LMFDB - Embedded newform 357.2.bh.a.331.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(25,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([0, 16, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bh (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$24$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			331.16
Character	$\chi$	$=$	357.331
Dual form			357.2.bh.a.151.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.225292 + 0.840803i) q^{2} +(0.991445 - 0.130526i) q^{3} +(1.07586 - 0.621147i) q^{4} +(0.173030 - 0.132771i) q^{5} +(0.333112 + 0.804203i) q^{6} +(-1.09410 - 2.40893i) q^{7} +(1.99567 + 1.99567i) q^{8} +(0.965926 - 0.258819i) q^{9} +(0.150616 + 0.115572i) q^{10} +(0.655950 - 0.854851i) q^{11} +(0.985578 - 0.756261i) q^{12} +1.49163i q^{13} +(1.77894 - 1.46263i) q^{14} +(0.154220 - 0.154220i) q^{15} +(0.0139413 - 0.0241470i) q^{16} +(2.16513 + 3.50888i) q^{17} +(0.435232 + 0.753843i) q^{18} +(-1.37549 - 5.13340i) q^{19} +(0.103686 - 0.250320i) q^{20} +(-1.39917 - 2.24551i) q^{21} +(0.866542 + 0.358933i) q^{22} +(-1.38324 - 0.182107i) q^{23} +(2.23908 + 1.71811i) q^{24} +(-1.28178 + 4.78368i) q^{25} +(-1.25417 + 0.336053i) q^{26} +(0.923880 - 0.382683i) q^{27} +(-2.67339 - 1.91207i) q^{28} +(2.90262 + 1.20230i) q^{29} +(0.164413 + 0.0949240i) q^{30} +(-7.12294 + 0.937752i) q^{31} +(5.47570 + 1.46721i) q^{32} +(0.538758 - 0.933156i) q^{33} +(-2.46249 + 2.61097i) q^{34} +(-0.509148 - 0.271554i) q^{35} +(0.878435 - 0.878435i) q^{36} +(-1.20885 - 1.57540i) q^{37} +(4.00629 - 2.31303i) q^{38} +(0.194697 + 1.47887i) q^{39} +(0.610277 + 0.0803444i) q^{40} +(-8.81025 + 3.64932i) q^{41} +(1.57281 - 1.68232i) q^{42} +(3.75109 + 3.75109i) q^{43} +(0.174721 - 1.32714i) q^{44} +(0.132771 - 0.173030i) q^{45} +(-0.158518 - 1.20406i) q^{46} +(0.912015 + 0.526552i) q^{47} +(0.0106702 - 0.0257601i) q^{48} +(-4.60590 + 5.27121i) q^{49} -4.31091 q^{50} +(2.60461 + 3.19625i) q^{51} +(0.926522 + 1.60478i) q^{52} +(1.50527 + 0.403336i) q^{53} +(0.529904 + 0.690585i) q^{54} -0.235006i q^{55} +(2.62397 - 6.99087i) q^{56} +(-2.03376 - 4.90994i) q^{57} +(-0.356963 + 2.71140i) q^{58} +(-2.80403 + 10.4648i) q^{59} +(0.0701255 - 0.261712i) q^{60} +(0.609357 - 4.62853i) q^{61} +(-2.39321 - 5.77772i) q^{62} +(-1.68029 - 2.04368i) q^{63} +4.87877i q^{64} +(0.198045 + 0.258097i) q^{65} +(0.905978 + 0.242756i) q^{66} +(-4.99373 - 8.64940i) q^{67} +(4.50890 + 2.43019i) q^{68} -1.39518 q^{69} +(0.113616 - 0.489272i) q^{70} +(2.61157 - 6.30489i) q^{71} +(2.44418 + 1.41115i) q^{72} +(-0.317144 - 2.40895i) q^{73} +(1.05226 - 1.37133i) q^{74} +(-0.646422 + 4.91006i) q^{75} +(-4.66842 - 4.66842i) q^{76} +(-2.77695 - 0.644849i) q^{77} +(-1.19957 + 0.496880i) q^{78} +(-8.57873 - 1.12941i) q^{79} +(-0.000793754 - 0.00602916i) q^{80} +(0.866025 - 0.500000i) q^{81} +(-5.05324 - 6.58551i) q^{82} +(-7.10788 + 7.10788i) q^{83} +(-2.90010 - 1.54677i) q^{84} +(0.840509 + 0.319676i) q^{85} +(-2.30883 + 3.99902i) q^{86} +(3.03472 + 0.813151i) q^{87} +(3.01505 - 0.396939i) q^{88} +(-1.70711 - 0.985601i) q^{89} +(0.175397 + 0.0726516i) q^{90} +(3.59324 - 1.63199i) q^{91} +(-1.60129 + 0.663276i) q^{92} +(-6.93960 + 1.85946i) q^{93} +(-0.237256 + 0.885453i) q^{94} +(-0.919566 - 0.705608i) q^{95} +(5.62037 + 0.739935i) q^{96} +(-11.0570 - 4.57996i) q^{97} +(-5.46972 - 2.68509i) q^{98} +(0.412348 - 0.995495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 8 q^{5} + 8 q^{11} - 80 q^{14} + 96 q^{16} - 16 q^{17} + 16 q^{22} + 8 q^{25} - 64 q^{26} - 88 q^{28} - 40 q^{32} - 32 q^{33} - 32 q^{35} + 32 q^{37} - 64 q^{40} - 64 q^{41} - 56 q^{42} - 32 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) $ 192 * q - 8 * q^5 + 8 * q^11 - 80 * q^14 + 96 * q^16 - 16 * q^17 + 16 * q^22 + 8 * q^25 - 64 * q^26 - 88 * q^28 - 40 * q^32 - 32 * q^33 - 32 * q^35 + 32 * q^37 - 64 * q^40 - 64 * q^41 - 56 * q^42 - 32 * q^43 + 32 * q^44 + 56 * q^49 + 64 * q^50 + 96 * q^52 + 64 * q^53 - 152 * q^56 - 32 * q^58 - 16 * q^59 + 40 * q^61 - 112 * q^62 + 32 * q^65 - 16 * q^67 + 48 * q^68 - 128 * q^69 - 120 * q^70 + 96 * q^71 + 8 * q^73 - 64 * q^74 - 112 * q^76 + 32 * q^77 - 16 * q^78 + 16 * q^79 + 192 * q^80 - 8 * q^82 - 16 * q^83 + 48 * q^84 - 64 * q^86 + 24 * q^87 - 136 * q^88 - 160 * q^92 + 48 * q^93 - 64 * q^94 - 104 * q^95 - 48 * q^96 - 96 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{8}\right)$	$1$

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 $

$2$	0.225292	+	0.840803i	0.159306	+	0.594537i	0.998698	+	0.0510113i	$0.0162444\pi$
$2$	0.225292	+	0.840803i	0.159306	+	0.594537i	−0.839392	+	0.543526i	$0.817089\pi$
$3$	0.991445	−	0.130526i	0.572411	−	0.0753593i
$3$	0.991445	−	0.130526i	0.572411	−	0.0753593i
$4$	1.07586	−	0.621147i	0.537929	−	0.310574i
$5$	0.173030	−	0.132771i	0.0773815	−	0.0593769i	−0.569346	−	0.822098i	$-0.692804\pi$
$5$	0.173030	−	0.132771i	0.0773815	−	0.0593769i	0.646728	+	0.762721i	$0.276137\pi$
$6$	0.333112	+	0.804203i	0.135992	+	0.328315i
$7$	−1.09410	−	2.40893i	−0.413530	−	0.910490i
$7$	−1.09410	−	2.40893i	−0.413530	−	0.910490i
$8$	1.99567	+	1.99567i	0.705574	+	0.705574i
$9$	0.965926	−	0.258819i	0.321975	−	0.0862730i
$10$	0.150616	+	0.115572i	0.0476291	+	0.0365471i
$11$	0.655950	−	0.854851i	0.197776	−	0.257747i	−0.683928	−	0.729550i	$-0.739730\pi$
$11$	0.655950	−	0.854851i	0.197776	−	0.257747i	0.881704	+	0.471802i	$0.156396\pi$
$12$	0.985578	−	0.756261i	0.284512	−	0.218314i
$13$			1.49163i			0.413704i	0.978372	+	0.206852i	$0.0663218\pi$
$13$			1.49163i			0.413704i	−0.978372	+	0.206852i	$0.933678\pi$
$14$	1.77894	−	1.46263i	0.475443	−	0.390905i
$15$	0.154220	−	0.154220i	0.0398194	−	0.0398194i
$16$	0.0139413	−	0.0241470i	0.00348532	−	0.00603675i
$17$	2.16513	+	3.50888i	0.525121	+	0.851028i
$17$	2.16513	+	3.50888i	0.525121	+	0.851028i
$18$	0.435232	+	0.753843i	0.102585	+	0.177683i
$19$	−1.37549	−	5.13340i	−0.315559	−	1.17768i	−0.923468	−	0.383675i	$-0.874658\pi$
$19$	−1.37549	−	5.13340i	−0.315559	−	1.17768i	0.607909	−	0.794006i	$-0.292008\pi$
$20$	0.103686	−	0.250320i	0.0231849	−	0.0559732i
$21$	−1.39917	−	2.24551i	−0.305323	−	0.490011i
$22$	0.866542	+	0.358933i	0.184747	+	0.0765248i
$23$	−1.38324	−	0.182107i	−0.288426	−	0.0379720i	−0.0150751	−	0.999886i	$-0.504799\pi$
$23$	−1.38324	−	0.182107i	−0.288426	−	0.0379720i	−0.273351	+	0.961914i	$0.588132\pi$
$24$	2.23908	+	1.71811i	0.457050	+	0.350707i
$25$	−1.28178	+	4.78368i	−0.256357	+	0.956736i
$26$	−1.25417	+	0.336053i	−0.245962	+	0.0659054i
$27$	0.923880	−	0.382683i	0.177801	−	0.0736475i
$28$	−2.67339	−	1.91207i	−0.505224	−	0.361348i
$29$	2.90262	+	1.20230i	0.539003	+	0.223262i	0.635541	−	0.772067i	$-0.280777\pi$
$29$	2.90262	+	1.20230i	0.539003	+	0.223262i	−0.0965382	+	0.995329i	$0.530777\pi$
$30$	0.164413	+	0.0949240i	0.0300176	+	0.0173307i
$31$	−7.12294	+	0.937752i	−1.27932	+	0.168425i	−0.739385	−	0.673283i	$-0.764884\pi$
$31$	−7.12294	+	0.937752i	−1.27932	+	0.168425i	−0.539932	+	0.841708i	$0.681550\pi$
$32$	5.47570	+	1.46721i	0.967977	+	0.259369i
$33$	0.538758	−	0.933156i	0.0937857	−	0.162442i
$34$	−2.46249	+	2.61097i	−0.422313	+	0.447777i
$35$	−0.509148	−	0.271554i	−0.0860617	−	0.0459010i
$36$	0.878435	−	0.878435i	0.146406	−	0.146406i
$37$	−1.20885	−	1.57540i	−0.198733	−	0.258994i	0.683347	−	0.730094i	$-0.260524\pi$
$37$	−1.20885	−	1.57540i	−0.198733	−	0.258994i	−0.882080	+	0.471100i	$0.843857\pi$
$38$	4.00629	−	2.31303i	0.649905	−	0.375223i
$39$	0.194697	+	1.47887i	0.0311764	+	0.236809i
$40$	0.610277	+	0.0803444i	0.0964932	+	0.0127036i
$41$	−8.81025	+	3.64932i	−1.37593	+	0.569929i	−0.943390	−	0.331686i	$-0.892382\pi$
$41$	−8.81025	+	3.64932i	−1.37593	+	0.569929i	−0.432540	+	0.901615i	$0.642382\pi$
$42$	1.57281	−	1.68232i	0.242690	−	0.259588i
$43$	3.75109	+	3.75109i	0.572036	+	0.572036i	0.932697	−	0.360661i	$-0.117449\pi$
$43$	3.75109	+	3.75109i	0.572036	+	0.572036i	−0.360661	+	0.932697i	$0.617449\pi$
$44$	0.174721	−	1.32714i	0.0263402	−	0.200074i
$45$	0.132771	−	0.173030i	0.0197923	−	0.0257938i
$46$	−0.158518	−	1.20406i	−0.0233722	−	0.177529i
$47$	0.912015	+	0.526552i	0.133031	+	0.0768055i	0.565039	−	0.825064i	$-0.308861\pi$
$47$	0.912015	+	0.526552i	0.133031	+	0.0768055i	−0.432007	+	0.901870i	$0.642195\pi$
$48$	0.0106702	−	0.0257601i	0.00154011	−	0.00371815i
$49$	−4.60590	+	5.27121i	−0.657986	+	0.753030i
$50$	−4.31091			−0.609655
$51$	2.60461	+	3.19625i	0.364718	+	0.447565i
$52$	0.926522	+	1.60478i	0.128485	+	0.222543i
$53$	1.50527	+	0.403336i	0.206765	+	0.0554025i	0.360715	−	0.932676i	$-0.382533\pi$
$53$	1.50527	+	0.403336i	0.206765	+	0.0554025i	−0.153950	+	0.988079i	$0.549199\pi$
$54$	0.529904	+	0.690585i	0.0721108	+	0.0939767i
$55$		−	0.235006i		−	0.0316882i
$56$	2.62397	−	6.99087i	0.350643	−	0.934195i
$57$	−2.03376	−	4.90994i	−0.269379	−	0.650338i
$58$	−0.356963	+	2.71140i	−0.0468715	+	0.356024i
$59$	−2.80403	+	10.4648i	−0.365054	+	1.36240i	0.502294	+	0.864697i	$0.332490\pi$
$59$	−2.80403	+	10.4648i	−0.365054	+	1.36240i	−0.867348	+	0.497703i	$0.834177\pi$
$60$	0.0701255	−	0.261712i	0.00905317	−	0.0337869i
$61$	0.609357	−	4.62853i	0.0780202	−	0.592622i	−0.907120	−	0.420872i	$-0.861724\pi$
$61$	0.609357	−	4.62853i	0.0780202	−	0.592622i	0.985140	−	0.171751i	$-0.0549424\pi$
$62$	−2.39321	−	5.77772i	−0.303938	−	0.733771i
$63$	−1.68029	−	2.04368i	−0.211697	−	0.257479i
$64$			4.87877i			0.609847i
$65$	0.198045	+	0.258097i	0.0245645	+	0.0320130i
$66$	0.905978	+	0.242756i	0.111518	+	0.0298812i
$67$	−4.99373	−	8.64940i	−0.610081	−	1.05669i	−0.991226	−	0.132177i	$-0.957803\pi$
