LMFDB - Embedded newform 828.2.o.a.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [828,2,Mod(47,828)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(828, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("828.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.o (of order $6$, degree $2$, 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:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$66$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.1
Character	$\chi$	$=$	828.47
Dual form			828.2.o.a.599.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 - 0.00214998i) q^{2} +(-1.34750 - 1.08823i) q^{3} +(1.99999 + 0.00608105i) q^{4} +(-1.10823 + 0.639837i) q^{5} +(1.90331 + 1.54189i) q^{6} +(-3.10783 - 1.79431i) q^{7} +(-2.82840 - 0.0128998i) q^{8} +(0.631500 + 2.93278i) q^{9} +O(q^{10})$	\(q+(-1.41421 - 0.00214998i) q^{2} +(-1.34750 - 1.08823i) q^{3} +(1.99999 + 0.00608105i) q^{4} +(-1.10823 + 0.639837i) q^{5} +(1.90331 + 1.54189i) q^{6} +(-3.10783 - 1.79431i) q^{7} +(-2.82840 - 0.0128998i) q^{8} +(0.631500 + 2.93278i) q^{9} +(1.56865 - 0.902482i) q^{10} +(-1.85048 + 3.20513i) q^{11} +(-2.68837 - 2.18465i) q^{12} +(-0.184963 - 0.320366i) q^{13} +(4.39127 + 2.54421i) q^{14} +(2.18963 + 0.343833i) q^{15} +(3.99993 + 0.0243241i) q^{16} +0.394694i q^{17} +(-0.886769 - 4.14893i) q^{18} -2.60714i q^{19} +(-2.22034 + 1.27293i) q^{20} +(2.23517 + 5.79987i) q^{21} +(2.62386 - 4.52875i) q^{22} +(0.500000 + 0.866025i) q^{23} +(3.79722 + 3.09534i) q^{24} +(-1.68122 + 2.91195i) q^{25} +(0.260889 + 0.453463i) q^{26} +(2.34060 - 4.63914i) q^{27} +(-6.20472 - 3.60750i) q^{28} +(3.05111 + 1.76156i) q^{29} +(-3.09586 - 0.490961i) q^{30} +(4.37957 - 2.52854i) q^{31} +(-5.65669 - 0.0429992i) q^{32} +(5.98144 - 2.30515i) q^{33} +(0.000848584 - 0.558182i) q^{34} +4.59226 q^{35} +(1.24516 + 5.86938i) q^{36} +2.69292 q^{37} +(-0.00560529 + 3.68705i) q^{38} +(-0.0993949 + 0.632975i) q^{39} +(3.14277 - 1.79542i) q^{40} +(2.91603 - 1.68357i) q^{41} +(-3.14854 - 8.20705i) q^{42} +(-9.58558 - 5.53424i) q^{43} +(-3.72043 + 6.39897i) q^{44} +(-2.57635 - 2.84614i) q^{45} +(-0.705244 - 1.22582i) q^{46} +(-1.51595 + 2.62570i) q^{47} +(-5.36342 - 4.38563i) q^{48} +(2.93908 + 5.09063i) q^{49} +(2.38386 - 4.11451i) q^{50} +(0.429519 - 0.531850i) q^{51} +(-0.367977 - 0.641853i) q^{52} +1.03499i q^{53} +(-3.32008 + 6.55569i) q^{54} -4.73602i q^{55} +(8.76704 + 5.11510i) q^{56} +(-2.83717 + 3.51311i) q^{57} +(-4.31114 - 2.49778i) q^{58} +(0.00783141 + 0.0135644i) q^{59} +(4.37715 + 0.700979i) q^{60} +(2.89682 - 5.01744i) q^{61} +(-6.19907 + 3.56648i) q^{62} +(3.29972 - 10.2477i) q^{63} +(7.99967 + 0.0729717i) q^{64} +(0.409964 + 0.236693i) q^{65} +(-8.46398 + 3.24711i) q^{66} +(12.0129 - 6.93565i) q^{67} +(-0.00240016 + 0.789385i) q^{68} +(0.268688 - 1.71108i) q^{69} +(-6.49442 - 0.00987325i) q^{70} +11.6120 q^{71} +(-1.74830 - 8.30322i) q^{72} +9.24391 q^{73} +(-3.80837 - 0.00578973i) q^{74} +(5.43432 - 2.09430i) q^{75} +(0.0158541 - 5.21425i) q^{76} +(11.5020 - 6.64066i) q^{77} +(0.141926 - 0.894948i) q^{78} +(3.90588 + 2.25506i) q^{79} +(-4.44840 + 2.53234i) q^{80} +(-8.20242 + 3.70410i) q^{81} +(-4.12751 + 2.37466i) q^{82} +(0.120747 - 0.209141i) q^{83} +(4.43505 + 11.6133i) q^{84} +(-0.252540 - 0.437412i) q^{85} +(13.5441 + 7.84719i) q^{86} +(-2.19438 - 5.69402i) q^{87} +(5.27524 - 9.04150i) q^{88} -9.36518i q^{89} +(3.63738 + 4.03058i) q^{90} +1.32752i q^{91} +(0.994729 + 1.73508i) q^{92} +(-8.65310 - 1.35878i) q^{93} +(2.14951 - 3.71003i) q^{94} +(1.66814 + 2.88931i) q^{95} +(7.57558 + 6.21374i) q^{96} +(0.343263 - 0.594549i) q^{97} +(-4.14553 - 7.20555i) q^{98} +(-10.5685 - 3.40302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 132 * q - 9 * q^8 + 2 * q^9	$ 132 q - 9 q^{8} + 2 q^{9} - 29 q^{12} - 15 q^{14} - 34 q^{18} - 21 q^{20} + 66 q^{23} + 15 q^{24} + 66 q^{25} - 54 q^{26} + 12 q^{27} + 77 q^{30} + 30 q^{32} - 22 q^{33} + 36 q^{36} - 24 q^{39} - 30 q^{41} - 11 q^{42} - 65 q^{48} + 66 q^{49} - 32 q^{51} - 64 q^{54} - 42 q^{56} - 6 q^{57} + 27 q^{58} + 36 q^{59} + 58 q^{60} + 63 q^{62} - 20 q^{63} - 9 q^{64} + 78 q^{66} - 15 q^{68} - 78 q^{70} + 36 q^{72} - 12 q^{73} - 21 q^{74} + 48 q^{75} - 87 q^{76} - 11 q^{78} + 72 q^{80} - 10 q^{81} - 9 q^{82} - 157 q^{84} - 24 q^{86} + 96 q^{87} + 108 q^{88} - 63 q^{90} - 12 q^{93} + 75 q^{94} - 9 q^{96} - 6 q^{97} + 20 q^{99}+O(q^{100}) $ 132 * q - 9 * q^8 + 2 * q^9 - 29 * q^12 - 15 * q^14 - 34 * q^18 - 21 * q^20 + 66 * q^23 + 15 * q^24 + 66 * q^25 - 54 * q^26 + 12 * q^27 + 77 * q^30 + 30 * q^32 - 22 * q^33 + 36 * q^36 - 24 * q^39 - 30 * q^41 - 11 * q^42 - 65 * q^48 + 66 * q^49 - 32 * q^51 - 64 * q^54 - 42 * q^56 - 6 * q^57 + 27 * q^58 + 36 * q^59 + 58 * q^60 + 63 * q^62 - 20 * q^63 - 9 * q^64 + 78 * q^66 - 15 * q^68 - 78 * q^70 + 36 * q^72 - 12 * q^73 - 21 * q^74 + 48 * q^75 - 87 * q^76 - 11 * q^78 + 72 * q^80 - 10 * q^81 - 9 * q^82 - 157 * q^84 - 24 * q^86 + 96 * q^87 + 108 * q^88 - 63 * q^90 - 12 * q^93 + 75 * q^94 - 9 * q^96 - 6 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.41421	−	0.00214998i	−0.999999	−	0.00152026i
$2$	−1.41421	−	0.00214998i	−0.999999	−	0.00152026i
$3$	−1.34750	−	1.08823i	−0.777978	−	0.628291i
$3$	−1.34750	−	1.08823i	−0.777978	−	0.628291i
$4$	1.99999	+	0.00608105i	0.999995	+	0.00304052i
$5$	−1.10823	+	0.639837i	−0.495616	+	0.286144i	−0.726901	−	0.686742i	$-0.759040\pi$
$5$	−1.10823	+	0.639837i	−0.495616	+	0.286144i	0.231286	+	0.972886i	$0.425707\pi$
$6$	1.90331	+	1.54189i	0.777022	+	0.629473i
$7$	−3.10783	−	1.79431i	−1.17465	−	0.678184i	−0.219879	−	0.975527i	$-0.570566\pi$
$7$	−3.10783	−	1.79431i	−1.17465	−	0.678184i	−0.954771	+	0.297343i	$0.903900\pi$
$8$	−2.82840	−	0.0128998i	−0.999990	−	0.00456078i
$9$	0.631500	+	2.93278i	0.210500	+	0.977594i
$10$	1.56865	−	0.902482i	0.496050	−	0.285390i
$11$	−1.85048	+	3.20513i	−0.557941	+	0.966382i	0.439728	+	0.898131i	$0.355075\pi$
$11$	−1.85048	+	3.20513i	−0.557941	+	0.966382i	−0.997668	+	0.0682504i	$0.978258\pi$
$12$	−2.68837	−	2.18465i	−0.776064	−	0.630654i
$13$	−0.184963	−	0.320366i	−0.0512996	−	0.0888535i	0.839235	−	0.543768i	$-0.183003\pi$
$13$	−0.184963	−	0.320366i	−0.0512996	−	0.0888535i	−0.890535	+	0.454915i	$0.849670\pi$
$14$	4.39127	+	2.54421i	1.17362	+	0.679969i
$15$	2.18963	+	0.343833i	0.565360	+	0.0887774i
$16$	3.99993	+	0.0243241i	0.999982	+	0.00608102i
$17$			0.394694i			0.0957275i	0.998854	+	0.0478637i	$0.0152413\pi$
$17$			0.394694i			0.0957275i	−0.998854	+	0.0478637i	$0.984759\pi$
$18$	−0.886769	−	4.14893i	−0.209014	−	0.977913i
$19$		−	2.60714i		−	0.598118i	−0.954235	−	0.299059i	$-0.903327\pi$
$19$		−	2.60714i		−	0.598118i	0.954235	−	0.299059i	$-0.0966728\pi$
$20$	−2.22034	+	1.27293i	−0.496483	+	0.284636i
$21$	2.23517	+	5.79987i	0.487754	+	1.26563i
$22$	2.62386	−	4.52875i	0.559409	−	0.965532i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	3.79722	+	3.09534i	0.775105	+	0.631833i
$25$	−1.68122	+	2.91195i	−0.336243	+	0.582391i
$26$	0.260889	+	0.453463i	0.0511644	+	0.0889314i
$27$	2.34060	−	4.63914i	0.450449	−	0.892802i
$28$	−6.20472	−	3.60750i	−1.17258	−	0.681753i
$29$	3.05111	+	1.76156i	0.566578	+	0.327114i	0.755781	−	0.654824i	$-0.227257\pi$
$29$	3.05111	+	1.76156i	0.566578	+	0.327114i	−0.189204	+	0.981938i	$0.560591\pi$
$30$	−3.09586	−	0.490961i	−0.565224	−	0.0896368i
$31$	4.37957	−	2.52854i	0.786593	−	0.454140i	−0.0521685	−	0.998638i	$-0.516613\pi$
$31$	4.37957	−	2.52854i	0.786593	−	0.454140i	0.838762	+	0.544498i	$0.183280\pi$
$32$	−5.65669	−	0.0429992i	−0.999971	−	0.00760125i
$33$	5.98144	−	2.30515i	1.04123	−	0.401274i
$34$	0.000848584	−	0.558182i	0.000145531	−	0.0957273i
$35$	4.59226			0.776233
$36$	1.24516	+	5.86938i	0.207527	+	0.978229i
$37$	2.69292			0.442714			0.221357	−	0.975193i	$-0.428951\pi$
$37$	2.69292			0.442714			0.221357	+	0.975193i	$0.428951\pi$
$38$	−0.00560529	+	3.68705i	−0.000909298	+	0.598118i
$39$	−0.0993949	+	0.632975i	−0.0159159	+	0.101357i
$40$	3.14277	−	1.79542i	0.496915	−	0.283880i
$41$	2.91603	−	1.68357i	0.455408	−	0.262930i	−0.254703	−	0.967019i	$-0.581978\pi$
$41$	2.91603	−	1.68357i	0.455408	−	0.262930i	0.710111	+	0.704089i	$0.248645\pi$
$42$	−3.14854	−	8.20705i	−0.485830	−	1.26637i
$43$	−9.58558	−	5.53424i	−1.46179	−	0.843963i	−0.462693	−	0.886519i	$-0.653117\pi$
$43$	−9.58558	−	5.53424i	−1.46179	−	0.843963i	−0.999094	+	0.0425558i	$0.986450\pi$
$44$	−3.72043	+	6.39897i	−0.560876	+	0.964681i
$45$	−2.57635	−	2.84614i	−0.384059	−	0.424278i
$46$	−0.705244	−	1.22582i	−0.103983	−	0.180737i
$47$	−1.51595	+	2.62570i	−0.221123	+	0.382997i	−0.955149	−	0.296124i	$-0.904306\pi$
$47$	−1.51595	+	2.62570i	−0.221123	+	0.382997i	0.734026	+	0.679121i	$0.237639\pi$
$48$	−5.36342	−	4.38563i	−0.774143	−	0.633011i
$49$	2.93908	+	5.09063i	0.419868	+	0.727233i
$50$	2.38386	−	4.11451i	0.337128	−	0.581879i
$51$	0.429519	−	0.531850i	0.0601447	−	0.0744739i
$52$	−0.367977	−	0.641853i	−0.0510292	−	0.0890091i
$53$			1.03499i			0.142167i	0.997470	+	0.0710837i	$0.0226457\pi$
$53$			1.03499i			0.142167i	−0.997470	+	0.0710837i	$0.977354\pi$
$54$	−3.32008	+	6.55569i	−0.451806	+	0.892116i
$55$		−	4.73602i		−	0.638605i
$56$	8.76704	+	5.11510i	1.17154	+	0.683535i
$57$	−2.83717	+	3.51311i	−0.375793	+	0.465323i
$58$	−4.31114	−	2.49778i	−0.566080	−	0.327975i
$59$	0.00783141	+	0.0135644i	0.00101956	+	0.00176593i	0.866535	−	0.499117i	$-0.166342\pi$
$59$	0.00783141	+	0.0135644i	0.00101956	+	0.00176593i	−0.865515	+	0.500883i	$0.833009\pi$
