+	0.579281i
$592$	1.17750	−	4.39450i	0.0483950	−	0.180613i
$593$	−16.7775	−	4.49553i	−0.688971	−	0.184609i	−0.102686	−	0.994714i	$-0.532744\pi$
$593$	−16.7775	−	4.49553i	−0.688971	−	0.184609i	−0.586285	+	0.810105i	$0.699410\pi$
$594$	5.62651	+	3.24847i	0.230859	+	0.133286i
$595$	−7.53393	+	5.50003i	−0.308861	+	0.225479i
$596$	4.07665	−	15.2143i	0.166986	−	0.623200i
$597$	4.52897	−	2.61480i	0.185358	−	0.107017i
$598$	−0.446196	+	0.701671i	−0.0182463	+	0.0286935i
$599$	−7.18140	+	12.4386i	−0.293424	+	0.508226i	−0.974617	−	0.223878i	$-0.928128\pi$
$599$	−7.18140	+	12.4386i	−0.293424	+	0.508226i	0.681193	+	0.732104i	$0.261461\pi$
$600$	11.8558	−	3.17674i	0.484010	−	0.129690i
$601$	−7.65598	+	4.42018i	−0.312294	+	0.180303i	−0.647952	−	0.761681i	$-0.724374\pi$
$601$	−7.65598	+	4.42018i	−0.312294	+	0.180303i	0.335659	+	0.941984i	$0.391041\pi$
$602$	−3.35470	−	31.2320i	−0.136727	−	1.27292i
$603$	7.19137	−	7.19137i	0.292855	−	0.292855i
$604$	17.6909	−	17.6909i	0.719833	−	0.719833i
$605$	−29.4044	−	7.87889i	−1.19546	−	0.320322i
$606$	2.29474	−	0.614874i	0.0932175	−	0.0249776i
$607$			27.1962i			1.10386i	0.833890	+	0.551930i	$0.186109\pi$
$607$			27.1962i			1.10386i	−0.833890	+	0.551930i	$0.813891\pi$
$608$	3.19666	+	5.53678i	0.129642	+	0.224546i
$609$	−7.71911	+	9.57691i	−0.312794	+	0.388076i
$610$		−	2.29085i		−	0.0927539i
$611$	−6.62702	−	4.21415i	−0.268100	−	0.170486i
$612$	−3.31012	−	1.91110i	−0.133804	−	0.0772516i
$613$	31.3428	−	31.3428i	1.26593	−	1.26593i	0.317751	−	0.948174i	$-0.397072\pi$
$613$	31.3428	−	31.3428i	1.26593	−	1.26593i	0.948174	−	0.317751i	$-0.102928\pi$
$614$	12.5717	+	7.25828i	0.507353	+	0.292920i
$615$	−4.54346	+	7.86951i	−0.183210	+	0.317329i
$616$	−18.7372	−	48.4811i	−0.754944	−	1.95336i
$617$	−7.15534	−	26.7041i	−0.288063	−	1.07507i	−0.946572	−	0.322493i	$-0.895479\pi$
$617$	−7.15534	−	26.7041i	−0.288063	−	1.07507i	0.658509	−	0.752573i	$-0.271188\pi$
$618$	−2.02705	−	2.02705i	−0.0815398	−	0.0815398i
$619$	−10.1905	−	38.0315i	−0.409591	−	1.52861i	−0.795429	−	0.606047i	$-0.792754\pi$
$619$	−10.1905	−	38.0315i	−0.409591	−	1.52861i	0.385838	−	0.922567i	$-0.373912\pi$
$620$	−3.67853	−	6.37141i	−0.147734	−	0.255882i
$621$	−0.116706	+	0.202140i	−0.00468324	+	0.00811161i
$622$	−12.1922	−	3.26689i	−0.488863	−	0.130990i
$623$	6.36523	+	8.71908i	0.255018	+	0.349322i
$624$	2.20513	+	2.40247i	0.0882757	+	0.0961757i
$625$	6.20963	+	10.7554i	0.248385	+	0.430216i
$626$	9.92861	+	9.92861i	0.396827	+	0.396827i
$627$	−8.27280			−0.330384
$628$	9.67233			0.385968
$629$	−13.2796	−	13.2796i	−0.529493	−	0.529493i
$630$	2.30259	−	0.889915i	0.0917373	−	0.0354551i
$631$	7.08811	−	1.89925i	0.282173	−	0.0756081i	−0.114957	−	0.993371i	$-0.536673\pi$
$631$	7.08811	−	1.89925i	0.282173	−	0.0756081i	0.397130	+	0.917762i	$0.370006\pi$
$632$	1.45706	−	5.43782i	0.0579588	−	0.216305i
$633$	9.62266	−	5.55565i	0.382466	−	0.220817i
$634$			18.4841i			0.734096i
$635$	−2.38358	−	8.89564i	−0.0945895	−	0.353013i
$636$	−4.17861			−0.165693
$637$	22.9096	−	10.5901i	0.907711	−	0.419595i
$638$	−30.2052			−1.19583
$639$	−0.433350	−	1.61728i	−0.0171431	−	0.0639787i
$640$			3.22481i			0.127472i
$641$	29.1101	−	16.8067i	1.14978	−	0.663826i	0.200946	−	0.979602i	$-0.435598\pi$
$641$	29.1101	−	16.8067i	1.14978	−	0.663826i	0.948834	+	0.315777i	$0.102265\pi$
$642$	2.83451	−	10.5785i	0.111869	−	0.417501i
$643$	−22.8004	+	6.10935i	−0.899160	+	0.240929i	−0.678655	−	0.734457i	$-0.737437\pi$
$643$	−22.8004	+	6.10935i	−0.899160	+	0.240929i	−0.220504	+	0.975386i	$0.570770\pi$
$644$	0.589703	−	0.227911i	0.0232376	−	0.00898096i
$645$	−8.02346	−	8.02346i	−0.315924	−	0.315924i
$646$	−4.64117			−0.182604
$647$	1.02762			0.0403998			0.0201999	−	0.999796i	$-0.493570\pi$