$67$	−4.99373	−	8.64940i	−0.610081	−	1.05669i	0.381145	−	0.924515i	$-0.375530\pi$
$68$	4.50890	+	2.43019i	0.546784	+	0.294704i
$69$	−1.39518			−0.167960
$70$	0.113616	−	0.489272i	0.0135797	−	0.0584792i
$71$	2.61157	−	6.30489i	0.309936	−	0.748253i	−0.689770	−	0.724028i	$-0.742288\pi$
$71$	2.61157	−	6.30489i	0.309936	−	0.748253i	0.999707	−	0.0242244i	$-0.00771161\pi$
$72$	2.44418	+	1.41115i	0.288050	+	0.166305i
$73$	−0.317144	−	2.40895i	−0.0371190	−	0.281946i	−0.999931	−	0.0117732i	$-0.996252\pi$
$73$	−0.317144	−	2.40895i	−0.0371190	−	0.281946i	0.962812	−	0.270173i	$-0.0870810\pi$
$74$	1.05226	−	1.37133i	0.122322	−	0.159414i
$75$	−0.646422	+	4.91006i	−0.0746424	+	0.566965i
$76$	−4.66842	−	4.66842i	−0.535505	−	0.535505i
$77$	−2.77695	−	0.644849i	−0.316463	−	0.0734873i
$78$	−1.19957	+	0.496880i	−0.135825	+	0.0562605i
$79$	−8.57873	−	1.12941i	−0.965182	−	0.127069i	−0.368572	−	0.929599i	$-0.620153\pi$
$79$	−8.57873	−	1.12941i	−0.965182	−	0.127069i	−0.596611	+	0.802531i	$0.703486\pi$
$80$	−0.000793754	−	0.00602916i	−8.87443e−5	−	0.000674080i
$81$	0.866025	−	0.500000i	0.0962250	−	0.0555556i
$82$	−5.05324	−	6.58551i	−0.558037	−	0.727248i
$83$	−7.10788	+	7.10788i	−0.780191	+	0.780191i	−0.979863	−	0.199672i	$-0.936012\pi$
$83$	−7.10788	+	7.10788i	−0.780191	+	0.780191i	0.199672	+	0.979863i	$0.436012\pi$
$84$	−2.90010	−	1.54677i	−0.316427	−	0.168766i
$85$	0.840509	+	0.319676i	0.0911660	+	0.0346738i
$86$	−2.30883	+	3.99902i	−0.248968	+	0.431225i
$87$	3.03472	+	0.813151i	0.325356	+	0.0871789i
$88$	3.01505	−	0.396939i	0.321406	−	0.0423139i
$89$	−1.70711	−	0.985601i	−0.180953	−	0.104474i	0.406787	−	0.913523i	$-0.366649\pi$
$89$	−1.70711	−	0.985601i	−0.180953	−	0.104474i	−0.587741	+	0.809049i	$0.699982\pi$
$90$	0.175397	+	0.0726516i	0.0184884	+	0.00765816i
$91$	3.59324	−	1.63199i	0.376673	−	0.171079i
$92$	−1.60129	+	0.663276i	−0.166946	+	0.0691513i
$93$	−6.93960	+	1.85946i	−0.719603	+	0.192817i
$94$	−0.237256	+	0.885453i	−0.0244711	+	0.0913275i
$95$	−0.919566	−	0.705608i	−0.0943455	−	0.0723939i
$96$	5.62037	+	0.739935i	0.573626	+	0.0755193i
$97$	−11.0570	−	4.57996i	−1.12267	−	0.465025i	−0.257386	−	0.966309i	$-0.582861\pi$
$97$	−11.0570	−	4.57996i	−1.12267	−	0.465025i	−0.865283	+	0.501284i	$0.832861\pi$
$98$	−5.46972	−	2.68509i	−0.552526	−	0.271235i
$99$	0.412348	−	0.995495i	0.0414425	−	0.100051i
$100$	1.59235	+	5.94274i	0.159235	+	0.594274i
$101$	−6.66428	−	11.5429i	−0.663121	−	1.14856i	−0.979791	−	0.200023i	$-0.935898\pi$
$101$	−6.66428	−	11.5429i	−0.663121	−	1.14856i	0.316670	−	0.948536i	$-0.397435\pi$
$102$	−2.10062	+	2.91005i	−0.207992	+	0.288138i
$103$	7.42358	−	12.8580i	0.731467	−	1.26694i	−0.224789	−	0.974407i	$-0.572169\pi$
$103$	7.42358	−	12.8580i	0.731467	−	1.26694i	0.956256	−	0.292530i	$-0.0944973\pi$
$104$	−2.97680	+	2.97680i	−0.291899	+	0.291899i
$105$	−0.540237	−	0.202774i	−0.0527217	−	0.0197887i
$106$			1.35650i			0.131755i
$107$	9.30206	−	7.13772i	0.899264	−	0.690030i	−0.0519206	−	0.998651i	$-0.516534\pi$
$107$	9.30206	−	7.13772i	0.899264	−	0.690030i	0.951185	+	0.308621i	$0.0998676\pi$
$108$	0.756261	−	0.985578i	0.0727712	−	0.0948373i
$109$	8.90628	+	6.83403i	0.853067	+	0.654581i	0.939828	−	0.341648i	$-0.110985\pi$
$109$	8.90628	+	6.83403i	0.853067	+	0.654581i	−0.0867613	+	0.996229i	$0.527652\pi$
$110$	0.197594	−	0.0529451i	0.0188398	−	0.00504812i
$111$	−1.40414	−	1.40414i	−0.133275	−	0.133275i
$112$	−0.0734216	−	0.00716440i	−0.00693769	−	0.000676972i
$113$	−2.43989	−	5.89041i	−0.229525	−	0.554123i	0.766594	−	0.642132i	$-0.221950\pi$
$113$	−2.43989	−	5.89041i	−0.229525	−	0.554123i	−0.996120	+	0.0880084i	$0.971950\pi$
$114$	3.67010	−	2.81617i	0.343736	−	0.263758i
$115$	−0.263522	+	0.152144i	−0.0245735	+	0.0141875i
$116$	3.86962	−	0.509445i	0.359285	−	0.0473007i
$117$	0.386062	+	1.44080i	0.0356915	+	0.133202i
$118$	−9.43055			−0.868153
$119$	6.08378	−	9.05470i	0.557700	−	0.830043i
$120$	0.615543			0.0561911
$121$	2.54651	+	9.50370i	0.231501	+	0.863973i
$122$	4.02896	−	0.530423i	0.364765	−	0.0480222i
$123$	−8.25854	+	4.76807i	−0.744648	+	0.429922i
$124$	−7.08079	+	5.43328i	−0.635873	+	0.487923i
$125$	0.830662	+	2.00540i	0.0742967	+	0.179368i
$126$	1.33977	−	1.87322i	0.119356	−	0.166880i
$127$	−0.377480	−	0.377480i	−0.0334959	−	0.0334959i	0.690160	−	0.723656i	$-0.257540\pi$
$127$	−0.377480	−	0.377480i	−0.0334959	−	0.0334959i	−0.723656	+	0.690160i	$0.757540\pi$
$128$	6.84932	−	1.83527i	0.605400	−	0.162216i
$129$	4.20861	+	3.22938i	0.370548	+	0.284331i
$130$	−0.172391	+	0.224664i	−0.0151197	+	0.0197043i
$131$	1.65277	−	1.26822i	0.144403	−	0.110805i	−0.534033	−	0.845463i	$-0.679324\pi$
$131$	1.65277	−	1.26822i	0.144403	−	0.110805i	0.678437	+	0.734659i	$0.262658\pi$
$132$		−	1.33859i		−	0.116509i
$133$	−10.8611	+	8.92989i	−0.941775	+	0.774320i
$134$	6.14739	−	6.14739i	0.531053	−	0.531053i
$135$	0.109050	−	0.188880i	0.00938553	−	0.0162562i
$136$	−2.68168	+	11.3234i	−0.229952	+	0.970975i
$137$	9.73326	+	16.8585i	0.831569	+	1.44032i	0.896794	+	0.442449i	$0.145890\pi$
$137$	9.73326	+	16.8585i	0.831569	+	1.44032i	−0.0652251	+	0.997871i	$0.520777\pi$
$138$	−0.314323	−	1.17307i	−0.0267570	−	0.0998584i
$139$	0.0370575	−	0.0894647i	0.00314317	−	0.00758829i	−0.922300	−	0.386474i	$-0.873693\pi$
$139$	0.0370575	−	0.0894647i	0.00314317	−	0.00758829i	0.925443	+	0.378886i	$0.123693\pi$
$140$	−0.716446	+	0.0241022i	−0.0605507	+	0.00203701i
$141$	0.972942	+	0.403006i	0.0819365	+	0.0339392i
$142$	5.88954	+	0.775372i	0.494239	+	0.0650678i
$143$	1.27512	+	0.978435i	0.106631	+	0.0818209i
$144$	0.00721654	−	0.0269325i	0.000601378	−	0.00224437i
$145$	0.661872	−	0.177348i	0.0549655	−	0.0147280i
$146$	1.95400	−	0.809374i	0.161714	−	0.0669843i
$147$	−3.87847	+	5.82731i	−0.319890	+	0.480628i
$148$	−2.27910	−	0.944035i	−0.187341	−	0.0775992i
$149$	−11.3521	−	6.55412i	−0.929998	−	0.536935i	−0.0431870	−	0.999067i	$-0.513751\pi$
$149$	−11.3521	−	6.55412i	−0.929998	−	0.536935i	−0.886811	+	0.462132i	$0.847084\pi$
$150$	−4.27403	+	0.562687i	−0.348973	+	0.0459432i
$151$	19.8391	+	5.31587i	1.61448	+	0.432599i	0.949374	−	0.314148i	$-0.101719\pi$
$151$	19.8391	+	5.31587i	1.61448	+	0.432599i	0.665108	+	0.746747i	$0.268386\pi$
$152$	7.49952	−	12.9896i	0.608292	−	1.05359i
$153$	2.99952	+	2.82894i	0.242497	+	0.228706i
$154$	−0.0834355	−	2.48015i	−0.00672343	−	0.199856i
$155$	−1.10798	+	1.10798i	−0.0889949	+	0.0889949i
$156$	1.12806	+	1.47012i	0.0903172	+	0.117704i
$157$	5.47198	−	3.15925i	0.436711	−	0.252135i	−0.265490	−	0.964114i	$-0.585534\pi$
$157$	5.47198	−	3.15925i	0.436711	−	0.252135i	0.702202	+	0.711978i	$0.252200\pi$
$158$	−0.983111	−	7.46747i	−0.0782121	−	0.594080i
$159$	1.54504	+	0.203408i	0.122530	+	0.0161313i
$160$	1.14227	−	0.473142i	0.0903040	−	0.0374051i
$161$	1.07472	+	3.53138i	0.0846997	+	0.278312i
$162$	0.615510	+	0.615510i	0.0483591	+	0.0483591i
$163$	−0.593869	+	4.51088i	−0.0465154	+	0.353319i	0.952321	+	0.305097i	$0.0986889\pi$
$163$	−0.593869	+	4.51088i	−0.0465154	+	0.353319i	−0.998837	+	0.0482223i	$0.984644\pi$
$164$	−7.21181	+	9.39861i	−0.563148	+	0.733908i
$165$	−0.0306745	−	0.232996i	−0.00238800	−	0.0181387i
$166$	−7.57767	−	4.37497i	−0.588142	−	0.339564i
$167$	−6.85435	+	16.5479i	−0.530406	+	1.28051i	0.400849	+	0.916144i	$0.368715\pi$
$167$	−6.85435	+	16.5479i	−0.530406	+	1.28051i	−0.931255	+	0.364369i	$0.881285\pi$
$168$	1.68903	−	7.27356i	0.130311	−	0.561168i
$169$	10.7750			0.828849
$170$	−0.0794244	+	0.778723i	−0.00609157	+	0.0597253i
$171$	−2.65724	−	4.60248i	−0.203204	−	0.351960i
$172$	6.36562	+	1.70566i	0.485374	+	0.130055i
$173$	5.34266	+	6.96269i	0.406195	+	0.529363i	0.950997	−	0.309202i	$-0.100062\pi$
$173$	5.34266	+	6.96269i	0.406195	+	0.529363i	−0.544802	+	0.838565i	$0.683395\pi$
$174$			2.73480i			0.207324i
$175$	12.9260	−	2.14609i	0.977111	−	0.162229i
$176$	−0.0114973	−	0.0277569i	−0.000866642	−	0.00209226i
$177$	−1.41411	+	10.7413i	−0.106291	+	0.807363i
$178$	0.444097	−	1.65739i	0.0332865	−	0.124227i
$179$	−6.25334	+	23.3378i	−0.467397	+	1.74435i	0.181421	+	0.983405i	$0.441930\pi$
$179$	−6.25334	+	23.3378i	−0.467397	+	1.74435i	−0.648818	+	0.760944i	$0.724736\pi$
$180$	0.0353653	−	0.268626i	0.00263597	−	0.0200222i
$181$	1.67474	+	4.04318i	0.124483	+	0.300528i	0.973819	−	0.227324i	$-0.0729977\pi$
$181$	1.67474	+	4.04318i	0.124483	+	0.300528i	−0.849337	+	0.527852i	$0.822998\pi$
$182$	2.18171	+	2.65353i	0.161719	+	0.196693i
$183$		−	4.66847i		−	0.345103i
$184$	−2.39707	−	3.12392i	−0.176714	−	0.230298i
$185$	−0.418334	−	0.112092i	−0.0307565	−	0.00824119i
$186$	−3.12688	−	5.41591i	−0.229274	−	0.397114i
$187$	4.41978	+	0.450787i	0.323207	+	0.0329648i
$188$	1.30827			0.0954151
$189$	−1.93267	−	1.80687i	−0.140581	−	0.131430i
$190$	0.386106	−	0.932142i	0.0280111	−	0.0676247i
$191$	−1.40634	−	0.811953i	−0.101759	−	0.0587508i	0.448257	−	0.893905i	$-0.352045\pi$
$191$	−1.40634	−	0.811953i	−0.101759	−	0.0587508i	−0.550016	+	0.835154i	$0.685378\pi$
$192$	0.636808	+	4.83703i	0.0459576	+	0.349083i
$193$	16.3244	−	21.2743i	1.17505	−	1.53136i	0.379818	−	0.925061i	$-0.375986\pi$
$193$	16.3244	−	21.2743i	1.17505	−	1.53136i	0.795236	−	0.606300i	$-0.207347\pi$
$194$	1.35979	−	10.3286i	0.0976269	−	0.741550i
$195$	0.230039	+	0.230039i	0.0164734	+	0.0164734i
$196$	−1.68110	+	8.53202i	−0.120078	+	0.609430i
$197$	8.69335	−	3.60090i	0.619376	−	0.256554i	−0.0508557	−	0.998706i	$-0.516195\pi$
$197$	8.69335	−	3.60090i	0.619376	−	0.256554i	0.670231	+	0.742152i	$0.266195\pi$
$198$	0.929914	+	0.122425i	0.0660861	+	0.00870040i
$199$	−0.0599294	−	0.455209i	−0.00424828	−	0.0322689i	0.989189	−	0.146643i	$-0.0468470\pi$