$60$	4.37715	+	0.700979i	0.565087	+	0.0904960i
$61$	2.89682	−	5.01744i	0.370900	−	0.642417i	−0.618804	−	0.785545i	$-0.712383\pi$
$61$	2.89682	−	5.01744i	0.370900	−	0.642417i	0.989704	+	0.143128i	$0.0457160\pi$
$62$	−6.19907	+	3.56648i	−0.787283	+	0.452944i
$63$	3.29972	−	10.2477i	0.415725	−	1.29109i
$64$	7.99967	+	0.0729717i	0.999958	+	0.00912146i
$65$	0.409964	+	0.236693i	0.0508498	+	0.0293581i
$66$	−8.46398	+	3.24711i	−1.04184	+	0.399691i
$67$	12.0129	−	6.93565i	1.46761	−	0.847324i	0.468266	−	0.883587i	$-0.344879\pi$
$67$	12.0129	−	6.93565i	1.46761	−	0.847324i	0.999342	+	0.0362632i	$0.0115455\pi$
$68$	−0.00240016	+	0.789385i	−0.000291062	+	0.0957270i
$69$	0.268688	−	1.71108i	0.0323463	−	0.205990i
$70$	−6.49442	−	0.00987325i	−0.776232	−	0.00118008i
$71$	11.6120			1.37809			0.689043	−	0.724721i	$-0.258031\pi$
$71$	11.6120			1.37809			0.689043	+	0.724721i	$0.258031\pi$
$72$	−1.74830	−	8.30322i	−0.206039	−	0.978544i
$73$	9.24391			1.08192			0.540959	−	0.841049i	$-0.318061\pi$
$73$	9.24391			1.08192			0.540959	+	0.841049i	$0.318061\pi$
$74$	−3.80837	−	0.00578973i	−0.442714	−	0.000673042i
$75$	5.43432	−	2.09430i	0.627501	−	0.241828i
$76$	0.0158541	−	5.21425i	0.00181859	−	0.598116i
$77$	11.5020	−	6.64066i	1.31077	−	0.756773i
$78$	0.141926	−	0.894948i	0.0160700	−	0.101333i
$79$	3.90588	+	2.25506i	0.439446	+	0.253714i	0.703362	−	0.710831i	$-0.251681\pi$
$79$	3.90588	+	2.25506i	0.439446	+	0.253714i	−0.263917	+	0.964545i	$0.585014\pi$
$80$	−4.44840	+	2.53234i	−0.497346	+	0.283125i
$81$	−8.20242	+	3.70410i	−0.911380	+	0.411567i
$82$	−4.12751	+	2.37466i	−0.455807	+	0.262237i
$83$	0.120747	−	0.209141i	0.0132538	−	0.0229562i	−0.859322	−	0.511434i	$-0.829114\pi$
$83$	0.120747	−	0.209141i	0.0132538	−	0.0229562i	0.872576	+	0.488478i	$0.162448\pi$
$84$	4.43505	+	11.6133i	0.483904	+	1.26711i
$85$	−0.252540	−	0.437412i	−0.0273918	−	0.0474440i
$86$	13.5441	+	7.84719i	1.46050	+	0.846184i
$87$	−2.19438	−	5.69402i	−0.235262	−	0.610463i
$88$	5.27524	−	9.04150i	0.562342	−	0.963827i
$89$		−	9.36518i		−	0.992707i	−0.868120	−	0.496354i	$-0.834672\pi$
$89$		−	9.36518i		−	0.992707i	0.868120	−	0.496354i	$-0.165328\pi$
$90$	3.63738	+	4.03058i	0.383414	+	0.424861i
$91$			1.32752i			0.139162i
$92$	0.994729	+	1.73508i	0.103708	+	0.180895i
$93$	−8.65310	−	1.35878i	−0.897285	−	0.140899i
$94$	2.14951	−	3.71003i	0.221705	−	0.382660i
$95$	1.66814	+	2.88931i	0.171148	+	0.296437i
$96$	7.57558	+	6.21374i	0.773180	+	0.634187i
$97$	0.343263	−	0.594549i	0.0348531	−	0.0603673i	−0.848073	−	0.529880i	$-0.822237\pi$
$97$	0.343263	−	0.594549i	0.0348531	−	0.0603673i	0.882926	+	0.469513i	$0.155570\pi$
$98$	−4.14553	−	7.20555i	−0.418762	−	0.727870i
$99$	−10.5685	−	3.40302i	−1.06218	−	0.342016i
$100$	−3.38013	+	5.81366i	−0.338013	+	0.581366i
$101$	3.64795	+	2.10615i	0.362985	+	0.209569i	0.670389	−	0.742010i	$-0.266127\pi$
$101$	3.64795	+	2.10615i	0.362985	+	0.209569i	−0.307405	+	0.951579i	$0.599460\pi$
$102$	−0.608575	+	0.751225i	−0.0602579	+	0.0743823i
$103$	16.1248	−	9.30963i	1.58882	−	0.917305i	0.595317	−	0.803491i	$-0.297026\pi$
$103$	16.1248	−	9.30963i	1.58882	−	0.917305i	0.993502	−	0.113815i	$-0.0363070\pi$
$104$	0.519017	+	0.908508i	0.0508938	+	0.0890865i
$105$	−6.18805	−	4.99744i	−0.603892	−	0.487700i
$106$	0.00222522	−	1.46370i	0.000216132	−	0.142167i
$107$	−8.96054			−0.866248			−0.433124	−	0.901334i	$-0.642589\pi$
$107$	−8.96054			−0.866248			−0.433124	+	0.901334i	$0.642589\pi$
$108$	4.70940	−	9.26399i	0.453162	−	0.891428i
$109$	9.26295			0.887229			0.443615	−	0.896218i	$-0.353696\pi$
$109$	9.26295			0.887229			0.443615	+	0.896218i	$0.353696\pi$
$110$	−0.0101823	+	6.69774i	−0.000970848	+	0.638604i
$111$	−3.62871	−	2.93053i	−0.344422	−	0.278153i
$112$	−12.3874	−	7.25269i	−1.17050	−	0.685315i
$113$	5.11925	−	2.95560i	0.481578	−	0.278039i	−0.239496	−	0.970897i	$-0.576982\pi$
$113$	5.11925	−	2.95560i	0.481578	−	0.278039i	0.721074	+	0.692858i	$0.243649\pi$
$114$	4.01992	−	4.96218i	0.376500	−	0.464751i
$115$	−1.10823	−	0.639837i	−0.103343	−	0.0596651i
$116$	6.09149	+	3.54166i	0.565581	+	0.328835i
$117$	0.822759	−	0.744768i	0.0760641	−	0.0688538i
$118$	−0.0110461	−	0.0191998i	−0.00101688	−	0.00176748i
$119$	0.708203	−	1.22664i	0.0649209	−	0.112446i
$120$	−6.18871	−	1.00074i	−0.564949	−	0.0913549i
$121$	−1.34855	−	2.33576i	−0.122596	−	0.212342i
$122$	−4.10751	+	7.08950i	−0.371876	+	0.641853i
$123$	−5.76147	−	0.904712i	−0.519494	−	0.0815752i
$124$	8.77447	−	5.03043i	0.787971	−	0.451746i
$125$		−	10.7012i		−	0.957144i
$126$	−4.68853	+	14.4853i	−0.417687	+	1.29045i
$127$			18.2365i			1.61823i	0.587653	+	0.809113i	$0.300052\pi$
$127$			18.2365i			1.61823i	−0.587653	+	0.809113i	$0.699948\pi$
$128$	−11.3131	−	0.120397i	−0.999943	−	0.0106417i
$129$	6.89401	+	17.8887i	0.606983	+	1.57501i
$130$	−0.579267	−	0.335615i	−0.0508051	−	0.0294354i
$131$	2.03659	+	3.52747i	0.177937	+	0.308197i	0.941174	−	0.337923i	$-0.109724\pi$
$131$	2.03659	+	3.52747i	0.177937	+	0.308197i	−0.763237	+	0.646119i	$0.776391\pi$
$132$	11.9768	−	4.57390i	1.04245	−	0.398107i
$133$	−4.67801	+	8.10254i	−0.405635	+	0.702580i
$134$	−17.0037	+	9.78265i	−1.46890	+	0.845092i
$135$	0.374362	+	6.63883i	0.0322200	+	0.571380i
$136$	0.00509149	−	1.11635i	0.000436592	−	0.0957265i
$137$	0.103434	+	0.0597179i	0.00883700	+	0.00510205i	0.504412	−	0.863463i	$-0.331709\pi$
$137$	0.103434	+	0.0597179i	0.00883700	+	0.00510205i	−0.495575	+	0.868565i	$0.665043\pi$
$138$	−0.383661	+	2.41926i	−0.0326594	+	0.205941i
$139$	−19.3255	+	11.1576i	−1.63916	+	0.946372i	−0.658043	+	0.752980i	$0.728616\pi$
$139$	−19.3255	+	11.1576i	−1.63916	+	0.946372i	−0.981122	+	0.193392i	$0.938051\pi$
$140$	9.18447	+	0.0279257i	0.776229	+	0.00236016i
$141$	4.90010	−	1.88842i	0.412663	−	0.159033i
$142$	−16.4218	−	0.0249654i	−1.37808	−	0.00209505i
$143$	1.36908			0.114489
$144$	2.45462	+	11.7463i	0.204551	+	0.978856i
$145$	−4.50845			−0.374406
$146$	−13.0729	−	0.0198742i	−1.08192	−	0.00164480i
$147$	1.57939	−	10.0580i	0.130266	−	0.829570i
$148$	5.38582	+	0.0163758i	0.442712	+	0.00134608i
$149$	1.71422	−	0.989705i	0.140434	−	0.0810798i	−0.428137	−	0.903714i	$-0.640830\pi$
$149$	1.71422	−	0.989705i	0.140434	−	0.0810798i	0.568571	+	0.822634i	$0.307496\pi$
$150$	−7.68978	+	2.95009i	−0.627868	+	0.240874i
$151$	9.09066	+	5.24850i	0.739787	+	0.427116i	0.821992	−	0.569499i	$-0.192863\pi$
$151$	9.09066	+	5.24850i	0.739787	+	0.427116i	−0.0822046	+	0.996615i	$0.526196\pi$
$152$	−0.0336316	+	7.37402i	−0.00272789	+	0.598112i
$153$	−1.15755	+	0.249249i	−0.0935826	+	0.0201506i
$154$	−16.2805	+	9.36657i	−1.31192	+	0.754780i
$155$	−3.23571	+	5.60442i	−0.259899	+	0.450158i
$156$	−0.202638	+	1.26534i	−0.0162240	+	0.101308i
$157$	5.41594	+	9.38069i	0.432239	+	0.748661i	0.997066	−	0.0765492i	$-0.0243902\pi$
$157$	5.41594	+	9.38069i	0.432239	+	0.748661i	−0.564826	+	0.825210i	$0.691057\pi$
$158$	−5.51889	−	3.19753i	−0.439059	−	0.254382i
$159$	1.12631	−	1.39465i	0.0893226	−	0.110603i
$160$	6.29643	−	3.57171i	0.497776	−	0.282368i
$161$		−	3.58861i		−	0.282822i
$162$	11.6079	−	5.22075i	0.912004	−	0.410181i
$163$			4.90778i			0.384407i	0.981355	+	0.192204i	$0.0615634\pi$
$163$			4.90778i			0.384407i	−0.981355	+	0.192204i	$0.938437\pi$
$164$	5.84228	−	3.34940i	0.456205	−	0.261544i
$165$	−5.15389	+	6.38178i	−0.401230	+	0.496821i
$166$	−0.171212	+	0.295510i	−0.0132886	+	0.0229360i
$167$	0.730123	+	1.26461i	0.0564987	+	0.0978585i	0.892891	−	0.450272i	$-0.148673\pi$
$167$	0.730123	+	1.26461i	0.0564987	+	0.0978585i	−0.836393	+	0.548131i	$0.815340\pi$
$168$	−6.24714	−	16.4332i	−0.481977	−	1.26785i
$169$	6.43158	−	11.1398i	0.494737	−	0.856909i
$170$	0.356205	+	0.619137i	0.0273197	+	0.0474856i
$171$	7.64617	−	1.64641i	0.584717	−	0.125904i
$172$	−19.1374	−	11.1267i	−1.45921	−	0.848404i
$173$	−16.5307	−	9.54400i	−1.25681	−	0.725617i	−0.284353	−	0.958720i	$-0.591779\pi$
$173$	−16.5307	−	9.54400i	−1.25681	−	0.725617i	−0.972452	+	0.233103i	$0.925112\pi$
$174$	3.09108	+	8.05727i	0.234334	+	0.610820i
$175$	10.4499	−	6.03324i	0.789937	−	0.456070i
$176$	−7.47974	+	12.7753i	−0.563807	+	0.962971i
$177$	0.00420842	−	0.0268004i	0.000316324	−	0.00201444i
$178$	−0.0201349	+	13.2444i	−0.00150918	+	0.992706i
$179$	1.73367			0.129581			0.0647904	−	0.997899i	$-0.479362\pi$
$179$	1.73367			0.129581			0.0647904	+	0.997899i	$0.479362\pi$
$180$	−5.13537	−	5.70792i	−0.382768	−	0.425443i
$181$	−19.7560			−1.46845			−0.734227	−	0.678904i	$-0.762455\pi$
$181$	−19.7560			−1.46845			−0.734227	+	0.678904i	$0.762455\pi$
$182$	0.00285415	−	1.87740i	0.000211563	−	0.139162i
$183$	−9.36360	+	3.60858i	−0.692177	+	0.266754i
$184$	−1.40303	−	2.45591i	−0.103433	−	0.181052i
$185$	−2.98438	+	1.72303i	−0.219416	+	0.126680i
$186$	12.2344	+	1.94021i	0.897069	+	0.142263i
$187$	−1.26505	−	0.730374i	−0.0925093	−	0.0534102i
$188$	−3.04784	+	5.24215i	−0.222287	+	0.382323i
$189$	−15.5982	+	10.2179i	−1.13460	+	0.743242i
$190$	−2.35290	−	4.08968i	−0.170697	−	0.296697i
$191$	−11.6305	+	20.1446i	−0.841552	+	1.45761i	0.0470300	+	0.998893i	$0.485024\pi$
$191$	−11.6305	+	20.1446i	−0.841552	+	1.45761i	−0.888582	+	0.458718i	$0.848309\pi$
$192$	−10.7001	−	8.80383i	−0.772215	−	0.635362i
$193$	5.96204	+	10.3265i	0.429157	+	0.743321i	0.996799	−	0.0799544i	$-0.0254775\pi$
$193$	5.96204	+	10.3265i	0.429157	+	0.743321i	−0.567642	+	0.823276i	$0.692144\pi$
$194$	−0.486725	+	0.840080i	−0.0349448	+	0.0603142i