$647$	1.02762			0.0403998			0.0201999	+	0.999796i	$0.493570\pi$
$648$	2.11257	+	2.11257i	0.0829897	+	0.0829897i
$649$	24.5364	+	42.4983i	0.963139	+	1.66821i
$650$	−7.85349	+	12.3501i	−0.308039	+	0.484411i
$651$	11.8720	+	16.2623i	0.465302	+	0.637369i
$652$	18.6233	+	4.99009i	0.729343	+	0.195427i
$653$	−11.2342	+	19.4582i	−0.439628	+	0.761458i	−0.997661	−	0.0683609i	$-0.978223\pi$
$653$	−11.2342	+	19.4582i	−0.439628	+	0.761458i	0.558033	+	0.829819i	$0.311556\pi$
$654$	−3.58843	−	6.21535i	−0.140319	−	0.243039i
$655$	4.15604	+	15.5105i	0.162390	+	0.606047i
$656$	−6.15420	−	6.15420i	−0.240281	−	0.240281i
$657$	2.10388	+	7.85180i	0.0820803	+	0.306328i
$658$	−2.05268	−	5.31115i	−0.0800217	−	0.207050i
$659$	−15.3326	+	26.5569i	−0.597275	+	1.03451i	0.395947	+	0.918273i	$0.370416\pi$
$659$	−15.3326	+	26.5569i	−0.597275	+	1.03451i	−0.993222	+	0.116237i	$0.962917\pi$
$660$	−5.50511	−	3.17838i	−0.214286	−	0.123718i
$661$	−24.4206	+	24.4206i	−0.949852	+	0.949852i	−0.998801	−	0.0489491i	$-0.984413\pi$
$661$	−24.4206	+	24.4206i	−0.949852	+	0.949852i	0.0489491	+	0.998801i	$0.484413\pi$
$662$	−3.37847	−	1.95056i	−0.131308	−	0.0758107i
$663$	13.1400	−	2.92450i	0.510314	−	0.113578i
$664$			42.0412i			1.63151i
$665$	−1.97258	+	2.44734i	−0.0764935	+	0.0949036i
$666$	2.48503	+	4.30419i	0.0962928	+	0.166784i
$667$		−	1.08516i		−	0.0420177i
$668$	−22.6870	+	6.07898i	−0.877788	+	0.235203i
$669$	−26.5785	−	7.12168i	−1.02758	−	0.275340i
$670$	6.70979	−	6.70979i	0.259222	−	0.259222i
$671$	11.4159	−	11.4159i	0.440708	−	0.440708i
$672$	−1.43586	−	13.3678i	−0.0553895	−	0.515673i
$673$	27.9964	−	16.1637i	1.07918	−	0.623066i	0.148506	−	0.988912i	$-0.452554\pi$
$673$	27.9964	−	16.1637i	1.07918	−	0.623066i	0.930675	+	0.365846i	$0.119220\pi$
$674$	14.4535	−	3.87281i	0.556729	−	0.149175i
$675$	−2.05414	+	3.55787i	−0.0790637	+	0.136942i
$676$	13.2600	+	1.13793i	0.509998	+	0.0437664i
$677$	−25.7232	+	14.8513i	−0.988623	+	0.570782i	−0.904862	−	0.425704i	$-0.860026\pi$
$677$	−25.7232	+	14.8513i	−0.988623	+	0.570782i	−0.0837606	+	0.996486i	$0.526693\pi$
$678$	−0.309102	+	1.15359i	−0.0118710	+	0.0443032i
$679$	−5.34713	+	3.90359i	−0.205204	+	0.149806i
$680$	−9.12208	−	5.26664i	−0.349816	−	0.201966i
$681$	−11.3401	−	3.03858i	−0.434554	−	0.116439i
$682$	−12.7968	+	47.7583i	−0.490015	+	1.82876i
$683$	4.83332	−	18.0382i	0.184942	−	0.690213i	−0.809701	−	0.586843i	$-0.800371\pi$
$683$	4.83332	−	18.0382i	0.184942	−	0.690213i	0.994643	−	0.103370i	$-0.0329626\pi$
$684$	−1.24412	−	0.333360i	−0.0475700	−	0.0127463i
$685$	−3.92244	−	2.26462i	−0.149869	−	0.0865267i
$686$	17.9248	+	3.68196i	0.684372	+	0.140578i
$687$	−3.62802	+	13.5399i	−0.138417	+	0.516581i
$688$	9.41190	−	5.43396i	0.358825	−	0.207168i
$689$	10.8420	−	9.95147i	0.413049	−	0.379121i
$690$	−0.108890	+	0.188604i	−0.00414539	+	0.00718002i
$691$	10.7277	−	2.87447i	0.408100	−	0.109350i	−0.0489282	−	0.998802i	$-0.515581\pi$
$691$	10.7277	−	2.87447i	0.408100	−	0.109350i	0.457028	+	0.889452i	$0.348914\pi$
$692$	7.61408	−	4.39599i	0.289444	−	0.167110i
$693$	15.9091	+	7.03974i	0.604338	+	0.267418i
$694$	4.74704	−	4.74704i	0.180195	−	0.180195i
$695$	−5.38002	+	5.38002i	−0.204076	+	0.204076i
$696$	−13.4166	−	3.59498i	−0.508556	−	0.136267i
$697$	−34.7029	+	9.29861i	−1.31447	+	0.352210i
$698$		−	0.386660i		−	0.0146353i
$699$	−3.04141	−	5.26788i	−0.115037	−	0.199249i
$700$	10.3794	−	4.01146i	0.392303	−	0.151619i
$701$		−	9.68156i		−	0.365668i	−0.983144	−	0.182834i	$-0.941473\pi$
$701$		−	9.68156i		−	0.365668i	0.983144	−	0.182834i	$-0.0585270\pi$
$702$	−3.55922	−	0.152440i	−0.134334	−	0.00575349i
$703$	−5.48069	−	3.16428i	−0.206708	−	0.119343i
$704$	31.7557	−	31.7557i	1.19684	−	1.19684i
