LMFDB - Embedded newform 640.2.bm.a.101.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

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

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.15
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.06065 + 0.935428i) q^{2} +(0.988226 - 0.528218i) q^{3} +(0.249949 - 1.98432i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-0.554050 + 1.48467i) q^{6} +(-1.61350 + 1.07810i) q^{7} +(1.59108 + 2.33847i) q^{8} +(-0.969134 + 1.45041i) q^{9} +(-1.39596 - 0.226463i) q^{10} +(-0.494740 + 0.150078i) q^{11} +(-0.801147 - 2.09298i) q^{12} +(3.45448 + 2.83502i) q^{13} +(0.702863 - 2.65280i) q^{14} +(1.03524 + 0.428811i) q^{15} +(-3.87505 - 0.991957i) q^{16} +(-5.14405 + 2.13073i) q^{17} +(-0.328846 - 2.44493i) q^{18} +(-0.0900704 - 0.914500i) q^{19} +(1.69247 - 1.06563i) q^{20} +(-1.02503 + 1.91769i) q^{21} +(0.384358 - 0.621974i) q^{22} +(-0.465669 + 0.0926273i) q^{23} +(2.80757 + 1.47050i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-6.31595 + 0.224461i) q^{26} +(-0.521086 + 5.29067i) q^{27} +(1.73601 + 3.47116i) q^{28} +(-0.523606 + 1.72610i) q^{29} +(-1.49915 + 0.513576i) q^{30} +(-0.516741 - 0.516741i) q^{31} +(5.03797 - 2.57271i) q^{32} +(-0.409641 + 0.409641i) q^{33} +(3.46288 - 7.07184i) q^{34} +(-1.85698 - 0.563308i) q^{35} +(2.63585 + 2.28560i) q^{36} +(3.16552 + 0.311777i) q^{37} +(0.950982 + 0.885708i) q^{38} +(4.91132 + 0.976922i) q^{39} +(-0.798294 + 2.71343i) q^{40} +(1.39813 + 7.02889i) q^{41} +(-0.706668 - 2.99283i) q^{42} +(9.65433 + 5.16035i) q^{43} +(0.174143 + 1.01923i) q^{44} +(-1.73600 + 0.170981i) q^{45} +(0.407264 - 0.533844i) q^{46} +(-0.796223 - 1.92225i) q^{47} +(-4.35340 + 1.06659i) q^{48} +(-1.23772 + 2.98812i) q^{49} +(-0.710532 - 1.22276i) q^{50} +(-3.95799 + 4.82282i) q^{51} +(6.48903 - 6.14619i) q^{52} +(2.01978 + 6.65832i) q^{53} +(-4.39636 - 6.09898i) q^{54} +(-0.429872 - 0.287231i) q^{55} +(-5.08832 - 2.05777i) q^{56} +(-0.572065 - 0.856156i) q^{57} +(-1.05928 - 2.32058i) q^{58} +(-2.47915 + 2.03458i) q^{59} +(1.10966 - 1.94707i) q^{60} +(-6.06772 - 11.3519i) q^{61} +(1.03146 + 0.0647064i) q^{62} -3.38506i q^{63} +(-2.93692 + 7.44140i) q^{64} +4.46887i q^{65} +(0.0512953 - 0.817675i) q^{66} +(0.510007 + 0.954156i) q^{67} +(2.94231 + 10.7400i) q^{68} +(-0.411259 + 0.337511i) q^{69} +(2.49653 - 1.13960i) q^{70} +(-2.65416 - 3.97222i) q^{71} +(-4.93372 + 0.0414272i) q^{72} +(6.17789 + 4.12794i) q^{73} +(-3.64915 + 2.63043i) q^{74} +(0.325275 + 1.07229i) q^{75} +(-1.83717 - 0.0498497i) q^{76} +(0.636462 - 0.775531i) q^{77} +(-6.12302 + 3.55802i) q^{78} +(1.33330 - 3.21887i) q^{79} +(-1.69151 - 3.62475i) q^{80} +(0.277024 + 0.668796i) q^{81} +(-8.05794 - 6.14732i) q^{82} +(-6.46372 + 0.636621i) q^{83} +(3.54910 + 2.51330i) q^{84} +(-4.91043 - 2.62468i) q^{85} +(-15.0670 + 3.55762i) q^{86} +(0.394315 + 1.98235i) q^{87} +(-1.13812 - 0.918151i) q^{88} +(-4.21414 - 0.838245i) q^{89} +(1.68134 - 1.80525i) q^{90} +(-8.63025 - 0.850005i) q^{91} +(0.0674088 + 0.947188i) q^{92} +(-0.783609 - 0.237705i) q^{93} +(2.64264 + 1.29402i) q^{94} +(0.649778 - 0.649778i) q^{95} +(3.61970 - 5.20357i) q^{96} +(0.0678790 + 0.0678790i) q^{97} +(-1.48239 - 4.32715i) q^{98} +(0.261795 - 0.863022i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.06065	+	0.935428i	−0.749991	+	0.661448i
$2$	−1.06065	+	0.935428i	−0.749991	+	0.661448i
$3$	0.988226	−	0.528218i	0.570553	−	0.304967i	−0.160777	−	0.986991i	$-0.551400\pi$
$3$	0.988226	−	0.528218i	0.570553	−	0.304967i	0.731330	+	0.682024i	$0.238900\pi$
$4$	0.249949	−	1.98432i	0.124974	−	0.992160i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$6$	−0.554050	+	1.48467i	−0.226190	+	0.606113i
$7$	−1.61350	+	1.07810i	−0.609844	+	0.407485i	−0.821785	−	0.569798i	$-0.807022\pi$
$7$	−1.61350	+	1.07810i	−0.609844	+	0.407485i	0.211941	+	0.977283i	$0.432022\pi$
$8$	1.59108	+	2.33847i	0.562532	+	0.826775i
$9$	−0.969134	+	1.45041i	−0.323045	+	0.483471i
$10$	−1.39596	−	0.226463i	−0.441442	−	0.0716138i
$11$	−0.494740	+	0.150078i	−0.149170	+	0.0452502i	−0.363987	−	0.931404i	$-0.618585\pi$
$11$	−0.494740	+	0.150078i	−0.149170	+	0.0452502i	0.214817	+	0.976654i	$0.431085\pi$
$12$	−0.801147	−	2.09298i	−0.231271	−	0.604192i
$13$	3.45448	+	2.83502i	0.958102	+	0.786294i	0.976937	−	0.213529i	$-0.0684958\pi$
$13$	3.45448	+	2.83502i	0.958102	+	0.786294i	−0.0188352	+	0.999823i	$0.505996\pi$
$14$	0.702863	−	2.65280i	0.187848	−	0.708990i
$15$	1.03524	+	0.428811i	0.267298	+	0.110719i
$16$	−3.87505	−	0.991957i	−0.968763	−	0.247989i
$17$	−5.14405	+	2.13073i	−1.24761	+	0.516779i	−0.906086	−	0.423093i	$-0.860944\pi$
$17$	−5.14405	+	2.13073i	−1.24761	+	0.516779i	−0.341528	+	0.939872i	$0.610944\pi$
$18$	−0.328846	−	2.44493i	−0.0775096	−	0.576276i
$19$	−0.0900704	−	0.914500i	−0.0206636	−	0.209801i	−0.999972	−	0.00742925i	$-0.997635\pi$
$19$	−0.0900704	−	0.914500i	−0.0206636	−	0.209801i	0.979309	−	0.202371i	$-0.0648648\pi$
$20$	1.69247	−	1.06563i	0.378447	−	0.238281i
$21$	−1.02503	+	1.91769i	−0.223679	+	0.418474i
$22$	0.384358	−	0.621974i	0.0819455	−	0.132605i
$23$	−0.465669	+	0.0926273i	−0.0970986	+	0.0193141i	−0.243400	−	0.969926i	$-0.578263\pi$
$23$	−0.465669	+	0.0926273i	−0.0970986	+	0.0193141i	0.146302	+	0.989240i	$0.453263\pi$
$24$	2.80757	+	1.47050i	0.573093	+	0.300165i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	−6.31595	+	0.224461i	−1.23866	+	0.0440204i
$27$	−0.521086	+	5.29067i	−0.100283	+	1.01819i
$28$	1.73601	+	3.47116i	0.328075	+	0.655988i
$29$	−0.523606	+	1.72610i	−0.0972312	+	0.320528i	−0.992040	−	0.125921i	$-0.959812\pi$
$29$	−0.523606	+	1.72610i	−0.0972312	+	0.320528i	0.894809	+	0.446449i	$0.147312\pi$
$30$	−1.49915	+	0.513576i	−0.273706	+	0.0937658i
$31$	−0.516741	−	0.516741i	−0.0928095	−	0.0928095i	0.659178	−	0.751987i	$-0.270904\pi$
$31$	−0.516741	−	0.516741i	−0.0928095	−	0.0928095i	−0.751987	+	0.659178i	$0.770904\pi$
$32$	5.03797	−	2.57271i	0.890596	−	0.454796i
$33$	−0.409641	+	0.409641i	−0.0713094	+	0.0713094i
$34$	3.46288	−	7.07184i	0.593878	−	1.21281i
$35$	−1.85698	−	0.563308i	−0.313886	−	0.0952164i
$36$	2.63585	+	2.28560i	0.439308	+	0.380933i
$37$	3.16552	+	0.311777i	0.520409	+	0.0512558i	0.354812	−	0.934938i	$-0.384545\pi$
$37$	3.16552	+	0.311777i	0.520409	+	0.0512558i	0.165597	+	0.986194i	$0.447045\pi$
$38$	0.950982	+	0.885708i	0.154270	+	0.143681i
$39$	4.91132	+	0.976922i	0.786441	+	0.156433i
$40$	−0.798294	+	2.71343i	−0.126221	+	0.429032i
$41$	1.39813	+	7.02889i	0.218352	+	1.09773i	0.922003	+	0.387182i	$0.126552\pi$
$41$	1.39813	+	7.02889i	0.218352	+	1.09773i	−0.703652	+	0.710545i	$0.748448\pi$
$42$	−0.706668	−	2.99283i	−0.109041	−	0.461804i
$43$	9.65433	+	5.16035i	1.47227	+	0.786946i	0.995739	−	0.0922109i	$-0.0293934\pi$
$43$	9.65433	+	5.16035i	1.47227	+	0.786946i	0.476533	+	0.879157i	$0.341893\pi$
$44$	0.174143	+	1.01923i	0.0262530	+	0.153655i
$45$	−1.73600	+	0.170981i	−0.258787	+	0.0254883i
$46$	0.407264	−	0.533844i	0.0600479	−	0.0787111i
$47$	−0.796223	−	1.92225i	−0.116141	−	0.280389i	0.855110	−	0.518446i	$-0.173489\pi$
$47$	−0.796223	−	1.92225i	−0.116141	−	0.280389i	−0.971251	+	0.238057i	$0.923489\pi$
$48$	−4.35340	+	1.06659i	−0.628359	+	0.153950i
$49$	−1.23772	+	2.98812i	−0.176817	+	0.426875i
$50$	−0.710532	−	1.22276i	−0.100484	−	0.172925i
$51$	−3.95799	+	4.82282i	−0.554229	+	0.675330i
$52$	6.48903	−	6.14619i	0.899867	−	0.852323i
$53$	2.01978	+	6.65832i	0.277438	+	0.914591i	0.979323	+	0.202301i	$0.0648419\pi$
$53$	2.01978	+	6.65832i	0.277438	+	0.914591i	−0.701885	+	0.712290i	$0.747658\pi$
$54$	−4.39636	−	6.09898i	−0.598268	−	0.829966i
$55$	−0.429872	−	0.287231i	−0.0579639	−	0.0387302i
$56$	−5.08832	−	2.05777i	−0.679956	−	0.274981i
$57$	−0.572065	−	0.856156i	−0.0757719	−	0.113401i
$58$	−1.05928	−	2.32058i	−0.139090	−	0.304707i
$59$	−2.47915	+	2.03458i	−0.322757	+	0.264880i	−0.781793	−	0.623537i	$-0.785695\pi$
$59$	−2.47915	+	2.03458i	−0.322757	+	0.264880i	0.459036	+	0.888418i	$0.348195\pi$
$60$	1.10966	−	1.94707i	0.143256	−	0.251366i
$61$	−6.06772	−	11.3519i	−0.776892	−	1.45346i	−0.888093	−	0.459664i	$-0.847970\pi$
$61$	−6.06772	−	11.3519i	−0.776892	−	1.45346i	0.111201	−	0.993798i	$-0.464530\pi$
$62$	1.03146	+	0.0647064i	0.130995	+	0.00821772i
$63$		−	3.38506i		−	0.426478i
$64$	−2.93692	+	7.44140i	−0.367115	+	0.930175i
$65$			4.46887i			0.554295i
$66$	0.0512953	−	0.817675i	0.00631402	−	0.100649i
$67$	0.510007	+	0.954156i	0.0623073	+	0.116569i	0.911147	−	0.412082i	$-0.135198\pi$
$67$	0.510007	+	0.954156i	0.0623073	+	0.116569i	−0.848840	+	0.528651i	$0.822698\pi$
$68$	2.94231	+	10.7400i	0.356807	+	1.30242i
$69$	−0.411259	+	0.337511i	−0.0495097	+	0.0406316i
$70$	2.49653	−	1.13960i	0.298393	−	0.136208i
$71$	−2.65416	−	3.97222i	−0.314990	−	0.471416i	0.639865	−	0.768487i	$-0.278990\pi$
$71$	−2.65416	−	3.97222i	−0.314990	−	0.471416i	−0.954855	+	0.297071i	$0.903990\pi$
$72$	−4.93372	+	0.0414272i	−0.581445	+	0.00488224i
$73$	6.17789	+	4.12794i	0.723068	+	0.483138i	0.861836	−	0.507186i	$-0.169314\pi$
$73$	6.17789	+	4.12794i	0.723068	+	0.483138i	−0.138769	+	0.990325i	$0.544314\pi$
$74$	−3.64915	+	2.63043i	−0.424205	+	0.305782i
$75$	0.325275	+	1.07229i	0.0375595	+	0.123817i
$76$	−1.83717	−	0.0498497i	−0.210738	−	0.00571815i
$77$	0.636462	−	0.775531i	0.0725316	−	0.0883800i
$78$	−6.12302	+	3.55802i	−0.693296	+	0.402866i