$195$	−0.294849	−	0.765079i	−0.0211145	−	0.0547884i
$196$	5.84717	+	10.1991i	0.417655	+	0.728506i
$197$			14.7571i			1.05140i	0.850669	+	0.525701i	$0.176197\pi$
$197$			14.7571i			1.05140i	−0.850669	+	0.525701i	$0.823803\pi$
$198$	14.9388	+	4.83531i	1.06165	+	0.343631i
$199$			14.7396i			1.04486i	0.852682	+	0.522431i	$0.174975\pi$
$199$			14.7396i			1.04486i	−0.852682	+	0.522431i	$0.825025\pi$
$200$	4.79271	−	8.21448i	0.338896	−	0.580851i
$201$	−23.7349	−	3.72705i	−1.67413	−	0.262886i
$202$	−5.15445	−	2.98638i	−0.362666	−	0.210121i
$203$	−6.32157	−	10.9493i	−0.443687	−	0.768488i
$204$	0.862269	−	1.06108i	0.0603709	−	0.0742906i
$205$	−2.15442	+	3.73157i	−0.150472	+	0.260624i
$206$	−22.8238	+	13.1311i	−1.59021	+	0.914889i
$207$	−2.22411	+	2.01329i	−0.154587	+	0.139933i
$208$	−0.732047	−	1.28594i	−0.0507583	−	0.0891638i
$209$	8.35620	+	4.82446i	0.578011	+	0.333715i
$210$	8.74048	+	7.08075i	0.603150	+	0.488618i
$211$	−11.7792	+	6.80073i	−0.810915	+	0.468182i	−0.847273	−	0.531157i	$-0.821757\pi$
$211$	−11.7792	+	6.80073i	−0.810915	+	0.468182i	0.0363588	+	0.999339i	$0.488424\pi$
$212$	−0.00629385	+	2.06998i	−0.000432264	+	0.142167i
$213$	−15.6471	−	12.6365i	−1.07212	−	0.865839i
$214$	12.6721	+	0.0192650i	0.866247	+	0.00131693i
$215$	14.1640			0.965979
$216$	−6.68000	+	13.0911i	−0.454517	+	0.890738i
$217$	−18.1479			−1.23196
$218$	−13.0998	−	0.0199151i	−0.887228	−	0.00134882i
$219$	−12.4562	−	10.0595i	−0.841709	−	0.679760i
$220$	0.0288000	−	9.47200i	0.00194169	−	0.638602i
$221$	0.126447	−	0.0730040i	0.00850572	−	0.00491078i
$222$	5.12546	+	4.15219i	0.343999	+	0.278677i
$223$	22.3283	+	12.8912i	1.49521	+	0.863262i	0.999985	−	0.00550083i	$-0.00175098\pi$
$223$	22.3283	+	12.8912i	1.49521	+	0.863262i	0.495229	+	0.868763i	$0.335084\pi$
$224$	17.5029	+	10.2835i	1.16946	+	0.687094i
$225$	−9.60181	−	3.09174i	−0.640121	−	0.206116i
$226$	−7.24606	+	4.16884i	−0.482001	+	0.277307i
$227$	13.3801	−	23.1750i	0.888068	−	1.53818i	0.0459111	−	0.998946i	$-0.485381\pi$
$227$	13.3801	−	23.1750i	0.888068	−	1.53818i	0.842157	−	0.539233i	$-0.181286\pi$
$228$	−5.69568	+	7.00894i	−0.377206	+	0.464178i
$229$	1.35043	+	2.33902i	0.0892392	+	0.154567i	0.907190	−	0.420722i	$-0.138223\pi$
$229$	1.35043	+	2.33902i	0.0892392	+	0.154567i	−0.817951	+	0.575289i	$0.804890\pi$
$230$	1.56590	+	0.907248i	0.103252	+	0.0598221i
$231$	−22.7254	−	3.56853i	−1.49522	−	0.234792i
$232$	−8.60704	−	5.02176i	−0.565080	−	0.329694i
$233$		−	17.8696i		−	1.17068i	−0.810789	−	0.585338i	$-0.800962\pi$
$233$		−	17.8696i		−	1.17068i	0.810789	−	0.585338i	$-0.199038\pi$
$234$	−1.16516	+	1.05149i	−0.0761687	+	0.0687381i
$235$		−	3.87983i		−	0.253092i
$236$	0.0155803	+	0.0271763i	0.00101419	+	0.00176903i
$237$	−2.80913	−	7.28919i	−0.182473	−	0.473484i
$238$	−1.00419	+	1.73321i	−0.0650917	+	0.112347i
$239$	−8.47098	−	14.6722i	−0.547942	−	0.949064i	−0.998415	−	0.0562741i	$-0.982078\pi$
$239$	−8.47098	−	14.6722i	−0.547942	−	0.949064i	0.450473	−	0.892790i	$-0.351255\pi$
$240$	8.74999	+	1.42857i	0.564809	+	0.0922137i
$241$	−0.188474	+	0.326446i	−0.0121407	+	0.0210282i	−0.872032	−	0.489449i	$-0.837198\pi$
$241$	−0.188474	+	0.326446i	−0.0121407	+	0.0210282i	0.859891	+	0.510477i	$0.170531\pi$
$242$	1.90212	+	3.30616i	0.122273	+	0.212528i
$243$	15.0837	+	3.93487i	0.967617	+	0.252422i
$244$	5.82413	−	10.0172i	0.372851	−	0.641287i
$245$	−6.51434	−	3.76106i	−0.416186	−	0.240285i
$246$	8.14599	+	1.29184i	0.519369	+	0.0823648i
$247$	−0.835238	+	0.482225i	−0.0531449	+	0.0306832i
$248$	−12.4198	+	7.09523i	−0.788656	+	0.450548i
$249$	−0.390301	+	0.150415i	−0.0247343	+	0.00953219i
$250$	−0.0230073	+	15.1338i	−0.00145511	+	0.957142i
$251$	29.0356			1.83271			0.916356	−	0.400364i	$-0.131116\pi$
$251$	29.0356			1.83271			0.916356	+	0.400364i	$0.131116\pi$
$252$	6.66172	−	20.4752i	0.419649	−	1.28982i
$253$	−3.70096			−0.232677
$254$	0.0392080	−	25.7902i	0.00246013	−	1.61822i
$255$	−0.135709	+	0.864234i	−0.00849843	+	0.0541204i
$256$	15.9988	+	0.194589i	0.999926	+	0.0121618i
$257$	26.0304	−	15.0287i	1.62373	−	0.937463i	0.637825	−	0.770181i	$-0.279834\pi$
$257$	26.0304	−	15.0287i	1.62373	−	0.937463i	0.985909	−	0.167282i	$-0.0534991\pi$
$258$	−9.71113	−	25.3132i	−0.604588	−	1.57593i
$259$	−8.36915	−	4.83193i	−0.520034	−	0.300242i
$260$	0.818485	+	0.475876i	0.0507603	+	0.0295126i
$261$	−3.23950	+	10.0607i	−0.200520	+	0.622740i
$262$	−2.87258	−	4.99297i	−0.177469	−	0.308467i
$263$	−4.46720	+	7.73741i	−0.275459	+	0.477109i	−0.970251	−	0.242102i	$-0.922163\pi$
$263$	−4.46720	+	7.73741i	−0.275459	+	0.477109i	0.694792	+	0.719211i	$0.255497\pi$
$264$	−16.9476	+	6.44271i	−1.04305	+	0.396521i
$265$	−0.662228	−	1.14701i	−0.0406803	−	0.0704604i
$266$	6.63311	−	11.4487i	0.406702	−	0.701962i
$267$	−10.1915	+	12.6196i	−0.623709	+	0.772304i
$268$	24.0679	−	13.7982i	1.47018	−	0.842858i
$269$			24.7292i			1.50777i	0.657008	+	0.753884i	$0.271822\pi$
$269$			24.7292i			1.50777i	−0.657008	+	0.753884i	$0.728178\pi$
$270$	−0.515154	−	9.38952i	−0.0313513	−	0.571428i
$271$		−	6.40805i		−	0.389261i	−0.980877	−	0.194631i	$-0.937649\pi$
$271$		−	6.40805i		−	0.389261i	0.980877	−	0.194631i	$-0.0623508\pi$
$272$	−0.00960058	+	1.57875i	−0.000582121	+	0.0957257i
$273$	1.44465	−	1.78884i	0.0874345	−	0.108265i
$274$	−0.146150	−	0.0846762i	−0.00882924	−	0.00511547i
$275$	−6.22212	−	10.7770i	−0.375208	−	0.649879i
$276$	0.547779	−	3.42052i	0.0329724	−	0.205891i
$277$	10.1168	−	17.5228i	0.607858	−	1.05284i	−0.383735	−	0.923443i	$-0.625362\pi$
$277$	10.1168	−	17.5228i	0.607858	−	1.05284i	0.991593	−	0.129397i	$-0.0413042\pi$
$278$	27.3543	−	15.7376i	1.64060	−	0.943879i
$279$	10.1814	+	11.2475i	0.609542	+	0.673372i
$280$	−12.9887	−	0.0592393i	−0.776225	−	0.00354023i
$281$	−26.2845	−	15.1754i	−1.56800	−	0.905286i	−0.996402	−	0.0847538i	$-0.972990\pi$
$281$	−26.2845	−	15.1754i	−1.56800	−	0.905286i	−0.571600	−	0.820532i	$-0.693677\pi$
$282$	−6.93384	+	2.66009i	−0.412904	+	0.158406i
$283$	−10.6115	+	6.12653i	−0.630786	+	0.364184i	−0.781056	−	0.624460i	$-0.785319\pi$
$283$	−10.6115	+	6.12653i	−0.630786	+	0.364184i	0.150270	+	0.988645i	$0.451986\pi$
$284$	23.2238	+	0.0706129i	1.37808	+	0.00419010i
$285$	0.896421	−	5.70866i	0.0530994	−	0.338152i
$286$	−1.93617	−	0.00294350i	−0.114488	−	0.000174053i
$287$	−12.0834			−0.713260
$288$	−3.44609	−	16.6170i	−0.203063	−	0.979166i
$289$	16.8442			0.990836
$290$	6.37590	+	0.00969307i	0.374406	+	0.000569197i
$291$	−1.10955	+	0.427603i	−0.0650432	+	0.0250665i
$292$	18.4877	+	0.0562127i	1.08191	+	0.00328960i
$293$	7.71107	−	4.45199i	0.450486	−	0.260088i	−0.257550	−	0.966265i	$-0.582915\pi$
$293$	7.71107	−	4.45199i	0.450486	−	0.260088i	0.708035	+	0.706177i	$0.249582\pi$
$294$	−2.25522	+	14.2208i	−0.131527	+	0.829371i
$295$	−0.0173580	−	0.0100217i	−0.00101062	−	0.000583483i
$296$	−7.61666	−	0.0347383i	−0.442709	−	0.00201912i
$297$	10.5378	+	16.0866i	0.611463	+	0.933437i
$298$	−2.42640	+	1.39597i	−0.140557	+	0.0808662i
$299$	0.184963	−	0.320366i	0.0106967	−	0.0185272i
$300$	10.8813	−	4.15553i	0.628234	−	0.239919i
$301$	19.8602	+	34.3989i	1.14472	+	1.98272i
$302$	−12.8448	−	7.44203i	−0.739137	−	0.428241i
$303$	−2.62363	−	6.80785i	−0.150724	−	0.391101i
$304$	0.0634162	−	10.4284i	0.00363717	−	0.598107i
$305$			7.41397i			0.424523i
$306$	1.63756	−	0.350003i	0.0936131	−	0.0200083i
$307$			26.1544i			1.49271i	0.665549	+	0.746354i	$0.268197\pi$
$307$			26.1544i			1.49271i	−0.665549	+	0.746354i	$0.731803\pi$
$308$	23.0442	−	13.2113i	1.31306	−	0.752784i
$309$	−31.8591	−	5.00278i	−1.81240	−	0.284598i
$310$	4.58803	−	7.91888i	0.260583	−	0.449762i
$311$	10.4210	+	18.0497i	0.590922	+	1.02351i	0.994109	+	0.108389i	$0.0345691\pi$
$311$	10.4210	+	18.0497i	0.590922	+	1.02351i	−0.403187	+	0.915118i	$0.632098\pi$
$312$	0.289294	−	1.78902i	0.0163780	−	0.101284i
$313$	11.3065	−	19.5834i	0.639081	−	1.10692i	−0.346554	−	0.938030i	$-0.612648\pi$
$313$	11.3065	−	19.5834i	0.639081	−	1.10692i	0.985635	−	0.168891i	$-0.0540186\pi$
$314$	−7.63912	−	13.2779i	−0.431101	−	0.749317i
$315$	2.90001	+	13.4681i	0.163397	+	0.758841i
$316$	7.79801	+	4.53385i	0.438672	+	0.255049i
$317$	−15.0237	−	8.67395i	−0.843817	−	0.487178i	0.0147430	−	0.999891i	$-0.495307\pi$
$317$	−15.0237	−	8.67395i	−0.843817	−	0.487178i	−0.858560	+	0.512713i	$0.828640\pi$
$318$	−1.59585	+	1.96991i	−0.0894906	+	0.110467i
$319$	−11.2921	+	6.51947i	−0.632234	+	0.365020i
$320$	−8.91216	+	5.03761i	−0.498205	+	0.281611i
$321$	12.0743	+	9.75115i	0.673922	+	0.544256i
$322$	−0.00771544	+	5.07506i	−0.000429965	+	0.282822i
$323$	1.02902			0.0572564
$324$	−16.4273	+	7.35829i	−0.912627	+	0.408794i
$325$	1.24385			0.0689966
$326$	0.0105516	−	6.94065i	0.000584401	−	0.384407i
$327$	−12.4818	−	10.0802i	−0.690245	−	0.557439i
$328$	−8.26942	+	4.72420i	−0.456602	+	0.260850i
$329$	9.42261	−	5.44014i	0.519485	−	0.299925i
$330$	7.30242	−	9.01411i	0.401985	−	0.496210i
$331$	−24.2777	−	14.0167i	−1.33442	−	0.770428i	−0.348447	−	0.937329i	$-0.613291\pi$
$331$	−24.2777	−	14.0167i	−1.33442	−	0.770428i	−0.985974	+	0.166900i	$0.946624\pi$
$332$	0.242766	−	0.417545i	0.0133235	−	0.0229158i
$333$	1.70058	+	7.89776i	0.0931913	+	0.432795i
$334$	−1.02983	−	1.79000i	−0.0563498	−	0.0979443i
$335$	−8.87537	+	15.3726i	−0.484913	+	0.839894i
$336$	8.79944	+	23.2534i	0.480049	+	1.26858i
$337$	0.634922	+	1.09972i	0.0345864	+	0.0599054i	0.882800	−	0.469748i	$-0.155655\pi$
$337$	0.634922	+	1.09972i	0.0345864	+	0.0599054i	−0.848214	+	0.529654i	$0.822322\pi$