$199$	−0.0599294	−	0.455209i	−0.00424828	−	0.0322689i	−0.993438	+	0.114374i	$0.963514\pi$
$200$	−12.1046	+	6.98862i	−0.855927	+	0.494170i
$201$	−6.07998	−	7.92359i	−0.428849	−	0.558887i
$202$	8.20387	−	8.20387i	0.577222	−	0.577222i
$203$	−0.279481	−	8.30765i	−0.0196157	−	0.583083i
$204$	4.78753	+	1.82087i	0.335194	+	0.127487i
$205$	−1.03992	+	1.80119i	−0.0726309	+	0.125800i
$206$	12.4835	+	3.34495i	0.869769	+	0.233054i
$207$	−1.38324	+	0.182107i	−0.0961420	+	0.0126573i
$208$	0.0360184	+	0.0207952i	0.00249743	+	0.00144189i
$209$	−5.29054	−	2.19141i	−0.365954	−	0.151583i
$210$	0.0487813	−	0.499916i	0.00336623	−	0.0344975i
$211$	13.0532	−	5.40683i	0.898623	−	0.372222i	0.114932	−	0.993373i	$-0.463335\pi$
$211$	13.0532	−	5.40683i	0.898623	−	0.372222i	0.783690	+	0.621152i	$0.213335\pi$
$212$	1.86999	−	0.501062i	0.128431	−	0.0344131i
$213$	1.76628	−	6.59183i	0.121023	−	0.451665i
$214$	8.09710	+	6.21312i	0.553507	+	0.424720i
$215$	1.14709	+	0.151017i	0.0782307	+	0.0102993i
$216$	2.60746	+	1.08005i	0.177415	+	0.0734878i
$217$	10.0522	+	16.1327i	0.682386	+	1.09516i
$218$	−3.73955	+	9.02808i	−0.253274	+	0.611459i
$219$	−0.628862	−	2.34695i	−0.0424946	−	0.158592i
$220$	−0.145973	−	0.252833i	−0.00984152	−	0.0170460i
$221$	−5.23395	+	3.22957i	−0.352073	+	0.217244i
$222$	0.864260	−	1.49694i	0.0580054	−	0.100468i
$223$	15.6591	−	15.6591i	1.04861	−	1.04861i	0.0498533	−	0.998757i	$-0.484125\pi$
$223$	15.6591	−	15.6591i	1.04861	−	1.04861i	0.998757	−	0.0498533i	$-0.0158754\pi$
$224$	−2.45655	−	14.7959i	−0.164135	−	0.988590i
$225$			4.95243i			0.330162i
$226$	4.40299	−	3.37853i	0.292882	−	0.224736i
$227$	9.73012	−	12.6805i	0.645811	−	0.841637i	−0.349643	−	0.936883i	$-0.613697\pi$
$227$	9.73012	−	12.6805i	0.645811	−	0.841637i	0.995454	+	0.0952458i	$0.0303637\pi$
$228$	−5.23784	−	4.01913i	−0.346884	−	0.266174i
$229$	−23.9810	+	6.42568i	−1.58471	+	0.424621i	−0.940379	−	0.340128i	$-0.889529\pi$
$229$	−23.9810	+	6.42568i	−1.58471	+	0.424621i	−0.644328	+	0.764749i	$0.722863\pi$
$230$	−0.187293	−	0.187293i	−0.0123497	−	0.0123497i
$231$	−2.83736	−	0.276867i	−0.186685	−	0.0182165i
$232$	3.39326	+	8.19206i	0.222779	+	0.537835i
$233$	−3.39828	+	2.60759i	−0.222628	+	0.170829i	−0.714054	−	0.700091i	$-0.753143\pi$
$233$	−3.39828	+	2.60759i	−0.222628	+	0.170829i	0.491425	+	0.870920i	$0.336476\pi$
$234$	−1.12446	+	0.649205i	−0.0735079	+	0.0424398i
$235$	0.227717	−	0.0299795i	0.0148546	−	0.00195565i
$236$	3.48343	+	13.0003i	0.226752	+	0.846251i
$237$	−8.65275			−0.562057
$238$	8.98385	+	3.07531i	0.582336	+	0.199343i
$239$	−15.3236			−0.991204			−0.495602	−	0.868550i	$-0.665052\pi$
$239$	−15.3236			−0.991204			−0.495602	+	0.868550i	$0.665052\pi$
$240$	−0.00157393	−	0.00587397i	−0.000101596	−	0.000379163i
$241$	6.35196	−	0.836251i	0.409166	−	0.0538677i	0.0768658	−	0.997041i	$-0.475509\pi$
$241$	6.35196	−	0.836251i	0.409166	−	0.0538677i	0.332300	+	0.943174i	$0.392175\pi$
$242$	−7.41703	+	4.28223i	−0.476785	+	0.275272i
$243$	0.793353	−	0.608761i	0.0508936	−	0.0390521i
$244$	−2.21941	−	5.35814i	−0.142083	−	0.343020i
$245$	−0.0970971	+	1.52361i	−0.00620331	+	0.0973398i
$246$	−5.86959	−	5.86959i	−0.374232	−	0.374232i
$247$	7.65713	−	2.05172i	0.487211	−	0.130548i
$248$	−16.0864	−	12.3436i	−1.02149	−	0.783817i
$249$	−6.11930	+	7.97483i	−0.387795	+	0.505384i
$250$	−1.49900	+	1.15022i	−0.0948051	+	0.0727465i
$251$			2.03781i			0.128626i	0.997930	+	0.0643128i	$0.0204855\pi$
$251$			2.03781i			0.128626i	−0.997930	+	0.0643128i	$0.979514\pi$
$252$	−3.07718	−	1.15500i	−0.193844	−	0.0727579i
$253$	−1.06301	+	1.06301i	−0.0668311	+	0.0668311i
$254$	0.232343	−	0.402429i	0.0145785	−	0.0252507i
$255$	0.875045	+	0.207233i	0.0547974	+	0.0129774i
$256$	7.96497	+	13.7957i	0.497811	+	0.862234i
$257$	4.64077	+	17.3196i	0.289483	+	1.08037i	0.945500	+	0.325621i	$0.105573\pi$
$257$	4.64077	+	17.3196i	0.289483	+	1.08037i	−0.656017	+	0.754746i	$0.727760\pi$
$258$	−1.76710	+	4.26617i	−0.110015	+	0.265600i
$259$	−2.47243	+	4.63567i	−0.153630	+	0.288047i
$260$	0.373385	+	0.154661i	0.0231563	+	0.00959167i
$261$	3.11490	+	0.410084i	0.192807	+	0.0253835i
$262$	1.43868	+	1.10394i	0.0888818	+	0.0682014i
$263$	−1.30494	+	4.87012i	−0.0804663	+	0.300304i	−0.994417	−	0.105521i	$-0.966349\pi$
$263$	−1.30494	+	4.87012i	−0.0804663	+	0.300304i	0.913951	+	0.405825i	$0.133016\pi$
$264$	2.93745	−	0.787087i	0.180787	−	0.0484419i
$265$	0.314009	−	0.130067i	0.0192894	−	0.00798993i
$266$	−9.95520	−	7.12019i	−0.610392	−	0.436567i
$267$	−1.82115	−	0.754346i	−0.111453	−	0.0461652i
$268$	−10.7451	−	6.20368i	−0.656361	−	0.378950i
$269$	−0.933003	+	0.122832i	−0.0568862	+	0.00748921i	−0.158916	−	0.987292i	$-0.550800\pi$
$269$	−0.933003	+	0.122832i	−0.0568862	+	0.00748921i	0.102029	+	0.994781i	$0.467466\pi$
$270$	0.183379	+	0.0491363i	0.0111601	+	0.00299034i
$271$	11.3324	−	19.6283i	0.688396	−	1.19234i	−0.283961	−	0.958836i	$-0.591649\pi$
$271$	11.3324	−	19.6283i	0.688396	−	1.19234i	0.972357	−	0.233500i	$-0.0750180\pi$
$272$	0.114914	−	0.00336311i	0.00696765	−	0.000203918i
$273$	3.34948	−	2.08704i	0.202720	−	0.126313i
$274$	−11.9818	+	11.9818i	−0.723850	+	0.723850i
$275$	3.24855	+	4.23359i	0.195895	+	0.255295i
$276$	−1.50101	+	0.866611i	−0.0903505	+	0.0521639i
$277$	−2.23281	−	16.9599i	−0.134157	−	1.01902i	−0.917585	−	0.397539i	$-0.869864\pi$
$277$	−2.23281	−	16.9599i	−0.134157	−	1.01902i	0.783429	−	0.621481i	$-0.213469\pi$
$278$	0.0835709	+	0.0110023i	0.00501225	+	0.000659875i
$279$	−6.63752	+	2.74935i	−0.397378	+	0.164599i
$280$	−0.474158	−	1.55802i	−0.0283364	−	0.0931095i
$281$	−22.3561	−	22.3561i	−1.33366	−	1.33366i	−0.902074	−	0.431581i	$-0.857956\pi$
$281$	−22.3561	−	22.3561i	−1.33366	−	1.33366i	−0.431581	−	0.902074i	$-0.642044\pi$
$282$	−0.119652	+	0.908846i	−0.00712517	+	0.0541210i
$283$	13.7779	−	17.9557i	0.819009	−	1.06735i	−0.177521	−	0.984117i	$-0.556808\pi$
$283$	13.7779	−	17.9557i	0.819009	−	1.06735i	0.996530	−	0.0832362i	$-0.0265256\pi$
$284$	−1.10658	−	8.40534i	−0.0656637	−	0.498765i
$285$	−1.00380	−	0.579544i	−0.0594600	−	0.0343292i
$286$	−0.535396	+	1.29256i	−0.0316586	+	0.0764307i
$287$	18.4302	+	17.2306i	1.08790	+	1.01709i
$288$	5.66887			0.334041
$289$	−7.62444	+	15.1943i	−0.448497	+	0.893784i
$290$	0.298230	+	0.516549i	0.0175126	+	0.0303328i
$291$	−11.5602	−	3.09755i	−0.677672	−	0.181582i
$292$	−1.83752	−	2.39470i	−0.107532	−	0.140139i
$293$		−	1.31519i		−	0.0768345i	−0.999262	−	0.0384172i	$-0.987768\pi$
$293$		−	1.31519i		−	0.0768345i	0.999262	−	0.0384172i	$-0.0122316\pi$
$294$	−5.77340	−	1.94818i	−0.336712	−	0.113620i
$295$	0.904236	+	2.18302i	0.0526467	+	0.127100i
$296$	0.731517	−	5.55643i	0.0425186	−	0.322961i
$297$	0.278882	−	1.04080i	0.0161824	−	0.0603934i
$298$	2.95319	−	11.0214i	0.171074	−	0.638455i
$299$	0.271637	−	2.06329i	0.0157092	−	0.119323i
$300$	2.35441	+	5.68406i	0.135932	+	0.328169i
$301$	4.93206	−	13.1402i	0.284279	−	0.757387i
$302$			17.8784i			1.02879i
$303$	−8.11392	−	10.5743i	−0.466132	−	0.607475i
$304$	−0.143132	−	0.0383521i	−0.00820919	−	0.00219965i
$305$	−0.509096	−	0.881780i	−0.0291508	−	0.0504906i
$306$	−1.70281	+	3.15934i	−0.0973432	+	0.180607i
$307$	21.7836			1.24325			0.621627	−	0.783314i	$-0.286472\pi$
$307$	21.7836			1.24325			0.621627	+	0.783314i	$0.286472\pi$
$308$	−3.38815	+	1.03113i	−0.193058	+	0.0587540i
$309$	5.68176	−	13.7170i	0.323224	−	0.780332i
$310$	−1.18121	−	0.681972i	−0.0670882	−	0.0387334i
$311$	−4.05687	−	30.8150i	−0.230044	−	1.74736i	−0.583690	−	0.811977i	$-0.698392\pi$
$311$	−4.05687	−	30.8150i	−0.230044	−	1.74736i	0.353646	−	0.935379i	$-0.384942\pi$
$312$	−2.56278	+	3.33988i	−0.145089	+	0.189083i
$313$	−2.88419	+	21.9076i	−0.163024	+	1.23829i	0.692841	+	0.721090i	$0.256359\pi$
$313$	−2.88419	+	21.9076i	−0.163024	+	1.23829i	−0.855865	+	0.517199i	$0.826975\pi$
$314$	3.88910	+	3.88910i	0.219475	+	0.219475i
$315$	−0.562082	−	0.130524i	−0.0316697	−	0.00735418i
$316$	−9.93102	+	4.11357i	−0.558664	+	0.231406i
$317$	−13.7699	−	1.81284i	−0.773395	−	0.101819i	−0.266509	−	0.963833i	$-0.585870\pi$
$317$	−13.7699	−	1.81284i	−0.773395	−	0.101819i	−0.506886	+	0.862013i	$0.669203\pi$
$318$	0.177059	+	1.34490i	0.00992899	+	0.0754182i
$319$	2.93177	−	1.69266i	0.164147	−	0.0947705i
$320$	0.647759	+	0.844175i	0.0362108	+	0.0471908i
$321$	8.29082	−	8.29082i	0.462749	−	0.462749i
$322$	−2.72707	+	1.69922i	−0.151974	+	0.0946938i
$323$	15.0343	−	15.9409i	0.836533	−	0.886974i
$324$	0.621147	−	1.07586i	0.0345082	−	0.0597699i
$325$	−7.13549	−	1.91195i	−0.395806	−	0.106056i
$326$	−3.92655	+	0.516941i	−0.217472	+	0.0286307i
$327$	9.72210	+	5.61306i	0.537633	+	0.310403i
$328$	−24.8651	−	10.2995i	−1.37295	−	0.568693i
$329$	0.270594	−	2.77308i	0.0149184	−	0.152885i
$330$	0.188993	−	0.0782833i	0.0104037	−	0.00430935i
$331$	−11.1108	+	2.97714i	−0.610707	+	0.163638i	−0.550900	−	0.834572i	$-0.685715\pi$
$331$	−11.1108	+	2.97714i	−0.610707	+	0.163638i	−0.0598073	+	0.998210i	$0.519049\pi$
$332$	−3.23203	+	12.0621i	−0.177381	+	0.661994i
$333$	−1.57540	−	1.20885i	−0.0863314	−	0.0662444i
$334$	−15.4577	−	2.03505i	−0.845809	−	0.111353i
$335$	−2.01245	−	0.833586i	−0.109952	−	0.0455437i
$336$	−0.0737286	+	0.00248033i	−0.00402222	+	0.000135313i
$337$	−6.12673	+	14.7912i	−0.333744	+	0.805730i	0.664544	+	0.747249i	$0.268626\pi$
$337$	−6.12673	+	14.7912i	−0.333744	+	0.805730i	−0.998289	+	0.0584813i	$0.981374\pi$
$338$	2.42753	+	9.05968i	0.132040	+	0.492782i
$339$	−3.18787	−	5.52155i	−0.173141	−	0.299889i
$340$	1.10283	−	0.178153i	0.0598096	−	0.00966172i
$341$	−3.87065	+	6.70417i	−0.209608	+	0.363051i
$342$	3.27112	−	3.27112i	0.176882	−	0.176882i
