LMFDB - Embedded newform 768.2.z.a.157.54

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(13,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 47, 0]))

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

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

chi := DirichletCharacter("768.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.z (of order $64$, degree $32$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$2048$
Relative dimension:	$64$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			157.54
Character	$\chi$	$=$	768.157
Dual form			768.2.z.a.181.54

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24142 - 0.677401i) q^{2} +(-0.740951 + 0.671559i) q^{3} +(1.08226 - 1.68188i) q^{4} +(-0.0647518 - 0.258504i) q^{5} +(-0.464918 + 1.33561i) q^{6} +(0.00672472 + 0.00551883i) q^{7} +(0.204226 - 2.82104i) q^{8} +(0.0980171 - 0.995185i) q^{9} +O(q^{10})$	\(q+(1.24142 - 0.677401i) q^{2} +(-0.740951 + 0.671559i) q^{3} +(1.08226 - 1.68188i) q^{4} +(-0.0647518 - 0.258504i) q^{5} +(-0.464918 + 1.33561i) q^{6} +(0.00672472 + 0.00551883i) q^{7} +(0.204226 - 2.82104i) q^{8} +(0.0980171 - 0.995185i) q^{9} +(-0.255495 - 0.277049i) q^{10} +(2.13233 - 1.00852i) q^{11} +(0.327584 + 1.97299i) q^{12} +(-1.81964 + 1.09065i) q^{13} +(0.0120867 + 0.00229587i) q^{14} +(0.221578 + 0.148054i) q^{15} +(-1.65745 - 3.64045i) q^{16} +(3.61800 - 2.41747i) q^{17} +(-0.552459 - 1.30184i) q^{18} +(5.02224 - 6.77171i) q^{19} +(-0.504850 - 0.170862i) q^{20} +(-0.00868891 + 0.000426859i) q^{21} +(1.96395 - 2.69644i) q^{22} +(-7.46058 + 2.26314i) q^{23} +(1.74318 + 2.22741i) q^{24} +(4.34697 - 2.32351i) q^{25} +(-1.52013 + 2.58658i) q^{26} +(0.595699 + 0.803208i) q^{27} +(0.0165599 - 0.00533739i) q^{28} +(4.67426 - 1.67248i) q^{29} +(0.375364 + 0.0336999i) q^{30} +(0.898765 + 2.16981i) q^{31} +(-4.52364 - 3.39657i) q^{32} +(-0.902674 + 2.17925i) q^{33} +(2.85386 - 5.45193i) q^{34} +(0.000991201 - 0.00209572i) q^{35} +(-1.56770 - 1.24190i) q^{36} +(-0.557933 + 3.76128i) q^{37} +(1.64756 - 11.8086i) q^{38} +(0.615827 - 2.03011i) q^{39} +(-0.742474 + 0.129874i) q^{40} +(-4.24157 - 2.26717i) q^{41} +(-0.0104974 + 0.00641579i) q^{42} +(-5.42356 + 5.98397i) q^{43} +(0.611520 - 4.67780i) q^{44} +(-0.263606 + 0.0391022i) q^{45} +(-7.72867 + 7.86332i) q^{46} +(0.491504 - 2.47096i) q^{47} +(3.67286 + 1.58432i) q^{48} +(-1.36562 - 6.86542i) q^{49} +(3.82248 - 5.82910i) q^{50} +(-1.05729 + 4.22092i) q^{51} +(-0.134970 + 4.24077i) q^{52} +(9.64013 + 3.44929i) q^{53} +(1.28361 + 0.593592i) q^{54} +(-0.398778 - 0.485912i) q^{55} +(0.0169422 - 0.0178436i) q^{56} +(0.826367 + 8.39024i) q^{57} +(4.66979 - 5.24260i) q^{58} +(-8.65553 - 5.18793i) q^{59} +(0.488813 - 0.212436i) q^{60} +(13.6797 + 0.672040i) q^{61} +(2.58558 + 2.08482i) q^{62} +(0.00615140 - 0.00615140i) q^{63} +(-7.91658 - 1.15226i) q^{64} +(0.399761 + 0.399761i) q^{65} +(0.355626 + 3.31684i) q^{66} +(-0.787007 + 16.0199i) q^{67} +(-0.150299 - 8.70136i) q^{68} +(4.00809 - 6.68710i) q^{69} +(-0.000189144 - 0.00327311i) q^{70} +(1.19466 - 0.117664i) q^{71} +(-2.78744 - 0.479754i) q^{72} +(4.11190 - 3.37455i) q^{73} +(1.85527 + 5.04728i) q^{74} +(-1.66052 + 4.64085i) q^{75} +(-5.95387 - 15.7755i) q^{76} +(0.0199052 + 0.00498598i) q^{77} +(-0.610698 - 2.93738i) q^{78} +(-7.93344 + 1.57806i) q^{79} +(-0.833747 + 0.664182i) q^{80} +(-0.980785 - 0.195090i) q^{81} +(-6.80136 + 0.0587357i) q^{82} +(1.99538 + 13.4518i) q^{83} +(-0.00868569 + 0.0150757i) q^{84} +(-0.859196 - 0.778730i) q^{85} +(-2.67937 + 11.1026i) q^{86} +(-2.34023 + 4.37826i) q^{87} +(-2.40959 - 6.22137i) q^{88} +(-13.3318 - 4.04415i) q^{89} +(-0.300758 + 0.227109i) q^{90} +(-0.0182556 - 0.00270797i) q^{91} +(-4.26791 + 14.9971i) q^{92} +(-2.12310 - 1.00415i) q^{93} +(-1.06367 - 3.40044i) q^{94} +(-2.07571 - 0.859788i) q^{95} +(5.63279 - 0.521193i) q^{96} +(2.26028 - 0.936237i) q^{97} +(-6.34595 - 7.59781i) q^{98} +(-0.794656 - 2.22092i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2048 q+O(q^{10}) $ 2048 * q	$ 2048 q+O(q^{100}) $ 2048 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{27}{64}\right)$

Coefficient data

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

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

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

$2$	1.24142	−	0.677401i	0.877818	−	0.478995i
$2$	1.24142	−	0.677401i	0.877818	−	0.478995i
$3$	−0.740951	+	0.671559i	−0.427788	+	0.387725i
$3$	−0.740951	+	0.671559i	−0.427788	+	0.387725i
$4$	1.08226	−	1.68188i	0.541128	−	0.840941i
$5$	−0.0647518	−	0.258504i	−0.0289579	−	0.115606i	0.953829	−	0.300352i	$-0.0971040\pi$
$5$	−0.0647518	−	0.258504i	−0.0289579	−	0.115606i	−0.982786	+	0.184745i	$0.940854\pi$
$6$	−0.464918	+	1.33561i	−0.189802	+	0.545260i
$7$	0.00672472	+	0.00551883i	0.00254170	+	0.00208592i	0.635663	−	0.771966i	$-0.280727\pi$
$7$	0.00672472	+	0.00551883i	0.00254170	+	0.00208592i	−0.633122	+	0.774052i	$0.718227\pi$
$8$	0.204226	−	2.82104i	0.0722049	−	0.997390i
$9$	0.0980171	−	0.995185i	0.0326724	−	0.331728i
$10$	−0.255495	−	0.277049i	−0.0807946	−	0.0876106i
$11$	2.13233	−	1.00852i	0.642922	−	0.304079i	−0.0781479	−	0.996942i	$-0.524901\pi$
$11$	2.13233	−	1.00852i	0.642922	−	0.304079i	0.721070	+	0.692862i	$0.243651\pi$
$12$	0.327584	+	1.97299i	0.0945654	+	0.569553i
$13$	−1.81964	+	1.09065i	−0.504676	+	0.302491i	−0.743690	−	0.668525i	$-0.766926\pi$
$13$	−1.81964	+	1.09065i	−0.504676	+	0.302491i	0.239014	+	0.971016i	$0.423176\pi$
$14$	0.0120867	+	0.00229587i	0.00323030	+	0.000613596i
$15$	0.221578	+	0.148054i	0.0572113	+	0.0382274i
$16$	−1.65745	−	3.64045i	−0.414362	−	0.910112i
$17$	3.61800	−	2.41747i	0.877493	−	0.586322i	−0.0331802	−	0.999449i	$-0.510564\pi$
$17$	3.61800	−	2.41747i	0.877493	−	0.586322i	0.910673	+	0.413127i	$0.135564\pi$
$18$	−0.552459	−	1.30184i	−0.130216	−	0.306847i
$19$	5.02224	−	6.77171i	1.15218	−	1.55354i	0.371707	−	0.928350i	$-0.378773\pi$
$19$	5.02224	−	6.77171i	1.15218	−	1.55354i	0.780475	−	0.625187i	$-0.214977\pi$
$20$	−0.504850	−	0.170862i	−0.112888	−	0.0382059i
$21$	−0.00868891		0.000426859i	−0.00189608		9.31482e-5i
$22$	1.96395	−	2.69644i	0.418716	−	0.574883i
$23$	−7.46058	+	2.26314i	−1.55564	+	0.471898i	−0.946915	−	0.321485i	$-0.895818\pi$
$23$	−7.46058	+	2.26314i	−1.55564	+	0.471898i	−0.608723	+	0.793383i	$0.708318\pi$
$24$	1.74318	+	2.22741i	0.355824	+	0.454667i
$25$	4.34697	−	2.32351i	0.869395	−	0.464701i
$26$	−1.52013	+	2.58658i	−0.298122	+	0.507269i
$27$	0.595699	+	0.803208i	0.114642	+	0.154577i
$28$	0.0165599	−	0.00533739i	0.00312952	−	0.00100867i
$29$	4.67426	−	1.67248i	0.867988	−	0.310571i	0.135027	−	0.990842i	$-0.456888\pi$
$29$	4.67426	−	1.67248i	0.867988	−	0.310571i	0.732961	+	0.680271i	$0.238138\pi$
$30$	0.375364	+	0.0336999i	0.0685318	+	0.00615273i
$31$	0.898765	+	2.16981i	0.161423	+	0.389709i	0.983809	−	0.179220i	$-0.0573576\pi$
$31$	0.898765	+	2.16981i	0.161423	+	0.389709i	−0.822386	+	0.568930i	$0.807358\pi$
$32$	−4.52364	−	3.39657i	−0.799673	−	0.600435i
$33$	−0.902674	+	2.17925i	−0.157135	+	0.379358i
$34$	2.85386	−	5.45193i	0.489434	−	0.934999i
$35$	0.000991201	−	0.00209572i	0.000167544	−	0.000354241i
$36$	−1.56770	−	1.24190i	−0.261284	−	0.206983i
$37$	−0.557933	+	3.76128i	−0.0917236	+	0.618351i	0.893756	+	0.448554i	$0.148061\pi$
$37$	−0.557933	+	3.76128i	−0.0917236	+	0.618351i	−0.985479	+	0.169796i	$0.945689\pi$
$38$	1.64756	−	11.8086i	0.267269	−	1.91561i
$39$	0.615827	−	2.03011i	0.0986112	−	0.325078i
$40$	−0.742474	+	0.129874i	−0.117395	+	0.0205350i
$41$	−4.24157	−	2.26717i	−0.662422	−	0.354072i	0.105679	−	0.994400i	$-0.466298\pi$
$41$	−4.24157	−	2.26717i	−0.662422	−	0.354072i	−0.768102	+	0.640328i	$0.778798\pi$
$42$	−0.0104974	+	0.00641579i	−0.00161979	+	0.000989978i
$43$	−5.42356	+	5.98397i	−0.827085	+	0.912547i	−0.997343	−	0.0728521i	$-0.976790\pi$
$43$	−5.42356	+	5.98397i	−0.827085	+	0.912547i	0.170258	+	0.985400i	$0.445540\pi$
$44$	0.611520	−	4.67780i	0.0921900	−	0.705205i
$45$	−0.263606	+	0.0391022i	−0.0392960	+	0.00582901i
$46$	−7.72867	+	7.86332i	−1.13953	+	1.15938i
$47$	0.491504	−	2.47096i	0.0716932	−	0.360426i	−0.928240	−	0.371982i	$-0.878678\pi$
$47$	0.491504	−	2.47096i	0.0716932	−	0.360426i	0.999933	+	0.0115558i	$0.00367840\pi$
$48$	3.67286	+	1.58432i	0.530132	+	0.228677i
$49$	−1.36562	−	6.86542i	−0.195088	−	0.980775i
$50$	3.82248	−	5.82910i	0.540581	−	0.824359i
$51$	−1.05729	+	4.22092i	−0.148050	+	0.591048i
$52$	−0.134970	+	4.24077i	−0.0187170	+	0.588089i
$53$	9.64013	+	3.44929i	1.32417	+	0.473797i	0.901615	−	0.432539i	$-0.142382\pi$
$53$	9.64013	+	3.44929i	1.32417	+	0.473797i	0.422558	+	0.906336i	$0.361132\pi$
$54$	1.28361	+	0.593592i	0.174677	+	0.0807776i
$55$	−0.398778	−	0.485912i	−0.0537712	−	0.0655204i
$56$	0.0169422	−	0.0178436i	0.00226400	−	0.00238446i
$57$	0.826367	+	8.39024i	0.109455	+	1.11131i
$58$	4.66979	−	5.24260i	0.613173	−	0.688386i
$59$	−8.65553	−	5.18793i	−1.12685	−	0.675410i	−0.175797	−	0.984426i	$-0.556250\pi$
$59$	−8.65553	−	5.18793i	−1.12685	−	0.675410i	−0.951057	+	0.309016i	$0.900000\pi$
$60$	0.488813	−	0.212436i	0.0631055	−	0.0274254i
$61$	13.6797	+	0.672040i	1.75151	+	0.0860459i	0.899346	−	0.437237i	$-0.144043\pi$
$61$	13.6797	+	0.672040i	1.75151	+	0.0860459i	0.852159	+	0.523283i	$0.175293\pi$
$62$	2.58558	+	2.08482i	0.328369	+	0.264773i
$63$	0.00615140	−	0.00615140i	0.000775003	−	0.000775003i
$64$	−7.91658	−	1.15226i	−0.989573	−	0.144033i
$65$	0.399761	+	0.399761i	0.0495843	+	0.0495843i
$66$	0.355626	+	3.31684i	0.0437746	+	0.408275i
$67$	−0.787007	+	16.0199i	−0.0961483	+	1.95714i	0.151902	+	0.988396i	$0.451460\pi$
$67$	−0.787007	+	16.0199i	−0.0961483	+	1.95714i	−0.248050	+	0.968747i	$0.579790\pi$