$79$	1.33330	−	3.21887i	0.150008	−	0.362151i	−0.830957	−	0.556337i	$-0.812206\pi$
$79$	1.33330	−	3.21887i	0.150008	−	0.362151i	0.980965	+	0.194186i	$0.0622065\pi$
$80$	−1.69151	−	3.62475i	−0.189117	−	0.405259i
$81$	0.277024	+	0.668796i	0.0307805	+	0.0743107i
$82$	−8.05794	−	6.14732i	−0.889851	−	0.678858i
$83$	−6.46372	+	0.636621i	−0.709485	+	0.0698782i	−0.446321	−	0.894873i	$-0.647266\pi$
$83$	−6.46372	+	0.636621i	−0.709485	+	0.0698782i	−0.263164	+	0.964751i	$0.584766\pi$
$84$	3.54910	+	2.51330i	0.387239	+	0.274224i
$85$	−4.91043	−	2.62468i	−0.532611	−	0.284686i
$86$	−15.0670	+	3.55762i	−1.62471	+	0.383628i
$87$	0.394315	+	1.98235i	0.0422750	+	0.212531i
$88$	−1.13812	−	0.918151i	−0.121324	−	0.0978752i
$89$	−4.21414	−	0.838245i	−0.446698	−	0.0888538i	−0.0333846	−	0.999443i	$-0.510629\pi$
$89$	−4.21414	−	0.838245i	−0.446698	−	0.0888538i	−0.413313	+	0.910589i	$0.635629\pi$
$90$	1.68134	−	1.80525i	0.177229	−	0.190290i
$91$	−8.63025	−	0.850005i	−0.904696	−	0.0891047i
$92$	0.0674088	+	0.947188i	0.00702786	+	0.0987511i
$93$	−0.783609	−	0.237705i	−0.0812565	−	0.0246489i
$94$	2.64264	+	1.29402i	0.272568	+	0.133468i
$95$	0.649778	−	0.649778i	0.0666658	−	0.0666658i
$96$	3.61970	−	5.20357i	0.369434	−	0.531087i
$97$	0.0678790	+	0.0678790i	0.00689207	+	0.00689207i	0.710544	−	0.703652i	$-0.248449\pi$
$97$	0.0678790	+	0.0678790i	0.00689207	+	0.00689207i	−0.703652	+	0.710544i	$0.748449\pi$
$98$	−1.48239	−	4.32715i	−0.149744	−	0.437108i
$99$	0.261795	−	0.863022i	0.0263114	−	0.0867370i
$100$	1.89743	+	0.632268i	0.189743	+	0.0632268i
$101$	−0.713637	+	7.24568i	−0.0710095	+	0.720972i	0.892096	+	0.451847i	$0.149235\pi$
$101$	−0.713637	+	7.24568i	−0.0710095	+	0.720972i	−0.963105	+	0.269125i	$0.913265\pi$
$102$	−0.313371	−	8.81773i	−0.0310284	−	0.873086i
$103$	3.26851	−	16.4319i	0.322056	−	1.61908i	−0.392671	−	0.919679i	$-0.628449\pi$
$103$	3.26851	−	16.4319i	0.322056	−	1.61908i	0.714727	−	0.699404i	$-0.246551\pi$
$104$	−1.13326	+	12.5890i	−0.111125	+	1.23445i
$105$	−2.13266	+	0.424213i	−0.208127	+	0.0413989i
$106$	−8.37066	−	5.17278i	−0.813030	−	0.502425i
$107$	3.11358	−	5.82509i	0.301001	−	0.563133i	−0.685266	−	0.728293i	$-0.740314\pi$
$107$	3.11358	−	5.82509i	0.301001	−	0.563133i	0.986267	+	0.165160i	$0.0528140\pi$
$108$	10.3681	+	2.35640i	0.997675	+	0.226745i
$109$	−1.69579	−	17.2176i	−0.162427	−	1.64915i	−0.638412	−	0.769694i	$-0.720409\pi$
$109$	−1.69579	−	17.2176i	−0.162427	−	1.64915i	0.475986	−	0.879453i	$-0.342091\pi$
$110$	0.724626	−	0.0974629i	0.0690904	−	0.00929272i
$111$	3.29294	−	1.36398i	0.312552	−	0.129463i
$112$	7.32181	−	2.57719i	0.691846	−	0.243522i
$113$	13.2501	+	5.48836i	1.24646	+	0.516302i	0.905729	−	0.423858i	$-0.139324\pi$
$113$	13.2501	+	5.48836i	1.24646	+	0.516302i	0.340734	+	0.940160i	$0.389324\pi$
$114$	1.40763	+	0.372954i	0.131837	+	0.0349304i
$115$	−0.367019	−	0.301205i	−0.0342247	−	0.0280875i
$116$	3.29426	+	1.47044i	0.305864	+	0.136527i
$117$	−7.45981	+	2.26291i	−0.689659	+	0.209206i
$118$	0.726296	−	4.47704i	0.0668610	−	0.412145i
$119$	6.00275	−	8.98375i	0.550271	−	0.823539i
$120$	0.644390	+	3.10316i	0.0588244	+	0.283278i
$121$	−8.92392	+	5.96277i	−0.811266	+	0.542070i
$122$	17.0546	+	6.36446i	1.54405	+	0.576211i
$123$	5.09445	+	6.20761i	0.459351	+	0.559721i
$124$	−1.15454	+	0.896221i	−0.103681	+	0.0804830i
$125$	−0.881921	+	0.471397i	−0.0788814	+	0.0421630i
$126$	3.16648	+	3.59036i	0.282093	+	0.319855i
$127$	13.4835			1.19647			0.598234	−	0.801322i	$-0.295870\pi$
$127$	13.4835			1.19647			0.598234	+	0.801322i	$0.295870\pi$
$128$	−3.84586	−	10.6400i	−0.339929	−	0.940451i
$129$	12.2665			1.08000
$130$	−4.18031	−	4.73990i	−0.366637	−	0.415717i
$131$	6.07604	−	3.24771i	0.530866	−	0.283754i	−0.184107	−	0.982906i	$-0.558939\pi$
$131$	6.07604	−	3.24771i	0.530866	−	0.283754i	0.714972	+	0.699153i	$0.246439\pi$
$132$	0.710470	+	0.915249i	0.0618385	+	0.0796622i
$133$	1.13125	+	1.37844i	0.0980922	+	0.119526i
$134$	−1.43348	−	0.534949i	−0.123834	−	0.0462125i
$135$	−4.42032	+	2.95356i	−0.380441	+	0.254202i
$136$	−13.1673	−	8.63905i	−1.12908	−	0.740793i
$137$	−5.92027	+	8.86032i	−0.505803	+	0.756988i	−0.993229	−	0.116177i	$-0.962936\pi$
$137$	−5.92027	+	8.86032i	−0.505803	+	0.756988i	0.487425	+	0.873165i	$0.337936\pi$
$138$	0.120483	−	0.742683i	0.0102562	−	0.0632214i
$139$	15.6396	−	4.74423i	1.32654	−	0.402400i	0.454023	−	0.890990i	$-0.349989\pi$
$139$	15.6396	−	4.74423i	1.32654	−	0.402400i	0.872514	+	0.488590i	$0.162489\pi$
$140$	−1.58193	+	3.54404i	−0.133698	+	0.299526i
$141$	−1.80222	−	1.47904i	−0.151774	−	0.124558i
$142$	6.53085	+	1.73036i	0.548057	+	0.145209i
$143$	−2.13455	−	0.884158i	−0.178500	−	0.0739370i
$144$	5.19419	−	4.65908i	0.432849	−	0.388257i
$145$	−1.66646	+	0.690272i	−0.138392	+	0.0573240i
$146$	−10.4140	+	1.40069i	−0.861865	+	0.115922i
$147$	0.355232	+	3.60673i	0.0292990	+	0.297478i
$148$	1.40988	−	6.20348i	0.115892	−	0.509923i
$149$	−6.78718	+	12.6979i	−0.556028	+	1.04025i	0.434203	+	0.900815i	$0.357030\pi$
$149$	−6.78718	+	12.6979i	−0.556028	+	1.04025i	−0.990231	+	0.139440i	$0.955470\pi$
$150$	−1.34805	−	0.833049i	−0.110068	−	0.0680181i
$151$	11.7411	−	2.33545i	0.955476	−	0.190056i	0.307357	−	0.951594i	$-0.400556\pi$
$151$	11.7411	−	2.33545i	0.955476	−	0.190056i	0.648120	+	0.761538i	$0.275556\pi$
$152$	1.99523	−	1.66567i	0.161834	−	0.135104i
$153$	1.89483	−	9.52595i	0.153188	−	0.770128i
$154$	0.0503914	+	1.41793i	0.00406066	+	0.114260i
$155$	0.0716292	−	0.727264i	0.00575340	−	0.0584152i
$156$	3.16610	−	9.50145i	0.253491	−	0.760725i
$157$	−1.09628	+	3.61396i	−0.0874929	+	0.288425i	−0.989758	−	0.142757i	$-0.954403\pi$
$157$	−1.09628	+	3.61396i	−0.0874929	+	0.288425i	0.902265	+	0.431182i	$0.141903\pi$
$158$	1.59686	+	4.66129i	0.127039	+	0.370832i
$159$	5.51304	+	5.51304i	0.437213	+	0.437213i
$160$	5.18479	+	2.26229i	0.409894	+	0.178850i
$161$	0.651493	−	0.651493i	0.0513448	−	0.0513448i
$162$	−0.919436	−	0.450221i	−0.0722377	−	0.0353727i
$163$	−16.0720	−	4.87539i	−1.25886	−	0.381870i	−0.410776	−	0.911736i	$-0.634742\pi$
$163$	−16.0720	−	4.87539i	−1.25886	−	0.381870i	−0.848082	+	0.529866i	$0.822242\pi$
$164$	14.2970	−	1.01748i	1.11641	−	0.0794519i
$165$	−0.576531	−	0.0567833i	−0.0448829	−	0.00442058i
$166$	6.26022	−	6.72158i	0.485887	−	0.521695i
$167$	19.6922	+	3.91703i	1.52383	+	0.303109i	0.884763	−	0.466042i	$-0.154320\pi$
$167$	19.6922	+	3.91703i	1.52383	+	0.303109i	0.639068	+	0.769150i	$0.279320\pi$
$168$	−6.11536	+	0.654201i	−0.471810	+	0.0504727i
$169$	1.35994	+	6.83687i	0.104611	+	0.525913i
$170$	7.66343	−	1.80949i	0.587759	−	0.138782i
$171$	1.41369	+	0.755634i	0.108108	+	0.0577848i
$172$	12.6529	−	17.8675i	0.964772	−	1.36238i
$173$	18.3904	−	1.81130i	1.39820	−	0.137711i	0.629341	−	0.777129i	$-0.283325\pi$
$173$	18.3904	−	1.81130i	1.39820	−	0.137711i	0.768859	+	0.639419i	$0.220825\pi$
$174$	−2.27258	−	1.73373i	−0.172284	−	0.131433i
$175$	−0.742611	−	1.79282i	−0.0561361	−	0.135525i
$176$	2.06601	−	0.0907984i	0.155732	−	0.00684419i
$177$	−1.37525	+	3.32016i	−0.103370	+	0.249558i
$178$	5.25384	−	3.05294i	0.393792	−	0.228828i
$179$	6.25132	−	7.61726i	0.467246	−	0.569340i	−0.485062	−	0.874480i	$-0.661203\pi$
$179$	6.25132	−	7.61726i	0.467246	−	0.569340i	0.952308	+	0.305139i	$0.0987030\pi$
$180$	−0.0946296	+	3.48751i	−0.00705327	+	0.259943i
$181$	−3.39629	−	11.1961i	−0.252444	−	0.832196i	−0.987963	−	0.154692i	$-0.950562\pi$
$181$	−3.39629	−	11.1961i	−0.252444	−	0.832196i	0.735519	−	0.677504i	$-0.236938\pi$
$182$	9.94877	−	7.17142i	0.737452	−	0.531581i
$183$	−11.9926	−	8.01317i	−0.886515	−	0.592350i
$184$	−0.957523	−	0.941577i	−0.0705895	−	0.0694140i
$185$	1.76718	+	2.64477i	0.129926	+	0.194447i
$186$	1.05349	−	0.480888i	0.0772456	−	0.0352604i
$187$	2.22519	−	1.82617i	0.162722	−	0.133543i
$188$	−4.01338	+	1.09950i	−0.292706	+	0.0801890i
$189$	−4.86313	−	9.09827i	−0.353740	−	0.661802i
$190$	−0.0813652	+	1.29701i	−0.00590285	+	0.0940947i
$191$		−	9.96170i		−	0.720803i	−0.932797	−	0.360402i	$-0.882640\pi$
$191$		−	9.96170i		−	0.720803i	0.932797	−	0.360402i	$-0.117360\pi$
$192$	1.02834	+	8.90512i	0.0742139	+	0.642672i
$193$		−	24.1750i		−	1.74016i	−0.492914	−	0.870078i	$-0.664068\pi$
$193$		−	24.1750i		−	1.74016i	0.492914	−	0.870078i	$-0.335932\pi$
$194$	−0.135492	−	0.00849981i	−0.00972773	−	0.000610251i
$195$	2.36054	+	4.41625i	0.169042	+	0.316255i
$196$	5.62002	+	3.20291i	0.401430	+	0.228779i
$197$	−3.59030	+	2.94648i	−0.255798	+	0.209928i	−0.753549	−	0.657392i	$-0.771659\pi$
$197$	−3.59030	+	2.94648i	−0.255798	+	0.209928i	0.497751	+	0.867320i	$0.334159\pi$
$198$	0.529623	+	1.16025i	0.0376387	+	0.0824556i
$199$	−8.86432	−	13.2664i	−0.628375	−	0.940429i	−0.999928	−	0.0120175i	$-0.996175\pi$
$199$	−8.86432	−	13.2664i	−0.628375	−	0.940429i	0.371553	−	0.928412i	$-0.378825\pi$
$200$	−2.60395	+	1.10430i	−0.184127	+	0.0780854i
$201$	1.00800	+	0.673527i	0.0710991	+	0.0475069i
$202$	−6.02089	−	8.35267i	−0.423628	−	0.587692i
$203$	−1.01608	−	3.34955i	−0.0713146	−	0.235093i
$204$	8.58073	+	9.05938i	0.600771	+	0.634283i
$205$	−4.54644	+	5.53985i	−0.317537	+	0.386920i
$206$	11.9041	+	20.4859i	0.829399	+	1.42732i
$207$	0.316948	−	0.765180i	0.0220294	−	0.0531837i
$208$	−10.5741	−	14.4126i	−0.733181	−	0.999331i
$209$	0.181808	+	0.438922i	0.0125759	+	0.0303609i
$210$	1.86518	−	2.44489i	0.128710	−	0.168714i