$705$	−1.78129	−	1.02843i	−0.0670872	−	0.0387328i
$706$	−9.86512	+	17.0869i	−0.371279	+	0.643074i
$707$	5.93373	−	2.29329i	0.223161	−	0.0862482i
$708$	1.97744	+	7.37989i	0.0743166	+	0.277353i
$709$	−1.06906	−	1.06906i	−0.0401494	−	0.0401494i	0.686747	−	0.726896i	$-0.259038\pi$
$709$	−1.06906	−	1.06906i	−0.0401494	−	0.0401494i	−0.726896	+	0.686747i	$0.759038\pi$
$710$	−0.404330	−	1.50898i	−0.0151742	−	0.0566310i
$711$	0.942160	+	1.63187i	0.0353338	+	0.0611999i
$712$	−6.09512	+	10.5571i	−0.228424	+	0.395643i
$713$	−1.71578	−	0.459743i	−0.0642566	−	0.0172175i
$714$	8.92527	+	3.94940i	0.334020	+	0.147803i
$715$	21.8533	−	4.86378i	0.817266	−	0.181895i
$716$	−6.98028	−	12.0902i	−0.260865	−	0.451832i
$717$	3.72605	+	3.72605i	0.139152	+	0.139152i
$718$	−27.3870			−1.02207
$719$	27.7174			1.03368			0.516842	−	0.856081i	$-0.327108\pi$
$719$	27.7174			1.03368			0.516842	+	0.856081i	$0.327108\pi$
$720$	0.603930	+	0.603930i	0.0225071	+	0.0225071i
$721$	−5.97654	−	4.81717i	−0.222578	−	0.179401i
$722$	16.6227	−	4.45404i	0.618632	−	0.165762i
$723$	−6.94938	+	25.9354i	−0.258450	+	0.964549i
$724$	−9.97910	+	5.76143i	−0.370870	+	0.214122i
$725$		−	19.0999i		−	0.709354i
$726$	8.24386	+	30.7665i	0.305958	+	1.14185i
$727$	29.0510			1.07744			0.538721	−	0.842484i	$-0.318908\pi$
$727$	29.0510			1.07744			0.538721	+	0.842484i	$0.318908\pi$
$728$	21.4040	+	18.8183i	0.793286	+	0.697452i
$729$	−1.00000			−0.0370370
$730$	1.96299	+	7.32600i	0.0726537	+	0.271147i
$731$		−	44.8623i		−	1.65929i
$732$	2.17682	−	1.25679i	0.0804576	−	0.0464522i
$733$	8.78993	−	32.8045i	0.324663	−	1.21166i	−0.589986	−	0.807413i	$-0.700867\pi$
$733$	8.78993	−	32.8045i	0.324663	−	1.21166i	0.914650	−	0.404247i	$-0.132466\pi$
$734$	6.37441	−	1.70802i	0.235284	−	0.0630441i
$735$	5.87597	−	3.02781i	0.216738	−	0.111683i
$736$	0.838703	+	0.838703i	0.0309150	+	0.0309150i
$737$	66.8735			2.46332
$738$	9.50785			0.349989
$739$	9.73435	+	9.73435i	0.358084	+	0.358084i	0.863106	−	0.505022i	$-0.168516\pi$
$739$	9.73435	+	9.73435i	0.358084	+	0.358084i	−0.505022	+	0.863106i	$0.668516\pi$
$740$	−2.43141	−	4.21132i	−0.0893803	−	0.154811i
$741$	4.02196	−	2.09794i	0.147750	−	0.0770699i
$742$	10.6091	−	1.13955i	0.389472	−	0.0418340i
$743$	−30.3940	−	8.14404i	−1.11505	−	0.298776i	−0.346169	−	0.938172i	$-0.612518\pi$
$743$	−30.3940	−	8.14404i	−1.11505	−	0.298776i	−0.768878	+	0.639396i	$0.779184\pi$
$744$	−11.3682	+	19.6904i	−0.416780	+	0.721884i
$745$	7.26442	+	12.5823i	0.266148	+	0.460981i
$746$	0.257288	+	0.960210i	0.00941997	+	0.0351558i
$747$	−9.95023	−	9.95023i	−0.364060	−	0.364060i
$748$	−6.50483	−	24.2764i	−0.237840	−	0.887632i
$749$	4.52145	−	28.9751i	0.165210	−	1.05873i
$750$	−4.24916	+	7.35977i	−0.155158	+	0.268741i
$751$	22.9765	+	13.2655i	0.838423	+	0.484064i	0.856728	−	0.515769i	$-0.172494\pi$
$751$	22.9765	+	13.2655i	0.838423	+	0.484064i	−0.0183050	+	0.999832i	$0.505827\pi$
$752$	1.39302	−	1.39302i	0.0507983	−	0.0507983i
$753$	−11.2292	−	6.48321i	−0.409217	−	0.236261i
$754$	14.6848	−	7.65990i	0.534788	−	0.278957i
$755$			23.0775i			0.839876i
$756$	2.10884	+	1.69975i	0.0766979	+	0.0618195i
$757$	7.38184	+	12.7857i	0.268298	+	0.464705i	0.968422	−	0.249315i	$-0.0802056\pi$
$757$	7.38184	+	12.7857i	0.268298	+	0.464705i	−0.700125	+	0.714021i	$0.746872\pi$
$758$		−	21.1143i		−	0.766908i
$759$	−1.48249	+	0.397233i	−0.0538111	+	0.0144186i
$760$	−3.42856	−	0.918680i	−0.124367	−	0.0333240i
$761$	23.1965	−	23.1965i	0.840873	−	0.840873i	−0.148100	−	0.988972i	$-0.547316\pi$
$761$	23.1965	−	23.1965i	0.840873	−	0.840873i	0.988972	+	0.148100i	$0.0473156\pi$
$762$	−6.81371	+	6.81371i	−0.246835	+	0.246835i
$763$	−11.3314	−	15.5217i	−0.410223	−	0.561922i