$343$	17.7373	+	5.32808i	0.957724	+	0.287689i
$344$			14.9718i			0.807227i
$345$	−0.241408	+	0.185239i	−0.0129970	+	0.00997294i
$346$	−4.65059	+	6.06076i	−0.250017	+	0.325829i
$347$	−18.2863	−	14.0316i	−0.981662	−	0.753256i	−0.0125615	−	0.999921i	$-0.503999\pi$
$347$	−18.2863	−	14.0316i	−0.981662	−	0.753256i	−0.969101	+	0.246665i	$0.920665\pi$
$348$	3.77001	−	1.01017i	0.202094	−	0.0541509i
$349$	13.3148	+	13.3148i	0.712726	+	0.712726i	0.967105	−	0.254379i	$-0.0818710\pi$
$349$	13.3148	+	13.3148i	0.712726	+	0.712726i	−0.254379	+	0.967105i	$0.581871\pi$
$350$	4.71656	+	10.3847i	0.252111	+	0.555085i
$351$	0.570822	+	1.37809i	0.0304682	+	0.0735568i
$352$	4.84603	−	3.71849i	0.258295	−	0.198196i
$353$	3.48667	−	2.01303i	0.185577	−	0.107143i	−0.404333	−	0.914612i	$-0.632496\pi$
$353$	3.48667	−	2.01303i	0.185577	−	0.107143i	0.589910	+	0.807469i	$0.299163\pi$
$354$	−9.34987	+	1.23093i	−0.496940	+	0.0654234i
$355$	−0.385224	−	1.43768i	−0.0204456	−	0.0763040i
$356$	−2.44881			−0.129787
$357$	4.84986	−	9.77133i	0.256682	−	0.517154i
$358$	−21.0313			−1.11154
$359$	−3.07558	−	11.4782i	−0.162323	−	0.605798i	−0.998366	−	0.0571346i	$-0.981804\pi$
$359$	−3.07558	−	11.4782i	−0.162323	−	0.605798i	0.836043	−	0.548663i	$-0.184863\pi$
$360$	0.610277	−	0.0803444i	0.0321644	−	0.00423452i
$361$	−8.00529	+	4.62186i	−0.421331	+	0.243256i
$362$	−3.02221	+	2.31903i	−0.158844	+	0.121885i
$363$	3.76521	+	9.09001i	0.197622	+	0.477102i
$364$	2.85211	−	3.98772i	0.149491	−	0.209013i
$365$	−0.374714	−	0.374714i	−0.0196134	−	0.0196134i
$366$	3.92526	−	1.05177i	0.205177	−	0.0549769i
$367$	0.159650	+	0.122504i	0.00833365	+	0.00639463i	0.612920	−	0.790145i	$-0.289995\pi$
$367$	0.159650	+	0.122504i	0.00833365	+	0.00639463i	−0.604586	+	0.796540i	$0.706662\pi$
$368$	−0.0236815	+	0.0308624i	−0.00123448	+	0.00160881i
$369$	−7.56553	+	5.80524i	−0.393846	+	0.302208i
$370$		−	0.376990i		−	0.0195988i
$371$	−0.675304	−	4.06738i	−0.0350601	−	0.211168i
$372$	−6.31103	+	6.31103i	−0.327211	+	0.327211i
$373$	1.59561	−	2.76368i	0.0826175	−	0.143098i	−0.821756	−	0.569840i	$-0.807005\pi$
$373$	1.59561	−	2.76368i	0.0826175	−	0.143098i	0.904373	+	0.426742i	$0.140339\pi$
$374$	0.616720	+	3.81772i	0.0318898	+	0.197410i
$375$	1.08531	+	1.87982i	0.0560453	+	0.0970733i
$376$	0.769255	+	2.87090i	0.0396713	+	0.148055i
$377$	−1.79339	+	4.32964i	−0.0923645	+	0.222988i
$378$	1.08380	−	2.03207i	0.0557449	−	0.104518i
$379$	−21.2202	−	8.78971i	−1.09001	−	0.451497i	−0.236000	−	0.971753i	$-0.575837\pi$
$379$	−21.2202	−	8.78971i	−1.09001	−	0.451497i	−0.854010	+	0.520256i	$0.825837\pi$
$380$	−1.42761	−	0.187948i	−0.0732348	−	0.00964155i
$381$	−0.423521	−	0.324979i	−0.0216977	−	0.0166492i
$382$	0.365854	−	1.36538i	0.0187187	−	0.0698591i
$383$	−17.5964	+	4.71493i	−0.899132	+	0.240922i	−0.678643	−	0.734468i	$-0.737432\pi$
$383$	−17.5964	+	4.71493i	−0.899132	+	0.240922i	−0.220488	+	0.975390i	$0.570765\pi$
$384$	6.55117	−	2.71358i	0.334313	−	0.138477i
$385$	−0.566114	+	0.257120i	−0.0288518	+	0.0131040i
$386$	21.5653	+	8.93263i	1.09764	+	0.454659i
$387$	4.59413	+	2.65242i	0.233533	+	0.134830i
$388$	−14.7406	+	1.94064i	−0.748341	+	0.0985210i
$389$	−2.55409	−	0.684367i	−0.129498	−	0.0346988i	0.193488	−	0.981103i	$-0.438020\pi$
$389$	−2.55409	−	0.684367i	−0.129498	−	0.0346988i	−0.322986	+	0.946404i	$0.604687\pi$
$390$	−0.141591	+	0.245244i	−0.00716976	+	0.0124184i
$391$	−2.35591	−	5.24792i	−0.119143	−	0.265399i
$392$	−19.7114	+	1.32774i	−0.995577	+	0.0670610i
$393$	1.47310	−	1.47310i	0.0743079	−	0.0743079i
$394$	4.98620	+	6.49814i	0.251201	+	0.327371i
$395$	−1.63433	+	0.943582i	−0.0822322	+	0.0474768i
$396$	−0.174721	−	1.32714i	−0.00878007	−	0.0666913i
$397$	−18.5158	−	2.43765i	−0.929279	−	0.122342i	−0.349335	−	0.936998i	$-0.613592\pi$
$397$	−18.5158	−	2.43765i	−0.929279	−	0.122342i	−0.579945	+	0.814656i	$0.696926\pi$
$398$	0.369240	−	0.152944i	0.0185083	−	0.00766639i
$399$	−9.60257	+	10.2712i	−0.480730	+	0.514201i
$400$	0.0976419	+	0.0976419i	0.00488209	+	0.00488209i
$401$	−0.988558	+	7.50885i	−0.0493663	+	0.374974i	0.948873	+	0.315658i	$0.102225\pi$
$401$	−0.988558	+	7.50885i	−0.0493663	+	0.374974i	−0.998239	+	0.0593159i	$0.981108\pi$
$402$	5.29240	−	6.89719i	0.263961	−	0.344001i
$403$	−1.39878	−	10.6248i	−0.0696782	−	0.529258i
$404$	−14.3396	−	8.27900i	−0.713424	−	0.411896i
$405$	0.0834632	−	0.201498i	0.00414732	−	0.0100125i
$406$	6.92213	−	2.10664i	0.343540	−	0.104551i
$407$	−2.13968			−0.106060
$408$	−1.18073	+	11.5766i	−0.0584549	+	0.573126i
$409$	3.32817	+	5.76456i	0.164567	+	0.285039i	0.936502	−	0.350663i	$-0.114044\pi$
$409$	3.32817	+	5.76456i	0.164567	+	0.285039i	−0.771934	+	0.635702i	$0.780711\pi$
$410$	−1.74873	−	0.468570i	−0.0863635	−	0.0231410i
$411$	11.8505	+	15.4438i	0.584541	+	0.761788i
$412$		−	18.4445i		−	0.908697i
$413$	28.2768	−	4.69478i	1.39141	−	0.231015i
$414$	−0.464751	−	1.12201i	−0.0228412	−	0.0551436i
$415$	−0.286159	+	2.17360i	−0.0140470	+	0.106698i
$416$	−2.18854	+	8.16773i	−0.107302	+	0.400456i
$417$	0.0250630	−	0.0935363i	0.00122734	−	0.00458049i
$418$	0.650628	−	4.94201i	0.0318233	−	0.241722i
$419$	10.4581	+	25.2480i	0.510911	+	1.23345i	0.943355	+	0.331786i	$0.107651\pi$
$419$	10.4581	+	25.2480i	0.510911	+	1.23345i	−0.432444	+	0.901661i	$0.642349\pi$
$420$	−0.707170	+	0.117411i	−0.0345064	+	0.00572907i
$421$			21.2726i			1.03676i	0.855149	+	0.518382i	$0.173465\pi$
$421$			21.2726i			1.03676i	−0.855149	+	0.518382i	$0.826535\pi$
$422$	7.48688	+	9.75709i	0.364456	+	0.474968i
$423$	1.01722	+	0.272564i	0.0494590	+	0.0132525i
$424$	2.19909	+	3.80894i	0.106797	+	0.184979i
$425$	−19.5606	+	5.85966i	−0.948828	+	0.284235i
$426$	5.94036			0.287811
$427$	−11.8165	+	3.59616i	−0.571841	+	0.174030i
$428$	5.57412	−	13.4571i	0.269435	−	0.650475i
$429$	1.39192	+	0.803628i	0.0672027	+	0.0387995i
$430$	0.131455	+	0.998497i	0.00633930	+	0.0481518i
$431$	17.4629	−	22.7581i	0.841159	−	1.09622i	−0.152993	−	0.988227i	$-0.548891\pi$
$431$	17.4629	−	22.7581i	0.841159	−	1.09622i	0.994152	−	0.107992i	$-0.0344422\pi$
$432$	0.00363940	−	0.0276440i	0.000175101	−	0.00133002i
$433$	10.9944	+	10.9944i	0.528355	+	0.528355i	0.920082	−	0.391726i	$-0.128122\pi$
$433$	10.9944	+	10.9944i	0.528355	+	0.528355i	−0.391726	+	0.920082i	$0.628122\pi$
$434$	−11.2997	+	12.0865i	−0.542404	+	0.580169i
$435$	0.633061	−	0.262223i	0.0303530	−	0.0125726i
$436$	13.8268	+	1.82034i	0.662185	+	0.0871783i
$437$	0.967807	+	7.35122i	0.0462965	+	0.351657i
$438$	1.83164	−	1.05750i	0.0875192	−	0.0505292i
$439$	−14.0778	−	18.3465i	−0.671895	−	0.875631i	0.325662	−	0.945486i	$-0.394413\pi$
$439$	−14.0778	−	18.3465i	−0.671895	−	0.875631i	−0.997557	+	0.0698556i	$0.977746\pi$
$440$	0.468994	−	0.468994i	0.0223584	−	0.0223584i
$441$	−3.08467	+	6.28369i	−0.146889	+	0.299224i
$442$	−3.89460	−	3.67312i	−0.185247	−	0.174713i
$443$	−3.28348	+	5.68716i	−0.156003	+	0.270205i	−0.933424	−	0.358776i	$-0.883194\pi$
$443$	−3.28348	+	5.68716i	−0.156003	+	0.270205i	0.777421	+	0.628981i	$0.216528\pi$
$444$	−2.38283	−	0.638476i	−0.113084	−	0.0303008i
$445$	−0.426241	+	0.0561157i	−0.0202058	+	0.00266014i
$446$	16.6941	+	9.63833i	0.790487	+	0.456388i
$447$	−12.1104	−	5.01631i	−0.572804	−	0.237263i
$448$	11.7526	−	5.33785i	0.555260	−	0.252190i
$449$	14.3056	−	5.92557i	0.675123	−	0.279645i	−0.0186636	−	0.999826i	$-0.505941\pi$
$449$	14.3056	−	5.92557i	0.675123	−	0.279645i	0.693786	+	0.720181i	$0.255941\pi$
$450$	−4.16402	+	1.11575i	−0.196294	+	0.0525967i
$451$	−2.65945	+	9.92522i	−0.125229	+	0.467360i
$452$	−6.28378	−	4.82172i	−0.295564	−	0.226795i
$453$	20.3632	+	2.68087i	0.956747	+	0.125958i
$454$	12.8540	+	5.32428i	0.603266	+	0.249881i
$455$	0.405058	−	0.759460i	0.0189894	−	0.0356040i
$456$	5.73989	−	13.8573i	0.268795	−	0.648928i
$457$	−9.95588	−	37.1558i	−0.465716	−	1.73808i	−0.654504	−	0.756059i	$-0.727122\pi$
$457$	−9.95588	−	37.1558i	−0.465716	−	1.73808i	0.188788	−	0.982018i	$-0.439544\pi$
$458$	−10.8055	−	18.7156i	−0.504906	−	0.874523i
$459$	3.34311	+	2.41322i	0.156043	+	0.112640i
$460$	−0.189008	+	0.327371i	−0.00881254	+	0.0152638i
$461$	16.3804	−	16.3804i	0.762911	−	0.762911i	−0.213937	−	0.976848i	$-0.568629\pi$
$461$	16.3804	−	16.3804i	0.762911	−	0.762911i	0.976848	+	0.213937i	$0.0686286\pi$
$462$	−0.406446	−	2.44804i	−0.0189096	−	0.113893i
$463$		−	23.4659i		−	1.09055i	−0.838256	−	0.545277i	$-0.816424\pi$
$463$		−	23.4659i		−	1.09055i	0.838256	−	0.545277i	$-0.183576\pi$
$464$	0.0694983	−	0.0533279i	0.00322638	−	0.00247569i
$465$	−0.953879	+	1.24312i	−0.0442351	+	0.0576483i
$466$	−2.95807	−	2.26981i	−0.137030	−	0.105147i
$467$	40.5700	−	10.8707i	1.87736	−	0.503036i	0.877637	−	0.479326i	$-0.159119\pi$
$467$	40.5700	−	10.8707i	1.87736	−	0.503036i	0.999719	−	0.0237103i	$-0.00754794\pi$
$468$	1.31030	+	1.31030i	0.0605686	+	0.0605686i
$469$	−15.3722	+	21.4928i	−0.709821	+	0.992447i
$470$	0.0765098	+	0.184711i	0.00352913	+	0.00852008i
$471$	5.01280	−	3.84646i	0.230978	−	0.177235i
$472$	−26.4801	+	15.2883i	−1.21885	+	0.703702i
$473$	5.66715	−	0.746094i	0.260576	−	0.0343054i
$474$	−1.94940	−	7.27526i	−0.0895389	−	0.334164i
$475$	26.3196			1.20763
$476$	0.920990	−	13.5205i	0.0422135	−	0.619711i
$477$	1.55837			0.0713529
$478$	−3.45230	−	12.8842i	−0.157905	−	0.589308i
$479$	19.8895	−	2.61850i	0.908774	−	0.119642i	0.338376	−	0.941011i	$-0.390122\pi$
$479$	19.8895	−	2.61850i	0.908774	−	0.119642i	0.570398	+	0.821368i	$0.306789\pi$
$480$	1.07074	−	0.618189i	0.0488722	−	0.0282164i
$481$	2.34991	−	1.80315i	0.107147	−	0.0822167i
$482$	2.13417	+	5.15234i	0.0972088	+	0.234683i