$68$	−0.150299	−	8.70136i	−0.0182264	−	1.05519i
$69$	4.00809	−	6.68710i	0.482517	−	0.805032i
$70$	−0.000189144	−	0.00327311i	−2.26070e−5	−	0.000391212i
$71$	1.19466	−	0.117664i	0.141780	−	0.0139641i	−0.0268781	−	0.999639i	$-0.508557\pi$
$71$	1.19466	−	0.117664i	0.141780	−	0.0139641i	0.168658	+	0.985675i	$0.446057\pi$
$72$	−2.78744	−	0.479754i	−0.328503	−	0.0565395i
$73$	4.11190	−	3.37455i	0.481261	−	0.394961i	−0.362243	−	0.932084i	$-0.617989\pi$
$73$	4.11190	−	3.37455i	0.481261	−	0.394961i	0.843504	+	0.537123i	$0.180489\pi$
$74$	1.85527	+	5.04728i	0.215670	+	0.586734i
$75$	−1.66052	+	4.64085i	−0.191741	+	0.535880i
$76$	−5.95387	−	15.7755i	−0.682955	−	1.80958i
$77$	0.0199052	+	0.00498598i	0.00226840	+	0.000568206i
$78$	−0.610698	−	2.93738i	−0.0691479	−	0.332593i
$79$	−7.93344	+	1.57806i	−0.892582	+	0.177546i	−0.620014	−	0.784591i	$-0.712873\pi$
$79$	−7.93344	+	1.57806i	−0.892582	+	0.177546i	−0.272568	+	0.962136i	$0.587873\pi$
$80$	−0.833747	+	0.664182i	−0.0932157	+	0.0742578i
$81$	−0.980785	−	0.195090i	−0.108976	−	0.0216767i
$82$	−6.80136	+	0.0587357i	−0.751085	+	0.00648628i
$83$	1.99538	+	13.4518i	0.219022	+	1.47652i	0.767872	+	0.640603i	$0.221316\pi$
$83$	1.99538	+	13.4518i	0.219022	+	1.47652i	−0.548850	+	0.835921i	$0.684934\pi$
$84$	−0.00868569	+	0.0150757i	−0.000947686	+	0.00164489i
$85$	−0.859196	−	0.778730i	−0.0931929	−	0.0844651i
$86$	−2.67937	+	11.1026i	−0.288924	+	1.19722i
$87$	−2.34023	+	4.37826i	−0.250899	+	0.469399i
$88$	−2.40959	−	6.22137i	−0.256864	−	0.663200i
$89$	−13.3318	−	4.04415i	−1.41317	−	0.428679i	−0.510818	−	0.859689i	$-0.670658\pi$
$89$	−13.3318	−	4.04415i	−1.41317	−	0.428679i	−0.902347	+	0.431009i	$0.858158\pi$
$90$	−0.300758	+	0.227109i	−0.0317027	+	0.0239394i
$91$	−0.0182556	−	0.00270797i	−0.00191371	−	0.000283872i
$92$	−4.26791	+	14.9971i	−0.444961	+	1.56356i
$93$	−2.12310	−	1.00415i	−0.220155	−	0.104125i
$94$	−1.06367	−	3.40044i	−0.109709	−	0.350729i
$95$	−2.07571	−	0.859788i	−0.212964	−	0.0882124i
$96$	5.63279	−	0.521193i	0.574895	−	0.0531941i
$97$	2.26028	−	0.936237i	0.229496	−	0.0950605i	−0.264972	−	0.964256i	$-0.585363\pi$
$97$	2.26028	−	0.936237i	0.229496	−	0.0950605i	0.494468	+	0.869196i	$0.335363\pi$
$98$	−6.34595	−	7.59781i	−0.641038	−	0.767495i
$99$	−0.794656	−	2.22092i	−0.0798660	−	0.223210i
$100$	0.796674	−	9.82572i	0.0796674	−	0.982572i
$101$	−12.3889	+	9.18821i	−1.23274	+	0.914261i	−0.998324	−	0.0578758i	$-0.981567\pi$
$101$	−12.3889	+	9.18821i	−1.23274	+	0.914261i	−0.234414	+	0.972137i	$0.575317\pi$
$102$	1.54672	+	5.95615i	0.153148	+	0.589747i
$103$	5.44302	+	10.1832i	0.536317	+	1.00338i	0.993481	+	0.113996i	$0.0363651\pi$
$103$	5.44302	+	10.1832i	0.536317	+	1.00338i	−0.457164	+	0.889382i	$0.651135\pi$
$104$	2.70515	+	5.35601i	0.265262	+	0.525200i
$105$	0.000672967		0.00221847i	6.56748e−5		0.000216501i
$106$	14.3040	−	2.24821i	1.38933	−	0.218365i
$107$	−0.755037	−	15.3691i	−0.0729922	−	1.48579i	−0.704103	−	0.710097i	$-0.748651\pi$
$107$	−0.755037	−	15.3691i	−0.0729922	−	1.48579i	0.631111	−	0.775692i	$-0.282599\pi$
$108$	1.99560	−	0.132620i	0.192027	−	0.0127614i
$109$	15.0190	+	11.1389i	1.43856	+	1.06691i	0.984391	+	0.175996i	$0.0563146\pi$
$109$	15.0190	+	11.1389i	1.43856	+	1.06691i	0.454171	+	0.890914i	$0.349935\pi$
$110$	−0.824209	−	0.333089i	−0.0785852	−	0.0317588i
$111$	−2.11252	−	3.16161i	−0.200512	−	0.300087i
$112$	0.00894516	−	0.0336282i	0.000845238	−	0.00317756i
$113$	−4.40401	+	6.59106i	−0.414294	+	0.620035i	−0.978659	−	0.205490i	$-0.934121\pi$
$113$	−4.40401	+	6.59106i	−0.414294	+	0.620035i	0.564365	+	0.825525i	$0.309121\pi$
$114$	6.70943	+	9.85604i	0.628396	+	0.923103i
$115$	1.06812	+	1.78204i	0.0996024	+	0.166176i
$116$	2.24583	−	9.67159i	0.208520	−	0.897985i
$117$	0.907040	+	1.91778i	0.0838559	+	0.177298i
$118$	−14.2595	−	0.577135i	−1.31269	−	0.0531296i
$119$	0.0376716	+	0.00371033i	0.00345335	+	0.000340125i
$120$	0.462919	−	0.594846i	0.0422585	−	0.0543018i
$121$	−3.44860	+	4.20213i	−0.313509	+	0.382012i
$122$	17.4375	−	8.43236i	1.57872	−	0.763430i
$123$	4.66534	−	1.16861i	0.420659	−	0.105370i
$124$	4.62206	+	0.836672i	0.415073	+	0.0751354i
$125$	−1.77693	−	1.96054i	−0.158933	−	0.175356i
$126$	0.00346951	−	0.0118034i	0.000309089	−	0.00105153i
$127$			16.0654i			1.42557i	0.701383	+	0.712785i	$0.252566\pi$
$127$			16.0654i			1.42557i	−0.701383	+	0.712785i	$0.747434\pi$
$128$	−10.6084	+	3.93226i	−0.937656	+	0.347566i
$129$		−	8.07607i		−	0.711058i
$130$	0.767071	+	0.225473i	0.0672765	+	0.0197753i
$131$	−0.182140	−	0.200961i	−0.0159136	−	0.0175580i	0.732942	−	0.680291i	$-0.238147\pi$
$131$	−0.182140	−	0.200961i	−0.0159136	−	0.0175580i	−0.748856	+	0.662733i	$0.769397\pi$
$132$	2.68831	+	3.87669i	0.233988	+	0.337423i
$133$	0.0711451	−	0.0178209i	0.00616906	−	0.00154527i
$134$	9.87489	+	20.4206i	0.853061	+	1.76407i
$135$	0.169059	−	0.206000i	0.0145503	−	0.0177296i
$136$	−6.08090	−	10.7002i	−0.521432	−	0.917538i
$137$	7.25966	+	0.715014i	0.620234	+	0.0610877i	0.403254	−	0.915088i	$-0.367879\pi$
$137$	7.25966	+	0.715014i	0.620234	+	0.0610877i	0.216981	+	0.976176i	$0.430379\pi$
$138$	0.445883	−	11.0166i	0.0379561	−	0.937794i
$139$	3.83707	+	8.11281i	0.325456	+	0.688120i	0.998682	−	0.0513171i	$-0.0163419\pi$
$139$	3.83707	+	8.11281i	0.325456	+	0.688120i	−0.673226	+	0.739437i	$0.735092\pi$
$140$	−0.00245202	−	0.00393518i	−0.000207233	−	0.000332584i
$141$	1.29521	+	2.16093i	0.109077	+	0.181983i
$142$	1.40337	−	0.955335i	0.117768	−	0.0801699i
$143$	−2.78013	+	4.16076i	−0.232486	+	0.347940i
$144$	−3.78538	+	1.29264i	−0.315448	+	0.107720i
$145$	−0.735008	−	1.10002i	−0.0610391	−	0.0913514i
$146$	2.81868	−	6.97464i	0.233275	−	0.577225i
$147$	5.62239	+	4.16985i	0.463727	+	0.343923i
$148$	5.72220	+	5.00904i	0.470362	+	0.411741i
$149$	0.515543	+	10.4941i	0.0422349	+	0.859712i	0.922681	+	0.385565i	$0.125993\pi$
$149$	0.515543	+	10.4941i	0.0422349	+	0.859712i	−0.880446	+	0.474147i	$0.842757\pi$
$150$	1.08231	+	6.88610i	0.0883703	+	0.562248i
$151$	3.69921	+	12.1947i	0.301037	+	0.992387i	0.968765	+	0.247981i	$0.0797671\pi$
$151$	3.69921	+	12.1947i	0.301037	+	0.992387i	−0.667728	+	0.744406i	$0.732733\pi$
$152$	−18.0776	−	15.5509i	−1.46629	−	1.26135i
$153$	−2.05120	−	3.83753i	−0.165830	−	0.310246i
$154$	0.0280882	−	0.00729408i	0.00226341	−	0.000587773i
$155$	0.502707	−	0.372833i	0.0403784	−	0.0299467i
$156$	−2.74792	−	3.23284i	−0.220010	−	0.258835i
$157$	−2.68654	−	7.50836i	−0.214409	−	0.599233i	0.785396	−	0.618994i	$-0.212459\pi$
$157$	−2.68654	−	7.50836i	−0.214409	−	0.599233i	−0.999805	+	0.0197611i	$0.993709\pi$
$158$	−8.77977	+	7.33316i	−0.698481	+	0.583395i
$159$	−9.45927	+	3.91816i	−0.750169	+	0.310730i
$160$	−0.585113	+	1.38931i	−0.0462573	+	0.109835i
$161$	−0.0626602	−	0.0259547i	−0.00493831	−	0.00204552i
$162$	−1.34972	+	0.422196i	−0.106044	+	0.0331708i
$163$	−5.98258	−	2.82955i	−0.468592	−	0.221628i	0.178649	−	0.983913i	$-0.442827\pi$
$163$	−5.98258	−	2.82955i	−0.468592	−	0.221628i	−0.647241	+	0.762285i	$0.724077\pi$
$164$	−8.40357	+	4.68017i	−0.656209	+	0.365460i
$165$	0.621793	+	0.0922343i	0.0484066	+	0.00718043i
$166$	11.5894	+	15.3476i	0.899509	+	1.19121i
$167$	−17.2100	−	5.22060i	−1.33175	−	0.403982i	−0.457394	−	0.889264i	$-0.651217\pi$
$167$	−17.2100	−	5.22060i	−1.33175	−	0.403982i	−0.874358	+	0.485282i	$0.838717\pi$
$168$	−0.000570316		0.0245990i	−4.40008e−5		0.00189785i
$169$	−4.00660	+	7.49582i	−0.308200	+	0.576601i
$170$	−1.59414	−	0.384712i	−0.122265	−	0.0295060i
$171$	−6.24684	−	5.66180i	−0.477708	−	0.432969i
$172$	4.19466	+	15.5980i	0.319840	+	1.18933i
$173$	−1.45295	−	9.79498i	−0.110466	−	0.744699i	−0.971653	−	0.236411i	$-0.924029\pi$
$173$	−1.45295	−	9.79498i	−0.110466	−	0.744699i	0.861187	−	0.508288i	$-0.169721\pi$
$174$	0.0606285	+	7.02054i	0.00459624	+	0.532226i
$175$	0.0420552	+	0.00836530i	0.00317908	+	0.000632357i
$176$	−7.20569	−	6.09108i	−0.543149	−	0.459132i
$177$	9.89732	−	1.96870i	0.743928	−	0.147977i
$178$	−19.2899	+	4.01047i	−1.44584	+	0.300597i
$179$	11.0591	+	2.77016i	0.826595	+	0.207051i	0.633120	−	0.774054i	$-0.281774\pi$
$179$	11.0591	+	2.77016i	0.826595	+	0.207051i	0.193475	+	0.981105i	$0.438024\pi$
$180$	−0.219523	+	0.485672i	−0.0163623	+	0.0361999i
$181$	−0.873662	+	2.44172i	−0.0649388	+	0.181492i	−0.969630	−	0.244576i	$-0.921351\pi$
$181$	−0.873662	+	2.44172i	−0.0649388	+	0.181492i	0.904691	+	0.426067i	$0.140101\pi$
$182$	−0.0244973	+	0.00900466i	−0.00181586	+	0.000667470i
$183$	−10.5873	+	8.68877i	−0.782636	+	0.642292i
$184$	4.86078	+	21.5088i	0.358341	+	1.58565i
$185$	1.00843	−	0.0993219i	0.0741414	−	0.00730229i
$186$	−3.31587	+	0.191615i	−0.243131	+	0.0140499i
$187$	5.27671	−	8.80366i	0.385871	−	0.643787i
$188$	−3.62392	−	3.50085i	−0.264302	−	0.255326i
$189$	−0.000426859		0.00868891i	−3.10494e−5		0.000632025i
$190$	−3.15925	+	0.338730i	−0.229196	+	0.0245741i
$191$	−11.4614	−	11.4614i	−0.829318	−	0.829318i	0.158104	−	0.987422i	$-0.449462\pi$
$191$	−11.4614	−	11.4614i	−0.829318	−	0.829318i	−0.987422	+	0.158104i	$0.949462\pi$
$192$	6.63961	−	4.46268i	0.479173	−	0.322066i
$193$	13.2928	−	13.2928i	0.956840	−	0.956840i	−0.0422667	−	0.999106i	$-0.513458\pi$
$193$	13.2928	−	13.2928i	0.956840	−	0.956840i	0.999106	+	0.0422667i	$0.0134579\pi$
$194$	2.17175	−	2.69338i	0.155922	−	0.193373i
$195$	−0.564666	−	0.0277403i	−0.0404366	−	0.00198652i
$196$	−13.0248	−	5.13333i	−0.930341	−	0.366667i
$197$	9.86695	+	5.91402i	0.702991	+	0.421357i	0.820448	−	0.571721i	$-0.193724\pi$
$197$	9.86695	+	5.91402i	0.702991	+	0.421357i	−0.117457	+	0.993078i	$0.537474\pi$
$198$	−2.49095	−	2.21879i	−0.177024	−	0.157683i
$199$	−1.96135	−	19.9139i	−0.139037	−	1.41166i	−0.771085	−	0.636733i	$-0.780286\pi$