$338$	−9.11956	+	15.7402i	−0.496039	+	0.856156i
$339$	−10.1146	−	1.58827i	−0.549347	−	0.0862630i
$340$	−0.502418	−	0.876356i	−0.0272474	−	0.0475271i
$341$			18.7161i			1.01353i
$342$	−10.8168	+	2.31193i	−0.584908	+	0.125015i
$343$			4.02588i			0.217377i
$344$	27.0404	+	15.7767i	1.45792	+	0.850621i
$345$	0.797046	+	2.06819i	0.0429115	+	0.111348i
$346$	23.3574	+	13.5328i	1.25570	+	0.727527i
$347$	10.9617	+	18.9863i	0.588457	+	1.01924i	0.994435	+	0.105354i	$0.0335976\pi$
$347$	10.9617	+	18.9863i	0.588457	+	1.01924i	−0.405978	+	0.913883i	$0.633069\pi$
$348$	−4.35412	−	11.4013i	−0.233405	−	0.611176i
$349$	8.86444	−	15.3537i	0.474503	−	0.821863i	−0.525071	−	0.851058i	$-0.675961\pi$
$349$	8.86444	−	15.3537i	0.474503	−	0.821863i	0.999574	+	0.0291955i	$0.00929454\pi$
$350$	−14.7913	+	8.50981i	−0.790629	+	0.454869i
$351$	−1.91915	+	0.108220i	−0.102436	+	0.00577637i
$352$	10.6054	−	18.0508i	0.565270	−	0.962113i
$353$	18.2661	+	10.5459i	0.972206	+	0.561303i	0.899908	−	0.436080i	$-0.143634\pi$
$353$	18.2661	+	10.5459i	0.972206	+	0.561303i	0.0722976	+	0.997383i	$0.476967\pi$
$354$	−0.00600921	+	0.0378924i	−0.000319386	+	0.00201396i
$355$	−12.8687	+	7.42976i	−0.683000	+	0.394331i
$356$	0.0569501	−	18.7303i	0.00301835	−	0.992703i
$357$	−2.28918	+	0.882210i	−0.121156	+	0.0466915i
$358$	−2.45178	−	0.00372736i	−0.129581	−	0.000196997i
$359$	15.4408			0.814933			0.407467	−	0.913220i	$-0.366412\pi$
$359$	15.4408			0.814933			0.407467	+	0.913220i	$0.366412\pi$
$360$	7.25023	+	8.08325i	0.382120	+	0.426025i
$361$	12.2028			0.642254
$362$	27.9392	+	0.0424750i	1.46845	+	0.00223244i
$363$	−0.724680	+	4.61497i	−0.0380358	+	0.242223i
$364$	−0.00807274	+	2.65504i	−0.000423126	+	0.139162i
$365$	−10.2444	+	5.91460i	−0.536216	+	0.309584i
$366$	13.2499	−	5.08316i	0.692582	−	0.265701i
$367$	−1.02787	−	0.593442i	−0.0536545	−	0.0309774i	0.472933	−	0.881098i	$-0.343195\pi$
$367$	−1.02787	−	0.593442i	−0.0536545	−	0.0309774i	−0.526587	+	0.850121i	$0.676529\pi$
$368$	1.97890	+	3.47620i	0.103157	+	0.181209i
$369$	6.77903	+	7.48891i	0.352902	+	0.389857i
$370$	4.22425	−	2.43032i	0.219608	−	0.126346i
$371$	1.85710	−	3.21659i	0.0964157	−	0.166997i
$372$	−17.2979	−	2.77017i	−0.896852	−	0.143626i
$373$	18.1443	+	31.4268i	0.939476	+	1.62722i	0.766451	+	0.642303i	$0.222021\pi$
$373$	18.1443	+	31.4268i	0.939476	+	1.62722i	0.173025	+	0.984917i	$0.444646\pi$
$374$	1.78747	+	1.03562i	0.0924279	+	0.0535508i
$375$	−11.6454	+	14.4198i	−0.601365	+	0.744637i
$376$	4.32157	−	7.40695i	0.222868	−	0.381985i
$377$		−	1.30330i		−	0.0671232i
$378$	22.0812	−	14.4167i	1.13573	−	0.741516i
$379$		−	30.9085i		−	1.58766i	−0.608139	−	0.793831i	$-0.708084\pi$
$379$		−	30.9085i		−	1.58766i	0.608139	−	0.793831i	$-0.291916\pi$
$380$	3.31870	+	5.78873i	0.170246	+	0.296956i
$381$	19.8455	−	24.5736i	1.01672	−	1.25894i
$382$	16.4913	−	28.4637i	0.843767	−	1.45633i
$383$	6.54128	+	11.3298i	0.334244	+	0.578927i	0.983339	−	0.181780i	$-0.0581859\pi$
$383$	6.54128	+	11.3298i	0.334244	+	0.578927i	−0.649096	+	0.760707i	$0.724853\pi$
$384$	15.1133	+	12.4735i	0.771248	+	0.636535i
$385$	−8.49788	+	14.7188i	−0.433092	+	0.750137i
$386$	−8.40938	−	14.6167i	−0.428026	−	0.743973i
$387$	10.1774	−	31.6073i	0.517347	−	1.60669i
$388$	0.690138	−	1.18700i	0.0350365	−	0.0602610i
$389$	−15.3101	−	8.83932i	−0.776255	−	0.448171i	0.0588462	−	0.998267i	$-0.481258\pi$
$389$	−15.3101	−	8.83932i	−0.776255	−	0.448171i	−0.835102	+	0.550096i	$0.814591\pi$
$390$	0.415333	+	1.08262i	0.0210312	+	0.0548205i
$391$	−0.341815	+	0.197347i	−0.0172863	+	0.00998028i
$392$	−8.24721	−	14.4362i	−0.416547	−	0.729140i
$393$	1.09441	−	6.96954i	0.0552059	−	0.351567i
$394$	0.0317275	−	20.8697i	0.00159841	−	1.05140i
$395$	−5.77148			−0.290395
$396$	−21.1162	−	6.87027i	−1.06113	−	0.345244i
$397$	−25.4796			−1.27878			−0.639392	−	0.768881i	$-0.720814\pi$
$397$	−25.4796			−1.27878			−0.639392	+	0.768881i	$0.720814\pi$
$398$	0.0316898	−	20.8449i	0.00158847	−	1.04486i
$399$	15.1211	−	5.82740i	0.756999	−	0.291735i
$400$	−6.79558	+	11.6067i	−0.339779	+	0.580335i
$401$	−16.2869	+	9.40324i	−0.813328	+	0.469575i	−0.848110	−	0.529820i	$-0.822260\pi$
$401$	−16.2869	+	9.40324i	−0.813328	+	0.469575i	0.0347820	+	0.999395i	$0.488926\pi$
$402$	33.5582	+	5.32187i	1.67373	+	0.265431i
$403$	−1.62012	−	0.935376i	−0.0807038	−	0.0465944i
$404$	7.28306	+	4.23446i	0.362346	+	0.210672i
$405$	6.72014	−	9.35321i	0.333927	−	0.464765i
$406$	8.91649	+	15.4982i	0.442518	+	0.769162i
$407$	−4.98320	+	8.63116i	−0.247008	+	0.427831i
$408$	−1.22171	+	1.49874i	−0.0604838	+	0.0741988i
$409$	−5.19191	−	8.99265i	−0.256723	−	0.444658i	0.708639	−	0.705572i	$-0.249310\pi$
$409$	−5.19191	−	8.99265i	−0.256723	−	0.444658i	−0.965362	+	0.260913i	$0.915976\pi$
$410$	3.05484	−	5.27260i	0.150868	−	0.260395i
$411$	−0.0743907	−	0.193031i	−0.00366942	−	0.00952149i
$412$	32.3060	−	18.5211i	1.59160	−	0.912470i
$413$		−	0.0562078i		−	0.00276581i
$414$	3.14970	−	2.84243i	0.154799	−	0.139698i
$415$			0.309035i			0.0151699i
$416$	1.03250	+	1.82016i	0.0506227	+	0.0892409i
$417$	38.1830	+	5.99581i	1.86983	+	0.293616i
$418$	−11.8071	−	6.84077i	−0.577503	−	0.334593i
$419$	−5.64852	−	9.78352i	−0.275948	−	0.477956i	0.694426	−	0.719564i	$-0.255658\pi$
$419$	−5.64852	−	9.78352i	−0.275948	−	0.477956i	−0.970374	+	0.241608i	$0.922325\pi$
$420$	−12.3457	−	10.0325i	−0.602407	−	0.489534i
$421$	9.55373	−	16.5475i	0.465620	−	0.806478i	−0.533609	−	0.845731i	$-0.679165\pi$
$421$	9.55373	−	16.5475i	0.465620	−	0.806478i	0.999229	+	0.0392532i	$0.0124979\pi$
$422$	16.6729	−	9.59235i	0.811625	−	0.466948i
$423$	−8.65791	−	2.78781i	−0.420962	−	0.135548i
$424$	0.0133513	−	2.92738i	0.000648394	−	0.142166i
$425$	−1.14933	−	0.663567i	−0.0557508	−	0.0321877i
$426$	22.1011	+	17.9043i	1.07080	+	0.867468i
$427$	−18.0057	+	10.3956i	−0.871355	+	0.503077i
$428$	−17.9210	−	0.0544895i	−0.866244	−	0.00263385i
$429$	−1.84484	−	1.48988i	−0.0890696	−	0.0719321i
$430$	−20.0309	−	0.0304524i	−0.965978	−	0.00146854i
$431$	21.7927			1.04972			0.524858	−	0.851190i	$-0.324119\pi$
$431$	21.7927			1.04972			0.524858	+	0.851190i	$0.324119\pi$
$432$	9.47508	−	18.4993i	0.455870	−	0.890046i
$433$	35.8713			1.72387			0.861933	−	0.507023i	$-0.169254\pi$
$433$	35.8713			1.72387			0.861933	+	0.507023i	$0.169254\pi$
$434$	25.6650	+	0.0390177i	1.23196	+	0.00187291i
$435$	6.07513	+	4.90624i	0.291280	+	0.235236i
$436$	18.5258	+	0.0563284i	0.887225	+	0.00269764i
$437$	2.25785	−	1.30357i	0.108007	−	0.0623582i
$438$	17.5940	+	14.2531i	0.840674	+	0.681039i
$439$	−5.18625	−	2.99428i	−0.247526	−	0.142909i	0.371105	−	0.928591i	$-0.378979\pi$
$439$	−5.18625	−	2.99428i	−0.247526	−	0.142909i	−0.618631	+	0.785682i	$0.712312\pi$
$440$	−0.0610939	+	13.3954i	−0.00291254	+	0.638598i
$441$	−13.0737	+	11.8344i	−0.622556	+	0.563543i
$442$	−0.178979	+	0.102971i	−0.00851317	+	0.00489784i
$443$	2.88316	−	4.99378i	0.136983	−	0.237262i	−0.789370	−	0.613918i	$-0.789593\pi$
$443$	2.88316	−	4.99378i	0.136983	−	0.237262i	0.926353	+	0.376656i	$0.122926\pi$
$444$	−7.23956	−	5.88310i	−0.343575	−	0.279199i
$445$	5.99219	+	10.3788i	0.284057	+	0.492001i
$446$	−31.5492	−	18.2790i	−1.49390	−	0.865534i
$447$	−3.38694	−	0.531844i	−0.160197	−	0.0251554i
$448$	−24.7307	−	14.5806i	−1.16841	−	0.688871i
$449$		−	25.1373i		−	1.18630i	−0.805091	−	0.593152i	$-0.797883\pi$
$449$		−	25.1373i		−	1.18630i	0.805091	−	0.593152i	$-0.202117\pi$
$450$	13.5724	+	4.39303i	0.639807	+	0.207089i
$451$			12.4617i			0.586797i
$452$	10.2564	−	5.88004i	0.482422	−	0.276574i
$453$	−6.53806	−	16.9651i	−0.307185	−	0.797089i
$454$	−18.9721	+	32.7456i	−0.890405	+	1.53683i
$455$	−0.849399	−	1.47120i	−0.0398204	−	0.0689710i
$456$	8.06997	−	9.89988i	0.377911	−	0.463604i
$457$	−4.72426	+	8.18266i	−0.220992	+	0.382769i	−0.955109	−	0.296254i	$-0.904263\pi$
$457$	−4.72426	+	8.18266i	−0.220992	+	0.382769i	0.734118	+	0.679022i	$0.237596\pi$
$458$	−1.90477	−	3.31077i	−0.0890041	−	0.154702i
$459$	1.83104	+	0.923823i	0.0854657	+	0.0431204i
$460$	−2.21256	−	1.28641i	−0.103161	−	0.0599790i
$461$	−18.6274	−	10.7545i	−0.867565	−	0.500889i	−0.00102659	−	0.999999i	$-0.500327\pi$
$461$	−18.6274	−	10.7545i	−0.867565	−	0.500889i	−0.866538	+	0.499111i	$0.833660\pi$
$462$	32.1309	+	5.09552i	1.49487	+	0.237065i
$463$	−14.6786	+	8.47472i	−0.682174	+	0.393853i	−0.800674	−	0.599101i	$-0.795525\pi$
$463$	−14.6786	+	8.47472i	−0.682174	+	0.393853i	0.118500	+	0.992954i	$0.462192\pi$
$464$	12.1614	+	7.12033i	0.564578	+	0.330553i
$465$	10.4590	−	4.03073i	0.485026	−	0.186921i
$466$	−0.0384192	+	25.2714i	−0.00177974	+	1.17067i
$467$	−23.6288			−1.09341			−0.546705	−	0.837325i	$-0.684118\pi$
$467$	−23.6288			−1.09341			−0.546705	+	0.837325i	$0.684118\pi$
$468$	1.65004	−	1.48453i	0.0762731	−	0.0686222i
$469$	−49.7787			−2.29857
$470$	−0.00834156	+	5.48691i	−0.000384767	+	0.253092i
$471$	2.91040	−	18.5343i	0.134104	−	0.854014i
$472$	−0.0219754	−	0.0384665i	−0.00101150	−	0.00177057i
$473$	35.4758	−	20.4820i	1.63118	−	0.941763i
$474$	3.95704	+	10.3145i	0.181753	+	0.473761i
$475$	7.59186	+	4.38316i	0.348339	+	0.201113i
$476$	1.42386	−	2.44897i	0.0652625	−	0.112248i
$477$	−3.03541	+	0.653599i	−0.138982	+	0.0299262i
$478$	11.9482	+	20.7678i	0.546499	+	0.949896i
$479$	12.2298	−	21.1827i	0.558796	−	0.967863i	−0.438802	−	0.898584i	$-0.644597\pi$
$479$	12.2298	−	21.1827i	0.558796	−	0.967863i	0.997597	−	0.0692787i	$-0.0220698\pi$
$480$	−12.3713	−	2.03911i	−0.564669	−	0.0930723i
$481$	−0.498092	−	0.862721i	−0.0227110	−	0.0393367i