$211$	−11.8225	+	1.16441i	−0.813893	+	0.0801615i	−0.496394	−	0.868097i	$-0.665343\pi$
$211$	−11.8225	+	1.16441i	−0.813893	+	0.0801615i	−0.317499	+	0.948259i	$0.602843\pi$
$212$	13.7171	−	2.34365i	0.942093	−	0.160963i
$213$	−4.72111	−	2.52348i	−0.323485	−	0.172906i
$214$	2.14655	+	9.09090i	0.146735	+	0.621441i
$215$	2.13564	+	10.7366i	0.145650	+	0.732230i
$216$	−13.2012	+	7.19934i	−0.898228	+	0.489853i
$217$	1.39086	+	0.276660i	0.0944178	+	0.0187809i
$218$	17.9045	+	16.6755i	1.21264	+	1.12941i
$219$	8.28561	+	0.816061i	0.559889	+	0.0551443i
$220$	−0.677404	+	0.781210i	−0.0456706	+	0.0526691i
$221$	−23.8107	−	7.22290i	−1.60168	−	0.485865i
$222$	−2.21674	+	4.52701i	−0.148778	+	0.303833i
$223$	1.54084	−	1.54084i	0.103183	−	0.103183i	−0.653631	−	0.756813i	$-0.726755\pi$
$223$	1.54084	−	1.54084i	0.103183	−	0.103183i	0.756813	+	0.653631i	$0.226755\pi$
$224$	−5.35509	+	9.58252i	−0.357802	+	0.640259i
$225$	−1.23347	−	1.23347i	−0.0822316	−	0.0822316i
$226$	−19.1876	+	6.57328i	−1.27634	+	0.437248i
$227$	−2.17656	+	7.17514i	−0.144463	+	0.476231i	−0.999073	−	0.0430390i	$-0.986296\pi$
$227$	−2.17656	+	7.17514i	−0.144463	+	0.476231i	0.854610	+	0.519270i	$0.173796\pi$
$228$	−1.84187	+	0.921165i	−0.121981	+	0.0610056i
$229$	−1.90227	+	19.3140i	−0.125705	+	1.27631i	0.700792	+	0.713366i	$0.252830\pi$
$229$	−1.90227	+	19.3140i	−0.125705	+	1.27631i	−0.826497	+	0.562941i	$0.809670\pi$
$230$	0.671033	−	0.0238477i	0.0442466	−	0.00157247i
$231$	0.219319	−	1.10259i	0.0144301	−	0.0725452i
$232$	−4.86954	+	1.52192i	−0.319701	+	0.0999191i
$233$	2.09065	−	0.415856i	0.136963	−	0.0272436i	−0.126133	−	0.992013i	$-0.540257\pi$
$233$	2.09065	−	0.415856i	0.136963	−	0.0272436i	0.263096	+	0.964770i	$0.415257\pi$
$234$	5.79544	−	9.37826i	0.378860	−	0.613076i
$235$	0.980803	−	1.83495i	0.0639805	−	0.119699i
$236$	3.41761	+	5.42796i	0.222467	+	0.353330i
$237$	−0.382663	−	3.88524i	−0.0248566	−	0.252373i
$238$	2.03685	+	15.1437i	0.132029	+	0.981623i
$239$	16.1164	−	6.67561i	1.04248	−	0.431809i	0.205278	−	0.978704i	$-0.434190\pi$
$239$	16.1164	−	6.67561i	1.04248	−	0.431809i	0.837202	+	0.546894i	$0.184190\pi$
$240$	−3.58625	−	2.68858i	−0.231492	−	0.173547i
$241$	16.2743	+	6.74103i	1.04832	+	0.434228i	0.839291	−	0.543682i	$-0.182970\pi$
$241$	16.2743	+	6.74103i	1.04832	+	0.434228i	0.209027	+	0.977910i	$0.432970\pi$
$242$	3.88739	−	14.6721i	0.249891	−	0.943158i
$243$	−11.7016	−	9.60323i	−0.750656	−	0.616048i
$244$	−24.0424	+	9.20290i	−1.53916	+	0.589155i
$245$	−3.09505	+	0.938874i	−0.197736	+	0.0599824i
$246$	−11.2102	−	1.81859i	−0.714736	−	0.115949i
$247$	2.28148	−	3.41448i	0.145167	−	0.217258i
$248$	0.386209	−	2.03056i	0.0245243	−	0.128941i
$249$	−6.05134	+	4.04338i	−0.383488	+	0.256239i
$250$	0.494450	−	1.32496i	0.0312718	−	0.0837978i
$251$	−6.00939	−	7.32246i	−0.379309	−	0.462190i	0.548004	−	0.836476i	$-0.315388\pi$
$251$	−6.00939	−	7.32246i	−0.379309	−	0.462190i	−0.927313	+	0.374286i	$0.877888\pi$
$252$	−6.71705	−	0.846092i	−0.423134	−	0.0532988i
$253$	0.216484	−	0.115713i	0.0136102	−	0.00727481i
$254$	−14.3012	+	12.6128i	−0.897340	+	0.791400i
$255$	−6.23902			−0.390702
$256$	14.0320	+	7.68776i	0.877003	+	0.480485i
$257$	−1.28731			−0.0803001			−0.0401500	−	0.999194i	$-0.512784\pi$
$257$	−1.28731			−0.0803001			−0.0401500	+	0.999194i	$0.512784\pi$
$258$	−13.0104	+	11.4744i	−0.809991	+	0.714364i
$259$	−5.44369	+	2.90971i	−0.338254	+	0.180801i
$260$	8.86767	+	1.11699i	0.549950	+	0.0692727i
$261$	−1.99611	−	2.43226i	−0.123556	−	0.150553i
$262$	−3.40654	+	9.12837i	−0.210457	+	0.563953i
$263$	−3.36412	+	2.24783i	−0.207441	+	0.138607i	−0.654951	−	0.755671i	$-0.727311\pi$
$263$	−3.36412	+	2.24783i	−0.207441	+	0.138607i	0.447510	+	0.894279i	$0.352311\pi$
$264$	−1.60971	−	0.306163i	−0.0990707	−	0.0188430i
$265$	−3.86562	+	5.78530i	−0.237463	+	0.355388i
$266$	−2.48929	−	0.403830i	−0.152628	−	0.0247604i
$267$	−4.60730	+	1.39761i	−0.281962	+	0.0855323i
$268$	2.02083	−	0.773527i	0.123442	−	0.0472507i
$269$	−14.7613	−	12.1143i	−0.900015	−	0.738623i	0.0658064	−	0.997832i	$-0.479038\pi$
$269$	−14.7613	−	12.1143i	−0.900015	−	0.738623i	−0.965821	+	0.259209i	$0.916538\pi$
$270$	1.92556	−	7.26758i	0.117186	−	0.442291i
$271$	−4.10726	−	1.70128i	−0.249499	−	0.103346i	0.254429	−	0.967091i	$-0.418112\pi$
$271$	−4.10726	−	1.70128i	−0.249499	−	0.103346i	−0.503928	+	0.863746i	$0.668112\pi$
$272$	22.0470	−	3.15403i	1.33680	−	0.191241i
$273$	−8.97762	+	3.71865i	−0.543350	+	0.225063i
$274$	−2.00886	−	14.9357i	−0.121360	−	0.902297i
$275$	−0.0506751	−	0.514513i	−0.00305582	−	0.0310263i
$276$	0.566937	+	0.900429i	0.0341256	+	0.0541995i
$277$	3.71029	−	6.94146i	0.222930	−	0.417072i	−0.745447	−	0.666565i	$-0.767764\pi$
$277$	3.71029	−	6.94146i	0.222930	−	0.417072i	0.968377	+	0.249493i	$0.0802639\pi$
$278$	−12.1503	+	19.6617i	−0.728724	+	1.17923i
$279$	1.25028	−	0.248696i	0.0748523	−	0.0148890i
$280$	−1.63732	−	5.23876i	−0.0978486	−	0.313076i
$281$	−2.82825	+	14.2186i	−0.168719	+	0.848208i	0.799991	+	0.600012i	$0.204838\pi$
$281$	−2.82825	+	14.2186i	−0.168719	+	0.848208i	−0.968710	+	0.248196i	$0.920162\pi$
$282$	3.29505	−	0.117102i	0.196218	−	0.00697332i
$283$	0.364323	−	3.69903i	0.0216567	−	0.219885i	−0.978265	−	0.207359i	$-0.933513\pi$
$283$	0.364323	−	3.69903i	0.0216567	−	0.219885i	0.999922	−	0.0125251i	$-0.00398697\pi$
$284$	−8.54557	+	4.27384i	−0.507086	+	0.253606i
$285$	0.298903	−	0.985352i	0.0177055	−	0.0583672i
$286$	3.09107	−	1.05893i	0.182779	−	0.0626161i
$287$	−9.83375	−	9.83375i	−0.580468	−	0.580468i
$288$	−1.15097	+	9.80044i	−0.0678217	+	0.577496i
$289$	9.90038	−	9.90038i	0.582375	−	0.582375i
$290$	1.12183	−	2.29099i	0.0658762	−	0.134532i
$291$	0.102935	+	0.0312249i	0.00603414	+	0.00183044i
$292$	9.73530	−	11.2271i	0.569716	−	0.657019i
$293$	2.53275	+	0.249454i	0.147965	+	0.0145733i	0.171728	−	0.985144i	$-0.445065\pi$
$293$	2.53275	+	0.249454i	0.147965	+	0.0145733i	−0.0237634	+	0.999718i	$0.507565\pi$
$294$	−3.75061	−	3.49317i	−0.218740	−	0.203726i
$295$	−3.14551	−	0.625681i	−0.183139	−	0.0364285i
$296$	4.30752	+	7.89855i	0.250370	+	0.459094i
$297$	−0.536211	−	2.69571i	−0.0311141	−	0.156421i
$298$	−4.67918	−	19.8170i	−0.271058	−	1.14797i
$299$	−1.87125	−	1.00020i	−0.108217	−	0.0578431i
$300$	2.20906	−	0.377433i	0.127540	−	0.0217911i
$301$	−21.1406	+	2.08217i	−1.21853	+	0.120014i
$302$	−10.2685	+	13.4600i	−0.590887	+	0.774538i
$303$	3.12206	+	7.53732i	0.179358	+	0.433008i
$304$	−0.558117	+	3.63308i	−0.0320102	+	0.208371i
$305$	4.92582	−	11.8920i	0.282052	−	0.680933i
$306$	6.90110	+	11.8762i	0.394509	+	0.678915i
$307$	−18.1670	+	22.1365i	−1.03684	+	1.26340i	−0.0728858	+	0.997340i	$0.523221\pi$
$307$	−18.1670	+	22.1365i	−1.03684	+	1.26340i	−0.963957	+	0.266057i	$0.914279\pi$
$308$	−1.37982	−	1.45679i	−0.0786225	−	0.0830082i
$309$	−5.44959	−	17.9649i	−0.310017	−	1.02199i
$310$	0.604329	+	0.838375i	0.0343236	+	0.0476165i
$311$	21.2283	+	14.1843i	1.20375	+	0.804318i	0.985183	−	0.171504i	$-0.0548628\pi$
$311$	21.2283	+	14.1843i	1.20375	+	0.804318i	0.218564	+	0.975823i	$0.429863\pi$
$312$	5.52980	+	13.0394i	0.313063	+	0.738208i
$313$	8.13343	+	12.1725i	0.459728	+	0.688032i	0.986828	−	0.161771i	$-0.0517206\pi$
$313$	8.13343	+	12.1725i	0.459728	+	0.688032i	−0.527100	+	0.849803i	$0.676721\pi$
$314$	−2.21783	−	4.85863i	−0.125159	−	0.274188i
$315$	2.61669	−	2.14746i	0.147434	−	0.120996i
$316$	−6.05401	−	3.45024i	−0.340564	−	0.194091i
$317$	4.76219	+	8.90943i	0.267471	+	0.500404i	0.979421	−	0.201827i	$-0.0646877\pi$
$317$	4.76219	+	8.90943i	0.267471	+	0.500404i	−0.711950	+	0.702230i	$0.752188\pi$
$318$	−11.0045	−	0.690343i	−0.617099	−	0.0387125i
$319$		−	0.932552i		−	0.0522129i
$320$	−7.61545	+	2.45050i	−0.425716	+	0.136987i
$321$		−	7.40115i		−	0.413092i
$322$	−0.0815800	+	1.30043i	−0.00454627	+	0.0724701i
$323$	2.41188	+	4.51231i	0.134201	+	0.251072i
$324$	1.39635	−	0.382540i	0.0775748	−	0.0212522i
$325$	−3.45448	+	2.83502i	−0.191620	+	0.157259i
$326$	21.6073	−	9.86314i	1.19672	−	0.546269i
$327$	−10.7705	−	16.1191i	−0.595608	−	0.891391i
$328$	−14.2123	+	14.4530i	−0.784744	+	0.798035i
$329$	3.35709	+	2.24314i	0.185082	+	0.123668i
$330$	0.664613	−	0.479076i	0.0365857	−	0.0263723i
$331$	3.93702	+	12.9786i	0.216398	+	0.713370i	0.996180	+	0.0873187i	$0.0278298\pi$
$331$	3.93702	+	12.9786i	0.216398	+	0.713370i	−0.779782	+	0.626051i	$0.784670\pi$
$332$	−0.352339	+	12.9852i	−0.0193371	+	0.712656i
$333$	−3.52002	+	4.28916i	−0.192896	+	0.235044i
$334$	−24.5506	+	14.2661i	−1.34335	+	0.780605i
$335$	−0.414027	+	0.999551i	−0.0226207	+	0.0546113i
$336$	5.87429	−	6.41436i	0.320469	−	0.349932i
$337$	12.3340	+	29.7770i	0.671877	+	1.62205i	0.778418	+	0.627747i	$0.216023\pi$
$337$	12.3340	+	29.7770i	0.671877	+	1.62205i	−0.106541	+	0.994308i	$0.533977\pi$
$338$	−7.83781	−	5.97939i	−0.426321	−	0.325236i
$339$	15.9931	−	1.57519i	0.868628	−	0.0855523i
$340$	−6.43556	+	9.08783i	−0.349017	+	0.492857i
$341$	0.333204	+	0.178101i	0.0180440	+	0.00964473i
$342$	−2.20627	+	0.520945i	−0.119301	+	0.0281695i
$343$	−3.87451	−	19.4785i	−0.209204	−	1.05174i
$344$	3.29348	+	30.7869i	0.177573	+	1.65992i
$345$	−0.521799	−	0.103792i	−0.0280927	−	0.00558799i
$346$	−17.8114	+	19.1241i	−0.957549	+	1.02812i
$347$	−24.0373	−	2.36746i	−1.29039	−	0.127092i	−0.570567	−	0.821251i	$-0.693276\pi$