$764$	10.1042	−	5.83367i	0.365558	−	0.211055i
$765$	3.40550	−	0.912500i	0.123126	−	0.0329915i
$766$	−11.2880	+	19.5513i	−0.407850	+	0.706418i
$767$	−22.7062	−	14.4390i	−0.819873	−	0.521361i
$768$	14.7517	−	8.51691i	0.532307	−	0.307328i
$769$	1.79577	−	6.70191i	0.0647572	−	0.241677i	−0.925959	−	0.377624i	$-0.876741\pi$
$769$	1.79577	−	6.70191i	0.0647572	−	0.241677i	0.990716	+	0.135947i	$0.0434078\pi$
$770$	14.8437	+	6.56832i	0.534932	+	0.236706i
$771$	−16.0849	−	9.28663i	−0.579284	−	0.334450i
$772$	−2.45551	−	0.657953i	−0.0883759	−	0.0236802i
$773$	−0.260414	+	0.971880i	−0.00936645	+	0.0349561i	−0.970451	−	0.241299i	$-0.922427\pi$
$773$	−0.260414	+	0.971880i	−0.00936645	+	0.0349561i	0.961084	+	0.276255i	$0.0890933\pi$
$774$	−3.07283	+	11.4680i	−0.110451	+	0.412207i
$775$	−30.1995	−	8.09193i	−1.08480	−	0.290671i
$776$	−6.47431	−	3.73794i	−0.232414	−	0.134184i
$777$	7.84708	+	10.7489i	0.281512	+	0.385615i
$778$	5.11020	−	19.0715i	0.183209	−	0.683747i
$779$	−10.4847	+	6.05336i	−0.375654	+	0.216884i
$780$	3.48243	+	0.149151i	0.124691	+	0.00534047i
$781$	5.50477	−	9.53455i	0.196976	−	0.341173i
$782$	−0.831702	+	0.222854i	−0.0297416	+	0.00796924i
$783$	4.02628	−	2.32457i	0.143887	−	0.0830734i
$784$	1.34457	+	6.18674i	0.0480205	+	0.220955i
$785$	−6.30870	+	6.30870i	−0.225167	+	0.225167i
$786$	11.8805	−	11.8805i	0.423762	−	0.423762i
$787$	−38.2900	−	10.2598i	−1.36489	−	0.365721i	−0.499281	−	0.866440i	$-0.666402\pi$
$787$	−38.2900	−	10.2598i	−1.36489	−	0.365721i	−0.865610	+	0.500719i	$0.833069\pi$
$788$	−14.4170	+	3.86303i	−0.513585	+	0.137615i
$789$			8.66221i			0.308383i
$790$	0.879067	+	1.52259i	0.0312758	+	0.0541713i
$791$	−0.493063	+	3.15973i	−0.0175313	+	0.112347i
$792$			19.6451i			0.698058i
$793$	−2.65502	+	8.44509i	−0.0942827	+	0.299894i
$794$	21.4026	+	12.3568i	0.759549	+	0.438526i
$795$	2.72546	−	2.72546i	0.0966622	−	0.0966622i
$796$	4.63651	+	2.67689i	0.164337	+	0.0948799i
$797$	18.4889	−	32.0238i	0.654912	−	1.13434i	−0.327004	−	0.945023i	$-0.606039\pi$
$797$	18.4889	−	32.0238i	0.654912	−	1.13434i	0.981916	−	0.189318i	$-0.0606276\pi$
$798$	3.24961	+	0.507089i	0.115035	+	0.0179508i
$799$	−2.10477	−	7.85511i	−0.0744614	−	0.277894i
$800$	14.7620	+	14.7620i	0.521916	+	0.521916i
$801$	−1.05604	−	3.94121i	−0.0373135	−	0.139256i
$802$	−0.694751	−	1.20334i	−0.0245325	−	0.0424915i
$803$	−26.7253	+	46.2896i	−0.943115	+	1.63352i
$804$	10.0569	+	2.69473i	0.354678	+	0.0950358i
$805$	−0.235976	+	0.533282i	−0.00831706	+	0.0187957i
$806$	−5.88991	−	26.4637i	−0.207463	−	0.932145i
$807$	3.64486	+	6.31308i	0.128305	+	0.222231i
$808$	5.07949	+	5.07949i	0.178696	+	0.178696i
$809$	19.6908			0.692293			0.346146	−	0.938181i	$-0.387490\pi$
$809$	19.6908			0.692293			0.346146	+	0.938181i	$0.387490\pi$
$810$	−0.933034			−0.0327835
$811$	25.0100	+	25.0100i	0.878220	+	0.878220i	0.993350	−	0.115131i	$-0.0367287\pi$
$811$	25.0100	+	25.0100i	0.878220	+	0.878220i	−0.115131	+	0.993350i	$0.536729\pi$
$812$	−12.4420	−	1.94152i	−0.436628	−	0.0681341i
$813$	22.6974	−	6.08174i	0.796032	−	0.213296i
$814$	−8.45832	+	31.5669i	−0.296464	+	1.10642i
$815$	−15.4016	+	8.89213i	−0.539495	+	0.311478i
$816$			3.37681i			0.118212i
$817$	−3.91275	−	14.6026i	−0.136890	−	0.510880i
$818$	−2.74007			−0.0958042
$819$	−9.51974	+	0.611992i	−0.332647	+	0.0213847i
$820$	−9.30270			−0.324865
$821$	−1.60713	−	5.99790i	−0.0560893	−	0.209328i	0.932194	−	0.361959i	$-0.117892\pi$
$821$	−1.60713	−	5.99790i	−0.0560893	−	0.209328i	−0.988283	+	0.152631i	$0.951225\pi$
$822$			4.73904i			0.165293i
$823$	−2.18495	+	1.26148i	−0.0761627	+	0.0439726i	−0.537598	−	0.843201i	$-0.680668\pi$
$823$	−2.18495	+	1.26148i	−0.0761627	+	0.0439726i	0.461435	+	0.887174i	$0.347335\pi$
$824$	2.24347	−	8.37275i	0.0781550	−	0.291679i