$482$	0.267243	−	0.461258i	0.0121726	−	0.0210097i
$483$	−3.90525	+	4.83565i	−0.177695	+	0.220030i
$484$	−2.68289	−	4.67970i	−0.121949	−	0.212714i
$485$			0.878529i			0.0398920i
$486$	−21.3230	−	5.59716i	−0.967232	−	0.253893i
$487$			32.5227i			1.47374i	0.676032	+	0.736872i	$0.263698\pi$
$487$			32.5227i			1.47374i	−0.676032	+	0.736872i	$0.736302\pi$
$488$	−8.25809	+	14.1540i	−0.373826	+	0.640719i
$489$	5.34081	−	6.61323i	0.241520	−	0.299060i
$490$	9.20458	+	5.33294i	0.415820	+	0.240918i
$491$	−3.03016	−	5.24840i	−0.136749	−	0.236857i	0.789515	−	0.613731i	$-0.210332\pi$
$491$	−3.03016	−	5.24840i	−0.136749	−	0.236857i	−0.926264	+	0.376874i	$0.876999\pi$
$492$	−11.5174	−	1.84445i	−0.519244	−	0.0831543i
$493$	−0.695279	+	1.20426i	−0.0313138	+	0.0542370i
$494$	1.18224	−	0.680172i	0.0531915	−	0.0306024i
$495$	13.8897	−	2.99080i	0.624296	−	0.134426i
$496$	17.5794	−	10.0075i	0.789340	−	0.449348i
$497$	−36.0880	−	20.8354i	−1.61877	−	0.934596i
$498$	0.552291	−	0.211880i	0.0247488	−	0.00949457i
$499$	18.0054	−	10.3954i	0.806034	−	0.465364i	−0.0395427	−	0.999218i	$-0.512590\pi$
$499$	18.0054	−	10.3954i	0.806034	−	0.465364i	0.845577	+	0.533854i	$0.179257\pi$
$500$	0.0650745	−	21.4023i	0.00291022	−	0.957139i
$501$	0.392351	−	2.49860i	0.0175290	−	0.111629i
$502$	−41.0625	−	0.0624260i	−1.83271	−	0.00278621i
$503$	27.7020			1.23517			0.617585	−	0.786504i	$-0.288111\pi$
$503$	27.7020			1.23517			0.617585	+	0.786504i	$0.288111\pi$
$504$	−9.46510	+	28.9420i	−0.421609	+	1.28918i
$505$	−5.39036			−0.239868
$506$	5.23394	+	0.00795698i	0.232677	+	0.000353731i
$507$	−20.7892	+	8.01183i	−0.923283	+	0.355818i
$508$	−0.110897	+	36.4728i	−0.00492025	+	1.61822i
$509$	23.9887	−	13.8499i	1.06328	−	0.613886i	0.136944	−	0.990579i	$-0.456272\pi$
$509$	23.9887	−	13.8499i	1.06328	−	0.613886i	0.926338	+	0.376693i	$0.122939\pi$
$510$	0.193779	−	1.22192i	0.00858070	−	0.0541075i
$511$	−28.7285	−	16.5864i	−1.27087	−	0.733740i
$512$	−22.6253	−	0.309587i	−0.999906	−	0.0136820i
$513$	−12.0949	−	6.10228i	−0.534001	−	0.269422i
$514$	−36.8449	+	21.1978i	−1.62516	+	0.934994i
$515$	−11.9133	+	20.6344i	−0.524962	+	0.909262i
$516$	13.6792	+	35.8192i	0.602192	+	1.57685i
$517$	−5.61045	−	9.71759i	−0.246748	−	0.427379i
$518$	11.8254	+	6.85137i	0.519577	+	0.301032i
$519$	11.8890	+	30.8498i	0.521868	+	1.35415i
$520$	−1.15649	−	0.674750i	−0.0507153	−	0.0295897i
$521$			7.71448i			0.337978i	0.985618	+	0.168989i	$0.0540502\pi$
$521$			7.71448i			0.337978i	−0.985618	+	0.168989i	$0.945950\pi$
$522$	4.60297	−	14.2210i	0.201466	−	0.622435i
$523$			3.10289i			0.135680i	0.997696	+	0.0678401i	$0.0216108\pi$
$523$			3.10289i			0.135680i	−0.997696	+	0.0678401i	$0.978389\pi$
$524$	4.05170	+	7.06729i	0.176999	+	0.308736i
$525$	−20.6468	−	3.24212i	−0.901098	−	0.141498i
$526$	6.33420	−	10.9327i	0.276184	−	0.476690i
$527$	0.998002	+	1.72859i	0.0434737	+	0.0752986i
$528$	23.9814	−	9.07492i	1.04366	−	0.394935i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	0.934064	+	1.62354i	0.0405732	+	0.0705222i
$531$	−0.0348359	+	0.0315337i	−0.00151175	+	0.00136845i
$532$	−9.40524	+	16.1766i	−0.407769	+	0.701343i
$533$	−1.07872	−	0.622798i	−0.0467245	−	0.0269764i
$534$	14.4401	−	17.8248i	0.624883	−	0.771355i
$535$	9.93034	−	5.73329i	0.429326	−	0.247872i
$536$	−34.0667	+	19.4618i	−1.47146	+	0.840622i
$537$	−2.33612	−	1.88664i	−0.100811	−	0.0814145i
$538$	0.0531673	−	34.9724i	0.00229221	−	1.50777i
$539$	−21.7548			−0.937046
$540$	0.708350	+	13.2799i	0.0304825	+	0.571475i
$541$	11.1002			0.477235			0.238618	−	0.971114i	$-0.423306\pi$
$541$	11.1002			0.477235			0.238618	+	0.971114i	$0.423306\pi$
$542$	−0.0137772	+	9.06234i	−0.000591780	+	0.389261i
$543$	26.6212	+	21.4991i	1.14242	+	0.922617i
$544$	0.0169715	−	2.23266i	0.000727648	−	0.0957247i
$545$	−10.2655	+	5.92678i	−0.439725	+	0.253875i
$546$	−2.04689	+	2.52669i	−0.0875990	+	0.108132i
$547$	−10.6669	−	6.15855i	−0.456084	−	0.263320i	0.254312	−	0.967122i	$-0.418151\pi$
$547$	−10.6669	−	6.15855i	−0.456084	−	0.263320i	−0.710396	+	0.703802i	$0.751484\pi$
$548$	0.206505	+	0.120064i	0.00882145	+	0.00512889i
$549$	16.5444	+	5.32723i	0.706098	+	0.227361i
$550$	8.77622	+	15.2544i	0.374219	+	0.650449i
$551$	4.59263	−	7.95468i	0.195653	−	0.338881i
$552$	−0.782030	+	4.83616i	−0.0332854	+	0.205841i
$553$	−8.09254	−	14.0167i	−0.344130	−	0.596050i
$554$	−14.3449	+	24.7591i	−0.609458	+	1.05191i
$555$	5.89651	+	0.925917i	0.250293	+	0.0393030i
$556$	−38.7186	+	22.1975i	−1.64203	+	0.941384i
$557$		−	17.8142i		−	0.754813i	−0.926048	−	0.377406i	$-0.876816\pi$
$557$		−	17.8142i		−	0.754813i	0.926048	−	0.377406i	$-0.123184\pi$
$558$	−14.3744	−	15.9283i	−0.608518	−	0.674298i
$559$			4.09452i			0.173180i
$560$	18.3687	+	0.111702i	0.776219	+	0.00472029i
$561$	0.909828	+	2.36084i	0.0384130	+	0.0996748i
$562$	37.1392	+	21.5177i	1.56662	+	0.907669i
$563$	−21.7000	−	37.5855i	−0.914546	−	1.58404i	−0.807564	−	0.589779i	$-0.799215\pi$
$563$	−21.7000	−	37.5855i	−0.914546	−	1.58404i	−0.106982	−	0.994261i	$-0.534119\pi$
$564$	9.81164	−	3.74702i	0.413145	−	0.157778i
$565$	−3.78220	+	6.55097i	−0.159119	+	0.275601i
$566$	15.0200	−	8.64140i	0.631339	−	0.363225i
$567$	32.1380	+	3.20593i	1.34967	+	0.134636i
$568$	−32.8432	−	0.149792i	−1.37807	−	0.00628514i
$569$	0.645353	+	0.372595i	0.0270546	+	0.0156200i	0.513466	−	0.858110i	$-0.328361\pi$
$569$	0.645353	+	0.372595i	0.0270546	+	0.0156200i	−0.486412	+	0.873730i	$0.661694\pi$
$570$	−1.28000	+	8.07133i	−0.0536134	+	0.338071i
$571$	−1.64385	+	0.949077i	−0.0687930	+	0.0397177i	−0.534002	−	0.845483i	$-0.679313\pi$
$571$	−1.64385	+	0.949077i	−0.0687930	+	0.0397177i	0.465209	+	0.885201i	$0.345979\pi$
$572$	2.73815	+	0.00832546i	0.114488	+	0.000348105i
$573$	37.5940	−	14.4881i	1.57051	−	0.605250i
$574$	17.0885	+	0.0259790i	0.713259	+	0.00108434i
$575$	−3.36243			−0.140223
$576$	4.83778	+	23.5074i	0.201574	+	0.979473i
$577$	4.46461			0.185864			0.0929321	−	0.995672i	$-0.470376\pi$
$577$	4.46461			0.185864			0.0929321	+	0.995672i	$0.470376\pi$
$578$	−23.8213	−	0.0362147i	−0.990835	−	0.00150633i
$579$	3.20386	−	20.4031i	0.133148	−	0.847923i
$580$	−9.01686	−	0.0274161i	−0.374405	−	0.00113839i
$581$	−0.750525	+	0.433316i	−0.0311370	+	0.0179770i
$582$	1.57006	−	0.602336i	0.0650812	−	0.0249676i
$583$	−3.31729	−	1.91524i	−0.137388	−	0.0793210i
$584$	−26.1455	−	0.119245i	−1.08191	−	0.00493439i
$585$	−0.435276	+	1.35181i	−0.0179964	+	0.0558903i
$586$	−10.9147	+	6.27948i	−0.450881	+	0.259403i
$587$	0.244393	−	0.423301i	0.0100872	−	0.0174715i	−0.860938	−	0.508710i	$-0.830122\pi$
$587$	0.244393	−	0.423301i	0.0100872	−	0.0174715i	0.871025	+	0.491239i	$0.163456\pi$
$588$	3.21993	−	20.1063i	0.132788	−	0.829170i
$589$	−6.59226	−	11.4181i	−0.271629	−	0.470476i
$590$	0.0245264	+	0.0142101i	0.00100973	+	0.000585019i
$591$	16.0592	−	19.8852i	0.660587	−	0.817968i
$592$	10.7715	+	0.0655029i	0.442706	+	0.00269215i
$593$		−	29.8507i		−	1.22582i	−0.790152	−	0.612911i	$-0.789998\pi$
$593$		−	29.8507i		−	1.22582i	0.790152	−	0.612911i	$-0.210002\pi$
$594$	−14.8681	−	22.7725i	−0.610044	−	0.934365i
$595$			1.81254i			0.0743068i
$596$	3.43444	−	1.96898i	0.140680	−	0.0806525i
$597$	16.0401	−	19.8616i	0.656478	−	0.812880i
$598$	−0.262266	+	0.452668i	−0.0107249	+	0.0185110i
$599$	−23.4079	−	40.5437i	−0.956420	−	1.65657i	−0.731084	−	0.682288i	$-0.760985\pi$
$599$	−23.4079	−	40.5437i	−0.956420	−	1.65657i	−0.225337	−	0.974281i	$-0.572348\pi$
$600$	−15.3974	+	5.85340i	−0.628598	+	0.238964i
$601$	−22.7279	+	39.3658i	−0.927089	+	1.60577i	−0.138922	+	0.990303i	$0.544364\pi$
$601$	−22.7279	+	39.3658i	−0.927089	+	1.60577i	−0.788167	+	0.615462i	$0.788969\pi$
$602$	−28.0126	−	48.6901i	−1.14171	−	1.98446i
$603$	27.9269	+	30.8513i	1.13727	+	1.25636i
$604$	18.1493	+	10.5522i	0.738485	+	0.429364i
$605$	2.98901	+	1.72571i	0.121521	+	0.0701600i
$606$	3.69573	+	9.63338i	0.150129	+	0.391329i
$607$	0.691231	−	0.399082i	0.0280562	−	0.0161983i	−0.485906	−	0.874011i	$-0.661510\pi$
$607$	0.691231	−	0.399082i	0.0280562	−	0.0161983i	0.513963	+	0.857813i	$0.328177\pi$
$608$	−0.112105	+	14.7478i	−0.00454645	+	0.598101i
$609$	−3.39706	+	21.6335i	−0.137656	+	0.876632i
$610$	0.0159399	−	10.4849i	0.000645387	−	0.424522i
$611$	1.12158			0.0453742
$612$	−2.31661	+	0.491457i	−0.0936434	+	0.0198660i
$613$	22.3953			0.904538			0.452269	−	0.891882i	$-0.350615\pi$
$613$	22.3953			0.904538			0.452269	+	0.891882i	$0.350615\pi$
$614$	0.0562313	−	36.9878i	0.00226931	−	1.49271i
$615$	6.96390	−	2.68377i	0.280812	−	0.108220i
$616$	−32.6178	+	18.6340i	−1.31421	+	0.750787i
$617$	−23.2366	+	13.4157i	−0.935470	+	0.540094i	−0.888537	−	0.458804i	$-0.848278\pi$
$617$	−23.2366	+	13.4157i	−0.935470	+	0.540094i	−0.0469326	+	0.998898i	$0.514945\pi$
$618$	45.0448	+	7.14348i	1.81197	+	0.287353i
$619$	16.0602	+	9.27238i	0.645515	+	0.372688i	0.786736	−	0.617290i	$-0.211769\pi$
$619$	16.0602	+	9.27238i	0.645515	+	0.372688i	−0.141221	+	0.989978i	$0.545103\pi$
$620$	−6.50547	+	11.1891i	−0.261266	+	0.449365i
$621$	5.18791	−	0.292545i	0.208184	−	0.0117394i
$622$	−14.6987	−	25.5485i	−0.589365	−	1.02440i
$623$	−16.8040	+	29.1054i	−0.673238	+	1.16608i
$624$	−0.412969	+	2.52944i	−0.0165320	+	0.101259i
$625$	−1.55907	−	2.70039i	−0.0623628	−	0.108016i
$626$	−16.0319	+	27.6708i	−0.640763	+	1.10595i
$627$	−6.00983	−	15.5944i	−0.240010	−	0.622782i
$628$	10.7748	+	18.7942i	0.429961	+	0.749971i
$629$			1.06288i			0.0423799i