$199$	−1.96135	−	19.9139i	−0.139037	−	1.41166i	0.632048	−	0.774929i	$-0.282214\pi$
$200$	−5.66695	−	12.7375i	−0.400714	−	0.900679i
$201$	−10.1752	−	12.3985i	−0.717702	−	0.874522i
$202$	−9.15570	+	19.7987i	−0.644193	+	1.39303i
$203$	0.0406632	+	0.0145495i	0.00285399	+	0.00102118i
$204$	5.95484	+	6.34635i	0.416922	+	0.444333i
$205$	−0.311422	+	1.24327i	−0.0217506	+	0.0868334i
$206$	13.6552	+	8.95450i	0.951401	+	0.623890i
$207$	1.52098	+	7.64648i	0.105715	+	0.531467i
$208$	6.98640	+	4.81660i	0.484419	+	0.333971i
$209$	3.87970	−	19.5046i	0.268364	−	1.34916i
$210$	0.00233823	+	0.00229819i	0.000161353	+	0.000158590i
$211$	8.36848	−	1.24135i	0.576110	−	0.0854578i	0.147684	−	0.989035i	$-0.452818\pi$
$211$	8.36848	−	1.24135i	0.576110	−	0.0854578i	0.428426	+	0.903577i	$0.359068\pi$
$212$	16.2344	−	12.4805i	1.11498	−	0.857167i
$213$	−0.806167	+	0.889468i	−0.0552377	+	0.0609454i
$214$	−11.3484	−	18.5681i	−0.775760	−	1.26929i
$215$	1.89806	+	1.01454i	0.129447	+	0.0691908i
$216$	2.38754	−	1.51646i	0.162452	−	0.103182i
$217$	−0.00593088	+	0.0195515i	−0.000402614	+	0.00132724i
$218$	26.1904	+	3.65413i	1.77384	+	0.247489i
$219$	−0.780508	+	5.26176i	−0.0527418	+	0.355557i
$220$	−1.24883	+	0.144816i	−0.0841958	+	0.00976349i
$221$	−3.94683	+	8.34487i	−0.265492	+	0.561337i
$222$	−4.76421	−	2.49387i	−0.319753	−	0.167377i
$223$	2.14745	−	5.18439i	0.143804	−	0.347173i	−0.835524	−	0.549454i	$-0.814836\pi$
$223$	2.14745	−	5.18439i	0.143804	−	0.347173i	0.979327	+	0.202282i	$0.0648357\pi$
$224$	−0.0116751	−	0.0478062i	−0.000780072	−	0.00319419i
$225$	−1.88624	−	4.55379i	−0.125749	−	0.303586i
$226$	−1.00244	+	11.1656i	−0.0666810	+	0.742722i
$227$	3.44755	−	1.23355i	0.228822	−	0.0818738i	−0.219982	−	0.975504i	$-0.570600\pi$
$227$	3.44755	−	1.23355i	0.228822	−	0.0818738i	0.448804	+	0.893630i	$0.351850\pi$
$228$	15.0057	+	7.69053i	0.993779	+	0.509318i
$229$	7.25048	+	9.77614i	0.479125	+	0.646025i	0.974957	−	0.222393i	$-0.0713868\pi$
$229$	7.25048	+	9.77614i	0.479125	+	0.646025i	−0.495832	+	0.868418i	$0.665137\pi$
$230$	2.53314	+	1.48872i	0.167030	+	0.0981636i
$231$	−0.0180971	+	0.00967312i	−0.00119070	+	0.000636445i
$232$	−3.76352	−	13.5278i	−0.247087	−	0.888147i
$233$	0.124903	−	0.0378890i	0.00818269	−	0.00248219i	−0.286191	−	0.958173i	$-0.592389\pi$
$233$	0.124903	−	0.0378890i	0.00818269	−	0.00248219i	0.294373	+	0.955690i	$0.404889\pi$
$234$	2.42512	+	1.76634i	0.158535	+	0.115469i
$235$	−0.670577	+	0.0329433i	−0.0437436	+	0.00214899i
$236$	−18.0930	+	8.94292i	−1.17775	+	0.582134i
$237$	4.81853	−	6.49704i	0.312997	−	0.422028i
$238$	0.0492797	−	0.0209127i	0.00319433	−	0.00135557i
$239$	2.73602	−	1.82815i	0.176979	−	0.118253i	−0.463926	−	0.885874i	$-0.653560\pi$
$239$	2.73602	−	1.82815i	0.176979	−	0.118253i	0.640904	+	0.767621i	$0.278560\pi$
$240$	0.171728	−	1.05204i	0.0110850	−	0.0679087i
$241$	−1.39188	−	0.930027i	−0.0896591	−	0.0599083i	0.509933	−	0.860214i	$-0.329670\pi$
$241$	−1.39188	−	0.930027i	−0.0896591	−	0.0599083i	−0.599592	+	0.800306i	$0.704670\pi$
$242$	−1.43464	+	7.55270i	−0.0922219	+	0.485506i
$243$	0.857729	−	0.514103i	0.0550233	−	0.0329797i
$244$	15.9352	−	22.2803i	1.02015	−	1.42635i
$245$	−1.68631	+	0.797566i	−0.107734	+	0.0509546i
$246$	5.00003	−	4.61104i	0.318790	−	0.293989i
$247$	−1.75310	+	17.7995i	−0.111547	+	1.13256i
$248$	6.30468	−	2.09232i	0.400348	−	0.132863i
$249$	−10.5121	−	8.62709i	−0.666180	−	0.546720i
$250$	−3.53399	−	1.23016i	−0.223509	−	0.0778022i
$251$	3.11417	+	12.4325i	0.196565	+	0.784731i	0.985418	+	0.170150i	$0.0544251\pi$
$251$	3.11417	+	12.4325i	0.196565	+	0.784731i	−0.788853	+	0.614581i	$0.789325\pi$
$252$	−0.00368854	−	0.0170033i	−0.000232356	−	0.00107111i
$253$	−13.6260	+	12.3499i	−0.856660	+	0.776431i
$254$	10.8827	+	19.9439i	0.682841	+	1.25139i
$255$	1.15959			0.0726161
$256$	−10.5057	+	12.0677i	−0.656608	+	0.754232i
$257$	−10.9234			−0.681381			−0.340691	−	0.940176i	$-0.610661\pi$
$257$	−10.9234			−0.681381			−0.340691	+	0.940176i	$0.610661\pi$
$258$	−5.47074	−	10.0258i	−0.340593	−	0.624180i
$259$	−0.0245098	+	0.0222144i	−0.00152297	+	0.00138034i
$260$	1.10499	−	0.239707i	0.0685288	−	0.0148660i
$261$	−1.20627	−	4.81568i	−0.0746659	−	0.298083i
$262$	−0.362243	−	0.126095i	−0.0223795	−	0.00779017i
$263$	−6.51856	−	5.34964i	−0.401952	−	0.329873i	0.411601	−	0.911364i	$-0.364970\pi$
$263$	−6.51856	−	5.34964i	−0.401952	−	0.329873i	−0.813553	+	0.581491i	$0.802470\pi$
$264$	5.96341	+	2.99154i	0.367022	+	0.184117i
$265$	0.267439	−	2.71536i	0.0164287	−	0.166803i
$266$	0.0762492	−	0.0703171i	0.00467514	−	0.00431142i
$267$	12.5941	−	5.95656i	0.770745	−	0.364535i
$268$	26.0918	+	18.6613i	1.59381	+	1.13992i
$269$	21.1165	−	12.6568i	1.28750	−	0.771697i	0.304010	−	0.952669i	$-0.401674\pi$
$269$	21.1165	−	12.6568i	1.28750	−	0.771697i	0.983488	+	0.180972i	$0.0579244\pi$
$270$	0.0703297	−	0.370253i	0.00428013	−	0.0225329i
$271$	14.2888	+	9.54749i	0.867985	+	0.579969i	0.907878	−	0.419235i	$-0.137702\pi$
$271$	14.2888	+	9.54749i	0.867985	+	0.579969i	−0.0398931	+	0.999204i	$0.512702\pi$
$272$	−14.7973	−	9.16430i	−0.897219	−	0.555668i
$273$	0.0153451	−	0.0102533i	0.000928727	−	0.000620556i
$274$	9.49665	−	4.03007i	0.573713	−	0.243465i
$275$	6.92589	−	9.33849i	0.417647	−	0.563132i
$276$	−6.90912	−	13.9783i	−0.415880	−	0.841393i
$277$	5.08949	−	0.250031i	0.305798	−	0.0150229i	0.104410	−	0.994534i	$-0.466705\pi$
$277$	5.08949	−	0.250031i	0.305798	−	0.0150229i	0.201388	+	0.979512i	$0.435455\pi$
$278$	10.2591	+	7.47218i	0.615297	+	0.448152i
$279$	2.24746	−	0.681758i	0.134552	−	0.0408158i
$280$	−0.00570968	−	0.00322422i	−0.000341219	−	0.000192684i
$281$	−4.17408	+	2.23109i	−0.249005	+	0.133096i	−0.591178	−	0.806541i	$-0.701337\pi$
$281$	−4.17408	+	2.23109i	−0.249005	+	0.133096i	0.342173	+	0.939637i	$0.388837\pi$
$282$	3.07172	+	1.80525i	0.182918	+	0.107501i
$283$	−2.96630	−	3.99959i	−0.176328	−	0.237751i	0.706198	−	0.708015i	$-0.250409\pi$
$283$	−2.96630	−	3.99959i	−0.176328	−	0.237751i	−0.882526	+	0.470263i	$0.844159\pi$
$284$	1.09503	−	2.13662i	0.0649781	−	0.126785i
$285$	2.11540	−	0.756902i	0.125305	−	0.0448350i
$286$	−0.632810	+	7.04851i	−0.0374188	+	0.416787i
$287$	−0.0160113	−	0.0386546i	−0.000945115	−	0.00228171i
$288$	−3.82361	+	4.16893i	−0.225309	+	0.245657i
$289$	0.740131	−	1.78683i	0.0435371	−	0.105108i
$290$	−1.65761	−	0.867689i	−0.0973380	−	0.0509525i
$291$	−1.04602	+	2.21162i	−0.0613186	+	0.129647i
$292$	−1.22547	−	10.5678i	−0.0717149	−	0.618436i
$293$	3.72689	−	25.1246i	0.217727	−	1.46780i	−0.554359	−	0.832278i	$-0.687036\pi$
$293$	3.72689	−	25.1246i	0.217727	−	1.46780i	0.772086	−	0.635518i	$-0.219214\pi$
$294$	9.80442	+	1.36793i	0.571805	+	0.0797791i
$295$	−0.780637	+	2.57341i	−0.0454504	+	0.149830i
$296$	10.4968	+	2.34211i	0.610114	+	0.136132i
$297$	2.08028	+	1.11193i	0.120710	+	0.0645208i
$298$	7.74874	+	12.6784i	0.448872	+	0.734440i
$299$	11.1072	−	12.2550i	0.642348	−	0.708722i
$300$	6.00826	+	7.81539i	0.346887	+	0.451222i
$301$	−0.0694964	+	0.0103088i	−0.00400571	+	0.000594191i
$302$	12.8529	+	12.6329i	0.739604	+	0.726939i
$303$	3.00912	−	15.1279i	0.172869	−	0.869073i
$304$	−32.9762	−	7.05946i	−1.89131	−	0.404888i
$305$	−0.712060	−	3.57977i	−0.0407724	−	0.204977i
$306$	−5.14595	−	3.37450i	−0.294175	−	0.192908i
$307$	−7.71716	+	30.8086i	−0.440442	+	1.75834i	0.189681	+	0.981846i	$0.439255\pi$
$307$	−7.71716	+	30.8086i	−0.440442	+	1.75834i	−0.630123	+	0.776496i	$0.716995\pi$
$308$	0.0299283	−	0.0280820i	0.00170532	−	0.00160012i
$309$	−10.8716	−	3.88993i	−0.618465	−	0.221290i
$310$	0.371514	−	0.803378i	0.0211006	−	0.0456288i
$311$	−18.2381	−	22.2232i	−1.03419	−	1.26016i	−0.964915	−	0.262563i	$-0.915432\pi$
$311$	−18.2381	−	22.2232i	−1.03419	−	1.26016i	−0.0692728	−	0.997598i	$-0.522068\pi$
$312$	−5.60126	−	2.15188i	−0.317109	−	0.121826i
$313$	−1.45044	−	14.7265i	−0.0819836	−	0.832394i	−0.944968	−	0.327163i	$-0.893907\pi$
$313$	−1.45044	−	14.7265i	−0.0819836	−	0.832394i	0.862984	−	0.505231i	$-0.168593\pi$
$314$	−8.42130	−	7.50118i	−0.475241	−	0.423316i
$315$	−0.00198847	−	0.00119184i	−0.000112038	−	6.71528e-5i
$316$	−5.93190	+	15.0510i	−0.333695	+	0.846683i
$317$	7.64506	+	0.375578i	0.429389	+	0.0210945i	0.262615	−	0.964901i	$-0.415415\pi$
$317$	7.64506	+	0.375578i	0.429389	+	0.0210945i	0.166774	+	0.985995i	$0.446665\pi$
$318$	−9.08877	+	11.2718i	−0.509673	+	0.632091i
$319$	8.28034	−	8.28034i	0.463610	−	0.463610i
$320$	0.214749	+	2.12108i	0.0120048	+	0.118572i
$321$	10.8807	+	10.8807i	0.607303	+	0.607303i
$322$	−0.0953694	+	0.0102254i	−0.00531473	+	0.000569837i
$323$	1.80006	−	36.6412i	0.100158	−	2.03877i
$324$	−1.38958	+	1.43843i	−0.0771988	+	0.0799126i
$325$	−5.37578	+	8.96895i	−0.298195	+	0.497508i
$326$	−9.34365	+	0.539944i	−0.517497	+	0.0299047i
$327$	−18.6088	+	1.83280i	−1.02907	+	0.101354i
$328$	−7.26202	+	11.5027i	−0.400978	+	0.635128i
$329$	0.0169420	−	0.0139040i	0.000934043	−	0.000766550i
$330$	0.834388	−	0.306702i	0.0459315	−	0.0168834i
$331$	11.5189	−	32.1930i	0.633134	−	1.76949i	−0.00550728	−	0.999985i	$-0.501753\pi$
$331$	11.5189	−	32.1930i	0.633134	−	1.76949i	0.638641	−	0.769505i	$-0.279497\pi$
$332$	24.7838	+	11.2023i	1.36019	+	0.614804i
$333$	3.68848	+	0.923916i	0.202128	+	0.0506303i
$334$	−24.9013	+	5.17712i	−1.36254	+	0.283279i
$335$	4.19216	−	0.833873i	0.229042	−	0.0455594i
$336$	0.0159554	+	0.0309240i	0.000870437	+	0.00168704i
$337$	31.8911	+	6.34354i	1.73722	+	0.345555i	0.959209	−	0.282697i	$-0.0912290\pi$
$337$	31.8911	+	6.34354i	1.73722	+	0.345555i	0.778010	+	0.628251i	$0.216229\pi$
$338$	0.103799	+	12.0195i	0.00564594	+	0.653777i
$339$	−1.16313	−	7.84121i	−0.0631727	−	0.425876i
$340$	−2.23960	+	0.602281i	−0.121459	+	0.0326633i
