LMFDB - Embedded newform 828.2.o.b.47.23

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			47.23
Character	$\chi$	$=$	828.47
Dual form			828.2.o.b.599.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.708968 - 1.22367i) q^{2} +(1.34750 + 1.08823i) q^{3} +(-0.994729 + 1.73508i) q^{4} +(-1.10823 + 0.639837i) q^{5} +(0.376303 - 2.42041i) q^{6} +(3.10783 + 1.79431i) q^{7} +(2.82840 - 0.0128998i) q^{8} +(0.631500 + 2.93278i) q^{9} +O(q^{10})$	\(q+(-0.708968 - 1.22367i) q^{2} +(1.34750 + 1.08823i) q^{3} +(-0.994729 + 1.73508i) q^{4} +(-1.10823 + 0.639837i) q^{5} +(0.376303 - 2.42041i) 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} +(-3.22857 + 1.25552i) q^{12} +(-0.184963 - 0.320366i) q^{13} +(-0.00771544 - 5.07506i) q^{14} +(-2.18963 - 0.343833i) q^{15} +(-2.02103 - 3.45188i) q^{16} +0.394694i q^{17} +(3.14104 - 2.85199i) q^{18} +2.60714i q^{19} +(-0.00778176 - 2.55934i) q^{20} +(2.23517 + 5.79987i) q^{21} +(-5.23394 + 0.00795698i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(3.82530 + 3.06057i) 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} +(1.13164 + 2.92315i) q^{30} +(-4.37957 + 2.52854i) q^{31} +(-2.79111 + 4.92034i) q^{32} +(5.98144 - 2.30515i) q^{33} +(0.482975 - 0.279826i) q^{34} -4.59226 q^{35} +(-5.71679 - 1.82162i) q^{36} +2.69292 q^{37} +(3.19027 - 1.84838i) q^{38} +(0.0993949 - 0.632975i) q^{39} +(-3.12626 + 1.82401i) q^{40} +(2.91603 - 1.68357i) q^{41} +(5.51245 - 6.84703i) 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} +(1.03311 - 6.85074i) q^{48} +(2.93908 + 5.09063i) q^{49} +(4.75520 - 0.00722916i) q^{50} +(-0.429519 + 0.531850i) q^{51} +(0.739850 - 0.00224954i) q^{52} +1.03499i q^{53} +(7.33618 - 0.424875i) q^{54} +4.73602i q^{55} +(8.81333 + 5.03492i) q^{56} +(-2.83717 + 3.51311i) q^{57} +(-0.00757464 - 4.98244i) q^{58} +(-0.00783141 - 0.0135644i) q^{59} +(2.77467 - 3.45717i) 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} +(-7.06138 - 5.68502i) q^{66} +(-12.0129 + 6.93565i) q^{67} +(-0.684828 - 0.392614i) q^{68} +(0.268688 - 1.71108i) q^{69} +(3.25576 + 5.61940i) q^{70} -11.6120 q^{71} +(1.82397 + 8.28693i) q^{72} +9.24391 q^{73} +(-1.90920 - 3.29525i) q^{74} +(-5.43432 + 2.09430i) q^{75} +(-4.52360 - 2.59340i) q^{76} +(11.5020 - 6.64066i) q^{77} +(-0.845020 + 0.327133i) 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} +(-12.2866 - 1.89109i) q^{84} +(-0.252540 - 0.437412i) q^{85} +(-0.0237970 - 15.6532i) q^{86} +(2.19438 + 5.69402i) q^{87} +(5.19255 - 9.08924i) q^{88} -9.36518i q^{89} +(-1.65618 + 5.17042i) q^{90} -1.32752i q^{91} +(1.99999 - 0.00608105i) q^{92} +(-8.65310 - 1.35878i) q^{93} +(-4.28774 + 0.00651850i) q^{94} +(-1.66814 - 2.88931i) q^{95} +(-9.11548 + 3.59277i) 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 + 3 q^{6} + 9 q^{8} + 2 q^{9}+O(q^{10}) $ 132 * q + 3 * q^6 + 9 * q^8 + 2 * q^9	$ 132 q + 3 q^{6} + 9 q^{8} + 2 q^{9} + 13 q^{12} - 15 q^{14} - 7 q^{18} - 21 q^{20} - 66 q^{23} - 37 q^{24} + 66 q^{25} + 54 q^{26} - 12 q^{27} - 39 q^{30} + 30 q^{32} - 22 q^{33} - 3 q^{36} + 24 q^{39} - 30 q^{41} + 53 q^{42} + 13 q^{48} + 66 q^{49} + 32 q^{51} - 9 q^{52} + 12 q^{54} - 42 q^{56} - 6 q^{57} - 36 q^{58} - 36 q^{59} - 34 q^{60} - 63 q^{62} + 20 q^{63} - 9 q^{64} - 78 q^{66} - 15 q^{68} + 78 q^{70} - 48 q^{72} - 12 q^{73} - 21 q^{74} - 48 q^{75} + 87 q^{76} + 46 q^{78} - 72 q^{80} - 10 q^{81} - 9 q^{82} + 71 q^{84} - 24 q^{86} - 96 q^{87} - 84 q^{88} + 47 q^{90} - 12 q^{93} - 42 q^{94} - 72 q^{96} - 6 q^{97} - 20 q^{99}+O(q^{100}) $ 132 * q + 3 * q^6 + 9 * q^8 + 2 * q^9 + 13 * q^12 - 15 * q^14 - 7 * q^18 - 21 * q^20 - 66 * q^23 - 37 * q^24 + 66 * q^25 + 54 * q^26 - 12 * q^27 - 39 * q^30 + 30 * q^32 - 22 * q^33 - 3 * q^36 + 24 * q^39 - 30 * q^41 + 53 * q^42 + 13 * q^48 + 66 * q^49 + 32 * q^51 - 9 * q^52 + 12 * q^54 - 42 * q^56 - 6 * q^57 - 36 * q^58 - 36 * q^59 - 34 * q^60 - 63 * q^62 + 20 * q^63 - 9 * q^64 - 78 * q^66 - 15 * q^68 + 78 * q^70 - 48 * q^72 - 12 * q^73 - 21 * q^74 - 48 * q^75 + 87 * q^76 + 46 * q^78 - 72 * q^80 - 10 * q^81 - 9 * q^82 + 71 * q^84 - 24 * q^86 - 96 * q^87 - 84 * q^88 + 47 * q^90 - 12 * q^93 - 42 * q^94 - 72 * 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 $

$2$	−0.708968	−	1.22367i	−0.501316	−	0.865264i
$2$	−0.708968	−	1.22367i	−0.501316	−	0.865264i
$3$	1.34750	+	1.08823i	0.777978	+	0.628291i
$3$	1.34750	+	1.08823i	0.777978	+	0.628291i
$4$	−0.994729	+	1.73508i	−0.497365	+	0.867542i
$5$	−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	$0.425707\pi$
$6$	0.376303	−	2.42041i	0.153625	−	0.988129i
$7$	3.10783	+	1.79431i	1.17465	+	0.678184i	0.954771	−	0.297343i	$-0.0961004\pi$
$7$	3.10783	+	1.79431i	1.17465	+	0.678184i	0.219879	+	0.975527i	$0.429434\pi$
$8$	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	$-0.644925\pi$
$11$	1.85048	−	3.20513i	0.557941	−	0.966382i	0.997668	−	0.0682504i	$-0.0217417\pi$
$12$	−3.22857	+	1.25552i	−0.932008	+	0.362439i
$13$	−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	$0.849670\pi$
$14$	−0.00771544	−	5.07506i	−0.00206204	−	1.35637i
$15$	−2.18963	−	0.343833i	−0.565360	−	0.0887774i
$16$	−2.02103	−	3.45188i	−0.505257	−	0.862969i
$17$			0.394694i			0.0957275i	0.998854	+	0.0478637i	$0.0152413\pi$
$17$			0.394694i			0.0957275i	−0.998854	+	0.0478637i	$0.984759\pi$
$18$	3.14104	−	2.85199i	0.740350	−	0.672222i
$19$			2.60714i			0.598118i	0.954235	+	0.299059i	$0.0966728\pi$
$19$			2.60714i			0.598118i	−0.954235	+	0.299059i	$0.903327\pi$
$20$	−0.00778176	−	2.55934i	−0.00174005	−	0.572285i
$21$	2.23517	+	5.79987i	0.487754	+	1.26563i
$22$	−5.23394	+	0.00795698i	−1.11588	+	0.00169643i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	3.82530	+	3.06057i	0.780836	+	0.624737i
$25$	−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	$0.560591\pi$
$30$	1.13164	+	2.92315i	0.206608	+	0.533691i
$31$	−4.37957	+	2.52854i	−0.786593	+	0.454140i	−0.838762	−	0.544498i	$-0.816720\pi$
$31$	−4.37957	+	2.52854i	−0.786593	+	0.454140i	0.0521685	+	0.998638i	$0.483387\pi$
$32$	−2.79111	+	4.92034i	−0.493403	+	0.869801i
$33$	5.98144	−	2.30515i	1.04123	−	0.401274i
$34$	0.482975	−	0.279826i	0.0828295	−	0.0479897i
$35$	−4.59226			−0.776233
$36$	−5.71679	−	1.82162i	−0.952799	−	0.303603i
$37$	2.69292			0.442714			0.221357	−	0.975193i	$-0.428951\pi$
$37$	2.69292			0.442714			0.221357	+	0.975193i	$0.428951\pi$
$38$	3.19027	−	1.84838i	0.517530	−	0.299846i
$39$	0.0993949	−	0.632975i	0.0159159	−	0.101357i
$40$	−3.12626	+	1.82401i	−0.494305	+	0.288401i
$41$	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	$0.248645\pi$
$42$	5.51245	−	6.84703i	0.850589	−	1.05652i
$43$	9.58558	+	5.53424i	1.46179	+	0.843963i	0.999094	−	0.0425558i	$-0.0135500\pi$
$43$	9.58558	+	5.53424i	1.46179	+	0.843963i	0.462693	+	0.886519i	$0.346883\pi$
$44$	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	−0.734026	−	0.679121i	$-0.762361\pi$
$47$	1.51595	−	2.62570i	0.221123	−	0.382997i	0.955149	+	0.296124i	$0.0956943\pi$
$48$	1.03311	−	6.85074i	0.149117	−	0.988820i
$49$	2.93908	+	5.09063i	0.419868	+	0.727233i
$50$	4.75520	−	0.00722916i	0.672486	−	0.00102236i
$51$	−0.429519	+	0.531850i	−0.0601447	+	0.0744739i
$52$	0.739850	−	0.00224954i	0.102599	−	0.000311955i
$53$			1.03499i			0.142167i	0.997470	+	0.0710837i	$0.0226457\pi$
$53$			1.03499i			0.142167i	−0.997470	+	0.0710837i	$0.977354\pi$
$54$	7.33618	−	0.424875i	0.998327	−	0.0578181i