$483$	1.52646	+	3.36089i	0.0694564	+	0.152926i
$484$	8.64288	+	8.64288i	0.392858	+	0.392858i
$485$	−2.52128	+	0.675576i	−0.114486	+	0.0306763i
$486$	0.690585	+	0.529904i	0.0313256	+	0.0240369i
$487$	15.1236	−	19.7095i	0.685316	−	0.893121i	−0.313081	−	0.949726i	$-0.601361\pi$
$487$	15.1236	−	19.7095i	0.685316	−	0.893121i	0.998397	+	0.0566056i	$0.0180278\pi$
$488$	10.4531	−	8.02092i	0.473188	−	0.363090i
$489$			4.54980i			0.205749i
$490$	−1.30293	+	0.261618i	−0.0588604	+	0.0118187i
$491$	−14.2099	+	14.2099i	−0.641285	+	0.641285i	−0.950871	−	0.309586i	$-0.899809\pi$
$491$	−14.2099	+	14.2099i	−0.641285	+	0.641285i	0.309586	+	0.950871i	$0.399809\pi$
$492$	−5.92335	+	10.2595i	−0.267045	+	0.462536i
$493$	2.06580	+	12.7881i	0.0930391	+	0.575946i
$494$	3.45019	+	5.97590i	0.155231	+	0.268868i
$495$	−0.0608241	−	0.226998i	−0.00273384	−	0.0102028i
$496$	−0.0766589	+	0.185071i	−0.00344209	+	0.00830993i
$497$	−18.0454	+	0.607070i	−0.809445	+	0.0272308i
$498$	−8.08389	−	3.34846i	−0.362248	−	0.150048i
$499$	−6.66659	−	0.877673i	−0.298437	−	0.0392900i	−0.0201794	−	0.999796i	$-0.506424\pi$
$499$	−6.66659	−	0.877673i	−0.298437	−	0.0392900i	−0.278258	+	0.960506i	$0.589757\pi$
$500$	2.13932	+	1.64156i	0.0956733	+	0.0734127i
$501$	−4.63578	+	17.3010i	−0.207111	+	0.772951i
$502$	−1.71340	+	0.459104i	−0.0764727	+	0.0204908i
$503$	37.9034	−	15.7001i	1.69003	−	0.700032i	0.690304	−	0.723520i	$-0.257477\pi$
$503$	37.9034	−	15.7001i	1.69003	−	0.700032i	0.999724	+	0.0234872i	$0.00747689\pi$
$504$	0.725187	−	7.43180i	0.0323024	−	0.331039i
$505$	−2.68568	−	1.11244i	−0.119511	−	0.0495031i
$506$	−1.13327	−	0.654296i	−0.0503801	−	0.0290870i
$507$	10.6829	−	1.40642i	0.474442	−	0.0624615i
$508$	−0.640585	−	0.171644i	−0.0284214	−	0.00761548i
$509$	−10.5680	+	18.3044i	−0.468421	+	0.811328i	−0.999349	−	0.0360888i	$-0.988510\pi$
$509$	−10.5680	+	18.3044i	−0.468421	+	0.811328i	0.530928	+	0.847417i	$0.321843\pi$
$510$	0.0228989	+	0.782428i	0.00101398	+	0.0346465i
$511$	−5.45601	+	3.39961i	−0.241360	+	0.150390i
$512$	0.223056	−	0.223056i	0.00985775	−	0.00985775i
$513$	−3.23525	−	4.21626i	−0.142840	−	0.186153i
$514$	−13.5168	+	7.80395i	−0.596202	+	0.344217i
$515$	−0.422665	−	3.21046i	−0.0186248	−	0.141470i
$516$	6.53379	+	0.860190i	0.287634	+	0.0378678i
$517$	1.04836	−	0.434245i	0.0461068	−	0.0190981i
$518$	−4.45471	−	1.03445i	−0.195729	−	0.0454510i
$519$	6.20576	+	6.20576i	0.272403	+	0.272403i
$520$	−0.119844	+	0.910307i	−0.00525552	+	0.0399196i
$521$	−11.4515	+	14.9239i	−0.501701	+	0.653830i	−0.973717	−	0.227760i	$-0.926860\pi$
$521$	−11.4515	+	14.9239i	−0.501701	+	0.653830i	0.472016	+	0.881590i	$0.343526\pi$
$522$	0.356963	+	2.71140i	0.0156238	+	0.118675i
$523$	11.8654	+	6.85050i	0.518838	+	0.299551i	0.736459	−	0.676482i	$-0.236496\pi$
$523$	11.8654	+	6.85050i	0.518838	+	0.299551i	−0.217621	+	0.976033i	$0.569830\pi$
$524$	0.990400	−	2.39104i	0.0432658	−	0.104453i
$525$	12.5353	−	3.81490i	0.547083	−	0.166496i
$526$	−4.38880			−0.191361
$527$	−18.7125	−	22.9632i	−0.815130	−	1.00029i
$528$	−0.0150219	−	0.0260188i	−0.000653746	−	0.00113232i
$529$	−20.3361	−	5.44904i	−0.884178	−	0.236915i
$530$	0.180104	+	0.234716i	0.00782323	+	0.0101954i
$531$			10.8339i			0.470153i
$532$	−6.13820	+	16.3536i	−0.266125	+	0.709020i
$533$	−5.44344	−	13.1416i	−0.235782	−	0.569227i
$534$	0.223964	−	1.70118i	0.00969189	−	0.0736172i
$535$	0.661857	−	2.47008i	0.0286146	−	0.106791i
$536$	7.29549	−	27.2271i	0.315117	−	1.17603i
$537$	−3.15365	+	23.9544i	−0.136090	+	1.03371i
$538$	−0.313476	−	0.756798i	−0.0135149	−	0.0326279i
$539$	1.48486	+	7.39501i	0.0639574	+	0.318526i
$540$		−	0.270944i		−	0.0116596i
$541$	−13.9965	−	18.2406i	−0.601756	−	0.784224i	0.388801	−	0.921322i	$-0.372889\pi$
$541$	−13.9965	−	18.2406i	−0.601756	−	0.784224i	−0.990558	+	0.137098i	$0.956223\pi$
$542$	19.0567	+	5.10622i	0.818554	+	0.219331i
$543$	2.18816	+	3.79000i	0.0939028	+	0.162644i
$544$	6.70734	+	22.3903i	0.287575	+	0.959975i
$545$	2.44841			0.104879
$546$	2.50940	+	2.34606i	0.107392	+	0.100402i
$547$	−8.74839	+	21.1205i	−0.374054	+	0.903046i	0.619000	+	0.785391i	$0.287538\pi$
$547$	−8.74839	+	21.1205i	−0.374054	+	0.903046i	−0.993054	+	0.117656i	$0.962462\pi$
$548$	20.9432	+	12.0916i	0.894650	+	0.516526i
$549$	−0.609357	−	4.62853i	−0.0260067	−	0.197541i
$550$	−2.82774	+	3.68518i	−0.120575	+	0.157137i
$551$	2.17938	−	16.5541i	0.0928448	−	0.705226i
$552$	−2.78431	−	2.78431i	−0.118508	−	0.118508i
$553$	6.66529	+	21.9013i	0.283437	+	0.931336i
$554$	13.7569	−	5.69828i	0.584473	−	0.242097i
$555$	−0.429386	−	0.0565298i	−0.0182264	−	0.00239956i
$556$	−0.0157021	−	0.119269i	−0.000665918	−	0.00505815i
$557$	12.0437	−	6.95345i	0.510309	−	0.294627i	−0.222652	−	0.974898i	$-0.571471\pi$
$557$	12.0437	−	6.95345i	0.510309	−	0.294627i	0.732961	+	0.680271i	$0.238138\pi$
$558$	−3.80704	−	4.96144i	−0.161165	−	0.210034i
$559$	−5.59524	+	5.59524i	−0.236653	+	0.236653i
$560$	−0.0136554	+	0.00850858i	−0.000577045	+	0.000359553i
$561$	4.44081	−	0.129967i	0.187491	−	0.00548719i
$562$	13.7604	−	23.8338i	0.580449	−	1.00537i
$563$	12.0282	+	3.22296i	0.506930	+	0.135831i	0.503214	−	0.864162i	$-0.332151\pi$
$563$	12.0282	+	3.22296i	0.506930	+	0.135831i	0.00371545	+	0.999993i	$0.498817\pi$
$564$	1.29707	−	0.170763i	0.0546166	−	0.00719042i
$565$	−1.20425	−	0.695274i	−0.0506631	−	0.0292504i
$566$	18.2012	+	7.53919i	0.765054	+	0.316896i
$567$	−2.15198	−	1.53915i	−0.0903748	−	0.0646381i
$568$	17.7943	−	7.37063i	0.746631	−	0.309265i
$569$	45.6779	−	12.2394i	1.91492	−	0.513100i	0.923264	−	0.384167i	$-0.125511\pi$
$569$	45.6779	−	12.2394i	1.91492	−	0.513100i	0.991653	−	0.128934i	$-0.0411554\pi$
$570$	0.261134	−	0.974564i	0.0109377	−	0.0408200i
$571$	−5.71065	−	4.38194i	−0.238983	−	0.183378i	0.482325	−	0.875992i	$-0.339792\pi$
$571$	−5.71065	−	4.38194i	−0.238983	−	0.183378i	−0.721309	+	0.692614i	$0.756459\pi$
$572$	1.97960	+	0.260620i	0.0827713	+	0.0108971i
$573$	−1.50029	−	0.621442i	−0.0626756	−	0.0259611i
$574$	−10.3353	+	19.3781i	−0.431388	+	0.808827i
$575$	2.64416	−	6.38357i	0.110269	−	0.266213i
$576$	1.26272	+	4.71253i	0.0526133	+	0.196356i
$577$	−7.37617	−	12.7759i	−0.307074	−	0.531868i	0.670647	−	0.741777i	$-0.266017\pi$
$577$	−7.37617	−	12.7759i	−0.307074	−	0.531868i	−0.977721	+	0.209909i	$0.932683\pi$
$578$	−14.4932	−	2.98748i	−0.602836	−	0.124263i
$579$	13.4079	−	23.2231i	0.557212	−	0.965119i
$580$	0.601921	−	0.601921i	0.0249934	−	0.0249934i
$581$	24.8991	+	9.34568i	1.03299	+	0.387724i
$582$		−	10.4177i		−	0.431829i
$583$	1.33217	−	1.02221i	0.0551730	−	0.0423358i
$584$	4.17455	−	5.44038i	0.172744	−	0.225124i
$585$	0.258097	+	0.198045i	0.0106710	+	0.00818815i
$586$	1.10582	−	0.296303i	0.0456810	−	0.0122402i
$587$	−16.8557	−	16.8557i	−0.695710	−	0.695710i	0.267772	−	0.963482i	$-0.413713\pi$
$587$	−16.8557	−	16.8557i	−0.695710	−	0.695710i	−0.963482	+	0.267772i	$0.913713\pi$
$588$	−0.553064	+	8.67845i	−0.0228080	+	0.357893i
$589$	14.6114	+	35.2750i	0.602051	+	1.45348i
$590$	−1.63177	+	1.25210i	−0.0671790	+	0.0515482i
$591$	8.14897	−	4.70481i	0.335204	−	0.193530i
$592$	−0.0548941	+	0.00722694i	−0.00225613	+	0.000297025i
$593$	1.49818	+	5.59128i	0.0615228	+	0.229606i	0.989841	−	0.142181i	$-0.0454116\pi$
$593$	1.49818	+	5.59128i	0.0615228	+	0.229606i	−0.928318	+	0.371788i	$0.878745\pi$
$594$	0.937938			0.0384841
$595$	−0.149521	−	2.37449i	−0.00612976	−	0.0973444i
$596$	−16.2843			−0.667031
$597$	−0.118833	−	0.443492i	−0.00486353	−	0.0181509i
$598$	1.79602	−	0.236450i	0.0734445	−	0.00966916i
$599$	−35.8128	+	20.6765i	−1.46327	+	0.844821i	−0.999161	−	0.0409560i	$-0.986960\pi$
$599$	−35.8128	+	20.6765i	−1.46327	+	0.844821i	−0.464112	+	0.885777i	$0.653626\pi$
$600$	−11.0889	+	8.50880i	−0.452702	+	0.347370i
$601$	−4.24262	−	10.2426i	−0.173060	−	0.417804i	0.813422	−	0.581674i	$-0.197602\pi$
$601$	−4.24262	−	10.2426i	−0.173060	−	0.417804i	−0.986482	+	0.163870i	$0.947602\pi$
$602$	12.1594	+	1.18651i	0.495582	+	0.0483584i
$603$	−7.06220	−	7.06220i	−0.287595	−	0.287595i
$604$	24.6460	−	6.60387i	1.00283	−	0.268708i
$605$	1.70244	+	1.30633i	0.0692139	+	0.0531097i
$606$	7.06286	−	9.20450i	0.286909	−	0.373907i
$607$	−12.9572	+	9.94243i	−0.525918	+	0.403551i	−0.837308	−	0.546731i	$-0.815872\pi$
$607$	−12.9572	+	9.94243i	−0.525918	+	0.403551i	0.311390	+	0.950282i	$0.399205\pi$
$608$		−	30.1271i		−	1.22181i
$609$	−1.36146	−	8.20010i	−0.0551690	−	0.332285i
$610$	0.626708	−	0.626708i	0.0253747	−	0.0253747i
$611$	−0.785421	+	1.36039i	−0.0317748	+	0.0550355i
$612$	4.98424	+	1.18040i	0.201476	+	0.0477147i
$613$	6.87929	+	11.9153i	0.277852	+	0.481254i	0.970851	−	0.239685i	$-0.0770442\pi$
$613$	6.87929	+	11.9153i	0.277852	+	0.481254i	−0.692999	+	0.720939i	$0.743711\pi$
$614$	4.90767	+	18.3157i	0.198057	+	0.739161i
$615$	−0.795917	+	1.92151i	−0.0320945	+	0.0774829i
$616$	−4.25496	−	6.82877i	−0.171437	−	0.275139i
$617$	12.1219	+	5.02105i	0.488009	+	0.202140i	0.613100	−	0.790005i	$-0.289922\pi$
$617$	12.1219	+	5.02105i	0.488009	+	0.202140i	−0.125091	+	0.992145i	$0.539922\pi$
$618$	12.8133	+	1.68691i	0.515428	+	0.0678574i
$619$	6.75593	+	5.18401i	0.271544	+	0.208363i	0.735552	−	0.677468i	$-0.236923\pi$
$619$	6.75593	+	5.18401i	0.271544	+	0.208363i	−0.464009	+	0.885831i	$0.653589\pi$
$620$	−0.503810	+	1.88024i	−0.0202335	+	0.0755124i
$621$	−1.34764	+	0.361099i	−0.0540789	+	0.0144904i
$622$	24.9953	−	10.3534i	1.00222	−	0.415134i
$623$	−0.506499	+	5.19066i	−0.0202925	+	0.207959i
$624$	0.0384246	+	0.0159160i	0.00153821	+	0.000637149i
$625$	−21.0347	−	12.1444i	−0.841387	−	0.485775i
$626$	−19.0697	+	2.51058i	−0.762180	+	0.100343i