$347$	−24.0373	−	2.36746i	−1.29039	−	0.127092i	−0.719822	+	0.694159i	$0.755776\pi$
$348$	4.03218	−	0.286960i	0.216148	−	0.0153826i
$349$	−5.98779	−	1.81638i	−0.320519	−	0.0972284i	0.125926	−	0.992040i	$-0.459810\pi$
$349$	−5.98779	−	1.81638i	−0.320519	−	0.0972284i	−0.446444	+	0.894811i	$0.647310\pi$
$350$	2.46470	+	1.20689i	0.131744	+	0.0645112i
$351$	−16.7993	+	16.7993i	−0.896678	+	0.896678i
$352$	−2.10638	+	2.02891i	−0.112270	+	0.108141i
$353$	3.48467	+	3.48467i	0.185470	+	0.185470i	0.793735	−	0.608264i	$-0.208134\pi$
$353$	3.48467	+	3.48467i	0.185470	+	0.185470i	−0.608264	+	0.793735i	$0.708134\pi$
$354$	−1.64711	−	4.80797i	−0.0875428	−	0.255541i
$355$	1.38679	−	4.57164i	0.0736033	−	0.242638i
$356$	−2.71667	+	8.15269i	−0.143983	+	0.432091i
$357$	1.18670	−	12.0487i	0.0628067	−	0.637687i
$358$	0.494944	+	13.9269i	0.0261586	+	0.736059i
$359$	4.83543	−	24.3093i	0.255204	−	1.28300i	−0.614300	−	0.789072i	$-0.710562\pi$
$359$	4.83543	−	24.3093i	0.255204	−	1.28300i	0.869504	−	0.493925i	$-0.164438\pi$
$360$	−3.16194	−	3.78754i	−0.166649	−	0.199621i
$361$	17.8067	−	3.54198i	0.937196	−	0.186420i
$362$	14.0754	+	8.69809i	0.739785	+	0.457162i
$363$	−5.66921	+	10.6063i	−0.297556	+	0.556689i
$364$	−3.84380	+	16.9127i	−0.201470	+	0.886467i
$365$	0.728276	+	7.39431i	0.0381197	+	0.387036i
$366$	20.2156	−	2.71902i	1.05669	−	0.142125i
$367$	−2.98789	+	1.23762i	−0.155966	+	0.0646034i	−0.459301	−	0.888281i	$-0.651900\pi$
$367$	−2.98789	+	1.23762i	−0.155966	+	0.0646034i	0.303334	+	0.952884i	$0.401900\pi$
$368$	1.89637	+	0.102988i	0.0988552	+	0.00536861i
$369$	−11.5498	−	4.78407i	−0.601256	−	0.249048i
$370$	−4.34835	−	1.15210i	−0.226060	−	0.0598949i
$371$	−10.4373	−	8.56565i	−0.541876	−	0.444706i
$372$	−0.667545	+	1.49552i	−0.0346106	+	0.0775390i
$373$	3.01844	−	0.915634i	0.156289	−	0.0474097i	−0.211171	−	0.977449i	$-0.567728\pi$
$373$	3.01844	−	0.915634i	0.156289	−	0.0474097i	0.367460	+	0.930039i	$0.380228\pi$
$374$	−0.651897	+	4.01843i	−0.0337088	+	0.207788i
$375$	−0.622537	+	0.931693i	−0.0321477	+	0.0481124i
$376$	3.22828	−	4.92041i	0.166486	−	0.253751i
$377$	−6.70231	+	4.47834i	−0.345187	+	0.230646i
$378$	13.6688	+	5.10096i	0.703049	+	0.262365i
$379$	22.8182	+	27.8040i	1.17209	+	1.42820i	0.882034	+	0.471186i	$0.156174\pi$
$379$	22.8182	+	27.8040i	1.17209	+	1.42820i	0.290056	+	0.957010i	$0.406326\pi$
$380$	−1.12696	−	1.45178i	−0.0578116	−	0.0744747i
$381$	13.3247	−	7.12222i	0.682647	−	0.364883i
$382$	9.31845	+	10.5659i	0.476774	+	0.540596i
$383$	−27.8992			−1.42558			−0.712792	−	0.701376i	$-0.752570\pi$
$383$	−27.8992			−1.42558			−0.712792	+	0.701376i	$0.752570\pi$
$384$	−9.42081	−	8.48327i	−0.480754	−	0.432910i
$385$	1.00326			0.0511309
$386$	22.6140	+	25.6412i	1.15102	+	1.30510i
$387$	−16.8410	+	9.00169i	−0.856075	+	0.457582i
$388$	0.151660	−	0.117727i	0.00769937	−	0.00597670i
$389$	−6.23656	−	7.59927i	−0.316206	−	0.385298i	0.590517	−	0.807026i	$-0.298924\pi$
$389$	−6.23656	−	7.59927i	−0.316206	−	0.385298i	−0.906723	+	0.421727i	$0.861424\pi$
$390$	−6.63479	−	2.47598i	−0.335966	−	0.125376i
$391$	2.19806	−	1.46870i	0.111161	−	0.0742751i
$392$	−8.95696	+	1.85997i	−0.452395	+	0.0939425i
$393$	4.28900	−	6.41894i	0.216351	−	0.323793i
$394$	1.05182	−	6.48364i	0.0529900	−	0.326641i
$395$	3.33405	−	1.01137i	0.167754	−	0.0508878i
$396$	−1.64708	−	0.735196i	−0.0827687	−	0.0369450i
$397$	12.4646	+	10.2294i	0.625579	+	0.513399i	0.892927	−	0.450201i	$-0.148648\pi$
$397$	12.4646	+	10.2294i	0.625579	+	0.513399i	−0.267349	+	0.963600i	$0.586148\pi$
$398$	21.8117	+	5.77904i	1.09332	+	0.289677i
$399$	1.84605	+	0.764659i	0.0924181	+	0.0382808i
$400$	1.72888	−	3.60707i	0.0864441	−	0.180354i
$401$	2.33563	−	0.967448i	0.116636	−	0.0483120i	−0.323603	−	0.946193i	$-0.604894\pi$
$401$	2.33563	−	0.967448i	0.116636	−	0.0483120i	0.440238	+	0.897881i	$0.354894\pi$
$402$	−1.69917	+	0.228540i	−0.0847471	+	0.0113986i
$403$	−0.320102	−	3.25005i	−0.0159454	−	0.161896i
$404$	14.1994	+	3.22713i	0.706445	+	0.160556i
$405$	−0.341244	+	0.638422i	−0.0169565	+	0.0317235i
$406$	4.21097	+	2.60223i	0.208987	+	0.129147i
$407$	−1.61290	+	0.320826i	−0.0799486	+	0.0159028i
$408$	−17.5755	−	1.58215i	−0.870118	−	0.0783282i
$409$	5.51773	−	27.7395i	0.272834	−	1.37163i	−0.564724	−	0.825280i	$-0.691017\pi$
$409$	5.51773	−	27.7395i	0.272834	−	1.37163i	0.837558	−	0.546349i	$-0.183983\pi$
$410$	−0.359961	−	10.1287i	−0.0177772	−	0.500221i
$411$	−1.17039	+	11.8832i	−0.0577312	+	0.586155i
$412$	−31.7892	−	10.5929i	−1.56614	−	0.521874i
$413$	1.80660	−	5.95557i	0.0888971	−	0.293055i
$414$	0.379600	+	1.10807i	0.0186563	+	0.0544586i
$415$	−4.59265	−	4.59265i	−0.225445	−	0.225445i
$416$	24.6973	+	5.39535i	1.21088	+	0.264529i
$417$	12.9495	−	12.9495i	0.634140	−	0.634140i
$418$	−0.603414	−	0.295474i	−0.0295139	−	0.0144521i
$419$	−21.6681	−	6.57296i	−1.05856	−	0.321110i	−0.287438	−	0.957799i	$-0.592803\pi$
$419$	−21.6681	−	6.57296i	−1.05856	−	0.321110i	−0.771121	+	0.636689i	$0.780303\pi$
$420$	0.308718	+	4.33792i	0.0150639	+	0.211669i
$421$	27.8458	+	2.74257i	1.35712	+	0.133665i	0.750260	−	0.661143i	$-0.229928\pi$
$421$	27.8458	+	2.74257i	1.35712	+	0.133665i	0.606861	+	0.794808i	$0.292428\pi$
$422$	11.4503	−	12.2941i	0.557390	−	0.598468i
$423$	3.55970	+	0.708069i	0.173079	+	0.0344275i
$424$	−12.3567	+	15.3171i	−0.600093	+	0.743866i
$425$	−1.08624	−	5.46089i	−0.0526903	−	0.264892i
$426$	7.36797	−	1.73973i	0.356979	−	0.0842900i
$427$	22.0288	+	11.7746i	1.06605	+	0.569814i
$428$	−10.7806	−	7.63431i	−0.521101	−	0.369018i
$429$	−2.57644	+	0.253757i	−0.124392	+	0.0122515i
$430$	−12.3085	−	9.39001i	−0.593567	−	0.452826i
$431$	9.49861	+	22.9317i	0.457532	+	1.10458i	0.969394	+	0.245512i	$0.0789560\pi$
$431$	9.49861	+	22.9317i	0.457532	+	1.10458i	−0.511862	+	0.859068i	$0.671044\pi$
$432$	7.26735	−	19.9847i	0.349651	−	0.961516i
$433$	14.3550	−	34.6561i	0.689859	−	1.66547i	−0.0552067	−	0.998475i	$-0.517582\pi$
$433$	14.3550	−	34.6561i	0.689859	−	1.66547i	0.745065	−	0.666991i	$-0.232418\pi$
$434$	−1.73401	+	1.00761i	−0.0832351	+	0.0483669i
$435$	−1.28223	+	1.56240i	−0.0614782	+	0.0749114i
$436$	−34.5891	−	0.938537i	−1.65652	−	0.0449477i
$437$	0.126651	+	0.417511i	0.00605852	+	0.0199723i
$438$	−9.55148	+	6.88503i	−0.456387	+	0.328980i
$439$	31.6012	+	21.1152i	1.50824	+	1.00778i	0.988120	+	0.153684i	$0.0491139\pi$
$439$	31.6012	+	21.1152i	1.50824	+	1.00778i	0.520123	+	0.854091i	$0.325886\pi$
$440$	−0.0122781	−	1.46225i	−0.000585338	−	0.0697101i
$441$	−3.13449	−	4.69110i	−0.149261	−	0.223386i
$442$	32.0113	−	14.6122i	1.52262	−	0.695034i
$443$	−23.8923	+	19.6079i	−1.13516	+	0.931602i	−0.998259	−	0.0589832i	$-0.981214\pi$
$443$	−23.8923	+	19.6079i	−1.13516	+	0.931602i	−0.136901	+	0.990585i	$0.543714\pi$
$444$	−1.88351	−	6.87517i	−0.0893872	−	0.326281i
$445$	−2.02545	−	3.78935i	−0.0960156	−	0.179633i
$446$	−0.192944	+	3.07564i	−0.00913619	+	0.145636i
$447$			16.1335i			0.763090i
$448$	−3.28389	−	15.1730i	−0.155149	−	0.716856i
$449$		−	16.1943i		−	0.764256i	−0.924109	−	0.382128i	$-0.875191\pi$
$449$		−	16.1943i		−	0.764256i	0.924109	−	0.382128i	$-0.124809\pi$
$450$	2.46211	+	0.154456i	0.116065	+	0.00728111i
$451$	−1.74659	−	3.26764i	−0.0822438	−	0.153867i
$452$	14.2025	−	24.9206i	0.668030	−	1.17217i
$453$	10.3692	−	8.50980i	0.487189	−	0.399825i
$454$	−4.40327	−	9.64631i	−0.206656	−	0.452724i
$455$	−4.81791	−	7.21051i	−0.225867	−	0.338034i
$456$	1.09190	−	2.69997i	0.0511327	−	0.126438i
$457$	9.33042	+	6.23439i	0.436459	+	0.291632i	0.754322	−	0.656504i	$-0.227966\pi$
$457$	9.33042	+	6.23439i	0.436459	+	0.291632i	−0.317864	+	0.948136i	$0.602966\pi$
$458$	−16.0493	−	22.2648i	−0.749932	−	1.04037i
$459$	−8.59253	−	28.3258i	−0.401065	−	1.32213i
$460$	−0.689422	+	0.652997i	−0.0321445	+	0.0304462i
$461$	13.0206	−	15.8656i	0.606428	−	0.738935i	−0.375784	−	0.926707i	$-0.622627\pi$
$461$	13.0206	−	15.8656i	0.606428	−	0.738935i	0.982213	+	0.187772i	$0.0601266\pi$
$462$	0.798774	+	1.37462i	0.0371623	+	0.0639530i
$463$	−11.9932	+	28.9541i	−0.557371	+	1.34561i	0.354469	+	0.935068i	$0.384662\pi$
$463$	−11.9932	+	28.9541i	−0.557371	+	1.34561i	−0.911840	+	0.410545i	$0.865338\pi$
$464$	3.74121	−	6.16932i	0.173682	−	0.286404i
$465$	−0.313368	−	0.756537i	−0.0145321	−	0.0350836i
$466$	−1.82844	+	2.39673i	−0.0847009	+	0.111026i
$467$	−28.7357	+	2.83022i	−1.32973	+	0.130967i	−0.737799	−	0.675020i	$-0.764135\pi$
$467$	−28.7357	+	2.83022i	−1.32973	+	0.130967i	−0.591933	+	0.805987i	$0.701635\pi$
$468$	2.62576	+	15.3683i	0.121376	+	0.710398i
$469$	−1.85157	−	0.989687i	−0.0854977	−	0.0456995i
$470$	0.676180	+	2.86371i	0.0311899	+	0.132093i
$471$	0.825583	+	4.15048i	0.0380408	+	0.191244i
$472$	−8.70235	−	2.56024i	−0.400558	−	0.117844i
$473$	−5.55084	−	1.10413i	−0.255228	−	0.0507680i
$474$	4.04023	+	3.76292i	0.185574	+	0.172837i
$475$	0.914500	+	0.0900704i	0.0419601	+	0.00413271i
$476$	−16.3263	−	14.1569i	−0.748313	−	0.648878i
$477$	−11.6147	−	3.52329i	−0.531803	−	0.161321i
$478$	−10.8492	+	22.1562i	−0.496232	+	1.01340i
$479$	7.63998	−	7.63998i	0.349080	−	0.349080i	−0.510687	−	0.859767i	$-0.670609\pi$
$479$	7.63998	−	7.63998i	0.349080	−	0.349080i	0.859767	+	0.510687i	$0.170609\pi$
$480$	6.31873	−	0.503044i	0.288409	−	0.0229607i
$481$	10.0514	+	10.0514i	0.458302	+	0.458302i
$482$	−23.5670	+	8.07356i	−1.07345	+	0.367741i