$55$			4.73602i			0.638605i
$56$	8.81333	+	5.03492i	1.17773	+	0.672820i
$57$	−2.83717	+	3.51311i	−0.375793	+	0.465323i
$58$	−0.00757464	−	4.98244i	−0.000994599	−	0.654227i
$59$	−0.00783141	−	0.0135644i	−0.00101956	−	0.00176593i	0.865515	−	0.500883i	$-0.166991\pi$
$59$	−0.00783141	−	0.0135644i	−0.00101956	−	0.00176593i	−0.866535	+	0.499117i	$0.833658\pi$
$60$	2.77467	−	3.45717i	0.358208	−	0.446318i
$61$	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
$66$	−7.06138	−	5.68502i	−0.869196	−	0.699778i
$67$	−12.0129	+	6.93565i	−1.46761	+	0.847324i	−0.999342	−	0.0362632i	$-0.988455\pi$
$67$	−12.0129	+	6.93565i	−1.46761	+	0.847324i	−0.468266	+	0.883587i	$0.655121\pi$
$68$	−0.684828	−	0.392614i	−0.0830476	−	0.0476114i
$69$	0.268688	−	1.71108i	0.0323463	−	0.205990i
$70$	3.25576	+	5.61940i	0.389138	+	0.671647i
$71$	−11.6120			−1.37809			−0.689043	−	0.724721i	$-0.741969\pi$
$71$	−11.6120			−1.37809			−0.689043	+	0.724721i	$0.741969\pi$
$72$	1.82397	+	8.28693i	0.214956	+	0.976624i
$73$	9.24391			1.08192			0.540959	−	0.841049i	$-0.318061\pi$
$73$	9.24391			1.08192			0.540959	+	0.841049i	$0.318061\pi$
$74$	−1.90920	−	3.29525i	−0.221940	−	0.383065i
$75$	−5.43432	+	2.09430i	−0.627501	+	0.241828i
$76$	−4.52360	−	2.59340i	−0.518893	−	0.297483i
$77$	11.5020	−	6.64066i	1.31077	−	0.756773i
$78$	−0.845020	+	0.327133i	−0.0956796	+	0.0370405i
$79$	−3.90588	−	2.25506i	−0.439446	−	0.253714i	0.263917	−	0.964545i	$-0.414986\pi$
$79$	−3.90588	−	2.25506i	−0.439446	−	0.253714i	−0.703362	+	0.710831i	$0.748319\pi$
$80$	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	−0.872576	−	0.488478i	$-0.837552\pi$
$83$	−0.120747	+	0.209141i	−0.0132538	+	0.0229562i	0.859322	+	0.511434i	$0.170886\pi$
$84$	−12.2866	−	1.89109i	−1.34058	−	0.206335i
$85$	−0.252540	−	0.437412i	−0.0273918	−	0.0474440i
$86$	−0.0237970	−	15.6532i	−0.00256609	−	1.68792i
$87$	2.19438	+	5.69402i	0.235262	+	0.610463i
$88$	5.19255	−	9.08924i	0.553527	−	0.968916i
$89$		−	9.36518i		−	0.992707i	−0.868120	−	0.496354i	$-0.834672\pi$
$89$		−	9.36518i		−	0.992707i	0.868120	−	0.496354i	$-0.165328\pi$
$90$	−1.65618	+	5.17042i	−0.174577	+	0.545010i
$91$		−	1.32752i		−	0.139162i
$92$	1.99999	−	0.00608105i	0.208513	−	0.000633993i
$93$	−8.65310	−	1.35878i	−0.897285	−	0.140899i
$94$	−4.28774	+	0.00651850i	−0.442246	+	0.000672332i
$95$	−1.66814	−	2.88931i	−0.171148	−	0.296437i
$96$	−9.11548	+	3.59277i	−0.930345	+	0.366686i
$97$	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	$0.599460\pi$
$102$	0.955323	+	0.148525i	0.0945911	+	0.0147061i
$103$	−16.1248	+	9.30963i	−1.58882	+	0.917305i	−0.595317	+	0.803491i	$0.702974\pi$
$103$	−16.1248	+	9.30963i	−1.58882	+	0.917305i	−0.993502	+	0.113815i	$0.963693\pi$
$104$	−0.527282	−	0.903736i	−0.0517043	−	0.0886186i
$105$	−6.18805	−	4.99744i	−0.603892	−	0.487700i
$106$	1.26649	−	0.733778i	0.123012	−	0.0712708i
$107$	8.96054			0.866248			0.433124	−	0.901334i	$-0.357411\pi$
$107$	8.96054			0.866248			0.433124	+	0.901334i	$0.357411\pi$
$108$	−5.72102	−	8.67582i	−0.550505	−	0.834832i
$109$	9.26295			0.887229			0.443615	−	0.896218i	$-0.353696\pi$
$109$	9.26295			0.887229			0.443615	+	0.896218i	$0.353696\pi$
$110$	5.79532	−	3.35769i	0.552562	−	0.320143i
$111$	3.62871	+	2.93053i	0.344422	+	0.278153i
$112$	−0.0872898	−	14.3542i	−0.00824811	−	1.35634i
$113$	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	$0.243649\pi$
$114$	6.31035	+	0.981074i	0.591018	+	0.0918860i
$115$	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
$120$	−6.19758	−	0.944251i	−0.565759	−	0.0861980i
$121$	−1.34855	−	2.33576i	−0.122596	−	0.212342i
$122$	−8.19344	+	0.0124562i	−0.741799	+	0.00112773i
$123$	5.76147	+	0.904712i	0.519494	+	0.0815752i
$124$	−0.0307524	−	10.1141i	−0.00276165	−	0.908276i
$125$		−	10.7012i		−	0.957144i
$126$	14.8792	−	3.22753i	1.32554	−	0.287531i
$127$		−	18.2365i		−	1.61823i	−0.587653	−	0.809113i	$-0.699948\pi$
$127$		−	18.2365i		−	1.61823i	0.587653	−	0.809113i	$-0.300052\pi$
$128$	−5.76080	−	9.73721i	−0.509188	−	0.860656i
$129$	6.89401	+	17.8887i	0.606983	+	1.57501i
$130$	−0.00101777	−	0.669467i	−8.92642e−5	−	0.0587162i
$131$	−2.03659	−	3.52747i	−0.177937	−	0.308197i	0.763237	−	0.646119i	$-0.223609\pi$
$131$	−2.03659	−	3.52747i	−0.177937	−	0.308197i	−0.941174	+	0.337923i	$0.890276\pi$
$132$	−1.95029	+	12.6713i	−0.169751	+	1.10289i
$133$	−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	$0.665043\pi$
$138$	−2.28429	+	0.884318i	−0.194452	+	0.0752781i
$139$	19.3255	−	11.1576i	1.63916	−	0.946372i	0.658043	−	0.752980i	$-0.271384\pi$
$139$	19.3255	−	11.1576i	1.63916	−	0.946372i	0.981122	−	0.193392i	$-0.0619490\pi$
$140$	4.56805	−	7.96795i	0.386071	−	0.673414i
$141$	4.90010	−	1.88842i	0.412663	−	0.159033i
$142$	8.23250	+	14.2092i	0.690856	+	1.19241i
$143$	−1.36908			−0.114489
$144$	8.84732	−	8.10709i	0.737276	−	0.675591i
$145$	−4.50845			−0.374406
$146$	−6.55364	−	11.3115i	−0.542383	−	0.936145i
$147$	−1.57939	+	10.0580i	−0.130266	+	0.829570i
$148$	−2.67873	+	4.67245i	−0.220190	+	0.384073i
$149$	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	$0.307496\pi$
$150$	6.41548	+	5.16502i	0.523822	+	0.421722i
$151$	−9.09066	−	5.24850i	−0.739787	−	0.427116i	0.0822046	−	0.996615i	$-0.473804\pi$
$151$	−9.09066	−	5.24850i	−0.739787	−	0.427116i	−0.821992	+	0.569499i	$0.807137\pi$
$152$	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
$156$	0.999394	+	0.802097i	0.0800155	+	0.0642192i
$157$	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	$0.691057\pi$
$158$	0.00969666	+	6.37826i	0.000771425	+	0.507427i
$159$	−1.12631	+	1.39465i	−0.0893226	+	0.110603i
$160$	−0.0550249	−	7.23872i	−0.00435010	−	0.572271i
$161$		−	3.58861i		−	0.282822i
$162$	10.3478	+	7.41095i	0.813003	+	0.582259i
$163$		−	4.90778i		−	0.384407i	−0.981355	−	0.192204i	$-0.938437\pi$
$163$		−	4.90778i		−	0.384407i	0.981355	−	0.192204i	$-0.0615634\pi$
$164$	0.0204758	+	6.73426i	0.00159889	+	0.525857i
$165$	−5.15389	+	6.38178i	−0.401230	+	0.496821i
$166$	0.341525		0.000519209i	0.0265075		4.02984e-5i
$167$	−0.730123	−	1.26461i	−0.0564987	−	0.0978585i	0.836393	−	0.548131i	$-0.184660\pi$
$167$	−0.730123	−	1.26461i	−0.0564987	−	0.0978585i	−0.892891	+	0.450272i	$0.851327\pi$
$168$	6.39677	+	16.3755i	0.493522	+	1.26340i
$169$	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	$0.925112\pi$
$174$	5.41185	−	6.72207i	0.410271	−	0.509599i
$175$	−10.4499	+	6.03324i	−0.789937	+	0.456070i
$176$	−14.8036	+	0.0900225i	−1.11586	+	0.00678570i
$177$	0.00420842	−	0.0268004i	0.000316324	−	0.00201444i
$178$	−11.4599	+	6.63961i	−0.858954	+	0.497660i
$179$	−1.73367			−0.129581			−0.0647904	−	0.997899i	$-0.520638\pi$
$179$	−1.73367			−0.129581			−0.0647904	+	0.997899i	$0.520638\pi$
$180$	7.50106	−	1.63904i	0.559096	−	0.122167i
$181$	−19.7560			−1.46845			−0.734227	−	0.678904i	$-0.762455\pi$
$181$	−19.7560			−1.46845			−0.734227	+	0.678904i	$0.762455\pi$
$182$	−1.62445	+	0.941172i	−0.120412	+	0.0697643i
$183$	9.36360	−	3.60858i	0.692177	−	0.266754i
$184$	−1.42537	−	2.44301i	−0.105080	−	0.180101i
$185$	−2.98438	+	1.72303i	−0.219416	+	0.126680i
$186$	4.47207	+	11.5519i	0.327908	+	0.847023i
$187$	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	$-0.514976\pi$
$191$	11.6305	−	20.1446i	0.841552	−	1.45761i	0.888582	−	0.458718i	$-0.151691\pi$
$192$	10.8589	+	8.60717i	0.783677	+	0.621169i
$193$	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	$0.692144\pi$