$825$	−26.0934	+	6.99170i	−0.908454	+	0.243420i
$826$	−7.03310	−	18.1976i	−0.244713	−	0.633176i
$827$	36.7114	+	36.7114i	1.27658	+	1.27658i	0.942569	+	0.334011i	$0.108402\pi$
$827$	36.7114	+	36.7114i	1.27658	+	1.27658i	0.334011	+	0.942569i	$0.391598\pi$
$828$	−0.238954			−0.00830422
$829$	26.2330			0.911111			0.455555	−	0.890207i	$-0.349441\pi$
$829$	26.2330			0.911111			0.455555	+	0.890207i	$0.349441\pi$
$830$	−9.28390	−	9.28390i	−0.322249	−	0.322249i
$831$	1.22578	+	2.12311i	0.0425218	+	0.0736499i
$832$	−7.38547	+	23.4917i	−0.256045	+	0.814427i
$833$	24.8922	+	7.96257i	0.862465	+	0.275887i
$834$	7.68967	+	2.06044i	0.266272	+	0.0713472i
$835$	10.8325	−	18.7624i	0.374873	−	0.649300i
$836$	−4.23462	−	7.33458i	−0.146457	−	0.253672i
$837$	−1.96967	−	7.35090i	−0.0680817	−	0.254084i
$838$	−13.5094	−	13.5094i	−0.466674	−	0.466674i
$839$	−9.29570	−	34.6920i	−0.320923	−	1.19770i	−0.918347	−	0.395776i	$-0.870476\pi$
$839$	−9.29570	−	34.6920i	−0.320923	−	1.19770i	0.597424	−	0.801926i	$-0.296191\pi$
$840$	5.81159	+	4.68422i	0.200519	+	0.161621i
$841$	3.69273	−	6.39600i	0.127336	−	0.220552i
$842$	2.90951	+	1.67981i	0.100268	+	0.0578900i
$843$	−9.26224	+	9.26224i	−0.319009	+	0.319009i
$844$	9.85116	+	5.68757i	0.339091	+	0.195774i
$845$	−9.39091	+	7.90650i	−0.323057	+	0.271992i
$846$			2.15213i			0.0739919i
$847$	30.7471	+	79.5558i	1.05648	+	2.73357i
$848$	1.84584	+	3.19709i	0.0633865	+	0.109789i
$849$		−	0.575760i		−	0.0197600i
$850$	−14.6388	+	3.92245i	−0.502106	+	0.134539i
$851$	−1.13408	−	0.303877i	−0.0388759	−	0.0104168i
$852$	1.21205	−	1.21205i	0.0415241	−	0.0415241i
$853$	−0.749751	+	0.749751i	−0.0256710	+	0.0256710i	−0.719826	−	0.694155i	$-0.755778\pi$
$853$	−0.749751	+	0.749751i	−0.0256710	+	0.0256710i	0.694155	+	0.719826i	$0.255778\pi$
$854$	−5.18401	+	3.78451i	−0.177393	+	0.129503i
$855$	1.02890	−	0.594034i	0.0351875	−	0.0203155i
$856$	31.9868	−	8.57083i	1.09329	−	0.292945i
$857$	1.48116	−	2.56544i	0.0505953	−	0.0876336i	−0.839619	−	0.543176i	$-0.817221\pi$
$857$	1.48116	−	2.56544i	0.0505953	−	0.0876336i	0.890214	+	0.455543i	$0.150555\pi$
$858$	−15.8400	−	17.2576i	−0.540770	−	0.589165i
$859$	20.5020	−	11.8368i	0.699518	−	0.403867i	−0.107650	−	0.994189i	$-0.534333\pi$
$859$	20.5020	−	11.8368i	0.699518	−	0.403867i	0.807168	+	0.590322i	$0.200999\pi$
$860$	3.00653	−	11.2205i	0.102522	−	0.382616i
$861$	25.3139	−	2.71902i	0.862695	−	0.0926638i
$862$	−0.593540	−	0.342681i	−0.0202161	−	0.0116717i
$863$	−18.8188	−	5.04247i	−0.640598	−	0.171648i	−0.0761238	−	0.997098i	$-0.524254\pi$
$863$	−18.8188	−	5.04247i	−0.640598	−	0.171648i	−0.564474	+	0.825451i	$0.690921\pi$
$864$	−1.31522	+	4.90846i	−0.0447446	+	0.166989i
$865$	−2.09897	+	7.83347i	−0.0713672	+	0.266346i
$866$	−20.0696	−	5.37764i	−0.681994	−	0.182740i
$867$	−2.65063	−	1.53034i	−0.0900201	−	0.0519731i
$868$	−8.34100	+	18.8498i	−0.283112	+	0.639806i
$869$	−3.20684	+	11.9681i	−0.108785	+	0.405990i
$870$	3.75665	−	2.16890i	0.127362	−	0.0735327i
$871$	−32.5117	+	16.9588i	−1.10162	+	0.574628i
$872$	10.8505	−	18.7936i	0.367445	−	0.636433i
$873$	2.41702	−	0.647638i	0.0818036	−	0.0219192i
$874$	−0.251281	+	0.145077i	−0.00849970	+	0.00490730i
$875$	−9.20834	+	20.8100i	−0.311299	+	0.703505i
$876$	−5.88441	+	5.88441i	−0.198816	+	0.198816i
$877$	24.3318	−	24.3318i	0.821626	−	0.821626i	−0.164715	−	0.986341i	$-0.552670\pi$
$877$	24.3318	−	24.3318i	0.821626	−	0.821626i	0.986341	+	0.164715i	$0.0526704\pi$
$878$	−21.7827	−	5.83666i	−0.735131	−	0.196978i
$879$	16.9291	−	4.53613i	0.571003	−	0.153000i
$880$			5.61602i			0.189316i
$881$	16.0850	+	27.8600i	0.541918	+	0.938629i	0.998794	+	0.0490986i	$0.0156348\pi$
$881$	16.0850	+	27.8600i	0.541918	+	0.938629i	−0.456876	+	0.889530i	$0.651032\pi$