$341$	4.10476	+	3.72033i	0.222285	+	0.201467i
$342$	−11.5903	−	2.79707i	−0.626730	−	0.151248i
$343$	0.0574118	−	0.107410i	0.00309994	−	0.00579959i
$344$	15.7734	+	16.5222i	0.850446	+	0.890816i
$345$	−1.98817	−	0.603105i	−0.107039	−	0.0324701i
$346$	−8.43886	−	11.1755i	−0.453676	−	0.600797i
$347$	−25.7484	−	3.81942i	−1.38225	−	0.205037i	−0.586149	−	0.810203i	$-0.699357\pi$
$347$	−25.7484	−	3.81942i	−1.38225	−	0.205037i	−0.796099	+	0.605166i	$0.793107\pi$
$348$	4.83099	+	8.67438i	0.258968	+	0.464996i
$349$	−10.2404	−	4.84337i	−0.548159	−	0.259260i	0.133351	−	0.991069i	$-0.457426\pi$
$349$	−10.2404	−	4.84337i	−0.548159	−	0.259260i	−0.681510	+	0.731809i	$0.738676\pi$
$350$	0.0578749	−	0.0181034i	0.00309354	−	0.000967667i
$351$	−1.95997	−	0.811847i	−0.104616	−	0.0433332i
$352$	−13.0714	−	2.68045i	−0.696708	−	0.142869i
$353$	−6.83664	+	2.83183i	−0.363877	+	0.150723i	−0.557128	−	0.830426i	$-0.688097\pi$
$353$	−6.83664	+	2.83183i	−0.363877	+	0.150723i	0.193251	+	0.981149i	$0.438097\pi$
$354$	10.9532	−	9.14845i	0.582153	−	0.486234i
$355$	−0.107773	−	0.301205i	−0.00571999	−	0.0159863i
$356$	−21.2302	+	18.0457i	−1.12520	+	0.956418i
$357$	−0.0304045	+	0.0225495i	−0.00160918	+	0.00119345i
$358$	15.6055	−	4.05251i	0.824777	−	0.214182i
$359$	−3.46787	−	6.48792i	−0.183027	−	0.342419i	0.773629	−	0.633638i	$-0.218439\pi$
$359$	−3.46787	−	6.48792i	−0.183027	−	0.342419i	−0.956656	+	0.291219i	$0.905939\pi$
$360$	0.0564739	+	0.751629i	0.00297643	+	0.0396143i
$361$	−15.1177	−	49.8365i	−0.795671	−	2.62297i
$362$	0.569443	+	3.62303i	0.0299293	+	0.190422i
$363$	−0.266735	−	5.42951i	−0.0139999	−	0.284975i
$364$	−0.0243117	+	0.0277731i	−0.00127428	+	0.00145571i
$365$	−1.13859	−	0.844433i	−0.0595963	−	0.0441996i
$366$	−7.25752	+	17.9583i	−0.379356	+	0.938694i
$367$	8.22162	+	12.3045i	0.429165	+	0.642291i	0.981529	−	0.191312i	$-0.0612742\pi$
$367$	8.22162	+	12.3045i	0.429165	+	0.642291i	−0.552364	+	0.833603i	$0.686274\pi$
$368$	20.6044	+	23.4088i	1.07408	+	1.22027i
$369$	−2.67200	+	3.99893i	−0.139099	+	0.208176i
$370$	1.18461	−	0.806413i	0.0615848	−	0.0419234i
$371$	0.0457911	+	0.0763978i	0.00237735	+	0.00396637i
$372$	−3.98659	+	2.48405i	−0.206695	+	0.128792i
$373$	7.87536	+	16.6511i	0.407771	+	0.862159i	0.998472	+	0.0552683i	$0.0176014\pi$
$373$	7.87536	+	16.6511i	0.407771	+	0.862159i	−0.590701	+	0.806891i	$0.701149\pi$
$374$	0.587012	−	14.5035i	0.0303537	−	0.749958i
$375$	2.63323	+	0.259351i	0.135980	+	0.0133928i
$376$	−6.87030	−	1.89119i	−0.354309	−	0.0975306i
$377$	−6.68136	+	8.14126i	−0.344108	+	0.419296i
$378$	0.00535597	+	0.0110758i	0.000275481	+	0.000569675i
$379$	−10.4625	+	2.62073i	−0.537424	+	0.134618i	−0.502183	−	0.864761i	$-0.667470\pi$
$379$	−10.4625	+	2.62073i	−0.537424	+	0.134618i	−0.0352406	+	0.999379i	$0.511220\pi$
$380$	−3.69251	+	2.56059i	−0.189422	+	0.131356i
$381$	−10.7888	−	11.9036i	−0.552729	−	0.609842i
$382$	−21.9924	−	6.46446i	−1.12523	−	0.330751i
$383$		−	0.529705i		−	0.0270667i	−0.999908	−	0.0135333i	$-0.995692\pi$
$383$		−	0.529705i		−	0.0270667i	0.999908	−	0.0135333i	$-0.00430793\pi$
$384$	5.21953	−	10.0378i	0.266358	−	0.512237i
$385$		−	0.00546841i		−	0.000278696i
$386$	7.49743	−	25.5066i	0.381609	−	1.29825i
$387$	5.42356	+	5.98397i	0.275695	+	0.304182i
$388$	0.871556	−	4.81477i	0.0442466	−	0.244433i
$389$	−35.5487	+	8.90448i	−1.80239	+	0.451475i	−0.991094	−	0.133161i	$-0.957487\pi$
$389$	−35.5487	+	8.90448i	−1.80239	+	0.451475i	−0.811295	+	0.584637i	$0.801237\pi$
$390$	−0.719780	+	0.348068i	−0.0364475	+	0.0176251i
$391$	−21.5213	+	26.2238i	−1.08838	+	1.32619i
$392$	−19.6466	+	2.45037i	−0.992301	+	0.123762i
$393$	0.269914	+	0.0265842i	0.0136153	+	0.00134099i
$394$	16.2552	+	0.657910i	0.818925	+	0.0331450i
$395$	0.921639	+	1.94864i	0.0463727	+	0.0980468i
$396$	−4.59534	−	1.06708i	−0.230924	−	0.0536228i
$397$	−4.98982	−	8.32501i	−0.250432	−	0.417820i	0.706683	−	0.707531i	$-0.250191\pi$
$397$	−4.98982	−	8.32501i	−0.250432	−	0.417820i	−0.957114	+	0.289711i	$0.906441\pi$
$398$	−15.9246	−	23.3930i	−0.798228	−	1.17258i
$399$	−0.0407473	+	0.0609826i	−0.00203991	+	0.00305295i
$400$	−15.6635	−	11.9738i	−0.783175	−	0.598692i
$401$	12.5909	+	18.8436i	0.628761	+	0.941007i	0.999923	+	0.0124385i	$0.00395941\pi$
$401$	12.5909	+	18.8436i	0.628761	+	0.941007i	−0.371162	+	0.928568i	$0.621041\pi$
$402$	−21.0304	−	8.49907i	−1.04890	−	0.423895i
$403$	−4.00192	−	2.96803i	−0.199350	−	0.147848i
$404$	2.04556	+	30.7806i	0.101771	+	1.53139i
$405$	0.0130760	+	0.266169i	0.000649754	+	0.0132260i
$406$	0.0603360	−	0.00948320i	0.00299442	−	0.000470643i
$407$	2.60362	+	8.58298i	0.129057	+	0.425442i
$408$	11.6915	+	3.84468i	0.578815	+	0.190340i
$409$	−8.55141	−	15.9986i	−0.422840	−	0.791078i	0.576827	−	0.816866i	$-0.304291\pi$
$409$	−8.55141	−	15.9986i	−0.422840	−	0.791078i	−0.999667	+	0.0257879i	$0.991791\pi$
$410$	0.455584	+	1.75437i	0.0224997	+	0.0866424i
$411$	−5.85922	+	4.34550i	−0.289014	+	0.214348i
$412$	23.0176	+	1.86628i	1.13400	+	0.0919450i
$413$	−0.0295747	−	0.0826558i	−0.00145528	−	0.00406722i
$414$	7.06791	+	8.46219i	0.347369	+	0.415894i
$415$	3.34813	−	1.38684i	0.164353	−	0.0680773i
$416$	11.9358	+	1.24683i	0.585202	+	0.0611310i
$417$	−8.29132	−	3.43438i	−0.406027	−	0.168182i
$418$	−8.39607	−	26.8415i	−0.410665	−	1.31286i
$419$	30.7024	+	14.5211i	1.49991	+	0.709404i	0.988680	−	0.150041i	$-0.0479406\pi$
$419$	30.7024	+	14.5211i	1.49991	+	0.709404i	0.511229	+	0.859445i	$0.329191\pi$
$420$	0.00445953	+	0.00126910i	0.000217603	+	6.19260e-5i
$421$	−0.845810	−	0.125464i	−0.0412223	−	0.00611474i	0.126087	−	0.992019i	$-0.459758\pi$
$421$	−0.845810	−	0.125464i	−0.0412223	−	0.00611474i	−0.167310	+	0.985904i	$0.553508\pi$
$422$	9.54792	−	7.20985i	0.464786	−	0.350970i
$423$	−2.41088	−	0.731333i	−0.117221	−	0.0355586i
$424$	11.6994	−	26.4908i	0.568172	−	1.28651i
$425$	10.1103	−	18.9151i	0.490423	−	0.917518i
$426$	−0.398266	+	1.65030i	−0.0192961	+	0.0799575i
$427$	0.0882832	+	0.0800152i	0.00427232	+	0.00387221i
$428$	−26.6662	−	15.3634i	−1.28896	−	0.742620i
$429$	−0.734254	−	4.94994i	−0.0354501	−	0.238985i
$430$	3.04355	−	0.0262837i	0.146773	−	0.00126751i
$431$	10.0791	+	2.00485i	0.485492	+	0.0965704i	0.431767	−	0.901985i	$-0.357890\pi$
$431$	10.0791	+	2.00485i	0.485492	+	0.0965704i	0.0537256	+	0.998556i	$0.482890\pi$
$432$	1.93669	−	3.49989i	0.0931793	−	0.168388i
$433$	−7.29381	+	1.45083i	−0.350518	+	0.0697224i	−0.367209	−	0.930138i	$-0.619687\pi$
$433$	−7.29381	+	1.45083i	−0.350518	+	0.0697224i	0.0166914	+	0.999861i	$0.494687\pi$
$434$	0.00588148	+	0.0282892i	0.000282320	+	0.00135793i
$435$	1.28333	+	0.321458i	0.0615310	+	0.0154127i
$436$	34.9887	−	13.2051i	1.67565	−	0.632411i
$437$	−22.1435	+	61.8869i	−1.05927	+	2.96045i
$438$	2.59538	+	7.06078i	0.124012	+	0.337377i
$439$	−17.2381	+	14.1469i	−0.822728	+	0.675196i	−0.948470	−	0.316867i	$-0.897369\pi$
$439$	−17.2381	+	14.1469i	−0.822728	+	0.675196i	0.125742	+	0.992063i	$0.459869\pi$
$440$	−1.45222	+	1.02573i	−0.0692319	+	0.0488999i
$441$	−6.96622	+	0.686113i	−0.331725	+	0.0326720i
$442$	0.753146	+	13.0331i	0.0358235	+	0.619921i
$443$	7.24127	−	12.0813i	0.344043	−	0.574001i	−0.636266	−	0.771470i	$-0.719522\pi$
$443$	7.24127	−	12.0813i	0.344043	−	0.574001i	0.980309	+	0.197468i	$0.0632720\pi$
$444$	−7.60374	+	0.131340i	−0.360857	+	0.00623310i
$445$	−0.182171	+	3.70818i	−0.00863574	+	0.175785i
$446$	−0.846029	−	7.89070i	−0.0400606	−	0.373635i
$447$	−7.42941	−	7.42941i	−0.351399	−	0.351399i
$448$	−0.0468776	−	0.0514389i	−0.00221476	−	0.00243026i
$449$	−11.3902	+	11.3902i	−0.537538	+	0.537538i	−0.922805	−	0.385267i	$-0.874109\pi$
$449$	−11.3902	+	11.3902i	−0.537538	+	0.537538i	0.385267	+	0.922805i	$0.374109\pi$
$450$	−5.42636	−	4.37543i	−0.255801	−	0.206260i
$451$	−11.3309	−	0.556652i	−0.533552	−	0.0262117i
$452$	6.31912	+	14.5402i	0.297227	+	0.683915i
$453$	−10.9304	−	6.55140i	−0.513553	−	0.307812i
$454$	3.44425	−	3.86674i	0.161647	−	0.181475i
$455$	0.000482066		0.00489449i	2.25996e−5		0.000229457i
$456$	23.8380	−	0.617709i	1.11632	−	0.0289269i
$457$	6.21305	+	7.57062i	0.290634	+	0.354139i	0.897774	−	0.440456i	$-0.145183\pi$
$457$	6.21305	+	7.57062i	0.290634	+	0.354139i	−0.607140	+	0.794595i	$0.707683\pi$
$458$	15.6233	+	7.22483i	0.730027	+	0.337594i
$459$	4.09697	+	1.46592i	0.191230	+	0.0684232i
$460$	4.15316	+	0.132182i	0.193642	+	0.00616301i
$461$	−0.763444	+	3.04784i	−0.0355571	+	0.141952i	−0.985210	−	0.171353i	$-0.945186\pi$
$461$	−0.763444	+	3.04784i	−0.0355571	+	0.141952i	0.949653	+	0.313305i	$0.101436\pi$
$462$	−0.0159136	+	0.0242674i	−0.000740367	+	0.00112902i
$463$	−6.24916	−	31.4167i	−0.290423	−	1.46006i	−0.800192	−	0.599744i	$-0.795269\pi$
$463$	−6.24916	−	31.4167i	−0.290423	−	1.46006i	0.509769	−	0.860312i	$-0.329731\pi$
$464$	−13.8359	−	14.2443i	−0.642316	−	0.661277i
$465$	−0.122102	+	0.613849i	−0.00566235	+	0.0284666i
$466$	0.129392	−	0.131646i	0.00599395	−	0.00609838i
$467$	19.7248	−	2.92590i	0.912754	−	0.135394i	0.326197	−	0.945302i	$-0.394233\pi$
$467$	19.7248	−	2.92590i	0.912754	−	0.135394i	0.586558	+	0.809908i	$0.300483\pi$
$468$	4.20712	+	0.549988i	0.194474	+	0.0254232i
$469$	−0.0937036	+	0.103386i	−0.00432683	+	0.00477392i
$470$	−0.810153	+	0.495146i	−0.0373696	+	0.0228394i
$471$	7.03290	+	3.75916i	0.324059	+	0.173213i
$472$	−16.4031	+	23.3581i	−0.755012	+	1.07515i
$473$	−5.52988	+	18.2296i	−0.254264	+	0.838196i
$474$	1.58073	−	11.3296i	0.0726052	−	0.520388i
$475$	6.09745	−	41.1057i	0.279770	−	1.88606i
$476$	0.0470106	−	0.0593436i	0.00215473	−	0.00272001i
$477$	4.37758	−	9.25562i	0.200436	−	0.423786i
$478$	2.15816	−	4.12289i	0.0987121	−	0.188577i
$479$	3.11272	−	7.51476i	0.142224	−	0.343358i	−0.836677	−	0.547697i	$-0.815505\pi$