$194$	−0.970893	+	0.00147602i	−0.0697061	+	0.000105972i
$195$	0.294849	+	0.765079i	0.0211145	+	0.0547884i
$196$	−11.7562	+	0.0357453i	−0.839732	+	0.00255324i
$197$			14.7571i			1.05140i	0.850669	+	0.525701i	$0.176197\pi$
$197$			14.7571i			1.05140i	−0.850669	+	0.525701i	$0.823803\pi$
$198$	−3.32857	−	15.3450i	−0.236551	−	1.09052i
$199$		−	14.7396i		−	1.04486i	−0.852682	−	0.522431i	$-0.825025\pi$
$199$		−	14.7396i		−	1.04486i	0.852682	−	0.522431i	$-0.174975\pi$
$200$	−4.71759	+	8.25785i	−0.333584	+	0.583918i
$201$	−23.7349	−	3.72705i	−1.67413	−	0.262886i
$202$	−0.00905633	−	5.95707i	−0.000637201	−	0.419138i
$203$	6.32157	+	10.9493i	0.443687	+	0.768488i
$204$	−0.495548	−	1.27430i	−0.0346953	−	0.0892187i
$205$	−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
$210$	−1.72808	+	11.1152i	−0.119249	+	0.767018i
$211$	11.7792	−	6.80073i	0.810915	−	0.468182i	−0.0363588	−	0.999339i	$-0.511576\pi$
$211$	11.7792	−	6.80073i	0.810915	−	0.468182i	0.847273	+	0.531157i	$0.178243\pi$
$212$	−1.79580	−	1.02954i	−0.123336	−	0.0707090i
$213$	−15.6471	−	12.6365i	−1.07212	−	0.865839i
$214$	−6.35274	−	10.9647i	−0.434264	−	0.749534i
$215$	−14.1640			−0.965979
$216$	−6.56031	+	13.1515i	−0.446373	+	0.894847i
$217$	−18.1479			−1.23196
$218$	−6.56713	−	11.3348i	−0.444782	−	0.767688i
$219$	12.4562	+	10.0595i	0.841709	+	0.679760i
$220$	−8.21739	−	4.71106i	−0.554017	−	0.317620i
$221$	0.126447	−	0.0730040i	0.00850572	−	0.00491078i
$222$	1.01336	−	6.51799i	0.0680120	−	0.437459i
$223$	−22.3283	−	12.8912i	−1.49521	−	0.863262i	−0.495229	−	0.868763i	$-0.664916\pi$
$223$	−22.3283	−	12.8912i	−1.49521	−	0.863262i	−0.999985	+	0.00550083i	$0.998249\pi$
$224$	−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	$0.514619\pi$
$227$	−13.3801	+	23.1750i	−0.888068	+	1.53818i	−0.842157	+	0.539233i	$0.818714\pi$
$228$	−3.27332	−	8.41732i	−0.216781	−	0.557451i
$229$	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	$0.804890\pi$
$230$	−0.00275127	−	1.80973i	−0.000181413	−	0.119330i
$231$	22.7254	+	3.56853i	1.49522	+	0.234792i
$232$	8.65249	+	4.94304i	0.568064	+	0.324526i
$233$		−	17.8696i		−	1.17068i	−0.810789	−	0.585338i	$-0.800962\pi$
$233$		−	17.8696i		−	1.17068i	0.810789	−	0.585338i	$-0.199038\pi$
$234$	−1.49466	−	0.478767i	−0.0977089	−	0.0312980i
$235$			3.87983i			0.253092i
$236$	0.0313255		9.52464e-5i	0.00203912		6.20001e-6i
$237$	−2.80913	−	7.28919i	−0.182473	−	0.473484i
$238$	2.00310	−	0.00304524i	0.129842	−	0.000197394i
$239$	8.47098	+	14.6722i	0.547942	+	0.949064i	0.998415	+	0.0562741i	$0.0179221\pi$
$239$	8.47098	+	14.6722i	0.547942	+	0.949064i	−0.450473	+	0.892790i	$0.648745\pi$
$240$	3.23843	+	8.25322i	0.209040	+	0.532743i
$241$	−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
$246$	−2.97763	−	7.69154i	−0.189847	−	0.490395i
$247$	0.835238	−	0.482225i	0.0531449	−	0.0306832i
$248$	−12.3545	+	7.20822i	−0.784514	+	0.457723i
$249$	−0.390301	+	0.150415i	−0.0247343	+	0.00953219i
$250$	−13.0947	+	7.58680i	−0.828182	+	0.479831i
$251$	−29.0356			−1.83271			−0.916356	−	0.400364i	$-0.868884\pi$
$251$	−29.0356			−1.83271			−0.916356	+	0.400364i	$0.868884\pi$
$252$	−14.4983	−	15.9190i	−0.913306	−	1.00280i
$253$	−3.70096			−0.232677
$254$	−22.3154	+	12.9291i	−1.40019	+	0.811242i
$255$	0.135709	−	0.864234i	0.00849843	−	0.0541204i
$256$	−7.83089	+	13.9527i	−0.489431	+	0.872042i
$257$	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	$-0.0534991\pi$
$258$	17.0022	−	21.1185i	1.05851	−	1.31478i
$259$	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	−0.694792	−	0.719211i	$-0.744503\pi$
$263$	4.46720	−	7.73741i	0.275459	−	0.477109i	0.970251	+	0.242102i	$0.0778368\pi$
$264$	16.8882	−	6.59703i	1.03939	−	0.406019i
$265$	−0.662228	−	1.14701i	−0.0406803	−	0.0704604i
$266$	13.2314	−	0.0201152i	0.811268	−	0.00123334i
$267$	10.1915	−	12.6196i	0.623709	−	0.772304i
$268$	−0.0843520	−	27.7425i	−0.00515262	−	1.69464i
$269$			24.7292i			1.50777i	0.657008	+	0.753884i	$0.271822\pi$
$269$			24.7292i			1.50777i	−0.657008	+	0.753884i	$0.728178\pi$
$270$	−7.85832	+	5.16482i	−0.478242	+	0.314321i
$271$			6.40805i			0.389261i	0.980877	+	0.194631i	$0.0623508\pi$
$271$			6.40805i			0.389261i	−0.980877	+	0.194631i	$0.937649\pi$
$272$	1.36244	−	0.797689i	0.0826098	−	0.0483670i
$273$	1.44465	−	1.78884i	0.0874345	−	0.108265i
$274$	−0.000256784	−	0.168908i	−1.55129e−5	−	0.0102041i
$275$	6.22212	+	10.7770i	0.375208	+	0.649879i
$276$	2.70160	+	2.16826i	0.162617	+	0.130514i
$277$	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	$-0.693677\pi$
$282$	−5.78481	−	4.65727i	−0.344480	−	0.277336i
$283$	10.6115	−	6.12653i	0.630786	−	0.364184i	−0.150270	−	0.988645i	$-0.548014\pi$
$283$	10.6115	−	6.12653i	0.630786	−	0.364184i	0.781056	+	0.624460i	$0.214681\pi$
$284$	11.5507	−	20.1477i	0.685411	−	1.19555i
$285$	0.896421	−	5.70866i	0.0530994	−	0.338152i
$286$	0.970636	+	1.67530i	0.0573949	+	0.0990628i
$287$	12.0834			0.713260
$288$	−16.1929	−	5.07851i	−0.954173	−	0.299254i
$289$	16.8442			0.990836
$290$	3.19635	+	5.51685i	0.187696	+	0.323960i
$291$	1.10955	−	0.427603i	0.0650432	−	0.0250665i
$292$	−9.19519	+	16.0390i	−0.538108	+	0.938609i
$293$	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	$0.249582\pi$
$294$	13.4274	−	5.19815i	0.783102	−	0.303163i
$295$	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
$300$	1.77190	−	11.5123i	0.102301	−	0.664660i
$301$	19.8602	+	34.3989i	1.14472	+	1.98272i
$302$	0.0225683	+	14.8450i	0.00129866	+	0.854232i
$303$	2.62363	+	6.80785i	0.150724	+	0.391101i
$304$	8.99951	−	5.26910i	0.516158	−	0.302204i
$305$			7.41397i			0.424523i
$306$	1.12567	+	1.23975i	0.0643501	+	0.0708718i
$307$		−	26.1544i		−	1.49271i	−0.665549	−	0.746354i	$-0.731803\pi$
$307$		−	26.1544i		−	1.49271i	0.665549	−	0.746354i	$-0.268197\pi$
$308$	0.0807643	+	26.5625i	0.00460198	+	1.51354i
$309$	−31.8591	−	5.00278i	−1.81240	−	0.284598i
$310$	−9.15196	+	0.0139134i	−0.519797	+	0.000790229i
$311$	−10.4210	−	18.0497i	−0.590922	−	1.02351i	−0.994109	−	0.108389i	$-0.965431\pi$
$311$	−10.4210	−	18.0497i	−0.590922	−	1.02351i	0.403187	−	0.915118i	$-0.367902\pi$
$312$	0.272963	−	1.79159i	0.0154535	−	0.101429i
$313$	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	$0.828640\pi$
$318$	2.50511	+	0.389472i	0.140480	+	0.0218405i
$319$	11.2921	−	6.51947i	0.632234	−	0.365020i
$320$	−8.81878	+	5.19935i	−0.492985	+	0.290653i
$321$	12.0743	+	9.75115i	0.673922	+	0.544256i
$322$	−4.39127	+	2.54421i	−0.244716	+	0.141783i
$323$	−1.02902			−0.0572564
$324$	1.73226	−	17.9165i	0.0962364	−	0.995359i
$325$	1.24385			0.0689966
$326$	−6.00550	+	3.47946i	−0.332614	+	0.192710i
$327$	12.4818	+	10.0802i	0.690245	+	0.557439i
$328$	8.22599	−	4.79943i	0.454204	−	0.265004i
$329$	9.42261	−	5.44014i	0.519485	−	0.299925i
$330$	11.4631	+	1.78218i	0.631024	+	0.0981058i
$331$	24.2777	+	14.0167i	1.33442	+	0.770428i	0.985974	−	0.166900i	$-0.0533758\pi$
$331$	24.2777	+	14.0167i	1.33442	+	0.770428i	0.348447	+	0.937329i	$0.386709\pi$
$332$	−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
$336$	15.5031	−	19.4372i	0.845762	−	1.06039i
$337$	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	$0.822322\pi$
$338$	−18.1912	+	0.0276555i	−0.989472	+	0.00150426i
$339$	10.1146	+	1.58827i	0.549347	+	0.0862630i
$340$	1.01016	−	0.00307142i	0.0547834	−	0.000166571i
$341$			18.7161i			1.01353i
$342$	7.43554	+	8.18912i	0.402068	+	0.442817i