$627$	−5.53132	−	1.48211i	−0.220899	−	0.0591898i
$628$	3.92472	−	6.79781i	0.156613	−	0.271262i
$629$	2.91058	−	7.65264i	0.116052	−	0.305131i
$630$	−0.0168882	−	0.502006i	−0.000672841	−	0.0200004i
$631$	8.03130	−	8.03130i	0.319721	−	0.319721i	−0.528939	−	0.848660i	$-0.677410\pi$
$631$	8.03130	−	8.03130i	0.319721	−	0.319721i	0.848660	+	0.528939i	$0.177410\pi$
$632$	−14.8663	−	19.3742i	−0.591351	−	0.770664i
$633$	12.2358	−	7.06437i	0.486331	−	0.280783i
$634$	−1.57801	−	11.9862i	−0.0626708	−	0.476032i
$635$	−0.115434	−	0.0151971i	−0.00458085	−	0.000603080i
$636$	1.78859	−	0.740858i	0.0709222	−	0.0293769i
$637$	−7.86270	−	6.87030i	−0.311532	−	0.272211i
$638$	2.08369	+	2.08369i	0.0824942	+	0.0824942i
$639$	0.890758	−	6.76598i	0.0352379	−	0.267658i
$640$	0.941470	−	1.22695i	0.0372149	−	0.0484993i
$641$	−2.67359	−	20.3079i	−0.105600	−	0.802114i	−0.959506	−	0.281687i	$-0.909106\pi$
$641$	−2.67359	−	20.3079i	−0.105600	−	0.802114i	0.853906	−	0.520427i	$-0.174227\pi$
$642$	8.83881	+	5.10309i	0.348840	+	0.201403i
$643$	−6.47266	+	15.6264i	−0.255257	+	0.616245i	−0.998613	−	0.0526512i	$-0.983233\pi$
$643$	−6.47266	+	15.6264i	−0.255257	+	0.616245i	0.743356	+	0.668896i	$0.233233\pi$
$644$	3.34975	+	3.13171i	0.131999	+	0.123407i
$645$	1.15699			0.0455562
$646$	16.7903	+	9.04956i	0.660604	+	0.356050i
$647$	7.46210	+	12.9247i	0.293365	+	0.508124i	0.974603	−	0.223938i	$-0.0718914\pi$
$647$	7.46210	+	12.9247i	0.293365	+	0.508124i	−0.681238	+	0.732062i	$0.738558\pi$
$648$	2.72613	+	0.730464i	0.107092	+	0.0286953i
$649$	7.10653	+	9.26141i	0.278956	+	0.363542i
$650$		−	6.43028i		−	0.252216i
$651$	12.0719	+	14.6826i	0.473135	+	0.575456i
$652$	2.16300	+	5.22195i	0.0847097	+	0.204507i
$653$	−0.680268	+	5.16715i	−0.0266209	+	0.202206i	−0.999587	−	0.0287427i	$-0.990850\pi$
$653$	−0.680268	+	5.16715i	−0.0266209	+	0.202206i	0.972966	+	0.230949i	$0.0741830\pi$
$654$	−2.52916	+	9.43895i	−0.0988979	+	0.369092i
$655$	0.117598	−	0.438880i	0.00459492	−	0.0171485i
$656$	−0.0347059	+	0.263617i	−0.00135504	+	0.0102925i
$657$	−0.929820	−	2.24479i	−0.0362758	−	0.0875774i
$658$	2.39258	−	0.397238i	0.0932724	−	0.0154859i
$659$			35.9750i			1.40139i	0.713463	+	0.700693i	$0.247126\pi$
$659$			35.9750i			1.40139i	−0.713463	+	0.700693i	$0.752874\pi$
$660$	−0.177726	−	0.231617i	−0.00691797	−	0.00901568i
$661$	−24.9096	−	6.67450i	−0.968870	−	0.259608i	−0.260519	−	0.965469i	$-0.583894\pi$
$661$	−24.9096	−	6.67450i	−0.968870	−	0.259608i	−0.708351	+	0.705861i	$0.750560\pi$
$662$	−5.00638	−	8.67130i	−0.194578	−	0.337019i
$663$	−4.76763	+	3.88511i	−0.185159	+	0.150885i
$664$	−28.3699			−1.10097
$665$	−0.693666	+	2.98718i	−0.0268992	+	0.115838i
$666$	0.661476	−	1.59694i	0.0256317	−	0.0618804i
$667$	−3.79608	−	2.19167i	−0.146985	−	0.0848617i
$668$	2.90435	+	22.0607i	0.112373	+	0.853555i
$669$	13.4812	−	17.5690i	0.521213	−	0.679258i
$670$	0.247491	−	1.87988i	0.00956140	−	0.0726260i
$671$	−3.55699	−	3.55699i	−0.137316	−	0.137316i
$672$	−4.36678	−	14.3486i	−0.168452	−	0.553511i
$673$	−30.2034	+	12.5107i	−1.16426	+	0.482250i	−0.879290	−	0.476287i	$-0.841982\pi$
$673$	−30.2034	+	12.5107i	−1.16426	+	0.482250i	−0.284966	+	0.958538i	$0.591982\pi$
$674$	−13.8168	−	1.81902i	−0.532204	−	0.0700660i
$675$	0.646422	+	4.91006i	0.0248808	+	0.188988i
$676$	11.5924	−	6.69288i	0.445862	−	0.257419i
$677$	17.0591	+	22.2318i	0.655633	+	0.854438i	0.996318	−	0.0857399i	$-0.0273254\pi$
$677$	17.0591	+	22.2318i	0.655633	+	0.854438i	−0.340684	+	0.940178i	$0.610659\pi$
$678$	3.92433	−	3.92433i	0.150713	−	0.150713i
$679$	1.06463	+	31.6465i	0.0408568	+	1.21448i
$680$	1.03941	+	2.31534i	0.0398595	+	0.0887893i
$681$	7.99174	−	13.8421i	0.306244	−	0.530430i
$682$	−6.50891	−	1.74406i	−0.249239	−	0.0667834i
$683$	−39.2720	+	5.17026i	−1.50270	+	0.197834i	−0.836512	−	0.547948i	$-0.815409\pi$
$683$	−39.2720	+	5.17026i	−1.50270	+	0.197834i	−0.666189	+	0.745783i	$0.732076\pi$
$684$	−5.71763	−	3.30107i	−0.218619	−	0.126220i
$685$	3.92247	+	1.62474i	0.149870	+	0.0620781i
$686$	−0.483784	+	16.1139i	−0.0184710	+	0.615233i
$687$	−22.9371	+	9.50085i	−0.875105	+	0.362480i
$688$	0.142872	−	0.0382826i	0.00544696	−	0.00145951i
$689$	−0.601628	+	2.24531i	−0.0229202	+	0.0855394i
$690$	−0.210137	−	0.161244i	−0.00799978	−	0.00613844i
$691$	−11.0966	−	1.46089i	−0.422134	−	0.0555750i	−0.0835329	−	0.996505i	$-0.526620\pi$
$691$	−11.0966	−	1.46089i	−0.422134	−	0.0555750i	−0.338601	+	0.940930i	$0.609954\pi$
$692$	10.0728	+	4.17229i	0.382910	+	0.158607i
$693$	−2.84923	+	0.0958519i	−0.108233	+	0.00364111i
$694$	7.67804	−	18.5364i	0.291454	−	0.703633i
$695$	−0.00546623	−	0.0204002i	−0.000207346	−	0.000773826i
$696$	4.43351	+	7.67906i	0.168052	+	0.291074i
$697$	−31.8803	−	23.0128i	−1.20755	−	0.871673i
$698$	−8.19541	+	14.1949i	−0.310201	+	0.537284i
$699$	−3.02884	+	3.02884i	−0.114561	+	0.114561i
$700$	12.5735	−	10.3378i	0.475232	−	0.390732i
$701$		−	32.2435i		−	1.21782i	−0.793240	−	0.608909i	$-0.791607\pi$
$701$		−	32.2435i		−	1.21782i	0.793240	−	0.608909i	$-0.208393\pi$
$702$	−1.03010	+	0.790421i	−0.0388785	+	0.0298325i
$703$	−6.42440	+	8.37244i	−0.242301	+	0.315772i
$704$	4.17062	+	3.20023i	0.157186	+	0.120613i
$705$	0.221856	−	0.0594461i	0.00835557	−	0.00223887i
$706$	2.47808	+	2.47808i	0.0932639	+	0.0932639i
$707$	−20.5146	+	28.6828i	−0.771532	+	1.07873i
$708$	5.15052	+	12.4344i	0.193568	+	0.467315i
$709$	−26.9347	+	20.6678i	−1.01156	+	0.776194i	−0.974789	−	0.223130i	$-0.928373\pi$
$709$	−26.9347	+	20.6678i	−1.01156	+	0.776194i	−0.0367668	+	0.999324i	$0.511706\pi$
$710$	1.12201	−	0.647796i	0.0421085	−	0.0243113i
$711$	−8.57873	+	1.12941i	−0.321727	+	0.0423562i
$712$	−1.43989	−	5.37375i	−0.0539623	−	0.201390i
$713$	10.0235			0.375384
$714$	9.30840	+	1.87637i	0.348358	+	0.0702214i
$715$	0.350542			0.0131095
$716$	7.76849	+	28.9924i	0.290322	+	1.08350i
$717$	−15.1925	+	2.00014i	−0.567376	+	0.0746965i
$718$	8.95802	−	5.17192i	0.334310	−	0.193014i
$719$	−13.6945	+	10.5082i	−0.510720	+	0.391889i	−0.831725	−	0.555189i	$-0.812646\pi$
$719$	−13.6945	+	10.5082i	−0.510720	+	0.391889i	0.321005	+	0.947078i	$0.395979\pi$
$720$	−0.00232717	−	0.00561828i	−8.67284e−5	−	0.000209381i
$721$	−39.0962	−	3.81497i	−1.45602	−	0.142077i
$722$	−5.68960	−	5.68960i	−0.211745	−	0.211745i
$723$	6.18847	−	1.65819i	0.230152	−	0.0616689i
$724$	4.31320	+	3.30963i	0.160299	+	0.123002i
$725$	−9.47198	+	12.3441i	−0.351780	+	0.458449i
$726$	−6.79464	+	5.21371i	−0.252173	+	0.193499i
$727$		−	22.9334i		−	0.850554i	−0.905063	−	0.425277i	$-0.860177\pi$
$727$		−	22.9334i		−	0.850554i	0.905063	−	0.425277i	$-0.139823\pi$
$728$	10.4278	+	3.91399i	0.386480	+	0.145062i
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	0.230640	−	0.399481i	0.00853638	−	0.0147854i
$731$	−5.04052	+	21.2837i	−0.186431	+	0.787206i
$732$	−2.89980	−	5.02261i	−0.107180	−	0.185641i
$733$	6.21114	+	23.1803i	0.229414	+	0.856184i	0.980588	+	0.196080i	$0.0628212\pi$
$733$	6.21114	+	23.1803i	0.229414	+	0.856184i	−0.751174	+	0.660104i	$0.770512\pi$
$734$	−0.0670334	+	0.161833i	−0.00247425	+	0.00597337i
$735$	0.102604	+	1.52325i	0.00378462	+	0.0561858i
$736$	−7.30704	−	3.02667i	−0.269341	−	0.111565i
$737$	−10.6696	−	1.40468i	−0.393019	−	0.0517420i
$738$	−6.58551	−	5.05324i	−0.242416	−	0.186012i
$739$	−8.30038	+	30.9774i	−0.305334	+	1.13952i	0.627323	+	0.778759i	$0.284151\pi$
$739$	−8.30038	+	30.9774i	−0.305334	+	1.13952i	−0.932657	+	0.360764i	$0.882516\pi$
$740$	−0.519694	+	0.139252i	−0.0191043	+	0.00511899i
$741$	7.32382	−	3.03362i	0.269047	−	0.111443i
$742$	3.26773	−	1.48415i	0.119962	−	0.0544848i
$743$	−47.7801	−	19.7912i	−1.75288	−	0.726067i	−0.997491	−	0.0707906i	$-0.977448\pi$
$743$	−47.7801	−	19.7912i	−1.75288	−	0.726067i	−0.755389	−	0.655276i	$-0.772552\pi$
$744$	−17.5600	−	10.1383i	−0.643780	−	0.371686i
$745$	−2.83445	+	0.373162i	−0.103846	+	0.0136716i
$746$	2.68318	+	0.718957i	0.0982384	+	0.0263229i
$747$	−5.02603	+	8.70534i	−0.183893	+	0.318512i
$748$	5.03507	−	2.26035i	0.184100	−	0.0826466i
$749$	−27.3717	−	14.5987i	−1.00014	−	0.533424i
$750$	−1.33604	+	1.33604i	−0.0487853	+	0.0487853i
$751$	4.50129	+	5.86620i	0.164254	+	0.214061i	0.868228	−	0.496166i	$-0.165259\pi$
$751$	4.50129	+	5.86620i	0.164254	+	0.214061i	−0.703973	+	0.710226i	$0.748593\pi$
$752$	0.0254293	−	0.0146816i	0.000927312	−	0.000535384i
$753$	0.265988	+	2.02038i	0.00969314	+	0.0736267i
$754$	−4.04441	−	0.532457i	−0.147289	−	0.0193909i
$755$	4.13855	−	1.71425i	0.150617	−	0.0623878i
$756$	−3.20161	−	0.743461i	−0.116442	−	0.0270394i
$757$	1.99870	+	1.99870i	0.0726441	+	0.0726441i	0.742495	−	0.669851i	$-0.233642\pi$
$757$	1.99870	+	1.99870i	0.0726441	+	0.0726441i	−0.669851	+	0.742495i	$0.733642\pi$
$758$	2.60965	−	19.8223i	0.0947869	−	0.719978i
$759$	−0.915168	+	1.19267i	−0.0332185	+	0.0432912i
$760$	−0.426989	−	3.24330i	−0.0154885	−	0.117647i
$761$	−32.4209	−	18.7182i	−1.17525	−	0.678534i	−0.220343	−	0.975422i	$-0.570718\pi$
$761$	−32.4209	−	18.7182i	−1.17525	−	0.678534i	−0.954912	+	0.296889i	$0.904051\pi$
$762$	0.177827	−	0.429313i	0.00644201	−	0.0155524i
$763$	6.71836	−	28.9317i	0.243221	−	1.04740i
$764$	−2.01737			−0.0729858
$765$	0.894608	+	0.0912438i	0.0323446	+	0.00329893i
$766$	−7.92865	−	13.7328i	−0.286474	−	0.496187i
$767$	−15.6096	−	4.18258i	−0.563630	−	0.151024i
$768$	9.69754	+	12.6381i	0.349930	+	0.456037i
$769$		−	20.5694i		−	0.741751i	−0.928683	−	0.370876i	$-0.879058\pi$
$769$		−	20.5694i		−	0.741751i	0.928683	−	0.370876i	$-0.120942\pi$
$770$	−0.343728	−	0.418063i	−0.0123871	−	0.0150659i
$771$	6.86173	+	16.5657i	0.247119	+	0.596599i
$772$	4.34822	−	33.0280i	0.156496	−	1.18870i