$479$	3.11272	−	7.51476i	0.142224	−	0.343358i	0.978900	+	0.204339i	$0.0655045\pi$
$480$	−0.499464	−	1.42235i	−0.0227973	−	0.0649211i
$481$	−3.08700	−	7.45267i	−0.140755	−	0.339812i
$482$	−2.35792	−	0.211692i	−0.107400	−	0.00964229i
$483$	0.0638582	−	0.0228488i	0.00290565	−	0.00103966i
$484$	3.33522	+	10.3479i	0.151601	+	0.470359i
$485$	−0.388378	−	0.523667i	−0.0176353	−	0.0237785i
$486$	0.716549	−	1.21924i	0.0325033	−	0.0553061i
$487$	3.58654	−	1.91705i	0.162522	−	0.0868696i	−0.388131	−	0.921604i	$-0.626879\pi$
$487$	3.58654	−	1.91705i	0.162522	−	0.0868696i	0.550652	+	0.834735i	$0.314379\pi$
$488$	4.68961	−	38.4538i	0.212289	−	1.74072i
$489$	6.33301	−	1.92110i	0.286389	−	0.0868750i
$490$	−1.55315	+	2.13242i	−0.0701642	+	0.0963331i
$491$	−1.94095	+	0.0953528i	−0.0875939	+	0.00430321i	−0.0928174	−	0.995683i	$-0.529587\pi$
$491$	−1.94095	+	0.0953528i	−0.0875939	+	0.00430321i	0.00522352	+	0.999986i	$0.498337\pi$
$492$	3.08363	−	9.11127i	0.139021	−	0.410768i
$493$	12.8683	−	17.3509i	0.579559	−	0.781444i
$494$	9.88110	+	23.2843i	0.444572	+	1.04761i
$495$	−0.522659	+	0.349230i	−0.0234918	+	0.0156967i
$496$	6.40943	−	6.86826i	0.287792	−	0.308394i
$497$	0.00868312	+	0.00580188i	0.000389491	+	0.000260250i
$498$	−18.8940	−	3.58892i	−0.846660	−	0.160823i
$499$	27.8253	−	16.6778i	1.24563	−	0.746602i	0.269335	−	0.963047i	$-0.413196\pi$
$499$	27.8253	−	16.6778i	1.24563	−	0.746602i	0.976295	+	0.216445i	$0.0694461\pi$
$500$	−5.22048	+	0.866780i	−0.233467	+	0.0387636i
$501$	16.2577	−	7.68933i	0.726342	−	0.343534i
$502$	12.2878	+	13.3244i	0.548430	+	0.594697i
$503$	−1.44581	+	14.6796i	−0.0644656	+	0.654530i	0.907602	+	0.419831i	$0.137911\pi$
$503$	−1.44581	+	14.6796i	−0.0644656	+	0.654530i	−0.972068	+	0.234700i	$0.924589\pi$
$504$	−0.0160971	−	0.0186096i	−0.000717021	−	0.000828939i
$505$	3.17739	+	2.60761i	0.141392	+	0.116037i
$506$	−8.54979	+	24.5617i	−0.380084	+	1.09190i
$507$	−2.06519	−	8.24470i	−0.0917183	−	0.366160i
$508$	27.0200	+	17.3868i	1.19882	+	0.771415i
$509$	21.0693	−	19.0961i	0.933880	−	0.846420i	−0.0544854	−	0.998515i	$-0.517352\pi$
$509$	21.0693	−	19.0961i	0.933880	−	0.846420i	0.988366	+	0.152095i	$0.0486018\pi$
$510$	1.43953	−	0.785505i	0.0637437	−	0.0347827i
$511$	0.0462749			0.00204708
$512$	−4.86736	+	22.0977i	−0.215109	+	0.976590i
$513$	8.43084			0.372231
$514$	−13.5605	+	7.39950i	−0.598128	+	0.326378i
$515$	2.27994	−	2.06642i	0.100466	−	0.0910573i
$516$	−13.5830	−	8.74037i	−0.597958	−	0.384773i
$517$	−1.44395	−	5.76459i	−0.0635050	−	0.253526i
$518$	−0.0153789	+	0.0441804i	−0.000675712	+	0.00194118i
$519$	7.65447	+	6.28186i	0.335994	+	0.275743i
$520$	1.20939	−	1.04610i	0.0530351	−	0.0458746i
$521$	−2.43692	+	24.7424i	−0.106763	+	1.08399i	0.781266	+	0.624198i	$0.214574\pi$
$521$	−2.43692	+	24.7424i	−0.106763	+	1.08399i	−0.888029	+	0.459787i	$0.847926\pi$
$522$	−4.75963	−	5.16116i	−0.208323	−	0.225898i
$523$	10.0733	−	4.76433i	0.440476	−	0.208330i	−0.194434	−	0.980916i	$-0.562287\pi$
$523$	10.0733	−	4.76433i	0.440476	−	0.208330i	0.634910	+	0.772586i	$0.281037\pi$
$524$	−0.535114	+	0.0888473i	−0.0233765	+	0.00388131i
$525$	−0.0367787	+	0.0220443i	−0.00160515	+	0.000962091i
$526$	−11.7161	−	2.22548i	−0.510848	−	0.0970357i
$527$	8.49718	+	5.67763i	0.370143	+	0.247322i
$528$	9.42958	−	0.325852i	0.410370	−	0.0141809i
$529$	31.4146	−	20.9906i	1.36585	−	0.912634i
$530$	−1.50738	−	3.55207i	−0.0654764	−	0.154292i
$531$	−6.01134	+	8.10535i	−0.260870	+	0.351742i
$532$	0.0470245	−	0.138944i	0.00203877	−	0.00602400i
$533$	10.1908	−	0.500642i	0.441412	−	0.0216852i
$534$	11.5996	−	15.9258i	0.501963	−	0.689179i
$535$	−3.92409	+	1.19036i	−0.169653	+	0.0514637i
$536$	45.0321	+	5.49187i	1.94509	+	0.237213i
$537$	−10.0546	+	5.37428i	−0.433887	+	0.231917i
$538$	17.6408	−	30.0168i	0.760550	−	1.29411i
$539$	−9.83585	−	13.2621i	−0.423660	−	0.571239i
$540$	−0.163501	−	0.507282i	−0.00703598	−	0.0218299i
$541$	−13.3190	+	4.76561i	−0.572628	+	0.204889i	−0.607250	−	0.794511i	$-0.707727\pi$
$541$	−13.3190	+	4.76561i	−0.572628	+	0.204889i	0.0346221	+	0.999400i	$0.488977\pi$
$542$	24.2059	+	2.17319i	1.03973	+	0.0933465i
$543$	−0.992420	−	2.39591i	−0.0425888	−	0.102818i
$544$	−24.5776	−	1.35305i	−1.05376	−	0.0580114i
$545$	1.90693	−	4.60374i	0.0816839	−	0.197202i
$546$	0.0121042	−	0.0231234i	0.000518010	−	0.000989590i
$547$	−10.8985	+	23.0429i	−0.465986	+	0.985245i	0.524978	+	0.851116i	$0.324074\pi$
$547$	−10.8985	+	23.0429i	−0.465986	+	0.985245i	−0.990964	+	0.134129i	$0.957176\pi$
$548$	9.05937	−	11.4361i	0.386997	−	0.488524i
$549$	2.00965	−	13.5479i	0.0857697	−	0.578212i
$550$	2.27205	−	16.2846i	0.0968806	−	0.694378i
$551$	12.1497	−	40.0523i	0.517596	−	1.70629i
$552$	−18.0460	−	12.6727i	−0.768090	−	0.539385i
$553$	−0.0620592	−	0.0331713i	−0.00263903	−	0.00141059i
$554$	6.14883	−	3.75802i	0.261239	−	0.159663i
$555$	−0.680498	+	0.750814i	−0.0288855	+	0.0318703i
$556$	17.7975	+	2.32663i	0.754781	+	0.0986710i
$557$	−29.2441	+	4.33795i	−1.23911	+	0.183805i	−0.733941	−	0.679213i	$-0.762321\pi$
$557$	−29.2441	+	4.33795i	−1.23911	+	0.183805i	−0.505172	+	0.863019i	$0.668571\pi$
$558$	2.32822	−	2.36878i	0.0985613	−	0.100278i
$559$	3.34249	−	16.8038i	0.141372	−	0.710727i
$560$	−0.00927222		0.000134872i	−0.000391823		5.69936e-6i
$561$	2.00239	+	10.0667i	0.0845410	+	0.425016i
$562$	−3.67045	+	5.59725i	−0.154828	+	0.236106i
$563$	0.451481	−	1.80241i	0.0190276	−	0.0759626i	−0.959774	−	0.280775i	$-0.909408\pi$
$563$	0.451481	−	1.80241i	0.0190276	−	0.0759626i	0.978801	+	0.204813i	$0.0656585\pi$
$564$	5.03618	+	0.160285i	0.212061	+	0.00674924i
$565$	1.98898	+	0.711669i	0.0836771	+	0.0299401i
$566$	−6.39176	−	2.95580i	−0.268666	−	0.124242i
$567$	−0.00551883	−	0.00672472i	−0.000231769	−	0.000282412i
$568$	−0.0879537	−	3.39422i	−0.00369046	−	0.142418i
$569$	2.49809	+	25.3636i	0.104725	+	1.06330i	0.893638	+	0.448789i	$0.148145\pi$
$569$	2.49809	+	25.3636i	0.104725	+	1.06330i	−0.788912	+	0.614506i	$0.789355\pi$
$570$	2.11338	−	2.37261i	0.0885196	−	0.0993776i
$571$	−7.77812	−	4.66203i	−0.325504	−	0.195100i	0.342011	−	0.939696i	$-0.388892\pi$
$571$	−7.77812	−	4.66203i	−0.325504	−	0.195100i	−0.667515	+	0.744596i	$0.732642\pi$
$572$	3.98909	+	9.17884i	0.166792	+	0.383787i
$573$	16.1894	+	0.795332i	0.676320	+	0.0332255i
$574$	−0.0460614	−	0.0371406i	−0.00192257	−	0.00155022i
$575$	−27.1725	+	27.1725i	−1.13317	+	1.13317i
$576$	−1.92268	+	7.76552i	−0.0801115	+	0.323563i
$577$	−13.7598	−	13.7598i	−0.572827	−	0.572827i	0.360090	−	0.932917i	$-0.382746\pi$
$577$	−13.7598	−	13.7598i	−0.572827	−	0.572827i	−0.932917	+	0.360090i	$0.882746\pi$
$578$	−0.291589	−	2.71958i	−0.0121285	−	0.113120i
$579$	−0.922419	+	18.7763i	−0.0383344	+	0.780315i
$580$	−2.64556	+	0.0456969i	−0.109851	+	0.00189746i
$581$	−0.0608197	+	0.101472i	−0.00252323	+	0.00420975i
$582$	0.199604	+	3.45412i	0.00827385	+	0.143178i
$583$	24.0346	−	2.36720i	0.995412	−	0.0980395i
$584$	−8.67999	−	12.2890i	−0.359181	−	0.508523i
$585$	0.437019	−	0.358653i	0.0180685	−	0.0148285i
$586$	−12.3928	−	33.7148i	−0.511943	−	1.39275i
$587$	4.20850	−	11.7620i	0.173703	−	0.485468i	−0.822866	−	0.568236i	$-0.807626\pi$
$587$	4.20850	−	11.7620i	0.173703	−	0.485468i	0.996569	+	0.0827679i	$0.0263760\pi$
$588$	13.0981	−	4.94335i	0.540155	−	0.203860i
$589$	19.2071	+	4.81114i	0.791417	+	0.198240i
$590$	0.774135	+	3.72350i	0.0318706	+	0.153294i
$591$	−11.2825	+	2.24424i	−0.464102	+	0.0923156i
$592$	14.6175	−	4.20300i	0.600775	−	0.172742i
$593$	5.37087	+	1.06833i	0.220555	+	0.0438712i	0.304131	−	0.952630i	$-0.401634\pi$
$593$	5.37087	+	1.06833i	0.220555	+	0.0438712i	−0.0835755	+	0.996501i	$0.526634\pi$
$594$	3.33572	−	0.0288069i	0.136866	−	0.00118196i
$595$	−0.00148017	−	0.00997850i	−6.06811e−5	−	0.000409079i
$596$	18.2078	+	10.4902i	0.745821	+	0.429697i
$597$	14.8267	+	13.4381i	0.606814	+	0.549985i
$598$	5.48725	−	22.7376i	0.224390	−	0.929811i
$599$	−15.1473	+	28.3385i	−0.618900	+	1.15788i	0.355841	+	0.934546i	$0.384194\pi$
$599$	−15.1473	+	28.3385i	−0.618900	+	1.15788i	−0.974742	+	0.223335i	$0.928306\pi$
$600$	12.7529	+	5.63220i	0.520636	+	0.229934i
$601$	−10.2961	−	3.12327i	−0.419985	−	0.127401i	0.0732168	−	0.997316i	$-0.476673\pi$
$601$	−10.2961	−	3.12327i	−0.419985	−	0.127401i	−0.493202	+	0.869915i	$0.664173\pi$
$602$	−0.0792912	+	0.0598746i	−0.00323167	+	0.00244031i
$603$	15.8656	+	2.35344i	0.646098	+	0.0958396i
$604$	24.5134	+	6.97610i	0.997438	+	0.283853i
$605$	1.30957	+	0.619380i	0.0532415	+	0.0251814i
$606$	−6.51205	−	20.8184i	−0.264534	−	0.845691i
$607$	−5.95380	−	2.46614i	−0.241657	−	0.100098i	0.258568	−	0.965993i	$-0.416749\pi$
$607$	−5.95380	−	2.46614i	−0.241657	−	0.100098i	−0.500225	+	0.865895i	$0.666749\pi$
$608$	−45.7194	+	13.5743i	−1.85417	+	0.550512i
$609$	−0.0399003	+	0.0165272i	−0.00161684	+	0.000669717i
$610$	−3.30890	−	3.96165i	−0.133974	−	0.160402i
$611$	1.80058	+	5.03230i	0.0728438	+	0.203585i
$612$	−8.67419	−	0.703307i	−0.350633	−	0.0284295i
$613$	−8.94456	+	6.63374i	−0.361267	+	0.267934i	−0.761074	−	0.648666i	$-0.775327\pi$
$613$	−8.94456	+	6.63374i	−0.361267	+	0.267934i	0.399806	+	0.916600i	$0.369077\pi$
$614$	11.2896	+	43.4741i	0.455609	+	1.75447i
$615$	−0.604178	−	1.13034i	−0.0243628	−	0.0455796i
$616$	0.0181308	−	0.0551351i	0.000730512	−	0.00222146i
$617$	4.31636	+	14.2291i	0.173770	+	0.572844i	0.999955	+	0.00944495i	$0.00300646\pi$
$617$	4.31636	+	14.2291i	0.173770	+	0.572844i	−0.826185	+	0.563399i	$0.809494\pi$
$618$	−16.1313	+	2.53541i	−0.648896	+	0.101989i
$619$	0.378356	+	7.70162i	0.0152074	+	0.309554i	0.994334	+	0.106302i	$0.0339011\pi$
$619$	0.378356	+	7.70162i	0.0152074	+	0.309554i	−0.979126	+	0.203252i	$0.934849\pi$
$620$	−0.0830035	−	1.24899i	−0.00333350	−	0.0501608i