$343$		−	4.02588i		−	0.217377i
$344$	27.1832	+	15.5294i	1.46562	+	0.837287i
$345$	0.797046	+	2.06819i	0.0429115	+	0.111348i
$346$	0.0410388	+	26.9945i	0.00220626	+	1.45123i
$347$	−10.9617	−	18.9863i	−0.588457	−	1.01924i	−0.994435	−	0.105354i	$-0.966402\pi$
$347$	−10.9617	−	18.9863i	−0.588457	−	1.01924i	0.405978	−	0.913883i	$-0.366931\pi$
$348$	−12.0624	−	1.85658i	−0.646613	−	0.0995229i
$349$	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	$0.476967\pi$
$354$	−0.0357784	+	0.0138509i	−0.00190160	+	0.000736168i
$355$	12.8687	−	7.42976i	0.683000	−	0.394331i
$356$	16.2494	+	9.31582i	0.861215	+	0.493737i
$357$	−2.28918	+	0.882210i	−0.121156	+	0.0466915i
$358$	1.22912	+	2.12144i	0.0649610	+	0.112122i
$359$	−15.4408			−0.814933			−0.407467	−	0.913220i	$-0.633588\pi$
$359$	−15.4408			−0.814933			−0.407467	+	0.913220i	$0.633588\pi$
$360$	−7.32366	−	8.01678i	−0.385991	−	0.422521i
$361$	12.2028			0.642254
$362$	14.0064	+	24.1748i	0.736159	+	1.27060i
$363$	0.724680	−	4.61497i	0.0380358	−	0.242223i
$364$	2.30336	+	1.32053i	0.120729	+	0.0692144i
$365$	−10.2444	+	5.91460i	−0.536216	+	0.309584i
$366$	−11.0542	−	8.89958i	−0.577812	−	0.465189i
$367$	1.02787	+	0.593442i	0.0536545	+	0.0309774i	0.526587	−	0.850121i	$-0.323471\pi$
$367$	1.02787	+	0.593442i	0.0536545	+	0.0309774i	−0.472933	+	0.881098i	$0.656805\pi$
$368$	−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
$372$	10.9651	−	13.6622i	0.568513	−	0.708354i
$373$	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	$0.444646\pi$
$374$	−0.00314058	−	2.06581i	−0.000162395	−	0.106820i
$375$	11.6454	−	14.4198i	0.601365	−	0.744637i
$376$	4.25383	−	7.44607i	0.219374	−	0.384002i
$377$		−	1.30330i		−	0.0671232i
$378$	23.5620	+	11.8429i	1.21190	+	0.609134i
$379$			30.9085i			1.58766i	0.608139	+	0.793831i	$0.291916\pi$
$379$			30.9085i			1.58766i	−0.608139	+	0.793831i	$0.708084\pi$
$380$	6.67254	−	0.0202881i	0.342294	−	0.00104076i
$381$	19.8455	−	24.5736i	1.01672	−	1.25894i
$382$	−32.8959	+	0.0500106i	−1.68310	+	0.00255876i
$383$	−6.54128	−	11.3298i	−0.334244	−	0.578927i	0.649096	−	0.760707i	$-0.275147\pi$
$383$	−6.54128	−	11.3298i	−0.334244	−	0.578927i	−0.983339	+	0.181780i	$0.941814\pi$
$384$	2.83368	−	19.3900i	0.144606	−	0.989489i
$385$	−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	$0.814591\pi$
$390$	0.727165	−	0.903213i	0.0368214	−	0.0457360i
$391$	0.341815	−	0.197347i	0.0172863	−	0.00998028i
$392$	8.37854	+	14.3604i	0.423180	+	0.725310i
$393$	1.09441	−	6.96954i	0.0552059	−	0.351567i
$394$	18.0579	−	10.4623i	0.909741	−	0.527085i
$395$	5.77148			0.290395
$396$	−16.4173	+	14.9522i	−0.825002	+	0.751375i
$397$	−25.4796			−1.27878			−0.639392	−	0.768881i	$-0.720814\pi$
$397$	−25.4796			−1.27878			−0.639392	+	0.768881i	$0.720814\pi$
$398$	−18.0364	+	10.4499i	−0.904082	+	0.523806i
$399$	−15.1211	+	5.82740i	−0.756999	+	0.291735i
$400$	13.4495	−	0.0817881i	0.672474	−	0.00408941i
$401$	−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	$0.488926\pi$
$402$	12.2666	+	31.6861i	0.611804	+	1.58036i
$403$	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
$408$	−1.20799	+	1.50982i	−0.0598044	+	0.0747474i
$409$	−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	$0.915976\pi$
$410$	6.09363	−	0.00926393i	0.300943	−	0.000457513i
$411$	0.0743907	+	0.193031i	0.00366942	+	0.00952149i
$412$	−0.113225	−	37.2384i	−0.00557818	−	1.83460i
$413$		−	0.0562078i		−	0.00276581i
$414$	−4.04042	−	1.29422i	−0.198576	−	0.0636076i
$415$		−	0.309035i		−	0.0151699i
$416$	2.09256	−	0.0159065i	0.102596	−	0.000779882i
$417$	38.1830	+	5.99581i	1.86983	+	0.293616i
$418$	−0.0207450	−	13.6456i	−0.00101467	−	0.667428i
$419$	5.64852	+	9.78352i	0.275948	+	0.477956i	0.970374	−	0.241608i	$-0.0776748\pi$
$419$	5.64852	+	9.78352i	0.275948	+	0.477956i	−0.694426	+	0.719564i	$0.744342\pi$
$420$	14.8264	−	5.76569i	0.723455	−	0.281337i
$421$	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
$426$	−4.36962	+	28.1057i	−0.211709	+	1.36173i
$427$	18.0057	−	10.3956i	0.871355	−	0.503077i
$428$	−8.91331	+	15.5473i	−0.430841	+	0.751507i
$429$	−1.84484	−	1.48988i	−0.0890696	−	0.0719321i
$430$	10.0418	+	17.3321i	0.484261	+	0.835827i
$431$	−21.7927			−1.04972			−0.524858	−	0.851190i	$-0.675881\pi$
$431$	−21.7927			−1.04972			−0.524858	+	0.851190i	$0.675881\pi$
$432$	20.7441	−	1.29635i	0.998053	−	0.0623707i
$433$	35.8713			1.72387			0.861933	−	0.507023i	$-0.169254\pi$
$433$	35.8713			1.72387			0.861933	+	0.507023i	$0.169254\pi$
$434$	12.8663	+	22.2071i	0.617602	+	1.06597i
$435$	−6.07513	−	4.90624i	−0.291280	−	0.235236i
$436$	−9.21412	+	16.0720i	−0.441276	+	0.769708i
$437$	2.25785	−	1.30357i	0.108007	−	0.0623582i
$438$	3.47851	−	22.3741i	0.166210	−	1.06907i
$439$	5.18625	+	2.99428i	0.247526	+	0.142909i	0.618631	−	0.785682i	$-0.287688\pi$
$439$	5.18625	+	2.99428i	0.247526	+	0.142909i	−0.371105	+	0.928591i	$0.621021\pi$
$440$	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	−0.926353	−	0.376656i	$-0.877074\pi$
$443$	−2.88316	+	4.99378i	−0.136983	+	0.237262i	0.789370	+	0.613918i	$0.210407\pi$
$444$	−8.69429	+	3.38103i	−0.412613	+	0.160457i
$445$	5.99219	+	10.3788i	0.284057	+	0.492001i
$446$	0.0554318	+	36.4619i	0.00262477	+	1.72652i
$447$	3.38694	+	0.531844i	0.160197	+	0.0251554i
$448$	24.9925	+	14.1271i	1.18079	+	0.667442i
$449$		−	25.1373i		−	1.18630i	−0.805091	−	0.593152i	$-0.797883\pi$
$449$		−	25.1373i		−	1.18630i	0.805091	−	0.593152i	$-0.202117\pi$
$450$	3.02411	+	13.9414i	0.142558	+	0.657203i
$451$		−	12.4617i		−	0.586797i
$452$	0.0359463	+	11.8223i	0.00169077	+	0.556076i
$453$	−6.53806	−	16.9651i	−0.307185	−	0.797089i
$454$	37.8446	−	0.0575338i	1.77613	−	0.00270020i
$455$	0.849399	+	1.47120i	0.0398204	+	0.0689710i
$456$	−7.97933	+	9.97308i	−0.373666	+	0.467032i
$457$	−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	$0.833660\pi$
$462$	−11.7449	−	30.3384i	−0.546423	−	1.41147i
$463$	14.6786	−	8.47472i	0.682174	−	0.393853i	−0.118500	−	0.992954i	$-0.537808\pi$
$463$	14.6786	−	8.47472i	0.682174	−	0.393853i	0.800674	+	0.599101i	$0.204475\pi$
$464$	−0.0856968	−	14.0922i	−0.00397837	−	0.654216i
$465$	10.4590	−	4.03073i	0.485026	−	0.186921i
$466$	−21.8665	+	12.6690i	−1.01294	+	0.586879i
$467$	23.6288			1.09341			0.546705	−	0.837325i	$-0.315882\pi$
$467$	23.6288			1.09341			0.546705	+	0.837325i	$0.315882\pi$
$468$	0.473812	+	2.16840i	0.0219020	+	0.100234i
$469$	−49.7787			−2.29857
$470$	4.74763	−	2.75068i	0.218992	−	0.126879i
$471$	−2.91040	+	18.5343i	−0.134104	+	0.854014i
$472$	−0.0223253	−	0.0382645i	−0.00102761	−	0.00176127i
$473$	35.4758	−	20.4820i	1.63118	−	0.941763i
$474$	−6.92797	+	8.60525i	−0.318212	+	0.395252i
$475$	−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	$0.355403\pi$
$479$	−12.2298	+	21.1827i	−0.558796	+	0.967863i	−0.997597	+	0.0692787i	$0.977930\pi$
$480$	7.80326	−	9.81404i	0.356169	−	0.447948i
$481$	−0.498092	−	0.862721i	−0.0227110	−	0.0393367i
$482$	0.533083		0.000810428i	0.0242813		3.69140e-5i
$483$	3.90525	−	4.83565i	0.177695	−	0.220030i
$484$	5.39418	−	0.0164012i	0.245190	−	0.000745510i
$485$			0.878529i			0.0398920i
$486$	5.87886	+	21.2471i	0.266670	+	0.963788i
$487$		−	32.5227i		−	1.47374i	−0.676032	−	0.736872i	$-0.736302\pi$
$487$		−	32.5227i		−	1.47374i	0.676032	−	0.736872i	$-0.263698\pi$
$488$	8.12864	−	14.2287i	0.367966	−	0.644102i
$489$	5.34081	−	6.61323i	0.241520	−	0.299060i