$882$	−5.81770	−	3.74042i	−0.195892	−	0.125947i
$883$			24.5604i			0.826522i	0.910613	+	0.413261i	$0.135610\pi$
$883$			24.5604i			0.826522i	−0.910613	+	0.413261i	$0.864390\pi$
$884$	9.31882	+	10.1528i	0.313426	+	0.341475i
$885$	−6.10324	−	3.52371i	−0.205158	−	0.118448i
$886$	11.7198	−	11.7198i	0.393734	−	0.393734i
$887$	−18.9519	−	10.9419i	−0.636343	−	0.367393i	0.146861	−	0.989157i	$-0.453083\pi$
$887$	−18.9519	−	10.9419i	−0.636343	−	0.367393i	−0.783204	+	0.621764i	$0.786416\pi$
$888$	−7.51409	+	13.0148i	−0.252156	+	0.436748i
$889$	−16.1924	+	20.0895i	−0.543076	+	0.673781i
$890$	−0.985325	−	3.67728i	−0.0330282	−	0.123263i
$891$	−4.64956	−	4.64956i	−0.155766	−	0.155766i
$892$	−7.29080	−	27.2096i	−0.244114	−	0.911045i
$893$	−1.37020	−	2.37325i	−0.0458519	−	0.0794178i
$894$	7.60092	−	13.1652i	0.254213	−	0.440310i
$895$	12.4386	+	3.33290i	0.415775	+	0.111407i
$896$	7.29748	−	5.32742i	0.243792	−	0.177976i
$897$	0.620004	−	0.569076i	0.0207013	−	0.0190009i
$898$	7.57109	+	13.1135i	0.252651	+	0.437604i
$899$	25.0181	+	25.0181i	0.834401	+	0.834401i
$900$	−4.20583			−0.140194
$901$	15.2391			0.507689
$902$	44.2074	+	44.2074i	1.47194	+	1.47194i
$903$	−4.90161	+	31.4113i	−0.163115	+	1.04530i
$904$	−3.48815	+	0.934647i	−0.116014	+	0.0310859i
$905$	2.75094	−	10.2666i	0.0914442	−	0.341275i
$906$	20.9115	−	12.0732i	0.694737	−	0.401107i
$907$			1.56364i			0.0519198i	0.999663	+	0.0259599i	$0.00826422\pi$
$907$			1.56364i			0.0519198i	−0.999663	+	0.0259599i	$0.991736\pi$
$908$	−3.11073	−	11.6094i	−0.103233	−	0.385272i
$909$	−2.40441			−0.0797493
$910$	−8.88224	+	0.571009i	−0.294443	+	0.0189288i
$911$	27.1812			0.900555			0.450277	−	0.892889i	$-0.351325\pi$
$911$	27.1812			0.900555			0.450277	+	0.892889i	$0.351325\pi$
$912$	0.294515	+	1.09914i	0.00975236	+	0.0363963i
$913$		−	92.5284i		−	3.06224i
$914$	11.9167	−	6.88013i	0.394171	−	0.227574i
$915$	−0.600084	+	2.23954i	−0.0198382	+	0.0740370i
$916$	−13.8615	+	3.71417i	−0.457996	+	0.122720i
$917$	28.2333	−	35.0283i	0.932345	−	1.15674i
$918$	−2.60848	−	2.60848i	−0.0860926	−	0.0860926i
$919$	−52.1835			−1.72137			−0.860687	−	0.509134i	$-0.829966\pi$
$919$	−52.1835			−1.72137			−0.860687	+	0.509134i	$0.829966\pi$
$920$	−0.658514			−0.0217106
$921$	−10.3888	−	10.3888i	−0.342324	−	0.342324i
$922$	−7.82204	−	13.5482i	−0.257605	−	0.446185i
$923$	−0.258322	+	6.03137i	−0.00850276	+	0.198525i
$924$	1.90209	+	17.7083i	0.0625740	+	0.582561i
$925$	−19.9610	−	5.34854i	−0.656314	−	0.175859i
$926$	−18.3537	+	31.7896i	−0.603141	+	1.04467i
$927$	1.45067	+	2.51263i	0.0476461	+	0.0825256i
$928$	−6.11463	−	22.8201i	−0.200723	−	0.749107i
$929$	19.3280	+	19.3280i	0.634133	+	0.634133i	0.949102	−	0.314969i	$-0.101994\pi$
$929$	19.3280	+	19.3280i	0.634133	+	0.634133i	−0.314969	+	0.949102i	$0.601994\pi$
$930$	−1.83777	−	6.85864i	−0.0602627	−	0.224904i
$931$	8.79685	+	0.420773i	0.288305	+	0.0137903i
$932$	3.11363	−	5.39297i	0.101990	−	0.176653i
$933$	11.0634	+	6.38744i	0.362199	+	0.209115i
$934$	23.3091	−	23.3091i	0.762697	−	0.762697i
$935$	20.0768	+	11.5913i	0.656582	+	0.379078i
$936$	−4.98191	−	9.55080i	−0.162839	−	0.312178i
$937$			33.8356i			1.10536i	0.833393	+	0.552680i	$0.186395\pi$
$937$			33.8356i			1.10536i	−0.833393	+	0.552680i	$0.813605\pi$
$938$	−26.2684	−	4.09907i	−0.857692	−	0.133839i
$939$	−7.10546	−	12.3070i	−0.231878	−	0.401624i
$940$		−	2.10570i		−	0.0686803i
$941$	−50.0997	+	13.4242i	−1.63320	+	0.437615i	−0.954842	−	0.297114i	$-0.903976\pi$
$941$	−50.0997	+	13.4242i	−1.63320	+	0.437615i	−0.678360	+	0.734729i	$0.737309\pi$
$942$	9.01704	+	2.41611i	0.293791	+	0.0787211i
$943$	−1.58821	+	1.58821i	−0.0517192	+	0.0517192i