$621$	−6.26203	−	4.64424i	−0.251287	−	0.186367i
$622$	−37.6952	−	15.2338i	−1.51144	−	0.610821i
$623$	−0.0673334	−	0.100772i	−0.00269766	−	0.00403733i
$624$	−8.41121	+	1.12291i	−0.336718	+	0.0449526i
$625$	13.3002	−	19.9052i	0.532009	−	0.796208i
$626$	−11.7764	−	17.2993i	−0.470679	−	0.691420i
$627$	10.2238	+	17.0574i	0.408299	+	0.681206i
$628$	−15.5357	−	3.60753i	−0.619942	−	0.143956i
$629$	7.07417	+	14.9571i	0.282066	+	0.596378i
$630$	−0.00327589		0.000132588i	−0.000130515		5.28242e-6i
$631$	−21.2099	−	2.08899i	−0.844354	−	0.0831616i	−0.333416	−	0.942780i	$-0.608201\pi$
$631$	−21.2099	−	2.08899i	−0.844354	−	0.0831616i	−0.510937	+	0.859618i	$0.670701\pi$
$632$	2.83156	+	22.7029i	0.112633	+	0.903072i
$633$	−5.36700	+	6.53970i	−0.213319	+	0.259930i
$634$	9.74516	−	4.71252i	0.387030	−	0.187158i
$635$	4.15295	−	1.04026i	0.164805	−	0.0412815i
$636$	−3.64747	+	20.1498i	−0.144631	+	0.798992i
$637$	9.97268	+	11.0032i	0.395132	+	0.435961i
$638$	4.67028	−	15.8885i	0.184898	−	0.629032i
$639$		−	1.20044i		−	0.0474887i
$640$	1.70341	+	2.48768i	0.0673333	+	0.0983342i
$641$			23.8719i			0.942882i	0.881898	+	0.471441i	$0.156266\pi$
$641$			23.8719i			0.942882i	−0.881898	+	0.471441i	$0.843734\pi$
$642$	20.8782	+	6.13695i	0.823996	+	0.242206i
$643$	−23.4029	−	25.8212i	−0.922922	−	1.01829i	−0.999774	−	0.0212446i	$-0.993237\pi$
$643$	−23.4029	−	25.8212i	−0.922922	−	1.01829i	0.0768527	−	0.997042i	$-0.475513\pi$
$644$	−0.111467	+	0.0772974i	−0.00439241	+	0.00304594i
$645$	−2.08769	+	0.522940i	−0.0822029	+	0.0205907i
$646$	−22.5861	−	46.7065i	−0.888639	−	1.83764i
$647$	20.9593	−	25.5390i	0.823995	−	1.00404i	−0.175813	−	0.984424i	$-0.556255\pi$
$647$	20.9593	−	25.5390i	0.823995	−	1.00404i	0.999808	−	0.0196171i	$-0.00624472\pi$
$648$	−0.750661	+	2.72700i	−0.0294887	+	0.107127i
$649$	−23.6886	−	2.33312i	−0.929858	−	0.0915830i
$650$	−0.598033	+	14.7758i	−0.0234568	+	0.579555i
$651$	−0.00873549	−	0.0184696i	−0.000342371	−	0.000723882i
$652$	−11.2336	+	6.99970i	−0.439944	+	0.274129i
$653$	15.8540	+	26.4507i	0.620414	+	1.03510i	0.994196	+	0.107581i	$0.0343106\pi$
$653$	15.8540	+	26.4507i	0.620414	+	1.03510i	−0.373783	+	0.927516i	$0.621939\pi$
$654$	−21.8598	+	14.8809i	−0.854786	+	0.581889i
$655$	−0.0401551	+	0.0600964i	−0.00156899	+	0.00234816i
$656$	−1.22332	+	19.1989i	−0.0477627	+	0.749593i
$657$	−2.95526	−	4.42286i	−0.115296	−	0.172552i
$658$	0.0116136	−	0.0287372i	0.000452746	−	0.00112029i
$659$	15.7390	+	11.6728i	0.613104	+	0.454709i	0.857159	−	0.515053i	$-0.172228\pi$
$659$	15.7390	+	11.6728i	0.613104	+	0.454709i	−0.244055	+	0.969762i	$0.578478\pi$
$660$	0.828066	−	0.945962i	0.0322324	−	0.0368215i
$661$	2.02217	+	41.1623i	0.0786534	+	1.60103i	0.636629	+	0.771170i	$0.280328\pi$
$661$	2.02217	+	41.1623i	0.0786534	+	1.60103i	−0.557976	+	0.829857i	$0.688422\pi$
$662$	−7.50785	−	47.7680i	−0.291801	−	1.85656i
$663$	−2.67966	−	8.83367i	−0.104070	−	0.343071i
$664$	38.3556	−	2.88186i	1.48848	−	0.111838i
$665$	−0.00921355	−	0.0172373i	−0.000357286	−	0.000668435i
$666$	5.20482	−	1.35161i	0.201683	−	0.0523739i
$667$	−31.0876	+	23.0561i	−1.20372	+	0.892737i
$668$	−27.4061	+	23.2952i	−1.06037	+	0.901318i
$669$	1.89047	+	5.28352i	0.0730899	+	0.204273i
$670$	4.63938	−	3.87497i	0.179235	−	0.149703i
$671$	29.8474	−	12.3632i	1.15225	−	0.477276i
$672$	0.0407553	+	0.0275816i	0.00157217	+	0.00106398i
$673$	2.15667	+	0.893322i	0.0831335	+	0.0344350i	0.423863	−	0.905726i	$-0.360674\pi$
$673$	2.15667	+	0.893322i	0.0831335	+	0.0344350i	−0.340729	+	0.940161i	$0.610674\pi$
$674$	43.8874	−	13.7281i	1.69048	−	0.528786i
$675$	4.45575	+	2.10741i	0.171502	+	0.0811143i
$676$	8.27091	+	14.8510i	0.318112	+	0.571192i
$677$	5.02755	+	0.745767i	0.193225	+	0.0286622i	0.242641	−	0.970116i	$-0.421986\pi$
$677$	5.02755	+	0.745767i	0.193225	+	0.0286622i	−0.0494167	+	0.998778i	$0.515736\pi$
$678$	−6.75558	−	8.94633i	−0.259447	−	0.343582i
$679$	0.0203667	+	0.00617816i	0.000781601	+	0.000237096i
$680$	−2.37230	+	2.26479i	−0.0909736	+	0.0868509i
$681$	−1.72606	+	3.22924i	−0.0661429	+	0.123745i
$682$	7.61589	+	1.83794i	0.291628	+	0.0703782i
$683$	0.250730	+	0.227248i	0.00959390	+	0.00869541i	0.676342	−	0.736588i	$-0.263564\pi$
$683$	0.250730	+	0.227248i	0.00959390	+	0.00869541i	−0.666748	+	0.745283i	$0.732314\pi$
$684$	−16.2832	+	4.37892i	−0.622602	+	0.167432i
$685$	−0.285242	−	1.92295i	−0.0108985	−	0.0734720i
$686$	−0.00148737	−	0.172232i	−5.67881e−5	−	0.00657584i
$687$	−11.9375	−	2.37452i	−0.455444	−	0.0905935i
$688$	30.7736	+	9.82606i	1.17323	+	0.374615i
$689$	−21.3035	+	4.23753i	−0.811598	+	0.161437i
$690$	−2.87670	+	0.598082i	−0.109514	+	0.0227686i
$691$	8.69114	+	2.17702i	0.330627	+	0.0828176i	0.404739	−	0.914432i	$-0.367362\pi$
$691$	8.69114	+	2.17702i	0.330627	+	0.0828176i	−0.0741124	+	0.997250i	$0.523612\pi$
$692$	−18.0465	−	8.15698i	−0.686023	−	0.310082i
$693$	0.00691302	−	0.0193206i	0.000262604	−	0.000733929i
$694$	−34.5520	+	12.7005i	−1.31157	+	0.482105i
$695$	1.84873	−	1.51722i	0.0701265	−	0.0575513i
$696$	11.8733	+	7.49605i	0.450058	+	0.284137i
$697$	−20.8268	+	2.05126i	−0.788872	+	0.0776971i
$698$	−15.9936	+	0.924227i	−0.605367	+	0.0349825i
$699$	−0.0671026	+	0.111954i	−0.00253805	+	0.00423448i
$700$	0.0595839	−	0.0616785i	0.00225206	−	0.00233123i
$701$	0.562011	−	11.4400i	0.0212269	−	0.432083i	−0.964537	−	0.263947i	$-0.914975\pi$
$701$	0.562011	−	11.4400i	0.0212269	−	0.432083i	0.985764	−	0.168135i	$-0.0537746\pi$
$702$	−2.98310	+	0.319843i	−0.112590	+	0.0120717i
$703$	22.6682	+	22.6682i	0.854948	+	0.854948i
$704$	−18.0429	+	5.52701i	−0.680016	+	0.208307i
$705$	0.474741	−	0.474741i	0.0178798	−	0.0178798i
$706$	−6.56886	+	8.14664i	−0.247222	+	0.306603i
$707$	−0.134020	−	0.00658397i	−0.00504033	−	0.000247616i
$708$	7.40031	−	18.7768i	0.278121	−	0.705674i
$709$	−35.2729	−	21.1418i	−1.32470	−	0.793996i	−0.335711	−	0.941965i	$-0.608976\pi$
$709$	−35.2729	−	21.1418i	−1.32470	−	0.793996i	−0.988992	+	0.147969i	$0.952726\pi$
$710$	−0.337828	−	0.300917i	−0.0126785	−	0.0112932i
$711$	0.792848	+	8.04992i	0.0297341	+	0.301896i
$712$	−14.1314	+	36.7836i	−0.529598	+	1.37852i
$713$	−11.6159	−	14.1540i	−0.435019	−	0.530072i
$714$	−0.0224697	+	0.0485895i	−0.000840909	+	0.00181842i
$715$	1.25559	+	0.449257i	0.0469564	+	0.0168013i
$716$	16.6278	−	15.6021i	0.621411	−	0.583076i
$717$	−0.799547	+	3.19197i	−0.0298596	+	0.119206i
$718$	−8.70001	−	5.70511i	−0.324682	−	0.212913i
$719$	3.12514	+	15.7112i	0.116548	+	0.585927i	0.994283	+	0.106780i	$0.0340540\pi$
$719$	3.12514	+	15.7112i	0.116548	+	0.585927i	−0.877734	+	0.479147i	$0.840946\pi$
$720$	0.579262	+	0.894833i	0.0215878	+	0.0333485i
$721$	−0.0195965	+	0.0985181i	−0.000729811	+	0.00366901i
$722$	−52.5268	−	51.6274i	−1.95485	−	1.92137i
$723$	1.65589	−	0.245627i	0.0615831	−	0.00913498i
$724$	3.16116	+	4.11196i	0.117484	+	0.152820i
$725$	16.4329	−	18.1309i	0.610301	−	0.673364i
$726$	−4.00909	−	6.55962i	−0.148791	−	0.243450i
$727$	44.3690	+	23.7157i	1.64555	+	0.879567i	0.992498	+	0.122258i	$0.0390136\pi$
$727$	44.3690	+	23.7157i	1.64555	+	0.879567i	0.653056	+	0.757309i	$0.273486\pi$
$728$	−0.0113676	+	0.0509469i	−0.000421310	+	0.00188822i
$729$	−0.290285	+	0.956940i	−0.0107513	+	0.0354422i
$730$	−1.98548	−	0.277018i	−0.0734861	−	0.0102529i
$731$	−5.15635	+	34.7613i	−0.190714	+	1.28569i
$732$	3.15532	+	27.2100i	0.116624	+	1.00571i
$733$	−10.4014	+	21.9920i	−0.384186	+	0.812293i	0.615522	+	0.788120i	$0.288945\pi$
$733$	−10.4014	+	21.9920i	−0.384186	+	0.812293i	−0.999708	+	0.0241734i	$0.992305\pi$
$734$	18.5416	+	9.70576i	0.684383	+	0.358246i
$735$	0.713862	−	1.72341i	0.0263312	−	0.0635691i
$736$	41.4359	+	15.1028i	1.52735	+	0.556696i
$737$	14.4782	+	34.9535i	0.533311	+	1.28753i
$738$	−0.608197	+	6.77437i	−0.0223881	+	0.249368i
$739$	−4.61991	+	1.65303i	−0.169946	+	0.0608077i	−0.420488	−	0.907298i	$-0.638141\pi$
$739$	−4.61991	+	1.65303i	−0.169946	+	0.0608077i	0.250542	+	0.968106i	$0.419391\pi$
$740$	0.924333	−	1.80355i	0.0339791	−	0.0663000i
$741$	−10.6545	−	14.3659i	−0.391402	−	0.527745i
$742$	0.108598	+	0.0638229i	0.00398676	+	0.00234301i
$743$	−14.6851	+	7.84937i	−0.538745	+	0.287965i	−0.718242	−	0.695793i	$-0.755053\pi$
$743$	−14.6851	+	7.84937i	−0.538745	+	0.287965i	0.179497	+	0.983759i	$0.442553\pi$
$744$	−3.26634	+	5.78428i	−0.119750	+	0.212062i
$745$	2.67939	−	0.812783i	0.0981651	−	0.0297781i
$746$	21.0561	+	15.3362i	0.770918	+	0.561498i
$747$	13.5826	−	0.667269i	0.496961	−	0.0244141i
$748$	−9.09596	−	18.4026i	−0.332581	−	0.672866i
$749$	0.0797422	−	0.107520i	0.00291372	−	0.00392869i
$750$	3.44464	−	1.46179i	0.125780	−	0.0533771i
$751$	28.7596	−	19.2165i	1.04945	−	0.701221i	0.0937610	−	0.995595i	$-0.470111\pi$
$751$	28.7596	−	19.2165i	1.04945	−	0.701221i	0.955690	+	0.294374i	$0.0951110\pi$
$752$	−9.81003	+	2.30619i	−0.357735	+	0.0840980i
$753$	−10.6566	−	7.12051i	−0.388348	−	0.259486i
$754$	−2.77948	+	14.6327i	−0.101223	+	0.532892i
$755$	2.91283	−	1.74588i	0.106009	−	0.0635392i
$756$	0.0141517	+	0.0101215i	0.000514694	+	0.000368117i
$757$	−41.5163	+	19.6358i	−1.50894	+	0.713674i	−0.989991	−	0.141134i	$-0.954925\pi$
$757$	−41.5163	+	19.6358i	−1.50894	+	0.713674i	−0.518945	+	0.854807i	$0.673675\pi$
$758$	−11.2131	+	10.3408i	−0.407279	+	0.375593i
$759$	1.80252	−	18.3013i	0.0654275	−	0.664296i
$760$	−2.84942	+	5.68008i	−0.103359	+	0.206038i
$761$	18.1653	+	14.9078i	0.658490	+	0.540409i	0.903217	−	0.429183i	$-0.141199\pi$
$761$	18.1653	+	14.9078i	0.658490	+	0.540409i	−0.244728	+	0.969592i	$0.578699\pi$
$762$	−21.4570	−	7.46907i	−0.777306	−	0.270576i
$763$	0.0395252	+	0.157793i	0.00143091	+	0.00571250i
$764$	−31.6809	+	6.87256i	−1.14617	+	0.248640i
$765$	−0.859196	+	0.778730i	−0.0310643	+	0.0281550i