$490$	0.0161724	+	10.6379i	0.000730594	+	0.480570i
$491$	3.03016	+	5.24840i	0.136749	+	0.236857i	0.926264	−	0.376874i	$-0.123001\pi$
$491$	3.03016	+	5.24840i	0.136749	+	0.236857i	−0.789515	+	0.613731i	$0.789668\pi$
$492$	−7.30085	+	9.09668i	−0.329148	+	0.410110i
$493$	−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
$498$	0.460769	+	0.370959i	0.0206476	+	0.0166231i
$499$	−18.0054	+	10.3954i	−0.806034	+	0.465364i	−0.845577	−	0.533854i	$-0.820743\pi$
$499$	−18.0054	+	10.3954i	−0.806034	+	0.465364i	0.0395427	+	0.999218i	$0.487410\pi$
$500$	18.5675	+	10.6448i	0.830362	+	0.476049i
$501$	0.392351	−	2.49860i	0.0175290	−	0.111629i
$502$	20.5853	+	35.5300i	0.918768	+	1.58578i
$503$	−27.7020			−1.23517			−0.617585	−	0.786504i	$-0.711889\pi$
$503$	−27.7020			−1.23517			−0.617585	+	0.786504i	$0.711889\pi$
$504$	−9.20072	+	29.0271i	−0.409832	+	1.29297i
$505$	−5.39036			−0.239868
$506$	2.62386	+	4.52875i	0.116645	+	0.201327i
$507$	20.7892	−	8.01183i	0.923283	−	0.355818i
$508$	31.6418	+	18.1404i	1.40388	+	0.804848i
$509$	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	$0.122939\pi$
$510$	−1.15375	+	0.446651i	−0.0510889	+	0.0197781i
$511$	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
$516$	−37.8961	−	5.83274i	−1.66828	−	0.256772i
$517$	−5.61045	−	9.71759i	−0.246748	−	0.427379i
$518$	−0.0207771	−	13.6668i	−0.000912893	−	0.600483i
$519$	−11.8890	−	30.8498i	−0.521868	−	1.35415i
$520$	1.16259	+	0.664173i	0.0509831	+	0.0291259i
$521$			7.71448i			0.337978i	0.985618	+	0.168989i	$0.0540502\pi$
$521$			7.71448i			0.337978i	−0.985618	+	0.168989i	$0.945950\pi$
$522$	14.6076	−	3.16863i	0.639359	−	0.138687i
$523$		−	3.10289i		−	0.135680i	−0.997696	−	0.0678401i	$-0.978389\pi$
$523$		−	3.10289i		−	0.135680i	0.997696	−	0.0678401i	$-0.0216108\pi$
$524$	8.14631	−	0.0247692i	0.355873	−	0.00108205i
$525$	−20.6468	−	3.24212i	−0.901098	−	0.141498i
$526$	−12.6351	+	0.0192088i	−0.550918	+	0.000837541i
$527$	−0.998002	−	1.72859i	−0.0434737	−	0.0752986i
$528$	−20.0457	−	15.9884i	−0.872379	−	0.695807i
$529$	−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
$534$	−22.6676	−	3.52415i	−0.980923	−	0.152505i
$535$	−9.93034	+	5.73329i	−0.429326	+	0.247872i
$536$	−33.8878	+	19.7717i	−1.46373	+	0.854009i
$537$	−2.33612	−	1.88664i	−0.100811	−	0.0814145i
$538$	30.2604	−	17.5322i	1.30462	−	0.755868i
$539$	21.7548			0.937046
$540$	11.8913	+	5.95429i	0.511721	+	0.256232i
$541$	11.1002			0.477235			0.238618	−	0.971114i	$-0.423306\pi$
$541$	11.1002			0.477235			0.238618	+	0.971114i	$0.423306\pi$
$542$	7.84133	−	4.54310i	0.336814	−	0.195143i
$543$	−26.6212	−	21.4991i	−1.14242	−	0.922617i
$544$	−1.94203	−	1.10163i	−0.0832638	−	0.0472322i
$545$	−10.2655	+	5.92678i	−0.439725	+	0.253875i
$546$	−3.21315	−	0.499552i	−0.137510	−	0.0213788i
$547$	10.6669	+	6.15855i	0.456084	+	0.263320i	0.710396	−	0.703802i	$-0.248516\pi$
$547$	10.6669	+	6.15855i	0.456084	+	0.263320i	−0.254312	+	0.967122i	$0.581849\pi$
$548$	−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
$552$	0.737884	−	4.84309i	0.0314064	−	0.206136i
$553$	−8.09254	−	14.0167i	−0.344130	−	0.596050i
$554$	−28.6145	+	0.0435017i	−1.21571	+	0.00184821i
$555$	−5.89651	−	0.925917i	−0.250293	−	0.0393030i
$556$	0.135699	+	44.6301i	0.00575494	+	1.89274i
$557$		−	17.8142i		−	0.754813i	−0.926048	−	0.377406i	$-0.876816\pi$
$557$		−	17.8142i		−	0.754813i	0.926048	−	0.377406i	$-0.123184\pi$
$558$	−6.54500	+	20.4328i	−0.277072	+	0.864988i
$559$		−	4.09452i		−	0.173180i
$560$	9.28108	+	15.8519i	0.392197	+	0.669865i
$561$	0.909828	+	2.36084i	0.0384130	+	0.0996748i
$562$	0.0652534	+	42.9224i	0.00275255	+	1.81057i
$563$	21.7000	+	37.5855i	0.914546	+	1.58404i	0.807564	+	0.589779i	$0.200785\pi$
$563$	21.7000	+	37.5855i	0.914546	+	1.58404i	0.106982	+	0.994261i	$0.465881\pi$
$564$	−1.59771	+	10.3805i	−0.0672758	+	0.437100i
$565$	−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	$0.661694\pi$
$570$	−7.62105	+	2.95034i	−0.319210	+	0.123576i
$571$	1.64385	−	0.949077i	0.0687930	−	0.0397177i	−0.465209	−	0.885201i	$-0.654021\pi$
$571$	1.64385	−	0.949077i	0.0687930	−	0.0397177i	0.534002	+	0.845483i	$0.320687\pi$
$572$	1.36187	−	2.37547i	0.0569425	−	0.0993236i
$573$	37.5940	−	14.4881i	1.57051	−	0.605250i
$574$	−8.56673	−	14.7861i	−0.357569	−	0.617158i
$575$	3.36243			0.140223
$576$	5.26580	+	23.4152i	0.219408	+	0.975633i
$577$	4.46461			0.185864			0.0929321	−	0.995672i	$-0.470376\pi$
$577$	4.46461			0.185864			0.0929321	+	0.995672i	$0.470376\pi$
$578$	−11.9420	−	20.6117i	−0.496722	−	0.857335i
$579$	−3.20386	+	20.4031i	−0.133148	+	0.847923i
$580$	4.48469	−	7.82254i	0.186216	−	0.324813i
$581$	−0.750525	+	0.433316i	−0.0311370	+	0.0179770i
$582$	−1.30988	−	1.05457i	−0.0542964	−	0.0437133i
$583$	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	−0.871025	−	0.491239i	$-0.836544\pi$
$587$	−0.244393	+	0.423301i	−0.0100872	+	0.0174715i	0.860938	+	0.508710i	$0.169878\pi$
$588$	−15.8804	−	12.7454i	−0.654897	−	0.525610i
$589$	−6.59226	−	11.4181i	−0.271629	−	0.470476i
$590$	−4.30927e−5	−	0.0283455i	−1.77410e−6	−	0.00116697i
$591$	−16.0592	+	19.8852i	−0.660587	+	0.817968i
$592$	−5.44248	−	9.29564i	−0.223684	−	0.382048i
$593$		−	29.8507i		−	1.22582i	−0.790152	−	0.612911i	$-0.789998\pi$
$593$		−	29.8507i		−	1.22582i	0.790152	−	0.612911i	$-0.210002\pi$
$594$	12.2137	−	24.2996i	0.501133	−	0.997024i
$595$		−	1.81254i		−	0.0743068i
$596$	0.0120369	+	3.95880i	0.000493050	+	0.162159i
$597$	16.0401	−	19.8616i	0.656478	−	0.812880i
$598$	0.523155		0.000795334i	0.0213934		3.25236e-5i
$599$	23.4079	+	40.5437i	0.956420	+	1.65657i	0.731084	+	0.682288i	$0.239015\pi$
$599$	23.4079	+	40.5437i	0.956420	+	1.65657i	0.225337	+	0.974281i	$0.427652\pi$
$600$	−15.3434	+	5.99360i	−0.626392	+	0.244688i
$601$	−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
$606$	6.47048	−	8.03700i	0.262845	−	0.326481i
$607$	−0.691231	+	0.399082i	−0.0280562	+	0.0161983i	−0.513963	−	0.857813i	$-0.671823\pi$
$607$	−0.691231	+	0.399082i	−0.0280562	+	0.0161983i	0.485906	+	0.874011i	$0.338490\pi$
$608$	−12.8280	−	7.27680i	−0.520244	−	0.295113i
$609$	−3.39706	+	21.6335i	−0.137656	+	0.876632i
$610$	9.07224	−	5.25627i	0.367324	−	0.212820i
$611$	−1.12158			−0.0453742
$612$	0.718982	−	2.25639i	0.0290631	−	0.0912090i
$613$	22.3953			0.904538			0.452269	−	0.891882i	$-0.350615\pi$
$613$	22.3953			0.904538			0.452269	+	0.891882i	$0.350615\pi$
$614$	−32.0043	+	18.5426i	−1.29159	+	0.748318i
$615$	−6.96390	+	2.68377i	−0.280812	+	0.108220i
$616$	32.4464	−	18.9308i	1.30730	−	0.762744i
$617$	−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	$0.514945\pi$
$618$	16.4654	+	42.5318i	0.662334	+	1.71088i
$619$	−16.0602	−	9.27238i	−0.645515	−	0.372688i	0.141221	−	0.989978i	$-0.454897\pi$
$619$	−16.0602	−	9.27238i	−0.645515	−	0.372688i	−0.786736	+	0.617290i	$0.788231\pi$
$620$	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
$624$	−2.38583	+	0.936162i	−0.0955097	+	0.0374765i
$625$	−1.55907	−	2.70039i	−0.0623628	−	0.108016i
$626$	−31.9796	+	0.0486175i	−1.27816	+	0.00194314i
$627$	6.00983	+	15.5944i	0.240010	+	0.622782i
$628$	−21.6637	+	0.0658692i	−0.864475	+	0.00262847i
$629$			1.06288i			0.0423799i
$630$	−14.4245	+	13.0971i	−0.574684	+	0.521800i
$631$			44.7068i			1.77975i	0.456205	+	0.889875i	$0.349209\pi$
$631$			44.7068i			1.77975i	−0.456205	+	0.889875i	$0.650791\pi$
$632$	−11.0765	−	6.32782i	−0.440598	−	0.251707i