$944$	4.77293	−	4.77293i	0.155346	−	0.155346i
$945$	−2.48413	+	0.266825i	−0.0808087	+	0.00867983i
$946$	−67.6083	+	39.0337i	−2.19814	+	1.26909i
$947$	31.3506	−	8.40036i	1.01876	−	0.272975i	0.289473	−	0.957186i	$-0.406520\pi$
$947$	31.3506	−	8.40036i	1.01876	−	0.272975i	0.729284	+	0.684211i	$0.239853\pi$
$948$	−0.964532	+	1.67062i	−0.0313266	+	0.0542592i
$949$	1.25413	−	29.2819i	0.0407109	−	0.950531i
$950$	−4.42279	+	2.55350i	−0.143494	+	0.0828465i
$951$	4.84186	−	18.0701i	0.157008	−	0.585962i
$952$	3.15180	+	29.3431i	0.102150	+	0.951014i
$953$	−4.71317	−	2.72115i	−0.152675	−	0.0881468i	0.421716	−	0.906728i	$-0.361428\pi$
$953$	−4.71317	−	2.72115i	−0.152675	−	0.0881468i	−0.574391	+	0.818581i	$0.694761\pi$
$954$	−3.89551	−	1.04380i	−0.126122	−	0.0337942i
$955$	−2.78543	+	10.3954i	−0.0901343	+	0.336386i
$956$	−1.39622	+	5.21075i	−0.0451569	+	0.168528i
$957$	29.5287	+	7.91218i	0.954526	+	0.255765i
$958$	4.54827	+	2.62595i	0.146948	+	0.0848405i
$959$	1.35525	+	12.6173i	0.0437634	+	0.407435i
$960$	−1.66925	+	6.22973i	−0.0538748	+	0.201064i
$961$	23.3093	−	13.4576i	0.751914	−	0.434118i
$962$	−3.89307	−	17.4918i	−0.125517	−	0.563958i
$963$	−5.54205	+	9.59911i	−0.178590	+	0.309327i
$964$	−26.5513	+	7.11440i	−0.855160	+	0.229139i
$965$	2.03073	−	1.17245i	0.0653717	−	0.0377423i
$966$	0.606683	−	0.0651650i	0.0195197	−	0.00209665i
$967$	17.2286	−	17.2286i	0.554035	−	0.554035i	−0.373568	−	0.927603i	$-0.621866\pi$
$967$	17.2286	−	17.2286i	0.554035	−	0.554035i	0.927603	+	0.373568i	$0.121866\pi$
$968$	−68.1027	+	68.1027i	−2.18890	+	2.18890i
$969$	4.53722	+	1.21574i	0.145756	+	0.0390553i
$970$	2.25516	−	0.604268i	0.0724088	−	0.0194019i
$971$		−	37.8393i		−	1.21432i	−0.794580	−	0.607160i	$-0.792309\pi$
$971$		−	37.8393i		−	1.21432i	0.794580	−	0.607160i	$-0.207691\pi$
$972$	−0.511873	−	0.886590i	−0.0164183	−	0.0284374i
$973$	21.0624	+	3.28670i	0.675229	+	0.105367i
$974$		−	13.7417i		−	0.440312i
$975$	10.9127	−	10.0163i	0.349485	−	0.320778i
$976$	−1.92316	−	1.11034i	−0.0615589	−	0.0355411i
$977$	42.0348	−	42.0348i	1.34481	−	1.34481i	0.453616	−	0.891197i	$-0.350134\pi$
$977$	42.0348	−	42.0348i	1.34481	−	1.34481i	0.891197	−	0.453616i	$-0.149866\pi$
$978$	16.1151	+	9.30403i	0.515303	+	0.297510i
$979$	13.4148	−	23.2350i	0.428737	−	0.742595i
$980$	5.69218	+	3.65972i	0.181830	+	0.116905i
$981$	1.87996	+	7.01612i	0.0600226	+	0.224008i
$982$	−5.43710	−	5.43710i	−0.173505	−	0.173505i
$983$	2.63615	+	9.83824i	0.0840800	+	0.313791i	0.995138	−	0.0984864i	$-0.0314001\pi$
$983$	2.63615	+	9.83824i	0.0840800	+	0.313791i	−0.911058	+	0.412277i	$0.864733\pi$
$984$	14.3747	+	24.8976i	0.458248	+	0.793708i
$985$	6.88375	−	11.9230i	0.219335	−	0.379899i
$986$	16.5660	+	4.43886i	0.527570	+	0.141362i
$987$	0.615458	+	5.72989i	0.0195903	+	0.182384i
$988$	3.91875	+	2.49195i	0.124672	+	0.0792795i
$989$	−1.40234	−	2.42892i	−0.0445918	−	0.0772352i
$990$	−4.33820	−	4.33820i	−0.137877	−	0.137877i
$991$	−51.8338			−1.64655			−0.823277	−	0.567640i	$-0.807857\pi$
$991$	−51.8338			−1.64655			−0.823277	+	0.567640i	$0.807857\pi$
$992$	−38.6721			−1.22784
$993$	2.79186	+	2.79186i	0.0885969	+	0.0885969i
$994$	−2.74674	+	3.40782i	−0.0871214	+	0.108089i
$995$	−4.77011	+	1.27815i	−0.151223	+	0.0405200i
$996$	3.72852	−	13.9150i	0.118143	−	0.440914i
$997$	−38.0778	+	21.9842i	−1.20593	+	0.696247i	−0.961869	−	0.273512i	$-0.911815\pi$
$997$	−38.0778	+	21.9842i	−1.20593	+	0.696247i	−0.244066	+	0.969759i	$0.578481\pi$
$998$			12.7513i			0.403635i
$999$	−1.30189	−	4.85874i	−0.0411901	−	0.153724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.a.262.7	yes	36
3.2	odd	2		819.2.gh.c.262.3		36
7.5	odd	6		273.2.bt.a.145.7	✓	36
13.7	odd	12		273.2.bt.a.241.7	yes	36
21.5	even	6		819.2.et.c.145.3		36