$766$	−0.358823	−	0.657588i	−0.0129648	−	0.0237596i
$767$	21.4081			0.773002
$768$	−0.319945	−	15.9968i	−0.0115450	−	0.577235i
$769$	−15.4130			−0.555807			−0.277904	−	0.960609i	$-0.589640\pi$
$769$	−15.4130			−0.555807			−0.277904	+	0.960609i	$0.589640\pi$
$770$	−0.00370431	−	0.00678860i	−0.000133494	−	0.000244644i
$771$	8.09368	−	7.33569i	0.291487	−	0.264188i
$772$	−7.97073	−	36.7432i	−0.286873	−	1.32242i
$773$	7.94660	+	31.7246i	0.285819	+	1.14105i	0.927422	+	0.374017i	$0.122020\pi$
$773$	7.94660	+	31.7246i	0.285819	+	1.14105i	−0.641602	+	0.767037i	$0.721730\pi$
$774$	10.7865	+	3.75471i	0.387712	+	0.134960i
$775$	8.94848	+	7.34383i	0.321439	+	0.263798i
$776$	−2.17956	−	6.56755i	−0.0782416	−	0.235761i
$777$	0.00324229	−	0.0329196i	0.000116317	−	0.00118098i
$778$	−38.0990	+	35.1349i	−1.36592	+	1.25965i
$779$	−36.6548	+	17.3364i	−1.31330	+	0.621143i
$780$	−0.657769	+	0.919680i	−0.0235519	+	0.0329298i
$781$	2.42875	−	1.45573i	0.0869074	−	0.0520903i
$782$	−8.95297	+	47.1333i	−0.320158	+	1.68548i
$783$	4.12780	+	2.75811i	0.147515	+	0.0985667i
$784$	−22.7298	+	16.3505i	−0.811778	+	0.583948i
$785$	−1.76698	+	1.18066i	−0.0630663	+	0.0421395i
$786$	0.353085	−	0.149838i	0.0125941	−	0.00534453i
$787$	9.10204	−	12.2727i	0.324453	−	0.437474i	−0.610623	−	0.791921i	$-0.709081\pi$
$787$	9.10204	−	12.2727i	0.324453	−	0.437474i	0.935076	+	0.354447i	$0.115331\pi$
$788$	20.6252	−	10.1946i	0.734744	−	0.363166i
$789$	8.42254	−	0.413773i	0.299850	−	0.0147307i
$790$	2.46416	+	1.79477i	0.0876707	+	0.0638549i
$791$	−0.0659907	+	0.0200181i	−0.00234636	+	0.000711760i
$792$	−6.42759	+	1.78819i	−0.228395	+	0.0635406i
$793$	−25.6250	+	13.6969i	−0.909971	+	0.486390i
$794$	−11.8338	−	6.95474i	−0.419967	−	0.246814i
$795$	1.62536	+	2.19155i	0.0576457	+	0.0777262i
$796$	−35.6156	−	18.2532i	−1.26236	−	0.646968i
$797$	−43.3860	+	15.5238i	−1.53681	+	0.549880i	−0.963092	−	0.269173i	$-0.913250\pi$
$797$	−43.3860	+	15.5238i	−1.53681	+	0.549880i	−0.573719	+	0.819052i	$0.694500\pi$
$798$	−0.00927485	+	0.103307i	−0.000328326	+	0.00365704i
$799$	−4.19520	−	10.1281i	−0.148415	−	0.358307i
$800$	−27.5561	−	4.25412i	−0.974255	−	0.150406i
$801$	−5.33142	+	12.8712i	−0.188376	+	0.454781i
$802$	28.3953	+	14.8638i	1.00267	+	0.524859i
$803$	5.36464	−	11.3426i	0.189314	−	0.400271i
$804$	−31.8649	+	3.69511i	−1.12379	+	0.130317i
$805$	−0.00265202	+	0.0178785i	−9.34716e−5	+	0.000630134i
$806$	−6.97862	−	0.973667i	−0.245811	−	0.0342959i
$807$	−7.14656	+	23.5590i	−0.251571	+	0.829318i
$808$	23.3902	+	36.8260i	0.822865	+	1.29553i
$809$	−5.97146	−	3.19181i	−0.209945	−	0.112218i	0.363073	−	0.931761i	$-0.381728\pi$
$809$	−5.97146	−	3.19181i	−0.209945	−	0.112218i	−0.573018	+	0.819543i	$0.694228\pi$
$810$	0.196536	+	0.321570i	0.00690558	+	0.0112988i
$811$	22.2008	−	24.4948i	0.779576	−	0.860129i	−0.213580	−	0.976926i	$-0.568512\pi$
$811$	22.2008	−	24.4948i	0.779576	−	0.860129i	0.993156	+	0.116796i	$0.0372625\pi$
$812$	0.0684785	−	0.0526443i	0.00240312	−	0.00184745i
$813$	−16.9990	+	2.52157i	−0.596182	+	0.0884352i
$814$	9.04631	+	8.89140i	0.317073	+	0.311643i
$815$	−0.344066	+	1.72974i	−0.0120521	+	0.0605901i
$816$	17.1185	−	3.14697i	0.599266	−	0.110166i
$817$	13.2833	+	66.7797i	0.464724	+	2.33633i
$818$	−21.4534	−	14.0682i	−0.750099	−	0.491884i
$819$	−0.00448429	+	0.0179023i	−0.000156694	+	0.000625557i
$820$	1.75399	+	1.86930i	0.0612519	+	0.0652790i
$821$	14.2661	+	5.10449i	0.497890	+	0.178148i	0.573846	−	0.818963i	$-0.305451\pi$
$821$	14.2661	+	5.10449i	0.497890	+	0.178148i	−0.0759559	+	0.997111i	$0.524201\pi$
$822$	−4.33012	+	9.36364i	−0.151030	+	0.326594i
$823$	13.3231	+	16.2343i	0.464415	+	0.565891i	0.951573	−	0.307423i	$-0.0994666\pi$
$823$	13.3231	+	16.2343i	0.464415	+	0.565891i	−0.487158	+	0.873314i	$0.661967\pi$
$824$	29.8388	−	13.2753i	1.03948	−	0.462468i
$825$	1.13960	+	11.5705i	0.0396756	+	0.402833i
$826$	−0.0927058	−	0.0825767i	−0.00322565	−	0.00287321i
$827$	44.4111	+	26.6190i	1.54433	+	0.925634i	0.995998	+	0.0893708i	$0.0284856\pi$
$827$	44.4111	+	26.6190i	1.54433	+	0.925634i	0.548328	+	0.836263i	$0.315264\pi$
$828$	14.5066	+	5.71733i	0.504138	+	0.198691i
$829$	−42.3119	−	2.07865i	−1.46955	−	0.0721945i	−0.701541	−	0.712630i	$-0.747504\pi$
$829$	−42.3119	−	2.07865i	−1.46955	−	0.0721945i	−0.768012	+	0.640435i	$0.778754\pi$
$830$	3.21699	−	3.98968i	0.111663	−	0.138484i
$831$	−3.60315	+	3.60315i	−0.124992	+	0.124992i
$832$	15.6620	−	6.53750i	0.542982	−	0.226647i
$833$	−21.5377	−	21.5377i	−0.746239	−	0.746239i
$834$	−12.6195	+	1.35304i	−0.436976	+	0.0468519i
$835$	−0.235165	+	4.78690i	−0.00813823	+	0.165657i
$836$	−28.6055	−	27.6341i	−0.989343	−	0.955745i
$837$	−1.20741	+	2.01445i	−0.0417343	+	0.0696296i
$838$	47.9512	−	2.77097i	1.65645	−	0.0957215i
$839$	−53.7157	+	5.29053i	−1.85447	+	0.182649i	−0.962832	−	0.270099i	$-0.912943\pi$
$839$	−53.7157	+	5.29053i	−1.85447	+	0.182649i	−0.891638	+	0.452749i	$0.850443\pi$
$840$	0.00639585	−	0.00144540i	0.000220678	−	4.98710e-5i
$841$	−3.36580	+	2.76224i	−0.116062	+	0.0952497i
$842$	−1.13500	+	0.417199i	−0.0391146	+	0.0143776i
$843$	1.59448	−	4.45627i	0.0549168	−	0.153482i
$844$	6.96903	−	15.4182i	0.239884	−	0.530718i
$845$	2.19713	+	0.550352i	0.0755836	+	0.0189327i
$846$	−3.48833	+	0.725242i	−0.119931	+	0.0249343i
$847$	−0.0463817	+	0.00922589i	−0.00159369	+	0.000317005i
$848$	−3.42104	−	40.8114i	−0.117479	−	1.40147i
$849$	4.88384	+	0.971457i	0.167613	+	0.0333403i
$850$	−0.261929	−	30.3304i	−0.00898411	−	1.04032i
$851$	−4.34980	−	29.3240i	−0.149109	−	1.00521i
$852$	0.623502	+	2.31851i	0.0213608	+	0.0794308i
$853$	−0.326774	−	0.296171i	−0.0111885	−	0.0101407i	0.665946	−	0.746000i	$-0.268028\pi$
$853$	−0.326774	−	0.296171i	−0.0111885	−	0.0101407i	−0.677134	+	0.735860i	$0.736778\pi$
$854$	0.163799	+	0.0395295i	0.00560509	+	0.00135267i
$855$	−1.05910	+	1.98144i	−0.0362206	+	0.0677639i
$856$	−43.5112	−	1.00879i	−1.48718	−	0.0344796i
$857$	16.6610	+	5.05404i	0.569127	+	0.172643i	0.561717	−	0.827330i	$-0.310141\pi$
$857$	16.6610	+	5.05404i	0.569127	+	0.172643i	0.00741062	+	0.999973i	$0.497641\pi$
$858$	−4.26461	−	5.64757i	−0.145591	−	0.192805i
$859$	−57.2395	−	8.49068i	−1.95299	−	0.289698i	−0.953072	−	0.302742i	$-0.902098\pi$
$859$	−57.2395	−	8.49068i	−1.95299	−	0.289698i	−0.999915	+	0.0130439i	$0.995848\pi$
$860$	3.76052	−	2.09433i	0.128233	−	0.0714161i
$861$	0.0378224	+	0.0178887i	0.00128898	+	0.000609644i
$862$	13.8705	−	4.33871i	0.472430	−	0.147777i
$863$	8.38197	+	3.47193i	0.285326	+	0.118186i	0.520756	−	0.853705i	$-0.325650\pi$
$863$	8.38197	+	3.47193i	0.285326	+	0.118186i	−0.235431	+	0.971891i	$0.575650\pi$
$864$	0.0334266	−	5.65676i	0.00113720	−	0.192447i
$865$	−2.43796	+	1.00984i	−0.0828931	+	0.0343354i
$866$	−8.07189	+	6.74192i	−0.274294	+	0.229100i
$867$	0.651563	+	1.82100i	0.0221283	+	0.0618443i
$868$	0.0264646	+	0.0311347i	0.000898266	+	0.00105678i
$869$	−15.3252	+	11.3660i	−0.519873	+	0.385564i
$870$	1.81091	−	0.470266i	0.0613956	−	0.0159435i
$871$	−16.0400	−	30.0087i	−0.543495	−	1.01681i
$872$	34.4905	−	40.0945i	1.16800	−	1.35777i
$873$	−0.710183	−	2.34116i	−0.0240361	−	0.0792363i
$874$	14.4329	+	91.8278i	0.488199	+	3.10612i
$875$	−0.00112946	−	0.0229906i	−3.81826e−5	−	0.000777225i
$876$	8.00494	+	7.00728i	0.270462	+	0.236754i
$877$	−37.1413	−	27.5458i	−1.25417	−	0.930157i	−0.254850	−	0.966981i	$-0.582026\pi$
$877$	−37.1413	−	27.5458i	−1.25417	−	0.930157i	−0.999322	+	0.0368239i	$0.988276\pi$
$878$	−11.8166	+	29.2394i	−0.398790	+	0.986781i
$879$	14.1112	+	21.1189i	0.475960	+	0.712324i
$880$	−1.10798	+	2.25710i	−0.0373502	+	0.0760870i
$881$	19.3839	−	29.0100i	0.653059	−	0.977371i	−0.346173	−	0.938171i	$-0.612519\pi$
$881$	19.3839	−	29.0100i	0.653059	−	0.977371i	0.999231	−	0.0392005i	$-0.0124811\pi$
$882$	−8.18324	+	5.57068i	−0.275544	+	0.187575i
$883$	19.5761	+	32.6608i	0.658789	+	1.09912i	0.987939	+	0.154845i	$0.0494877\pi$
$883$	19.5761	+	32.6608i	0.658789	+	1.09912i	−0.329150	+	0.944278i	$0.606762\pi$
$884$	9.76360	+	15.6694i	0.328386	+	0.527018i
$885$	−1.14979	−	2.43102i	−0.0386496	−	0.0817178i
$886$	0.805561	−	19.9033i	0.0270633	−	0.668663i
$887$	9.34152	+	0.920059i	0.313657	+	0.0308926i	0.253621	−	0.967304i	$-0.418378\pi$
$887$	9.34152	+	0.920059i	0.313657	+	0.0308926i	0.0600363	+	0.998196i	$0.480878\pi$
$888$	−9.35047	+	5.31383i	−0.313781	+	0.178320i
$889$	−0.0886620	+	0.108035i	−0.00297363	+	0.00362338i
$890$	2.28577	+	4.72682i	0.0766193	+	0.158443i
$891$	−2.28811	+	0.573142i	−0.0766546	+	0.0192010i
$892$	−6.39545	−	9.22258i	−0.214135	−	0.308795i
$893$	−14.2642	−	15.7381i	−0.477332	−	0.526654i
$894$	−14.2557	−	4.19034i	−0.476783	−	0.140146i
$895$		−	3.03819i		−	0.101555i
$896$	−0.0930397	−	0.0321024i	−0.00310824	−	0.00107247i
$897$			16.5395i			0.552237i
$898$	−6.42431	+	21.8558i	−0.214382	+	0.729338i
$899$	7.83001	+	8.63909i	0.261146	+	0.288130i
$900$	−9.70032	−	1.75593i	−0.323344	−	0.0585309i
$901$	43.2165	−	10.8252i	1.43975	−	0.360639i
$902$	−14.4435	+	6.98454i	−0.480917	+	0.232560i
$903$	0.0445705	−	0.0543093i	0.00148321	−	0.00180730i
$904$	17.6943	+	13.7700i	0.588503	+	0.457982i
$905$	0.687766	+	0.0677390i	0.0228621	+	0.00225172i
$906$	−18.0071	−	0.728816i	−0.598246	−	0.0242133i
$907$	−2.00385	−	4.23680i	−0.0665369	−	0.140680i	0.867980	−	0.496599i	$-0.165418\pi$
$907$	−2.00385	−	4.23680i	−0.0665369	−	0.140680i	−0.934517	+	0.355919i	$0.884168\pi$
$908$	1.65644	−	7.13339i	0.0549709	−	0.236730i
$909$	7.92964	+	13.2298i	0.263010	+	0.438805i
$910$	0.00391398	+	0.00574958i	0.000129747	+	0.000190597i
$911$	9.73218	−	14.5652i	0.322441	−	0.482568i	−0.634470	−	0.772947i	$-0.718782\pi$
$911$	9.73218	−	14.5652i	0.322441	−	0.482568i	0.956911	+	0.290380i	$0.0937816\pi$