$633$	23.2732	+	3.65455i	0.925028	+	0.145255i
$634$	0.0372976	+	24.5336i	0.00148128	+	0.974355i
$635$	11.6684	+	20.2102i	0.463045	+	0.802018i
$636$	−1.29946	−	3.34155i	−0.0515270	−	0.132501i
$637$	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	$0.313825\pi$
$642$	3.37188	−	21.6882i	0.133078	−	0.855965i
$643$	−3.66731	+	2.11732i	−0.144624	+	0.0834990i	−0.570566	−	0.821252i	$-0.693276\pi$
$643$	−3.66731	+	2.11732i	−0.144624	+	0.0834990i	0.425942	+	0.904751i	$0.359943\pi$
$644$	6.22654	+	3.56970i	0.245360	+	0.140666i
$645$	−19.0860	−	15.4138i	−0.751511	−	0.606916i
$646$	0.729544	+	1.25918i	0.0287035	+	0.0495419i
$647$	−21.7240			−0.854060			−0.427030	−	0.904237i	$-0.640440\pi$
$647$	−21.7240			−0.854060			−0.427030	+	0.904237i	$0.640440\pi$
$648$	−23.1519	+	10.5825i	−0.909493	+	0.415719i
$649$	−0.0579675			−0.00227542
$650$	−0.881853	−	1.52206i	−0.0345891	−	0.0597003i
$651$	−24.4543	−	19.7492i	−0.958440	−	0.774031i
$652$	8.51541	+	4.88192i	0.333489	+	0.191191i
$653$	−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	$0.506321\pi$
$654$	3.48568	−	22.4201i	0.136301	−	0.876697i
$655$	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	−0.969775	−	0.244003i	$-0.921539\pi$
$659$	−7.02293	+	12.1641i	−0.273575	+	0.473845i	0.696200	+	0.717848i	$0.254873\pi$
$660$	−5.94619	−	15.2906i	−0.231455	−	0.595185i
$661$	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	$0.732608\pi$
$662$	−0.0602712	−	39.6452i	−0.00234251	−	1.54085i
$663$	0.249832	+	0.0392306i	0.00970266	+	0.00152359i
$664$	−0.338824	+	0.593091i	−0.0131489	+	0.0230164i
$665$		−	11.9726i		−	0.464279i
$666$	8.45858	−	7.68021i	0.327763	−	0.297602i
$667$		−	3.52312i		−	0.136416i
$668$	2.92048	−	0.00887983i	0.112997	−	0.000343571i
$669$	−16.0587	−	41.6693i	−0.620863	−	1.61103i
$670$	−25.1033	+	0.0381637i	−0.969825	+	0.00147439i
$671$	−10.7210	−	18.5693i	−0.413880	−	0.716862i
$672$	−34.7759	−	5.19025i	−1.34151	−	0.200218i
$673$	−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	$0.717309\pi$
$678$	−5.22738	−	13.5029i	−0.200756	−	0.518576i
$679$	2.13361	−	1.23184i	0.0818803	−	0.0472736i
$680$	−0.719926	−	1.23392i	−0.0276079	−	0.0473186i
$681$	−43.2494	+	16.6676i	−1.65732	+	0.638704i
$682$	22.9023	−	13.2691i	0.876973	−	0.508100i
$683$	19.2584			0.736903			0.368451	−	0.929647i	$-0.379888\pi$
$683$	19.2584			0.736903			0.368451	+	0.929647i	$0.379888\pi$
$684$	4.74921	−	14.9045i	0.181591	−	0.569886i
$685$	−0.152839			−0.00583968
$686$	−4.92635	+	2.85422i	−0.188089	+	0.108975i
$687$	−0.725692	+	4.62141i	−0.0276869	+	0.176318i
$688$	−0.269230	−	44.2731i	−0.0102643	−	1.68789i
$689$	0.331577	−	0.191436i	0.0126321	−	0.00729313i
$690$	1.96570	−	2.44160i	0.0748329	−	0.0929502i
$691$	−24.1291	−	13.9310i	−0.917916	−	0.529959i	−0.0349463	−	0.999389i	$-0.511126\pi$
$691$	−24.1291	−	13.9310i	−0.917916	−	0.529959i	−0.882970	+	0.469430i	$0.844459\pi$
$692$	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
$696$	6.28003	+	16.0767i	0.238044	+	0.609384i
$697$	0.664497	+	1.15094i	0.0251696	+	0.0435950i
$698$	−25.0724	+	0.0381167i	−0.949005	+	0.00144274i
$699$	19.4463	−	24.0792i	0.735526	−	0.910760i
$700$	−0.0733769	−	24.1328i	−0.00277338	−	0.912136i
$701$			28.7292i			1.08509i	0.840028	+	0.542543i	$0.182538\pi$
$701$			28.7292i			1.08509i	−0.840028	+	0.542543i	$0.817462\pi$
$702$	−1.49304	−	2.27167i	−0.0563511	−	0.0857388i
$703$			7.02082i			0.264795i
$704$	14.5693	−	25.7750i	0.549103	−	0.971431i
$705$	−4.22216	+	5.22807i	−0.159016	+	0.196900i
$706$	−0.0453470	−	29.8284i	−0.00170666	−	1.12260i
$707$	7.55814	+	13.0911i	0.284253	+	0.492341i
$708$	0.0423147	+	0.0339611i	0.00159028	+	0.00127634i
$709$	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
$714$	2.70248	+	2.17573i	0.101138	+	0.0814248i
$715$	1.51726	−	0.875990i	0.0567423	−	0.0327602i
$716$	1.72454	−	3.00807i	0.0644489	−	0.112417i
$717$	−4.55211	+	28.9891i	−0.170002	+	1.08262i
$718$	10.9470	+	18.8944i	0.408539	+	0.705133i
$719$	−30.2369			−1.12765			−0.563823	−	0.825895i	$-0.690670\pi$
$719$	−30.2369			−1.12765			−0.563823	+	0.825895i	$0.690670\pi$
$720$	−4.61765	+	14.6454i	−0.172090	+	0.545801i
$721$	−66.8174			−2.48841
$722$	−8.65142	−	14.9322i	−0.321972	−	0.555720i
$723$	−0.609217	+	0.234782i	−0.0226570	+	0.00873163i
$724$	19.6519	−	34.2783i	0.730357	−	1.27394i
$725$	−10.2592	+	5.92314i	−0.381016	+	0.219980i
$726$	−6.16097	+	2.38510i	−0.228655	+	0.0885193i
$727$	2.51826	+	1.45392i	0.0933970	+	0.0539228i	0.545971	−	0.837804i	$-0.316161\pi$
$727$	2.51826	+	1.45392i	0.0933970	+	0.0539228i	−0.452574	+	0.891727i	$0.649494\pi$
$728$	−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
$732$	−3.05307	+	19.8362i	−0.112845	+	0.733166i
$733$	−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	$0.913870\pi$
$734$	−0.00255178	−	1.67851i	−9.41878e−5	−	0.0619548i
$735$	−4.68516	−	12.1571i	−0.172815	−	0.448423i
$736$	5.65669	−	0.0429992i	0.208508	−	0.00158497i
$737$			51.3371i			1.89103i
$738$	4.35784	−	13.6047i	0.160414	−	0.500795i
$739$			37.2005i			1.36844i	0.729274	+	0.684222i	$0.239858\pi$
$739$			37.2005i			1.36844i	−0.729274	+	0.684222i	$0.760142\pi$
$740$	−0.0209557	−	6.89210i	−0.000770347	−	0.253359i
$741$	1.65025	+	0.259136i	0.0606236	+	0.00951961i
$742$	5.25266	−	0.00798544i	0.192831	−	0.000293155i
$743$	16.0794	+	27.8503i	0.589895	+	1.02173i	0.994246	+	0.107124i	$0.0341643\pi$
$743$	16.0794	+	27.8503i	0.589895	+	1.02173i	−0.404351	+	0.914604i	$0.632502\pi$
$744$	−24.4919	−	3.73155i	−0.897918	−	0.136805i
$745$	−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
$750$	−25.9013	−	4.02689i	−0.945781	−	0.147041i
$751$	−40.1801	+	23.1980i	−1.46619	+	0.846506i	−0.999285	−	0.0378003i	$-0.987965\pi$
$751$	−40.1801	+	23.1980i	−1.46619	+	0.846506i	−0.466907	+	0.884307i	$0.654632\pi$
$752$	−12.1273	+	0.0737480i	−0.442239	+	0.00268931i
$753$	−39.1254	−	31.5975i	−1.42581	−	1.15148i
$754$	−1.59480	+	0.923996i	−0.0580793	+	0.0336499i
$755$	13.4327			0.488867
$756$	−2.21287	−	37.2283i	−0.0804812	−	1.35398i
$757$	34.2669			1.24545			0.622726	−	0.782440i	$-0.286025\pi$
$757$	34.2669			1.24545			0.622726	+	0.782440i	$0.286025\pi$
$758$	37.8217	−	21.9131i	1.37375	−	0.795920i
$759$	−4.98703	−	4.02751i	−0.181018	−	0.146189i
$760$	−4.75544	−	8.15060i	−0.172498	−	0.295653i
$761$	−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	$0.377907\pi$
$762$	−44.1398	−	6.86245i	−1.59902	−	0.248600i
$763$	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
$768$	−25.7359	+	10.2794i	−0.928663	+	0.370925i
$769$	−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	$-0.397372\pi$
$770$	24.0356	−	0.0365405i	0.866183	−	0.00131683i
$771$	51.4307	+	8.07606i	1.85223	+	0.290852i
$772$	−23.8480	+	0.0725109i	−0.858310	+	0.00260972i
$773$			19.5827i			0.704342i	0.935936	+	0.352171i	$0.114556\pi$
$773$			19.5827i			0.704342i	−0.935936	+	0.352171i	$0.885444\pi$
$774$	45.8923	−	9.95476i	1.64956	−	0.357817i
$775$		−	17.0041i		−	0.610806i
$776$	0.963215	−	1.68605i	0.0345774	−	0.0605256i
$777$	6.01915	+	15.6186i	0.215936	+	0.560314i
$778$	0.0380087	+	25.0013i	0.00136268	+	0.896341i
$779$	4.38931	+	7.60250i	0.157263	+	0.272388i
$780$	−1.62077	−	0.249459i	−0.0580329	−	0.00893208i
$781$	−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
$786$	−9.30431	+	3.60198i	−0.331874	+	0.128478i
$787$	0.368525	−	0.212768i	0.0131365	−	0.00758436i	−0.493417	−	0.869793i	$-0.664252\pi$