39.20	even	12		819.2.et.c.514.3		36
91.33	even	12	inner	273.2.cg.a.124.7	yes	36
273.215	odd	12		819.2.gh.c.397.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.7	✓	36	7.5	odd	6
273.2.bt.a.241.7	yes	36	13.7	odd	12
273.2.cg.a.124.7	yes	36	91.33	even	12	inner
273.2.cg.a.262.7	yes	36	1.1	even	1	trivial
819.2.et.c.145.3		36	21.5	even	6
819.2.et.c.514.3		36	39.20	even	12
819.2.gh.c.262.3		36	3.2	odd	2
819.2.gh.c.397.3		36	273.215	odd	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.255728 + 0.954388i) q^{2} -1.00000i q^{3} +(0.886590 - 0.511873i) q^{4} +(-0.244406 + 0.912136i) q^{5} +(0.954388 - 0.255728i) q^{6} +(2.46785 - 0.953787i) q^{7} +(2.11257 + 2.11257i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.255728 + 0.954388i) q^{2} -1.00000i q^{3} +(0.886590 - 0.511873i) q^{4} +(-0.244406 + 0.912136i) q^{5} +(0.954388 - 0.255728i) q^{6} +(2.46785 - 0.953787i) q^{7} +(2.11257 + 2.11257i) q^{8} -1.00000 q^{9} -0.933034 q^{10} +(-4.64956 - 4.64956i) q^{11} +(-0.511873 - 0.886590i) q^{12} +(3.43957 + 1.08136i) q^{13} +(1.54138 + 2.11138i) q^{14} +(0.912136 + 0.244406i) q^{15} +(-0.452226 + 0.783279i) q^{16} +(1.86677 + 3.23334i) q^{17} +(-0.255728 - 0.954388i) q^{18} +(0.889632 + 0.889632i) q^{19} +(0.250210 + 0.933796i) q^{20} +(-0.953787 - 2.46785i) q^{21} +(3.24847 - 5.62651i) q^{22} +(0.202140 + 0.116706i) q^{23} +(2.11257 - 2.11257i) q^{24} +(3.55787 + 2.05414i) q^{25} +(-0.152440 + 3.55922i) q^{26} +1.00000i q^{27} +(1.69975 - 2.10884i) q^{28} +(-2.32457 - 4.02628i) q^{29} +0.933034i q^{30} +(-7.35090 + 1.96967i) q^{31} +(4.90846 + 1.31522i) q^{32} +(-4.64956 + 4.64956i) q^{33} +(-2.60848 + 2.60848i) q^{34} +(0.266825 + 2.48413i) q^{35} +(-0.886590 + 0.511873i) q^{36} +(-4.85874 + 1.30189i) q^{37} +(-0.621551 + 1.07656i) q^{38} +(1.08136 - 3.43957i) q^{39} +(-2.44328 + 1.41063i) q^{40} +(-2.49056 + 9.29490i) q^{41} +(2.11138 - 1.54138i) q^{42} +(-10.4062 - 6.00801i) q^{43} +(-6.50224 - 1.74227i) q^{44} +(0.244406 - 0.912136i) q^{45} +(-0.0596897 + 0.222765i) q^{46} +(-2.10393 - 0.563747i) q^{47} +(0.783279 + 0.452226i) q^{48} +(5.18058 - 4.70761i) q^{49} +(-1.05060 + 3.92089i) q^{50} +(3.23334 - 1.86677i) q^{51} +(3.60301 - 0.801905i) q^{52} +(2.04084 - 3.53484i) q^{53} +(-0.954388 + 0.255728i) q^{54} +(5.37742 - 3.10465i) q^{55} +(7.22846 + 3.19857i) q^{56} +(0.889632 - 0.889632i) q^{57} +(3.24817 - 3.24817i) q^{58} +(-7.20872 - 1.93157i) q^{59} +(0.933796 - 0.250210i) q^{60} +2.45527i q^{61} +(-3.75966 - 6.51191i) q^{62} +(-2.46785 + 0.953787i) q^{63} +6.82982i q^{64} +(-1.82700 + 2.87307i) q^{65} +(-5.62651 - 3.24847i) q^{66} +(-7.19137 + 7.19137i) q^{67} +(3.31012 + 1.91110i) q^{68} +(0.116706 - 0.202140i) q^{69} +(-2.30259 + 0.889915i) q^{70} +(0.433350 + 1.61728i) q^{71} +(-2.11257 - 2.11257i) q^{72} +(-2.10388 - 7.85180i) q^{73} +(-2.48503 - 4.30419i) q^{74} +(2.05414 - 3.55787i) q^{75} +(1.24412 + 0.333360i) q^{76} +(-15.9091 - 7.03974i) q^{77} +(3.55922 + 0.152440i) q^{78} +(-0.942160 - 1.63187i) q^{79} +(-0.603930 - 0.603930i) q^{80} +1.00000 q^{81} -9.50785 q^{82} +(9.95023 + 9.95023i) q^{83} +(-2.10884 - 1.69975i) q^{84} +(-3.40550 + 0.912500i) q^{85} +(3.07283 - 11.4680i) q^{86} +(-4.02628 + 2.32457i) q^{87} -19.6451i q^{88} +(1.05604 + 3.94121i) q^{89} +0.933034 q^{90} +(9.51974 - 0.611992i) q^{91} +0.238954 q^{92} +(1.96967 + 7.35090i) q^{93} -2.15213i q^{94} +(-1.02890 + 0.594034i) q^{95} +(1.31522 - 4.90846i) q^{96} +(-2.41702 + 0.647638i) q^{97} +(5.81770 + 3.74042i) q^{98} +(4.64956 + 4.64956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 - 36 * q^9	\( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

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