$483$	0.299692	−	0.987953i	0.0136365	−	0.0449534i
$484$	9.60153	+	19.1983i	0.436433	+	0.872650i
$485$	−0.00940920	+	0.0955332i	−0.000427250	+	0.00433794i
$486$	21.3944	−	0.760329i	0.970469	−	0.0344892i
$487$	2.98648	−	15.0140i	0.135330	−	0.680351i	−0.852237	−	0.523155i	$-0.824755\pi$
$487$	2.98648	−	15.0140i	0.135330	−	0.680351i	0.987568	−	0.157195i	$-0.0502452\pi$
$488$	16.8919	−	32.2510i	0.764660	−	1.45993i
$489$	−18.4581	+	3.67154i	−0.834702	+	0.166033i
$490$	2.40451	−	3.89101i	0.108625	−	0.175778i
$491$	8.50573	−	15.9131i	0.383858	−	0.718148i	−0.613584	−	0.789630i	$-0.710273\pi$
$491$	8.50573	−	15.9131i	0.383858	−	0.718148i	0.997442	+	0.0714814i	$0.0227727\pi$
$492$	13.5912	−	8.55744i	0.612740	−	0.385799i
$493$	−0.984401	−	9.99479i	−0.0443352	−	0.450143i
$494$	0.774150	+	5.75572i	0.0348306	+	0.258962i
$495$	0.833206	−	0.345125i	0.0374498	−	0.0155122i
$496$	1.48981	+	2.51498i	0.0668946	+	0.112926i
$497$	8.56494	+	3.54771i	0.384190	+	0.159137i
$498$	2.63606	−	9.94919i	0.118124	−	0.445834i
$499$	20.1868	+	16.5668i	0.903683	+	0.741634i	0.966574	−	0.256387i	$-0.0825321\pi$
$499$	20.1868	+	16.5668i	0.903683	+	0.741634i	−0.0628912	+	0.998020i	$0.520032\pi$
$500$	0.714967	+	1.86784i	0.0319743	+	0.0835323i
$501$	21.5294	−	6.53088i	0.961863	−	0.291778i
$502$	13.2235	+	2.14520i	0.590193	+	0.0957451i
$503$	−16.8060	+	25.1520i	−0.749343	+	1.12147i	0.239264	+	0.970955i	$0.423094\pi$
$503$	−16.8060	+	25.1520i	−0.749343	+	1.12147i	−0.988607	+	0.150517i	$0.951906\pi$
$504$	7.91588	−	5.38591i	0.352601	−	0.239907i
$505$	−6.05371	+	4.04496i	−0.269387	+	0.179998i
$506$	−0.121372	+	0.325236i	−0.00539564	+	0.0144585i
$507$	4.95528	+	6.03803i	0.220072	+	0.268158i
$508$	3.37018	−	26.7556i	0.149528	−	1.18709i
$509$	21.0236	−	11.2373i	0.931853	−	0.498086i	0.0656859	−	0.997840i	$-0.479076\pi$
$509$	21.0236	−	11.2373i	0.931853	−	0.498086i	0.866167	+	0.499755i	$0.166576\pi$
$510$	6.61740	−	5.83615i	0.293023	−	0.258429i
$511$	−14.4184			−0.637831
$512$	−22.0744	+	4.97195i	−0.975560	+	0.219731i
$513$	4.88526			0.215689
$514$	1.36538	−	1.20418i	0.0602244	−	0.0531143i
$515$	14.7755	−	7.89769i	0.651088	−	0.348014i
$516$	3.06598	−	24.3406i	0.134972	−	1.07153i
$517$	0.682411	+	0.831520i	0.0300124	+	0.0365702i
$518$	3.05201	−	8.17836i	0.134098	−	0.359336i
$519$	17.2172	−	11.5041i	0.755749	−	0.504975i
$520$	−10.4503	+	7.11034i	−0.458278	+	0.311809i
$521$	−2.36248	+	3.53570i	−0.103502	+	0.154902i	−0.879606	−	0.475704i	$-0.842193\pi$
$521$	−2.36248	+	3.53570i	−0.103502	+	0.154902i	0.776104	+	0.630606i	$0.217193\pi$
$522$	4.39238	+	0.712561i	0.192249	+	0.0311880i
$523$	39.3799	−	11.9458i	1.72196	−	0.522352i	0.734284	−	0.678843i	$-0.237518\pi$
$523$	39.3799	−	11.9458i	1.72196	−	0.522352i	0.987679	+	0.156491i	$0.0500183\pi$
$524$	−4.92580	−	12.8686i	−0.215184	−	0.562166i
$525$	−1.68087	−	1.37945i	−0.0733591	−	0.0602042i
$526$	1.46546	−	5.53106i	0.0638972	−	0.241165i
$527$	3.75918	+	1.55710i	0.163752	+	0.0678285i
$528$	1.99373	−	1.18103i	0.0867659	−	0.0513979i
$529$	−21.0410	+	8.71545i	−0.914824	+	0.378933i
$530$	−1.31168	−	9.75218i	−0.0569756	−	0.423608i
$531$	−0.548358	−	5.56757i	−0.0237967	−	0.241612i
$532$	3.01802	−	1.90023i	0.130848	−	0.0823855i
$533$	−15.0972	+	28.2449i	−0.653933	+	1.22342i
$534$	3.57936	−	5.79217i	0.154894	−	0.250652i
$535$	6.47809	−	1.28857i	0.280072	−	0.0557098i
$536$	−1.41981	+	2.71078i	−0.0613263	+	0.117088i
$537$	2.15415	−	10.8296i	0.0929583	−	0.467333i
$538$	26.9887	−	0.959142i	1.16356	−	0.0413516i
$539$	0.163899	−	1.66410i	0.00705965	−	0.0716778i
$540$	4.75596	+	9.50957i	0.204664	+	0.409227i
$541$	9.52625	−	31.4038i	0.409566	−	1.35016i	−0.473453	−	0.880819i	$-0.656993\pi$
$541$	9.52625	−	31.4038i	0.409566	−	1.35016i	0.883019	−	0.469338i	$-0.155507\pi$
$542$	5.94779	−	2.03759i	0.255480	−	0.0875218i
$543$	−9.27025	−	9.27025i	−0.397825	−	0.397825i
$544$	−20.4338	+	23.9687i	−0.876091	+	1.02765i
$545$	12.2336	−	12.2336i	0.524030	−	0.524030i
$546$	6.04357	−	12.3421i	0.258641	−	0.528193i
$547$	−44.2239	−	13.4152i	−1.89088	−	0.573591i	−0.990311	−	0.138869i	$-0.955653\pi$
$547$	−44.2239	−	13.4152i	−1.89088	−	0.573591i	−0.900565	−	0.434722i	$-0.856847\pi$
$548$	16.1019	+	13.9623i	0.687841	+	0.596442i
$549$	22.3454	+	2.20083i	0.953677	+	0.0939290i
$550$	0.535038	+	0.498314i	0.0228141	+	0.0212482i
$551$	1.62568	+	0.323367i	0.0692562	+	0.0137759i
$552$	−1.44361	−	0.424710i	−0.0614440	−	0.0180769i
$553$	1.31900	+	6.63107i	0.0560896	+	0.281982i
$554$	2.55793	+	10.8332i	0.108676	+	0.460257i
$555$	3.14339	+	1.68018i	0.133429	+	0.0713195i
$556$	−5.50496	−	32.2198i	−0.233462	−	1.36643i
$557$	−26.8197	+	2.64151i	−1.13639	+	0.111924i	−0.648664	−	0.761075i	$-0.724672\pi$
$557$	−26.8197	+	2.64151i	−1.13639	+	0.111924i	−0.487722	+	0.872999i	$0.662172\pi$
$558$	−1.09347	+	1.43333i	−0.0462902	+	0.0606775i
$559$	18.7210	+	45.1966i	0.791816	+	1.91161i
$560$	6.63710	+	4.02489i	0.280469	+	0.170083i
$561$	1.23438	−	2.98005i	0.0521155	−	0.125818i
$562$	−10.3007	−	17.7265i	−0.434507	−	0.747748i
$563$	7.94644	−	9.68276i	0.334902	−	0.408080i	−0.578144	−	0.815934i	$-0.696223\pi$
$563$	7.94644	−	9.68276i	0.334902	−	0.408080i	0.913047	+	0.407855i	$0.133723\pi$
$564$	−3.38535	+	3.20649i	−0.142549	+	0.135018i
$565$	4.16320	+	13.7242i	0.175147	+	0.577383i
$566$	3.07376	+	4.26417i	0.129200	+	0.179236i
$567$	−1.16801	−	0.780439i	−0.0490518	−	0.0327754i
$568$	5.06597	−	12.5268i	0.212563	−	0.525613i
$569$	4.98494	+	7.46049i	0.208980	+	0.312760i	0.921121	−	0.389276i	$-0.127275\pi$
$569$	4.98494	+	7.46049i	0.208980	+	0.312760i	−0.712142	+	0.702036i	$0.752275\pi$
$570$	0.604695	+	1.32471i	0.0253279	+	0.0554862i
$571$	−8.91235	+	7.31418i	−0.372970	+	0.306089i	−0.802141	−	0.597135i	$-0.796306\pi$
$571$	−8.91235	+	7.31418i	−0.372970	+	0.306089i	0.429171	+	0.903223i	$0.358806\pi$
$572$	−2.28798	+	4.01463i	−0.0956652	+	0.167860i
$573$	−5.26195	−	9.84441i	−0.219821	−	0.411256i
$574$	19.6289	+	1.23138i	0.819295	+	0.0513969i
$575$		−	0.474792i		−	0.0198002i
$576$	−7.94683	−	11.4715i	−0.331118	−	0.477978i
$577$			15.2702i			0.635708i	0.948140	+	0.317854i	$0.102962\pi$
$577$			15.2702i			0.635708i	−0.948140	+	0.317854i	$0.897038\pi$
$578$	−1.23973	+	19.7619i	−0.0515658	+	0.821987i
$579$	−12.7697	−	23.8904i	−0.530690	−	0.992851i
$580$	0.953190	+	3.47933i	0.0395791	+	0.144471i
$581$	9.74285	−	7.99575i	0.404201	−	0.331719i
$582$	−0.138386	+	0.0631694i	−0.00573629	+	0.00261845i
$583$	−1.99853	−	2.99101i	−0.0827707	−	0.123875i
$584$	0.176455	+	21.0147i	0.00730177	+	0.869596i
$585$	−6.48170	−	4.33094i	−0.267985	−	0.179062i
$586$	−2.91971	+	2.10463i	−0.120612	+	0.0869413i
$587$	8.69635	+	28.6680i	0.358937	+	1.18326i	0.931606	+	0.363469i	$0.118408\pi$
$587$	8.69635	+	28.6680i	0.358937	+	1.18326i	−0.572670	+	0.819786i	$0.694092\pi$
$588$	7.24569	+	0.196604i	0.298807	+	0.00810780i
$589$	−0.426017	+	0.519103i	−0.0175537	+	0.0213893i
$590$	3.92156	−	2.27877i	0.161448	−	0.0938155i
$591$	−1.99164	+	4.80825i	−0.0819252	+	0.197785i
$592$	−11.9573	−	4.34821i	−0.491442	−	0.178710i
$593$	6.72631	+	16.2387i	0.276216	+	0.666846i	0.999725	−	0.0234704i	$-0.00747155\pi$
$593$	6.72631	+	16.2387i	0.276216	+	0.666846i	−0.723508	+	0.690316i	$0.757472\pi$
$594$	3.09038	+	2.35762i	0.126800	+	0.0967342i
$595$	10.7526	−	1.05904i	0.440815	−	0.0434165i
$596$	23.5003	+	16.6418i	0.962610	+	0.681674i
$597$	−15.7675	−	8.42790i	−0.645320	−	0.344931i
$598$	2.92035	−	0.689554i	0.119422	−	0.0281979i
$599$	−4.15266	−	20.8768i	−0.169673	−	0.853005i	−0.968033	−	0.250824i	$-0.919299\pi$
$599$	−4.15266	−	20.8768i	−0.169673	−	0.853005i	0.798360	−	0.602181i	$-0.205701\pi$
$600$	−1.98998	+	2.46674i	−0.0812405	+	0.100704i
$601$	7.26541	+	1.44518i	0.296362	+	0.0589501i	0.341032	−	0.940052i	$-0.389224\pi$
$601$	7.26541	+	1.44518i	0.296362	+	0.0589501i	−0.0446697	+	0.999002i	$0.514224\pi$
$602$	20.4750	−	21.9840i	0.834501	−	0.896000i
$603$	−1.87818	−	0.184985i	−0.0764855	−	0.00753317i
$604$	−1.69961	−	23.8818i	−0.0691560	−	0.971738i
$605$	−10.2706	−	3.11554i	−0.417558	−	0.126665i
$606$	−10.3620	−	5.07398i	−0.420929	−	0.206116i
$607$	−32.5607	+	32.5607i	−1.32160	+	1.32160i	−0.409117	+	0.912482i	$0.634163\pi$
$607$	−32.5607	+	32.5607i	−1.32160	+	1.32160i	−0.912482	+	0.409117i	$0.865837\pi$
$608$	−2.80652	−	4.37550i	−0.113819	−	0.177450i
$609$	−2.77341	−	2.77341i	−0.112384	−	0.112384i
$610$	5.89953	+	17.2210i	0.238865	+	0.697256i
$611$	2.69909	−	8.89770i	0.109193	−	0.359962i
$612$	−18.4289	−	6.14095i	−0.744945	−	0.248233i
$613$	−1.76006	+	17.8702i	−0.0710881	+	0.721770i	0.891901	+	0.452230i	$0.149371\pi$
$613$	−1.76006	+	17.8702i	−0.0710881	+	0.721770i	−0.962989	+	0.269540i	$0.913129\pi$
$614$	−1.43836	−	40.4729i	−0.0580473	−	1.63335i
$615$	−1.56666	+	7.87613i	−0.0631738	+	0.317596i
$616$	2.82622	+	0.254417i	0.113872	+	0.0102508i
$617$	−27.0268	+	5.37597i	−1.08806	+	0.216428i	−0.706356	−	0.707857i	$-0.749662\pi$
$617$	−27.0268	+	5.37597i	−1.08806	+	0.216428i	−0.381703	+	0.924285i	$0.624662\pi$
$618$	22.5850	+	13.9567i	0.908501	+	0.561422i
$619$	−11.1471	+	20.8547i	−0.448039	+	0.838222i	0.551952	+	0.833876i	$0.313883\pi$
$619$	−11.1471	+	20.8547i	−0.448039	+	0.838222i	−0.999991	+	0.00434590i	$0.998617\pi$
$620$	−1.42522	−	0.323914i	−0.0572382	−	0.0130087i
$621$	−0.247407	−	2.51197i	−0.00992811	−	0.100802i
$622$	−35.7842	+	4.81300i	−1.43481	+	0.192984i