$787$	0.368525	−	0.212768i	0.0131365	−	0.00758436i	0.506554	+	0.862208i	$0.330919\pi$
$788$	−25.6049	−	14.6794i	−0.912136	−	0.522931i
$789$	14.4396	−	5.56480i	0.514065	−	0.198112i
$790$	−4.09180	−	7.06238i	−0.145580	−	0.251268i
$791$	21.2130			0.754248
$792$	29.9358	+	9.48875i	1.06372	+	0.337168i
$793$	−2.14322			−0.0761081
$794$	18.0642	+	31.1786i	0.641075	+	1.10649i
$795$	0.355866	−	2.26625i	0.0126213	−	0.0803758i
$796$	25.5744	+	14.6619i	0.906461	+	0.519677i
$797$	−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	$0.513046\pi$
$798$	17.8511	+	14.3717i	0.631924	+	0.508753i
$799$	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
$804$	30.0766	−	37.4747i	1.06072	−	1.32163i
$805$	2.29613	+	3.97701i	0.0809279	+	0.140171i
$806$	−0.00402207	−	2.64564i	−0.000141672	−	0.0931887i
$807$	−26.9112	+	33.3226i	−0.947317	+	1.17301i
$808$	10.3450	+	5.90996i	0.363937	+	0.207912i
$809$			2.22808i			0.0783350i	0.999233	+	0.0391675i	$0.0124706\pi$
$809$			2.22808i			0.0783350i	−0.999233	+	0.0391675i	$0.987529\pi$
$810$	−16.2096	−	1.59210i	−0.569547	−	0.0559408i
$811$		−	9.52445i		−	0.334449i	−0.985919	−	0.167224i	$-0.946520\pi$
$811$		−	9.52445i		−	0.334449i	0.985919	−	0.167224i	$-0.0534804\pi$
$812$	−25.2861	+	0.0768835i	−0.887370	+	0.00269808i
$813$	−6.97345	+	8.63483i	−0.244570	+	0.302837i
$814$	−14.0946	+	0.0214276i	−0.494016	+	0.000751035i
$815$	3.14018	+	5.43895i	0.109996	+	0.190518i
$816$	2.70395	+	0.407764i	0.0946572	+	0.0142746i
$817$	−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	$0.283541\pi$
$822$	0.183465	−	0.227882i	0.00639907	−	0.00794830i
$823$	4.55420	−	2.62937i	0.158749	−	0.0916539i	−0.418521	−	0.908207i	$-0.637451\pi$
$823$	4.55420	−	2.62937i	0.158749	−	0.0916539i	0.577270	+	0.816553i	$0.304118\pi$
$824$	−45.4871	+	26.5393i	−1.58462	+	0.924542i
$825$	−3.34362	+	21.2931i	−0.116410	+	0.741332i
$826$	−0.0687797	+	0.0398495i	−0.00239315	+	0.00138654i
$827$	−41.1698			−1.43161			−0.715807	−	0.698298i	$-0.753941\pi$
$827$	−41.1698			−1.43161			−0.715807	+	0.698298i	$0.753941\pi$
$828$	1.28083	+	5.86170i	0.0445119	+	0.203708i
$829$	26.1956			0.909812			0.454906	−	0.890539i	$-0.349673\pi$
$829$	26.1956			0.909812			0.454906	+	0.890539i	$0.349673\pi$
$830$	−0.378156	+	0.219096i	−0.0131260	+	0.00760492i
$831$	32.7012	−	12.6025i	1.13439	−	0.437175i
$832$	−1.50302	−	2.54932i	−0.0521079	−	0.0883819i
$833$	−2.00924	+	1.16004i	−0.0696161	+	0.0401929i
$834$	−19.7337	−	50.9742i	−0.683321	−	1.76509i
$835$	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	−0.969121	−	0.246587i	$-0.920691\pi$
$839$	−7.84993	+	13.5965i	−0.271010	+	0.469402i	0.698111	+	0.715989i	$0.254024\pi$
$840$	−17.5667	−	14.0549i	−0.606110	−	0.484941i
$841$	−8.29380	−	14.3653i	−0.285993	−	0.495355i
$842$	−27.0220	+	0.0410806i	−0.931240	+	0.00141573i
$843$	−18.9040	−	49.0524i	−0.651088	−	1.68945i
$844$	0.0827112	+	27.2028i	0.00284704	+	0.936359i
$845$			16.4606i			0.566263i
$846$	−2.72682	−	12.5709i	−0.0937501	−	0.432196i
$847$		−	9.67887i		−	0.332570i
$848$	3.57267	−	2.09175i	0.122686	−	0.0718311i
$849$	20.9660	+	3.29225i	0.719552	+	0.112990i
$850$	0.00285331	+	1.87685i	9.78677e−5	+	0.0643754i
$851$	−1.34646	−	2.33214i	−0.0461561	−	0.0799448i
$852$	37.4900	−	14.5791i	1.28439	−	0.499471i
$853$	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	$0.487461\pi$
$858$	−0.515191	+	3.31375i	−0.0175883	+	0.113129i
$859$	3.70952	−	2.14169i	0.126567	−	0.0730735i	−0.435380	−	0.900247i	$-0.643386\pi$
$859$	3.70952	−	2.14169i	0.126567	−	0.0730735i	0.561947	+	0.827173i	$0.310053\pi$
$860$	14.0894	−	24.5758i	0.480444	−	0.838027i
$861$	16.2823	+	13.1495i	0.554900	+	0.448135i
$862$	15.4503	+	26.6670i	0.526239	+	0.908281i
$863$	50.4891			1.71867			0.859334	−	0.511415i	$-0.170878\pi$
$863$	50.4891			1.71867			0.859334	+	0.511415i	$0.170878\pi$
$864$	−16.2932	−	24.4649i	−0.554307	−	0.832312i
$865$	24.4264			0.830523
$866$	−25.4316	−	43.8946i	−0.864201	−	1.49160i
$867$	22.6975	+	18.3304i	0.770849	+	0.622534i
$868$	18.0523	−	31.4882i	0.612734	−	1.06878i
$869$	−14.4555	+	8.34588i	−0.490369	+	0.283115i
$870$	−1.69654	+	10.9123i	−0.0575182	+	0.369962i
$871$	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
$876$	−29.8446	+	11.6060i	−1.00836	+	0.392129i
$877$	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	$0.784567\pi$
$878$	−0.0128753	−	8.46909i	−0.000434519	−	0.285818i
$879$	15.2355	+	2.39239i	0.513879	+	0.0806935i
$880$	16.3482	−	9.57163i	0.551096	−	0.322660i
$881$			41.6939i			1.40470i	0.711830	+	0.702352i	$0.247867\pi$
$881$			41.6939i			1.40470i	−0.711830	+	0.702352i	$0.752133\pi$
$882$	23.7502	+	7.60763i	0.799711	+	0.256162i
$883$			29.5890i			0.995749i	0.867249	+	0.497875i	$0.165886\pi$
$883$			29.5890i			0.995749i	−0.867249	+	0.497875i	$0.834114\pi$
$884$	0.000887882		0.292015i	2.98627e−5		0.00982151i
$885$	0.0124840	+	0.0323937i	0.000419645	+	0.00108890i
$886$	8.15480	−	0.0123975i	0.273966	−	0.000416501i
$887$	−23.3218	−	40.3946i	−0.783070	−	1.35632i	−0.930145	−	0.367192i	$-0.880319\pi$
$887$	−23.3218	−	40.3946i	−0.783070	−	1.35632i	0.147075	−	0.989125i	$-0.453014\pi$
$888$	10.3012	+	8.24189i	0.345687	+	0.276580i
$889$	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
$894$	−1.75043	−	4.52155i	−0.0585431	−	0.151223i
$895$	1.92131	−	1.10927i	0.0642223	−	0.0370788i
$896$	−0.432057	−	40.5982i	−0.0144340	−	1.35629i
$897$	−0.597870	+	0.230409i	−0.0199623	+	0.00769314i
$898$	−30.7597	+	17.8216i	−1.02647	+	0.594713i
$899$	−17.8167			−0.594222
$900$	14.9156	−	13.5845i	0.497188	−	0.452817i
$901$	−0.408507			−0.0136093
$902$	−15.2490	+	8.83492i	−0.507735	+	0.294171i
$903$	−10.6724	+	67.9650i	−0.355156	+	2.26173i
$904$	14.4411	−	8.42565i	0.480305	−	0.280233i
$905$	21.8942	−	12.6406i	0.727788	−	0.420189i
$906$	−16.1244	+	20.0281i	−0.535696	+	0.665390i
$907$	−8.24112	−	4.75802i	−0.273642	−	0.157987i	0.356900	−	0.934143i	$-0.383834\pi$
$907$	−8.24112	−	4.75802i	−0.273642	−	0.157987i	−0.630542	+	0.776155i	$0.717167\pi$
$908$	−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	$-0.656303\pi$
$911$	15.9343	−	27.5989i	0.527926	−	0.914394i	0.999470	−	0.0325516i	$-0.0103633\pi$
$912$	17.8608	+	2.69347i	0.591431	+	0.0891896i
$913$	0.446882	+	0.774022i	0.0147896	+	0.0256164i
$914$	13.3622	−	0.0203141i	0.441983	−	0.000671931i
$915$	−8.06813	+	9.99031i	−0.266724	+	0.330269i
$916$	−5.40171	+	0.0164241i	−0.178478	+	0.000542668i
$917$		−	14.6170i		−	0.482697i
$918$	0.167696	+	2.89555i	0.00553478	+	0.0955673i
$919$		−	6.99591i		−	0.230774i	−0.993321	−	0.115387i	$-0.963189\pi$
$919$		−	6.99591i		−	0.230774i	0.993321	−	0.115387i	$-0.0368108\pi$
$920$	3.14277	+	1.79542i	0.103614	+	0.0591932i
$921$	28.4620	−	35.2429i	0.937856	−	1.16129i
$922$	0.0462440	+	30.4184i	0.00152297	+	1.00178i
$923$	2.14778	+	3.72007i	0.0706952	+	0.122448i
$924$	−28.7974	+	35.8808i	−0.947364	+	1.18039i
$925$	−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	$0.927415\pi$
$930$	−12.3474	−	9.94072i	−0.404887	−	0.325969i
$931$	−13.2720	+	7.66257i	−0.434971	+	0.251131i
$932$	31.0052	+	17.7754i	1.01561	+	0.582253i
$933$	5.60001	−	35.6625i	0.183336	−	1.16754i
$934$	−16.7521	−	28.9138i	−0.548144	−	0.946089i
$935$	−1.86928			−0.0611320
$936$	2.31748	−	2.11711i	0.0757493	−	0.0692000i
$937$	−44.7887			−1.46318			−0.731592	−	0.681743i	$-0.761222\pi$
$937$	−44.7887			−1.46318			−0.731592	+	0.681743i	$0.761222\pi$