$773$	11.4755	−	42.8270i	0.412744	−	1.54038i	−0.376569	−	0.926389i	$-0.622896\pi$
$773$	11.4755	−	42.8270i	0.412744	−	1.54038i	0.789313	−	0.613992i	$-0.210437\pi$
$774$	−1.19514	+	4.46032i	−0.0429584	+	0.160323i
$775$	4.64416	−	35.2759i	0.166823	−	1.26715i
$776$	−12.9260	−	31.2062i	−0.464017	−	1.12024i
$777$	−1.84621	+	4.91873i	−0.0662323	+	0.176458i
$778$		−	2.30167i		−	0.0825189i
$779$	30.8518	+	40.2069i	1.10538	+	1.44056i
$780$	0.390378	+	0.104601i	0.0139778	+	0.00374533i
$781$	−3.67668	−	6.36820i	−0.131562	−	0.227872i
$782$	3.88170	−	3.16317i	0.138809	−	0.113115i
$783$	3.14177			0.112278
$784$	0.0630718	+	0.184706i	0.00225257	+	0.00659665i
$785$	0.527362	−	1.27316i	0.0188224	−	0.0454412i
$786$	1.57046	+	0.906707i	0.0560165	+	0.0323412i
$787$	3.71997	+	28.2560i	0.132603	+	1.00722i	0.920316	+	0.391175i	$0.127931\pi$
$787$	3.71997	+	28.2560i	0.132603	+	1.00722i	−0.787713	+	0.616042i	$0.788735\pi$
$788$	7.11612	−	9.27391i	0.253501	−	0.330369i
$789$	−0.658102	+	4.99878i	−0.0234291	+	0.177961i
$790$	−1.16157	−	1.16157i	−0.0413268	−	0.0413268i
$791$	−11.5201	+	12.3222i	−0.409608	+	0.438127i
$792$	2.80958	−	1.16377i	0.0998342	−	0.0413527i
$793$	6.90405	+	0.908936i	0.245170	+	0.0322773i
$794$	−2.12188	−	16.1173i	−0.0753027	−	0.571981i
$795$	0.294345	−	0.169940i	0.0104393	−	0.00602716i
$796$	−0.347227	−	0.452516i	−0.0123071	−	0.0160390i
$797$	−12.4444	+	12.4444i	−0.440802	+	0.440802i	−0.892282	−	0.451479i	$-0.850896\pi$
$797$	−12.4444	+	12.4444i	−0.440802	+	0.440802i	0.451479	+	0.892282i	$0.350896\pi$
$798$	−10.7994	−	5.75986i	−0.382295	−	0.203897i
$799$	0.127022	+	4.34020i	0.00449372	+	0.153545i
$800$	−14.0373	+	24.3134i	−0.496295	+	0.859608i
$801$	−1.90403	−	0.510185i	−0.0672758	−	0.0180265i
$802$	−6.53617	+	0.860504i	−0.230800	+	0.0303854i
$803$	−2.26733	−	1.30904i	−0.0800122	−	0.0461950i
$804$	−11.4629	−	4.74809i	−0.404266	−	0.167452i
$805$	0.654823	+	0.468345i	0.0230795	+	0.0165070i
$806$	8.61822	−	3.56978i	0.303564	−	0.125740i
$807$	−0.908988	+	0.243563i	−0.0319979	+	0.00857381i
$808$	9.73604	−	36.3354i	0.342513	−	1.27827i
$809$	17.9557	+	13.7779i	0.631288	+	0.484404i	0.874150	−	0.485657i	$-0.161419\pi$
$809$	17.9557	+	13.7779i	0.631288	+	0.484404i	−0.242862	+	0.970061i	$0.578086\pi$
$810$	0.188224	+	0.0247801i	0.00661351	+	0.000870685i
$811$	−34.7562	−	14.3965i	−1.22046	−	0.505529i	−0.322901	−	0.946433i	$-0.604658\pi$
$811$	−34.7562	−	14.3965i	−1.22046	−	0.505529i	−0.897555	+	0.440903i	$0.854658\pi$
$812$	−5.46095	−	8.76426i	−0.191642	−	0.307565i
$813$	8.67346	−	20.9396i	0.304192	−	0.734383i
$814$	−0.482053	−	1.79905i	−0.0168959	−	0.0630565i
$815$	0.496156	+	0.859367i	0.0173796	+	0.0301023i
$816$	0.113491	−	0.0183336i	0.00397299	−	0.000641803i
$817$	14.0962	−	24.4154i	0.493165	−	0.854187i
$818$	−4.09705	+	4.09705i	−0.143250	+	0.143250i
$819$	3.04841	−	2.50638i	0.106520	−	0.0875800i
$820$			2.58376i			0.0902289i
$821$	42.0992	−	32.3039i	1.46927	−	1.12741i	0.504799	−	0.863237i	$-0.331567\pi$
$821$	42.0992	−	32.3039i	1.46927	−	1.12741i	0.964474	−	0.264176i	$-0.0851001\pi$
$822$	−10.3154	+	13.4433i	−0.359791	+	0.468888i
$823$	12.9144	+	9.90954i	0.450167	+	0.345425i	0.808831	−	0.588042i	$-0.200101\pi$
$823$	12.9144	+	9.90954i	0.450167	+	0.345425i	−0.358664	+	0.933467i	$0.616768\pi$
$824$	40.4753	−	10.8453i	1.41002	−	0.377815i
$825$	3.77335	+	3.77335i	0.131371	+	0.131371i
$826$	10.3179	+	22.7176i	0.359007	+	0.790445i
$827$	3.35156	+	8.09138i	0.116545	+	0.281365i	0.971378	−	0.237538i	$-0.0763405\pi$
$827$	3.35156	+	8.09138i	0.116545	+	0.281365i	−0.854833	+	0.518903i	$0.826341\pi$
$828$	−1.37506	+	1.05512i	−0.0477866	+	0.0366679i
$829$	22.8359	−	13.1843i	0.793124	−	0.457910i	−0.0479371	−	0.998850i	$-0.515265\pi$
$829$	22.8359	−	13.1843i	0.793124	−	0.457910i	0.841061	+	0.540940i	$0.181931\pi$
$830$	−1.89204	+	0.249091i	−0.0656735	+	0.00864608i
$831$	−4.42741	−	16.5233i	−0.153585	−	0.573188i
$832$	−7.27733			−0.252296
$833$	−28.4684	−	4.74869i	−0.986372	−	0.164532i
$834$	0.0842920			0.00291879
$835$	1.01106	+	3.77334i	0.0349893	+	0.130582i
$836$	−7.05306	+	0.928553i	−0.243935	+	0.0321147i
$837$	−6.22187	+	3.59220i	−0.215059	+	0.124165i
$838$	−18.8725	+	14.4814i	−0.651939	+	0.500251i
$839$	3.73445	+	9.01576i	0.128927	+	0.311258i	0.975141	−	0.221586i	$-0.0711232\pi$
$839$	3.73445	+	9.01576i	0.128927	+	0.311258i	−0.846213	+	0.532844i	$0.821123\pi$
$840$	−0.673464	−	1.48280i	−0.0232367	−	0.0511615i
$841$	−13.5264	−	13.5264i	−0.466429	−	0.466429i
$842$	−17.8861	+	4.79256i	−0.616394	+	0.165162i
$843$	−25.0829	−	19.2468i	−0.863902	−	0.662895i
$844$	10.6850	−	13.9250i	0.367793	−	0.479317i
$845$	1.86441	−	1.43061i	0.0641376	−	0.0492145i
$846$			0.916689i			0.0315164i
$847$	20.1076	−	16.5323i	0.690907	−	0.568058i
$848$	0.0307248	−	0.0307248i	0.00105509	−	0.00105509i
$849$	11.3163	−	19.6004i	0.388375	−	0.672685i
$850$	−9.33367	−	15.1265i	−0.320142	−	0.518833i
$851$	1.38524	+	2.39930i	0.0474853	+	0.0822470i
$852$	−2.19423	−	8.18899i	−0.0751732	−	0.280550i
$853$	−14.2568	+	34.4190i	−0.488144	+	1.17848i	0.467509	+	0.883988i	$0.345152\pi$
$853$	−14.2568	+	34.4190i	−0.488144	+	1.17848i	−0.955653	+	0.294496i	$0.904848\pi$
$854$	−5.68583	−	9.12516i	−0.194565	−	0.312257i
$855$	−1.07086	−	0.443564i	−0.0366226	−	0.0151696i
$856$	32.8083	+	4.31930i	1.12137	+	0.147631i
$857$	13.9991	+	10.7419i	0.478200	+	0.366935i	0.819557	−	0.572998i	$-0.194220\pi$
$857$	13.9991	+	10.7419i	0.478200	+	0.366935i	−0.341357	+	0.939934i	$0.610887\pi$
$858$	−0.362103	+	1.35138i	−0.0123620	+	0.0461355i
$859$	−42.9916	+	11.5196i	−1.46685	+	0.393042i	−0.901851	−	0.432046i	$-0.857792\pi$
$859$	−42.9916	+	11.5196i	−1.46685	+	0.393042i	−0.565003	+	0.825089i	$0.691125\pi$
$860$	1.32791	−	0.550037i	0.0452812	−	0.0187561i
$861$	20.5216	+	14.6775i	0.699374	+	0.500209i
$862$	23.0693	+	9.55564i	0.785745	+	0.325466i
$863$	17.5436	+	10.1288i	0.597192	+	0.344789i	0.767936	−	0.640527i	$-0.221284\pi$
$863$	17.5436	+	10.1288i	0.597192	+	0.344789i	−0.170744	+	0.985315i	$0.554617\pi$
$864$	5.62037	−	0.739935i	0.191209	−	0.0251731i
$865$	1.84888	+	0.495407i	0.0628639	+	0.0168443i
$866$	−6.76714	+	11.7210i	−0.229957	+	0.398297i
$867$	−5.57596	+	16.0595i	−0.189369	+	0.545410i
$868$	20.8355	+	11.1126i	0.707202	+	0.377186i
$869$	−6.59270	+	6.59270i	−0.223642	+	0.223642i
$870$	0.363101	+	0.473203i	0.0123103	+	0.0160431i
$871$	12.9017	−	7.44880i	0.437158	−	0.252393i
$872$	4.13552	+	31.4124i	0.140046	+	1.06376i
$873$	−11.8656	−	1.56214i	−0.401591	−	0.0528705i
$874$	−5.96289	+	2.46991i	−0.201698	+	0.0835459i
$875$	3.92203	−	4.19511i	0.132589	−	0.141820i
$876$	−2.13437	−	2.13437i	−0.0721135	−	0.0721135i
$877$	−4.44055	+	33.7293i	−0.149947	+	1.13896i	0.736603	+	0.676325i	$0.236429\pi$
$877$	−4.44055	+	33.7293i	−0.149947	+	1.13896i	−0.886550	+	0.462633i	$0.846905\pi$
$878$	12.2542	−	15.9700i	0.413558	−	0.538960i
$879$	−0.171667	−	1.30394i	−0.00579019	−	0.0439809i
$880$	−0.00567469	−	0.00327629i	−0.000191294	−	0.000110444i
$881$	−8.08150	+	19.5105i	−0.272273	+	0.657324i	−0.999580	−	0.0289880i	$-0.990772\pi$
$881$	−8.08150	+	19.5105i	−0.272273	+	0.657324i	0.727307	+	0.686312i	$0.240772\pi$
$882$	−5.97830	−	1.17793i	−0.201300	−	0.0396629i
$883$	−33.2848			−1.12012			−0.560061	−	0.828452i	$-0.689222\pi$
$883$	−33.2848			−1.12012			−0.560061	+	0.828452i	$0.689222\pi$
$884$	−3.62495	+	6.72561i	−0.121920	+	0.226207i
$885$	1.18144	+	2.04632i	0.0397137	+	0.0687862i
$886$	−5.52152	−	1.47949i	−0.185499	−	0.0497044i
$887$	1.13818	+	1.48330i	0.0382162	+	0.0498043i	0.812071	−	0.583559i	$-0.198340\pi$
$887$	1.13818	+	1.48330i	0.0382162	+	0.0498043i	−0.773854	+	0.633364i	$0.781674\pi$
$888$		−	5.60437i		−	0.188070i
$889$	−0.496323	+	1.32232i	−0.0166461	+	0.0443493i
$890$	−0.143211	−	0.345742i	−0.00480045	−	0.0115893i
$891$	0.140644	−	1.06830i	0.00471175	−	0.0357893i
$892$	7.12036	−	26.5735i	0.238407	−	0.889748i
$893$	1.44853	−	5.40600i	0.0484733	−	0.180905i
$894$	1.48934	−	11.3126i	0.0498108	−	0.378351i
$895$	2.01656	+	4.86841i	0.0674062	+	0.162733i
$896$	−11.9149	−	14.4916i	−0.398048	−	0.484130i
$897$		−	2.08109i		−	0.0694856i
$898$	8.20518	+	10.6932i	0.273810	+	0.356837i
$899$	−21.8026	−	5.84200i	−0.727159	−	0.194842i
$900$	3.07619	+	5.32812i	0.102540	+	0.177604i
$901$	1.84385	+	6.15508i	0.0614274	+	0.205056i
$902$	−8.94431			−0.297813
$903$	3.17473	−	13.6715i	0.105648	−	0.454960i
$904$	6.88609	−	16.6245i	0.229028	−	0.552922i
$905$	0.826598	+	0.477237i	0.0274770	+	0.0158639i
$906$	2.33360	+	17.7254i	0.0775286	+	0.588888i
$907$	8.65553	−	11.2801i	0.287402	−	0.374550i	−0.627232	−	0.778832i	$-0.715812\pi$
$907$	8.65553	−	11.2801i	0.287402	−	0.374550i	0.914634	+	0.404283i	$0.132479\pi$
$908$	2.59175	−	19.6863i	0.0860103	−	0.653313i
$909$	−9.42472	−	9.42472i	−0.312598	−	0.312598i
$910$	0.729813	+	0.169473i	0.0241931	+	0.00561798i
$911$	−33.5613	+	13.9015i	−1.11194	+	0.460579i	−0.861604	−	0.507581i	$-0.830540\pi$
$911$	−33.5613	+	13.9015i	−1.11194	+	0.460579i	−0.250332	+	0.968160i	$0.580540\pi$
$912$	−0.146914	−	0.0193415i	−0.00486480	−	0.000640463i
$913$	1.41376	+	10.7386i	0.0467887	+	0.355395i
$914$	28.9977	−	16.7419i	0.959160	−	0.553771i
$915$	−0.619836	−	0.807786i	−0.0204912	−	0.0267046i
$916$	−21.8088	+	21.8088i	−0.720584	+	0.720584i
$917$	−4.86334	−	2.59386i	−0.160602	−	0.0856569i
$918$	−1.27587	+	3.35457i	−0.0421099	+	0.110717i
$919$	−2.80953	+	4.86625i	−0.0926779	+	0.160523i	−0.908637	−	0.417587i	$-0.862876\pi$
$919$	−2.80953	+	4.86625i	−0.0926779	+	0.160523i	0.815959	+	0.578109i	$0.196209\pi$
$920$	−0.829530	−	0.222272i	−0.0273488	−	0.00732808i