$630$	−4.07227	−	19.0530i	−0.162243	−	0.759088i
$631$		−	44.7068i		−	1.77975i	−0.456205	−	0.889875i	$-0.650791\pi$
$631$		−	44.7068i		−	1.77975i	0.456205	−	0.889875i	$-0.349209\pi$
$632$	−11.0183	−	6.42859i	−0.438284	−	0.255716i
$633$	23.2732	+	3.65455i	0.925028	+	0.145255i
$634$	21.2281	+	12.2991i	0.843075	+	0.488460i
$635$	−11.6684	−	20.2102i	−0.463045	−	0.802018i
$636$	2.26110	−	2.78244i	0.0896585	−	0.110331i
$637$	1.08724	−	1.88316i	0.0430781	−	0.0746135i
$638$	15.9834	−	9.19563i	0.632788	−	0.364059i
$639$	7.33295	+	34.0553i	0.290087	+	1.34721i
$640$	12.6145	−	7.10509i	0.498633	−	0.280853i
$641$	39.2486	+	22.6602i	1.55023	+	0.895024i	0.998123	+	0.0612487i	$0.0195083\pi$
$641$	39.2486	+	22.6602i	1.55023	+	0.895024i	0.552104	+	0.833775i	$0.313825\pi$
$642$	−17.0547	−	13.8162i	−0.673094	−	0.545280i
$643$	3.66731	−	2.11732i	0.144624	−	0.0834990i	−0.425942	−	0.904751i	$-0.640057\pi$
$643$	3.66731	−	2.11732i	0.144624	−	0.0834990i	0.570566	+	0.821252i	$0.306724\pi$
$644$	0.0218225	−	7.17719i	0.000859929	−	0.282821i
$645$	−19.0860	−	15.4138i	−0.751511	−	0.606916i
$646$	−1.45526	−	0.00221238i	−0.0572563	−	8.70448e-5i
$647$	21.7240			0.854060			0.427030	−	0.904237i	$-0.359560\pi$
$647$	21.7240			0.854060			0.427030	+	0.904237i	$0.359560\pi$
$648$	23.2475	−	10.3709i	0.913247	−	0.407406i
$649$	−0.0579675			−0.00227542
$650$	−1.75907	−	0.00267426i	−0.0689965	−	0.000104893i
$651$	24.4543	+	19.7492i	0.958440	+	0.774031i
$652$	−0.0298445	+	9.81552i	−0.00116880	+	0.384406i
$653$	−22.8871	+	13.2138i	−0.895640	+	0.517098i	−0.875783	−	0.482705i	$-0.839654\pi$
$653$	−22.8871	+	13.2138i	−0.895640	+	0.517098i	−0.0198567	+	0.999803i	$0.506321\pi$
$654$	17.6302	+	14.2824i	0.689397	+	0.558487i
$655$	−4.51401	−	2.60617i	−0.176377	−	0.101831i
$656$	11.7049	−	6.66324i	0.456998	−	0.260156i
$657$	5.83753	+	27.1104i	0.227744	+	1.05768i
$658$	−13.3373	+	7.67326i	−0.519940	+	0.299135i
$659$	7.02293	−	12.1641i	0.273575	−	0.473845i	−0.696200	−	0.717848i	$-0.745127\pi$
$659$	7.02293	−	12.1641i	0.273575	−	0.473845i	0.969775	+	0.244003i	$0.0784606\pi$
$660$	−10.3465	+	12.7322i	−0.402739	+	0.495599i
$661$	8.00051	+	13.8573i	0.311184	+	0.538986i	0.978619	−	0.205682i	$-0.0659412\pi$
$661$	8.00051	+	13.8573i	0.311184	+	0.538986i	−0.667435	+	0.744668i	$0.732608\pi$
$662$	34.3036	+	19.8748i	1.33325	+	0.772456i
$663$	−0.249832	−	0.0392306i	−0.00970266	−	0.00152359i
$664$	−0.344220	+	0.589976i	−0.0133583	+	0.0228955i
$665$		−	11.9726i		−	0.464279i
$666$	−2.38800	−	11.1728i	−0.0925332	−	0.432936i
$667$			3.52312i			0.136416i
$668$	1.45255	+	2.53365i	0.0562008	+	0.0980299i
$669$	−16.0587	−	41.6693i	−0.620863	−	1.61103i
$670$	12.5847	−	21.7210i	0.486189	−	0.839156i
$671$	10.7210	+	18.5693i	0.413880	+	0.716862i
$672$	−12.3943	−	32.9042i	−0.478120	−	1.26931i
$673$	−16.1774	+	28.0201i	−0.623594	+	1.08010i	0.365217	+	0.930922i	$0.380995\pi$
$673$	−16.1774	+	28.0201i	−0.623594	+	1.08010i	−0.988811	+	0.149173i	$0.952339\pi$
$674$	−0.895550	−	1.55660i	−0.0344953	−	0.0599579i
$675$	9.57388	+	14.6151i	0.368499	+	0.562536i
$676$	12.9308	−	22.2404i	0.497340	−	0.855401i
$677$	−7.13980	−	4.12216i	−0.274405	−	0.158428i	0.356483	−	0.934302i	$-0.383976\pi$
$677$	−7.13980	−	4.12216i	−0.274405	−	0.158428i	−0.630888	+	0.775874i	$0.717309\pi$
$678$	14.3007	+	2.26790i	0.549215	+	0.0870980i
$679$	−2.13361	+	1.23184i	−0.0818803	+	0.0472736i
$680$	0.708641	+	1.24043i	0.0271751	+	0.0475685i
$681$	−43.2494	+	16.6676i	−1.65732	+	0.638704i
$682$	0.0402392	−	26.4685i	0.00154084	−	1.01353i
$683$	−19.2584			−0.736903			−0.368451	−	0.929647i	$-0.620112\pi$
$683$	−19.2584			−0.736903			−0.368451	+	0.929647i	$0.620112\pi$
$684$	15.3023	−	3.24630i	0.585097	−	0.124125i
$685$	−0.152839			−0.00583968
$686$	0.00865556	−	5.69345i	0.000330471	−	0.217377i
$687$	0.725692	−	4.62141i	0.0276869	−	0.176318i
$688$	−38.2070	−	22.3697i	−1.45663	−	0.852836i
$689$	0.331577	−	0.191436i	0.0126321	−	0.00729313i
$690$	−1.12275	−	2.92657i	−0.0427422	−	0.111413i
$691$	24.1291	+	13.9310i	0.917916	+	0.529959i	0.882970	−	0.469430i	$-0.155541\pi$
$691$	24.1291	+	13.9310i	0.917916	+	0.529959i	0.0349463	+	0.999389i	$0.488874\pi$
$692$	−33.0032	−	19.1884i	−1.25459	−	0.729435i
$693$	26.7391	+	29.5392i	1.01573	+	1.12210i
$694$	−15.4614	−	26.8742i	−0.586907	−	1.02013i
$695$	14.2780	−	24.7303i	0.541597	−	0.938074i
$696$	6.13313	+	16.1333i	0.232476	+	0.611530i
$697$	0.664497	+	1.15094i	0.0251696	+	0.0435950i
$698$	−12.5692	+	21.6943i	−0.475752	+	0.821141i
$699$	−19.4463	+	24.0792i	−0.735526	+	0.910760i
$700$	20.9363	−	12.0029i	0.791320	−	0.453666i
$701$			28.7292i			1.08509i	0.840028	+	0.542543i	$0.182538\pi$
$701$			28.7292i			1.08509i	−0.840028	+	0.542543i	$0.817462\pi$
$702$	2.71431	−	0.148920i	0.102445	−	0.00562063i
$703$		−	7.02082i		−	0.264795i
$704$	−15.0371	+	25.5049i	−0.566732	+	0.961252i
$705$	−4.22216	+	5.22807i	−0.159016	+	0.196900i
$706$	−25.8094	−	14.9534i	−0.971351	−	0.562780i
$707$	−7.55814	−	13.0911i	−0.284253	−	0.492341i
$708$	0.00857977	−	0.0535750i	0.000322447	−	0.00201347i
$709$	9.86295	−	17.0831i	0.370411	−	0.641571i	−0.619218	−	0.785219i	$-0.712550\pi$
$709$	9.86295	−	17.0831i	0.370411	−	0.641571i	0.989629	+	0.143649i	$0.0458835\pi$
$710$	18.2151	−	10.4796i	0.683599	−	0.393292i
$711$	−4.14704	+	12.8792i	−0.155526	+	0.483006i
$712$	−0.120809	+	26.4885i	−0.00452752	+	0.992697i
$713$	4.37957	+	2.52854i	0.164016	+	0.0946947i
$714$	3.23928	−	1.24271i	0.121227	−	0.0465072i
$715$	−1.51726	+	0.875990i	−0.0567423	+	0.0327602i
$716$	3.46733	+	0.0105426i	0.129580	+	0.000393994i
$717$	−4.55211	+	28.9891i	−0.170002	+	1.08262i
$718$	−21.8365	−	0.0331974i	−0.814933	−	0.00123891i
$719$	30.2369			1.12765			0.563823	−	0.825895i	$-0.309330\pi$
$719$	30.2369			1.12765			0.563823	+	0.825895i	$0.309330\pi$
$720$	−10.2360	−	11.4470i	−0.381472	−	0.426605i
$721$	−66.8174			−2.48841
$722$	−17.2574	−	0.0262358i	−0.642254	−	0.000976396i
$723$	0.609217	−	0.234782i	0.0226570	−	0.00873163i
$724$	−39.5119	−	0.120137i	−1.46845	−	0.00446487i
$725$	−10.2592	+	5.92314i	−0.381016	+	0.219980i
$726$	1.03477	−	6.52499i	0.0384040	−	0.242165i
$727$	−2.51826	−	1.45392i	−0.0933970	−	0.0539228i	0.452574	−	0.891727i	$-0.350506\pi$
$727$	−2.51826	−	1.45392i	−0.0933970	−	0.0539228i	−0.545971	+	0.837804i	$0.683839\pi$
$728$	0.0171248	−	3.75477i	0.000634688	−	0.139161i
$729$	−16.0431	−	21.7168i	−0.594191	−	0.804324i
$730$	14.5004	−	8.34247i	0.536686	−	0.308769i
$731$	2.18433	−	3.78337i	0.0807904	−	0.139933i
$732$	−18.7491	+	7.16018i	−0.692985	+	0.264648i
$733$	−6.77724	−	11.7385i	−0.250323	−	0.433572i	0.713292	−	0.700867i	$-0.247203\pi$
$733$	−6.77724	−	11.7385i	−0.250323	−	0.433572i	−0.963615	+	0.267295i	$0.913870\pi$
$734$	1.45235	+	0.841463i	0.0536073	+	0.0310590i
$735$	4.68516	+	12.1571i	0.172815	+	0.448423i
$736$	−2.79111	−	4.92034i	−0.102882	−	0.181366i
$737$			51.3371i			1.89103i
$738$	−9.57088	−	10.6055i	−0.352309	−	0.390393i
$739$		−	37.2005i		−	1.36844i	−0.729274	−	0.684222i	$-0.760142\pi$
$739$		−	37.2005i		−	1.36844i	0.729274	−	0.684222i	$-0.239858\pi$
$740$	−5.97921	+	3.42790i	−0.219800	+	0.126012i
$741$	1.65025	+	0.259136i	0.0606236	+	0.00951961i
$742$	−2.63325	+	4.54494i	−0.0966695	+	0.166850i
$743$	−16.0794	−	27.8503i	−0.589895	−	1.02173i	−0.994246	−	0.107124i	$-0.965836\pi$
$743$	−16.0794	−	27.8503i	−0.589895	−	1.02173i	0.404351	−	0.914604i	$-0.367498\pi$
$744$	24.4569	+	3.95479i	0.896633	+	0.144990i
$745$	−1.26650	+	2.19364i	−0.0464010	+	0.0803689i
$746$	−25.5923	−	44.4832i	−0.937001	−	1.62865i
$747$	0.689616	+	0.222054i	0.0252317	+	0.00812452i
$748$	−2.52564	−	1.46843i	−0.0923464	−	0.0536913i
$749$	27.8479	+	16.0780i	1.01754	+	0.587476i
$750$	16.5000	−	20.3677i	0.602496	−	0.743722i
$751$	40.1801	−	23.1980i	1.46619	−	0.846506i	0.466907	−	0.884307i	$-0.345368\pi$
$751$	40.1801	−	23.1980i	1.46619	−	0.846506i	0.999285	+	0.0378003i	$0.0120351\pi$
$752$	−6.12754	+	10.4657i	−0.223448	+	0.381645i
$753$	−39.1254	−	31.5975i	−1.42581	−	1.15148i
$754$	−0.00280206	+	1.84314i	−0.000102045	+	0.0671231i
$755$	−13.4327			−0.488867
$756$	−31.2585	+	20.3408i	−1.13686	+	0.739789i
$757$	34.2669			1.24545			0.622726	−	0.782440i	$-0.286025\pi$
$757$	34.2669			1.24545			0.622726	+	0.782440i	$0.286025\pi$
$758$	−0.0664525	+	43.7111i	−0.00241366	+	1.58766i
$759$	4.98703	+	4.02751i	0.181018	+	0.146189i
$760$	−4.68090	−	8.19363i	−0.169794	−	0.297214i
$761$	−6.66901	+	3.85035i	−0.241751	+	0.139575i	−0.615981	−	0.787761i	$-0.711240\pi$
$761$	−6.66901	+	3.85035i	−0.241751	+	0.139575i	0.374230	+	0.927336i	$0.377907\pi$
$762$	−28.1186	+	34.7096i	−1.01863	+	1.25740i
$763$	−28.7877	−	16.6206i	−1.04218	−	0.601705i
$764$	−23.3834	+	40.2183i	−0.845980	+	1.45505i
$765$	1.12336	−	1.01687i	0.0406150	−	0.0367650i
$766$	−9.22639	−	16.0368i	−0.333363	−	0.579434i
$767$	0.00289705	−	0.00501783i	0.000104606	−	0.000181183i
$768$	−21.3466	−	17.6726i	−0.770279	−	0.637707i
$769$	−18.3848	−	31.8434i	−0.662972	−	1.14830i	−0.979831	−	0.199828i	$-0.935962\pi$
$769$	−18.3848	−	31.8434i	−0.662972	−	1.14830i	0.316859	−	0.948473i	$-0.397372\pi$
$770$	12.0494	−	20.7972i	0.434232	−	0.749478i
$771$	−51.4307	−	8.07606i	−1.85223	−	0.290852i
$772$	11.8612	+	20.6893i	0.426895	+	0.744623i
$773$			19.5827i			0.704342i	0.935936	+	0.352171i	$0.114556\pi$
$773$			19.5827i			0.704342i	−0.935936	+	0.352171i	$0.885444\pi$
$774$	−14.4610	+	44.6775i	−0.519789	+	1.60590i
$775$			17.0041i			0.610806i
$776$	−0.978554	+	1.67719i	−0.0351280	+	0.0602077i