$912$	29.1746	−	16.9147i	0.966067	−	0.560103i
$913$	17.8212	+	26.6713i	0.589795	+	0.882690i
$914$	12.8414	+	5.18961i	0.424754	+	0.171657i
$915$	2.93163	+	2.17424i	0.0969166	+	0.0718782i
$916$	24.2892	−	1.61417i	0.802537	−	0.0533336i
$917$	−0.000115772	−	0.00235660i	−3.82314e−6	−	7.78219e-5i
$918$	6.07908	−	0.955468i	0.200639	−	0.0315351i
$919$	13.1334	+	43.2950i	0.433231	+	1.42817i	0.853653	+	0.520842i	$0.174382\pi$
$919$	13.1334	+	43.2950i	0.433231	+	1.42817i	−0.420422	+	0.907329i	$0.638118\pi$
$920$	5.24536	−	2.64926i	0.172935	−	0.0873436i
$921$	−14.9718	−	28.0102i	−0.493337	−	0.922968i
$922$	1.11685	+	4.30081i	0.0367816	+	0.141640i
$923$	−2.04552	+	1.51706i	−0.0673290	+	0.0499346i
$924$	−0.00331668	+	0.0409060i	−0.000109111	+	0.00134571i
$925$	6.31404	+	17.6465i	0.207604	+	0.580215i
$926$	−29.0395	−	34.7681i	−0.954298	−	1.14255i
$927$	10.6676	−	4.41869i	0.350372	−	0.145129i
$928$	−26.8253	−	8.31079i	−0.880584	−	0.272815i
$929$	21.7518	+	9.00991i	0.713655	+	0.295605i	0.709816	−	0.704387i	$-0.248778\pi$
$929$	21.7518	+	9.00991i	0.713655	+	0.295605i	0.00383879	+	0.999993i	$0.498778\pi$
$930$	0.264242	+	0.844757i	0.00866483	+	0.0277007i
$931$	−53.3491	−	25.2323i	−1.74845	−	0.826954i
$932$	0.0714525	−	0.251078i	0.00234050	−	0.00822434i
$933$	28.4377	+	4.21834i	0.931009	+	0.138102i
$934$	22.5048	−	16.9939i	0.736379	−	0.556056i
$935$	−2.61745	−	0.793996i	−0.0855999	−	0.0259664i
$936$	5.59537	−	2.16714i	0.182890	−	0.0708352i
$937$	13.3777	−	25.0280i	0.437031	−	0.817628i	−0.562929	−	0.826505i	$-0.690326\pi$
$937$	13.3777	−	25.0280i	0.437031	−	0.817628i	0.999961	+	0.00887684i	$0.00282562\pi$
$938$	−0.0462918	+	0.191820i	−0.00151148	+	0.00626316i
$939$	10.9644	+	9.93760i	0.357811	+	0.324301i
$940$	−0.670328	+	1.16348i	−0.0218637	+	0.0379487i
$941$	−7.10488	−	47.8972i	−0.231612	−	1.56140i	−0.723239	−	0.690598i	$-0.757348\pi$
$941$	−7.10488	−	47.8972i	−0.231612	−	1.56140i	0.491627	−	0.870806i	$-0.336402\pi$
$942$	11.2773	−	0.0973890i	0.367433	−	0.00317311i
$943$	36.7755	+	7.31510i	1.19758	+	0.238213i
$944$	−4.54028	+	40.1087i	−0.147774	+	1.30543i
$945$	0.00227375		0.000452278i	7.39652e−5		1.47126e-5i
$946$	5.48382	+	26.3765i	0.178294	+	0.857575i
$947$	6.77249	+	1.69642i	0.220076	+	0.0551262i	0.351450	−	0.936207i	$-0.385689\pi$
$947$	6.77249	+	1.69642i	0.220076	+	0.0551262i	−0.131374	+	0.991333i	$0.541939\pi$
$948$	−5.71237	−	15.1357i	−0.185529	−	0.491583i
$949$	−3.80171	+	10.6251i	−0.123409	+	0.344905i
$950$	−20.2755	−	55.1599i	−0.657825	−	1.78962i
$951$	−5.91684	+	4.85582i	−0.191867	+	0.157461i
$952$	0.0181605	−	0.105516i	0.000588586	−	0.00341978i
$953$	−19.7670	+	1.94688i	−0.640315	+	0.0630655i	−0.412964	−	0.910747i	$-0.635506\pi$
$953$	−19.7670	+	1.94688i	−0.640315	+	0.0630655i	−0.227351	+	0.973813i	$0.573006\pi$
$954$	−0.835344	−	14.4555i	−0.0270452	−	0.468014i
$955$	−2.22067	+	3.70496i	−0.0718591	+	0.119890i
$956$	−0.113660	−	6.58019i	−0.00367602	−	0.212819i
$957$	−0.574591	+	11.6961i	−0.0185739	+	0.378080i
$958$	−1.22632	−	11.4375i	−0.0396205	−	0.369530i
$959$	0.0448731	+	0.0448731i	0.00144903	+	0.00144903i
$960$	−1.58355	−	1.42740i	−0.0511087	−	0.0460691i
$961$	18.0200	−	18.0200i	0.581291	−	0.581291i
$962$	−8.88071	−	7.16077i	−0.286325	−	0.230872i
$963$	−15.3691	−	0.755037i	−0.495263	−	0.0243307i
$964$	−3.07057	+	1.33446i	−0.0988963	+	0.0429800i
$965$	−4.29698	−	2.57551i	−0.138325	−	0.0829087i
$966$	0.0637972	−	0.0716227i	0.00205264	−	0.00230442i
$967$	−1.35475	−	13.7550i	−0.0435657	−	0.442330i	−0.992081	−	0.125599i	$-0.959915\pi$
$967$	−1.35475	−	13.7550i	−0.0435657	−	0.442330i	0.948515	−	0.316731i	$-0.102585\pi$
$968$	11.1501	+	10.5868i	0.358378	+	0.340274i
$969$	23.2729	+	28.3582i	0.747634	+	0.910995i
$970$	−0.836873	−	0.387004i	−0.0268704	−	0.0124259i
$971$	40.6928	+	14.5601i	1.30589	+	0.467256i	0.895666	−	0.444727i	$-0.146699\pi$
$971$	40.6928	+	14.5601i	1.30589	+	0.467256i	0.410228	+	0.911983i	$0.365449\pi$
$972$	0.0636214	−	1.99899i	0.00204066	−	0.0641176i
$973$	−0.0189700	+	0.0757325i	−0.000608151	+	0.00242787i
$974$	3.15380	−	4.80939i	0.101054	−	0.154103i
$975$	−2.03999	−	10.2557i	−0.0653319	−	0.328446i
$976$	−20.2269	−	50.9141i	−0.647446	−	1.62972i
$977$	−6.87834	+	34.5797i	−0.220058	+	1.10630i	0.699886	+	0.714254i	$0.253234\pi$
$977$	−6.87834	+	34.5797i	−0.220058	+	1.10630i	−0.919944	+	0.392050i	$0.871766\pi$
$978$	6.56058	−	6.67488i	0.209784	−	0.213439i
$979$	−32.5064	+	4.82186i	−1.03891	+	0.154107i
$980$	−0.483608	+	3.69934i	−0.0154483	+	0.118171i
$981$	12.5574	−	13.8549i	0.400926	−	0.442353i
$982$	−2.34495	+	1.43318i	−0.0748303	+	0.0457345i
$983$	−29.8550	−	15.9578i	−0.952227	−	0.508976i	−0.0793126	−	0.996850i	$-0.525273\pi$
$983$	−29.8550	−	15.9578i	−0.952227	−	0.508976i	−0.872914	+	0.487874i	$0.837773\pi$
$984$	−2.34390	−	13.3998i	−0.0747209	−	0.427169i
$985$	0.889893	−	2.93359i	0.0283544	−	0.0934718i
$986$	4.22146	−	30.2568i	0.134439	−	0.963571i
$987$	−0.00321588	+	0.0216797i	−0.000102363	+	0.000690073i
$988$	28.0394	+	22.2122i	0.892053	+	0.706663i
$989$	26.9203	−	56.9182i	0.856016	−	1.80989i
$990$	−0.412272	+	0.787592i	−0.0131029	+	0.0250313i
$991$	15.3716	−	37.1102i	0.488294	−	1.17885i	−0.467284	−	0.884107i	$-0.654768\pi$
$991$	15.3716	−	37.1102i	0.488294	−	1.17885i	0.955578	−	0.294738i	$-0.0952324\pi$
$992$	3.30424	−	12.8682i	0.104910	−	0.408564i
$993$	13.0846	+	31.5891i	0.415228	+	1.00245i
$994$	0.0147096	+	0.00132062i	0.000466561	+	4.18874e-5i
$995$	−5.02083	+	1.79648i	−0.159171	+	0.0569522i
$996$	−25.8866	+	8.34346i	−0.820247	+	0.264373i
$997$	4.59887	+	6.20085i	0.145648	+	0.196383i	0.870007	−	0.493040i	$-0.164114\pi$
$997$	4.59887	+	6.20085i	0.145648	+	0.196383i	−0.724359	+	0.689423i	$0.757864\pi$
$998$	23.2453	−	39.5531i	0.735817	−	1.25203i
$999$	−3.35345	+	1.79246i	−0.106098	+	0.0567108i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.157.54	✓	2048
256.181	even	64	inner	768.2.z.a.181.54	yes	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.157.54	✓	2048	1.1	even	1	trivial
768.2.z.a.181.54	yes	2048	256.181	even	64	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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24142 - 0.677401i) q^{2} +(-0.740951 + 0.671559i) q^{3} +(1.08226 - 1.68188i) q^{4} +(-0.0647518 - 0.258504i) q^{5} +(-0.464918 + 1.33561i) q^{6} +(0.00672472 + 0.00551883i) q^{7} +(0.204226 - 2.82104i) q^{8} +(0.0980171 - 0.995185i) q^{9} +O(q^{10})\)	\(q+(1.24142 - 0.677401i) q^{2} +(-0.740951 + 0.671559i) q^{3} +(1.08226 - 1.68188i) q^{4} +(-0.0647518 - 0.258504i) q^{5} +(-0.464918 + 1.33561i) q^{6} +(0.00672472 + 0.00551883i) q^{7} +(0.204226 - 2.82104i) q^{8} +(0.0980171 - 0.995185i) q^{9} +(-0.255495 - 0.277049i) q^{10} +(2.13233 - 1.00852i) q^{11} +(0.327584 + 1.97299i) q^{12} +(-1.81964 + 1.09065i) q^{13} +(0.0120867 + 0.00229587i) q^{14} +(0.221578 + 0.148054i) q^{15} +(-1.65745 - 3.64045i) q^{16} +(3.61800 - 2.41747i) q^{17} +(-0.552459 - 1.30184i) q^{18} +(5.02224 - 6.77171i) q^{19} +(-0.504850 - 0.170862i) q^{20} +(-0.00868891 + 0.000426859i) q^{21} +(1.96395 - 2.69644i) q^{22} +(-7.46058 + 2.26314i) q^{23} +(1.74318 + 2.22741i) q^{24} +(4.34697 - 2.32351i) q^{25} +(-1.52013 + 2.58658i) q^{26} +(0.595699 + 0.803208i) q^{27} +(0.0165599 - 0.00533739i) q^{28} +(4.67426 - 1.67248i) q^{29} +(0.375364 + 0.0336999i) q^{30} +(0.898765 + 2.16981i) q^{31} +(-4.52364 - 3.39657i) q^{32} +(-0.902674 + 2.17925i) q^{33} +(2.85386 - 5.45193i) q^{34} +(0.000991201 - 0.00209572i) q^{35} +(-1.56770 - 1.24190i) q^{36} +(-0.557933 + 3.76128i) q^{37} +(1.64756 - 11.8086i) q^{38} +(0.615827 - 2.03011i) q^{39} +(-0.742474 + 0.129874i) q^{40} +(-4.24157 - 2.26717i) q^{41} +(-0.0104974 + 0.00641579i) q^{42} +(-5.42356 + 5.98397i) q^{43} +(0.611520 - 4.67780i) q^{44} +(-0.263606 + 0.0391022i) q^{45} +(-7.72867 + 7.86332i) q^{46} +(0.491504 - 2.47096i) q^{47} +(3.67286 + 1.58432i) q^{48} +(-1.36562 - 6.86542i) q^{49} +(3.82248 - 5.82910i) q^{50} +(-1.05729 + 4.22092i) q^{51} +(-0.134970 + 4.24077i) q^{52} +(9.64013 + 3.44929i) q^{53} +(1.28361 + 0.593592i) q^{54} +(-0.398778 - 0.485912i) q^{55} +(0.0169422 - 0.0178436i) q^{56} +(0.826367 + 8.39024i) q^{57} +(4.66979 - 5.24260i) q^{58} +(-8.65553 - 5.18793i) q^{59} +(0.488813 - 0.212436i) q^{60} +(13.6797 + 0.672040i) q^{61} +(2.58558 + 2.08482i) q^{62} +(0.00615140 - 0.00615140i) q^{63} +(-7.91658 - 1.15226i) q^{64} +(0.399761 + 0.399761i) q^{65} +(0.355626 + 3.31684i) q^{66} +(-0.787007 + 16.0199i) q^{67} +(-0.150299 - 8.70136i) q^{68} +(4.00809 - 6.68710i) q^{69} +(-0.000189144 - 0.00327311i) q^{70} +(1.19466 - 0.117664i) q^{71} +(-2.78744 - 0.479754i) q^{72} +(4.11190 - 3.37455i) q^{73} +(1.85527 + 5.04728i) q^{74} +(-1.66052 + 4.64085i) q^{75} +(-5.95387 - 15.7755i) q^{76} +(0.0199052 + 0.00498598i) q^{77} +(-0.610698 - 2.93738i) q^{78} +(-7.93344 + 1.57806i) q^{79} +(-0.833747 + 0.664182i) q^{80} +(-0.980785 - 0.195090i) q^{81} +(-6.80136 + 0.0587357i) q^{82} +(1.99538 + 13.4518i) q^{83} +(-0.00868569 + 0.0150757i) q^{84} +(-0.859196 - 0.778730i) q^{85} +(-2.67937 + 11.1026i) q^{86} +(-2.34023 + 4.37826i) q^{87} +(-2.40959 - 6.22137i) q^{88} +(-13.3318 - 4.04415i) q^{89} +(-0.300758 + 0.227109i) q^{90} +(-0.0182556 - 0.00270797i) q^{91} +(-4.26791 + 14.9971i) q^{92} +(-2.12310 - 1.00415i) q^{93} +(-1.06367 - 3.40044i) q^{94} +(-2.07571 - 0.859788i) q^{95} +(5.63279 - 0.521193i) q^{96} +(2.26028 - 0.936237i) q^{97} +(-6.34595 - 7.59781i) q^{98} +(-0.794656 - 2.22092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2048 q+O(q^{10}) \) 2048 * q	\( 2048 q+O(q^{100}) \) 2048 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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