$938$	35.2915	+	60.9127i	1.15231	+	1.98887i
$939$	36.5468	−	14.0845i	1.19266	−	0.459631i
$940$	−6.73183	−	3.85938i	−0.219568	−	0.125879i
$941$	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	$0.327246\pi$
$942$	24.7432	−	9.57883i	0.806176	−	0.312095i
$943$	−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	−0.580852	−	0.814009i	$-0.697281\pi$
$947$	12.7564	−	22.0947i	0.414526	−	0.717980i	0.995379	+	0.0960286i	$0.0306140\pi$
$948$	15.4417	+	2.37669i	0.501522	+	0.0771914i
$949$	−1.70978	−	2.96143i	−0.0555020	−	0.0961322i
$950$	0.0188474	+	12.3974i	0.000611491	+	0.402226i
$951$	−10.8052	−	28.0374i	−0.350381	−	0.909176i
$952$	−1.98726	+	3.47857i	−0.0644073	+	0.112741i
$953$		−	42.7058i		−	1.38338i	−0.722196	−	0.691689i	$-0.756867\pi$
$953$		−	42.7058i		−	1.38338i	0.722196	−	0.691689i	$-0.243133\pi$
$954$	2.95180	+	3.25096i	0.0955680	+	0.105254i
$955$			29.7664i			0.963220i
$956$	−33.8838	+	0.103025i	−1.09588	+	0.00333207i
$957$	22.3107	+	3.50341i	0.721203	+	0.113249i
$958$	34.5912	−	0.0525878i	1.11759	−	0.00169903i
$959$	0.214305	+	0.371186i	0.00692026	+	0.0119862i
$960$	−17.5414	−	2.59077i	−0.566146	−	0.0836168i
$961$	−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
$966$	−8.68593	−	1.35041i	−0.279465	−	0.0434486i
$967$	−15.5707	+	8.98975i	−0.500720	+	0.289091i	−0.729011	−	0.684502i	$-0.760020\pi$
$967$	−15.5707	+	8.98975i	−0.500720	+	0.289091i	0.228291	+	0.973593i	$0.426686\pi$
$968$	−3.84437	−	6.58907i	−0.123563	−	0.211781i
$969$	−1.38661	−	1.11982i	−0.0445442	−	0.0359737i
$970$	1.07503	−	0.622849i	0.0345171	−	0.0199985i
$971$	−40.8665			−1.31147			−0.655734	−	0.754992i	$-0.727641\pi$
$971$	−40.8665			−1.31147			−0.655734	+	0.754992i	$0.727641\pi$
$972$	21.8315	−	22.2573i	0.700245	−	0.713903i
$973$	80.0804			2.56726
$974$	−39.7970	+	23.0576i	−1.27518	+	0.738812i
$975$	1.67609	+	1.35360i	0.0536779	+	0.0433500i
$976$	−23.1741	+	0.140925i	−0.741786	+	0.00451090i
$977$	−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	$0.365432\pi$
$978$	−11.8789	−	1.84682i	−0.379844	−	0.0590546i
$979$	−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	−0.716695	−	0.697387i	$-0.754346\pi$
$983$	7.70050	−	13.3377i	0.245608	−	0.425405i	0.962302	+	0.271982i	$0.0876791\pi$
$984$	16.3074	+	2.48456i	0.519861	+	0.0792050i
$985$	−9.44217	−	16.3543i	−0.300852	−	0.521092i
$986$	1.96654	−	0.00298967i	0.0626275	−	9.52104e-5i
$987$	18.6171	+	2.92341i	0.592588	+	0.0930530i
$988$	0.00586487	+	1.92889i	0.000186586	+	0.0613662i
$989$		−	11.0685i		−	0.351957i
$990$	13.5071	+	14.8760i	0.429284	+	0.472791i
$991$			14.9086i			0.473589i	0.971560	+	0.236794i	$0.0760968\pi$
$991$			14.9086i			0.473589i	−0.971560	+	0.236794i	$0.923903\pi$
$992$	−0.217451	−	28.6064i	−0.00690406	−	0.908254i
$993$	17.4606	+	45.3072i	0.554097	+	1.43778i
$994$	0.0895913	+	58.9314i	0.00284166	+	1.86919i
$995$	9.43094	+	16.3349i	0.298981	+	0.517850i
$996$	0.127260	−	0.826827i	0.00403240	−	0.0261990i
$997$	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.b.47.23	yes	132
4.3	odd	2		828.2.o.a.47.1	✓	132
9.5	odd	6		828.2.o.a.599.1	yes	132
36.23	even	6	inner	828.2.o.b.599.23	yes	132

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

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)

\(f(q)\)	\(=\)	\(q+(-0.708968 - 1.22367i) q^{2} +(1.34750 + 1.08823i) q^{3} +(-0.994729 + 1.73508i) q^{4} +(-1.10823 + 0.639837i) q^{5} +(0.376303 - 2.42041i) q^{6} +(3.10783 + 1.79431i) q^{7} +(2.82840 - 0.0128998i) q^{8} +(0.631500 + 2.93278i) q^{9} +O(q^{10})\)	\(q+(-0.708968 - 1.22367i) q^{2} +(1.34750 + 1.08823i) q^{3} +(-0.994729 + 1.73508i) q^{4} +(-1.10823 + 0.639837i) q^{5} +(0.376303 - 2.42041i) 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} +(-3.22857 + 1.25552i) q^{12} +(-0.184963 - 0.320366i) q^{13} +(-0.00771544 - 5.07506i) q^{14} +(-2.18963 - 0.343833i) q^{15} +(-2.02103 - 3.45188i) q^{16} +0.394694i q^{17} +(3.14104 - 2.85199i) q^{18} +2.60714i q^{19} +(-0.00778176 - 2.55934i) q^{20} +(2.23517 + 5.79987i) q^{21} +(-5.23394 + 0.00795698i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(3.82530 + 3.06057i) 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} +(1.13164 + 2.92315i) q^{30} +(-4.37957 + 2.52854i) q^{31} +(-2.79111 + 4.92034i) q^{32} +(5.98144 - 2.30515i) q^{33} +(0.482975 - 0.279826i) q^{34} -4.59226 q^{35} +(-5.71679 - 1.82162i) q^{36} +2.69292 q^{37} +(3.19027 - 1.84838i) q^{38} +(0.0993949 - 0.632975i) q^{39} +(-3.12626 + 1.82401i) q^{40} +(2.91603 - 1.68357i) q^{41} +(5.51245 - 6.84703i) 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} +(1.03311 - 6.85074i) q^{48} +(2.93908 + 5.09063i) q^{49} +(4.75520 - 0.00722916i) q^{50} +(-0.429519 + 0.531850i) q^{51} +(0.739850 - 0.00224954i) q^{52} +1.03499i q^{53} +(7.33618 - 0.424875i) q^{54} +4.73602i q^{55} +(8.81333 + 5.03492i) q^{56} +(-2.83717 + 3.51311i) q^{57} +(-0.00757464 - 4.98244i) q^{58} +(-0.00783141 - 0.0135644i) q^{59} +(2.77467 - 3.45717i) 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} +(-7.06138 - 5.68502i) q^{66} +(-12.0129 + 6.93565i) q^{67} +(-0.684828 - 0.392614i) q^{68} +(0.268688 - 1.71108i) q^{69} +(3.25576 + 5.61940i) q^{70} -11.6120 q^{71} +(1.82397 + 8.28693i) q^{72} +9.24391 q^{73} +(-1.90920 - 3.29525i) q^{74} +(-5.43432 + 2.09430i) q^{75} +(-4.52360 - 2.59340i) q^{76} +(11.5020 - 6.64066i) q^{77} +(-0.845020 + 0.327133i) 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} +(-12.2866 - 1.89109i) q^{84} +(-0.252540 - 0.437412i) q^{85} +(-0.0237970 - 15.6532i) q^{86} +(2.19438 + 5.69402i) q^{87} +(5.19255 - 9.08924i) q^{88} -9.36518i q^{89} +(-1.65618 + 5.17042i) q^{90} -1.32752i q^{91} +(1.99999 - 0.00608105i) q^{92} +(-8.65310 - 1.35878i) q^{93} +(-4.28774 + 0.00651850i) q^{94} +(-1.66814 - 2.88931i) q^{95} +(-9.11548 + 3.59277i) q^{96} +(0.343263 - 0.594549i) q^{97} +(4.14553 - 7.20555i) q^{98} +(10.5685 + 3.40302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{6} + 9 q^{8} + 2 q^{9}+O(q^{10}) \) 132 * q + 3 * q^6 + 9 * q^8 + 2 * q^9	\( 132 q + 3 q^{6} + 9 q^{8} + 2 q^{9} + 13 q^{12} - 15 q^{14} - 7 q^{18} - 21 q^{20} - 66 q^{23} - 37 q^{24} + 66 q^{25} + 54 q^{26} - 12 q^{27} - 39 q^{30} + 30 q^{32} - 22 q^{33} - 3 q^{36} + 24 q^{39} - 30 q^{41} + 53 q^{42} + 13 q^{48} + 66 q^{49} + 32 q^{51} - 9 q^{52} + 12 q^{54} - 42 q^{56} - 6 q^{57} - 36 q^{58} - 36 q^{59} - 34 q^{60} - 63 q^{62} + 20 q^{63} - 9 q^{64} - 78 q^{66} - 15 q^{68} + 78 q^{70} - 48 q^{72} - 12 q^{73} - 21 q^{74} - 48 q^{75} + 87 q^{76} + 46 q^{78} - 72 q^{80} - 10 q^{81} - 9 q^{82} + 71 q^{84} - 24 q^{86} - 96 q^{87} - 84 q^{88} + 47 q^{90} - 12 q^{93} - 42 q^{94} - 72 q^{96} - 6 q^{97} - 20 q^{99}+O(q^{100}) \) 132 * q + 3 * q^6 + 9 * q^8 + 2 * q^9 + 13 * q^12 - 15 * q^14 - 7 * q^18 - 21 * q^20 - 66 * q^23 - 37 * q^24 + 66 * q^25 + 54 * q^26 - 12 * q^27 - 39 * q^30 + 30 * q^32 - 22 * q^33 - 3 * q^36 + 24 * q^39 - 30 * q^41 + 53 * q^42 + 13 * q^48 + 66 * q^49 + 32 * q^51 - 9 * q^52 + 12 * q^54 - 42 * q^56 - 6 * q^57 - 36 * q^58 - 36 * q^59 - 34 * q^60 - 63 * q^62 + 20 * q^63 - 9 * q^64 - 78 * q^66 - 15 * q^68 + 78 * q^70 - 48 * q^72 - 12 * q^73 - 21 * q^74 - 48 * q^75 + 87 * q^76 + 46 * q^78 - 72 * q^80 - 10 * q^81 - 9 * q^82 + 71 * q^84 - 24 * q^86 - 96 * q^87 - 84 * q^88 + 47 * q^90 - 12 * q^93 - 42 * q^94 - 72 * q^96 - 6 * q^97 - 20 * q^99

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