$623$	7.70322	−	3.19078i	0.308623	−	0.127836i
$624$	−18.0626	−	8.65744i	−0.723081	−	0.346575i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	−20.0132	−	5.30254i	−0.799890	−	0.211932i
$627$	0.411514	+	0.337720i	0.0164343	+	0.0134873i
$628$	6.89724	+	3.07868i	0.275230	+	0.122853i
$629$	−16.9479	+	5.14109i	−0.675757	+	0.204989i
$630$	−0.766590	+	4.72542i	−0.0305417	+	0.188265i
$631$	2.83681	−	4.24559i	0.112932	−	0.169014i	−0.770698	−	0.637200i	$-0.780092\pi$
$631$	2.83681	−	4.24559i	0.112932	−	0.169014i	0.883630	+	0.468186i	$0.155092\pi$
$632$	9.64862	−	2.00359i	0.383802	−	0.0796987i
$633$	−11.0682	+	7.39555i	−0.439922	+	0.293947i
$634$	−13.3851	−	4.99509i	−0.531592	−	0.198380i
$635$	8.55384	+	10.4229i	0.339449	+	0.413620i
$636$	12.3176	−	9.56166i	0.488425	−	0.379145i
$637$	−12.7471	+	6.81346i	−0.505058	+	0.269959i
$638$	0.872335	+	0.989109i	0.0345361	+	0.0391592i
$639$	8.33359			0.329672
$640$	5.78504	−	9.72282i	0.228674	−	0.384328i
$641$	29.3296			1.15845			0.579224	−	0.815168i	$-0.303356\pi$
$641$	29.3296			1.15845			0.579224	+	0.815168i	$0.303356\pi$
$642$	6.92325	+	7.85002i	0.273239	+	0.309816i
$643$	6.53263	−	3.49176i	0.257622	−	0.137702i	−0.337531	−	0.941315i	$-0.609592\pi$
$643$	6.53263	−	3.49176i	0.257622	−	0.137702i	0.595152	+	0.803613i	$0.297092\pi$
$644$	−1.12993	−	1.45561i	−0.0445255	−	0.0573591i
$645$	7.78176	+	9.48210i	0.306406	+	0.373357i
$646$	−6.77910	−	2.52984i	−0.266720	−	0.0995350i
$647$	14.0181	−	9.36656i	0.551106	−	0.368238i	−0.248621	−	0.968601i	$-0.579977\pi$
$647$	14.0181	−	9.36656i	0.551106	−	0.368238i	0.799727	+	0.600363i	$0.204977\pi$
$648$	−1.12319	+	1.71192i	−0.0441232	+	0.0672507i
$649$	0.921188	−	1.37866i	0.0361598	−	0.0541170i
$650$	1.01203	−	6.23838i	0.0396952	−	0.244689i
$651$	1.52062	−	0.461276i	0.0595979	−	0.0180788i
$652$	−13.6915	+	30.6734i	−0.536201	+	1.20126i
$653$	33.7687	+	27.7133i	1.32147	+	1.08450i	0.990004	+	0.141037i	$0.0450438\pi$
$653$	33.7687	+	27.7133i	1.32147	+	1.08450i	0.331468	+	0.943467i	$0.392456\pi$
$654$	26.5020	+	7.02174i	1.03631	+	0.274572i
$655$	6.36511	+	2.63651i	0.248705	+	0.103017i
$656$	1.55451	−	28.6242i	0.0606936	−	1.11759i
$657$	−11.9744	+	4.95997i	−0.467166	+	0.193507i
$658$	−5.65899	+	0.761139i	−0.220610	+	0.0296723i
$659$	3.14107	+	31.8919i	0.122359	+	1.24233i	0.838705	+	0.544586i	$0.183313\pi$
$659$	3.14107	+	31.8919i	0.122359	+	1.24233i	−0.716346	+	0.697745i	$0.754187\pi$
$660$	−0.256779	+	1.12983i	−0.00999513	+	0.0439785i
$661$	−4.43010	+	8.28813i	−0.172311	+	0.322371i	−0.953222	−	0.302271i	$-0.902255\pi$
$661$	−4.43010	+	8.28813i	−0.172311	+	0.322371i	0.780911	+	0.624642i	$0.214755\pi$
$662$	−16.3164	−	10.0830i	−0.634154	−	0.391885i
$663$	−27.3456	+	5.43938i	−1.06202	+	0.211248i
$664$	−11.7730	−	14.1023i	−0.456882	−	0.547276i
$665$	−0.347886	+	1.74894i	−0.0134905	+	0.0678211i
$666$	−0.278695	−	7.84201i	−0.0107992	−	0.303872i
$667$	0.0839432	−	0.852290i	0.00325029	−	0.0330008i
$668$	12.6947	−	38.0966i	0.491172	−	1.47400i
$669$	0.708801	−	2.33660i	0.0274038	−	0.0903383i
$670$	−0.495870	−	1.44746i	−0.0191571	−	0.0559204i
$671$	4.70561	+	4.70561i	0.181658	+	0.181658i
$672$	−0.230383	+	12.2984i	−0.00888724	+	0.474419i
$673$	31.1304	−	31.1304i	1.19999	−	1.19999i	0.225820	−	0.974169i	$-0.427494\pi$
$673$	31.1304	−	31.1304i	1.19999	−	1.19999i	0.974169	−	0.225820i	$-0.0725061\pi$
$674$	−40.9363	−	20.0453i	−1.57681	−	0.772116i
$675$	−5.08736	−	1.54323i	−0.195812	−	0.0593991i
$676$	13.9064	−	0.989685i	0.534863	−	0.0380648i
$677$	41.6925	+	4.10635i	1.60237	+	0.157820i	0.859329	−	0.511423i	$-0.170881\pi$
$677$	41.6925	+	4.10635i	1.60237	+	0.157820i	0.743044	+	0.669243i	$0.233381\pi$
$678$	−15.4896	+	16.6311i	−0.594875	+	0.638715i
$679$	−0.182703	−	0.0363419i	−0.00701150	−	0.00139467i
$680$	−1.67515	−	15.6590i	−0.0642389	−	0.600495i
$681$	1.63911	+	8.24036i	0.0628108	+	0.315771i
$682$	−0.520013	+	0.122786i	−0.0199123	+	0.00470171i
$683$	−17.9851	−	9.61325i	−0.688182	−	0.367841i	0.0899462	−	0.995947i	$-0.471330\pi$
$683$	−17.9851	−	9.61325i	−0.688182	−	0.367841i	−0.778128	+	0.628106i	$0.783830\pi$
$684$	1.85277	−	2.61635i	0.0708424	−	0.100039i
$685$	−10.6049	+	1.04449i	−0.405192	+	0.0399080i
$686$	22.3302	+	17.0355i	0.852570	+	0.650417i
$687$	8.32215	+	20.0914i	0.317510	+	0.766536i
$688$	−32.2922	−	29.5733i	−1.23113	−	1.12747i
$689$	−11.8992	+	28.7272i	−0.453323	+	1.09442i
$690$	0.650536	−	0.378019i	0.0247655	−	0.0143909i
$691$	3.98360	−	4.85402i	0.151543	−	0.184656i	−0.691705	−	0.722180i	$-0.743140\pi$
$691$	3.98360	−	4.85402i	0.151543	−	0.184656i	0.843248	+	0.537524i	$0.180640\pi$
$692$	1.00247	−	36.9453i	0.0381081	−	1.40445i
$693$	0.508023	+	1.67473i	0.0192982	+	0.0636176i
$694$	27.7097	−	19.9741i	1.05185	−	0.758206i
$695$	13.5890	+	9.07989i	0.515461	+	0.344420i
$696$	−4.00829	+	4.07618i	−0.151934	+	0.154507i
$697$	−22.1687	−	33.1779i	−0.839701	−	1.25670i
$698$	8.05002	−	3.67461i	0.304698	−	0.139086i
$699$	1.84637	−	1.51528i	0.0698362	−	0.0573131i
$700$	−3.74315	+	1.02546i	−0.141478	+	0.0387589i
$701$	3.15303	+	5.89890i	0.119088	+	0.222798i	0.934401	−	0.356222i	$-0.115935\pi$
$701$	3.15303	+	5.89890i	0.119088	+	0.222798i	−0.815313	+	0.579020i	$0.803435\pi$
$702$	2.10360	−	33.5326i	0.0793954	−	1.26561i
$703$		−	2.92295i		−	0.110241i
$704$	0.336225	−	4.12233i	0.0126719	−	0.155366i
$705$		−	2.33143i		−	0.0878066i
$706$	−6.95566	−	0.436350i	−0.261780	−	0.0164223i
$707$	−6.66014	−	12.4602i	−0.250480	−	0.468616i
$708$	6.24451	+	3.55881i	0.234683	+	0.133748i
$709$	6.58171	−	5.40147i	0.247181	−	0.202856i	−0.502642	−	0.864495i	$-0.667639\pi$
$709$	6.58171	−	5.40147i	0.247181	−	0.202856i	0.749823	+	0.661638i	$0.230139\pi$
$710$	2.80554	+	6.14615i	0.105290	+	0.230661i
$711$	3.37654	+	5.05335i	0.126630	+	0.189515i
$712$	−4.74483	−	11.1884i	−0.177820	−	0.419302i
$713$	0.288495	+	0.192766i	0.0108042	+	0.00721914i
$714$	10.0121	+	13.8895i	0.374692	+	0.519803i
$715$	−0.670678	−	2.21093i	−0.0250819	−	0.0826841i
$716$	−13.5526	−	14.3085i	−0.506483	−	0.534735i
$717$	12.4004	−	15.1100i	0.463102	−	0.564292i
$718$	17.6109	+	30.3068i	0.657235	+	1.13104i
$719$	−10.0150	+	24.1783i	−0.373495	+	0.901698i	0.619657	+	0.784873i	$0.287272\pi$
$719$	−10.0150	+	24.1783i	−0.373495	+	0.901698i	−0.993153	+	0.116825i	$0.962728\pi$
$720$	6.89668	+	1.05947i	0.257024	+	0.0394842i
$721$	12.4416	+	30.0366i	0.463348	+	1.11862i
$722$	−15.5734	+	20.4137i	−0.579582	+	0.759719i
$723$	19.6434	−	1.93471i	0.730546	−	0.0719525i
$724$	−23.0654	+	3.94088i	−0.857221	+	0.146462i
$725$	−1.59078	−	0.850290i	−0.0590801	−	0.0315790i
$726$	−3.90844	−	16.5527i	−0.145056	−	0.614330i
$727$	4.48197	+	22.5324i	0.166227	+	0.835679i	0.970441	+	0.241339i	$0.0775866\pi$
$727$	4.48197	+	22.5324i	0.166227	+	0.835679i	−0.804214	+	0.594340i	$0.797413\pi$
$728$	−11.7437	−	21.5340i	−0.435251	−	0.798104i
$729$	−18.7664	−	3.73286i	−0.695051	−	0.138254i
$730$	−7.68929	−	7.16151i	−0.284593	−	0.265060i
$731$	−60.6577	−	5.97426i	−2.24351	−	0.220966i
$732$	−18.8982	+	21.7942i	−0.698498	+	0.805536i
$733$	−17.0735	−	5.17918i	−0.630623	−	0.191297i	−0.0412375	−	0.999149i	$-0.513130\pi$
$733$	−17.0735	−	5.17918i	−0.630623	−	0.191297i	−0.589385	+	0.807852i	$0.700630\pi$
$734$	2.01139	−	4.10764i	0.0742417	−	0.151616i
$735$	−2.56268	+	2.56268i	−0.0945259	+	0.0945259i
$736$	−2.10772	+	1.66469i	−0.0776916	+	0.0613611i
$737$	−0.395518	−	0.395518i	−0.0145691	−	0.0145691i
$738$	16.7254	−	5.72976i	0.615670	−	0.210915i
$739$	0.364513	−	1.20164i	0.0134088	−	0.0442030i	−0.949981	−	0.312309i	$-0.898898\pi$
$739$	0.364513	−	1.20164i	0.0134088	−	0.0442030i	0.963389	+	0.268106i	$0.0863977\pi$
$740$	5.68978	−	2.84559i	0.209160	−	0.104606i
$741$	0.451031	−	4.57939i	0.0165690	−	0.168228i
$742$	19.0828	−	0.678179i	0.700552	−	0.0248967i
$743$	−1.66873	+	8.38929i	−0.0612199	+	0.307773i	−0.999247	−	0.0387874i	$-0.987650\pi$
$743$	−1.66873	+	8.38929i	−0.0612199	+	0.307773i	0.938028	+	0.346561i	$0.112650\pi$
$744$	−0.690918	−	2.21066i	−0.0253303	−	0.0810467i
$745$	−14.1214	+	2.80892i	−0.517367	+	0.102911i
$746$	−2.34499	+	3.79470i	−0.0858563	+	0.138934i
$747$	5.34085	−	9.99203i	0.195411	−	0.365589i
$748$	−3.06752	−	4.87194i	−0.112159	−	0.178136i
$749$	1.25631	+	12.7555i	0.0459046	+	0.466077i
$750$	−0.211239	−	1.57054i	−0.00771335	−	0.0573479i
$751$	28.3671	−	11.7500i	1.03513	−	0.428764i	0.200568	−	0.979680i	$-0.435721\pi$
$751$	28.3671	−	11.7500i	1.03513	−	0.428764i	0.834561	+	0.550916i	$0.185721\pi$
$752$	1.17861	+	8.23865i	0.0429796	+	0.300433i
$753$	−9.80649	−	4.06198i	−0.357368	−	0.148027i
$754$	2.91963	−	11.0195i	0.106327	−	0.401306i
$755$	9.25380	+	7.59439i	0.336780	+	0.276388i
$756$	−19.2694	+	7.37590i	−0.700822	+	0.268259i
$757$	−22.6627	+	6.87467i	−0.823691	+	0.249864i	−0.673871	−	0.738849i	$-0.735370\pi$
$757$	−22.6627	+	6.87467i	−0.823691	+	0.249864i	−0.149821	+	0.988713i	$0.547870\pi$
$758$	−50.2107	−	8.14552i	−1.82373	−	0.295859i
$759$	0.152813	−	0.228701i	0.00554677	−	0.00830132i
$760$	2.55334	+	0.485640i	0.0926193	+	0.0176160i
$761$	−8.20918	+	5.48520i	−0.297583	+	0.198838i	−0.695394	−	0.718629i	$-0.744770\pi$
$761$	−8.20918	+	5.48520i	−0.297583	+	0.198838i	0.397811	+	0.917467i	$0.369770\pi$
$762$	−7.47054	+	20.0185i	−0.270629	+	0.725194i
$763$	21.2985	+	25.9523i	0.771058	+	0.939537i
$764$	−19.7672	−	2.48991i	−0.715152	−	0.0900819i