$777$	6.01915	+	15.6186i	0.215936	+	0.560314i
$778$	21.6328	+	12.5336i	0.775573	+	0.449351i
$779$	−4.38931	−	7.60250i	−0.157263	−	0.272388i
$780$	−0.585042	−	1.53194i	−0.0209479	−	0.0548524i
$781$	−21.4877	+	37.2178i	−0.768890	+	1.33176i
$782$	0.483824	−	0.278356i	0.0173015	−	0.00995399i
$783$	15.3136	−	10.0314i	0.547262	−	0.358493i
$784$	11.6323	+	20.4336i	0.415438	+	0.729772i
$785$	−12.0042	−	6.93064i	−0.428449	−	0.247365i
$786$	−1.56272	+	9.85405i	−0.0557403	+	0.351482i
$787$	−0.368525	+	0.212768i	−0.0131365	+	0.00758436i	−0.506554	−	0.862208i	$-0.669081\pi$
$787$	−0.368525	+	0.212768i	−0.0131365	+	0.00758436i	0.493417	+	0.869793i	$0.335748\pi$
$788$	−0.0897389	+	29.5142i	−0.00319682	+	1.05140i
$789$	14.4396	−	5.56480i	0.514065	−	0.198112i
$790$	8.16210	+	0.0124086i	0.290394	+	0.000441477i
$791$	−21.2130			−0.754248
$792$	29.8481	+	9.76142i	1.06060	+	0.346857i
$793$	−2.14322			−0.0761081
$794$	36.0335	+	0.0547805i	1.27878	+	0.00194409i
$795$	−0.355866	+	2.26625i	−0.0126213	+	0.0803758i
$796$	−0.0896322	+	29.4790i	−0.00317693	+	1.04486i
$797$	−26.1635	+	15.1055i	−0.926758	+	0.535064i	−0.885785	−	0.464096i	$-0.846379\pi$
$797$	−26.1635	+	15.1055i	−0.926758	+	0.535064i	−0.0409734	+	0.999160i	$0.513046\pi$
$798$	−21.3969	+	8.20867i	−0.757442	+	0.290584i
$799$	−1.03635	−	0.598335i	−0.0366633	−	0.0211676i
$800$	9.63534	−	16.3997i	0.340661	−	0.579818i
$801$	27.4660	−	5.91411i	0.970464	−	0.208965i
$802$	23.0533	−	13.2632i	0.814041	−	0.468338i
$803$	−17.1057	+	29.6279i	−0.603646	+	1.04555i
$804$	−47.4470	−	7.59841i	−1.67333	−	0.267975i
$805$	2.29613	+	3.97701i	0.0809279	+	0.140171i
$806$	2.28918	+	1.32630i	0.0806329	+	0.0467170i
$807$	26.9112	−	33.3226i	0.947317	−	1.17301i
$808$	−10.2907	−	6.00408i	−0.362025	−	0.211223i
$809$			2.22808i			0.0783350i	0.999233	+	0.0391675i	$0.0124706\pi$
$809$			2.22808i			0.0783350i	−0.999233	+	0.0391675i	$0.987529\pi$
$810$	−9.52382	+	13.2130i	−0.334633	+	0.464256i
$811$			9.52445i			0.334449i	0.985919	+	0.167224i	$0.0534804\pi$
$811$			9.52445i			0.334449i	−0.985919	+	0.167224i	$0.946520\pi$
$812$	−12.5765	−	21.9369i	−0.441348	−	0.769834i
$813$	−6.97345	+	8.63483i	−0.244570	+	0.302837i
$814$	7.06586	−	12.1956i	0.247658	−	0.427455i
$815$	−3.14018	−	5.43895i	−0.109996	−	0.190518i
$816$	1.73098	−	2.11691i	0.0605965	−	0.0741067i
$817$	−14.4285	+	24.9909i	−0.504790	+	0.874322i
$818$	7.32313	+	12.7287i	0.256047	+	0.445048i
$819$	−3.89334	+	0.838331i	−0.136044	+	0.0292937i
$820$	−4.33152	+	7.45001i	−0.151263	+	0.260166i
$821$	46.3207	+	26.7433i	1.61660	+	0.933347i	0.987790	+	0.155791i	$0.0497928\pi$
$821$	46.3207	+	26.7433i	1.61660	+	0.933347i	0.628814	+	0.777555i	$0.283541\pi$
$822$	0.104789	+	0.273146i	0.00365494	+	0.00952706i
$823$	−4.55420	+	2.62937i	−0.158749	+	0.0916539i	−0.577270	−	0.816553i	$-0.695882\pi$
$823$	−4.55420	+	2.62937i	−0.158749	+	0.0916539i	0.418521	+	0.908207i	$0.362549\pi$
$824$	−45.7273	+	26.1233i	−1.59299	+	0.910050i
$825$	−3.34362	+	21.2931i	−0.116410	+	0.741332i
$826$	−0.000120846		0.0794898i	−4.20476e−6		0.00276580i
$827$	41.1698			1.43161			0.715807	−	0.698298i	$-0.246059\pi$
$827$	41.1698			1.43161			0.715807	+	0.698298i	$0.246059\pi$
$828$	−4.46045	+	4.01303i	−0.155011	+	0.139462i
$829$	26.1956			0.909812			0.454906	−	0.890539i	$-0.349673\pi$
$829$	26.1956			0.909812			0.454906	+	0.890539i	$0.349673\pi$
$830$	0.000664418	−	0.437041i	2.30623e−5	−	0.0151699i
$831$	−32.7012	+	12.6025i	−1.13439	+	0.437175i
$832$	−1.45627	−	2.57632i	−0.0504870	−	0.0893177i
$833$	−2.00924	+	1.16004i	−0.0696161	+	0.0401929i
$834$	−53.9860	−	8.56144i	−1.86938	−	0.296458i
$835$	−1.61829	−	0.934320i	−0.0560032	−	0.0323335i
$836$	16.6830	+	9.69968i	0.576993	+	0.335471i
$837$	−1.47943	−	26.2357i	−0.0511365	−	0.906839i
$838$	7.96717	+	13.8481i	0.275221	+	0.478375i
$839$	7.84993	−	13.5965i	0.271010	−	0.469402i	−0.698111	−	0.715989i	$-0.745976\pi$
$839$	7.84993	−	13.5965i	0.271010	−	0.469402i	0.969121	+	0.246587i	$0.0793092\pi$
$840$	17.4378	+	14.2146i	0.601662	+	0.490450i
$841$	−8.29380	−	14.3653i	−0.285993	−	0.495355i
$842$	−13.5466	+	23.3812i	−0.466846	+	0.805769i
$843$	18.9040	+	49.0524i	0.651088	+	1.68945i
$844$	−23.5997	+	13.5298i	−0.812334	+	0.465714i
$845$			16.4606i			0.566263i
$846$	12.2381	+	3.96117i	0.420755	+	0.136188i
$847$			9.67887i			0.332570i
$848$	−0.0251753	+	4.13990i	−0.000864523	+	0.142165i
$849$	20.9660	+	3.29225i	0.719552	+	0.112990i
$850$	1.62397	+	0.940895i	0.0557018	+	0.0322724i
$851$	1.34646	+	2.33214i	0.0461561	+	0.0799448i
$852$	−31.2172	−	25.3680i	−1.06948	−	0.869095i
$853$	26.1469	−	45.2877i	0.895252	−	1.55062i	0.0617596	−	0.998091i	$-0.480329\pi$
$853$	26.1469	−	45.2877i	0.895252	−	1.55062i	0.833492	−	0.552531i	$-0.186338\pi$
$854$	25.4862	−	14.6628i	0.872119	−	0.501752i
$855$	−7.42028	+	6.71690i	−0.253768	+	0.229713i
$856$	25.3440	+	0.115589i	0.866239	+	0.00395077i
$857$	27.0622	+	15.6244i	0.924427	+	0.533718i	0.885045	−	0.465506i	$-0.154128\pi$
$857$	27.0622	+	15.6244i	0.924427	+	0.533718i	0.0393824	+	0.999224i	$0.487461\pi$
$858$	2.60579	+	2.11097i	0.0889601	+	0.0720675i
$859$	−3.70952	+	2.14169i	−0.126567	+	0.0730735i	−0.561947	−	0.827173i	$-0.689947\pi$
$859$	−3.70952	+	2.14169i	−0.126567	+	0.0730735i	0.435380	+	0.900247i	$0.356614\pi$
$860$	28.3279	+	0.0861322i	0.965975	+	0.00293708i
$861$	16.2823	+	13.1495i	0.554900	+	0.448135i
$862$	−30.8194	−	0.0468537i	−1.04971	−	0.00159584i
$863$	−50.4891			−1.71867			−0.859334	−	0.511415i	$-0.829122\pi$
$863$	−50.4891			−1.71867			−0.859334	+	0.511415i	$0.829122\pi$
$864$	−13.4396	+	26.1415i	−0.457223	+	0.889352i
$865$	24.4264			0.830523
$866$	−50.7296	−	0.0771225i	−1.72386	−	0.00262073i
$867$	−22.6975	−	18.3304i	−0.770849	−	0.622534i
$868$	−36.2957	−	0.110358i	−1.23196	−	0.00374581i
$869$	−14.4555	+	8.34588i	−0.490369	+	0.283115i
$870$	−8.58097	−	6.95153i	−0.290922	−	0.235679i
$871$	−4.44389	−	2.56568i	−0.150575	−	0.0869348i
$872$	−26.1993	−	0.119490i	−0.887220	−	0.00404646i
$873$	1.96045	+	0.631258i	0.0663513	+	0.0213648i
$874$	−3.19588	+	1.83867i	−0.108102	+	0.0621939i
$875$	−19.2012	+	33.2575i	−0.649120	+	1.12431i
$876$	−24.8510	−	20.1947i	−0.839638	−	0.682316i
$877$	4.51928	+	7.82763i	0.152605	+	0.264320i	0.932184	−	0.361984i	$-0.117900\pi$
$877$	4.51928	+	7.82763i	0.152605	+	0.264320i	−0.779579	+	0.626304i	$0.784567\pi$
$878$	7.32801	+	4.24570i	0.247308	+	0.143285i
$879$	−15.2355	−	2.39239i	−0.513879	−	0.0806935i
$880$	0.115199	−	18.9437i	0.00388337	−	0.638593i
$881$			41.6939i			1.40470i	0.711830	+	0.702352i	$0.247867\pi$
$881$			41.6939i			1.40470i	−0.711830	+	0.702352i	$0.752133\pi$
$882$	18.5144	−	16.7082i	0.623412	−	0.562596i
$883$		−	29.5890i		−	0.995749i	−0.867249	−	0.497875i	$-0.834114\pi$
$883$		−	29.5890i		−	0.995749i	0.867249	−	0.497875i	$-0.165886\pi$
$884$	0.253336	−	0.145238i	0.00852061	−	0.00488489i
$885$	0.0124840	+	0.0323937i	0.000419645	+	0.00108890i
$886$	−4.08814	+	7.05607i	−0.137344	+	0.237053i
$887$	23.3218	+	40.3946i	0.783070	+	1.35632i	0.930145	+	0.367192i	$0.119681\pi$
$887$	23.3218	+	40.3946i	0.783070	+	1.35632i	−0.147075	+	0.989125i	$0.546986\pi$
$888$	10.2256	+	8.33551i	0.343150	+	0.279721i
$889$	32.7218	−	56.6759i	1.09746	−	1.90085i
$890$	−8.45191	−	14.6907i	−0.283309	−	0.492432i
$891$	3.30629	−	33.1441i	0.110765	−	1.11037i
$892$	44.5780	+	25.9182i	1.49258	+	0.867804i
$893$	6.84555	+	3.95228i	0.229078	+	0.132258i
$894$	4.78870	+	0.759422i	0.160158	+	0.0253989i
$895$	−1.92131	+	1.10927i	−0.0642223	+	0.0370788i
$896$	34.9431	+	20.6733i	1.16737	+	0.690646i
$897$	−0.597870	+	0.230409i	−0.0199623	+	0.00769314i
$898$	−0.0540447	+	35.5495i	−0.00180349	+	1.18630i
$899$	17.8167			0.594222
$900$	−19.1847	−	6.24185i	−0.639491	−	0.208062i
$901$	−0.408507			−0.0136093
$902$	0.0267923	−	17.6234i	0.000892087	−	0.586797i
$903$	10.6724	−	67.9650i	0.355156	−	2.26173i
$904$	−14.5174	+	8.29357i	−0.482841	+	0.275840i
$905$	21.8942	−	12.6406i	0.727788	−	0.420189i
$906$	9.20973	+	24.0063i	0.305973	+	0.797555i
$907$	8.24112	+	4.75802i	0.273642	+	0.157987i	0.630542	−	0.776155i	$-0.282833\pi$
$907$	8.24112	+	4.75802i	0.273642	+	0.157987i	−0.356900	+	0.934143i	$0.616166\pi$
$908$	26.9010	−	46.2684i	0.892740	−	1.53547i
$909$	−3.87318	+	12.0287i	−0.128465	+	0.398966i
$910$	1.19807	+	2.08242i	0.0397155	+	0.0690315i
$911$	−15.9343	+	27.5989i	−0.527926	+	0.914394i	0.471544	+	0.881842i	$0.343697\pi$
$911$	−15.9343	+	27.5989i	−0.527926	+	0.914394i	−0.999470	+	0.0325516i	$0.989637\pi$
$912$	−11.4339	+	13.9832i	−0.378615	+	0.463029i
$913$	0.446882	+	0.774022i	0.0147896	+	0.0256164i
$914$	6.69870	−	11.5619i	0.221573	−	0.382432i
$915$	8.06813	−	9.99031i	0.266724	−	0.330269i
$916$	2.68663	+	4.68623i	0.0887688	+	0.154837i
$917$		−	14.6170i		−	0.482697i
$918$	−2.58749	−	1.31042i	−0.0854000	−	0.0432503i
$919$			6.99591i			0.230774i	0.993321	+	0.115387i	$0.0368108\pi$
$919$			6.99591i			0.230774i	−0.993321	+	0.115387i	$0.963189\pi$
$920$	3.12626	+	1.82401i	0.103070	+	0.0601358i
$921$	28.4620	−	35.2429i	0.937856	−	1.16129i
$922$	26.3200	+	15.2492i	0.866802	+	0.502207i
$923$	−2.14778	−	3.72007i	−0.0706952	−	0.122448i
$924$	−45.4290	−	7.27523i	−1.49450	−	0.239337i
$925$	−4.52739	+	7.84167i	−0.148860	+	0.257833i
$926$	20.7769	−	11.9535i	0.682772	−	0.392816i
$927$	37.4859	+	41.4114i	1.23120	+	1.36013i
$928$	−17.1835	−	10.0958i	−0.564075	−	0.331411i
$929$	−38.5686	−	22.2676i	−1.26540	−	0.730576i	−0.291282	−	0.956637i	$-0.594082\pi$