$921$	21.5972	−	2.84333i	0.711652	−	0.0936908i
$922$	17.4631	+	10.0823i	0.575115	+	0.332043i
$923$	9.40457	+	3.89550i	0.309555	+	0.128222i
$924$	−3.22458	+	1.46455i	−0.106081	+	0.0481802i
$925$	9.08570	−	3.76342i	0.298736	−	0.123740i
$926$	19.7302	−	5.28670i	0.648375	−	0.173732i
$927$	3.84273	−	14.3413i	0.126212	−	0.471028i
$928$	14.1299	+	10.8422i	0.463835	+	0.355913i
$929$	−9.41236	−	1.23916i	−0.308809	−	0.0406555i	−0.0254711	−	0.999676i	$-0.508109\pi$
$929$	−9.41236	−	1.23916i	−0.308809	−	0.0406555i	−0.283338	+	0.959020i	$0.591442\pi$
$930$	−1.26012	−	0.521958i	−0.0413209	−	0.0171157i
$931$	33.3946	+	16.3934i	1.09446	+	0.537272i
$932$	−2.03637	+	4.91622i	−0.0667034	+	0.161036i
$933$	−8.04432	−	30.0218i	−0.263359	−	0.982870i
$934$	18.2802	+	31.6623i	0.598147	+	1.03602i
$935$	0.824608	−	0.508818i	0.0269676	−	0.0166401i
$936$	−2.10491	+	3.64581i	−0.0688012	+	0.119167i
$937$	13.7900	−	13.7900i	0.450499	−	0.450499i	−0.445021	−	0.895520i	$-0.646804\pi$
$937$	13.7900	−	13.7900i	0.450499	−	0.450499i	0.895520	+	0.445021i	$0.146804\pi$
$938$	−21.5345	−	8.08279i	−0.703126	−	0.263913i
$939$			22.0966i			0.721096i
$940$	0.226370	−	0.173699i	0.00738336	−	0.00566545i
$941$	−30.3941	+	39.6104i	−0.990821	+	1.29126i	−0.0343577	+	0.999410i	$0.510939\pi$
$941$	−30.3941	+	39.6104i	−0.990821	+	1.29126i	−0.956463	+	0.291853i	$0.905728\pi$
$942$	4.36346	+	3.34820i	0.142169	+	0.109090i
$943$	12.8513	−	3.44349i	0.418495	−	0.112135i
$944$	0.213602	+	0.213602i	0.00695214	+	0.00695214i
$945$	−0.574310	−	0.0560406i	−0.0186823	−	0.00182300i
$946$	1.90408	+	4.59686i	0.0619071	+	0.149457i
$947$	1.94716	−	1.49411i	0.0632741	−	0.0485519i	−0.576640	−	0.816998i	$-0.695637\pi$
$947$	1.94716	−	1.49411i	0.0632741	−	0.0485519i	0.639914	+	0.768446i	$0.278970\pi$
$948$	−9.30914	+	5.37463i	−0.302347	+	0.174560i
$949$	3.59327	−	0.473062i	0.116642	−	0.0153563i
$950$	5.92961	+	22.1296i	0.192382	+	0.717979i
$951$	−13.8887			−0.450373
$952$	30.2113	−	5.92895i	0.979155	−	0.192158i
$953$	33.7181			1.09224			0.546119	−	0.837708i	$-0.316105\pi$
$953$	33.7181			1.09224			0.546119	+	0.837708i	$0.316105\pi$
$954$	0.351089	+	1.31028i	0.0113669	+	0.0424220i
$955$	−0.351144	+	0.0462289i	−0.0113627	+	0.00149593i
$956$	−16.4861	+	9.51823i	−0.533197	+	0.307842i
$957$	2.68575	−	2.06085i	0.0868179	−	0.0666177i
$958$	6.68260	+	16.1332i	0.215905	+	0.521241i
$959$	29.9618	−	41.8916i	0.967518	−	1.35275i
$960$	0.752404	+	0.752404i	0.0242837	+	0.0242837i
$961$	19.9131	−	5.33571i	0.642359	−	0.172120i
$962$	2.04551	+	1.56958i	0.0659500	+	0.0506052i
$963$	7.13772	−	9.30206i	0.230010	−	0.299755i
$964$	6.31437	−	4.84519i	0.203372	−	0.156053i
$965$		−	5.84851i		−	0.188270i
$966$	−2.48195	+	2.04064i	−0.0798553	+	0.0656564i
$967$	26.9308	−	26.9308i	0.866036	−	0.866036i	−0.125995	−	0.992031i	$-0.540212\pi$
$967$	26.9308	−	26.9308i	0.866036	−	0.866036i	0.992031	+	0.125995i	$0.0402124\pi$
$968$	−13.8842	+	24.0482i	−0.446256	+	0.772938i
$969$	12.8250	−	17.7669i	0.411999	−	0.570754i
$970$	−1.13605	−	1.96770i	−0.0364764	−	0.0631790i
$971$	−6.54195	−	24.4149i	−0.209941	−	0.783512i	−0.987886	−	0.155179i	$-0.950404\pi$
$971$	−6.54195	−	24.4149i	−0.209941	−	0.783512i	0.777945	−	0.628332i	$-0.216262\pi$
$972$	0.475405	−	1.14773i	0.0152486	−	0.0368135i
$973$	−0.256059	+	0.00861416i	−0.00820887	+	0.000276157i
$974$	19.9790	+	8.27557i	0.640168	+	0.265166i
$975$	−7.32400	−	0.964223i	−0.234556	−	0.0308798i
$976$	−0.103270	−	0.0792417i	−0.00330559	−	0.00253647i
$977$	−5.65949	+	21.1215i	−0.181063	+	0.675737i	0.814376	+	0.580338i	$0.197079\pi$
$977$	−5.65949	+	21.1215i	−0.181063	+	0.675737i	−0.995439	+	0.0953994i	$0.969587\pi$
$978$	−3.82549	+	1.02504i	−0.122326	+	0.0327771i
$979$	−1.96232	+	0.812820i	−0.0627161	+	0.0259778i
$980$	0.841922	+	1.69950i	0.0268942	+	0.0542885i
$981$	10.3716	+	4.29605i	0.331139	+	0.137162i
$982$	−15.1491	−	8.74636i	−0.483428	−	0.279107i
$983$	47.6946	−	6.27912i	1.52122	−	0.200273i	0.676887	−	0.736087i	$-0.263329\pi$
$983$	47.6946	−	6.27912i	1.52122	−	0.200273i	0.844336	+	0.535815i	$0.179995\pi$
$984$	−25.9968	−	6.96581i	−0.828746	−	0.222062i
$985$	1.02612	−	1.77729i	0.0326948	−	0.0566291i
$986$	−10.2868	+	4.61799i	−0.327600	+	0.147067i
$987$	−0.0936803	−	2.78468i	−0.00298188	−	0.0886373i
$988$	6.96356	−	6.96356i	0.221540	−	0.221540i
$989$	−4.50557	−	5.87177i	−0.143269	−	0.186711i
$990$	0.177158	−	0.102282i	0.00563044	−	0.00325074i
$991$	3.79029	+	28.7901i	0.120403	+	0.914548i	0.939896	+	0.341460i	$0.110921\pi$
$991$	3.79029	+	28.7901i	0.120403	+	0.914548i	−0.819494	+	0.573088i	$0.805745\pi$
$992$	−40.3790	−	5.31599i	−1.28203	−	0.168783i
$993$	−10.6272	+	4.40193i	−0.337244	+	0.139691i
$994$	−4.57591	−	15.0358i	−0.145139	−	0.476907i
$995$	−0.0708081	−	0.0708081i	−0.00224477	−	0.00224477i
$996$	−1.62996	+	12.3808i	−0.0516473	+	0.392300i
$997$	6.68310	−	8.70959i	0.211656	−	0.275835i	−0.675445	−	0.737410i	$-0.736049\pi$
$997$	6.68310	−	8.70959i	0.211656	−	0.275835i	0.887101	+	0.461575i	$0.152715\pi$
$998$	−0.763982	−	5.80302i	−0.0241834	−	0.183691i
$999$	−1.71971	−	0.992874i	−0.0544092	−	0.0314132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bh.a.331.16	yes	192
7.4	even	3	inner	357.2.bh.a.25.9	✓	192
17.15	even	8	inner	357.2.bh.a.100.9	yes	192
119.32	even	24	inner	357.2.bh.a.151.16	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bh.a.25.9	✓	192	7.4	even	3	inner
357.2.bh.a.100.9	yes	192	17.15	even	8	inner
357.2.bh.a.151.16	yes	192	119.32	even	24	inner
357.2.bh.a.331.16	yes	192	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.225292 + 0.840803i) q^{2} +(0.991445 - 0.130526i) q^{3} +(1.07586 - 0.621147i) q^{4} +(0.173030 - 0.132771i) q^{5} +(0.333112 + 0.804203i) q^{6} +(-1.09410 - 2.40893i) q^{7} +(1.99567 + 1.99567i) q^{8} +(0.965926 - 0.258819i) q^{9} +(0.150616 + 0.115572i) q^{10} +(0.655950 - 0.854851i) q^{11} +(0.985578 - 0.756261i) q^{12} +1.49163i q^{13} +(1.77894 - 1.46263i) q^{14} +(0.154220 - 0.154220i) q^{15} +(0.0139413 - 0.0241470i) q^{16} +(2.16513 + 3.50888i) q^{17} +(0.435232 + 0.753843i) q^{18} +(-1.37549 - 5.13340i) q^{19} +(0.103686 - 0.250320i) q^{20} +(-1.39917 - 2.24551i) q^{21} +(0.866542 + 0.358933i) q^{22} +(-1.38324 - 0.182107i) q^{23} +(2.23908 + 1.71811i) q^{24} +(-1.28178 + 4.78368i) q^{25} +(-1.25417 + 0.336053i) q^{26} +(0.923880 - 0.382683i) q^{27} +(-2.67339 - 1.91207i) q^{28} +(2.90262 + 1.20230i) q^{29} +(0.164413 + 0.0949240i) q^{30} +(-7.12294 + 0.937752i) q^{31} +(5.47570 + 1.46721i) q^{32} +(0.538758 - 0.933156i) q^{33} +(-2.46249 + 2.61097i) q^{34} +(-0.509148 - 0.271554i) q^{35} +(0.878435 - 0.878435i) q^{36} +(-1.20885 - 1.57540i) q^{37} +(4.00629 - 2.31303i) q^{38} +(0.194697 + 1.47887i) q^{39} +(0.610277 + 0.0803444i) q^{40} +(-8.81025 + 3.64932i) q^{41} +(1.57281 - 1.68232i) q^{42} +(3.75109 + 3.75109i) q^{43} +(0.174721 - 1.32714i) q^{44} +(0.132771 - 0.173030i) q^{45} +(-0.158518 - 1.20406i) q^{46} +(0.912015 + 0.526552i) q^{47} +(0.0106702 - 0.0257601i) q^{48} +(-4.60590 + 5.27121i) q^{49} -4.31091 q^{50} +(2.60461 + 3.19625i) q^{51} +(0.926522 + 1.60478i) q^{52} +(1.50527 + 0.403336i) q^{53} +(0.529904 + 0.690585i) q^{54} -0.235006i q^{55} +(2.62397 - 6.99087i) q^{56} +(-2.03376 - 4.90994i) q^{57} +(-0.356963 + 2.71140i) q^{58} +(-2.80403 + 10.4648i) q^{59} +(0.0701255 - 0.261712i) q^{60} +(0.609357 - 4.62853i) q^{61} +(-2.39321 - 5.77772i) q^{62} +(-1.68029 - 2.04368i) q^{63} +4.87877i q^{64} +(0.198045 + 0.258097i) q^{65} +(0.905978 + 0.242756i) q^{66} +(-4.99373 - 8.64940i) q^{67} +(4.50890 + 2.43019i) q^{68} -1.39518 q^{69} +(0.113616 - 0.489272i) q^{70} +(2.61157 - 6.30489i) q^{71} +(2.44418 + 1.41115i) q^{72} +(-0.317144 - 2.40895i) q^{73} +(1.05226 - 1.37133i) q^{74} +(-0.646422 + 4.91006i) q^{75} +(-4.66842 - 4.66842i) q^{76} +(-2.77695 - 0.644849i) q^{77} +(-1.19957 + 0.496880i) q^{78} +(-8.57873 - 1.12941i) q^{79} +(-0.000793754 - 0.00602916i) q^{80} +(0.866025 - 0.500000i) q^{81} +(-5.05324 - 6.58551i) q^{82} +(-7.10788 + 7.10788i) q^{83} +(-2.90010 - 1.54677i) q^{84} +(0.840509 + 0.319676i) q^{85} +(-2.30883 + 3.99902i) q^{86} +(3.03472 + 0.813151i) q^{87} +(3.01505 - 0.396939i) q^{88} +(-1.70711 - 0.985601i) q^{89} +(0.175397 + 0.0726516i) q^{90} +(3.59324 - 1.63199i) q^{91} +(-1.60129 + 0.663276i) q^{92} +(-6.93960 + 1.85946i) q^{93} +(-0.237256 + 0.885453i) q^{94} +(-0.919566 - 0.705608i) q^{95} +(5.62037 + 0.739935i) q^{96} +(-11.0570 - 4.57996i) q^{97} +(-5.46972 - 2.68509i) q^{98} +(0.412348 - 0.995495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 8 q^{5} + 8 q^{11} - 80 q^{14} + 96 q^{16} - 16 q^{17} + 16 q^{22} + 8 q^{25} - 64 q^{26} - 88 q^{28} - 40 q^{32} - 32 q^{33} - 32 q^{35} + 32 q^{37} - 64 q^{40} - 64 q^{41} - 56 q^{42} - 32 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) \) 192 * q - 8 * q^5 + 8 * q^11 - 80 * q^14 + 96 * q^16 - 16 * q^17 + 16 * q^22 + 8 * q^25 - 64 * q^26 - 88 * q^28 - 40 * q^32 - 32 * q^33 - 32 * q^35 + 32 * q^37 - 64 * q^40 - 64 * q^41 - 56 * q^42 - 32 * q^43 + 32 * q^44 + 56 * q^49 + 64 * q^50 + 96 * q^52 + 64 * q^53 - 152 * q^56 - 32 * q^58 - 16 * q^59 + 40 * q^61 - 112 * q^62 + 32 * q^65 - 16 * q^67 + 48 * q^68 - 128 * q^69 - 120 * q^70 + 96 * q^71 + 8 * q^73 - 64 * q^74 - 112 * q^76 + 32 * q^77 - 16 * q^78 + 16 * q^79 + 192 * q^80 - 8 * q^82 - 16 * q^83 + 48 * q^84 - 64 * q^86 + 24 * q^87 - 136 * q^88 - 160 * q^92 + 48 * q^93 - 64 * q^94 - 104 * q^95 - 48 * q^96 - 96 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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