$765$	8.56573	−	4.57848i	0.309695	−	0.165535i
$766$	29.5913	−	26.0977i	1.06918	−	0.942949i
$767$	−14.3323			−0.517508
$768$	17.9276	+	0.185273i	0.646908	+	0.00668548i
$769$	1.32484			0.0477748			0.0238874	−	0.999715i	$-0.492396\pi$
$769$	1.32484			0.0477748			0.0238874	+	0.999715i	$0.492396\pi$
$770$	−1.06411	+	0.938479i	−0.0383478	+	0.0338204i
$771$	−1.27215	+	0.679979i	−0.0458154	+	0.0244888i
$772$	−47.9710	−	6.04252i	−1.72651	−	0.217475i
$773$	16.6242	+	20.2567i	0.597931	+	0.728581i	0.980756	−	0.195240i	$-0.0625486\pi$
$773$	16.6242	+	20.2567i	0.597931	+	0.728581i	−0.382824	+	0.923821i	$0.625049\pi$
$774$	9.44192	−	25.3011i	0.339383	−	0.909431i
$775$	0.607624	−	0.406001i	0.0218265	−	0.0145840i
$776$	−0.0507323	+	0.266734i	−0.00182118	+	0.00957520i
$777$	−3.84263	+	5.75091i	−0.137854	+	0.206313i
$778$	13.7234	+	2.22630i	0.492007	+	0.0798167i
$779$	6.30199	−	1.91169i	0.225792	−	0.0684933i
$780$	9.35328	−	3.58022i	0.334901	−	0.128193i
$781$	1.90926	+	1.56689i	0.0683187	+	0.0560677i
$782$	−0.957507	+	3.61389i	−0.0342404	+	0.129233i
$783$	−8.85938	−	3.66967i	−0.316608	−	0.131143i
$784$	7.76032	−	10.3514i	0.277154	−	0.369692i
$785$	−3.48910	+	1.44523i	−0.124531	+	0.0515826i
$786$	1.45534	+	10.8203i	0.0519102	+	0.385947i
$787$	3.73206	+	37.8922i	0.133033	+	1.35071i	0.797466	+	0.603364i	$0.206173\pi$
$787$	3.73206	+	37.8922i	0.133033	+	1.35071i	−0.664433	+	0.747348i	$0.731327\pi$
$788$	4.94937	+	7.86076i	0.176314	+	0.280028i
$789$	−2.13717	+	3.99836i	−0.0760852	+	0.142345i
$790$	−2.59019	+	4.19148i	−0.0921548	+	0.149126i
$791$	−27.2960	+	5.42951i	−0.970534	+	0.193051i
$792$	2.43469	−	0.760938i	0.0865130	−	0.0270387i
$793$	11.2221	−	56.4171i	0.398507	−	2.00343i
$794$	−22.7894	+	0.809906i	−0.808766	+	0.0287425i
$795$	−0.764202	+	7.75908i	−0.0271035	+	0.275186i
$796$	−28.5404	+	14.2737i	−1.01159	+	0.505919i
$797$	15.4970	−	51.0868i	0.548933	−	1.80959i	−0.0371133	−	0.999311i	$-0.511816\pi$
$797$	15.4970	−	51.0868i	0.548933	−	1.80959i	0.586046	−	0.810278i	$-0.300684\pi$
$798$	−2.67329	+	0.915813i	−0.0946335	+	0.0324194i
$799$	8.19162	+	8.19162i	0.289799	+	0.289799i
$800$	1.54042	+	5.44308i	0.0544621	+	0.192442i
$801$	5.29987	−	5.29987i	0.187262	−	0.187262i
$802$	−1.57230	+	3.21093i	−0.0555198	+	0.113382i
$803$	−3.67596	−	1.11509i	−0.129722	−	0.0393507i
$804$	1.58844	−	1.83186i	0.0560200	−	0.0646046i
$805$	0.916914	+	0.0903081i	0.0323170	+	0.00318294i
$806$	3.37970	+	3.14772i	0.119045	+	0.110874i
$807$	−20.9865	−	4.17448i	−0.738761	−	0.146949i
$808$	−18.0793	+	9.85964i	−0.636027	+	0.346861i
$809$	0.0905960	+	0.455457i	0.00318519	+	0.0160130i	0.982345	−	0.187077i	$-0.0599015\pi$
$809$	0.0905960	+	0.455457i	0.00318519	+	0.0160130i	−0.979160	+	0.203090i	$0.934901\pi$
$810$	−0.235259	−	0.996350i	−0.00826614	−	0.0350082i
$811$	1.42211	+	0.760132i	0.0499370	+	0.0266919i	0.496176	−	0.868222i	$-0.334737\pi$
$811$	1.42211	+	0.760132i	0.0499370	+	0.0266919i	−0.446239	+	0.894914i	$0.647237\pi$
$812$	−6.90056	+	1.17900i	−0.242162	+	0.0413749i
$813$	−4.95755	+	0.488276i	−0.173869	+	0.0171246i
$814$	1.41061	−	1.84904i	0.0494419	−	0.0648087i
$815$	−6.42725	−	15.5168i	−0.225137	−	0.543528i
$816$	20.1214	−	14.7625i	0.704391	−	0.516792i
$817$	3.84957	−	9.29368i	0.134679	−	0.325145i
$818$	20.0959	+	34.5833i	0.702638	+	1.20918i
$819$	9.59672	−	11.6936i	0.335337	−	0.408609i
$820$	9.85646	+	10.4063i	0.344202	+	0.363402i
$821$	5.57038	+	18.3631i	0.194408	+	0.640877i	0.998899	+	0.0469120i	$0.0149380\pi$
$821$	5.57038	+	18.3631i	0.194408	+	0.640877i	−0.804491	+	0.593965i	$0.797562\pi$
$822$	−9.87450	−	13.6987i	−0.344413	−	0.477797i
$823$	−36.7264	−	24.5398i	−1.28020	−	0.855403i	−0.285517	−	0.958374i	$-0.592165\pi$
$823$	−36.7264	−	24.5398i	−1.28020	−	0.855403i	−0.994684	+	0.102970i	$0.967165\pi$
$824$	43.6260	−	18.5012i	1.51978	−	0.644518i
$825$	−0.321853	−	0.481687i	−0.0112055	−	0.0167702i
$826$	3.65484	+	8.00671i	0.127168	+	0.278589i
$827$	33.3754	−	27.3905i	1.16058	−	0.952460i	0.161169	−	0.986927i	$-0.448473\pi$
$827$	33.3754	−	27.3905i	1.16058	−	0.952460i	0.999406	+	0.0344672i	$0.0109734\pi$
$828$	−1.43914	−	0.820181i	−0.0500136	−	0.0285033i
$829$	15.1069	+	28.2630i	0.524683	+	0.981614i	0.995072	+	0.0991542i	$0.0316137\pi$
$829$	15.1069	+	28.2630i	0.524683	+	0.981614i	−0.470389	+	0.882459i	$0.655886\pi$
$830$	9.16729	+	0.575092i	0.318201	+	0.0199618i
$831$		−	8.81958i		−	0.305948i
$832$	−31.2421	+	17.3800i	−1.08312	+	0.602542i
$833$		−	18.0083i		−	0.623950i
$834$	−1.62154	+	25.8482i	−0.0561492	+	0.895050i
$835$	9.46471	+	17.7072i	0.327540	+	0.612784i
$836$	0.916405	−	0.251056i	0.0316945	−	0.00868296i
$837$	3.00318	−	2.46464i	0.103805	−	0.0851905i
$838$	29.1308	−	13.2974i	1.00631	−	0.459351i
$839$	−10.1181	−	15.1429i	−0.349317	−	0.522790i	0.614654	−	0.788797i	$-0.289296\pi$
$839$	−10.1181	−	15.1429i	−0.349317	−	0.522790i	−0.963971	+	0.266007i	$0.914296\pi$
$840$	−4.38525	−	4.31222i	−0.151305	−	0.148786i
$841$	21.4074	+	14.3039i	0.738185	+	0.493240i
$842$	−32.1001	+	23.1388i	−1.10624	+	0.797417i
$843$	4.71555	+	15.5451i	0.162412	+	0.535401i
$844$	−0.644447	+	23.7506i	−0.0221828	+	0.817530i
$845$	−4.42224	+	5.38851i	−0.152130	+	0.185370i
$846$	−4.43794	+	2.57884i	−0.152580	+	0.0886622i
$847$	7.97023	−	19.2418i	0.273860	−	0.661157i
$848$	−1.22198	−	27.8049i	−0.0419631	−	0.954823i
$849$	−1.59386	−	3.84792i	−0.0547012	−	0.132060i
$850$	6.26039	+	4.77599i	0.214730	+	0.163815i
$851$	−1.50296	+	0.148029i	−0.0515209	+	0.00507437i
$852$	−6.18743	+	8.73744i	−0.211978	+	0.299340i
$853$	26.8125	+	14.3316i	0.918044	+	0.490705i	0.861535	−	0.507697i	$-0.169503\pi$
$853$	26.8125	+	14.3316i	0.918044	+	0.490705i	0.0565086	+	0.998402i	$0.482003\pi$
$854$	−34.3791	+	8.11760i	−1.17643	+	0.277778i
$855$	0.312724	+	1.57217i	0.0106949	+	0.0537670i
$856$	18.5758	−	1.98717i	0.634907	−	0.0679202i
$857$	16.6589	+	3.31366i	0.569057	+	0.113192i	0.471229	−	0.882011i	$-0.343811\pi$
$857$	16.6589	+	3.31366i	0.569057	+	0.113192i	0.0978279	+	0.995203i	$0.468811\pi$
$858$	2.49533	−	2.67922i	0.0851890	−	0.0914672i
$859$	−30.7261	−	3.02625i	−1.04836	−	0.103254i	−0.440861	−	0.897575i	$-0.645327\pi$
$859$	−30.7261	−	3.02625i	−1.04836	−	0.103254i	−0.607498	+	0.794321i	$0.707827\pi$
$860$	21.8386	−	1.55420i	0.744691	−	0.0529977i
$861$	−14.9123	−	4.52361i	−0.508211	−	0.154164i
$862$	−31.5256	−	15.4372i	−1.07377	−	0.525792i
$863$	−25.4088	+	25.4088i	−0.864924	+	0.864924i	−0.991905	−	0.126981i	$-0.959471\pi$
$863$	−25.4088	+	25.4088i	−0.864924	+	0.864924i	0.126981	+	0.991905i	$0.459471\pi$
$864$	10.9862	+	27.9949i	0.373757	+	0.952405i
$865$	13.0669	+	13.0669i	0.444289	+	0.444289i
$866$	17.1927	+	50.1860i	0.584230	+	1.70539i
$867$	4.55425	−	15.0134i	0.154671	−	0.509881i
$868$	0.896625	−	2.69076i	0.0304334	−	0.0913304i
$869$	−0.176556	+	1.79260i	−0.00598925	+	0.0608098i
$870$	−0.101520	−	2.85659i	−0.00344184	−	0.0968475i
$871$	−0.943242	+	4.74200i	−0.0319605	+	0.160676i
$872$	37.5648	−	31.3602i	1.27210	−	1.06199i
$873$	−0.164236	+	0.0326686i	−0.00555856	+	0.00110567i
$874$	−0.524883	−	0.324360i	−0.0177544	−	0.0109716i
$875$	0.914762	−	1.71140i	0.0309246	−	0.0578559i
$876$	3.69030	−	16.2373i	0.124684	−	0.548608i
$877$	3.03245	+	30.7890i	0.102399	+	1.03967i	0.899824	+	0.436254i	$0.143695\pi$
$877$	3.03245	+	30.7890i	0.102399	+	1.03967i	−0.797425	+	0.603418i	$0.793805\pi$
$878$	−53.2695	+	7.16480i	−1.79776	+	0.241800i
$879$	2.63470	−	1.09133i	0.0888662	−	0.0368096i
$880$	1.38085	+	1.53945i	0.0465486	+	0.0518948i
$881$	−11.0644	−	4.58303i	−0.372769	−	0.154406i	0.188430	−	0.982087i	$-0.439660\pi$
$881$	−11.0644	−	4.58303i	−0.372769	−	0.154406i	−0.561200	+	0.827680i	$0.689660\pi$
$882$	7.71277	+	2.04351i	0.259703	+	0.0688086i
$883$	43.7989	+	35.9448i	1.47395	+	1.20964i	0.928412	+	0.371553i	$0.121175\pi$
$883$	43.7989	+	35.9448i	1.47395	+	1.20964i	0.545538	+	0.838086i	$0.316325\pi$
$884$	−20.2840	+	45.4427i	−0.682225	+	1.52840i
$885$	−3.43897	+	1.04320i	−0.115600	+	0.0350668i
$886$	6.99955	−	43.1467i	0.235155	−	1.44954i
$887$	25.1529	−	37.6440i	0.844553	−	1.26396i	−0.118039	−	0.993009i	$-0.537661\pi$
$887$	25.1529	−	37.6440i	0.844553	−	1.26396i	0.962592	−	0.270954i	$-0.0873392\pi$
$888$	8.42896	+	5.53025i	0.282857	+	0.185583i
$889$	−21.7556	+	14.5366i	−0.729659	+	0.487542i
$890$	5.69296	+	2.12451i	0.190828	+	0.0712136i
$891$	−0.237426	−	0.289305i	−0.00795409	−	0.00969208i
$892$	−2.67239	−	3.44266i	−0.0894784	−	0.115269i
$893$	−1.68618	+	0.901284i	−0.0564260	+	0.0301603i
$894$	−15.0918	−	17.1120i	−0.504744	−	0.572311i
$895$	9.85401			0.329383
$896$	17.6763	+	13.0214i	0.590523	+	0.435013i
$897$	−2.37754			−0.0793837
$898$	15.1486	+	17.1764i	0.505515	+	0.573185i
$899$	1.16252	−	0.621377i	0.0387720	−	0.0207241i
$900$	−2.75591	+	2.13930i	−0.0918637	+	0.0713100i
$901$	−24.5770	−	29.9471i	−0.818777	−	0.997683i
$902$	4.90916	+	1.83201i	0.163457	+	0.0609992i
$903$	−19.7919	+	13.2245i	−0.658633	+	0.440084i
$904$	8.24756	+	39.7174i	0.274310	+	1.32098i
$905$	6.50009	−	9.72807i	0.216070	−	0.323372i
$906$	−3.03779	+	18.7256i	−0.100924	+	0.622115i
$907$	29.5645	−	8.96828i	0.981672	−	0.297787i	0.241645	−	0.970365i	$-0.422313\pi$
$907$	29.5645	−	8.96828i	0.981672	−	0.297787i	0.740026	+	0.672578i	$0.234813\pi$
$908$	13.6937	+	6.11240i	0.454443	+	0.202847i
$909$	−9.81760	−	8.05710i	−0.325629	−	0.267237i