$929$	−38.5686	−	22.2676i	−1.26540	−	0.730576i	−0.974113	+	0.226061i	$0.927415\pi$
$930$	−14.7999	+	5.67782i	−0.485309	+	0.186183i
$931$	13.2720	−	7.66257i	0.434971	−	0.251131i
$932$	0.108666	−	35.7390i	0.00355947	−	1.17067i
$933$	5.60001	−	35.6625i	0.183336	−	1.16754i
$934$	33.4161	+	0.0508014i	1.09341	+	0.00166227i
$935$	1.86928			0.0611320
$936$	−2.33670	+	2.09589i	−0.0763773	+	0.0685062i
$937$	−44.7887			−1.46318			−0.731592	−	0.681743i	$-0.761222\pi$
$937$	−44.7887			−1.46318			−0.731592	+	0.681743i	$0.761222\pi$
$938$	70.3977	+	0.107023i	2.29857	+	0.00349443i
$939$	−36.5468	+	14.0845i	−1.19266	+	0.459631i
$940$	0.0235935	−	7.75963i	0.000769534	−	0.253091i
$941$	1.01597	−	0.586571i	0.0331197	−	0.0191217i	−0.483349	−	0.875428i	$-0.660580\pi$
$941$	1.01597	−	0.586571i	0.0331197	−	0.0191217i	0.516468	+	0.856306i	$0.327246\pi$
$942$	−4.15577	+	26.2051i	−0.135402	+	0.853809i
$943$	2.91603	+	1.68357i	0.0949591	+	0.0548247i
$944$	0.0309951	+	0.0544471i	0.00100881	+	0.00177210i
$945$	10.7487	−	21.3041i	0.349654	−	0.693022i
$946$	−50.2144	+	28.8896i	−1.63261	+	0.939282i
$947$	−12.7564	+	22.0947i	−0.414526	+	0.717980i	−0.995379	−	0.0960286i	$-0.969386\pi$
$947$	−12.7564	+	22.0947i	−0.414526	+	0.717980i	0.580852	+	0.814009i	$0.302719\pi$
$948$	−5.57391	−	14.5954i	−0.181032	−	0.474036i
$949$	−1.70978	−	2.96143i	−0.0555020	−	0.0961322i
$950$	−10.7271	−	6.21505i	−0.348032	−	0.201643i
$951$	10.8052	+	28.0374i	0.350381	+	0.909176i
$952$	−2.01890	+	3.46030i	−0.0654330	+	0.112149i
$953$		−	42.7058i		−	1.38338i	−0.722196	−	0.691689i	$-0.756867\pi$
$953$		−	42.7058i		−	1.38338i	0.722196	−	0.691689i	$-0.243133\pi$
$954$	4.29412	−	0.917801i	0.139027	−	0.0297149i
$955$		−	29.7664i		−	0.963220i
$956$	−16.8527	−	29.3957i	−0.545054	−	0.950726i
$957$	22.3107	+	3.50341i	0.721203	+	0.113249i
$958$	−17.3411	+	29.9305i	−0.560267	+	0.967012i
$959$	−0.214305	−	0.371186i	−0.00692026	−	0.0119862i
$960$	17.4912	+	2.91033i	0.564526	+	0.0939306i
$961$	−2.71293	+	4.69893i	−0.0875139	+	0.151579i
$962$	0.702553	+	1.22114i	0.0226512	+	0.0393712i
$963$	−5.65858	−	26.2793i	−0.182345	−	0.846839i
$964$	−0.378931	+	0.651743i	−0.0122045	+	0.0209912i
$965$	−13.2146	−	7.62946i	−0.425394	−	0.245601i
$966$	5.53324	−	6.83024i	0.178029	−	0.219759i
$967$	15.5707	−	8.98975i	0.500720	−	0.289091i	−0.228291	−	0.973593i	$-0.573314\pi$
$967$	15.5707	−	8.98975i	0.500720	−	0.289091i	0.729011	+	0.684502i	$0.239980\pi$
$968$	3.78411	+	6.62386i	0.121626	+	0.212899i
$969$	−1.38661	−	1.11982i	−0.0445442	−	0.0359737i
$970$	0.00188882	−	1.24243i	6.06463e−5	−	0.0398919i
$971$	40.8665			1.31147			0.655734	−	0.754992i	$-0.272359\pi$
$971$	40.8665			1.31147			0.655734	+	0.754992i	$0.272359\pi$
$972$	30.1433	+	7.96142i	0.966845	+	0.255363i
$973$	80.0804			2.56726
$974$	0.0699231	−	45.9940i	0.00224048	−	1.47374i
$975$	−1.67609	−	1.35360i	−0.0536779	−	0.0433500i
$976$	11.7091	−	19.9989i	0.374800	−	0.640150i
$977$	−5.45021	+	3.14668i	−0.174368	+	0.100671i	−0.584644	−	0.811290i	$-0.698766\pi$
$977$	−5.45021	+	3.14668i	−0.174368	+	0.100671i	0.410276	+	0.911961i	$0.365432\pi$
$978$	−7.56726	+	9.34102i	−0.241974	+	0.298693i
$979$	30.0166	+	17.3301i	0.959334	+	0.553872i
$980$	−13.0058	−	7.56170i	−0.415454	−	0.241549i
$981$	5.84955	+	27.1662i	0.186762	+	0.867350i
$982$	4.27401	+	7.42886i	0.136389	+	0.237064i
$983$	−7.70050	+	13.3377i	−0.245608	+	0.425405i	−0.962302	−	0.271982i	$-0.912321\pi$
$983$	−7.70050	+	13.3377i	−0.245608	+	0.425405i	0.716695	+	0.697387i	$0.245654\pi$
$984$	16.2841	+	2.63321i	0.519117	+	0.0839436i
$985$	−9.44217	−	16.3543i	−0.300852	−	0.521092i
$986$	0.985860	−	1.70158i	0.0313962	−	0.0541894i
$987$	−18.6171	−	2.92341i	−0.592588	−	0.0930530i
$988$	−1.67340	+	0.959366i	−0.0532380	+	0.0305215i
$989$		−	11.0685i		−	0.351957i
$990$	−19.6494	+	4.19976i	−0.624500	+	0.133477i
$991$		−	14.9086i		−	0.473589i	−0.971560	−	0.236794i	$-0.923903\pi$
$991$		−	14.9086i		−	0.473589i	0.971560	−	0.236794i	$-0.0760968\pi$
$992$	−24.8826	+	14.1149i	−0.790023	+	0.448148i
$993$	17.4606	+	45.3072i	0.554097	+	1.43778i
$994$	50.9913	+	29.5433i	1.61734	+	0.937056i
$995$	−9.43094	−	16.3349i	−0.298981	−	0.517850i
$996$	−0.781512	+	0.298456i	−0.0247632	+	0.00945694i
$997$	9.48322	−	16.4254i	0.300337	−	0.520198i	−0.675875	−	0.737016i	$-0.736234\pi$
$997$	9.48322	−	16.4254i	0.300337	−	0.520198i	0.976212	+	0.216817i	$0.0695676\pi$
$998$	−25.4859	+	14.6626i	−0.806741	+	0.464138i
$999$	6.30307	−	12.4928i	0.199420	−	0.395256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.o.a.47.1	✓	132
4.3	odd	2		828.2.o.b.47.23	yes	132
9.5	odd	6		828.2.o.b.599.23	yes	132
36.23	even	6	inner	828.2.o.a.599.1	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
828.2.o.a.47.1	✓	132	1.1	even	1	trivial
828.2.o.a.599.1	yes	132	36.23	even	6	inner
828.2.o.b.47.23	yes	132	4.3	odd	2
828.2.o.b.599.23	yes	132	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 0.00214998i) q^{2} +(-1.34750 - 1.08823i) q^{3} +(1.99999 + 0.00608105i) q^{4} +(-1.10823 + 0.639837i) q^{5} +(1.90331 + 1.54189i) q^{6} +(-3.10783 - 1.79431i) q^{7} +(-2.82840 - 0.0128998i) q^{8} +(0.631500 + 2.93278i) q^{9} +O(q^{10})\)	\(q+(-1.41421 - 0.00214998i) q^{2} +(-1.34750 - 1.08823i) q^{3} +(1.99999 + 0.00608105i) q^{4} +(-1.10823 + 0.639837i) q^{5} +(1.90331 + 1.54189i) q^{6} +(-3.10783 - 1.79431i) q^{7} +(-2.82840 - 0.0128998i) q^{8} +(0.631500 + 2.93278i) q^{9} +(1.56865 - 0.902482i) q^{10} +(-1.85048 + 3.20513i) q^{11} +(-2.68837 - 2.18465i) q^{12} +(-0.184963 - 0.320366i) q^{13} +(4.39127 + 2.54421i) q^{14} +(2.18963 + 0.343833i) q^{15} +(3.99993 + 0.0243241i) q^{16} +0.394694i q^{17} +(-0.886769 - 4.14893i) q^{18} -2.60714i q^{19} +(-2.22034 + 1.27293i) q^{20} +(2.23517 + 5.79987i) q^{21} +(2.62386 - 4.52875i) q^{22} +(0.500000 + 0.866025i) q^{23} +(3.79722 + 3.09534i) q^{24} +(-1.68122 + 2.91195i) q^{25} +(0.260889 + 0.453463i) q^{26} +(2.34060 - 4.63914i) q^{27} +(-6.20472 - 3.60750i) q^{28} +(3.05111 + 1.76156i) q^{29} +(-3.09586 - 0.490961i) q^{30} +(4.37957 - 2.52854i) q^{31} +(-5.65669 - 0.0429992i) q^{32} +(5.98144 - 2.30515i) q^{33} +(0.000848584 - 0.558182i) q^{34} +4.59226 q^{35} +(1.24516 + 5.86938i) q^{36} +2.69292 q^{37} +(-0.00560529 + 3.68705i) q^{38} +(-0.0993949 + 0.632975i) q^{39} +(3.14277 - 1.79542i) q^{40} +(2.91603 - 1.68357i) q^{41} +(-3.14854 - 8.20705i) q^{42} +(-9.58558 - 5.53424i) q^{43} +(-3.72043 + 6.39897i) q^{44} +(-2.57635 - 2.84614i) q^{45} +(-0.705244 - 1.22582i) q^{46} +(-1.51595 + 2.62570i) q^{47} +(-5.36342 - 4.38563i) q^{48} +(2.93908 + 5.09063i) q^{49} +(2.38386 - 4.11451i) q^{50} +(0.429519 - 0.531850i) q^{51} +(-0.367977 - 0.641853i) q^{52} +1.03499i q^{53} +(-3.32008 + 6.55569i) q^{54} -4.73602i q^{55} +(8.76704 + 5.11510i) q^{56} +(-2.83717 + 3.51311i) q^{57} +(-4.31114 - 2.49778i) q^{58} +(0.00783141 + 0.0135644i) q^{59} +(4.37715 + 0.700979i) q^{60} +(2.89682 - 5.01744i) q^{61} +(-6.19907 + 3.56648i) q^{62} +(3.29972 - 10.2477i) q^{63} +(7.99967 + 0.0729717i) q^{64} +(0.409964 + 0.236693i) q^{65} +(-8.46398 + 3.24711i) q^{66} +(12.0129 - 6.93565i) q^{67} +(-0.00240016 + 0.789385i) q^{68} +(0.268688 - 1.71108i) q^{69} +(-6.49442 - 0.00987325i) q^{70} +11.6120 q^{71} +(-1.74830 - 8.30322i) q^{72} +9.24391 q^{73} +(-3.80837 - 0.00578973i) q^{74} +(5.43432 - 2.09430i) q^{75} +(0.0158541 - 5.21425i) q^{76} +(11.5020 - 6.64066i) q^{77} +(0.141926 - 0.894948i) q^{78} +(3.90588 + 2.25506i) q^{79} +(-4.44840 + 2.53234i) q^{80} +(-8.20242 + 3.70410i) q^{81} +(-4.12751 + 2.37466i) q^{82} +(0.120747 - 0.209141i) q^{83} +(4.43505 + 11.6133i) q^{84} +(-0.252540 - 0.437412i) q^{85} +(13.5441 + 7.84719i) q^{86} +(-2.19438 - 5.69402i) q^{87} +(5.27524 - 9.04150i) q^{88} -9.36518i q^{89} +(3.63738 + 4.03058i) q^{90} +1.32752i q^{91} +(0.994729 + 1.73508i) q^{92} +(-8.65310 - 1.35878i) q^{93} +(2.14951 - 3.71003i) q^{94} +(1.66814 + 2.88931i) q^{95} +(7.57558 + 6.21374i) q^{96} +(0.343263 - 0.594549i) q^{97} +(-4.14553 - 7.20555i) q^{98} +(-10.5685 - 3.40302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 132 * q - 9 * q^8 + 2 * q^9	\( 132 q - 9 q^{8} + 2 q^{9} - 29 q^{12} - 15 q^{14} - 34 q^{18} - 21 q^{20} + 66 q^{23} + 15 q^{24} + 66 q^{25} - 54 q^{26} + 12 q^{27} + 77 q^{30} + 30 q^{32} - 22 q^{33} + 36 q^{36} - 24 q^{39} - 30 q^{41} - 11 q^{42} - 65 q^{48} + 66 q^{49} - 32 q^{51} - 64 q^{54} - 42 q^{56} - 6 q^{57} + 27 q^{58} + 36 q^{59} + 58 q^{60} + 63 q^{62} - 20 q^{63} - 9 q^{64} + 78 q^{66} - 15 q^{68} - 78 q^{70} + 36 q^{72} - 12 q^{73} - 21 q^{74} + 48 q^{75} - 87 q^{76} - 11 q^{78} + 72 q^{80} - 10 q^{81} - 9 q^{82} - 157 q^{84} - 24 q^{86} + 96 q^{87} + 108 q^{88} - 63 q^{90} - 12 q^{93} + 75 q^{94} - 9 q^{96} - 6 q^{97} + 20 q^{99}+O(q^{100}) \) 132 * q - 9 * q^8 + 2 * q^9 - 29 * q^12 - 15 * q^14 - 34 * q^18 - 21 * q^20 + 66 * q^23 + 15 * q^24 + 66 * q^25 - 54 * q^26 + 12 * q^27 + 77 * q^30 + 30 * q^32 - 22 * q^33 + 36 * q^36 - 24 * q^39 - 30 * q^41 - 11 * q^42 - 65 * q^48 + 66 * q^49 - 32 * q^51 - 64 * q^54 - 42 * q^56 - 6 * q^57 + 27 * q^58 + 36 * q^59 + 58 * q^60 + 63 * q^62 - 20 * q^63 - 9 * q^64 + 78 * q^66 - 15 * q^68 - 78 * q^70 + 36 * q^72 - 12 * q^73 - 21 * q^74 + 48 * q^75 - 87 * q^76 - 11 * q^78 + 72 * q^80 - 10 * q^81 - 9 * q^82 - 157 * q^84 - 24 * q^86 + 96 * q^87 + 108 * q^88 - 63 * q^90 - 12 * q^93 + 75 * q^94 - 9 * q^96 - 6 * q^97 + 20 * q^99

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