$910$	11.8550	+	3.14101i	0.392990	+	0.104123i
$911$	−33.1861	−	13.7461i	−1.09950	−	0.455429i	−0.242192	−	0.970228i	$-0.577866\pi$
$911$	−33.1861	−	13.7461i	−1.09950	−	0.455429i	−0.857311	+	0.514799i	$0.827866\pi$
$912$	1.36751	+	3.88511i	0.0452828	+	0.128649i
$913$	3.10232	−	1.28502i	0.102672	−	0.0425280i
$914$	−15.7281	+	2.11544i	−0.520240	+	0.0699727i
$915$	−1.41373	−	14.3539i	−0.0467366	−	0.474524i
$916$	37.8497	+	8.60222i	1.25059	+	0.284225i
$917$	−6.30230	+	11.7908i	−0.208120	+	0.389365i
$918$	35.6104	+	22.0060i	1.17532	+	0.726306i
$919$	−26.7916	+	5.32918i	−0.883773	+	0.175793i	−0.616054	−	0.787704i	$-0.711270\pi$
$919$	−26.7916	+	5.32918i	−0.883773	+	0.175793i	−0.267719	+	0.963497i	$0.586270\pi$
$920$	0.120403	−	1.33751i	0.00396955	−	0.0440962i
$921$	−6.26017	+	31.4720i	−0.206280	+	1.03704i
$922$	1.03089	+	29.0076i	0.0339507	+	0.955315i
$923$	2.09260	−	21.2466i	0.0688789	−	0.699340i
$924$	−2.13307	−	0.710790i	−0.0701730	−	0.0233833i
$925$	−0.923349	+	3.04387i	−0.0303595	+	0.100082i
$926$	−14.3640	−	41.9289i	−0.472029	−	1.37787i
$927$	20.6654	+	20.6654i	0.678740	+	0.678740i
$928$	1.80285	+	10.0431i	0.0591813	+	0.329681i
$929$	−42.4048	+	42.4048i	−1.39126	+	1.39126i	−0.568738	+	0.822519i	$0.692568\pi$
$929$	−42.4048	+	42.4048i	−1.39126	+	1.39126i	−0.822519	+	0.568738i	$0.807432\pi$
$930$	1.04006	+	0.509286i	0.0341049	+	0.0167002i
$931$	2.84412	+	0.862754i	0.0932123	+	0.0282756i
$932$	−0.302636	−	4.25246i	−0.00991318	−	0.139294i
$933$	28.4708	+	2.80413i	0.932091	+	0.0918030i
$934$	27.8310	−	29.8821i	0.910660	−	0.977772i
$935$	2.82329	+	0.561588i	0.0923315	+	0.0183659i
$936$	−17.1609	−	13.8441i	−0.560922	−	0.452508i
$937$	−6.27065	−	31.5247i	−0.204853	−	1.02987i	−0.937162	−	0.348894i	$-0.886557\pi$
$937$	−6.27065	−	31.5247i	−0.204853	−	1.02987i	0.732309	−	0.680973i	$-0.238443\pi$
$938$	2.88965	−	0.682304i	0.0943504	−	0.0222780i
$939$	14.4674	+	7.73299i	0.472126	+	0.252357i
$940$	−3.39598	−	2.40487i	−0.110765	−	0.0784382i
$941$	−14.6632	+	1.44420i	−0.478006	+	0.0470795i	−0.334151	−	0.942519i	$-0.608450\pi$
$941$	−14.6632	+	1.44420i	−0.478006	+	0.0470795i	−0.143854	+	0.989599i	$0.545950\pi$
$942$	−4.75813	−	3.62993i	−0.155028	−	0.118269i
$943$	−1.30213	−	3.14363i	−0.0424033	−	0.102371i
$944$	11.6250	−	5.42491i	0.378363	−	0.176566i
$945$	3.94792	−	9.53113i	0.128426	−	0.310048i
$946$	6.92032	−	4.02132i	0.224999	−	0.130744i
$947$	8.07130	−	9.83491i	0.262282	−	0.319592i	−0.625173	−	0.780486i	$-0.714971\pi$
$947$	8.07130	−	9.83491i	0.262282	−	0.319592i	0.887455	+	0.460895i	$0.152471\pi$
$948$	−7.80521	−	0.211786i	−0.253501	−	0.00687847i
$949$	9.63865	+	31.7744i	0.312884	+	1.03144i
$950$	−1.05422	+	0.759916i	−0.0342033	+	0.0246549i
$951$	9.41224	+	6.28906i	0.305213	+	0.203937i
$952$	30.5591	−	0.256597i	0.990427	−	0.00831636i
$953$	−15.5042	−	23.2037i	−0.502231	−	0.751641i	0.490572	−	0.871400i	$-0.336788\pi$
$953$	−15.5042	−	23.2037i	−0.502231	−	0.751641i	−0.992803	+	0.119759i	$0.961788\pi$
$954$	15.6149	−	7.12778i	0.505552	−	0.230770i
$955$	7.70050	−	6.31964i	0.249182	−	0.204499i
$956$	−9.21829	−	33.6486i	−0.298141	−	1.08827i
$957$	−0.492590	−	0.921572i	−0.0159232	−	0.0297902i
$958$	−0.956678	+	15.2500i	−0.0309089	+	0.492704i
$959$		−	20.6788i		−	0.667752i
$960$	−6.23138	+	6.44427i	−0.201117	+	0.207988i
$961$		−	30.4660i		−	0.982773i
$962$	−20.0633	−	1.25863i	−0.646866	−	0.0405799i
$963$	5.43131	+	10.1613i	0.175021	+	0.327442i
$964$	17.4441	−	30.6085i	0.561836	−	0.985832i
$965$	18.6875	−	15.3365i	0.601573	−	0.493699i
$966$	0.606291	+	1.32821i	0.0195071	+	0.0427345i
$967$	−23.3004	−	34.8716i	−0.749291	−	1.12139i	−0.988617	−	0.150454i	$-0.951926\pi$
$967$	−23.3004	−	34.8716i	−0.749291	−	1.12139i	0.239326	−	0.970939i	$-0.423074\pi$
$968$	−28.1425	−	11.3811i	−0.904533	−	0.365803i
$969$	4.76697	+	3.18519i	0.153137	+	0.102323i
$970$	−0.0793846	−	0.110129i	−0.00254888	−	0.00353602i
$971$	−14.8553	−	48.9712i	−0.476728	−	1.57156i	−0.784517	−	0.620107i	$-0.787089\pi$
$971$	−14.8553	−	48.9712i	−0.476728	−	1.57156i	0.307789	−	0.951455i	$-0.400411\pi$
$972$	−21.9807	+	20.8193i	−0.705031	+	0.667781i
$973$	−20.1197	+	24.5159i	−0.645009	+	0.785945i
$974$	10.8769	+	18.7182i	0.348520	+	0.599771i
$975$	−1.91630	+	4.62636i	−0.0613708	+	0.148162i
$976$	12.2521	+	50.0081i	0.392181	+	1.60072i
$977$	−2.31201	−	5.58169i	−0.0739678	−	0.178574i	0.882571	−	0.470179i	$-0.155811\pi$
$977$	−2.31201	−	5.58169i	−0.0739678	−	0.178574i	−0.956539	+	0.291605i	$0.905811\pi$
$978$	16.1430	−	21.1604i	0.516198	−	0.676635i
$979$	2.21071	−	0.217736i	0.0706545	−	0.00695886i
$980$	1.08942	+	6.37624i	0.0348003	+	0.203682i
$981$	26.6161	+	14.2266i	0.849785	+	0.454220i
$982$	5.86398	+	24.8347i	0.187127	+	0.792507i
$983$	6.57554	+	33.0575i	0.209727	+	1.05437i	0.931916	+	0.362674i	$0.118136\pi$
$983$	6.57554	+	33.0575i	0.209727	+	1.05437i	−0.722189	+	0.691696i	$0.756864\pi$
$984$	−6.41065	+	21.7901i	−0.204364	+	0.694642i
$985$	−4.55532	−	0.906109i	−0.145145	−	0.0288710i
$986$	10.3935	+	9.68012i	0.330997	+	0.308278i
$987$	4.50243	+	0.443451i	0.143314	+	0.0141152i
$988$	−6.20516	−	5.38063i	−0.197412	−	0.171181i
$989$	−4.97371	−	1.50876i	−0.158155	−	0.0479757i
$990$	−0.560899	+	1.14546i	−0.0178265	+	0.0364051i
$991$	28.2383	−	28.2383i	0.897020	−	0.897020i	−0.0981514	−	0.995171i	$-0.531293\pi$
$991$	28.2383	−	28.2383i	0.897020	−	0.897020i	0.995171	+	0.0981514i	$0.0312930\pi$
$992$	−3.93276	−	1.27390i	−0.124865	−	0.0404463i
$993$	10.7462	+	10.7462i	0.341021	+	0.341021i
$994$	−12.4030	+	4.24901i	−0.393400	+	0.134770i
$995$	4.63159	−	15.2683i	0.146831	−	0.484038i
$996$	6.51083	+	13.0184i	0.206304	+	0.412505i
$997$	0.938317	−	9.52689i	0.0297168	−	0.301720i	−0.968825	−	0.247744i	$-0.920311\pi$
$997$	0.938317	−	9.52689i	0.0297168	−	0.301720i	0.998542	−	0.0539754i	$-0.0171893\pi$
$998$	−36.9081	+	1.31167i	−1.16831	+	0.0415201i
$999$	−3.29902	+	16.5853i	−0.104376	+	0.524735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.15	✓	1024
128.109	even	32	inner	640.2.bm.a.621.15	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.15	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.15	yes	1024	128.109	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06065 + 0.935428i) q^{2} +(0.988226 - 0.528218i) q^{3} +(0.249949 - 1.98432i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-0.554050 + 1.48467i) q^{6} +(-1.61350 + 1.07810i) q^{7} +(1.59108 + 2.33847i) q^{8} +(-0.969134 + 1.45041i) q^{9} +(-1.39596 - 0.226463i) q^{10} +(-0.494740 + 0.150078i) q^{11} +(-0.801147 - 2.09298i) q^{12} +(3.45448 + 2.83502i) q^{13} +(0.702863 - 2.65280i) q^{14} +(1.03524 + 0.428811i) q^{15} +(-3.87505 - 0.991957i) q^{16} +(-5.14405 + 2.13073i) q^{17} +(-0.328846 - 2.44493i) q^{18} +(-0.0900704 - 0.914500i) q^{19} +(1.69247 - 1.06563i) q^{20} +(-1.02503 + 1.91769i) q^{21} +(0.384358 - 0.621974i) q^{22} +(-0.465669 + 0.0926273i) q^{23} +(2.80757 + 1.47050i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-6.31595 + 0.224461i) q^{26} +(-0.521086 + 5.29067i) q^{27} +(1.73601 + 3.47116i) q^{28} +(-0.523606 + 1.72610i) q^{29} +(-1.49915 + 0.513576i) q^{30} +(-0.516741 - 0.516741i) q^{31} +(5.03797 - 2.57271i) q^{32} +(-0.409641 + 0.409641i) q^{33} +(3.46288 - 7.07184i) q^{34} +(-1.85698 - 0.563308i) q^{35} +(2.63585 + 2.28560i) q^{36} +(3.16552 + 0.311777i) q^{37} +(0.950982 + 0.885708i) q^{38} +(4.91132 + 0.976922i) q^{39} +(-0.798294 + 2.71343i) q^{40} +(1.39813 + 7.02889i) q^{41} +(-0.706668 - 2.99283i) q^{42} +(9.65433 + 5.16035i) q^{43} +(0.174143 + 1.01923i) q^{44} +(-1.73600 + 0.170981i) q^{45} +(0.407264 - 0.533844i) q^{46} +(-0.796223 - 1.92225i) q^{47} +(-4.35340 + 1.06659i) q^{48} +(-1.23772 + 2.98812i) q^{49} +(-0.710532 - 1.22276i) q^{50} +(-3.95799 + 4.82282i) q^{51} +(6.48903 - 6.14619i) q^{52} +(2.01978 + 6.65832i) q^{53} +(-4.39636 - 6.09898i) q^{54} +(-0.429872 - 0.287231i) q^{55} +(-5.08832 - 2.05777i) q^{56} +(-0.572065 - 0.856156i) q^{57} +(-1.05928 - 2.32058i) q^{58} +(-2.47915 + 2.03458i) q^{59} +(1.10966 - 1.94707i) q^{60} +(-6.06772 - 11.3519i) q^{61} +(1.03146 + 0.0647064i) q^{62} -3.38506i q^{63} +(-2.93692 + 7.44140i) q^{64} +4.46887i q^{65} +(0.0512953 - 0.817675i) q^{66} +(0.510007 + 0.954156i) q^{67} +(2.94231 + 10.7400i) q^{68} +(-0.411259 + 0.337511i) q^{69} +(2.49653 - 1.13960i) q^{70} +(-2.65416 - 3.97222i) q^{71} +(-4.93372 + 0.0414272i) q^{72} +(6.17789 + 4.12794i) q^{73} +(-3.64915 + 2.63043i) q^{74} +(0.325275 + 1.07229i) q^{75} +(-1.83717 - 0.0498497i) q^{76} +(0.636462 - 0.775531i) q^{77} +(-6.12302 + 3.55802i) q^{78} +(1.33330 - 3.21887i) q^{79} +(-1.69151 - 3.62475i) q^{80} +(0.277024 + 0.668796i) q^{81} +(-8.05794 - 6.14732i) q^{82} +(-6.46372 + 0.636621i) q^{83} +(3.54910 + 2.51330i) q^{84} +(-4.91043 - 2.62468i) q^{85} +(-15.0670 + 3.55762i) q^{86} +(0.394315 + 1.98235i) q^{87} +(-1.13812 - 0.918151i) q^{88} +(-4.21414 - 0.838245i) q^{89} +(1.68134 - 1.80525i) q^{90} +(-8.63025 - 0.850005i) q^{91} +(0.0674088 + 0.947188i) q^{92} +(-0.783609 - 0.237705i) q^{93} +(2.64264 + 1.29402i) q^{94} +(0.649778 - 0.649778i) q^{95} +(3.61970 - 5.20357i) q^{96} +(0.0678790 + 0.0678790i) q^{97} +(-1.48239 - 4.32715i) q^{98} +(0.261795 - 0.863022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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